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1. NoSim Probability StDv Prob C of V Beta Log10 Prob 100 3 50000E 01 4 79372E 02 0 137 0 38532 4 55932E 01 200 3 30000E 01 3 33325E 02 0 101 0 43991 4 81486E 01 300 3 06667E 01 2 66667E 02 0 087 0 50532 5 13333E 01 400 3 20000E 01 2 33530E 02 0 073 0 46770 4 94850E 01 500 3 12000E 01 2 07406E 02 0 066 0 49019 5 05845E 01 600 3 23333E 01 1 91117E 02 0 059 0 45840 4 90350E 01 700 3 27143E 01 1 77456E 02 0 054 0 44782 4 85263E 01 800 3 25000E 01 1 65699E 02 0 051 0 45376 4 88117E 01 900 3 31111E 01 1 56958E 02 0 047 0 43685 4 80026E 01 1000 3 30000E 01 1 48769E 02 0 045 0 43991 4 81486E 01 The table is useful to check if the simulation has stabilised This can be seen from the development of the coefficient of variation It should decrease steadily If it does not the result may actually be more inaccurate than it appears and further simulation is recommended see RUN RESTART The number of lines in the table is controlled by using the command DEFINE RESULT OPTION INTERMEDIATE RESULTS The simulation may be restarted from the previous result by using the command RUN RESTART The stop criteria may be changed before the run is restarted This is useful e g for estimating the time a simulation need to run in order to produce a required accuracy on the result or for continuing a simulation that did not produce the desired accuracy Proban SESAM 3 22 01 OCT 2004 Program version
2. It may be that the model requires a number of distribution variables other than the stochastic process varia bles to be integrated in the inner loop of the nested FORM analysis implied by the model If the variable x is such a distribution variable then it is pushed to the inner loop by the command ASSIGN SUB LEVEL INTEGRATION x ON The outer loop integration of x is restored by the command SESAM Proban Program version 4 4 01 OCT 2004 3 29 ASSIGN SUB LEVEL INTEGRATION x OFF The calculation proceeds as for an ordinary probability calculation The major difference is that importance factors are calculated only for the outer loop variables if a nested FORM analysis is implied by the model 3 5 Crossing Rate and Results 3 5 1 Definition of a Stochastic Process for Calculation of Crossing Rate A stochastic process is defined as above for the calculation of first passage probability If there is no time variable in the model then neither starting time nor duration is made use of If there is a time variable in the model then the crossing rate is calculated at the starting time for this varia ble or if not assigned at the default starting time If a duration is assigned to the time variable then the crossing rate is averaged over the duration taken from the starting time If a time variable is assigned a dura tion then this value is used If not the default value is used In order t
3. SESAM Proban Program version 4 4 01 OCT 2004 5 25 CHANGE EVENT CONDITIONED event condition INTERSECTION subevent EVENT name desc SINGLE ld variable lt gt threshold UNION subevent PURPOSE To change an event PARAMETERS name desc CONDITIONED event condition INTERSECTION UNION subevent SINGLE 1d variable threshold NOTES Name of event to be changed Descriptive text for the event The event is a conditioned event Name of event being conditioned Name of event conditioned on The event is an intersection of other events i e it is fulfilled only when all subevents are fulfilled The event is a union of other events i e it is fulfilled when at least one subevent is fulfilled A selection of events forming either an intersection or a union These cannot be conditioned events The event is a simple in equality Name of one dimensional variable that is the left hand side of the in equality One of lt less than equal gt greater than Numerical right hand side of the single event 1 When the event name is selected the existing state of the event is presented as defaults unless the type of the event is changed 2 The events that are created by this program should not be changed by the user Proban 5 26 01 OCT 2004 See also e CREATE EVENT e COPY EVENT e RENAME EVENT DISPLAY EVENT e PRINT EVENT A
4. Y FUNCTION FUNCTION FUNCTION Figure 3 18 Organisation of the function library In addition to this function library tree Proban has some built in function libraries and is able to use the Proban Version 2 function library LIBLIM Also simple functions can be created on input The built in libraries are described in Section 3 10 1 and the compatibility issues regarding Proban Version 3 are described in Section 3 10 4 Section 3 10 2 shows an example of how to create a function formula on input Proban is delivered with a library that contains the examples from the example manual in one sublibrary called Examples This library is separated into several FORTRAN routines The location of these rou tines is described in the installation guide Section 3 10 3 describes how to create a private function library and add model functions to this The contents of a sublibrary may be printed using the PRINT FUNCTION LIBRARY command The description of each function may be printed using the PRINT FUNCTION DESCRIPTION command SESAM Proban Program version 4 4 01 OCT 2004 3 61 3 10 1 The Built in Function Libraries Proban Version 4 3 contains three built in function libraries with the names Misc Math and Prob Logical The Math library contains a large number of basic mathematical functions the Prob Logical library contains probability functions and
5. SESAM Proban Program version 4 4 01 OCT 2004 5 69 DEFINE ANALYSIS OPTION DIFFERENTIATION uspacel uspace2 rel abs limit GENERATED DISTRIBUTION ANALYTICAL ONEWAY INCREMENTATION GRADIENT CALCULATION TWOWAY INCREMENTATION NUMERICAL U SPACE BOUNDS Value ON IMPORTANCE FACTORS OFF ON GRADIENT VALUES OFF NONE LOW LEVEL MEDIUM ANALYSIS OPTION INTERMEDIATE RESULTS EXCESSIVE ON POINT VALUES OFF ON NESTED ANALYSIS SHOW DURING ANALYSIS OFF ON PARAMETER STUDY OFF DEFAULT SEEDS RANDOM seed seed2 seed3 ALL SENSITIVITY NONE SELECTED Proban 5 70 PURPOSE 01 OCT 2004 SESAM Program version 4 4 Define analysis options for probability and distribution analyses PARAMETERS DIFFERENTIATION uspacel uspace2 rel abs limit GENERATED DISTRIBUTION GRADIENT CALCULATION U SPACE BOUNDS IMPORTANCE FACTORS INTERMEDIATE RESULTS GRADIENT VALUES LEVEL POINT VALUES Define differentiation increments for use in FORM SORM op timization and in calculation of sensitivity values The differentiation increment in U space It must be positive The differentiation increment for the Hessian matrix in U space Used during the FORM SORM optimization It must be positive Relative parameter increment It must be positive Absolute parameter increment It must be positive Limit for application of relative parameter increme
6. The same command cannot be entered recursive e g a DISPLAY FUNCTION command cannot be issued inside another DISPLAY FUNCTION command Commands can be nested this way to as many levels as desired However to nest with more than one level may be confusing and is not recommended The current status may be seen by typing 4 4 11 Aborting All or Parts of a Command To abort a command type two dots after each other Please note that all entries on the command line up to the double dot will be processed before the command is aborted The double dot clears all loops and previous input in the command and then presents the main prompt A double dot is only logged if a part of the current command has already been written to the journal file To abort parts of a command going back to the last LOOP or to the point of a left parenthesis in a multiple selection or a vector or a matrix type lt lt lt CtrIC may also be used to abort a command hold the Control key while typing C Usage of CtrlC will throw away all of the input of the command line as well as abort the command Unlike the double dot the input before the CtrlC is not processed CtrlC may also be used to abort a running analysis 4 4 12 Access to the Operating System It is possible to issue a command to the operating system at any level in a Proban command not from pro gramming mode This is done by typing an exclamation mark followed by the operating
7. This puts 20 integration points in the interval 9000 to 10800 If there is periodicity in the stochastic process only one period needs to be integrated The number of peri ods is input by the command DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS NUMBER OF TIME SPLITS 2 Proban SESAM 3 30 01 OCT 2004 Program version 4 4 The calculation proceeds as for an ordinary probability calculation The major difference is that importance factors are calculated only for the outer loop variables if a nested FORM analysis is implied by the model 3 6 Distribution Analysis and Results Performing a distribution analysis requires the following steps after the model has been specified 1 Select the method to be used for distribution analysis using SELECT ANALYSIS METHOD DISTRI BUTION ANALYSIS The default method is MONTE CARLO SIMULATION when Proban starts from a new database 2 Define the desired options for the chosen method and or general analysis options These options are explained in the DEFINE command The default options will be sufficient in most cases 3 ASSIGN SENSITIVITY CALCULATION to the required parameters and or decide the extent of sensi tivity calculation using DEFINE ANALYSIS OPTION SENSITIVITY 4 Run the analysis using RUN DISTRIBUTION ANALYSIS 5 Present the results using PRINT RESULT DISPLAY RESULT and PLOT The different analysis methods are described in separate sections using the examples from Se
8. SESAM Proban Program version 4 4 01 OCT 2004 5 1 5 COMMAND DESCRIPTION This chapter describes all the commands available in Proban As described in Chapter 4 Proban has two user interfaces A graphical user interface also called graphics mode and a text based command interface also called line mode The first section of this chapter lists the correspondence between the pulldown menus available in the graphical user interface and the line mode commands The line mode input is journalled also when the graphical user interface is used The line mode input is therefore described in full in this chapter The second section lists the line mode commands alphabetically The hierarchical structure of the line mode commands and numerical data is documented in this chapter by use of tables How to interpret these tables is explained below Examples are used to illustrate how the com mand structure may diverge into multiple choices and converge to a single choice In the example below command A is followed by either of the commands B and C Thereafter command D is given Legal alternatives are therefore A B D and A C D A ED C In the example below command A is followed by three selections of either of commands B and C as indi cated by 3 For example A B B B or A B BC or A C BC etc B A 3 C In the example below the three dots in the left most column indicate that the command sequ
9. Proban 5 78 SESAM 01 OCT 2004 Program version 4 4 DEFINE CONTINUOUS PROCESS ANALYSIS OPTION ANALYSIS OPTION INTEGRATION INTERVAL upperend lowerend OFF MINIMUM EXTREME VALUE integernumber NUMBER OF TIME SPLITS integernumber POINTS IN QUADRATURE integernumber PURPOSE Define analysis options default duration and default starting time for a continuous stochastic process PARAMETERS INTEGRATION INTERVAL MINIMUM EXTREME VALUE NUMBER OF TIME SPLITS POINTS IN QUADRATURE lowerend upperend OFF integernumber NOTES Reduce integration interval for crossing rate to contributory part The integration will be carried out between lower end and upper end The failure set is a series system of an integer number of equal but independent events Periodicity in a stochastic process may be exploited in order to reduce the integration effort If the number of periods time splits in the process is n then the actual duration is n D where D is the duration assigned to the process The integration is over the assigned duration D and the calculated expected number of crossings is multiplied by n The number of points in the quadrature used to calculate the ex pected number of crossings in the duration of the process Lower end of the reduced integration interval Upper end of the reduced integration interval Turn off assignment of reduced integration interval
10. lt dim gt The dimension of the distribution if this is not fixed input seq The sequence of parameters used to define the distributions parameter The parameter value s for the chosen input sequence Each parameter value may be either a numerical value or the name of an existing one dimensional variable Please note that the name of a variable cannot be abbreviated here SPLINE 1DIM The variable is assigned a distribution fitted to input data See a following page for details NOTES 1 The variable may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command 2 The distribution function and density values may be printed by use of the PRINT DISTRIBUTION com mand 3 The moments of the distribution are calculated and printed if possible by use of the PRINT VARIA BLE command 4 The distributions are listed in SESAM User s Manual Proban Distributions See also CHANGE VARIABLE DISPLAY DISTRIBUTION PRINT VARIABLE PRINT DISTRIBUTION e ASSIGN CORRELATION SESAM Proban Program version 4 4 01 OCT 2004 5 59 e ASSIGN EXTREME VALUE EXAMPLES CREATE VARIABLE X DISTRIBUTION Normal Mean CoV 22 0 2 CREATE VARIABLE Y DISTRIBUTION Normal Mean Std X 3 1 Proban 5 60 SESAM 01 OCT 2004 Program version 4 4 CREATE VARIABLE DISTRIBUTION SPLINE 1DIM UNWEIGHTED
11. 4644 1611 7 3 72 94 10628 74 83 23 9962 9227 8584 ga SESAM Proban Program version 4 4 01 OCT 2004 3 45 DISTRIBUTION END SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Distribution function Distribution T 1 20000 40000 60000 Variable 2 NPY_01 4 NPY_05 D NPY_10 m NPV_15 Figure 3 10 The distribution of NPV for different rates of return The density function plot clearly shows the change in both mean and standard deviation Proban SESAM 3 46 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Density function gt T 1 20000 40000 60000 Variable 2 NPV_01 4 NPY_05 D NP _10 m NPV_15 Figure 3 11 The density of NPV for different rates of return The 15 individual results may also be examined independently by selecting one in DISPLAY or any number in PRINT of the parameter values with the usual DISPLAY RESULT and PRINT RESULT com mand The probability of a loss is examined using a FORM analysis SELECT ANALYSIS METHOD PROBABILITY FORM RUN PROBABILITY ANALYSIS SINGLE EVENT NPV lt 0 Starting Probability Analysis of NPV lt 0 0 Parameter study r 0 100000E 01 Starting FORM calculation Starting linearization of SESAM Program version 4 4 01 OCT 2004 Single event NPV lt 0 0 Linearization completed Calculating importance factors FORM Reliability index FORM Proba
12. CPU time limit exceeded Number of simulations 50 Estimated Probability 2 9244E 01 Standard dev of Probability 9 5408E 03 Coeff of Var of Probability 0 033 Estimated Reliability index 0 5463 The messages are very similar to the messages produced by the other simulation methods This time the CPU time limit was the effective stop criterion It is also possible to demand a stop if a required coefficient of variation has been reached The stop criteria are manipulated using the command DEFINE PROBABIL ITY SIMULATION DIRECTIONAL This command is also used to define the search method and the simu lation method The summary print is identical to the print for Monte Carlo simulation The importance factors are printed using the ALL or IMPORTANCE FACTORS option SESAM Proban Program version 4 4 01 OCT 2004 3 23 PRINT RESULT IMPORTANCE FACTORS e ae a E ee a ee ee A a ee a a ia e ee ee Probability of NPV lt 0 0 Net Present Value Analysis method Directional simulation Ho Importance factors Variable Importance StDv Imp I2 55 1 4 8 11 35 4 4 5 ImpGroup 1 6 5 1 0 S 3 1 0 6 ImpGroup 1 El E2 Note the importance group that is created from the two correlated expense variables When two or more distribution variables are correlated they will generate only one importance factor together Note also that standard deviations are given This table shows clearly that if the
13. DEFINE ANALYSIS OPTION NEST ED ANALYSIS DIFFERENTIATION GLOBAL 1 0E 2 1 0E 2 1 0E 3 1 0E 3 1 0E 10 DEFINE ANALYSIS OPTION NEST ED ANALYSIS INTERMEDIATE RESULTS NONE SESAM Proban Program version 4 4 01 OCT 2004 5 77 DEFINE CONTINUOUS PROCESS ANALYSIS OPTION CONTINUOUS PROCESS DURATION Value STARTING TIME NONE PURPOSE Define analysis options default duration and default starting time for a continuous stochastic process PARAMETERS DURATION Default duration Will be used if the continuous process does not contain a TIME variable or if duration is not specified for the TIME variable If the model contains no TIME variable and a crossing rate is calculated the duration is not used STARTING POINT Default starting point Will be used if starting time is not spec ified for the TIME variable If the model contains no TIME var iable the starting time is not used Value Duration value or starting time value Can be a numerical value or the name of a one dimensional variable NONE Turn off assignment of duration value or starting point value NOTES See also e ASSIGN CONTINUOUS PROCESS EXAMPLES DEFINE CONTINUOUS PROCESS DURATION DurVar DEFINE CONTINUOUS PROCESS DURATION NONE DEFINE CONTINUOUS PROCESS STARTING TIME 0 0 DEFINE CONTINUOUS PROCESS STARTING TIME NONE
14. DEFINE PARAMETER STUDY e SELECT ANALYSIS METHOD CROSSING RATE ANALYSIS SAVE RESULT e PRINT RESULT SESAM Program version 4 4 DISPLAY RESULT EXAMPLES RUN CONTINUOUS PROCI 01 OCT 2004 ESS ANALYSIS CROSSING RAT RUN CONTINUOUS PROC ESS ANALYSIS CROSSING RAT E Cross E SINGLE en Proban GV EVENT Cross_Var gt 50 5 175 Proban SESAM 5 176 01 OCT 2004 Program version 4 4 RUN CONTINUOUS PROCESS ANALYSIS FIRST PASSAGE PROBA BILITY event SINGLE EVENT ld variable lt gt threshold FIRST PASSAGE PROBABILITY PURPOSE Run a first passage probability analysis PARAMETERS event Name of the event to be analysed The event cannot be a condi tional event or contain equality events SINGLE EVENT Event is specified directly as a simple inequality 1d variable Name of a one dimensional variable can be a coordinate of a multidimensional variable lt gt One of lt less than gt greater than threshold Numerical right hand side of the single event NOTES 1 The type of analysis being run is selected by use of the SELECT ANALYSIS METHOD FIRST PAS SAGE PROBABILITY ANALYSIS command The options to be used for the analysis are set by use of the DEFINE command 2 The result is stored under the name LastAnalysis and is overwritten the next time an analysis is per formed unless saved under another name using the SAVE RESULT com
15. Print distribution and density functions and fractile values for the variables assigned distributions with fixed or numerical parameters PARAMETERS valuel value2 LOW RESOLUTION HIGH RESOLUTION n ALL SIMULATIONS FRACTILE probability PROBABILITY fractile NOTES This input is only required if the selected result is a parameter study Valuel is then a selection of the first parameter values for which the study was run The particular results from the analysis using the selected value s will be printed This input is only required if the selected result is a two param eter study Value2 is then a selection of the second parameter values for which the study was run The particular results from the analysis using the selected value s will be printed Print a table of the distribution complementary distribution and density function values at 19 fixed probability values ranging from 0 001 to 0 999 Print a table of the distribution complementary distribution and density function values at n points ranging from median 4 standard deviations to median 4 standard deviations The sampled values are printed in sorted order increasing probability Print fractile values at the specified probabilities Also prints the complementary probabilities Print probabilities distribution function values at the specified fractiles Also prints the complementary probabilities at the specified points If a LOOP is s
16. Variable has a fixed value Numerical value of a fixed variable Variable assigned a model function See a following page for details The distribution of the variable is generated from the distribu tion of another variable Variable specifying a generated distribution This is a one di mensional variable or a coordinate in a multidimensional vari able The variable is the probability of an event The variable is generic time SESAM Proban Program version 4 4 01 OCT 2004 5 57 NOTES 1 Some of the variables in a generated distribution may be shared between the generated variable and the generating variable by using the ASSIGN CONDITIONING command 2 A generated distribution may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command See also e CHANGE VARIABLE e COPY VARIABLE DELETE VARIABLE e RENAME VARIABLE PRINT VARIABLE ASSIGN CONDITIONING e ASSIGN EXTREME VALUE EXAMPLES CREATE VARIABLI CREATE VARIABLI Width Width of plate FIXED 22 5 Amplitude Wave amplitude GENERATED Var44 o Fl Proban SESAM 5 58 01 OCT 2004 Program version 4 4 CREATE VARIABLE DISTRIBUTION distribution dim input seq parameter SPLINE 1DIM DISTRIBUTION PURPOSE To create a variable to be based on a distribution PARAMETERS distribution Name of the distribution excepting the spline distribution
17. Is a sophistication of the ORTHOGONAL 1 method Instead of using the simulated directions and their opposites all possible averages of two of these directions are used This gives a better coverage of u space but increases computation time consider ably As ORTHOGONAL 2 except that averages are formed of all possible combinations of three directions instead of two This method can be very time consuming Specifies how the line search for points on the limit state sur face is performed along the simulated direction This search method simply checks one point far out on the line and looks for a solution only if the sign of the function is differ ent at the origin and at the end point This method is generally sufficient for single events It is generally not recommended for analysis of other events This search method steps out to the first solution if any then takes one step to the end to see if there should be another solu tion This method is sufficiently accurate in most cases This search method steps out in the u space to the end of the line where the probability becomes negligible without skip ping any larger pieces The search method steps out in the u space until the probability of the remaining line becomes negligible as specified by the search limit The search limit may be entered as a PROBABIL ITY with value probval or as a STANDARD NORMAL ar gval which is the u space search limit Notice the corresp
18. Name Description Arguments Pl Applied load 1 P2 Applied load 2 L1 Location of load 1 L2 Location of load 2 Span Beam span Proban SESAM 3 68 01 OCT 2004 Program version 4 4 Formula P1 1 11 Span P2 L2 Span The formula is printed at the end of the function description The command PRINT FUNCTION FORMULA MomForml produces MomForml Moment at end of beam Gradients must be calculated numerically Name Description Value Index Pl Applied load at end position v1 P2 Applied load at other position V2 L1 Location load at end position v3 L2 Location load at other position v4 Span Beam span V5 Depth Effective Depth v6 Ts Steel yield stress V7 As Steel area v8 K Stress strain coefficient v9 Width Width of beam v10 Tc Concrete compressive strength Vel Formula Interpretation SUB PAGE 2 NOMENCLATURE Operator Function Name Operands Positions of Operand Values Result Position of Resulting Value Operator Operands Result x v8 v6 v12 V12 V7 V13 WRK v8 2 0 v14 K v9 V14 V15 EK V7 2 0 v16 v16 V10 V17 v17 V11 v18 SESAM Proban Program version 4 4 01 OCT 2004 3 69 R v15 V18 V19 V13 V19 V20 LoadPart V1 V2 V3 V4 V5 V21 X V3 V21 V22 V20 V22 V23 Formula As Depth Ts K As 2 Ts 2 Width Tc Ll LoadPart P1 P2 L1 L2 Span the print is of the function arguments the order of calculation and the input formula text The or
19. time derivative variable value NONE NOTES See also A variable with type attribute TIME A variable with type attribute DISTRIBUTION FITTED DIS TRIBUTION or GENERATED Time derivative of process variable A variable with type at tribute DISTRIBUTION FITTED DISTRIBUTION or GEN ERATED Duration value or starting time value Can be a numerical value or the name of a one dimensional variable Turn off assignment of duration value or starting point value or time derivative variable DEFINE CONTINUOUS PROCESS EXAMPLES CREATE ASSIGN ASSIGN CREATE CREATE ASSIGN ASSIGN VARIABLE CON CON VARIABLE VARIABLE CON CON Time TINUOUS PROC TINUOUS PROC PVar TDVar TINUOUS PROCESS TINUOUS PROCESS Time Variable ESS STA Process Process Variabl a a ESS DURATION Time DurVar RTING TIME Time 0 0 Variable DISTRIBUTION NORMAL e DISTRIBUTION NORMAL TIME DERIVATIVI TIME DERIVATIVE PVar TDVar PVar NONE SESAM Proban Program version 4 4 01 OCT 2004 5 13 ASSIGN CORRELATION BASIC value CORRELATION univariate NORMALIZED NONE PURPOSE Assign the same correlation or no correlation to a number of variables PARAMETERS univariate A selection of variables that are defined as one dimensional distributions with nu merical or fixed parameter values All pairs of the selected variables
20. DNY SESAM USER MANUAL Proban General Purpose Probabilistic Analysis Program DET NORSKE VERITAS SESAM User Manual Proban General Purpose Probabilistic Analysis Program Octber Ist 2004 Valid from program version 4 4 Developed and marketed by DET NORSKE VERITAS DNV Software Report No 92 7049 Revision 5 November 1st 2004 Copyright O 2004 Det Norske Veritas All rights reserved No part of this book may be reproduced in any form or by any means without permission in writing from the publisher Published by Det Norske Veritas Veritasveien 1 N 1322 Hovik Norway Telephone 47 67 57 99 00 Facsimile 47 67 57 72 72 E mail sales software sesam dnv com E mail support software support dnv com Website www dnv com If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas then Det Norske Veritas shall pay compensation to such person for his proved direct loss or damage However the compensation shall not exceed an amount equal to ten times the fee charged for the service in question provided that the maximum compensation shall never exceed USD 2 millions In this provision Det Norske Veritas shall mean the Foundation Det Norske Veritas as well as all its subsidiaries directors officers employees agents and any other acting on behalf of Det Norske Veritas 1 1 1 2 1 3 1 4 2 1 22 2 3 2 4 2 5
21. It is not possible to write plots with different colour options to the same file The DISPLAY command remembers the last command it executed and presents it as default the next time DISPLAY is entered Thus the command DISPLAY semicolon is a simple way of repeating the previous display command To display the input distributions in Example 3 1 and take a copy ona file use the following commands DISPLAY DISTRIBUTION ONLY Load RAl RB RC LOOP DISTRIBUTION PLOT DENSITY PLOT END Note the inserted plot commands that are executed without leaving the loop Proban may also be used to display events The plot in Figure 3 1 was generated by using the command DISPLAY EVENT System MULTIPLE The two distribution plots looks like this with the display frame off Proban SESAM 3 10 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 23 JUN 2000 11 28 Distribution function Distribution Variable 2 Load ARA D RB RC Figure 3 2 Distribution functions for variables in Example 3 1 SESAM Proban Program version 4 4 01 OCT 2004 3 11 SESAM PROBAN 4 3 03 23 JUN 2000 11 28 Density function Density Variable 2 Load ARA RB PRO Figure 3 3 Density functions for variables in Example 3 1 3 3 Probability Analysis and Results Performing a probability analysis requires the following steps after the model has been specified 1 Select the method to be used for proba
22. MEDIUM LOW FREE UNIMODAL EQUAL The fractiles and probability values to which the distribution function is fitted All probabilities must be greater than 0 and smaller than 1 The fractiles and probability values to which the distribution function is fitted with corresponding weights All probabilities must be greater than 0 and smaller than 1 Use high accuracy when fitting the spline distribution to the da ta In some cases it may be difficult to get convergence when high accuracy is used Use medium accuracy when fitting the spline distribution to the data Use low accuracy when fitting the spline distribution to the da ta The fitted distribution need not be unimodal The fitted distribution must be unimodal The tail values of a FREE fit must be identical Proban SESAM PB OCA Programversion 4 4 FREE No restriction on the tail values of a FREE fit except that they are non negative VANISH Both tail values of a FREE fit must be zero NOTES 1 The existing values are presented as defaults whenever this is possible If changing from UNWEIGHTED to WEIGHTED the existing fractiles and probabilities are kept as defaults and the weights are all set to 1 If the spline will not fit try relaxing the demands on accuracy or check if any of the points have been specified wrongly The variable may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command The distribution function and den
23. NAME and STATUS is specified the prompt for database and journal file file name is disabled and defaults are used for any unspecified values 5 Proban will issue a message when an error is found in the command line specification Table 4 1 Command line arguments HEADER SHORT Give the usual start up header SHORT or no start up header NONE NOHEADER Same as HEADER NONE PREFIX prefix Specifies the database and journal file prefix NAME name Specifies the database and journal file name STATUS status Specifies the database and journal file status as OLD or NEW INTERFACE LINE Start the program in line mode ignoring the graphics user interface INTERFACE WINDOW Start the program in graphics mode COMMAND FILE filename NOCOMMAND FILE Read the specified command input file just after the database has been opened and initialised Do not read an initial command input file FORCED EXIT Exit Proban after the database has been opened and initialised and any initial command file has been read NOFORCED EXIT Disable the forced exit COMPANY NAME value Specifies the header in the display see also SET COMPANY NAME PRINT FORMFEED value Use FORTRAN or ASCII formfeed character on LIS files PLOT COLOUR value Specifies the plot colour see also SET PLOT COLOUR SESAM Proban Program version 4 4 01 OCT 2004 4 3 Table
24. See also e CHANGE VARIABLE e COPY VARIABLE e RENAME VARIABLE PRINT VARIABLE e ASSIGN CONDITIONING EXAMPLES CREATE VARIABLE P EVENT PROBABILITY RELIABILITY INDEX EVENAM Proban 5 68 01 OCT 2004 DEFINE DEFINE ANALYSIS OPTION CONTINUOUS PROCESS DISTRIBUTION SIMULATION FORM SORM MEAN VALUE FORM PARAMETER STUDY PRESENTATION PROBABILITY SIMULATION TWO PARAMETER STUDY SESAM Program version 4 4 PURPOSE Define global parameters or analysis options PARAMETERS ANALYSIS OPTION CONTINUOUS PROCESS DISTRIBUTION SIMULATION FORM SORM MEAN VALUE FORM PARAMETER STUDY PRESENTATION PROBABILITY SIMULATION PARAMETER STUDY Define general options for distribution and probability analysis Define general options for crossing rate and first passage anal ysis Define simulation of distributions Define options for FORM and SORM probability analysis Define how a mean based FORM distribution analysis is per formed Define values of a parameter for repeated analysis as a function of this parameter Define options used for presentation print and display Define options for simulation of probabilities Define for each of two parameters an array of values for repeat ed analysis covering the matrix of values defined by the two ar rays
25. tion guide for the location of this file These files are self explanatory please read the comments in the files To get started take a copy of the function library FUNCLB that is delivered with Proban and of the source code that is delivered with it as well as the file that is used to maintain the object library This function library contains a dummy LIBLIM routine as well as the example sublibrary If you need to incorporate an existing LIBLIM remove the LIBLIM delivered with Proban and simply com pile your own LIBLIM routine s including all sublibraries and functions and add them to the FUNCLB Proban SESAM 3 70 01 OCT 2004 Program version 4 4 object library If you do not need to program a new function you are ready to link Proban see step 5 below The example library may be removed by editing the call to EXAMLB out of FUNCLB Remember to change the number of sublibraries in FUNCLB To add a function to the function library follow the procedure described here The location of the templates is described in the installation guide The templates contain much documentation that will not be mentioned here 1 Program the function using FORTRAN 90 There is a number of templates available for different types of functions The complexity of the function is dependent on the capabilities of the function Use the template that fits the functions capabilities in order to avoid unnecessary work FUNC10 DOC is used for a func
26. 3 889E 05 0 29169 El Lognormal Mean 5 000E 03 1 146E 06 0 00057 E2 Triangle Mean 5 000E 04 5 882E 05 0 29412 E2 Lognormal Mean 1 000E 04 9 519E 07 0 00095 S Normal Mean 1 000E 04 4 203E 19 0 00000 Parametric sensitivity result for Kurtosis 2 7728764069 Variable Type Parameter Value dKurt dPar Measure 11 Triangle Mean 7 500E 04 1 298E 05 0 09733 El Lognormal Mean 5 000E 03 6 829E 07 0 00034 12 Triangle Mean 5 000E 04 2 853E 06 0 01427 E2 Lognormal Mean 1 000E 04 2 508E 07 0 00025 SESAM Proban Program version 4 4 01 OCT 2004 3 35 S Normal Mean 1 000E 04 1 714E 18 0 00000 A change in the mean will cause a shift in the distribution affecting the profit while a change in the stand ard deviation will cause a change in the slope of the distribution function at the centre of the distribution affecting the risk See also Figure 2 9 and Figure 2 10 The sensitivity measure is useful for getting an overview of the effect of the different parameters The meas ure is described in Section 2 8 The ALL option gives the print shown above plus a list of intermediate simulation results and a table show ing the empirical distribution The table of intermediate results is useful for checking if the simulation has stabilised If the mean or stand ard deviation fluctuate it may be necessary to continue the simulation see RUN RESTART The skewness and kurtosis can be expected to fluctuate They describe the tail b
27. CREATE EVENT CHANGE EVENT DISPLAY EVENT ASSIGN STARTING POINT ASSIGN MEASURED VALUE SET TITLE SESAM Program version 4 4 01 OCT 2004 Proban 5 139 EXAMPLES PRINT EVENT J3220 CGFail J5 I1 INA11 Generates the following print J3220 CGFail Crack growth failure for fatigue point J3220 Event type Subevent Subtype J5 I1 INAl1 All inspections up to J5 I1 Event type Subevent Subtype Contents Intersection J5 I1 INLen Single J5 I1 INLen 0 0 Proban SESAM 5 140 01 OCT 2004 Program version 4 4 PRINT FUNCTION DESCRIPTION FORMULA FUNCTION GRADIENT LIBRARY VALUE PURPOSE Print information about the model functions that are available in the program PARAMETERS DESCRIPTION FORMULA GRADIENT LIBRARY VALUE NOTES None Print a description of one or more functions Print a description and a calculation scheme for one of more function formulas Calculate and print a gradient for a function Print a description of a selection of function libraries Calculate and print a gradient for a function SESAM Proban Program version 4 4 01 OCT 2004 5 141 PRINT FUNCTION DESCRIPTION DESCRIPTION name PURPOSE Print a description of a selection of functions PARAMETERS lt name gt Name s of the function s to be printed NOTES The selection of functions presented is determined by the cu
28. Controls the limits of the x axis The limits are determined by the data that are being presented The limits are fixed to the minimum value xmin and the maxi mum value xmax Controls the spacing of numbers along the axis The axis has a LINEAR spacing The axis has a logarithmic spacing with base 10 Set the title at the x axis Proban SESAM FB OCA Program version 4 4 DEFAULT The title is specified by Proban according to the current graphs being drawn SPECIFIED xtitle The specified xtitle text is used NOTES See also DISPLAY PLOT SET GRAPH YAXIS ATTRIBUTTES SET GRAPH ZAXIS ATTRIBUTTES EXAMPLES The following is default when the program starts with a new database SET GRAPH XAXIS ATTRIBUTES DECIMAL FORMAT GENERAL SET GRAPH XAXIS ATTRIBUTES LIMITS FREE SET GRAPH XAXIS ATTRIBUTES SPACING LINEAR SET GRAPH XAXIS ATTRIBUTES TITLE DEFAULT SESAM Program version 4 4 Proban 01 OCT 2004 5 209 SET GRAPH YAXIS ATTRIBUTES YAXIS ATTRIBUTES EXPONENTIAL FIXED GENERAL INTEGER DECIMAL FORMAT FIXED ymin ymax FREE LIMITS LINEAR LOGARITHMIC SPACING DEFAULT SPECIFIED ytitle TITLE PURPOSE Control the drawing of the Y axis in a graph display PARAMETERS DECIMAL FORMAT EXPONENTIAL FIXED GENERAL INTEGER LIMITS FREE FIXED ymin ymax SPACING LINEAR LOGAR
29. PRINT DISTRIBUTION PRINT VARIABLE e SET EXAMPLES DISPLAY FITTED DISTRIBUTION Sp133 Proban SESAM 5 116 01 OCT 2004 Program version 4 4 DISPLAY FUNCTION FUNCTION name coord from ONE ARGUMENT argx tox SURFACE TWO ARGUMENTS argx tox argy toy CONTOUR min max step PURPOSE Display distribution and density functions for existing variables PARAMETERS name coord from ONE ARGUMENT argx tox TWO ARGUMENT argy toy SURFACE CONTOUR min max step NOTES Name of the function Coordinate of the function if multidimensional Argument value s where the calculation of the function is started Display the function as a graph with one argument along the ab scissa and the function value as the ordinate Name of the argument to be used as abscissa End value along the abscissa axis Display the function as a surface or contour plot This option is not available for functions with only one argument Name of the argument to be used as ordinate End value along the ordinate axis Show a surface plot Show a contour plot Contour specification min min step until max is reached 1 Functions where the number of coordinates is defined by the user cannot be displayed 2 The function option values in effect at the time of display will be used Note that these may affect the number of arguments of the function as
30. PROBABILITY fractile q PURPOSE Print distribution and density functions and fractile values for the variables assigned distributions with fixed or numerical parameters PARAMETERS univar LOW RESOLUTION HIGH RESOLUTION n FRACTILE probability PROBABILITY fractile NOTES Selection of variables that are defined as one dimensional dis tributions with numerical or fixed parameters Print a table of the distribution complementary distribution and density function values at 19 fixed probability values ranging from 0 001 to 0 999 Print a table of the distribution complementary distribution and density function values at n points ranging from median 4 standard deviations to median 4 standard deviations Print fractile values at the specified probabilities Also prints the complementary distribution and density function at the specified points Print probabilities distribution function values at the specified fractiles Also prints the complementary distribution and densi ty function at the specified points If a LOOP is specified in line mode input after DISTRIBUTION any specified fractiles or probabilities are kept as defaults Otherwise the default set of fractiles and probabilities is empty See also DISPLAY DISTRIBUTION e PRINT VARIABLE e SET TITLE SESAM Program version 4 4 EXAMPLES Proban 01 OCT 2004 5 137 PRINT DISTRIBUTION StdNormal LOW RESOLUTION Generates the followi
31. SELECT ANALYSIS METHOD DISTRIBUTION ANALYSIS PRINT ANALYSIS SETTINGS e RUN DISTRIBUTION ANALYSIS EXAMPLES The following values are default when the program starts up with a new database DEFINE DISTRIBUTION SIMULATION MONTE CARLO SIMULATION 1000 DEFINE DISTRIBUTION SIMULATION LATIN HYPERCUBE SIMULATION 100 SESAM Proban Program version 4 4 01 OCT 2004 5 81 DEFINE FORM SORM ON BOUNDS OFF ON INACTIVE CONSTRAINTS OFF SQP MULTINORMAL CRUDE SQP maxit maxstep conv GLOBAL NLPQL NESTED ANALYSIS RFCRC SYSTEM RSM SQP maxit maxstep conv FORM SORM NLPQL OPTIMIZATION RFCRC RSM ONE WAY ANALYTICAL SENSITIVITY TWO WAY ASYMPTOTIC ASSIGNED INITIAL DEFAULT STARTING POINT PREVIOUS SOLUTION PARAMETER STUDY SAME AS INITIAL RESET PURPOSE Define FORM SORM analysis options PARAMETERS BOUNDS Control the usage of bounds in probability calculation in a large intersection If ON bounds are used If OFF the probability is calculated using the multinormal distribution on the comple mentary set Proban 5 82 INACTIVE CONSTRAINTS MULTINORMAL NESTED ANALYSIS GLOBAL SYSTEM OPTIMISATION SQP maxit maxstep conv NLPQL RFCRC RSM SENSITIVITY STARTING POINT INITIAL SESAM 01 OCT 2004 Program version 4 4 Control linearisation of constraints that a
32. The name of the distribution excepting the spline distribution and multidimensional distributions The sequence of parameters used to define the distributions The parameter specification for the chosen input sequence Each parameter value may be either specified as a numerical value in which case it is not fitted as FIT in which case it is fitted or as FIT lt value gt where lt value gt is a numerical value used as starting point for an iterative fit A lower bound on the fitted value is specified by L lt value gt An upper bound on the fitted value is specified by U lt value gt Fit to cumulative input data The input data are weighted The weights must be positive The input data are not weighted Successive values of fractiles cumulative probabilities and weights The probabilities must be in the interval 0 1 The in put data will be sorted in order of increasing probability Successive values of fractiles and cumulative probabilities The probabilities must be in the interval 0 1 The input data will be sorted in order of increasing probability Proban SESAM 01 OCT 2004 Program version 4 4 5 40 OBSERVATIONS OBSERVATION MOMENTFIT Observation Weight Observation RESULT RESULT MOMENTFIT result name NOTES The input data are observed values of the variable The input data are observed values of the variable and first mo ments fit is used Successive values of observations and wei
33. The particular re sults from the analysis using the selected value s will be printed value2 This input is only required if the selected result is a two parameter study value2 is then a selection of the parameter values for which the study was run The particular results from the analysis using the selected value s will be printed NOTES The print does not contain the sample resulting from a simulation This sample will often be very large and it can be printed by use of PRINT RESULT SAMPLE See also SELECT RESULT e SET TITLE EXAMPLES PRINT RESULT ALL no parameter study DISPLAY RESULT ALL all results from a study oe Proban SESAM 5 154 01 OCT 2004 Program version 4 4 PRINT RESULT ANALYSIS SETTINGS ANALYSIS SETTINGS PURPOSE Print analysis options applied to a probability a crossing rate a first passage probability or a distribution analysis PARAMETERS None NOTES This print contains the date time and cpu time consumption for the analysis See also DEFINE RUN CONTINUOUS PROCESS ANALYSIS RUN DETERMINISTIC ANALYSIS e RUN PROBABILITY ANALYSIS e RUN DISTRIBUTION ANALYSIS e SELECT RESULT e SET TITLE EXAMPLES PRINT RESULT ANALYSIS SETTINGS SESAM Proban Program version 4 4 01 OCT 2004 5 155 PRINT RESULT IMPORTANCE FACTORS IMPORTANCE FACTORS valuel value2 PURPOSE Print importance factors
34. aA LVA DALNI Figure 1 1 SESAM overview SESAM Proban Program version 4 4 01 OCT 2004 1 3 SESAM is comprised of preprocessors environmental analysis programs structural analysis programs and postprocessors An overview of SESAM is shown in Figure 1 1 1 3 How to Read this Manual Chapter 2 FEATURES OF PROBAN describes the features of Proban i e what the program can do Chapter 3 USER S GUIDE TO PROBAN is the user s guide It contains guidance on how to exploit the fea tures of Proban Chapter 4 EXECUTION OF PROBAN describes how to start the program and how to navigate the user interface It also describes the files used by Proban and the program s requirements and limitations Chapter 5 COMMAND DESCRIPTION provides a description of all commands and associated input data Appendix A PROBAN LINK IN FUNCTIONS AND DISTRIBUTION explains how to link in functions and distributions defined and coded by the user The distribution models available are described in detail in SESAM User s Manual Proban Distributions DNV SESAM Report NO 94 7089 Rev 1 June 1996 The theory is described in detail in SESAM Theory Manual Proban No 96 7017 Rev 0 29 September 1996 1 4 Changes from the Previous Revision The following changes have been made with respect to the previous revision of the manual generally described e Distribution simulation of vector variables e Simple response surface for functions e Moment fit of distr
35. c cc ccccccssccsccesscesseeseeeseeeseceseceeeeeeeeesecsaecseseeeseeeeseecaeseeeeeeaes 4 21 4 5 6 Entering a Vector or a Matrix of Values ccccccccescesceeceesceesseneceseeeseeeseenseceeeseeseneeaaes 4 21 4 5 7 Journalling from Graphics Mode 0 cccccccecssesseesseceeceeeceeceeseecscenseceseceaeeeseceaeceseeeeeseneeaaes 4 22 COMMAND DESCRIPTION ssccsscssscecssscevnstocsueethscosencnbvcia ceooncteaensdevnsnssoveusechossvencesecdoccous 5 1 Graphical User Interface Menus cccceccecsseesseeseceeeceseeeseeesecaecneeseneeseecsaecseceseeseeeseecseeeseseesereeaaes 5 2 Dold Whe E E EAEE EA E E E 5 2 1 2 The Fun O ME e e a e a dE 5 3 S13 The Variable Me dias 5 3 SLA The Process Menik esea ooo e aE aa E E e e a ETE 5 4 51 5 ThesE vert Ment meer e r A A E A Ea EE 5 4 1 67 The Analysisi Ment 0 ts E ca A E AAA E E Ea 5 4 5170 The Result Men ii plea ssagausded ead a e aaa S 5 6 58 The Options MENU a tilda iria 5 7 5 2 S19 The Help Me it A A A at A AAA IA 5 7 Line Mode Command Syntax assaiant iii aini a a A a a iane 5 8 A A E E a a 5 9 ASSIGN CONDITION dE tc 5 11 ASSIGN CONTINUOUS PROCESS 0 dci Na 5 12 ASSIGN CORRELATION o otto Ganbavaasteesasebavasantesteas 5 13 ASSIGN EC DREN TUE iso Mas IEG AiG Sado 5 14 AUS SIGN FUNC TIQINGOP TIOIN td A AAA eR 5 15 ASSIGN MEASURED VALUE ibid 5 16 ASSIGN OPTIMISATION BOUNDS latas id ine avectoig telne nave Seeivelsanistcbets 5 17 ASSIGN SENSED TE Y CALCUL
36. event PROBABILITY ANALYSIS SINGLE EVENT ld variable lt gt threshold CONDITIONED event SINGLE EVENT 1d variable gt threshold conditioning event SINGLE EVENT 1d variable threshold PURPOSE Run a probability analysis PARAMETERS event SINGLE EVENT 1d variable threshold CONDITIONED conditioning event NOTES The name of the event to be analysed The event is specified directly as a simple in equality The name of a one dimensional variable can be a coordinate of a multidimensional variable One of lt less than equal gt greater than The numerical right hand side of the single event Analyse the conditioned probability of one event given another The name of the conditioning event This event cannot be of the conditioned type The type of analysis being run is selected by use of the SELECT ANALYSIS METHOD PROBABIL ITY ANALYSIS command The options to be used for the analysis are set by use of the DEFINE com mand The result is stored under the name LastAnalysis and is overwritten the next time an analysis is per formed unless saved under another name using the SAVE RESULT command 3 See also The results are examined by use of the commands PRINT RESULT or DISPLAY RESULT Proban 5 184 DEFIN e DEFIN DEFIN E FORM SORM 01 OCT 2004 E ANALYSIS OPTION E PROBABILITY SIMULATION DEFINE
37. fractile probability SPLINE 1DIM lower upper WEIGHTED fractile probability weight HIGH EQUAL MEDIUM FREE FREE VANISH LOW UNIMODAL PURPOSE To create a variable to have a fitted distribution based on splines PARAMETERS lower upper UNWEIGHTED WEIGHTED fractile probability fractile probability weighted HIGH MEDIUM LOW FREE UNIMODAL EQUAL The lower bound of the distribution The upper bound of the distribution Do not apply user defined weights to the spline fit Apply user defined weights to the input points in the spline fit The fractiles and probability values to which the distribution function is fitted All probabilities must be greater than 0 and smaller than 1 The fractiles and probability values to which the distribution function is fitted with corresponding weights All probabilities must be greater than 0 and smaller than 1 Use high accuracy when fitting the spline distribution to the da ta In some cases it may be difficult to get convergence when high accuracy is used Use medium accuracy when fitting the spline distribution to the data Use low accuracy when fitting the spline distribution to the da ta The fitted distribution need not be unimodal The fitted distribution must be unimodal The tail values of a FREE fit must be identical SESAM Proban Program version 4 4 01 OCT 2004 5 61 FREE No restriction on the tail values of a FREE fit excep
38. input space Secondly the V space is mapped into U space so that the U space variables are uncorrelated The event that is being analysed is formulated inside Proban as G x lt 0 where G is an appropriate func tion The terminology used here derives from structural reliability analysis calculation of small probabili ties The function G is called the limit state function The set where the event is fulfilled is formulated as G x lt 0 and is called the failure set The surface where G x 0 is called the failure surface or the limit state surface The set where G x gt 0 is called the safe set These terms and the transformation is illustrated in Figure 2 3 g u 0 failure set G x 0 failure set Safe set Safe set 19 ke F k PPP PY x space wspace j S N OSB a 21 exp uTu 2 UY Figure 2 3 Transformation from input space to U space The required probability P g u lt 0 is approximated using the following steps An approximation point is found using an optimization method the nearest point to the origin on the failure surface This point is called the design point u The failure surface is approximated at this point using either a linear approximation FORM or a second order approximation SORM The probability content in the failure set is approximated by the probability content in the approximated failure set The Reliability Index B is defined as the standard norm
39. 1000 SESAM Proban Program version 4 4 01 OCT 2004 5 105 DEFINE TWO PARAMETER STUDY TWO PARAMETER STUDY parameterl ma valuel parameter2 value2 PURPOSE Define two parameter study values Each parameter is one of a fixed variable or of a numerical parameter in a distribution or of a numerical argument in a function PARAMETERS parameter 1 The name of a fixed variable or the name of a numerical parameter in a distribution or of a numerical argument in a function value Those parameter values of parameter for which the parameter study is to be per formed parameter2 The name of a fixed variable or the name of a numerical parameter in a distribution or of a numerical argument in a function value2 Those parameter values of parameter2 for which the parameter study is to be per formed NOTES 1 The parameter study is performed over the matrix valuel value2 so that all combinations of values are covered 2 A parameter study may be modified by entering the command again and selecting the same parameters The current values are then presented as defaults 3 Usage of the parameter study is controlled by the command DEFINE ANALYSIS OPTION PARAME TER STUDY 4 This command is described in the User s Manual for Proban Version 3 as ASSIGN PARAMETER STUDY See also DEFINE ANALYSIS OPTION PARAMETER STUDY PRINT PARAMETER STUDY PRINT RESULT PARAM
40. 2 CHANGE FUNCTION FORMULA SYMFOR2 Symbolic Formula A FUNOPT OPT NAM 1 Quot 1 OPT NAM 2 file name OPT NAM 3 MENU_ENTRY OPT_NAM 4 3 OPT NAM 5 0 5E 3 B 3 A SESAM Program version 4 4 Proban 01 OCT 2004 5 29 CHANGE FUNCTION INTEGRAL INTEGRAL ma value argname argdesc function integrator a method lowerbound upperbound tolerance PURPOSE To change an integration function PARAMETERS argname argdesc function value integrator method lowerbound upperbound tolerance NOTES Matrix of argument names and corresponding argument descriptions At least one argument must be defined Name of function to be integrated integrand Value can be a numerical value or an argument name argname Text value integrator Case insensitive The text value integrator is inserted in order to identify the single integration variable Integration method to be used One of ROMBERG SIMPSON or TRAPEZOI DAL Lower bound for integrator Must be a numerical value or an argument name ar gname Upper bound for integrator Must be a numerical value or an argument name ar gname Relative precision in result of integration 1 An argument name consists of maximum 12 alphanumeric characters and _ The first character must be alphabetic 2 An argument description co
41. 2004 5 85 DEFINE RFCRC RFCRC method maxit conv test PURPOSE Options for RFCRC PARAMETERS method One of RF Racwitz Fiessler method and RFCRC Rackwitz Fiessler method robusted with circle steps maxit Maximum number of general iterations gradient evaluations conv Optimality criterion Test for the U space distance between the two last iterates test Progress test If RFstep i 1 suggested by the algorithm is less than RFstep i test then accept the step else proceed with a cir cle step NOTES A RF step is performed initially Then the next step suggested by the RF method is examined If the progress is unsatisfactory then a circle step is performed This step defines a u space circle with center at u 0 and passing through the current iteration point in the plane defined by the u space gradient at that point The minimum point um of the event function g u on this circle is found and an iteration is performed on the line from 0 to um to find g unext 0 The method is restricted to a single event The analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also PRINT ANALYSIS SETTINGS EXAMPLES The following values are default when the program starts up with a new database DEFINE FORM SORM OPTIMIZATION RFCRC CIRCLE 40 0 001 4 0 Proban SESAM 5 86 01 OCT 2004 Program version 4 4 DEFINE RSM RSM method contribution ma
42. 21 NOV 2000 13 25 Skewness Measure of symmetry Skewness of x_2 Skewness of x_4 1 0 Skewness of x 3 1 0 Distribution function 1 0 0 8 Distr ibut ton 0 4 0 6 lt 2 0 0 0 Var table A x_i ata X2 s aS Figure 2 14 Illustration of Skewness SESAM Program version 4 4 SESAM Proban Program version 4 4 01 OCT 2004 2 23 SESAM PROBAN 4 3 03 07 JUN 2000 15 21 Kurtosis Measure of relative tail thickness Kurtosis of x 1 5 0 0 Kurtosis of X_2 3 0 Kurtosis of x 3 1 5 Density function i Po a E Ol ea 0 pel o Nu oO a4 B o 4 4 Var Lab le AL x_i ak x_2 O x_3 SESAM PROBAN 4 3 03 O7 JUN 2000 15 21 Kurtosis Measure of relative tail thickness Kurtosis of x 1 5 0 0 Kurtosis of X_2 3 0 Kurtosis of x 3 1 5 Distribution function O E En 3 39 hes a6 ee aso Es oO A a a o 4 Var Lab Le An x_ E ae eae O x_3 Figure 2 15 Illustration of Kurtosis Proban fits if possible a Hermite transformation distribution to the sample using the estimates of the first four moments This is stored in a variable called Hermite Fit Proban will also fit a normal distribution using the estimated mean and standard deviation This is stored in a variable called Normal Fit Proban SESAM 2 24 01 OCT 2004 Program version 4 4 It is also possible to fit other distrib
43. 4 DEFINE PRESENTATION FUNCTION 1D FUNCTION DISPLAY nval 2D FUNCTION DISPLAY nx ny FUNCTION PURPOSE Define options for presentation of model functions PARAMETERS 1D FUNCTION DISPLAY nval The number of function evaluations used in a one dimensional graph of a model function 2D FUNCTION DISPLAY nx ny The number of abscissa nx and ordinate ny values used in a two dimensional display of a model function The total number of function evaluations will be nx ny NOTES See also e DISPLAY FUNCTION EXAMPLES The following values are default when the program starts up with a new database DEFINE PRESENTATION FUNCTION 1D FUNCTION DISPLAY 101 DEFINE PRESENTATION FUNCTION 2D FUNCTION DISPLAY 21 21 SESAM Program version 4 4 Proban 01 OCT 2004 5 93 DEFINE PRESENTATION RESULT CONFIDENCE VALUE conf IMPORTANCE CUTOFF cutoff IMPORTANCE LIMIT limit INTERMEDIATE SIMULATIONS intsim RESULT SENSITIVITY MEASURE inc lim ON V SPACE POINT OFF RESET PURPOSE Define options for presentation of results PARAMETERS CONFIDENCE VALUE conf IMPORTANCE CUTOFF cutoff IMPORTANCE LIMIT limit INTERMEDIATE SIMULATIONS intsim SENSITIVITY MEASURE inc lim The confidence value that is used with print and display of con fidence limits This value must be given in e g a value of 95 will print display 95 confiden
44. 4 1 Command line arguments PLOT FORMAT format Specifies the plot file format see also SET PLOT FORMAT PLOT PAGE SIZE value Specifies the plot page size see also SET PLOT PAGE SIZE DISPLAY COLOUR value Specifies display colour see also SET DISPLAY COLOUR DISPLAY DEVICE device Specifies display device see also SET DISPLAY DEVICE 4 1 2 Starting Proban in Graphics Mode To start Proban in graphics mode the computer must be running under the Motif window manager Proban reads a resource file with the name faceitClass on Unix systems note the use of upper and lower case letters This file is placed in the directory where private X application resource files are kept often the home directory Proban must use a fixed width font otherwise the messages and prints will be misaligned If running on a Unix system the command to be used to start Proban in graphics mode is simply prompt gt proban If running on an NT system the command to be used to start Proban in graphics mode is simply prompt gt proban or proban exe If running on an NT system notice that the funclib dll containing the functions must be in the user LIB path or on the same directory as the executable Proban responds by opening the main window and overlaying it with a dialog box requesting the database file prefix name and status provided that none of these were specified as command line arguments see Section 4 1 1 Note
45. 990 3 618389864E 04 0 999 The final print option gives a print of the whole sample the first column showing the values in the order they were sampled and the second column showing the values in increasing order The length of this print is usually very large a typical sample is 1000 values producing more than 1000 lines of print so be careful with this one The following lists the beginning and end of a print of a sample PRINT RESULT SAMPLE MCS NPV Monte carlo simulation of the Net Present Value NPV Distribution of Net Present Value Monte Car o simu Analysis method SimNo Observation Sorted 1 1 091962657E 03 2 188313507E 04 2 4 877797384E 03 2 167421873E 04 3 2 817265088E 02 1 898907363E 04 4 6 398132552E 03 1 813028770E 04 5 8 561568457E 03 1 749456502E 04 997 5 078346459E 03 2 883378727E 04 998 1 332132339E 04 3 004064064E 04 999 8 859116186E 03 3 060224454E 04 1000 2 935722632E 03 3 618948588E 04 The simulation may be restarted using the RUN RESTART command continuing from the previous result The number of simulations to be done can be changed before the restart SESAM Proban Program version 4 4 01 OCT 2004 3 37 Consider now the situation in Example 3 2 after 6 months where the manager has obtained information that the income after the first year will exceed 70000 The updated distribution for the Net Present value is calcu lat
46. CREATE VARIABLE DISPLAY DISTRIBUTION DISPLAY FITTED DISTRIBUTION PRINT VARIABLE PRINT DISTRIBUTION Proban 5 64 01 OCT 2004 Program version 4 4 e ASSIGN EXTREME VALUE EXAMPLES CREATE VARIABLE X FITTED DISTRIBUTION Normal Mean CoV FIT FIT OBS UNW ONLY 1 34 2456 8 65 4 32 4 67 6 66 5 23 3 25 CREATE VARIABLE Y FITTED DISTRIBUTION Normal Mean Std FIT15 FIT CUMULATIVE WEIGHTED ONLY 12 0 1 1 15 0 3 2170 7 1 200 91 CREATE VARIABLE RES FITTED DISTRIBUTION Lognormal Mean Std L FIT FIT 0 RESULT LastAnalysis SESAM SESAM Proban Program version 4 4 01 OCT 2004 5 65 CREATE VARIABLE FUNCTION FUNCTION function dim argument PURPOSE To create a variable to be a function of numerical values or other variables PARAMETERS function The name of the function The functions can be listed by use of the commands PRINT FUNCTION LIBRARY and PRINT FUNCTION DESCRIPTION dim The dimension of the function if this is not fixed argument The argument value s for the chosen function Each argument value may be either a numerical value or the name of an existing one dimensional variable Please note that the name of a variable cannot be abbreviated here NOTES The selection of functions presented is determined by the current selection of sub libraries see SELECT FUNCTION LIBRARY This is because some libraries may contai
47. DISPLAY RESULT IMPORTANCE FACTORS e SELECT RESULT e SET EXAMPLES DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR ONLY Depth ImpGroup 1 DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR ONLY T Proban SESAM 5 124 01 OCT 2004 Program version 4 4 DISPLAY RESULT PARAMETER STUDY MAIN RESULT MAIN RESULT mainres coordinate PURPOSE Display main results as a function of the parameters in a parameter study PARAMETERS mainres A selection of main results The list of available results depend on the analysis per formed All possible main results are presented in the list even though they may not all be calculated for all the individual analyses in the parameter study For de terministic analysis of a variable there will be one result for each coordinate and for an event there will be one result These results will be named after the variable or event analysed coordinate A coordinate of a vector if a vector variable with more than one coordinate is sam pled NOTES See also e PRINT RESULT PARAMETER STUDY MAIN RESULT e SELECT RESULT e SET EXAMPLES DISPLAY RESULT PARAMETER STUDY MAIN RESULT ONLY Prob Conf DISPLAY RESULT PARAMETER STUDY MAIN RESULT ONLY Mean SESAM Proban Program version 4 4 01 OCT 2004 5 125 EXIT EXIT PURPOSE Close all open files and stop execution of Proban PARAMETERS
48. DISTRIBUTION ANALYSIS MI RUN DISTRIBUTION ANALYSIS NPV SESAM Program version 4 4 01 OCT 2004 Starting Distribution Analysis of NPV Starting Mean Value based FORM calculation Using 19 points from probability 1 0E 02 to 0 99 Mean Value based FORM calculation completed The result may be printed PRINT R ESULT ALL es ag eng a sg tos Se Sey eg ig EES yt Ss gg a gi int it ey eg ag ad iy Soest ai Distribution of NPV Net Present Value Analysis method Mean Value FORM in is et anh pas en ey he Sgn a es dl feta npn sh el Se Set eee ISA Fractile Prob Beta 1 645756331E 04 0 010000 2 3263 1 441564890E 04 0 019326 2 0679 1 220139988E 04 0 035196 1 8094 9 839270797E 03 0 060463 1 5509 7 362152817E 03 0 098107 1 2924 4 810213974E 03 0 150584 1 0339 2 229028106E 03 0 219037 0 7754 3 328901273E 02 0 302590 0 5170 2 826943311E 03 0 398017 0 2585 5 207437625E 03 0 500000 0 0000 7 587310473E 03 0 601983 0 2585 1 007949922E 04 0 697410 0 5170 1 263830995E 04 0 780963 0 7754 1 521514507E 04 0 849416 1 0339 1 776148968E 04 0 901893 1 2924 2 023176963E 04 0 939537 1 5509 2 258581651E 04 0 964804 1 8094 2 479073870E 04 0 980674 2 0679 2 682208115E 04 0 990000 2 3263 The only other available print option is ANALYSIS SETTINGS Proban 3 39 The result may also be displayed together with other distributions in this case the hermite fit to the simu lated di
49. Ed T Colour Page Size Ad y Format SESAM NEUTRAL POSTSCRIPT HPGL 7550 WINDOWS PRINTER HPGL Z CGM BINARY OK Apply Cancel Figure 4 5 The Set Plot dialog box A Pushbutton is a button that causes an action when it is clicked on OK Apply and Cancel buttons are represented in the Set Plot box shown above All dialog boxes have a standard set of buttons at the bottom of the box These buttons are described later in this section If the label of a pushbutton is followed by three dots the button will open a new dialog box The Assign dia log boxes often contain pushbuttons that provide a short cut to boxes placed under the Select main com mand In addition to these items there are a few more complex input items that are described in the following sec tions 4 5 4 The Standard Buttons in a Dialog Box A dialog box will contain one or more of these standard buttons placed at the bottom of the box Table 4 8 The standard buttons of a dialog box OK Accept the contents of the box and close the box The box will not be closed if the processing of the contents of the box gives an error Apply Accept the contents of the box The box is not closed Cancel Close the box without accepting the contents Close Close the box without accepting the contents SESAM Proban Program version 4 4 01 OCT 2004 4 21 Table 4 8 The standard buttons of a dialog box Update Update the contents of the
50. Integer number The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e ASSIGN CONTINUOUS PROCESS SESAM Proban Program version 4 4 01 OCT 2004 5 79 PRINT ANALYSIS SETTINGS EXAMPLES DEFINE CONTINUOUS PROCESS ANALYSIS OPTION INTEGRATION INTERVAL 10 1000 The following values are default when the program starts up with a new database DEFINE CONTINUOUS PROCESS ANALYSIS OPTION INTEGRATION INTERVAL OFF DEFINE CONTINUOUS PROCESS ANALYSIS OPTION MINIMUM EXTREME VALUE 1 DEFINE CONTINUOUS PROCESS ANALYSIS OPTION NUMBER OF TIME SPLITS 1 DEFINE CONTINUOUS PROCESS ANALYSIS OPTION POINTS IN QUADRATURE 6 CI py Ea Proban SESAM 5 80 01 OCT 2004 Program version 4 4 DEFINE DISTRIBUTION SIMULATION MONTE CARLO SIMULATION nsim DISTRIBUTION SIMULATION LATIN HYPERCUBE SIMULATION nsim RESET PURPOSE Define analysis options for simulation of distributions PARAMETERS MONTE CARLO SIMULATION Define Monte Carlo simulation of distributions LATIN HYPERCUBE SIMULATION Define Latin Hypercube simulation of distributions nsim The number of simulations to be performed RESET Reset all values and options to the default values used when in itialising a new database NOTES The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also
51. LINE C F test_in jnl FORCED EXIT Proban SESAM 4 6 01 OCT 2004 Program version 4 4 Note that it is necessary to use the line mode interface and that the forced exit tells the program to exit when the command input file has been read This command assumes that the program is started at the directory for both the database file and the command input file The command can be enclosed in a batch command file script During a run Proban reads commands from standard input so the commands can be typed into the batch file after the program start up On a UNIX platforms the user may create a batch input file e g proban and then issue one of the commands below in order to execute PROBAN as a background process prompt gt proban lt Proban inp gt Proban log or prompt gt proban NAM TEST STA N INT L C F test_in jnl F EX gt Proban log The header and messages given by Proban will appear on the log file On an NT platform the background process requires that the script is coded in a proban bat file 4 1 5 Files and Data Safety Proban makes use of the files shown in Table below File type Extension PREBRAN Format Reads from Writes to DATABASE mod YES YES Binary JOURNAL jnl NO YES ASCII COM INPUT Jnl YES NO ASCII PRINT lis NO YES ASCII PLOT varies NO YES Binary ASCII The DATABASE also called MODEL file is a direct access file that is used to keep the probabilistic m
52. None NOTES 1 This command is not available from the menu bar in graphics mode Use FILE EXIT instead 2 This command is not journalled 3 EXIT cannot be abbreviated EXAMPLES EXIT Proban SESAM 5 126 01 OCT 2004 Program version 4 4 FILE PLOT EXIT FILE PURPOSE To manage file access and close the program PARAMETERS EXIT Close all open files and exit the program See the command description for EXIT PLOT Execute the last DISPLAY command and write the result to the currently selected plot file See the command description for PLOT NOTES None SESAM Proban Program version 4 4 01 OCT 2004 5 127 GET U SPACE event variable xvalue X SPACE event variable uvalue MAIN RESULT mresname GET SENSITIVITY target parameter RESULT U SPACE DESIGN POINT _ inters sevent variable V SPACE X SPACE PURPOSE Access specific values in the database and transmit them to the controlling process or write them to standard output if Proban runs by itself PARAMETERS U SPACE X SPACE RESULT MAIN RESULT SENSITIVITY DESIGN POINT event variable xvalue variable uvalue U SPACE is used to calculate the u space standard normal space values of all variables used in the definition of the spec ified event Those values that are not specified in the command are set to their median value before calc
53. PRINT RESULT DISPLAY RESULT PLOT and possibly also DEFINE RESULT OPTION and SET This process will be illustrated using the following examples Proban SESAM 3 2 01 OCT 2004 Program version 4 4 Example 3 1 A System Network Consider a simple system network with three components connected in series and with the first components set up with two redundant spares SESAM PROBAN 4 3 03 23 JUN 2000 11 28 Shgk Shak Shak System Failure ofthe system Figure 3 1 A system network Each component is subjected to a load and has a built in resistance and the component fails if the load is greater than the resistance The load is the same on all components but their resistance are different The distributions of the load and the resistance are Table 3 1 Network Variables Variable Type Parameter Value Load Inv Gauss distribution Mean 80 Stdv 10 Lower 0 Resistance of A1 A2 A3 Inv Gauss distribution Mean 110 CoV 0 1 Lower 0 SESAM Proban Program version 4 4 01 OCT 2004 3 3 Table 3 1 Network Variables Resistance of B Normal distribution Mean 120 CoV 0 1 Resistance of C Normal distribution Mean 130 CoV 0 1 There are three questions that must be answered 1 What is the probability that the system will fail 2 What is the probability that the system will fail if the redundancy inside the A component is remove
54. Skewness Skewness Mean Stand Dev Skewness Kurtosis Mean Variance Third C Mom Fourth C Mom Stand Dev gt 0 Kurtosis gt 0 Variance gt 0 Fourth C Mom gt 0 8 9 Kurtosis gt Skewness Skewness Mean Stand Dev Lower Bound Mean Coef of Var Lower Bound Ksi Lambda Lower Bound Mean gt Lower Bound Mean Coef of Var gt 0 Stand Dev gt 0 Coef of Var gt 0 Ksi gt 0 Lambda gt 0 Mean Stand Dev Lower Bound Mean Coef of Var Lower Bound Sigma Mu Lower Bound Mean gt Lower Bound Mean Coef of Var gt 0 Stand Dev gt 0 Coef of Var gt 0 Sigma gt 0 N Cycles Delta N Cycles gt 0 Delta gt 0 Mean Lower Bound Theta Lower bound SESAM Program version 4 4 Multi Normal Normal Onesi Normal Oval Poisson Rayleigh Student t Triangle Trunc Normal Uniform Cor Std Mean Covar Mean Mean StD Mean Cov Mean Low Sigma Low Mean Scale Mean Mean Low Theta Low Dof Mean Deg of Freed gt 0 Low MostL Up Low Mean Up Mu Sigma Lim Mu Cov Lim Limits Mean Low Proban 01 OCT 2004 3 55 Mean gt Lower Bound Theta gt 0 Correlations 1 2 1 3 2 3 Stdv1 Stdv2 Meanl Mean Covariances 1 1 1 2 2 2 2 3 3 3 Meanl Mean The dimension lt 40 must be specified before the input sequence 1 lt Correlation lt 1 Stdv gt 0 Covar i 1 gt 0 Covari ance and correlation matr
55. The functions are calculated within a range of three standard deviations five standard deviations if limited by a bound on each side of the mean See also DISPLAY RESULT DISTRIBUTION DISPLAY FITTED DISTRIBUTION PRINT DISTRIBUTION PRINT VARIABLE SET GRAPH EXAMPLES DISPLAY DISTRIBUTION ONLY Width Height DENSITY Proban SESAM 5 114 01 OCT 2004 Program version 4 4 DISPLAY EVENT SINGLE MULTIPLE EVENT event PURPOSE Display the definition of an event as a network PARAMETERS event The name of the event to be displayed SINGLE Display only the first level subevents MULTIPLE Display the first two levels of subevents as network NOTES Unions are displayed horizontally and intersections vertically See also PRINT EVENT e SET EXAMPLES DISPLAY EVENT Beam Fail MULTIPLE SESAM Proban Program version 4 4 01 OCT 2004 5 115 DISPLAY FITTED DISTRIBUTION FITTED DISTRIBUTION variable PURPOSE Display a fitted distribution with the points it is fitted to PARAMETERS variable Name of a variable assigned a fitted distribution NOTES 1 A spline fit or cumulative fit is displayed as a distribution function curve 2 A fit to observations is displayed as a histogram with the density function of the fitted distribution This display can be regulated by use of the SET GRAPH HISTOGRAM command See also DISPLAY DISTRIBUTION
56. The selection of functions presented is determined by the current selection of sub libraries see SELECT FUNCTION LIBRARY This is because some libraries may contain a large number of functions and or not be relevant to the current problem 2 Ifa LOOP is specified in line mode input after lt function gt any specified argument values are kept as defaults Otherwise the default set of argument values is empty See also SELECT FUNCTION LIBRARY PRINT FUNCTION GRADIENT e SET TITLE Proban SESAM 5 150 01 OCT 2004 Program version 4 4 EXAMPLES PRINT FUNCTION VALUE Polynomium 2 SINGLE POINT 11 0 4 2 6 Generates the following print Polynom 2 Polynomium of degree 2 Name Value Arguments Argument 1 100000000E 01 Shift 0 000000000E 00 Coef 0 4 000000000E 00 Coef 1 2 000000000E 00 Coef 2 6 000000000E 00 Function Polynom 2 7 000000000E 02 SESAM Program version 4 4 01 OCT 2004 PRINT PARAMETER STUDY PARAMETER STUDY PURPOSE Print the currently assigned parameter study PARAMETERS None NOTES See also DEFINE PARAMETER STUDY DEFINE ANALYSIS OPTION PARAMETER STUDY SET TITLE EXAMPLES PRINT PARAMETER STUDY Generates the following print Variable Parameter Number Nyears Constant 10 E AA NE E e o a DyN O 00 00 0001 0 00 O AR AAA eee Ea Te Sh le tele Ate l
57. U Student U Triangle U Trunc No U Weibull MMMM KM MM MM KM KM XK GE GEOCE Cer Gh qu Ge ck ck sarod Function Difference Division Identity Linear Comb Log Diff Maximum Minimum Polynom 1 Pol ynom 2 Pol ynom 3 Polynom 4 Polynom N Power Diff Product Sequence SignLogDiff SignPowDiff Sum Dimen Proban 01 OCT 2004 3 65 5 O Hermit trans distribution Standard Normal fractil 4 O Inv Gauss distribution Standard Normal fractile 4 O Lognormal distribution Standard Normal fractile 3 O Long Higgins distribution Standard Normal fractil 3 O Maxwell distribution Standard Normal fractile 3 O Onesi Normal distribution Standard Normal fractil 3 0 Oval distribution Standard Normal fractile 3 0 Rayleigh distribution Standard Normal fractile 3 O Student t distribution Standard Normal fractile 4 O Triangle distribution Standard Normal fractile 5 0 Trunc Normal distribution Standard Normal fractil 4 0 Weibull distribution Standard Normal fractile Sublibrary Misc Miscellaneous general functions NArg NOp Description 2 O Difference X1 X2 2 0 Division X1 X2 1 O Identity f x x Input O Linear combination x1 x2 x3 x4 2 O Difference Log X1 Log X2 Input O Maximum of any number of variables Input O Minimum of any number of variables 4 O Polynomium of degree 1 5 0 Polynomium of degr
58. a number Log Natural logarithm Log10 1 Logarithm with base 10 Power ac 2 Power function X1 X2 Round Nearest integer to a number 0 5 gt 1 0 5 gt 1 Sign The sign of a number or 0 if it is 0 Sinus of an argument in degrees 0 360 Sinus of an argument in radians Sin Degrees Sin Radians oO0oO0DO0O0OO0OO0OO00O0OO0OO0OO0O0O0O0O0O0O0O0O0O0O0O0O0O0O0O0O0O0O00O0Oo00O0O0Oo0OooOo Sinh Hyperbolic sinus exp x exp x 2 Sgrt Square root Square Square of a value Proban 3 62 E Pan Degrees Tan Radians Tanh A Lo o ON A U U D BB Q oo ct OO H I O a 5 O zZ lt J andado Q Q WU rt tt BOB oo OO Og ti ti HOE Q Q Q Bs 0 H 5 I Tj Q Ps 0 H 5 I Function Special Fu SESAM 01 OCT 2004 Program version 4 4 1 O Tangent of an argument in degrees 0 360 1 0 Tangent of an argument in radians dl O Hyperbolic tangent Sublibrary Prob Logical Probability functions for logical systems NArg NOp Description 2 O AND gate Prob p n 2 0 EQV gate Prob p n 1 p n 2 O NEQV gate Prob 1 p n 1 p n 2 0 OR gate Prob 1 1 p n 2 O AND gate B InvPHI PHI B N 2 O EQV gate PHI F PHI B N PHI B N 2 O NEQV gate PHI F 1 PHI B N PHI B N 2 0O OR gate B InvPHI PHI B N Input 0 AND gate Prob pl
59. and especially in the calculation of gradients A possible remedy is to change the KTO to a larger value using the command DEFINE FORM SORM OPTIMIZATION DEFINE FORM SORM NESTED ANALYSIS GLOBAL DEFINE FORM SORM NESTED ANALYSIS SYSTEM It may also be that the precision of a numeric derivative is poor Differentiation increments can be adjusted by using the commands DEFINE ANALYSIS OPTION DIFFERENTIATION DEFINE ANALYSIS OPTION NESTED ANALYSIS DIFFERENTIATION DEFINE ANALYSIS OPTION GENERATED DISTRIBUTION DIFFERENTIATION Analytic derivatives can be coded together with the corresponding function and be linked into the program in order to increase numerical precision in the derivatives and also to reduce computational work In other cases the design point search does not find a path leading to the target A remedy is to set starting point and optimization bounds for selected variables in order to restrict the search This is particularly use ful in connection with nested reliability analyses where ill conditioned inner loop calculations may arise if the outer loop optimization variables are unrestricted This is done by using the commands ASSIGN STARTING POINT ASSIGN OPTIMISATION BOUNDS A further possibility is to re formulate the event function so that it better assists the design point search Often it helps to use a log difference log resistance log load if both resistance and load are always positive values 2 The calculat
60. another parameter because the two parameters may have values of different magnitude For this reason Proban uses a concept called a sensitivity measure in order to quantify sensitivity values on the same scale The sensitivity measure is defined as the change in the target value estimated from a fixed relative increase in the parameter the default increase is 10 This value will have the same scale as the target value inde pendent of the scale of the magnitude of the parameter used The sensitivity measure is not properly defined if the parameter value is very close to 0 thus a limit at which it is applied must be set The relative incre ment and the limit at which it is applied are controlled using the DEFINE RESULT OPTION command Another kind of sensitivity that is of interest is the degree of importance the uncertainty of a random varia ble in the model has on the probability or reliability index This can be used to identify those random varia bles in the model that could just as well be fixed at the 50 fractile and to identify those random variables for which it would pay to reduce the uncertainty if possible These sensitivities are presented in Proban as importance factors They are presented in and will always sum to 100 The usage of importance factors can be illustrated by the following example If a variable has the impor tance factor a in the effect on the FORM reliability index of fixing the variable to a const
61. are masked out shown grey in graphics mode Use of Proban in graphics mode is described in Section 4 5 Tutorial examples of line mode command input are given in Chapter 3 The HELP command is not described here It is intended purely to serve as on line help Usage of the HELP command is not logged When in doubt how to do things try the HELP command 5 1 Graphical User Interface Menus The pulldown menus of the graphical user interface are listed here from left to right and top to bottom together with the line mode commands to which they correspond The line mode commands can be found alphabetically in the next section Please note that some line mode commands are available through more than one pulldown menu This is purely for convenience and does not affect the journalling of these actions Some dialog boxes are also available through short cut buttons inside other dialog boxes 5 1 1 The File Menu This pulldown menu contains file manipulation commands and the command used to exit Proban Open FILE OPEN Plot PLOT Exit EXIT SESAM Program version 4 4 5 1 2 The Function Menu Create Function Change Function Delete Function Copy Function Function Option Select Library Display Function Presentation Options Print Description Print Formula Print Response Surface Print Value Print Gradient Print Library 5 1 3 The Variable Menu Proban 01 OCT 2004 5 3 CREATE FUNCTION CHANGE FUNCTION DELETE FUNCTION C
62. be included in the selection until the status is changed Set the current selection to the item s matching lt text gt Set the default status to ONLY lt text gt INCLUDE Any items specified after this will be included in the selection until the status is changed Exclude the item s matching lt text gt from the selection Set the default status to EXCLUDE lt text gt EXCLUDE Any items specified after this will be excluded from the selection until the status is changed Include or exclude the items matching lt text gt depending on the default status RS The initial default status is INCLUDE In the case of a selection of numerical values or of a selection between names GROUP lt from gt lt to gt which can be integer values the lt text gt can be substituted with this interval lt step gt expression which expands to the values lt from gt lt from gt lt step gt lt from gt 2 lt step gt up to but not exceeding lt to gt When a default selection is being presented or if the left parentheses has been typed as input Proban presents the right parenthesis as default A single question mark will show all items in the list listing the currently selected items in parenthesis Prefixing the question mark with a text lt text gt will show all items in the list matching lt text gt Example 4 1 DISPLAY DISTRIBUTION will display all distributions currently stored in the da
63. be set to Overwrite The input fields will be cleared Insert the contents of the input fields before the selected row Only one row can Insert before be selected in the scrollable box The default status will be set to Insert before The input fields will be cleared Clear the contents of the matrix NOTE There is no way to get the cleared con Clear tents back other than perhaps cancelling closing the dialog box and opening it again Pressing this is equivalent to pressing the help button while the scrollable box Help has the input focus It provide on line access to a description of how to use the matrix vector 4 5 7 Journalling from Graphics Mode All commands that are accepted from graphics mode are logged on the journal file The commands are logged in a format that can be read into the corresponding line mode command There is one case that deserves attention Some dialog boxes contain many line mode commands An example is the Set Plot dialog box Figure 4 4 and Figure 4 5 Since all the visible contents of a dialog box are selected when the OK or Apply button is pressed even if only parts of the box has been changed all possible commands in the box will be logged Pressing the OK or Apply button in this box will generate the following log SET PLOT COLOUR OFF SET PLOT FILE PROBAN SET PLOT FORMAT SESAM NEUTRAL S PLOT PAGE SIZE A4 CJ 5 tz Gl GI 3 3
64. cases where the accuracy of the multinormal probability calculation is in doubt i e the probability is close to 0 5 the failure probability can be estimated using bounds In some cases a subevent may be inactive in the first linearisation because it is partly hidden behind the others An example is seen in Figure 2 5 Proban will subsequently attempt a separate linearisation of this event in order to obtain the best estimate possible of the probability However this linearisation of inactive constraints can be turned off if desired If a union of intersections is being analysed Proban will analyse each intersection first then estimate the total failure probability using the same bounding technique as for large intersections 2 3 2 Monte Carlo Simulation Monte Carlo simulation is the simplest simulation method available in Proban It consists of sampling ran dom points and checking if each point is inside or outside of the event of interest The probability of the event is estimated as the average number of hits in the event during the simulation SESAM Proban Program version 4 4 01 OCT 2004 2 13 f u ua failure set safeset ae u space Oe fy u Figure 2 7 Monte Carlo hit miss simulation of a probability This method is not efficient except perhaps for mid range probabilities or for sufficiently simple model functions but it has the definite advantage that it will produce unbiased estimates Thus it may be used to ch
65. if possible Show the value size of the pie segment ON or hide it OFF When running the program on a black and white screen it the it usually a good idea to change the default SOLID filling to a HOLLOW or HATCHED See also e DISPLAY RESULT IMPORTANCE FACTORS e PLOT EXAMPLES The following is default when the program starts with a new database l GRAPH PII GRAPH PII GRAPH PII Fl EF Fl FF E 3 3 3 3 3 3 S S S SET S S GRAPH PII ENT OFF l FILLING SOLID VISIBILITY SHOW ENTATION HORIZONTAL ITION AUTOMATIC UE ON GRAPH PIE l GRAPH PIE CHART SESAM Program version 4 4 Proban 01 OCT 2004 5 207 SET GRAPH XAXIS ATTRIBUTES XAXIS ATTRIBUTES EXPONENTIAL FIXED GENERAL INTEGER DECIMAL FORMAT FIXED xmin xmax FREE LIMITS LINEAR LOGARITHMIC SPACING DEFAULT SPECIFIED xtitle TITLE PURPOSE Control the drawing of the X axis in a graph display PARAMETERS DECIMAL FORMAT EXPONENTIAL FIXED GENERAL INTEGER LIMITS FREE xmin xmax FIXED SPACING LINEAR LOGARITHMIC TITLE Controls the presentation of numbers labelling the x axis The numbers are presented in exponential format e g 1 233E 01 The numbers are presented in fixed format e g 12 33 The numbers are presented in general free format The numbers are presented as integers
66. in Section 3 9 3 After the routines have been written compiled and placed in the object library user a UNIX the user should take a private copy of UNIX Makefile and modify it to contain the name and address of the new user a NT This facility is not available on NT Proban can the be linked with the new distribution It is not necessarily a trivial matter to include a new distribution into Proban because it requires program ming skills and because Proban requires a very high accuracy of the inverse distribution function in the tails of the distribution Please contact DNV Sesam AS if you need help to do this
67. in the database The effect is to prohibit use of some commands and generate some error messages when the commands are used The commands that in particu lar may create problems include DEFINE PARAMETER STUDY SSIGN SENSITIVITY RINT VARIABLE UN CROSSING RATE ANALYSIS UN FIRST PASSAGE PROBABILITY ANALYSIS UN PROBABILITY ANALYSIS AWD Pp Proban SESAM 4 8 01 OCT 2004 Program version 4 4 RUN DISTRIBUTION ANALYSIS RUN DETERMINISTIC ANALYSIS 4 4 Using the Line Mode User Interface The line mode environment in Proban is very powerful It has many features and provides a great flexibility to the user This section describes the facilities one by one Even when running graphics mode the line mode environment is available through the command input line There are two modes of operation inside the line mode environment called command mode and pro gramming mode Command mode is the commonly used mode it is used to give commands to Proban A new input line always starts in command mode To switch to from programming mode inside an input line type the dollar sign Programming mode is used basically to calculate numerical values These values can then be used in a com mand if desired or they can be viewed as results When moving through the commands Proban will present a prompt possibly followed by a default inside The main command level is signified by the prompt No defa
68. load at other position Span Beam span Depth Effective Depth Ts Steel yield stress As Steel area K Stress strain coefficient Width Width of beam Tc Concrete compressive strength As Depth Ts K As 2 Ts 2 Width Tc Ll LoadPart P1 P2 L1 L2 Span CREATE FUNCTION ShrForml Shear at end of beam FORMULA ONLY Pl Applied load at end position P2 Applied load at other position L1 Location load at end position L2 Location load at other position Span Beam span Depth Effective Depth Ts Steel yield stress Width Width of beam Tc Concrete compressive strength Av Shear steel area Spacing Shear steel spacing 0 2 Sqrt Tc Width Depth Av Depth Ts Spacing LoadPart P1 P2 L1 L2 Span CREATE VARIABLE LOOP Pal Applied load 1 DISTR Normal Mean StD 28000 8400 P2 Applied load 2 DISTR Normal Mean StD 28000 8400 L1 Location load 1 DISTR Normal Mean StD 750 60 L2 Location load 2 DISTR Normal Mean StD 750 60 Depth Effective Depth DISTR Normal Mean StD 300 15 SESAM Proban Program version 4 4 01 OCT 2004 3 67 Ts Steel yield stress DISTR Normal Mean StD 360 36 As Steel area DISTR Normal Mean StD 452 22 6 K Stress strain coefficient DISTR Normal Mean StD 0 55 0 055 Width Width of beam DISTR Normal Mean StD 120 6 Te Concrete compressive strength DISTR
69. must know whether a nested reliability analysis is implied by the model at hand or not The rule is rather simple If the model includes a distribution variable not assigned a time derivative or assigned as a time derivative then Proban sets up a nested reliability analysis and the options for nested reliability analysis applies When a time variable is present in the model the integration over time employs a trapezoidal rule The inte gration is by default over the duration taken from the starting point This interval may be reduced in order to capture the significant part of the time interval The integration interval in the above example is restricted to the end of the interval by use of the command DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS INTEGRATION INTERVAL 9000 10800 The number of points in the quadrature may be manipulated by the command DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS POINTS IN QUADRATURE 20 This puts 20 integration points in the interval 9000 to 10800 If there is periodicity in the stochastic process only one period needs to be integrated The number of peri ods is input by the command DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS NUMBER OF TIME SPLITS 2 The first passage probability may be the minimum of a number of independent realisations of the process This number is entered by the command DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS MINIMUM EXTREME VALUE 3
70. p2 pn Input O EQV gate Prob 1 p1 1 pn p1 pn Input O NEQV gate Prob 1 1 p1 1 pn p1 pn 1 O NOT gate Prob 1 p Input 0 OR gate Prob 1 1 pl 1 p2 1 pn Input 0 AND gate B InvPhi PHI B1 PHI BN Input O EQV gate PHI F PROD PHI Bi PROD PHI Bi Input O NEQV gate PHI F 1 PROD PHI Bi PROD PHI Bi 1 O NOT gate Reliability Index B Input O OR gate B InvPHI PHI B1 PHI BN Error Function Complementary error function Gamma Function Logarithm of Gamma function SESAM Program version 4 4 Den Beta Den Burr Den Chi squa Den Exponent Den Gamma Den Gen Gamm Den Gumbel Den Hermit s Den Hermit t Den Inv Gaus Den Lognorma Den Long Hig Den Maxwell Den Normal Den Onesi No Den Oval Den Rayleigh Den Student Den Triangle Den Trunc No Den Weibull Dis Beta Dis Burr Dis Chi squa Dis Exponent Dis Gamma Dis Gen Gamm Dis Gumbel Dis Hermit s Dis Hermit t Dis Inv Gaus Dis Lognorma Dis Long Hig Dis Maxwell Dis Normal Dis Onesi No Dis Oval Dis Rayleigh Dis Student Dis Triangle Dis Trunc No Dis Weibull Proban 01 OCT 2004 3 63 Sublibrary Distribution Functions related to
71. result to be unreliable in the middle of the distribution and the importance factors to have a strange behaviour at the same area See also the end of Section 3 8 Consider Example 3 1 described in Section 3 1 An analysis of the probability of failure of component A with the default settings is done with the following command RUN PROBABILITY ANALYSIS A and produces the following messages while the analysis is running Starting Probability Analysis of A Starting FORM calculation Starting linearization of Intersection of Al A2 A3 Linearization completed Calculating importance factors FORM Reliability index 2 8249 FORM Probability 2 36457E 03 The following commands can be used to see the results PRINT RESULT ALL PRINT RESULT ANALYSIS SETTINGS PRINT RESULT SUMMARY PRINT RESULT IMPORTANCE FACTORS There is also a command that is used to print sensitivity results PRINT RESULT SENSITIVITY This command is not available after this analysis because no parametric sensitivity values were calculated The summary print produces the following output PRINT RESULT SUMMARY SESAM Proban Program version 4 4 01 OCT 2004 3 13 Probability of A Failure of all A components Analysis method FORM FORM Probability 2 36457E 03 FORM Reliability index 2 8249 U space Geometry Small Intersection Number of linearization points 1 Description of subevents Subevent De
72. s and possibly a measured value dProb FORM dProb SORM Derivative of probability Derivative of probability SORM only Main results for Monte Carlo and Directional simulation of a probability Probability Stdv Prob CoV Prob Conf Prob Lo Conf Prob Up Beta Conf Beta Lo Conf Beta Up Log10P Conf LogP Lo Conf LogP Up The probability estimate Estimated standard deviation of Probability Coefficient of variation for Probability Lower confidence bound for Probability Upper confidence bound for Probability Reliability index corresponding to Probability Lower confidence bound for Beta Upper confidence bound for Beta Log10 Probability Lower confidence bound for Log10P Upper confidence bound for Log10P Main results for Axis orthogonal simulation of a probability Probability Conf Prob Lo Conf Prob Up Beta Conf Beta Lo Conf Beta Up Log10P Conf LogP Lo Conf LogP Up The probability estimate Lower confidence bound for Probability Upper confidence bound for Probability Reliability index corresponding to Probability Lower confidence bound for Beta Upper confidence bound for Beta Log10 Probability Lower confidence bound for Log10P Upper confidence bound for Log10P SESAM Proban Program version 44 AR ODD Correction The estimated correction to the FORM probability Stdv Corr Estimated standard deviation of Correction CoV Corr Coefficient of variation for Correction Conf Corr Lo Lower confidence bound for Co
73. some of these remove them from the selection 2 The command DEFINE ANALYSIS OPTION SENSITIVITY is used to confirm or override the selec tion specified here See also ASSIGN SENSITIVITY CALCULATION INCREMENT DEFINE ANALYSIS OPTION SENSITIVITY DEFINE FORM SORM SENSITIVITY EXAMPLES ASSIGN SENSITIVITY CALCULATION VARIABLE Mean ASSIGN SENSITIVITY CALCULATION VARIABLE INCLUDE P1 1nC Stdv SESAM Proban Program version 4 4 01 OCT 2004 5 21 ASSIGN SIMULATION DENSITY SIMULATION DENSITY varsim varadjsim PURPOSE Assign a variable as adjusted simulation density in a sampling of probability PARAMETERS varsim Variable representing the coordinate for which the adjusted simulation applies varadjsim Variable defining the adjusted simulation density NOTES 1 Adjusted simulation means that the sampling is according to the following formula in which fU is the u space distributions and fA is the adjusted sampling density P folwdu 0040 0 du g u lt 0 g u lt 0 2 The adjusted simulation density replaces the variable in u space 3 The adjustment is restricted to Normal random variables 4 Correlated variables and variables conditioned on the value of other variables cannot be assigned an adjusted sampling density See also e SELECT ANALYSIS METHOD PROBABILITY DESIGN POINT SIMULATION ADJUSTED e SELECT ANALYSIS METHOD PROBABILITY MONTE CARLO SIMULATION ADJUSTE
74. ss Sosscestdshees Madina dandoles 5 126 GEL raspa oa si ins 5 127 O at 5 129 PELOT scaler tata Dutti lia TO ii 5 131 PRIN Tiida E aaa toda EI ir s 5 132 PRINT ANALY SIS SETIINGS iere deiavs act a A E sed eadaselys cb cs ibid 5 134 PRINT CORRELA TION centa oss add ci o a Aa d E 5 135 PRINT DISTRIBUTION adan att 5 136 IN RN 5 138 PRINTEUNCIION wicsccsuessdesscescciatest coop tebiaaeaesdnestebvassaecdessoetsaciauts estos ias pita ii 5 140 PRINT EUNCTION DESCRIPTION cctsis ccsehatsstaitasadens ns dausancdetssassetssnsdeessasseuseaabesgcscbdarevcdspannads 5 141 PRINT FUNCTION FORMULA onae aaa aa aa raana TEA E a E A aasi 5 142 PRINT FUNCTION GRADIENT e aaa eie a E sno E EA EEEE A EE AEAEE 5 144 PRINT FUNCTION EIBRARY airada atleta tock italia iii 5 146 PRINT FUNCTION RESPONSESURFACE nininini i a a a a i a 5 147 PRINT FUNCTION VALUE caia AAA Att 5 149 PRINTPARAMETER STUD Y gurnita ea e a aa a A ir daa aE E aa A 5 151 PRINT RESULT eieae e E E E T E E E E dar n 5 152 PRINT RESUETAE Dinani ae E ET T E E E AA 5 153 PRINT RESULT ANALYSIS SETTINGS eeeeeseseseeeesrsereesresrsssseserresrsersrresresreseessesentssrsereesenee 5 154 PRINT RESULT IMPORTANCE FACTORS eeseesseeesessseeeseerssssesesresrrerseseeresrsersesenrestnsreeseese 5 155 PRINT RESULT INTERMEDIATE RESULTS sssssssssesssesressseseersseserststerrsessesessesesesseseenrsrses 5 156 PRINT RESUETPARAMETERSSTUDY union noenten a E ARAR R 5 157 PRINT RESULT PARAMET
75. the fitting parameters being Mean and COV The input required to do this is R SET G S C TG UN DISTRIBUTION ANALYSIS NPV RAPH HISTOGRAM COLUMNS 20 RAPH HISTOGRAM FILLING HOLLOW REATI RI E VARIABLE FitNPV FITTED DISTRIBUTION Normal Mean CoV FIT FIT ESULT LastAnalysis SESAM Proban 01 OCT 2004 3 57 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 14 54 Nomal distribution fit of FitNPV istogram itted curve Observations 20000 0 20000 40000 60000 FitNPV Mean 4646 8327577 Coef of Var 1 9850182914 Figure 3 16 NPV fitted to normal distribution Mean and COV This input produces a fit that can be displayed as in Figure 3 16 by the following command DISPLAY FITTED DISTRIBUTION FitNPV The parameters are fitted to the result from a Proban distribution analysis by means of the Maximum Likeli hood method The vertical lines on the observation axis shows the density of the sampled observations The histogram shows the contribution from each of the twenty intervals on the observation axis In the next example the distribution of a beta distributed random variable is calculated using a parameter study on a threshold value x The result is fitted to the beta distribution REATE VARIABLI E VARIABLI a a E H D Zea a ESI T UN PROBABILITY ANALYSIS betax QAawmuuvaa FIT
76. the probability of the union event A union of single events may also be analysed using the bounding technique Use the command DEFINE FORM SORM BOUNDS ON to achieve this The first questions in Example 3 1 can now be answered Using SORM the probability of failure is about 0 01 corresponding to a reliability index of about 2 33 The effect of removing the redundancy in compo nent A is to increase the failure probability to about 0 028 corresponding to a reliability index of about 1 9 A print of the summary results and of all results yield in addition to the bounds and the summary result for each of the subevents a list of intersection probabilities Subevent Intersection Probabilities Subi Subj Probability Subi Subj Probability Subi Subj Probability 1 1 2 35961E 03 2 1 5 69582E 04 2 2 6 75823E 03 3 1 2 28220E 04 3 2 2 57420E 04 3 3 1 71569E 03 The intersection probabilities are used to calculate the probability bounds They are probabilities of the intersections between pairs of the subevents SESAM Proban Program version 4 4 01 OCT 2004 3 17 The importance factors are the key to the last question of Example 3 1 regarding the importance of the uncertainty of the resistance values A print of the importance factors produces because this is a bounds analysis a table for the main event and a table for each subevent The main table is shown here Probability of System Failure of the system Analysis met
77. tion of Intersection of NPV lt 0 Linearization completed Ca Ca cu cu FORM Reliabi ndex SORM Reliabi ity 1 ity 1 ndex FORM Probability SORM Probability Analysing conditioning event in conditional Starting SORM calculation Starting linearization of 0 tz Y 11 gt 70000 0 ating importance factors ating 5 para 1 0238 0 9621 52965E 01 67999E 01 3 19 metric sensitivity values calculation Calculating importance factors and 5 parametric sensitivity values 7 Ts Single event 11 gt 70000 0 Linearization completed FORM Reliability index SORM Reliability index FORM Probability SORM Probability Final results SORM Reliability index SORM Probability 2 0 7647 0 7647 777786 01 777786 01 0 7858 15999E 01 NPV lt 0 0 given 11 gt 70000 0 Only the conditional result itself is printed The results from the intersection event and the conditioning event are not available If they are of interest the corresponding models must be defined and analysed sepa rately 3 3 2 Monte Carlo Simulation Monte Carlo simulation is the simplest way to simulate a probability The result is unbiased but it may have a large standard deviation It is not possible in Proban to calculate sensitivities or importance factors using Monte Carlo simulation of a probability Consider the probabil
78. to the Mean of El Assigned sensitivity calculation to the Mean of E2 SESAM Proban Program version 4 4 01 OCT 2004 3 31 Assigned sensitivity calculation to the Mean of I1 Assigned sensitivity calculation to the Mean of 12 Assigned sensitivity calculation to the Mean of S RUN DISTRIBUTION ANALYSIS NPV Starting Distribution Analysis of NPV Starting Monte Carlo simulation Stopping after 1000 simulations Simulating 5 sensitivity values 250 simulations completed 500 simulations completed 750 simulations completed 1000 simulations completed Number of simulations 1000 Estimated Mean 4 96924E 03 Estimated Standard Deviation 9 23969E 03 Estimated Skewness 0 121 Estimated Kurtosis 2eh13 Normal distribution fit to simulation of NPV stored in a variable called Normal Fit Hermit trans distribution fit to simulation of NPV stored in a variab ca d Hermite Fit SAVE RESULT MCS NPV Monte Carlo simulation of the Net Present Value CS NPV is now the selected result After the analysis the result was saved under the name MCS NPV The fitted distributions are based on the estimated moments From the skewness and kurtosis it can be seen that the distribution fits well to a normal distribution which has skewness 0 and kurtosis 3 This may also be checked using the DISPLAY command SET GRAPH HISTOGRAM FILLING HOLLOW DISPLAY RESULT DI
79. version 4 4 01 OCT 2004 2 11 FORM SORM can be used on a single event a union of single events an intersection of single events or a union of intersections with each intersection containing single events Proban handles union and intersection events a little differently than single events but the basic principle is the same Unions and intersections may generate two different geometries in U space the so called Large intersection and Small intersection A large intersection is generated from a small probability in a union event or a large probability in an intersection event A small intersection is generated in the converse cir cumstance The situations are described in Figure 2 5 and Figure 2 6 Safe set u space Figure 2 5 Small intersection geometry in a FORM SORM analysis In the case of a small intersection the approximation of the failure set becomes convex and the probability of this set can be calculated directly using known methods for calculating probabilities in the multinormal distribution Proban SESAM 2 12 01 OCT 2004 Program version 4 4 safe set Qj g u 0 E b IN A C g u 0 failure set u space Figure 2 6 Large intersection geometry in a FORM SORM analysis In the case of a large intersection the safe set is the convex set and the failure probability is calculated as 1 the probability of the safe set when the direct multinormal probability calculation is used Alternatively for
80. will be as signed the specified correlation BASIC The correlation is specified in the physical space NORMALIZED The correlation is specified in the transformed standard normal space value Correlation value Can be a numerical value or the name of a one dimensional var iable NOTES It is possible to do sensitivity analysis on correlation coefficients by creating them as fixed variables first then using the fixed variable to specify the correlation value see example below See also e PRINT CORRELATION EXAMPLES ASSIGN CORRELATION P 1nC P m BASIC 0 9 CREATE VARIABLE StrCorr Stress correlation FIXED 0 8 ASSIGN CORRELATION FP 1nA FP 1dB NORMALIZED StrCorr ASSIGN SENSITITIVY VARIABLE INCLUDE StrCorr ASSIGN CORRELATION PP NONE Proban 5 14 01 OCT 2004 ASSIGN EXTREME VALUE MIN OF N n min EXTREME VALUE variable MAX OF N n max NONE PURPOSE Assign extreme type to a distribution variable PARAMETERS variable MIN OF N n min MAX OF N n max NONE NOTES 1 All variables have by default no extreme type assigned SESAM Program version 4 4 A one dimensional distribution variable or a generated distribu tion variable The extreme distribution is the minimum of n_ min independ ent identically distributed variables with the distribution that was input when the selected variable was created changed n_min must be a positi
81. with caution It is possible to fit other distributions to the sample by creating a variable with type attribute Fitted Distribu tion see Section 3 9 2 2 8 Sensitivity Results It is often desirable to investigate the sensitivity of a target value with respect to one or more parameters in the model The target value can be the calculated probability or reliability index or the moments of a simu lated distribution Proban SESAM 2 26 01 OCT 2004 Program version 4 4 Examples are the sensitivity of the reliability index with respect to the standard deviation of the strength of a material or the sensitivity of the mean and standard deviation of the Net Present Value of an investment with respect to the oil price The change in e g the reliability index given a change in a parameter T is estimated as dp A Brew B dt F Proban can calculate the sensitivity of the target value with respect to any fixed variable or constant distribu tion parameter or constant function argument in the model The sensitivity of the probability and reliability index with respect to a parameter can be calculated using FORM SORM and Directional simulation The sensitivity of the mean standard deviation skewness and kurtosis of a distribution can be calculated using Monte Carlo or Latin hypercube simulation of a distribution The derivative of a target value with respect to a parameter is not very easily compared to a derivative with respect to
82. 05836358575 Installation DNVS OSLPCMSL Copyright DET NORSKE VERITAS aS P O Box 300 N 1322 Hovik Norway Initializing new database gt Proban mod Discrete process analysis Monte Carlo simulation Parameter study Not assigned Importance factors Or Parametric sensitivity Selected parameters Current display device is WINDOWS Current plot format is SESAM NEUTRAL Figure 4 2 The main dialog window at start up In addition to the parts seen in Figure 4 2 the graphics area and command line area may be visible as shown in Figure 4 3 e The command line and prompt at the bottom as well as the command list at the right and the six short cut buttons are used to give line mode commands to Proban A command can be entered by clicking in the command list or by typing text in the command line followed by lt Enter gt The short cut buttons all have explanatory text attached visible when the mouse pointer is paused over the button Two extra but tons appear when a command input file is open SESAM Proban Program version 4 4 01 OCT 2004 4 17 E BEE File Function Variable Process Event Analysis Result Options Help FILE ASSIGN CHANGE COPY CREATE DEFINE for x_normal DELETE DISPLAY ibuted var ob le PLOT FRINT RENAME RUN SELECT SET HELP EXIT DISTRIBUTION x_normal Lol DENSITY 3 Figure 4 3 The main window with graphics area and li
83. 1 The following command calculates the event function Beam Fail at the starting point for a FORM SORM analysis RUN DETERMINISTIC ANALYSIS EVENT Beam Fail STARTING POINT The following command calculates an event function at the U space origin RUN DETERMINISTIC ANALYSIS EVENT Beam Fail USPACE ORIGIN and produces the result Value of event Beam Fail 30136 798306 False The points of the union event Beam Fail have negative function values Therefore if the value was nega tive then the assertion that the point is in the Beam Fail event it would be True However the point takes a positive value and therefore the assertion 1s False 3 8 Parameter Study Analysis and Results It is often desirable to monitor the development of a target value as a function of a parameter in the model e g as a function of time This can be done in Proban by use of the parameter study facility 1 The steps in performing a parameter study are 2 Enter the model into Proban 3 Assign a parameter study to parameter specifying the desired values This is done using the ASSIGN PARAMETER STUDY command 4 Ifnecessary make sure that a parameter study will be run by entering the command DEFINE ANALY SIS OPTION PARAMETER STUDY ON The default status is ON so this is only necessary if the cur rent status has been set to OFF 5 Run the analysis using the RUN command One analysis will be performed for each para
84. 2 6 2s 2 8 Table of Contents INTRODUCTION ciscsiscccsvacsssercesctess eecdsecscdeseRevaacscedaelatessiactevecsuseesseoscustedeveacsecvacdavecovsscesecs 1 1 Proban Probabilistic Analysis Program cccccsccesscesseesseeseceseceseeeneeeseesaecsaececseeeeesecseecssenseeseenats 1 1 Proban in the SESAM yt ae id dat 1 2 How to Read this Manual i c ccessssccscccsessosctccceccoscenectedeccvsssecntesseseesseecesecoesovsetecesecvsvtteedeccovewenveecs 1 3 Changes from the Previous ReVisiOn ccccsccesccesscescesseeesecseceseeeeceseecseecsecesecsseeeseeeseeseceseeneeenaeeaaes 1 3 FEATURES OF PROBA cccccsssssscscccccccccssvsscccccsceccesesescscosscsccsscesessscoccesceecesesecscces 2 1 General Description ici a tad Cede asta 2 1 Mode Det ii tada lic 2 2 2 2 1 A lt p A E EE A AE A EEEE E 2 2 2 2 2 Events dt T 2 3 2 2 3 EXE VS A EEE E o dede 2 4 2 2 4 CO aaa 2 4 2 2 5 Time DEL Vatives aa ais 2 5 2 2 6 Measured Values ccccnnonocononinonnnnnananoconanannnnnnocononannnnnccnononann nn nono conannn none rononnnnan nan ccnonnnnnss 2 6 DDT Model FU cl A dese aa ai aeS 2 6 2 2 8 Generated Distribuida balas Li laa ies 2 7 Probability Analysis ani ea EE AAA da 2 8 2 3 1 EORM SOR Mist le daeeaa ee 2 8 2 32 Monte Carlo Simulation oococccnnnnnonononinnnnnnnnnanononnnnnnnnanononanann conoce nana nn nono ronnnann na neronnananes 2 12 2 3 3 Directional Simulation c csscccccsssssossccccvcssssssencceseesessseccesc
85. 2 r2 Linear Comb ONLY 1 CO 1 Y1 1 Y2 Note that expression 12 E2 S is conveniently modelled as a linear combination using the Linear Comb function with arguments 1 12 1 E2 1 S I2 E2 S 1 0 D 1 0 E2 1 0 S Note also that the inclusion of a function in Proban with the following syntax f a rn a 1 r n would ease the modelling in this case As a further benefit this function would most likely be reusable in other economical models The example illustrates how complex functions can be built through variables referencing variables How ever the same formula can be created using the function formula facility Proban SESAM 3 6 01 OCT 2004 Program version 4 4 CREATE FUNCTION NPV Net present value FORMULA ONLY r Required rate of return CO Initial investment 11 Income first year 12 Income second year El Expense first year E2 Expense second year S Scrap value CO 11 E1 1 R 12 E2 S 1 R 2 A set of formulas can be kept on a journal file and be read into the program whenever needed The questions will be answered in the following sections However the following commands can be used to get the information needed to answers the questions ASSIGN SENSITIVITY CALCULATION VARIABLE Mean RUN DISTRIBUTION ANALYSIS NPV SET GRAPH HISTOGRAM FILLING HOLLOW DISPLAY DISTRIBUTION Empirical Fit OOP ENSITY ISTRIBUTION END PRINT RESULT ALL RUN PRO
86. 4 4 A conditional probability is calculated just like any other probability In this case Proban counts the number of hits in the conditioning event and the number of hits in the intersection event The probability estimate is then the division of these two values 3 3 3 Directional Simulation Directional simulation is a more sophisticated version of Monte Carlo simulation It can be used to simulate sensitivities and importance factors Consider again the probability of a loss in Example 3 2 The following commands will simulate this proba bility including parametric sensitivities for all the mean parameters the messages given by Proban are also shown SELECT ANALYSIS METHOD PROBABILITY ANALYSIS DIRECTIONAL SIMULATION ASSIGN SENSITIVITY CALCULATION VARIABLE ONLY Mean Assigned sensitivity calculation to the Mean of El Assigned sensitivity calculation to the Mean of E2 Assigned sensitivity calculation to the Mean of I1 Assigned sensitivity calculation to the Mean of I2 Assigned sensitivity calculation to the Mean of S RUN PROBABILITY ANALYSIS SINGLE EVENT NPV lt 0 Starting Probability Analysis of NPV lt 0 0 Starting Directional simulation Stopping after 50 simulations or 60 0 CPUsec Simulating importance factors and 5 sensitivity values 12 simulations completed 24 simulations completed 36 simulations completed 48 simulations completed
87. 5 169 RENAME FUNCTION FUNCTION from to PURPOSE To change the name of a function formula or function integral PARAMETERS from The original name of the function to The new name of the function This cannot be the name of an existing function NOTES If the renamed function is referenced in other function formulas or function integrals then the name must be changed in these functions too See also CHANGE FUNCTION e CREATE FUNCTION DELETE FUNCTION e PRINT FUNCTION e DISPLAY FUNCTION EXAMPLES RENAME FUNCTION SYMFUN SYMFOR Proban 5 170 01 OCT 2004 RENAME RESULT RESULT from to PURPOSE To change the name of a result PARAMETERS from to NOTES See also The original name of the result SESAM Program version 4 4 The new name of the result This cannot be the name of an existing result SAVE RESULT DELETE RESULT RUN PRINT RESULT DISPLAY RESULT EXAMPLES RI ENAM E RI ESULT SORM Result Global Fail SESAM Proban Program version 4 4 01 OCT 2004 5 171 RENAME VARIABLE VARIABLE from to PURPOSE To change the name of a variable PARAMETERS from The original name of the variable to The new name of the variable This cannot be the name of an existing variable NOTES Renaming a variable does not affect the usage of the variable in other vari
88. 5E 01 3 545E 01 Beta 0 4399 0 3733 0 5085 Log10 Prob 4 815E 01 5 149E 01 4 504E 01 This gives confidence intervals in addition to the previous information shown during the run The confi dence level may be set using the command DEFINE RESULT OPTION CONFIDENCE VALUE The print option PRINT RESULT ANALYSIS SETTINGS shows the analysis settings used among other things the seeds used by the random generator PRINT RESULT ANALYSIS SETTINGS Probability of NPV lt 0 0 Net Present Value Analysis method Monte Carlo simulation SESAM Proban Program version 4 4 01 OCT 2004 3 21 Method Option Value Analysis Method Probability Monte Carlo simulation Monte Carlo Sim Prob Stop Criteria Simulations 1000 CPU seconds 60 0 Coef of Var No requirement Analysis Option Parameter Study off Sensitivity Selected Seeds Seed 1 216264090 Seed 2 276250807 Seed 3 326643946 General info Time of analysis 00 15 50 10 FEB 1992 CPU time used 16 seconds The results may be reproduced exactly by using the same seeds and the same number of simulations The seeds are manipulated using the command DEFINE ANA LYSIS OPTION SEEDS This also applies to all other simulation methods in Proban The PRINT RESULT ALL command generates the summary print plus a history of intermediate results dur ing the simulation This history table is Intermediate simulation results
89. 640E 03 0 096 2 607 1 50000E 01 1 61194E 03 8 58423E 03 0 096 2 607 The only parameter that varies considerably is the mean The standard deviation decreases slightly when r increases The mean with confidence limits is displayed as a function ofr and a file copy is created SET DRAWING FONT SIZE RELATIVE 1 5 Proban 3 44 E OT nuunuu ET GRAPH LIN ISPLAY RESULT PARAMET ET GRAPH LIN E 0P7 E 0P7 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 15000 20000 o o O o pe ia PIONS MARK ER ST PIONS MARK ER OFF UDY MAIN R ER ON 01 OCT 2004 ESULT Mean NPV Net Present Value Parameter study using SESAM Program version 4 4 Main resu Mea Conf Mean Lo Conf Mean Up It n Figure 3 9 Parameter study of mean of NPV with respect to internal rate of return To get a visual impression of the development of the whole distribution here is a display of four of the fitted Gl ct Gh Ge Gt to to to to NPV NPV NPV NPV with with with with E E r E O 10 00 DISPLAY DISTRIBUTION ONLY NPV amp amp distributions CREATE VARIABLI LOOP NPV_01 Fi NPV_05 Fi NPV_10 Fi NPV_15 Fi END LOOP DENSITY o 05 10 alot DISTR Normal DISTR Normal DISTR Normal DISTR Normal Mean StD Mean StD Mean StD Mean StD 17952 11675
90. ABLE DELETE VARIABLE RENAME VARIABLE PRINT VARIABLE DISPLAY VARIABLE ASSIGN CONDITIONING ASSIGN CORRELATION ASSIGN EXTREME VALUE ASSIGN FUNCTION OPTION ASSIGN OPTIMISATION BOUNDS ASSIGN SENSITIVITY CALCULATION ASSIGN STARTING POINT EXAMPLES COPY VARIABLE Widthl Width2 Proban SESAM 5 46 01 OCT 2004 Program version 4 4 CREATE EVENT FORMULA CREATE FUNCTION INTEGRATION VARIABLE PURPOSE Create a named object PARAMETERS EVENT Create an event FUNCTION Create a function VARIABLE Create a random variable NOTES None SESAM Proban Program version 4 4 01 OCT 2004 5 47 CREATE EVENT CONDITIONED event condition INTERSECTION subevent EVENT name desc SINGLE 1d variable lt gt threshold UNION subevent PURPOSE To create an event PARAMETERS name desc CONDITIONED event condition INTERSECTION UNION subevent SINGLE 1d variable threshold NOTES See also e CHANGE EVENT Name of event This cannot be the name of an existing event Event names are matched case insensitive and can not be longer than 12 characters Descriptive text for the event It can be up to 50 characters long Event is a conditioned event Name of event being conditioned Name of event conditioned on Event is an intersection of other events i e it is fulfilled only when all subevents are fulfilled Even
91. ANALYSIS AXIS ORTHOGONAL COEFFICIENT OF VARIATION 0 AXIS ORTHOGONAL CP AXIS ORTHOGONAL DENSITY CONDITIONED AXIS ORTHOGONAL SE AXIS ORTHOGONAL SIMULATIONS 50 PU TIME 60 ARCH MEDIUM SAFE Proban SESAM 5 98 01 OCT 2004 Program version 4 4 DEFINE PROBABILITY SIMULATION DESIGN POINT COEFFICIENT OF VARIATION cov CPU TIME cpu DESIGN POINT SIMULATIONS nsim RESET PURPOSE Define analysis options for design point simulation of a probability PARAMETERS COEFFICIENT OF VARIATION cov The simulations will stop if the coefficient of variation of the simulated result becomes lower than or equal to cov To disable this stop criterion set cov to 0 cov must be non negative CPU TIME cpu The simulations will stop when the cpu time cpu in seconds has been exceeded The check is performed after each simula tion is completed To disable this stop criterion set cpu to 0 cpu must be non negative SIMULATIONS nsim The simulation will stop after nsim simulations has been com pleted nsim must be a positive whole number RESET Reset all values and options to the default values used when in itialising a new database NOTES 1 The design point simulation first finds the design point Then it performs a Monte Carlo probability sim ulation with sampling density centered at the design point 2 The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS comma
92. ANALYSIS METHOD PROBABILITY SORM PARABOLIC UN PROBABILITY ANALYSIS NPVx ET DRAWING FONT SIZE RELATIVE 1 5 DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR ANDNAPAQQA u u H Q Z Proban SESAM 3 50 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 14 54 NPVx Parameter study using x Importance factors OT E E Fs gt ba jaz T kar gt a r e e i 2 1 1 eet te IO X 1 g B R uo GES gt a At A A AA Loe 4 o LA I 1 1 1 oo a Soles owe Sort ag e aa tel E a i E ame e o i I I 1 i m1 j E E al a 5 a a 7 vi a o a 7 Ne 1 1 1 1 1 1 8 4 N E O AE E a XK 1 1 f 1 1 Sle aa es EA A AS gt i E A ee See a 1 Mo Ao a gt 8 376 1 T T T T T 1 30000 20000 10000 0 10000 20000 30000 x Variable A 1 A 12 mMS ImpGroup 1 Figure 3 13 The importance factors across the distribution of NPV The spike in the middle is caused by the application of FORM SORM to a model containing the non differ entiable density function of the triangle distribution The spikes will disappear if the triangle distributions are changed to Beta distributions with the same mean standard deviation and limits or if Directional simulation is used One can also display importance factor pie charts simultaneously for a selection of parameter values from a parameter study by using the command
93. ATION ita 5 18 ASSIGN SENSITIVITY CALCULATION INCREMENT ccccsscsssesesseseeseeeceecseeaeeeeecaeeeeeaees 5 19 ASSIGN SENSITIVITY CALCULATION VARIABLE 0 cccecsssssssseesceeeseeseeesecaeeeceeeeeaeenseeeas 5 20 ASSIGN SIMULATION EN SUEY ata 5 21 ASSIGN STARTING POIN Tn s 5 22 ASSIGN SUB LEVEL IN TEGRA BION aan 5 23 GA eV LG E rene rte an ty pea te Teen My hea be Meo E Oo dee CE as een ey eT TCR errr e rect et 5 24 CHANGE EVEN Do oia 5 25 CHANGE FUNCTION cor dar 5 27 CHANGE FUNCTION FORMULA re 5 28 CHANGE FUNCTION INTEGRAL tia a tos 5 29 CHANGE FUNCTION RESPONSESURFACE ccscsssssssssncsssssescsssonsessnssescncsnsensocsasonseesnss 5 31 CHANGE VARTABEE us aii 5 33 CHANGE VARIABLE DISTRIBUTION iaa 5 35 CHANGE VARIABLE DISTRIBUTION SPLINE 1DIM 0 0 ce cccececsesceseeecteeseeseeeeeeneeaeeeeaes 5 37 CHANGE VARIABLE FITTED DISTRIBUTION 0 cc cceecscsssesseseeeceeeseeeeeceeeeeeaeeeeeecaeeneees 5 39 CHANGE VARIABLE FUNCION ted liada 5 42 CHANGE VARIABLE PROBABILITY isidro 5 43 COPY PVEN 55005 So sats to O 5 44 COPY VARIA BUE da Eo Selb es A E N ia es 5 45 CRE AST ide 5 46 EREATREVEN Dar 5 47 CREATE FUNCTION es 5 49 CREATE FUNCTION FORMULA diet 5 50 CREATE FUNCTION INTEGRAL is 5 52 CREATE FUNCTION RESPONSESURFACE cssssssssossrcssssscsssscsscssseccasensesssnsesencenesasenenss 5 54 CREATE VARIABLE tidad 5 56 CREATE VARIABLE DISTRIBUTION 0 iio 5 58 CREATE VARIABLE DISTRIBUTION
94. B The outer integration level averages this crossing rate over the variables of Set B The implied nested optimization employs the optimization criteria defined for nested reliability analysis see above If a random variable which is not a stochastic process is to be integrated on the inner integration level then this is achieved by pushing the variable to the inner level 2 7 Distribution Analysis In many cases the distribution of a random variable is of interest Proban supplies three different ways of calculating this distribution The Mean Value Based FORM method is analytical though not very accurate The two simulation methods Monte Carlo simulation and Latin hypercube simulation are recommended for use when possible 2 7 1 Monte Carlo Simulation Monte Carlo simulation is a straightforward simulation technique where points are sampled randomly and the target value is calculated each time The sample of target values is stored on the database and can be used for display or printed presentation after the analysis The first four moments of the distribution are fit ted from the sample and presented as a summary result after the analysis is complete SESAM Proban Program version 4 4 01 OCT 2004 2 19 The first four moments are illustrated in Figure 2 12 to Figure 2 15 A normal distribution has a skewness of 0 0 and a kurtosis of 3 0 A lognormal distribution has a positive skewness and a kurtosis that is larger than 3 0 P
95. BABILITY ANALYSIS SINGLE EVENT NPV lt 0 U UE ti Proban can also be used to do a probability or distribution analysis conditional on some obtained informa tion Suppose that the manager decides to go for the project After 6 months he is certain that the income after the first year will exceed 70000 This information can be used to update the distribution of the NPV and the probability of a loss This can be formulated as a conditional probability P NPV lt 0 I gt 70000 P NPV lt 0 T gt 70000 P 1 gt 70000 The following commands will recalculate the values conditioned on the new information RUN DISTRIBUTION ANALYSIS CONDITIONED NPV SINGLE EVENT 11 gt 70000 RUN PROBABILITY ANALYSIS CONDITIONED SINGLE EVENT NPV lt 0 SINGLE EVENT 11 gt 70000 Result presentation is as above 3 2 Presentation of Model Data and Results Results and input data are presented using the PRINT DISPLAY and PLOT commands The SET command may be used to control print and display options and to control the output print and plot file s The DEFINE RESULT OPTION command is used to set some options specific to the presentation of a selected results SESAM Proban Program version 4 4 01 OCT 2004 3 7 When many results are stored simultaneously only the currently selected result can be presented Use SELECT RESULT to access a particular result After
96. CESS ANALYSIS PURPOSE Run an analysis PARAMETERS CROSSING RATE Run a crossing rate analysis FIRST PASSAGE PROBABILITY Run a first passage probability analysis NOTES None Proban SESAM 5 174 01 OCT 2004 Program version 4 4 RUN CONTINUOUS PROCESS ANALYSIS CROSSING RATE event SINGLE EVENT 1d variable lt gt threshold CROSSING RATE PURPOSE Run a crossing rate analysis PARAMETERS event Name of event to be analysed The event cannot be a condition al event or contain equality events SINGLE EVENT Event is specified directly as a simple inequality 1d variable Name of a one dimensional variable can be a coordinate of a multidimensional variable lt gt One of lt less than gt greater than threshold Numerical right hand side of the single event NOTES 1 The type of analysis being run is selected by use of the SELECT ANALYSIS METHOD CROSSING RATE ANALYSIS command The options to be used for the analysis are set by use of the DEFINE com mand 2 The result is stored under the name LastAnalysis and is overwritten the next time an analysis is per formed unless saved under another name using the SAVE RESULT command 3 The results are examined by use of the commands PRINT RESULT or DISPLAY RESULT 4 Variables with type attribute PROBABILITY cannot be used in a crossing rate analysis See also DEFINE ANALYSIS OPTION DEFINE FORM SORM
97. Create a response surface function Proban 5 50 SESAM 01 OCT 2004 Program version 4 4 CREATE FUNCTION FORMULA FORMULA argname argdesc formula text PURPOSE To create a function formula PARAMETERS argname argdesc formula text NOTES A matrix of argument names and corresponding argument descriptions At least one argument must be defined Formula text lines 1 An argument name consists of maximum 12 alphanumeric characters and _ The first character must be alphabetic 2 An argument description consists of maximum 50 characters 3 A formula is input through a number of lines that are concatenated The order of calculation is according to the FORTRAN syntax See the syntax below Unary operators Binary operators Separator Delimiters Operators FUNAM O ok Unary Unary binary binary Quotes Blanks Hyphen plus sign minus sign addition subtraction multiplication division exponentiation separates the elements of a function argument option list left parenthesis right parenthesis Delimits a function argument option list and a portion of a formula Association Precedence left to right 5 right to left 4 right to left 3 left to right 2 left to right 1 delimits a character value An apostrophe within a quoted text must be entered as in graphics mode and as in line mode on journ
98. D EXAMPLES ASSIGN SIMULATION DENSITY VarSim VarAdjSim SESAM Program version 4 4 Proban 5 22 01 OCT 2004 ASSIGN STARTING POINT event numerical STARTING POINT VARIABLE variable default PURPOSE Assign a starting point for the FORM SORM optimization to an event or a variable PARAMETERS event VARIABLE variable numerical default NOTES Name of the event to which the starting point is assigned This must be a single event Assign the starting point to a variable This must be a one dimensional distribution variable or a generated distribution variable This assignment causes the starting point value to be used in all events that depend on the variable except when over ridden by a direct assignment to the event Name of the variable to which the starting point is assigned Numerical starting point value The value must be specified in the physical model space not in U space The text default implies a default starting point value that is the origin in U space 1 The starting point assignment can be printed by use of the PRINT STARTING POINT command 2 The use of starting points in the FORM SORM optimization is determined by the DEFINE FORM SORM STARTING POINT INITIAL command 3 The starting point assignment can be printed by use of the PRINT STARTING POINT command 4 Anevent may depend on several variables and a variable may be multidimensional It may therefore b
99. DISPLAY RESULT CHANGE TRANSFER FUNCTION CREATE TRANSFER FUNCTION DISPLAY TRANSFER FUNCTION PRINT TRANSFER FUNCTION EXAMPLE The following values are default when the program starts up with a new database 000 0 U y EFINE PRESENTATION RESULT CONFIDENCE VALUE 90 EFINE PRESENTATION EFINE PRESENTATION ESULT IMPORTANCE CUTOFF 0 E SULT PORTANCE LIMIT 5 NTERMEDIATE SIMULATIONS 10 EFINE PRESENTATION R R EFINE PRESENTATION RESULT R R EFINE PRESENTATION I I ESULT SENSITIVITY MEASURE 0 1 0 0001 ESULT V SPACE POINT OFF SESAM Proban Program version 4 4 01 OCT 2004 5 95 DEFINE PROBABILITY SIMULATION AXIS ORTHOGONAL DESIGN POINT DIRECTIONAL MONTE CARLO PROBABILITY ANALYSIS PURPOSE Define analysis options that apply to simulation of a probability PARAMETERS AXIS ORTHOGONAL Define analysis options for axis orthogonal simulation DESIGN POINT Define analysis options for design point simulation DIRECTIONAL Define analysis options for directional simulation MONTE CARLO Define analysis options for Monte Carlo simulation NOTES None Proban 5 96 SESAM 01 OCT 2004 Program version 4 4 DEFINE PROBABILITY SIMULATION AXIS ORTHOGONAL COEFFICIENT OF VARIATION cov CPU TIME cpu CONDITIONED re STANDARD NORMAL AXIS ORTHOGONAL RISK Y AND FAST S
100. E Define Mean value based FORM analysis options PARAMETERS POINTS number LOWER PROBABILITY lower UPPER PROBABILITY upper GRADIENT RESET NOTES The number of points to be calculated These are spaced equal ly in distance in U space from the distance corresponding to lower probability bound to the distance corresponding to upper probability bound The lower probability bound for the range in which values are calculated Must be positive and less than 1 The upper probability bound for the range in which values are calculated Must be positive and less than 1 The method uses either ONE gradient at the origin of U space or THREE gradients the remaining two are calculated at the lower and upper bound Reset all values and options to the default values used when in itialising a new database The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e PRINT ANALYSIS SETTINGS e SELECT ANALYSIS METHOD DISTRIBUTION ANALYSIS EXAMPLES The following values are default when the program starts up with a new database SESAM Program version 4 4 01 OCT 2004 DEFINE MEAN VALUE FORM POINTS 19 DEFINE MEAN VALUE FORM LOWER PROBABILITY 0 01 DEFINE MEAN VALUE FORM UPPER PROBABILITY 0 99 DEFINE MEAN VALUE FORM GRADIENT ONE Proban 5 89 Proban SESAM 5 90 01 OCT 2004 Program version 4 4 DEFINE PARAMETER STUDY PARAM
101. E HARDWARE SOFTWAREE FONT SIZE ABSOLUTE size RELATIVE factor DRAWING _ FONT TYPE SIMPLE GROTESQUE ROMAN NORMAL ROMAN ITALIC PURPOSE To set drawing characteristics PARAMETERS CHARACTER TYPE FONT SIZE ABSOLUTE size RELATIVE factor FONT TYPE FRAME GRID ROMAN BOLD ON FRAME OFF ON GRID OFF Set the character type to SOFTWARE i e scaleable or HARDWARE i e fixed Set the font size This affects all text Set the font size to an ABSOLUTE size in mm Set the font size to a RELATIVE value scaleable by a factor where 40 80 characters are fitted into the window when the factor is 1 Select the font to be used The list of fonts may be machine de pendent Set frame on drawing ON or OFF This command has currently no effect Set grid on a graph drawing ON or OFF Proban 5 200 01 OCT 2004 NOTES See also e DISPLAY PLOT EXAMPLES The following is default when the program starts with a new database SET DRAWING CHARACTER TYPE SOFTWARE SET DRAWING FONT SIZE RELATIVE 1 0 SET DRAWING FONT TYPE SIMPLE S ET DRAWING GRID ON Ed PaPa Ea SESAM Program version 4 4 SESAM Proban Program version 4 4 01 OCT 2004 5 201 SET GRAPH HISTOGRAM LINE OPTIONS PIE CHART XAXIS ATTRIBUTES YAXIS ATTRIBUTES ZAXIS ATTRIBUTES GRAPH PURPOSE To
102. EARCH MEDIUM SAFE SAFE AND SLOW SIMULATIONS nsim RESET PURPOSE Define analysis options for axis orthogonal simulation of a probability PARAMETERS COEFFICIENT OF VARIATION cov CPU TIME cpu DENSITY CONDITIONED STANDARD NORMAL SEARCH RISK Y AND FAST The simulations will stop if the coefficient of variation of the simulated result becomes lower than or equal to cov To disable this stop criterion set cov to 0 cov must be non negative The simulations will stop when the cpu time cpu in seconds has been exceeded The check is performed after each simula tion is completed To disable this stop criterion set cpu to 0 cpu must be non negative Specifies the sampling density This density has a shape that is dependent on the shape of the limit state surface and produces a result that is a multiplicative correction to the FORM probability This is generally quite fast and accurate but it depends on a reasonable FORM approxima tion to the limit state surface This density is not dependent on the shape of the limit state sur face and produces an additive correction to the FORM proba bility This option is the slowest and safest of the two Specifies how the line search for points on the limit state sur face is performed along the simulated direction This search method simply checks one point far out on the line and looks for a solution only if the sign of the function is differ ent at the origin
103. ER STUDY IMPORTANCE FACTOR oooconccccccccononnonnanancnaninnnoo 5 158 PRINT RESULT PARAMETER STUDY MAIN RESULT cococconcccocccncononnninnconcnnanncrncrononncnncnnnos 5 159 PRINT RESULT SAMPLE cial E E e e E do aii 5 160 PRINT RESULT SENSITIVITY tna E a e a e EA 5 162 PRINT RESUETESUMMAR Y india TE EE GRE EERTE E A E caca EAA 5 164 PRINT VARIABLEPRINT VARIABLE pinces i ie oe EEE E ans 5 165 RENAME n N a E E EE E a a E T A A R SET 5 167 RENAM BEVEN Pore mort eE T AE E E E ES E E acts 5 168 RENAME FUNCTION atiina a a aA Ea a EENE 5 169 RENAME RESU DT a Tus a a a ea a a becado A E EA a dieta 5 170 RENAME VARIABLE 5000 dona a nia ci 5 171 A ssdoebegnseserestavensbesseesteduasies Sosvaoedebeee ds gUnedbeabeaseveieesssuuss veseuseesteueeyen 5 172 RUN CONTINUOUS PROCESS ANALYSIS coconcoconcocconcnnnonacnonncnnnnnnnnnonnononon nro rana no rn nonncnncnnnos 5 173 RUN CONTINUOUS PROCESS ANALYSIS CROSSING RATE ccooonconcoconicnconcnncnnonanonncnncnnnns 5 174 RUN CONTINUOUS PROCESS ANALYSIS FIRST PASSAGE PROBABILITY 0 5 176 RUN DETERMINISTIC ANALY SI Sgen aroia a A aa a Aaa E E 5 178 RUN DISTRIBUTION ANALYSIS a e ea a E aata aT E EEE a NE TREA 5 180 RUN INPUT CHECK riip i A E EAE A RER E E aca A 5 182 RUN PROBABILITY ANALY SIS ernie a rbd a eiei eiie 5 183 RUN RESTAR Torah id a aa a a ae a ET 5 185 SAVE AORE E EN S E E E EE EEE 5 186 SAV EU RESUS Pornos eio e OE e E E a A EA EAE O a Ea RIRE T 5 187 SELECT cto E osndgitegupdstasasuita sraledacoautedseundverten
104. ETER STUDY DISPLAY RESULT PARAMETER STUDY EXAMPLES DEFINE TWO PARAMETER STUDY StrCorr GROUP 0 1 0 9 0 1 StrStd GROUP 1 2 0 2 Proban SESAM 5 106 01 OCT 2004 Program version 4 4 DEFINE TWO PARAMETER STUDY XX abc ONLY 22 24 25 29 6 XX def ONLY 3 4 5 SESAM Program version 4 4 DELETE DELETE EVENT FUNCTION RESULT VARIABLE PURPOSE Delete a named object PARAMETERS EVENT FUNCTION RESULT VARIABLE NOTES None Delete an event 01 OCT 2004 Delete a function formula Delete an analysis result Delete a random variable Proban 5 107 Proban SESAM 5 108 01 OCT 2004 Program version 4 4 DELETE EVENT EVENT name PURPOSE Delete one or more events PARAMETERS name Name s of the event s to be deleted NOTES Deletion cannot be undone The only way to undo a deletion is to edit the command s generating the deleted object from the journal file and then read the command input file into the program again See also e CREATE EVENT e CHANGE EVENT e COPY EVENT RENAME EVENT e DISPLAY EVENT PRINT EVENT EXAMPLES DELETE EVENT PFC SESAM Proban Program version 4 4 01 OCT 2004 5 109 DELETE FUNCTION FUNCTION name PURPOSE Delete one or more function formulas or function integrals PARAMETERS name Name s of the fu
105. ETER STUDY parameter value PURPOSE Define parameter study values of a fixed variable or of a numerical parameter in a distribution or of a numerical argument in a function PARAMETERS parameter The name of a fixed variable or the name of a numerical parameter in a distribution or of a numerical argument in a function value Those parameter values for which the parameter study is to be performed NOTES A parameter study may be modified by entering the command again and selecting the same parameter The current values are then presented as defaults Usage of the parameter study is controlled by the command DEFINE ANALYSIS OPTION PARAME TER STUDY This command is described in the User s Manual for Proban Version 3 as ASSIGN PARAMETER STUDY See also DEFINE ANALYSIS OPTION PARAMETER STUDY PRINT PARAMETER STUDY PRINT RESULT PARAMETER STUDY DISPLAY RESULT PARAMETER STUDY EXAMPLES EFINE PARAMETER STUDY StrCorr GROUP 0 1 0 9 0 1 EFINE PARAMETER STUDY XX abc ONLY 22 24 25 29 6 SESAM Program version 4 4 01 OCT 2004 DEFINE PRESENTATION FUNCTION RESULT PRESENTATION PURPOSE Define presentation of results and input data PARAMETERS FUNCTION Define presentation of model functions RESULT Define presentation of analysis results NOTES None Proban 5 91 Proban SESAM 5 92 01 OCT 2004 Program version 4
106. FORM SORM optimization It must be positive Relative parameter increment It must be positive Absolute parameter increment It must be positive Limit for application of relative parameter increment The ab solute increment is used if the absolute value of the parameter is less than limit It must be positive Determines if the gradients that have been programmed into the model functions are used ANALYTICAL or if one way Proban 5 74 U SPACE BOUNDS INTERMEDIATE RESULTS FRACTILE FROM PROBABILITY UNMIN maxit maxstep conv PROBABILITY FROM FRACTILE SQP NLPQL RFCRC NOTES SESAM 01 OCT 2004 Program version 4 4 u du or two way ut du and u du incrementation is used to determine the gradient Initialises the u space optimisation upper bounds to Value and the u space lower bounds to Value Controls the amount of intermediate results to be generated The possible alternatives are NONE LOW MEDIUM EX CESSIVE Defines the optimization method used to calculate a fractile from a probability value Unconstrained minimisation in polar coordinates The maximal number of iterations allowed The maximal number of steps in one search direction Convergence criterion Defines the optimization method used to calculate a probability from a fractile value Sequential quadratic programming Sequential quadratic programming Extended options set See DEFINE NLPQL Robusted Rackwitz Fiessler
107. FUNCTION OPTION e ASSIGN OPTIMISATION BOUNDS e ASSIGN SENSITIVITY CALCULATION e SET TITLE Proban 5 166 EXAMPLES PRINT VARIABLE 01 OCT 2004 J3220 1nC J3220 m May generate the following print J3220 1 nc SESAM Program version 4 4 Distribution Normal Calculated parameters Dim Parameter Value 1 Mean 31 0 Stand Dev 0 77 Skewness 0 0 Kurtosis 3 0 Median 31 0 Variable J3220 m m material parameter Dim Parameter Value SESAM Program version 4 4 01 OCT 2004 RENAME EVENT FUNCTION RESULT VARIABLE RENAME PURPOSE Rename a named object PARAMETERS EVENT Rename an event FUNCTION Rename a function formula RESULT Rename an analysis result VARIABLE Rename a random variable NOTES None Proban 5 167 Proban SESAM 5 168 01 OCT 2004 Program version 4 4 RENAME EVENT EVENT from to PURPOSE To change the name of an event PARAMETERS from The original name of the event to The new name of the event This cannot be the name of an existing event NOTES Renaming of an event does not affect the usage of the event in other events See also CHANGE EVENT CREATE EVENT DELETE EVENT COPY EVENT PRINT EVENT DISPLAY EVENT EXAMPLES R ENAME EV ENT Moment 1 Moment 2 SESAM Proban Program version 4 4 01 OCT 2004
108. G CONTINUOUS PROCESS CORRELATION EXTREME VALUE FUNCTION OPTION ASSIGN MEASURED VALUE OPTIMISATION BOUNDS SENSITIVITY CALCULATION SIMULATION DENSITY STARTING POINT SUB LEVEL INTEGRATION PURPOSE Assign attribute s to one or more named objects PARAMETERS CONDITIONING CONTINUOUS PROCESS CORRELATION EXTREME VALUE FUNCTION OPTION MEASURED VALUE OPTIMISATION BOUNDS SENSITIVITY CALCULATION SIMULATION DENSITY Assign conditioning variables to a generated distribution varia ble Assign duration and starting time to a type time variable and time derivative to a time dependent process variable Assign correlation between random variables Assign extreme value distribution type to a random variable Assign optional function input to a random variable that is a function of other variables or to a model function Assign the measured value to an event with equality constraint Assign bounds to a variable limiting the range of values al lowed in FORM SORM optimization Assign sensitivity calculation and increment to parameters Assign a variable as adjusted simulation density in a sampling of probability Proban SESAM 5 10 01 OCT 2004 Program version 4 4 STARTING POINT Assign a starting point for the FORM SORM analysis to an event SUB LEVEL INTEGRATION Assign variables to be integrated together with time dependent process variabl
109. GS SESAM Program version 4 4 Summary All Importance Factors Sensitivity Sample Parameter Study Main Result Parameter Study Importance Intermediate Results 5 1 8 The Options Menu Proban 01 OCT 2004 5 7 PRINT RESULT SUMMARY PRINT RESULT ALL PRINT RESULT IMPORTANCE FACTORS PRINT RESULT SENSITIVITY PRINT RESULT SAMPLE PRINT RESULT PARAMETER STUDY MAIN RESULT PRINT RESULT PARAMETER STUDYIMPORTANCE FAC TOR PRINT RESULT INTERMEDIATE RESULTS This menu contains the commands available in the line mode SET command i e print and display settings Company Name Display Drawing Graph gt Lines and Markers X Axis Y Axis Z Axis Histogram Pie Chart Plot Print Title 5 1 9 The Help Menu SET COMPANY NAME SET DISPLAY SET DRAWING SET GRAPH LINE OPTIONS SET GRAPH X AXIS ATTRIBUTES SET GRAPH Y AXIS ATTRIBUTES SET GRAPH Z AXIS ATTRIBUTES SET GRAPH HISTOGRAM SET GRAPH PIE CHART SET PLOT SET PRINT SET TITLE The contents of the Help menu is the same as is described with the HELP command in the next section Proban SESAM 5 8 01 OCT 2004 Program version 4 4 5 2 Line Mode Command Syntax This section describes the complete syntax of the line mode command input The commands are presented alphabetically As the line mode input is case insensitive all alternatives are presented in upper case SESAM Program version 4 4 ASSIGN Proban 01 OCT 2004 5 9 CONDITIONIN
110. IGNED see AS SIGN STARTING POINT or DEFAULT The default starting point is a small shift from the origin in U space STARTING POINT PARAMETER STUDY Controls the usage of starting points in a parameter study Ei RESET ther the PREVIOUS SOLUTION is used whenever possible or the starting point is defined as above SAME AS INITIAL Reset all values and options to the default values used when in itialising a new database SESAM Proban Program version 4 4 01 OCT 2004 5 83 NOTES The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e ASSIGN STARTING POINT DEFINE ANALYSIS OPTION PRINT ANALYSIS SETTINGS SELECT ANALYSIS METHOD PROBABILITY ANALYSIS EXAMPLES The following values are default when the program starts up with a new database DEFINE FORM SORM BOUNDS OFF DEFINE FORM SORM INACTIVE CONSTRAINTS ON DEFINE FORM SORM MULTINORMAL SQP DEFINE FORM SORM NESTED ANALYSIS GLOBAL SQP 40 10 0 0025 DEFINE FORM SORM OPTIMIZATION SQP 40 10 0 0025 DEFINE FORM SORM SENSITIVITY ANALYTICAL ONE WAY DEFINE FORM SORM STARTING POINT INITIAL ASSIGNED DEFINE FORM SORM STARTING POINT PARAMETER STUDY PREVIOUS SOLUTION Proban 5 84 DEFINE NEPQL SESAM 01 OCT 2004 Program version 4 4 NLPQL search method maxit maximum step lenght maxfun conv cnsv b
111. IMITS LINEAR LOGARITHMIC SPACING DEFAULT SPECIFIED ztitle TITLE PURPOSE Control the drawing of the Z axis in a graph display PARAMETERS DECIMAL FORMAT EXPONENTIAL FIXED GENERAL INTEGER LIMITS FREE FIXED zmin zmax SPACING LINEAR LOGARITHMIC TITLE Controls the presentation of numbers labelling the z axis The numbers are presented in exponential format e g 1 233E 01 The numbers are presented in fixed format e g 12 33 The numbers are presented in general free format The numbers are presented as integers Controls the limits of the z axis The limits are determined by the data that are being presented The limits are fixed to the min value zmin and the max value zmax Controls the spacing of numbers along the axis The axis has a LINEAR spacing The axis has a logarithmic spacing with base 10 Set the title at the z axis Proban SESAM FEAR OCA Programversion 4 4 DEFAULT The title is specified by Proban according to the current graphs being drawn SPECIFIED ztitle The specified ztitle text is used NOTES See also DISPLAY e PLOT SET GRAPH XAXIS ATTRIBUTTES SET GRAPH YAXIS ATTRIBUTTES EXAMPLES The following is default when the program starts with a new database SET GRAPH ZAXIS ATTRIBUTES DECIMAL FORMAT GENERAL SET GRAPH ZAXIS ATTRIBUTES LIMITS FREE SET GRAPH ZAXIS ATTRIBUTES SPACING LINEAR SET GRAPH ZAXIS ATTRIBUTES T
112. IMPORTANCE LIMIT 3 The form of the pie charts may be manipulated by use of the command SET GRAPH PIE CHART 4 Examples of the display can be seen in Figure 3 4 and Figure 3 14 See also DEFINE PRESENTATION RESULT IMPORTANCE LIMIT DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR PRINT RESULT e SELECT RESULT e SET EXAMPLES DISPLAY RESULT IMPORTANCE FACTORS DISPLAY RESULT IMPORTANCE FACTORS ONLY 22 5 DISPLAY RESULT IMPORTANCE FACTORS ONLY ole no parameter study pick one from a study all results from a study J m aO E oo Proban SESAM 5 122 01 OCT 2004 Program version 4 4 DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR MAIN RESUL PARAMETER STUDY PURPOSE Display results as a function of the parameters in a parameter study PARAMETERS IMPORTANCE FACTOR Display importance factors as a function of the parameters MAIN RESULT Display one or more main results as a function of the parame ters NOTES None SESAM Proban Program version 4 4 01 OCT 2004 5 123 DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR IMPORTANCE FACTOR variable PURPOSE Display importance factor for variable as a function of the parameters in a parameter study PARAMETERS variable Name of variable or importance group NOTES An example of the display can be seen in Figure 3 14 See also PRINT RESULT PARAMETER STUDY IMPORTANCE FACTOR
113. INT DIS PLAY NOTES None SESAM Program version 4 4 SELECT ANALYSIS METHOD ANALYSIS METHOD 01 OCT 2004 Proban 5 189 CROSSING RATE ANALYSIS FORM MONTE CARLO SIMULATION DISTRIBUTION ANALYSIS LATIN HYPERCUBE SIMULATION MEAN VALUE FORM FIRST PASSAGE PROBABILITY ANALYSIS FORM FORM PARABOLIC DIAGONAL SORM FULL EXPANSION ASYMPTOTIC PROBABILITY ANALYSIS AXIS ORTHOGONAL SIMULATION DEFAULT DESIGN POINT SIMULATION ADJUSTED DIRECTIONAL SIMULATION CENTRAL NORMAL MONTE CARLO SIMULATION ADJUSTED PURPOSE Select analysis method for probability and distribution analyses PARAMETERS CROSSING RATE ANALYSIS FIRST PASSAGE PROBABILITY ANALYSIS DISTRIBUTION ANALYSIS MONTE CARLO SIMULATION Select the method used for crossing rate analysis Select the method used for first passage probabil ity analysis Select the method used for distribution analysis The simplest simulation method where points are picked randomly and sample values are kept dis tribution analysis or the frequency of occurrences counted probability analysis Proban 5 190 LATIN HYPERCUBE SIMULATION MEAN VALUE FORM PROBABILITY ANALYSIS FORM SORM PARABOLIC DIAGONAL FULL EXPANSION ASYMPTOTIC AXIS ORTHOGONAL SIMULATION DESIGN POINT SIMULATION DIRECTIONAL SIMULATION MONTE CARLO SIMULATION CENTRAL NORMAL ADJUSTED
114. ION DESIGN POINT coococonocccocononconcconccnnncnnnonncconannnannncnnnos 5 98 DEFINE PROBABILITY SIMULATION DIRECTIONA Lo coooconocinoccnnncnoncnnccnnncnnonnnonnccnacnnanncs 5 100 DEFINE PROBABILITY SIMULATION MONTE CARLO oodconcccoccconnonnnonnonnnannnanancnnncnnncnnccnns 5 103 DEFINE TWO PARAMETER STUDY neroet iei AE a E E ee aaa 5 105 A O 5 107 DELETE EVENT A O O ONE 5 108 DEEETE FUNCTION laa a a a renato rod Deals Faroe Panor cia 5 109 DEBETE RRESUET 2 a ai laa 5 110 DELETE VARIABEE settar adinei desscesSdondeuss ashes tdandes stavbus aaa a e a a i bates 5 111 DISPLAY rhac aan triar Te ETT A SE A ER E Aa oS Raa ROS 5 112 DISPLAY DISTRIBUTION saiia aaa A a A S 5 113 DISPLAY EVENTS piena a At ia 5 114 DISPLAY FITTED DISTRIBUTION croira a A E E 5 115 DISPLAY FUNCTION Yeer e e a a EEEE E E Conebucutelteens 5 116 DISPLAY RESULT Grada EE E A a te 5 118 DISPLAY RESULT DISTRIBUTION se heet enii E E E E nana rnn ancora oran E EE 5 119 DISPLAY RESULT IMPORTANCE FACTORS coocccoccconinnonnnnnonnonacnnnnnnnanonnonno no ncancanrancnncrncra nens 5 121 DISPLAY RESULT PARAMETER STUD Y cooccocnnicnociononicnnninncnncnncnononnonncnncnnn nn kereis asii kasis 5 122 DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR eserse 5 123 DISPLAY RESULT PARAMETER STUDY MAIN RESULT conconcccnccnioncnnncnnnannninnnonnononannnannos 5 124 EA orilla EA dust suiesatsaustiaeasodcanevoudea reine ies CRA Goss decesesees lestiaestes 5 125 HE rincon ticos ts cnet EEEE A E A E bebonenscanie
115. IONS MARKER SIZE 7j NU EFAULT for all lines 0 u ed SESAM Program version 4 4 01 OCT 2004 SET GRAPH PIE CHART OFF EXPLODED SEGMENT SEGMENT NAME name HATCHED FILLING HOLLOW SOLID HIDE VISIBILITY SHOW PIE CHART HORIZONTAL ORIENTATION ROTATED LABEL OUTSIDE POSITION AUROMATIC INSIDE ON VALUE OFF PURPOSE Set options controlling display of a pie chart PARAMETERS EXPLODED SEGMENT OFF No segment is to be exploded SEGMENT NAME name Proban 5 205 Controls if a segment of the pie is to be shown exploded i e detached from the rest Explode the segment with the given name No segment will be exploded if the name does not match nay of the segment names in the pie to be displayed The name can be abbreviated and the matching of names disregards the text case FILLING The columns in the histogram can be filled with a HATCHED pattern or not filled at all HOLLOW or be filled with a SOL ID pattern LABEL VISIBILITY Define the drawing of the pie segment labels HIDE or SHOW the pie segment labels Proban 5 206 ORIENTATION POSITION VALUE NOTES SESAM 01 OCT 2004 Program version 4 4 Draw the pie segment labels HORIZONTAL or ROTATED to follow the segment angle Draw the pie segment labels OUTSIDE the pie INSIDE the pie or use an AUTOMATIC placement where they are drawn in side
116. ITHMIC TITLE Controls the presentation of numbers labelling the y axis The numbers are presented in exponential format e g 1 233E 01 The numbers are presented in fixed format e g 12 33 The numbers are presented in general free format The numbers are presented as integers Controls the limits of the y axis The limits are determined by the data that are being presented The limits are fixed to the min value ymin and the max value ymax Controls the spacing of numbers along the axis The axis has a LINEAR spacing The axis has a logarithmic spacing with base 10 Set the title at the y axis Proban SESAM 5210 OCA Programversion 4 4 DEFAULT The title is specified by Proban according to the current graphs being drawn SPECIFIED ytitle The specified ytitle text is used NOTES See also DISPLAY e PLOT SET GRAPH XAXIS ATTRIBUTTES SET GRAPH ZAXIS ATTRIBUTTES EXAMPLES The following is default when the program starts with a new database SET GRAPH YAXIS ATTRIBUTES DECIMAL FORMAT GENERAL l GRAPH YAXIS ATTRIBUTES LIMITS FREE l GRAPH YAXIS ATTRIBUTES SPACING LINEAR GRAPH YAXIS ATTRIBUTES TITLE DEFAULT Ae d S S S SESAM Program version 4 4 Proban 01 OCT 2004 5 211 SET GRAPH ZAXIS ATTRIBUTES ZAXIS ATTRIBUTES EXPONENTIAL FIXED GENERAL INTEGER DECIMAL FORMAT FIXED zmin zmax FREE L
117. ITLE DEFAULT SESAM Proban Program version 4 4 01 OCT 2004 5 213 SET PLOT ON COLOUR O SESAM NEUTRAL POSTSCRIPT FORMAT HPGL 7550 HPGL 2 PLOT CGM BINARY FILE prefix name Al A2 PAGE SIZE A3 A4 A5 PURPOSE To set plot file characteristics PARAMETERS COLOUR FORMAT SESAM NEUTRAL POSTSCRIPT HPGL 7550 HPGL 2 CGM BINARY Sets the output to the plot file to be in colours ON or mono chrome OFF Set the type of plot file to be used Please note that the actual range of devices is machine dependent SESAM Neutral format This is the default format It can be converted to other formats and or manipulated by use if the utility program PLTCNV PostScript format PostScript is a trademark of Adobe Systems Incorporated Note that this requires access to a printer that ac cepts PostScript files HP 7550 plotter HP Laserjet printer ISO 8632 3 Computer Graphics Metafile CGM plot format Proban SESAM 5 214 01 OCT 2004 Program version 4 4 FILE prefix name Set the prefix and name of the plot file The prefix and name are concatenated The suffix of the file will depend on the format of the file PAGE SIZE Sets the size of the plot to one of Al A2 A3 A4 or A5 NOTES 1 When one of these settings is changed a new plot file will be opened the next time a plot is written 2 One plot fi
118. L2 1 SESAM Proban Program version 4 4 01 OCT 2004 5 33 CHANGE VARIABLE DISTRIBUTION VARIABLE name desc FITTED DISTRIBUTION FIXED value FUNCTION GENERATED 1d variable PROBABILITY TIME PURPOSE To change a variable PARAMETERS name desc DISTRIBUTION FITTED DISTRIBUTION FIXED value FUNCTION GENERATED 1d variable PROBABILITY TIME Name of variable to be changed Descriptive text for the variable The variable is assigned a distribution See a following page for details The variable is assigned a distribution that is fitted to input da ta See a following page for details The variable has a fixed value The numerical value of a fixed variable The variable is assigned a model function See a following page for details The distribution of the variable is generated from the distribu tion of another variable The variable specifying a generated distribution This is a one dimensional variable or a coordinate in a multidimensional var iable The variable is the probability of an event as calculated by Proban The variable is the generic time variable Proban SESAM 5 34 01 OCT 2004 Program version 4 4 NOTES 1 When the variable name is selected the existing state of the variable is presented as defaults unless the type of the variable is changed 2 Some of the variables in a generated distribution may be sh
119. NE PROBABILITY SIMULATIONAXIS ORTHOGONAL DEFINE PROBABILITY SIMULATION DIRECTIONAL DEFINE PROBABILITY SIMULATION MONTE CARLO DEFINE DISTRIBUTION SIMULATION DEFINE MEAN VALUE FORM DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS Proban 5 6 Sub Level Integration Check Analysis Input Probability Distribution Continuous Process Print Analysis Setup Analysis Setup Parameter Study FORM SORM Starting Point 5 1 7 The Result Menu SESAM 01 OCT 2004 Program version 4 4 ASSIGN SUB LEVEL INTEGRATION RUN INPUT CHECK PROBABILITY ANALYSIS RUN INPUT CHECK DISTRIBUTION ANALYSIS RUN INPUT CHECK CONTINUOUS PROCESS ANALYSIS PRINT ANALYSIS SETTINGS PRINT PARAMETER STUDY PRINT STARTING POINT This menu contains commands used to access results created while running probabilistic or deterministic analysis The results created during general probabilistic or deterministic analysis must be accessible through this menu Save Result Select Result Delete Result Rename Result Result Presentation Display Result gt Distribution Importance Factors Parameter Study Main Result Parameter Study Importance Print Result gt Analysis Settings SAVE RESULT SELECT RESULT DELETE RESULT RENAME RESULT DEFINE PRESENTATION RESULT DISPLAY RESULT DISTRIBUTION DISPLAY RESULT IMPORTANCE FACTORS DISPLAY RESULT PARAMETER STUDY MAIN RESULT DISPLAY RESULT PARAMETER STUDY IMPORTANCE FAC TOR PRINT RESULT ANALYSIS SETTIN
120. Normal Mean StD 40 6 Av Shear steel area DISTR Normal Mean StD 35 1 75 Spacing Shear steel spacing DISTR Normal Mean StD 300 45 Span Beam span FIXED 3000 Momentl Moment limit state at 1 FUNCTION MomForml P1 P2 L1 L2 Span Depth Ts As K Width Tc Moment2 Moment limit state at 2 FUNCTION MomForml P2 Pl L2 L1 Span Depth Ts As K Width Tc Shear0 Shear limit state at 0 FUNCTION ShrForml P1 P2 L1 L2 Span Depth Ts Width Tc Av Spacing Shear3 Shear limit state at 3 FUNCTION ShrForml P2 Pl L2 L1 Span Depth Ts Width Tc Av Spacing END PRINT FUNCTION DESCRIPTION LoadPart PRINT FUNCTION FORMULA MomForml As can be seen from the input the moment formula and the shear formula have a common load part This load part is created separately as a function formula The load part formula is then used in the definition of the moment formula and the shear formula Any one dimensional function in any user defined function library and any formula created on input can be used as a reference in the definition of a function formula The only limitation is that a function formula cannot in directly reference itself Notice that it is possible and often useful to divide a function formula into a number of smaller formulas The command PRINT FUNCTION DESCRIPTION LoadPart produces LoadPart Load part of moment and shear The function belongs to sublibrary SYMBOLIC Gradients must be calculated numerically
121. O 5LO FIT4 5U5 RESULT LastAnal REATE VARIABLE beta fit FIT beta DISTRIBUTION Beta R S Lim 2 3 1 3 betax FUNCTION DIFFERENCE betax E ANALYSIS OPTION PARAMET EFINE PARAMETER STUDY X ONLY GROUP 1 1 2 9 0 1 ER STUDY ON PTED DISTRIBUTION Beta R S Lim FITL1U4 FITL1U4 lysis Proban SESAM 3 58 01 OCT 2004 Program version 4 4 The resulting fit becomes SESAM PROBAN 4 3 03 22 JUN 2000 14 54 Beta distribution fit of beta_fit Distribution function beta_fit 2 Fitted curve R 1 9998617004 x Input points S 2 9998966821 Lower Bound 1 0000182728 Upper Bound 2 9999942066 Figure 3 17 Fitting of beta distribution By inspecting the input we see that the fitted parameters are given starting point value and a lower or an upper bound It is often necessary to specify an initial value and parameter bounds to the optimization algo rithm in order to reach the best fit The value after FIT is the starting point The value after L is a lower bound on the parameter and the value after U is an upper bound Proban can also fit a distribution to the result of a parameter study on probability by means of the Least Squares method For more details see command CREATE VARIABLE FITTED DISTRIBUTION 3 9 3 User Defined Distributions To add a user defined distribution to Proban requires that the distribution is programmed and then linked into Proban Use the following sequence to ad
122. OPY EVENT Rename Event RENAME EVENT Measured Value ASSIGN MEASURED VALUE Display Event DISPLAY EVENT Print Event PRINT EVENT 5 1 6 The Analysis Menu This menu contains commands used to set up and execute probabilistic and deterministic analyses in gen eral Results from such an analysis are examined by use of the Result menu Select Analysis Method SELECT ANALYSIS METHOD General Analysis Setup DEFINE ANALYSIS OPTION SESAM Program version 4 4 Sensitivity Calculation gt Selection Increment Parameter Study Run Analysis gt Probability Distribution Deterministic Continuous Process Restart Simulation FORM SORM Analysis Setup gt General FORM SORM Setup Optimization Bounds Starting Point Nested Analysis Optimization Nested Analysis General Generated Distribution Probability Simulation Setup Axis Orthogonal Simulation Directional Simulation Monte Carlo Simulation Distribution Analysis Setup Simulation Mean Value FORM Continuous Process Setup General Analysis Setup Proban 01 OCT 2004 5 5 ASSIGN SENSITIVITY VARIABLE ASSIGN SENSITIVITY INCREMENT DEFINE PARAMETER STUDY RUN PROBABILITY ANALYSIS RUN DISTRIBUTION ANALYSIS RUN DETERMINISTIC ANALYSIS RUN CONTINUOUS PROCESS RUN RESTART DEFINE FORM SORM ASSIGN OPTIMISATION BOUNDS ASSIGN STARTING POINT DEFINE FORM SORM NESTED ANALYSIS DEFINE ANALYSIS OPTION NESTED ANALYSIS DEFINE FORM SORM GENERATED DISTRIBUTION DEFI
123. OPY FUNCTION ASSIGN FUNCTION OPTION SELECT FUNCTION LIBRARY DISPLAY FUNCTION DEFINE PRESENTATION FUNCTION PRINT FUNCTION DESCRIPTION PRINT FUNCTION FORMULA PRINT FUNCTION RESPONSESURFACE PRINT FUNCTION VALUE PRINT FUNCTION GRADIENT PRINT FUNCTION LIBRARY This menu contains commands used to define random variables Create Variable Change Variable Delete Variable Copy Variable Rename Variable Extreme Type Function Option Conditioning Display gt One Dimensional Distribution Fitted Distribution CREATE VARIABLE CHANGE VARIABLE DELETE VARIABLE COPY VARIABLE RENAME VARIABLE ASSIGN EXTREME VALUE ASSIGN FUNCTION OPTION ASSIGN CONDITIONING DISPLAY DISTRIBUTION DISPLAY FITTED DISTRIBUTION Proban SESAM 5 4 01 OCT 2004 Program version 4 4 Print gt Print Basic Information PRINT VARIABLE Print Distribution PRINT DISTRIBUTION Print Correlation PRINT CORRELATION Correlation gt Correlate Variables ASSIGN CORRELATION 5 1 4 The Process Menu Continuous Process gt Time Derivative ASSIGN CONTINUOUS PROCESS TIME DERIVATIVES Stationary Process Duration DEFINE CONTINUOUS PROCESS DURATION General Process Start Time ASSIGN CONTINUOUS PROCESS STARTING TIME General Process Duration ASSIGN CONTINUOUS PROCESS DURATION 5 1 5 The Event Menu This menu contains commands used to model events Create Event CREATE EVENT Change Event CHANGE EVENT Delete Event DELETE EVENT Copy Event C
124. PARAMETER STUDY e SELECT ANALYSIS METHOD PROBABILITY ANALYSIS e SAVE RESULT e PRINT RESULT DISPLAY RESULT EXAMPLES RUN RUN RUN RUN PROBABILI PROBABILI PROBABILI PY ANALYSIS PY ANALYSIS PY ANALYSIS PROBABILI PY ANALYSIS Beam Fail SINGLE EV CONDITION CONDITION ED Loss SINGLE ENT NPV gt 100000 ED Failure NoFi nd EV ENT SESAM Program version 4 4 Expense gt 100000 SESAM Proban Program version 4 4 01 OCT 2004 5 185 RUN RESTART RESTART PURPOSE Continue a simulation PARAMETERS None NOTES 1 The selected result defines the analysis to be restarted 2 Only simulations resulting from RUN PROBABILITY ANALYSIS or RUN DISTRIBUTION ANALY SIS can be restarted The simulations will add to the previously established sample The stop criteria for the simulation can be modified before the analysis is restarted 3 The new result will be stored under the default name LastAnalysis The previous result is deleted if it was also stored under this name See also RUN DISTRIBUTION ANALYSIS e RUN PROBABILITY ANALYSIS DEFINE DISTRIBUTION SIMULATION DEFINE PROBABILITY SIMULATION SAVE RESULT PRINT RESULT e DISPLAY RESULT EXAMPLES RUN RESTART Proban 5 186 01 OCT 2004 SAVE SAVERESULT PURPOSE Save an analysis result under a name PARAMETERS RESULT Save an analysis re
125. PARAMETER STUDY IMPORTANCE FACTOR ONLY T 1 EI E SESAM Program version 4 4 Proban 01 OCT 2004 5 159 PRINT RESULT PARAMETER STUDY MAIN RESULT MAIN RESULT mainres PURPOSE Print main results as a function of the parameter in a parameter study PARAMETERS mainres coordinate NOTES None See also A selection of main results The list of available results depend on the analysis per formed All possible main results are presented in the list even though they may not all be calculated for all the individual analyses in the parameter study For de terministic analysis of a variable there will be one result for each coordinate and for an event there will be one result These results will be named after the variable or event analysed A coordinate of a vector if a vector variable with more than one coordinate is sam pled e DISPLAY RESULT PARAMETER STUDY MAIN RESULT e SELECT RESULT e SET TITLE EXAMPLES PRINT RESULT PRINT RESULT PARAMET PARAMET ER STUDY MAIN RESULT ONLY Prob Conf ER STUDY MAIN RESULT ONLY Mean Proban SESAM 5 160 01 OCT 2004 Program version 4 4 PRINT RESULT SAMPLE LOW RESOLUTION HIGH RESOLUTION n SAMPLE valuel value2 ALL SIMULATIONS FRACTILE probability PROBABILITY fractile po PURPOSE
126. PARAMETERS valuel This input is only required if the selected result is a parameter study valuel is then a selection of the parameter values for which the study was run The particular re sults from the analysis using the selected value s will be printed value2 This input is only required if the selected result is a two parameter study value2 is then a selection of the parameter values for which the study was run The particular results from the analysis using the selected value s will be printed NOTES The smallest importance factor values may be removed from the print see DEFINE PRESENTATION RESULT IMPORTANCE CUTOFF See also DEFINE PRESENTATION RESULT IMPORTANCE CUTOFF PRINT RESULT PARAMETER STUDY IMPORTANCE FACTOR PRINT RESULT SELECT RESULT e SET TITLE EXAMPLES PRINT RESULT IMPORTANCE FACTORS no parameter study Proban SESAM 5 156 01 OCT 2004 Program version 4 4 PRINT RESULT INTERMEDIATE RESULTS INTERMEDIATE RESULTS PURPOSE Print all intermediate results from the selected analysis result PARAMETERS None NOTES 1 The intermediate results are generated during the analysis The amount of intermediate results is control led by use of the commands DEFINE ANALYSIS OPTION INTERMEDIATE RESULTS and DEFINE ANALYSIS OPTIONS GENERATED DISTRIBUTION INTERMEDIATE RESULTS 2 The print may be very long depending on the amount of intermediate results requested 3 The intermed
127. RAM FILLING SOLID dd E 3 O SESAM Program version 4 4 01 OCT 2004 SET GRAPH LINE OPTIONS LINE OPTIONS LINE TYPE line linetype ON MARKER OFF MARKER TYPE line marker type MARKER SIZE size PURPOSE To set options controlling how lines are drawn and marked PARAMETERS LINE TYPE line linetype MARKER MARKER TYPE marker type MARKER SIZE size NOTES Proban 5 203 Controls how lines are drawn Only six lines can be controlled A line number from 1 to 6 The line type to use Legal values BLANK END POINT DASHED DASH DOT DEFAULT DOTTED SOLID Turn usage of markers ON or OFF Control the marker type The type of marker to use Legal values CROSS DEFAULT DELTA DIAMOND NABLA PLUS SQUARE STAR Set the size of the markers Even when the MARKER option is ON not all points on the curve need be marked If more than 20 points are drawn and the line type is not BLANK only a few points are marked in order to not clutter the curve with markers See also DISPLAY PLOT EXAMPLES The following is default when the program starts with a new database S S a 3043 l GRAPH LIN l GRAPH LIN a Es a 0P1 0P1 TIONS LINE TYPE DI EFAULT PIONS MARKER ON o for all lines Proban SESAM 5 204 01 OCT 2004 Program version 4 4 T GRAPH LINE OPTIONS MARKER TYPE T GRAPH LINE OPT
128. RINT VARIA BLE command 6 The distribution itself may be displayed using DISPLAY DISTRIBUTION The accuracy of the fit may be examined using DISPLAY FITTED DISTRIBUTION 7 The distributions are listed in SESAM User s Manual Proban Distributions See also e CREATE VARIABLE SESAM Proban Program version 4 4 01 OCT 2004 5 41 e DISPLAY DISTRIBUTION e DISPLAY FITTED DISTRIBUTION e PRINT VARIABLE PRINT DISTRIBUTION e ASSIGN EXTREME VALUE EXAMPLES CHANGE VARIABLE X FITTED DISTRIBUTION Normal Mean CoV FIT FIT OBS UNW ONLY 1 34 2 56 8 65 4 32 4 67 6 66 5 23 3 25 CHANGE VARIABLE Y FITTED DISTRIBUTION Normal Mean Std FIT15 FIT CUMULATIVE WEIGHTED ONLY 12 0 1 1 15 0 3 2 17 0 7 1 20 0 9 1 CHANGE VARIABLE RES FITTED DISTRIBUTION Lognormal Mean Std L FIT FIT 0 RESULT LastAnalysis Proban 5 42 01 OCT 2004 CHANGE VARIABLE FUNCTION FUNCTION function dim argument PURPOSE SESAM Program version 4 4 To change a variable to be based on a model function or to change a function already assigned PARAMETERS function The name of the function The functions can be listed by use of the commands PRINT FUNCTION LIBRARY and PRINT FUNCTION DESCRIPTION dim The dimension of the function if this is not fixed argument The argument value s for the chosen function Each argument value may be either a numerical value or the
129. SESAM Program version 4 4 A stratified simulation technique where the sam pling points are spread systematically over the sample space A simple FORM estimation of a distribution Quick but not generally reliable Select the method used for probability analysis First Order Reliability method Second Order Reliability Method Uses a parabolic approximation to the failure sur face If the U space dimension is n this method requires n 1 2 second order derivations Uses an approximation to the failure surface based on the diagonal of the second order differential matrix If the U space dimension is n this method requires n second order derivations Uses a full second order approximation to the fail ure surface If the U space dimension is n this method requires n2 second order derivations Note that this method is not invariant art different formulations of the problem that give the same failure surface Asymptotic second order approximation Not nec essarily accurate but fast A simulation method based on a FORM result It simulates the difference between the correct prob ability and the FORM approximation Design point simulation of probability Monte Carlo sampling of points around the design point Directional simulation of probability Samples di rections in U space instead of points Monte Carlo simulation of probability The simulation density is entered at the u space origin The simulation densi
130. SET DRAWING FONT SIZE RELATIVE 1 0 DISPLAY RESULT MAIN RESULT ONLY 15000 0 15000 SESAM Program version 4 4 SESAM PROBAN 4 3 03 x 15000 0 01 OCT 2004 22 JUN 2000 14 54 Importance Factors NPY AANA E AAA PESA SSA sere oe SA SER A x 15000 0 Proban 3 51 Figure 3 14 Multiple pie charts for parameter study of importance factors While the results are available it is instructing to see the distribution as calculated with FORM and SORM DISPLAY RESULT PARAMETER STUDY MAIN RESULT ONLY Prob Proban 3 52 01 OCT 2004 SESAM PROBAN 4 3 03 NPVx Parameter study using x SESAM Program version 4 4 22 JUN 2000 14 54 Main result 4 Prob FORM Prob SORM o T 30000 20000 10000 0 10000 20000 30000 x Figure 3 15 The distribution of NPV calculated by FORM and SORM The SORM distribution has a nasty drop at the middle This is not a Proban error it is caused by an improper usage of SORM Again the triangle distributions used here have a non differentiable density at the middle of the distributions If similar Beta distributions were used the SORM result would give a cor rect distribution function try it 3 9 Distributions Proban contains an extensive list of distributions that can be used to model uncertainty The list includes 21 continuous distributions two discrete distributions and a spline distribution that fi
131. SPLINE 1DIM oooooccnnccccnonoonnnononnnnnonnnncnonnnonononnnnnnnnoss 5 60 CREATE VARIABLE FITTED DISTRIBUTION c ccoooocnnonoonnnononnnnnnnnnnncnonnnnnnnnnnnnnnnnnnncnnnnnnnnnoss 5 62 CREATE VARIABLE y FUNCION dond 5 65 CREATE VARIABLE PROBABILITY rd inuin 5 67 DEFINEN la RR 5 68 DEFINE ANALYSIS O TON sae 5 69 DEFINE ANALYSIS OPTION GENERATED DISTRIBUTION oocococcocononcnnonnnncnnonnonnconinanncnnonos 5 73 DEFINE ANALYSIS OPTION NESTED ANALYSIS cccscssssscrcssssrssssssesecnssneseceesenesnsereees 5 75 DEFBINE CONTINUOQUS PROCESS tis er eea tarta tdi it 5 77 DEFINE CONTINUOUS PROCESS ANALYSIS OPTION coocococcccccnonnonnonnnnnnnancnnconanncrnncnncnncnnnn 5 78 DEFINE DISTRIBUTION SIMULATION eee cee cnceneeceeseeeeecesceseeaesaeeeeseeesaeeaesaeeaaeeaee 5 80 DEBINE FORMS ORM usina A a ii 5 81 DEFINE cy NEPO Dorru ennen it tie Id 5 84 DEFINE RECREO ismo eo eE T E AEEA EE E las inode tan cea paite Cove het See tee 5 85 DERINE RSM ii ii 5 86 DEFINE MEAN VALUE FORM peili ra E E E A a noria ranonn n 5 88 DEFINE PARAM PTER U D Y tte aa do il EE NaS 5 90 DEFINE PRESENTATION eoar ataa a aa Bar ape do dd p ae aT S aa E a 5 91 DEFINE PRESENTATION FUNC TION chretien enintaan aiee a E R aa a aiai 5 92 DEFINE PRESENTATION RESULT eriei aliia a anae ia aa S 5 93 DEFINE PROBABILITY SIMULATION credere dikain i diarsir srias 5 95 DEFINE PROBABILITY SIMULATION AXIS ORTHOGONAL eeeseeereeresrersrrsrerrsres 5 96 DEFINE PROBABILITY SIMULAT
132. SSIGN STARTING POINT e ASSIGN MEASURED VALUE EXAMPLES CHANGE EVENT Loss NPV lt 0 SESAM Program version 4 4 CHANGE EVENT Nol Crack2 INTERSECTION ONLY NoCrack 1 Crack2 CHANGE EVENT Fail Cond Failure given nofind then find Crack2 CONDITION ED Failure Nol SESAM Program version 4 4 01 OCT 2004 CHANGE FUNCTION FORMULA FUNCTION name desc INTEGRAL RESPONSESURFACE PURPOSE To change a function PARAMETERS name Name of the function Cannot be changed desc Descriptive text associated with the function formula FORMULA Change a function formula INTEGRAL Change an integration function RESPONSESURFACE Change a response surface function NOTES None Proban 5 27 Proban SESAM 5 28 01 OCT 2004 Program version 4 4 CHANGE FUNCTION FORMULA FORMULA arguments adesc formula text PURPOSE Change a function formula PARAMETERS argument Name of a formula argument At least one argument must be defined adesc Description of argument formula text Formula text lines NOTES Formula syntax is described in command CREATE FUNCTION FORMULA See also e CREATE FUNCTION FORMULA DELETE FUNCTION FORMULA DISPLAY FUCTION PRINT FUNCTION e RENAME FUNCTION EXAMPLES CHANGE FUNCTION FORMULA SYMFOR1 Symbolic Formula ONLY A Arg 1 B Arg 2 A B
133. STRIBUTION INCLUD LOOP DENSITY SET DRAWING GRID ON PLOT DISTRIBUTION END CJ Empirical Normal Fit Hermite Fit PLOT These commands generate the following two plots Proban SESAM 3 32 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Simulation of NPV Net Present Value Density function 00 20000 10000 40000 Variable E Simulation of NPV Hermite Fit 0 Normal Fit Figure 3 5 Histogram of NPV with fitted distributions As can be seen the difference between the normal distribution fit and hermite transformation distribution fit is small SESAM Proban Program version 4 4 01 OCT 2004 3 33 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Simulation of NPV Net Present Value Distribution function Distribution 1 10000 20000 30000 40000 od MN o 30000 20000 10000 Variable Simulation of NPY Hermite Fit 0 Normal Fit Figure 3 6 Empirical distribution function for NPV with fitted distributions The result print includes the options ANALYSIS SETTINGS SUMMARY ALL SENSITIVITY and SAMPLE The print of ANALYSIS SETTINGS contains the analysis settings used with the analysis plus the cpu time usage and the time and date of the run The summary print contains simply the estimated moments PRINT RESULT SUMMARY Result name MCS NPV Monte carlo simulation of the Net P
134. Study Analysis and Results 0 cccccsccsssceseeseesseeseecsseceecseeeeseecseecssenseeseeesseeeseceeeseenes 3 4 DIS EIDUTLON Ss A Pose tee UA GS AA UGA ER RT GAM JO eA pela 3 52 3 9 1 EAO DistriPUtOns s 3se eds cee A dla 3 53 3 92 Distribution Fitting osorno lili nad AR aiii 3 56 3 9 3 User Defined DistributiOWS occccnnnnonononononananananocnnnnannnnnnononanannn nn nono cnnnnnn nono rononanannnancanos 3 58 Model FUN CHLONS dE de Tao od road 3 60 3 10 1 The Built in Function Librarles oooooccncnnnnnnoananononanonancnnononananana nono nnnnnan an nono cnnannnnonacinnns 3 61 3 10 2 Create Function Formula Interactively ccccccccccescsescesseessecsseeseceeeceseeeseecsecnseceeseeeennes 3 65 3 10 3 Creating and Updating a Private Function Library cccccccscceseceteeeecenceeseeesecnseeeeeeenes 3 69 3 10 4 Compatibility with Proban Version 2 LIBLIM ccccccccsecseceteceteeeeceeeeesseeeenneeeneenaes 3 71 Various A CN 3 71 3 11 1 Importing Plot Files into Documents cccccesseeseceseceseeeseeesecaeceseseeeseeeeseecseeneenteeenes 3 71 3 11 2 Ifthe Required Plot Format is not Available ooononnnnincnincnionnoonconnconnconnonncconocononanonnno 3 72 3 11 3 Problems with Convergence During FORM SORM AnialySis ccccceeseetceceeseeeseenees 3 72 EXECUTION OF PROBAN ieccic cocctaiccvcctcccdacicscacecccvesdaetansncccsdedbelesedscccvadsbsbdesevseccoacedeuts 4 1 Program EnvirOnmMent ccccecccessessse
135. Successive values of fractiles and cumulative probabilities The probabilities must be in the interval 0 1 The input data will be sorted in order of increasing probability The input data are observed values of the variable and first mo ments fit is used Successive values of observations and weights The input data will be sorted in order of increasing observation values Observed values of the random variable to which a distribution is fitted The input data will be sorted in order of increasing ob servation values The input data are sampled values of the variable and first mo ments fit is used The name of the result for which the distribution is to be fitted 1 The existing values are presented as defaults whenever this is possible 2 The RESULT option can be useful for substituting a variable requiring lengthy computation time with a fitted distribution 3 The variable may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command 4 The distribution function and density values may be printed by use of the PRINT DISTRIBUTION com mand 5 The moments of the distribution are calculated and printed if possible by use of the PRINT VARIA BLE command 6 The distribution itself may be displayed using DISPLAY DISTRIBUTION The accuracy of the fit may be examined using DISPLAY FITTED DISTRIBUTION 7 The distributions are listed in SESAM User s Manual Proban Distributions See also
136. T SAVE RESULT PRINT RESULT e DISPLAY RESULT EXAMPLES RUN DETERMINISTIC ANALYSIS VARIABLE P SNTime MEAN VALUE Proban 5 180 01 OCT 2004 SESAM Program version 4 4 RUN DISTRIBUTION ANALYSIS DISTRIBUTION ANALYSIS 1d variable CONDITIONED 1d variable event SINGLE EVENT 1d condvar lt gt _ threshold PURPOSE Run a distribution analysis PARAMETERS 1d variable CONDITIONED event SINGLE EVENT 1d condvar lt gt gt threshold NOTES The name of a one dimensional variable can be a coordinate of a multidimensional variable Analyse the conditioned distribution of lt 1d variable gt given an event The name of the conditioning event This event cannot be of the conditioned type The conditioning event is specified directly as a simple inJequality The name of the one dimensional variable that is forming the left hand side if the in equality One of lt less than gt greater than The numerical right hand side of the conditioning single event 1 The type of analysis being run is selected by use of the SELECT ANALYSIS METHOD DISTRIBU TION ANALYSIS command The options to be used for the analysis are set by use of the DEFINE com mand 2 The result is stored under the name LastAnalysis and is overwritten the next time an analysis is per formed unless saved under another name usin
137. UNCTION GRADIENT SESAM Program version 4 4 ANALYTICAL GRADIENT function SINGLE POINT NUMERICAL dim arguments CHECK PURPOSE Calculate and print the gradient of a function PARAMETERS function Name of the function to be printed SINGLE POINT The gradient is to be calculated in a single point ANALYTICAL Calculate only analytical gradients i e those that are pro grammed into the function This option is not available if the function cannot calculate gradients NUMERICAL Calculate gradients by numerical differentiation only CHECK Calculate both analytical and numerical gradients and print both dim The dimension of the value calculated by the function Is not re quired as input if the dimension is fixed lt arguments gt The arguments of the function NOTES 1 The selection of functions presented is determined by the current selection of sub libraries see SELECT FUNCTION LIBRARY This is because some libraries may contain a large number of functions and or not be relevant to the current problem 2 Ifa LOOP is specified in line mode input after lt function gt any specified argument values are kept as defaults Otherwise the default set of argument values is empty See also SELECT FUNCTION LIBRARY PRINT FUNCTION VALUE e SET TITLE SESAM Proban Program version 4 4 01 OCT 2004 5 145 EXAMPLES PRINT FUNCTION GRADIENT Power SINGLE POINT CHECK 4 3 Generates
138. VITY NON RUN PROBABILITY ANALYSIS System Gl Starting Probability Analysis of System Starting SORM calculation Starting linearization of Intersection of Al A2 A3 Linearization completed Calculating importance factors FORM Reliability index 2 8249 SORM Reliability index 2 8256 FORM Probability 2 36457E 03 SORM Probability 2 35961E 03 Starting linearization of Single event B Linearization completed Proban SESAM 3 16 01 OCT 2004 Program version 4 4 Calculating importance factors FORM Reliability index 2 4915 SORM Reliability index 2 4699 FORM Probability 6 36053E 03 SORM Probability 6 75823E 03 Starting linearization of Single event C Linearization completed Calculating importance factors FORM Reliability index 2 9483 SORM Reliability index 2 9262 FORM Probability 1 59742E 03 SORM Probability 1 71569E 03 Lower bound on Reliability index 2 3261 Upper bound on Reliability index 2 3347 Lower bound on Probability 9 77831E 03 Upper bound on Probability 1 00065E 02 This analysis provides bounds instead of a direct probability because of the geometry of the limit state sur face in U space The system event is a union of events with at least one intersection between the subevents The only way Proban can treat this using FORM SORM is to analyse each subevent by itself and then use these results to bound
139. YSIS OPTION DIFFERENTIATION 0 001 0 1 0 0001 0 001 1 0E 10 GRADIENT CALCULATION ANALYTICAL IMPORTANCE FACTORS ON INTERMEDIATE RESULTS GRADIENT VALUES OFF INTERMEDIATE RESULTS LEVEL NONE INTERMEDIATE RESULTS POINT VALUES OFF INTERMEDIATE RESULTS SHOW DURING ANALYSIS OFF PARAMETER STUDY ON Proban SESAM 5 72 01 OCT 2004 Program version 4 4 DEFINE ANALYSIS OPTION SEEDS RANDOM DEFINE ANALYSIS OPTION SENSITIVITY SELECTED T T T SESAM Program version 4 4 Proban 01 OCT 2004 5 73 DEFINE ANALYSIS OPTION GENERATED DISTRIBUTION GENERATED DISTRIBUTION DIFFERENTIATION uspacel uspace2 rel abs limit ANALYTICAL GRADIENT CALCULATION ONEWAY INCREMENTATION TWOWAY INCREMENTATION U SPACE BOUNDS Value NONE INTERMEDIATE RESULTS ast MEDIUM EXCESSIVE FRACTILE FROM PROBABILITY UNMIN maxit maxstep conv SQP maxit maxstep conv PROBABILITY FROM FRACTILE NLPQL RFCRC PURPOSE Define analysis options for usage of generated distributions PARAMETERS DIFFERENTIATION uspacel uspace2 rel abs limit GRADIENT CALCULATION Define differentiation increments for use in optimization The differentiation increment in U space It must be positive The differentiation increment for the Hessian matrix in U space Used during the
140. abilities The con fidence level default 90 may be changed by use of the command DEFINE RESULT OPTION CONFIDENCE VALUE PRINT RESULT ALL produces in addition to the summary table a table of intermediate results showing again the simulated correction SESAM Proban Program version 4 4 01 OCT 2004 3 27 NoSim Correction StDv Corr C of V Beta Log10 Prob Probability 5 1 03647E 00 1 06515E 02 0 010 0 51621 5 18768E 0 3 02853E 01 10 1 03600E 00 7 99191E 03 0 008 0 51661 5 18965E 0 3 02716E 01 15 1 03659E 00 6 77490E 03 0 007 0 51611 5 18715E 0 3 02890E 01 20 1 03716E 00 5 34914E 03 0 005 0 51563 5 18478E 0 3 03055E 01 25 1 03699E 00 4 74850E 03 0 005 0 51577 5 18548E 0 3 03007E 01 30 1 03869E 00 5 50507E 03 0 005 0 51436 5 17839E 0 3 03502E 01 35 1 03980E 00 8 50778E 03 0 008 0 51343 5 17376E 0 3 03825E 01 40 1 04274E 00 8 05059E 03 0 008 0 51097 5 16147E 0 3 04686E 01 45 1 03252E 00 1 10480E 02 0 011 0 51952 5 20426E 0 3 01699E 01 50 1 03399E 00 1 01512E 02 0 010 0 51829 5 19807E 0 3 02130E 01 It is interesting to note that the coefficient of variation fluctuates This is most likely because the simulation once in a while produces a result that is somewhat different from the others This can happen because the simulation is based on the FORM result If there is some probability content that is not covered well by the FORM approximation the simulation will on
141. ables or in single events nor does it affect any correlation assignments See also e CHANGE VARIABLE CREATE VARIABLE DELETE VARIABLE e COPY VARIABLE e PRINT VARIABLE e DISPLAY VARIABLE EXAMPLES RENAME VARIABLE Widthl Width2 Proban 5 172 RUN SESAM 01 OCT 2004 Program version 4 4 CONTINUOUS PROCESS ANALYSIS DETERMINISTIC ANALYSIS DISTRIBUTION ANALYSIS RUN INPUT CHECK PROBABILITY ANALYSIS RESTART PURPOSE Run an analysis PARAMETERS CONTINUOUS PROCESS ANALYSIS DETERMINISTIC ANALYSIS DISTRIBUTION ANALYSIS INPUT CHECK INSPECTION ANALYSIS PROBABILITY ANALYSIS RESTART NOTES None Run a first passage probability analysis or a crossing rate anal ysis Run a deterministic analysis Run an analysis of the distribution of a variable Check the input for a probability analysis or distribution analy Sis Run an analysis of the probability of failure for a fatigue point throughout the service life taking all inspections into account Run an analysis of the probability of an event possibly condi tioned on another event or of the probability of failure for a fa tigue point throughout the service life Restart a probability or distribution simulation from the results obtained SESAM Proban Program version 4 4 01 OCT 2004 5 173 RUN CONTINUOUS PROCESS ANALYSIS CROSSING RATE FIRST PASSAGE PROBABILITY CONTINUOUS PRO
142. al file Blanks are deleted except within quoted texts A hyphen in the defined name for a function function option or function option menu entry must be entered as _ Names should be unique when is replaced by _ SESAM Proban Program version 4 4 01 OCT 2004 5 51 The formula text is case insensitive except within a quoted string function option value Function option A function option is entered as OPTION NAME OPTION VALUE Case sensitivity See also CHANGE FUNCTION DISPLAY FUNCTION PRINT FUNCTION e RENAME FUNCTION EXAMPLES CREATE FUNCTION SYMFOR1 Symbolic formula FORMULA ONLY A Arg A B Arg B A B 2 CREATE FUNCTION SYMFOR2 Symbolic formula FORMULA A FUNOPT OPT NAM 1 Quot 1 OPT_NAM 2 file name OPT NAM 3 MENU_ENTRY OPT_NAM 4 OPT NAM 5 0 5E 3 B 3 A 3 Proban 5 52 SESAM 01 OCT 2004 Program version 4 4 CREATE FUNCTION INTEGRAL INTEGRAL ma value argname argdesc y function t integrator a method lowerbound upperbound tolerance PURPOSE To create an integration function PARAMETERS argname argdesc function value integrator method lowerbound upperbound tolerance NOTES Matrix of argument names and corresponding argument descriptions At least one argument must be defined Name of function to be integrated i
143. al fractile corresponding to the prob Proban SESAM 2 10 01 OCT 2004 Program version 4 4 ability of the safe set In the simplest case P defaults to the distance from the origin to the design point in U space The process is illustrated in Figure 2 4 SORM failure set FORM A a V9 u Vg u C7 u Ba N safe set u u space Figure 2 4 FORM SORM approximation to failure surface The stop criteria of the optimization method may be controlled A starting point other than the origin for the optimization may be defined together with bounds on the optimization variables Analytical differentiation of the model function is used when possible if this facility has not been turned off Step lengths for numeri cal differentiation can be defined Using FORM the failure probability is estimated as the probability outside the linear hyperplane approxi mation to the failure surface This probability is Prorm DP where O is the standard normal distribution function and is the distance from the origin to the design point Using SORM the failure surface is approximated with a second order surface and the probability outside this surface is calculated The reliability index in this case becomes a function of the failure probability p 0 Psorm Various types of second order approximations are available giving different accuracies and requiring differ ent numbers of second order derivatives SESAM Proban Program
144. alysis using the selected value s will be printed coordinate A coordinate of a vector if a vector vareiable with more than one coordinate is sam pled NOTES 1 The sensitivity values are printed for the probability itself the logarithm of the probability and for the reliability index 2 The sensitivity measure is calculated as the change in the target value resulting from a fixed percentage increase in the parameter This value provides a dimensionless sensitivity measure The definition of the sensitivity measure can be changed using the command See also DEFINE PRESENTATION RESULT SENSITIVITY MEASURE ASSIGN SENSITIVITY DEFINE ANALYSIS OPTION SENSITIVITY SELECT RESULT SET TITLE SESAM Proban Program version 4 4 01 OCT 2004 5 163 EXAMPLES PRINT RESULT SENSITIVITY may generate the following print Probability of Fatigue lt 0 0 Fatigue Life SN II Analysis method SORM Parametric sensitivity result for Probability 1 67162275386E 08 Variable Type Parameter Value dProb dPar Measure Scale Normal Mean 5 048E 00 7 229E 08 3 65E 08 Stand Dev 6 000E 01 1 815E 07 1 09E 08 Parametric sensitivity result for Beta 5 5224397018 Variable Type Parameter Value dBeta dPar Measure Scale Normal Mean 5 048E 00 7 596E 01 0 38347 Stand Dev 6 000E 01 1 907E 00 0 11442 Parametric sensitivity result for Log10 Prob 7 7768617259 Variable Type Parameter Value dLg10 dP
145. an analysis is completed the result is named LastA nalysis and becomes the selected result It is necessary to save the result under another name using SAVE RESULT if it is not to be over written in the next run 3 2 1 Print The PRINT command is used to present data in tabular formats By default the print is sent to the screen that is the terminal window when running in line mode or a sep arate print window when running in graphics mode This destination is always effective when the program starts even if the setting was changed in a previous session using the same database The print may also be directed to a file The print destination and print file name is controlled by use of the SET PRINT command The default file name is identical to the database and journal file name The print file always has the exten sion lis The printed output on a file will be slightly different from the screen print A page header is added and in some cases also a nomenclature On printing to screen in an interactive line mode session Proban will prompt at the end of each page for an action At this prompt it is possible to abort the print or to browse through the previous print or to continue printing These prompts are not issued when running graphics mode Instead the print window has a scroll bar that may be used to examine the print after it has been presented The number of lines in a screen page may be set using the SET PRINT co
146. ance factor Importance factor Importance factor NPV lt 0 0 Net Present Value SORM study Y for 11 for 12 for S SESAM Proban Program version 4 4 01 OCT 2004 3 49 ImpGroup 1 Importance factor for Group number 1 Value TI 12 S ImpGroup 1 1 00000E 02 35 4 535 8 353 pes 2 00000E 02 359 54 3 32 Tyt 3 00000E 02 3965 54 7 3 0 6 7 4 00000E 02 35 20 Soek 2 9 6 4 5 00000E 02 35 6 55 4 2 8 6 2 6 00000E 02 357 5979 2 8 6 0 7 00000E 02 35 8 55x9 2 8 5 9 8 00000E 02 36 0 55 4 Qed 5 8 9 00000E 02 36 2 552 2 7 5 8 1 00000E 01 36 5 54 9 2 8 D9 1 10000E 01 36 8 54 4 2 8 6 0 1 20000E 01 TL 53 8 2 9 6 2 1 30000E 01 Shed 53 0 351 6 4 1 40000E 01 37 9 52 1 32 6 7 1 50000E 01 38 5 52 2 3 1 6 3 In this case there is practically no difference in the importance factors for different values of the rate of return If the importance factors are mapped across the distribution of the NPV they will often be seen to change considerably This can be done by finding the probability of the event NPV lt x as a function of x The same type of parameter study may be used to map the distribution function using a probability analysis method The following commands will do the trick REATE VARIABLE x FIXED 0 REATE VARIABLE NPVx FUNCTION Difference NPV x REATE EVENT NPVx SINGLE NPVx lt 0 NPV x lt 0 is identical to NPV lt x PARAMETER STUDY x ONLY GROUP 25000 30000 1000 ELECT
147. and at the end point This method is generally SESAM Program version 4 4 MEDIUM SAFE SAFE AND SLOW SIMULATIONS nsim RESET NOTES Proban 01 OCT 2004 5 97 sufficient for single events It is generally not recommended for analysis of other events This search method steps out to the first solution if any then takes one step to the end to see if there should be another solu tion This method is sufficiently accurate in most cases This search method steps out to the end of the line where the probability becomes negligible without skipping any larger pieces The simulation will stop after nsim simulations has been com pleted nsim must be a positive whole number Reset all values and options to the default values used when in itialising a new database 1 The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command 2 The simulation will run until any one of the stop criteria has been met 3 Sensitivity calculation is not possible with this analysis method See also PRINT ANALYSIS SETTINGS SELECT ANALYSIS METHOD PROBABILITY ANALYSIS3 EXAMPLES The following values are default when the program starts up with a new database D D D D D EFINE ES EFINE EFINE EFINE EFINE PROBABILI PROBABILI PROBABILI PROBABILI PY ANALYSIS PY ANALYSIS PY ANALYSIS PY ANALYSIS PROBABILI PY
148. ant value is estimated to be EEE 1 2 100 Please note that this formula applies only to FORM analysis of single events B If two or more variables are correlated only one importance factor will be presented for the group The same applies to distribution variables where one variable enters the distribution of another variable as a parameter Importance factors can be calculated using FORM SORM and Directional simulation SESAM Proban Program version 4 4 01 OCT 2004 2 27 2 9 Deterministic Analysis It is often desirable to evaluate the value of a variable or an event function at a given point This is achieved through performing a deterministic analysis The analysis of a variable can be done at the mean value or at the median value of the stochastic variables involved or at a point modified from one of these The analysis of an event function can be done at the u space origin or at the starting point for a FORM SORM analysis Thus in order to calculate an event function at an arbitrary point specify the point as a starting point for a FORM SORM analysis Parameter study as well as print and display commands are available also for deter ministic analyses 2 10 Parameter Study It is often desirable to see the evolution of a result probability reliability index crossing rate moment sen sitivity function value over time or as function of any parameter in the model In Proban this is accom plished by use of the paramete
149. any cases a vector or matrix of values must be input An example is entering fractiles cumulative prob abilities and weights in the CREATE VARIABLE FITTED DISTRIBUTION command The graphics mode input of this is quite flexible The values are presented in columns in a scrollable box Under the box is one input field for each column in the matrix one field if it is a vector Under the input field s are two rows of buttons that are used to manipulate the contents of the box Type values into the input fields and hit lt Return gt in the last bottom field The values are then inserted at the bottom or before the selected row or overwrites the selected row depending on the default status The Proban SESAM 4 22 01 OCT 2004 Program version 4 4 initial status is Include which inserts values at the bottom The input fields are cleared after the insertion is complete Instead of pressing lt Return gt a button may be pressed The effect of this is Table 4 9 Entering a vector or matrix of values in graphics mode Include the values in the input field s at the bottom then clear the input fields ies Sets the default status to Include Exclude all selected rows from the matrix vector Sets the default status to Exclude Exclude Overwrite the selected row with the contents of the input fields Only one row Te can be selected in the scrollable box The next row if any will then be selected and the default status will
150. ar Measure Scale Normal Mean 5 048E 00 1 878E 00 0 94814 Stand Dev 6 000E 01 4 715E 00 0 28290 Proban SESAM 5 164 01 OCT 2004 Program version 4 4 PRINT RESULT SUMMARY SUMMARY value PURPOSE Print a short summary for the selected result PARAMETERS value This input is only required if the selected result is a parameter study lt value gt is then a selection of the parameter values for which the study was run The particular results from the analysis using the selected value s will be printed NOTES See also e SELECT RESULT SET PRINT EXAMPLES PRINT RESULT SUMMARY may generate the following print Probability of Fatigue lt 0 0 Fatigue Life SN II Analysis method SORM 4 FORM Probability 1 72486E 08 SORM Probability 1 67162E 08 FORM Reliability index 5 5169 SORM Reliability index 5 5224 SESAM Proban Program version 4 4 01 OCT 2004 5 165 PRINT VARIABLEPRINT VARIABLE VARIABLE name PURPOSE Print information about one or more variables PARAMETERS name Name s of variable s to be printed NOTES The printout contains information about the variable data including all assignments except starting point and correlation See also CREATE VARIABLE e CHANGE VARIABLE DISPLAY VARIABLE ASSIGN CONDITIONING e ASSIGN EXTREME VALUE e ASSIGN
151. aracteristics PLOT Set plot file characteristics PRINT Set print characteristics NOTES All sub commands and data are fully explained subsequently as each command is described in detail SESAM Program version 4 4 01 OCT 2004 SET COMPANY NAME COMPANY NAME text PURPOSE To set the company name for use with result presentation PARAMETERS text The name of the company NOTES The text is used at the top of a display plot It is not used with printed results See also DISPLAY PLOT EXAMPLES SET COMPANY NAME Det Norske Veritas Proban 5 195 Proban SESAM 5 196 01 OCT 2004 Program version 4 4 SET DISPLAY ON COLOUR OFF FILE DISPLAY DESTINATION SCREEN DEVICE device WORKSTATION WINDOW left right bottom top PURPOSE Set display characteristics PARAMETERS COLOUR DESTINATION DEVICE WORKSTATION WINDOW left right bottom top Sets the output to the display device to be in colours ON or monochrome OFF Set the destination of the graphics produced in the DISPLAY command to the current plot file FILE or to the screen SCREEN Set the current screen display device type The available device types depend on the computer on which the program runs Here is a selection of the some device types that may be available VGA PC with VGA resolution X WINDOW for X windows VT340 Digital VT 340 screen DUMMY u
152. are described in Section 4 2 and Section 4 3 4 1 Program Environment Proban is on Unix platforms delivered as an executable and an object file to be linked with user developed code On NT platforms the delivery is an executable and a DLL Dynamic Link Library for functions The user replaces the DLL when he wants to run his own coded functions The Unix version requires that the Motif window manager is installed Proban supports both graphics and line mode execution of the program How to start the program in the different modes is described below Proban SESAM 4 2 01 OCT 2004 Program version 4 4 4 1 1 Command Line Arguments It is possible to specify command line arguments when starting Proban The command line arguments are simply added to the usual command starting the program prompt gt proban NOHEADER STAT OLD INT LINE C F test_in jnl FORCED EXIT Please note that 1 Command line arguments and values can be abbreviated as described in Section 4 4 4 However other input will be accepted and used when possible 2 Each argument name must begin with a slash and each argument value must be prefixed by an equal sign Spaces can be freely distributed around the equal sign and before each slash 3 Texts with blank space and special characters e g file names can be protected in quotes Please note that some operating systems change the case of the input text if it is not protected in quotes 4 Ifat least one of PREFIX
153. ared between the generated variable and the generating variable by using the ASSIGN CONDITIONING command 3 A generated distribution may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command See also CREATE VARIABLE e COPY VARIABLE e RENAME VARIABLE e PRINT VARIABLE ASSIGN CONDITIONING ASSIGN EXTREME VALUE EXAMPLES CHANGE VARIABLE Width FIXED 22 5 CHANGE VARIABLE Amplitude GENERATED Var44 SESAM Proban Program version 4 4 01 OCT 2004 5 35 CHANGE VARIABLE DISTRIBUTION distribution dim input seq parameter SPLINE 1DIM DISTRIBUTION PURPOSE To change a variable to be based on a distribution or to change a distribution already assigned PARAMETERS distribution The name of the distribution excepting the spline distribution dim The dimension of the distribution if this is not fixed input seq The sequence of parameters used to define the distributions parameter The parameter value s for the chosen input sequence Each parameter value may be either a numerical value or the name of an existing one dimensional variable Please note that the name of a variable cannot be abbreviated here SPLINE 1DIM The variable is assigned a distribution fitted to input data See a following page for details NOTES 1 The existing values are presented as defaults whenever this is possible 2 The variable may be assigned an ex
154. ate a response surface function PARAMETERS argname argdesc function point argname method increment NOTES Matrix of argument names and corresponding argument descriptions At least one argument must be defined Name of function to be approximated Centre of approximations Argument name This approximated function argument becomes the argument ar gname of the approximation Function fit method to be used L or L1 Linear approximation based on positive incrementation L2 Linear approximation based on two way incrementation D Quadratic diagonal approximation No cross derivatives with other argu ments QName Q followed by name Quadratic approximation including cross terms for arguments that have the same group Name Q alone is treated as a group Increment to be used with the fit 1 An argument name consists of maximum 12 alphanumeric characters and _ The first character must be alphabetic 2 An argument description consists of maximum 50 characters 3 Point argname method and increment are comma separated See also e CHANGE FUNCTION RESPONSESURFACE e DISPLAY FUNCTION SESAM Proban Program version 4 4 01 OCT 2004 5 55 e PRINT FUNCTION e PRINT RESPONSESURFACE RENAME FUNCTION EXAMPLES Fit a quadratic response surface function to appfunc centred around 1 2 3 with increment 1 for the second argument of appfunc and increment 2 for the third argument of appfunc includin
155. ban session but only one can be open at a time If the database file has been corrupted the information may be reconstructed by use of the journal file It is therefore recommended to take backup copies of the journal and database file at regular intervals 4 2 Program Requirements 4 2 1 Execution Time Most of Proban can be run interactively with no significant timing problems However the following situa tions may require so much computation time that a batch run is advisable e Calculating a result with computational costly functions e Calculating a result by use of extensive simulation Because of an internal buffer limit the database access performance may degrade considerably when a cer tain size of the database has been reached It is not possible to predict exactly when this will happen 4 2 2 Storage Space The initial size of the program on NT is about 4Mb The initial size of the program on Unix is about 9Mb The initial size of the database is about 230Kb 4 3 Program Limitations The following limitations apply See also the status list for current updates to this The names functions variables and events are limited to 12 characters All names are case insensitive when matched with input text Descriptive texts are in most cases limited to 50 characters There is a limit on the number of random variables that can be presented through the user interface this limit does not apply to the number that can be stored
156. bilit Parameter study y EN 1 6589 4 85693E 02 0 200000E 01 Starting FORM calculation and so on The results can be presented in a table PRINT RESULT PARAMETER STUDY MAIN R PrRrRRrRPRO WAND Na l O RRRPRRPRRRPNDNDNNDNDNNNDNNDNDN Beta FORI 0 10 00 10 10 0 DO 214 Re Rte Y o Oy o Prob FORM Log10P FORM ESULT 4 85693E 02 6 26036E 02 7 93830E 02 9 91689E 02 1 22202E 01 1 48698E 01 1 78836E 01 2 12752E 01 2 50535E 01 2 92197E 01 3 37676E 01 3 86808E 01 4 39316E 0 4 94 779E 0 5 51104E 0 and they can also be displayed as with the main results above SET DRAWING FONT SIZE RELA TIVE 1 5 DISPLAY RESULT PARAMET ER S7 TUDY MAIN R ESULT ONLY Prob edd 20 10 00 91 82 74 67 60 23 47 41 35 30 25 36 34 03 36 29 77 75 21 11 43 15 25 72 56 88 Proban 3 47 Proban 3 48 SESAM 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 NPV lt 0 0 Net Present Value Parameter study using r Figure 3 12 The probability of a loss different rates of return The importance factor pie charts can be displayed simultaneously for a selection of parameter values It is also possible to print and display the variation of the importance factors with the internal rate of return Value I1 I2 Parameter r Import
157. bility analysis using SELECT ANALYSIS METHOD PROBA BILITY ANALYSIS The default method is FORM when Proban starts from a new database 2 Define the desired options for the chosen method and or general analysis options These options are explained in the DEFINE command The default options will be sufficient in most cases 3 ASSIGN SENSITIVITY CALCULATION to the required parameters and or decide the extent of sensi tivity calculation using DEFINE ANALYSIS OPTION SENSITIVITY 4 Decide if importance factors are to be calculated by use of the DEFINE ANALYSIS OPTION IMPOR TANCE FACTORS Proban SESAM 3 12 01 OCT 2004 Program version 4 4 5 Run the analysis using RUN PROBABILITY ANALYSIS 6 Present the results using PRINT RESULT DISPLAY RESULT and PLOT The different analysis methods are described in separate sections using the examples from Section 3 1 FORM and SORM are treated together because of their similarity 3 3 1 FORM SORM First a word of caution FORM requires the model function s and distribution function s to be differentia ble and SORM requires them also to be twice differentiable at the design point If they are not the results will be unreliable when the design point is close to a point with a lack of differentiability The model in Example 3 2 exemplifies this The triangle distribution has a density function that is not differentiable at its most likely argument in the middle of the distribution This causes the SORM
158. box to correctly represent information changed elsewhere Help Provide context sensitive help Most dialog boxes have a default pushbutton that is activated by typing lt Return gt when the dialog box is active This pushbutton is usually the OK or the Apply button The default button will be highlighted or framed 4 5 5 Entering a Prefixed List The prefixed list is used to enter a number of values that is unknown until the time the box is used where each value has a prefix or prompt It is for example used to input distribution parameters function argu ments and starting point values In line mode the list is simply traversed sequential from top to bottom In graphics mode the accompanying input field located just below the box is used to input and change values The procedure used to change or input a value is e Select the corresponding row in the box Doubleclick on the row if desired to transfer the current value to the input field If no row is selected the first row is implicitly used Type the new value in the input field Hit lt Return gt in the input field to transfer the value to the box The next row in the box will then be selected and the input field will be cleared Thus it is possible to input values sequential into the box by clicking on the input field and then typing the values one by one with each value followed by a lt Return gt 4 5 6 Entering a Vector or a Matrix of Values In m
159. bservation OBSERVATION WEIGHTED observation weight dd MOMENTFIT UNWEIGHTED observation RESULT result name RESULI MOMENTFIT _ result name PURPOSE To create a variable to be fitted to a distribution PARAMETERS distribution input seq parameter CUMULATIVE WEIGHTED UNWEIGHTED fractile probability weight The name of the distribution excepting the spline distribution and multidimensional distributions The sequence of parameters used to define the distributions The parameter specification for the chosen input sequence Each parameter value may be either specified as a numerical value in which case it is not fitted as FIT in which case it is fitted or as FIT lt value gt where lt value gt is a numerical value used as starting point for an iterative fit A lower bound on the fitted value is specified by L lt value gt An upper bound on the fitted value is specified by U lt value gt Fit to cumulative input data The input data are weighted The weights must be positive The input data are not weighted Successive values of fractiles cumulative probabilities and weights The probabilities must be in the interval 0 1 The in put data will be sorted in order of increasing probability SESAM Program version 4 4 fractile probability OBSERVATION MOMENTFIT observation weight observation RESULI MOMENTFIT result name NOTES Proban 01 OCT 2004 5 63
160. can be copied and used to maintain a function library a In order to use this Makefile you should keep all source files of your function in one directory b First copy the Makefile from SESAM_ HOME proban funclb Makefile to the directory where your mod el function routines are placed c Modify the Makefile Follow the description in the Makefile itself d Usage of the Makefile to link Proban is described at the top of the Makefile itself The commands must be typed from the directory where the Makefile is placed e To add a new model function insert the file names in the definition of SOURCE in the Makefile and then execute the make command A1 2 NT Proban comes with a set of batch files bat and option files opt which can be copied and used to maintain a function library a In order to use these files you should keep all source files of your function in one directory b First copy the bat and opt files from SESAM_ HOME proban funclb to the directory where your model function routines are placed Proban SESAM A 2 01 OCT 2004 Program version 4 4 c Modify the files Follow the description in the files themselves d To add a new model function insert the file names in the opt files and then execute the bat files A 1 3 Implementing New Distributions into Proban Each user may make his own library of distributions extending the distributions library which is already available in Proban How to do this is described
161. can be useful as some func tion libraries may have a large number of functions and or be irrelevant for the current modelling 2 The program starts on a new database with two libraries masked off Distribution and Verification See also e PRINT FUNCTION e CREATE VARIABLE FUNCTION e CHANGE VARIABLE FUNCTION EXAMPLES SELECT FUNCTION LIBRARY SESAM Proban Program version 4 4 01 OCT 2004 5 193 SELECT RESULT RESULT name PURPOSE Select a result from probability crossing rate first passage probability distribution analysis or deterministic analysis for presentation PARAMETERS name The name of a result NOTES Only one analysis result can be presented at one time Other types of result presentations are not affected by this command See also PRINT RESULT DISPLAY RESULT DELETE RESULT RUN CONTINUOUS PROCESS ANALYSIS e RUN DETERMINISTIC ANALYSIS e RUN DISTRIBUTION ANALYSIS e RUN PROBABILITY ANALYSIS e SAVE RESULT EXAMPLES SELECT RESULT Fail 444S Proban SESAM 5 194 01 OCT 2004 Program version 4 4 SET COMPANY NAME DISPLAY DRAWING SET GRAPH PLOT PRINT PURPOSE Set or re set global file device environment characteristics PARAMETERS COMPANY NAME Set company name on display and plot DISPLAY Set display characteristics DRAWING Set drawing characteristics GRAPH Set graph ch
162. ce limits This value is used to cut off the smallest importance factor val ues from the print of importance factors This value must be given in e g if input as 5 all importance factor values less than 5 will not be printed This value is used to group the smallest importance factor val ues in the display of importance factors This value must be given in e g if input as 5 all importance factor values less than 5 will be shown in one pie slice named Other Determines how many lines of intermediate results will be printed with the PRINT RESULT ALL command after a simu lation analysis To see all intermediate simulation results set intsim to a value equal to or greater than the number of sim lations performed Defines how sensitivity measures are calculated A sensitivity measure is dimensionless in that it measures the change in the target value when a parameter is multiplied by 1 inc As this definition does not work when the parameter value is zero lim denotes the smallest parameter value to which it can be applied Proban SESAM 5 94 01 OCT 2004 Program version 4 4 V SPACE POINT Defines if the V space coordinates of a FORM linearisation point are to be printed ON or not OFF RESET Reset all values and options to the default values used when in itialising a new database NOTES This command is documented in the Proban Users Manual as DEFINE RESULT OPTION See also PRINT RESULT
163. cost computation time Proban comes with three different search methods giving different trade off between speed and accuracy There are ways to further sophisticate this sampling Proban always samples also the probability in the opposite direction of any given direction A set of orthogonal directions spanning the whole space may be sampled instead of just one direction and linear combinations of these may be considered This still pro vides unbiased probability estimates because it utilises the rotational symmetry of the U space However the required time to produce a single estimate of the probability increases considerably with the number of random variables in the problem so the sophisticated methods are not recommended for problems with many variables Proban supplies a default method that is efficient in most cases The length of a Directional simulation my be controlled by defining the maximal number of simulations by restricting the time to be used or by demanding a stop when a certain coefficient of variation has been reached 2 3 4 Axis Orthogonal Simulation Axis Orthogonal simulation is also a directional simulation technique However instead of shooting from the origin as in Directional simulation it shoots from a hyperplane based on a FORM approximation out towards the limit state surface Axis Orthogonal simulation does not simulate the probability itself it simu lates a correction to the FORM approximation to the probabili
164. ction 3 1 Monte Carlo simulation and latin hypercube simulation are treated together because the presentation of results is the same for both 3 6 1 Monte Carlo and Latin Hypercube Simulation The default distribution sampling method is Monte carlo simulation This is a straightforward sampling method that repeatedly samples all the random variables in the model and calculates the target value from them Latin hypercube simulation follows the same principle but uses a stratified sampling technique that is usu ally more economical These methods may be used to calculate parametric sensitivity values but not to calculate importance fac tors Each sensitivity calculation requires numerical differentiation and consequently the sampling of an extra value for each differentiation done This can increase computation time considerably In the run listed below 5 sensitivity values are simulated This increases the time the simulation need to run approximately a factor of 6 The number of simulations can be controlled using the command DEFINE DISTRIBUTION SIMULA TION The cpu time usage cannot be controlled Consider the calculation of the distribution of the Net Present Value in Example 3 2 The following com mand produces a simulation including a sensitivity calculation with respect to the mean of all variables the messages generated by Proban are included ASSIGN SENSITIVITY CALCULATION VARIABLE Mean Assigned sensitivity calculation
165. d 3 Is there a significant effect of replacing any of the components with a component that has a better pro duction quality i e a smaller standard deviation on the resistance Inside Proban the failure criterion on the components can be modelled as differences between the load and the resistance There is no need to program a model function as the difference function is already available in Proban The following variables are needed in the Proban model CREATE VARIABLI LOOP Gl Load The common load DISTRIBUTION Inv Gauss Mean StD Low 80 0 10 0 0 0 RA1l Resistance of A DISTRIBUTION Inv Gauss Mean CoV Low 110 0 1 0 0 RB Resistance of B DISTRIBUTION Normal Mean CoV 120 0 1 RC Resistance of C DISTRIBUTION Normal Mean Cov 130 0 1 END COPY VARIABLE RA1 RA2 COPY VARIABLE RA1 RA3 CREATE VARIABLE LOOP Al Failure criterion for component Al FUNCTION Difference RA1 Load A2 Failure criterion for component A2 FUNCTION Difference RA2 Load A3 Failure criterion for component A3 FUNCTION Difference RA3 Load B Failure criterion for component B FUNCTION Difference RB Load C Failure criterion for component C FUNCTION Difference RC Load The event of failure for each component is modelled as a single event Resistance Load lt 0 The event of failure of all three A components is modelled as an intersection of the three subevents that the individual A components fail The wh
166. d a user defined distribution SESAM Proban Program version 4 4 01 OCT 2004 3 59 1 Select a three character routine prefix for the distribution This prefix should begin the name of each rou tine programmed with the distribution For illustration of the process assume that the chosen prefix is XXX These prefixes cannot be used ATR BET BPM CDI CH2 CGR CHK CIQ COP CPM DDI DES DFU DIM DIS EXP EXT FOX FU FX GAM GGM GUM HTM ICO IDI IIQ ING INI IPM IQ IQC LNM LOH LSC LSD LSI MNR MOM MSG MXW NAM NMS NPM NRM NUM ONE OP OVA PAR PM PMI PMN PTZ RAY SP1 SP2 STN STU TAC TOC TPA TRA TRI TRU TST UAT UNI USR VTZ WBL ZTV ZVP 2 The distribution input sequence and parameter s must be installed by modifying the routine USRINI During start up Proban calls USRINI to install any user defined distributions The delivered version of USRINI does not install any user defined distributions The distribution is allowed to have one input sequence The input sequences that are in use in Proban al ready may be reused or a new input sequence may be installed The same applies to the parameters in the input sequence If an existing input sequence or parameter is used all restrictions that apply to the input sequence and parameters will also be in effect for the new distributions These restrictions are described in the previous section Other details about the installation are described in USRINI itself The location of USRINI is described in the installation gu
167. der calcula tion has the arguments first and the function value last and provides an additional means to verify the for mula Values of function options for a function referenced by a function formula can be entered in the argument list for that function The function options applied to a function referenced in a function formula are its cur rent default options overwritten by options entered in the argument list If a function with dimension defined by a function option is to be referenced then its dimension must be set to one prior to the creation of the function formula as shown below ASSIGN FUNCTION OPTION FUNCTION FuncOptTest Opt 5 Menu SumTerm ASSIGN FUNCTION OPTION FUNCTION FuncOptTest Opt 7 NCoord 1 CREATE FUNCTION FUNSYM Symbolic Function involving options FORMULA ONLY A Arg A B Arg B CG Arg C 3 A B C FUNCOPTTEST Opt_1 Text ab c Opt 2 intege 2 Opt_3 double 4 2 Opt_5 menu SumTerm Opt 6 Narg 3 A 2 B 3 C The usage of apostrophes in the input file above gives text value of Opt 1 Text ab c 3 10 3 Creating and Updating a Private Function Library The routines that must be programmed should be kept in one directory It is also recommended to compile all the routines and keep the object code in an object library which is then linked into Proban Proban is delivered with tools that facilitate maintenance of the object library a Makefile on Unix See the installa
168. distribution fct tion Inverse distribution tion Inverse distribution tion Inverse distribution fct tion Inverse distribution fct tion Inverse distribution fc Maxwell distribu tion Normal dis Ova Ray tributio Onesi Normal dis 1 distribution eigh distribution Inverse distribution Inverse distribution fct Ny tribu Inverse distribution fct tion Inverse distribution fc Inverse distribution fct fet Student t distribution Description Inverse distribution fct I Triangle Inv Trunc No Inv Weibull UtX Beta UtX Burr UtX Chi squa Utx Exponent UtX Gamma UtX Gen Gamm UtX Gumbel UtX Hermit s UtX Hermit t UtX Inv Gaus Utx Lognorma UtX Long Hig UtX Maxwell UtX Onesi No UtX Oval UtX Rayleigh UtX Student UtX Triangle tX Trunc No tX Weibull tU Beta tU Burr tU Chi squa tU Exponent tU Gamma tU Gen Gamm tU Gumbel tU Hermit s C x MM KM KM XM KM OX C 00 0 GUY Y YU 0 4 OP Y Y Y UY MY UY Ys 01 01 Y YN 4 Y Y 01 Y os oOoOoO0DODO0OO0OO00O00O00O00O00O0O0OO0O0O0O0O0O0O0O0O0O0O0O0O0O0O0O0O00O00O000O000O0oO0OooOo Priang e distribution Inverse distribution fct Weibul Trunc Normal distribution distribution Beta distribution Burr distribution Chi square distribution Inverse distribution fc Inverse distribution fct Inverse of Std Nor
169. distributions Beta distribution Density function Burr distribution Density function Chi square distribution Density function Exponential distribution Density function Gamma distribution Density function Gen Gamma distribution Density function Gumbel distribution Density function Hermit secon distribution Density function Hermit trans distribution Density function Inv Gauss distribution Density function Lognormal distribution Density function Long Higgins distribution Density function Maxwell distribution Density function Normal distribution Density function Onesi Normal distribution Density function Oval distribution Density function Rayleigh distribution Density function Student t distribution Density function Triangle distribution Density function Trunc Normal distribution Density function Weibull distribution Density function Beta distribution Distribution function Burr distribution Distribution function Chi square distribution Distribution function Exponential distribution Distribution function Gamma distribution Distribution function Gen Gamma distribution Distribution function Gumbel distribution Distribution function Hermit secon distribution Distribution function Hermit trans distribution Distribution function Inv Gauss distribution Distribution function Lognormal distribution Distribution function Long Higgins distribution Distribution function Maxwell distribution Distribution function Normal di
170. e A eke Sb Gh O O oOo 2 0 OOO N hRPRRRPRPOOOO Proban 5 151 Proban 5 152 01 OCT 2004 PRINT RESULT RESULT ALL ANALYSIS SETTINGS IMPORTANCE FACTORS INTERMEDIATE RESULTS PARAMETER STUDY SAMPLE SENSITIVITY SUMMARY SESAM Program version 4 4 PURPOSE Print the currently selected result in tabular form to screen or to file PARAMETERS ALL ANALYSIS SETTINGS IMPORTANCE FACTORS INTERMEDIATE RESULTS PARAMETER STUDY SAMPLE SENSITIVITY SUMMARY NOTES None Print all the results from a probability or distribution analysis Print analysis options applied to the result Print the importance factors resulting from a probability analy Sis Print the intermediate debug results from a probability or dis tribution analysis Print results as a function of the parameter in a parameter study Print the sample resulting from application of a simulation method Print parametric sensitivity results Print a summary of the results from a probability or distribution analysis SESAM Proban Program version 4 4 01 OCT 2004 5 153 PRINT RESULT ALL ALL valuel value2 PURPOSE Print all information from the selected result PARAMETERS valuel This input is only required if the selected result is a parameter study valuel is then a selection of the parameter values for which the study was run
171. e necessary to specify more than one numerical or default value The identification of each value i e the name of the variable parameter is given as prompt for each needed input value See also e PRINT STARTING POINT DEFINE FORM SORM STARTING POINT INITIAL EXAMPLES ASSIGN ST ASSIGN ST ART ART PING POINT PING POINT EP1 7 52 DI EFAULT D VARIABLE VAR7 DEFA ULT DEFAULT EFAULT 2200 8 65 SESAM Proban Program version 4 4 01 OCT 2004 5 23 ASSIGN SUB LEVEL INTEGRATION ON OFF SUB LEVEL INTEGRATION variable PURPOSE Assign a sub level integration property to a variable PARAMETERS variable Name of the variable to which the sub level integration property is assigned This must be a variable with type attribute distribution or type attribute generated ON The variable is pushed to the inner integration loop in a continuous process analy sis OFF The variable is integrated in the outer integration loop in a continuous process anal ysis NOTES See also e ASSIGN CONTINUOUS PROCESS TIME DERIVATIVE EXAMPLES ASSIGN SUB LEVEL INTEGRATION X ON Proban SESAM 5 24 01 OCT 2004 Program version 4 4 CHANGE EVENT CHANGE FUNCTION VARIABLE PURPOSE Change a named object PARAMETERS EVENT Change an event FUNCTION Change a function VARIABLE Change a random variable NOTES None
172. e 3 Name of variable for which the design point value is sought Name of single event Proban is prepared for use as a sub process controlled by another program which transmits commands to Proban The GET command is used to access the calculated results As an example one can invoke Proban from a code calibration program in order to calculate the reliability indexes required for the code calibration EXAMPLES GET U SPACI ET RESULT E Beam ONLY P1 30000 P2 30000 MAIN RESULT Beta FORM S ENSITIVITY Beta L1 Mean G GET RESULT GET RESULT D ESIGN POINT Beam L1 X SPACE SESAM Program version 4 4 Proban 01 OCT 2004 5 129 HELP ABOUT HELP COMMAND INPUT FILE COMMANDS DEFAULTS LINE MODE SELECTING OTHER FACILITIES HELP BUILT IN EXPRESSIONS PROGRAMMING MODE OVERVIEW VARIABLES STATUS LIST SUPPORT PURPOSE Provide guidance to the user PARAMETERS ABOUT HELP COMMAND INPUT FILE LINE MODE COMMANDS DEFAULTS SELECTING OTHER FACILITIES PROGRAMMING MODE BUILT IN EXPRESSIONS Provide information about the HELP command Provide information about command input files Provide information specific for usage in line mode Provide information about specifying commands in line mode Provide information about usage of defaults in line mode Provide information about selection and abbreviation in line mode Provid
173. e factors may be presented as function of the parameter The same values can be printed in a table In addition the individual results can be examined one by one Proban SESAM 2 30 01 OCT 2004 Program version 4 4 SESAM Proban Program version 4 4 01 OCT 2004 3 1 3 USER S GUIDE TO PROBAN This chapter describes the usage of Proban with illustrating examples Chapter 3 is divided into three parts Section 3 1 to Section 3 8 go through the modelling analysis and presentation of results using the differ ent methods available in Proban Section 3 9 and Section 3 10 treat distributions and functions listing those available in Proban and describing how to extend the list Section 3 11 contains various hints For a quick introduction read Section 3 1 first 3 1 Howto Do an Analysis A Proban analysis typically consists of the following steps 1 2 Define the model and the questions that are to be answered by Proban Ifnecessary program the model function s and link with Proban see Section 3 10 3 Enter the model in Proban and verify it The commands that are of main interest here are CREATE COPY CHANGE DELETE ASSIGN PRINT DISPLAY PLOT RUN DETERMINISTIC ANALY SIS and RUN INPUT CHECK Set up the analysis and run it This typically requires usage of DEFINE SELECT ANALYSIS METHOD RUN and possibly SAVE If the summary results presented during the analysis are not sufficient examine the results using
174. e information about special facilities in line mode Provide information about the programming mode Provide information about built in functions procedures and constants accessible in programming mode Provide information about the use of calculation expressions in programming mode Proban SESAM 5 130 01 OCT 2004 Program version 4 4 OVERVIEW Provide an overview of the facilities available in programming mode VARIABLES Provide information about the usage of variables in program ming mode STATUS LIST Examine the status list for Proban SUPPORT Provide information that is helpful at a support request This in clude information about the versions of the program and linked in libraries and about the environment in which the pro gram runs NOTES 1 This command is not journalled 2 There is no guarantee that this command will remain compatible over time 3 All information except the status list is treated as a program message i e it is written into the message window in graphics mode and echoed at the terminal in line mode The status list is presented in the print window when running in graphics mode and presented one full screen at a time when running in line mode 4 See also the sections in Chapter 4 on getting help when running in line mode and in graphics mode SESAM Proban Program version 4 4 01 OCT 2004 5 131 PLOT PLOT PURPOSE Execute the last DISPLAY command and write the result to t
175. e input in free format in Proban Floating point numbers as 1000 1 54 le 44 and le5 are all accepted Whole numbers can be specified as floating point numbers Examples of whole numbers 1000 1 1e4 SESAM Proban Program version 4 4 01 OCT 2004 4 11 Names may contain any alphanumeric character as well as the underscore _ and the hyphen An inte ger will be accepted as a name but will not work when referenced in situations which permits numerical input Good practice is to start a name with an alphabetic character The maximal length of a name is docu mented with the command where the named object is created Text must be encapsulated in single quotes if it contains blank space s and or special characters This is a text containing 10 spaces and a single 4 4 6 Selecting a Single Alternative from a List In many cases Proban will require a selection of a single alternative from a list An example is right at the start at the main prompt where the main commands are presented for selection The selection need not be a selection between commands it could also be a selection between named objects or between numerical values In selection of a single value abbreviation is allowed but wildcards cannot be used An exact match is always preferred Thus it is possible to select an item that is an abbreviation of another item in the list by typing the item exactly A single question mark will show all items in
176. each analysis This will make the results correlated but will remove the random fluctuation between analyses If this was not done comparison between results for different parameter values would be very difficult A simulated parameter study may be continued using the command RUN RESTART The main results can be printed and displayed as shown below PRINT RESULT PARAMETER STUDY MAIN RESULT Mean Stand Dev Skewness Kurtosis Distribution of NPV Net Present Value Analysis method Monte Carlo simulation Parameter study r Value LSE Mean Estimated Mean Standard Dev Estimated Standard Deviation Skewness Estimated Skewness Kurtosis Estimated Kurtosis Value Mean Standard Dev Skewness Kurtosis 1 00000E 02 1 79527E 04 1 06288E 04 0 092 2 604 2 00000E 02 1 63237E 04 1 04551E 04 0 093 2 604 3 00000E 02 1 47354E 04 1 02863E 04 00 93 2 605 4 00000E 02 1 31864E 04 1 01222E 04 0 093 2 605 5 00000E 02 1 16753E 04 9 96274E 03 0 094 2 605 6 00000E 02 1 02008E 04 9 80762E 03 0 094 2 606 7 00000E 02 8 76168E 03 9 65672E 03 0 094 2 606 8 00000E 02 7 35671E 03 9 50988E 03 0 095 2 606 9 00000E 02 5 98475E 03 9 36697E 03 0 095 2 606 1 00000E 01 4 64472E 03 9 22783E 03 0 095 2 606 1 10000E 01 3 33555E 03 9 09233E 03 0 095 2 607 1 20000E 01 2 05624E 03 8 96034E 03 0 095 2 607 1 30000E 01 8 05832E 02 8 83174E 03 0 096 2 607 1 40000E 01 4 16599E 02 8 70
177. ean 10000 Stdv 2000 The expenses are assumed to be positively correlated with a correlation coefficient of 0 75 The questions the manager of the company wish to pose are 1 What is the distribution of the NPV 2 What is the probability of a loss i e NPV lt 0 3 What can be done to increase the profit and or reduce the risk The model function can be modelled directly using the built in functions as shown here It may also be pro grammed into Proban The model can be entered into Proban as follows CREATE VARIABLE LOOP r Required rate of return FIXED 0 1 CO Initial investment FIXED 100000 Il Income first year DISTRIBUTION Triangle Low Mean Up 60000 75000 90000 12 Income second year DISTRIBUTION Triangle Low Mean Up 30000 50000 70000 El EZ Expense second year END S Scrap value Expense first year DISTRIBUTION Lognormal Mean StD Low 5000 1000 0 DISTRIBUTION Lognormal Mean StD Low 10000 2000 O DISTRIBUTION Normal Mean StD 10000 2000 ASSIGN CORRELATION ONLY El E2 BASIC 0 75 CREATE VARIABLI Gl 2 J LOOP IE1l TAS LA FUNCTION sl Ed FUNCTION Yi Year 1 FUNCTION IES2 I2 E2 S FUNCTION r2 141 02 FUNCTION Y2 Year 2 FUNCTION NPV Net Present Value FUNCTION Difference I1 El Sum ONLY 1 0 r Division IEl rl Linear Comb ONLY 1 12 1 E2 1 S Square rl Division IES
178. eck if the approximate result delivered by other methods is accurate Its other main use is in cases where the more sophisticated methods cannot be used e g because the model function is not differentiable The length of a Monte Carlo simulation may be controlled by defining the maximal number of simulations by restricting the time to be used or by demanding a stop when a certain coefficient of variation has been reached 2 3 3 Directional Simulation Directional simulation is a sophistication of the principle used in Monte Carlo simulation The rotational symmetry of U space is used to make sampling more efficient Instead of sampling points randomly in the U space directions are sampled randomly and the probability of the event along the sampled direction is calculated Because of the rotational symmetry each directional probability estimate is an unbiased estimate of the correct probability Proban SESAM 2 14 01 OCT 2004 Program version 4 4 failure set zon g 0 Be 1 safe set Tr an Y g u 0 wy a Figure 2 8 Directional simulation This method is in theory unbiased but may still produce biased results because it requires correct evaluation of the probability in a given direction which in turn requires solving a nonlinear equation to find the point s where the limit state surface crosses the line In complicated cases there may be more than one of these points in a given direction and to be sure to find them all will
179. econds has been exceeded The check is performed after each simulation is completed To disable this stop criterion set cpu to 0 The cpu must be non negative Specifies the sampling method The default sampling method is selected on the basis of the di mension of the u space This method is recommended in most cases If the model contains a time consuming model function it may be better to use the random direction method SESAM Program version 4 4 RANDOM DIRECTION ORTHOGONAL 1 ORTHOGONAL 2 ORTHOGONAL 3 SEARCH RISKY AND FAST MEDIUM SAFE SAFE AND SLOW SEARCH LIMIT STEP LENGTH length Proban 01 OCT 2004 5 101 The probability is calculated in a simulated direction and in the opposite direction and the average of the two probabilities is used as the sample probability This reduces the sample vari ance because the two probabilities can be assumed to be nega tively correlated This is the simplest technique It is mostly useful when the more sophisticated techniques take too long time to produce results An orthogonal set of directions that span the u space is simu lated The probability is then found in each of these directions and their opposite directions and the average value is calculat ed and used as the sample value The sample variance is further reduced by this method The drawback is that it may take some time to produce each sample value because of the large number of calculations involved
180. ection of variables The general print options can be manipulated through the SET PRINT command See also SESAM Proban Program version 4 4 01 OCT 2004 5 133 SET PRINT Proban SESAM 5 134 01 OCT 2004 Program version 4 4 PRINT ANALYSIS SETTINGS ANALYSIS SETTINGS PURPOSE Print all analysis options PARAMETERS None NOTES All analysis options related to probability and distribution analysis are printed including those for analysis methods that are currently not selected See also DEFINE e SELECT ANALYSIS METHOD EXAMPLES PRINT ANALYSIS SETTINGS SESAM Program version 4 4 Proban 01 OCT 2004 5 135 PRINT CORRELATION CORRELATION univar PURPOSE Print assigned correlations PARAMETERS univar NOTES See also A selection of variables that are defined as one dimensional distributions with nu merical or fixed parameters All correlations assigned to pairs of these variables are printed If only one variable is selected all correlations assigned to this variable will be printed e ASSIGN CORRELATION e SET TITLE EXAMPLES PRINT CORR ELATION Generates the following print Variabl Variab le 2 Input Basic Normalized Proban 5 136 01 OCT 2004 Program version 4 4 PRINT DISTRIBUTION LOW RESOLUTION HIGH RESOLUTION n DISTRIBUTION univar FRACTILE probability
181. ed Deassigned sensitivity ca ENSITIVITY CALCULATION VARIABLE cu EXCL UDE ation sensitivity ca cu ation sensitivity ca cu ation sensitivity ca cu ation ca cu ation sensitivity for for for FOr for the the the the the Mean Mean Mean Mean Mean of of of of of S SESAM Program version 4 4 E 02 3 0E 02 E 02 0 1 0 11 0 12 0 13 0 14 The distribution analysis will take some time Proban gives the standard analysis message for each analysis and shows the parameter value used in the analysis Only parts of these messages are shown here SELECT ANALYSIS METHOD DISTRIBUTION ANALYSIS MONTE CARLO SIMULATION RUN DISTRIBUTION ANALYSIS NPV Starting Distribution Analysis of NPV Parameter study r 0 100000E 01 Starting Monte Carlo simulation after 1000 simulations completed Stopping 250 simulations 500 simulations completed 750 simulations completed 1000 simulations completed Number of simulations 1000 Estimated Mean 1 85046E 04 Estimated Standard Deviation 1 07176E 04 Estimated Skewness 0 018 Estimated Kurtosis 2 812 Parameter study r 0 200000E 01 Starting Monte Carlo simulation and so on SESAM Proban Program version 4 4 01 OCT 2004 3 43 When using a simulation in a parameter study Proban will use the same seeds in
182. ed as follows showing also the Proban messages RENAME VARIABLE Hermite Fit Original Fit Renamed variable Hermite Fit to Original Fit RUN DISTRIBUTION ANALYSIS CONDITIONED NPV SINGLE EVENT 11 gt 70000 Starting Distribution Analysis of NPV given I1 gt 7000 Starting Monte Carlo simulation Stopping after 1000 simulations Simulating 5 sensitivity values 250 simulations completed 500 simulations completed 750 simulations completed 1000 simulations completed Number of simulations 1000 Number in conditioning event 786 Estimated Mean 7 34214E 03 Estimated Standard Deviation 8 19665E 03 Estimated Skewness 0 013 Estimated Kurtosis 2 663 Normal distribution fit to simulation of NPV stored in a variable called Normal Fit Hermit trans distribution fit to simulation of NPV stored in a variab ca d Hermite Fit RENAME VARIABLE Hermite Fit Updated Fit Renamed variable Hermite Fit to Updated Fit ESULT Updated Distribution of NPV given 11 gt 70000 Updated is now the selected result SAVE y Proban prints the number of hits in the conditioning event as well as the usual information The distribution cannot be estimated if there is no hit in the conditioning event Note that the fitted distributions were renamed so that they will not be overwritten during the next analysis This enables a comparison bet
183. ee 2 6 O Polynomium of degree 3 a O Polynomium of degree 4 Input O Polynomium N X X0 C0 Sum of Ci X X0 i 3 O Difference X1 X3 X2 X3 Input O Product of any number of variables 2 1 F 1 X i Arguments gt Vector 2 O 1 X1 1 X2 1 X 1 log X X 1 log X lt 1 gt 1 3 O Sign X1 Abs X1 X3 Sign X2 Abs X2 X3 0 Sum of any number of variables 3 10 2 Create Function Formula Interactively Functions can be modelled on input by using the command CREATE FUNCTION FORMULA and CHANGE FUNCTION FORMULA As an example consider the beam example in the example manual 3 Rather than programming the formula and linking it into Proban the function formula can be created on input as shown below The syntax is described under the command CREATE FUNCTION FORMULA However notice that the order of calculation is according to the FORTRAN syntax Proban SESAM 3 66 01 OCT 2004 Program version 4 4 CREATE FUNCTION LoadPart Load part of moment and shear FORMULA ONLY P1 Applied load 1 P2 Applied load 2 L1 Location of load 1 L2 Location of load 2 Span Beam span P1 1 L1 Span P2 L2 Span CREATE FUNCTION MomForml Moment at end of beam FORMULA ONLY Pl Applied load at end position P2 Applied load at other position L1 Location load at end position L2 Location
184. een words This may cause some function argument names to be identical inside the same function This may again give prob lems when assigning sensitivity calculation or a parameter study to such parameters because Proban cannot distinguish between the different arguments The chance of this being a problem is in reality very small The function names from Proban Version 2 are unchanged except that blank spaces between words in the names are substituted with hyphens e g Func 1 is changed to Func 1 The sublibraries under LIBLIM will be named LIBLIM 1 LIBLIM 2 etc Proban needs both a FUNCLB and a LIBLIM routine in order to run It needs to call both in order to be able to provide the compatibility to Proban Version 2 Thus if only LIBLIM is used a dummy version of FUN CLB must be linked in and vice versa Proban is delivered with a dummy version of LIBLIM that has no sublibraries Users that do not need LIBLIM can simply use this while users that have their own LIBLIM will need to substitute their LIBLIM with the one provided It is possible to mix old LIBLIM routines with routines that are programmed in the new format The two hierarchies of functions are completely separate and the routines are simply placed in the same object library 3 11 Various Hints This section contains various hints on how to facilitate the use of Proban 3 11 1 Importing Plot Files into Documents Proban will orient plots along the long ed
185. eeseceseceeeeeceeeeessecaeneenerennes 4 11 4 4 7 Selecting Several Alternatives from a List cccccccccsscesseessecsteeseceeeceseeeseeesecesecseeeneeenes 4 11 4 48 Entering a Vector or a Matrix of Values cccceccccesccescesseeeseeeecneeeeceneceseeeseecseesaeeneenses 4 12 4 49 Setting and Clearing Loops in a Command ccceccecccesseesseeseceeeceseeeseecsecesecneeeeeenseesnees 4 13 4 4 10 Inserting a Command into Another Command ccceccccseesseeseceeeceseeeseeesecneenseneneenaes 4 14 4 4 11 Aborting All or Parts of a Command ccc ccceescceteeeeceeeeescecceeseceeceseeeseenseceaeeeeeeeneeaaes 4 14 4 4 12 Access to the Operating System cccccccessccssecseceeeceeeecseeesceeseceseceseeeseeeseceaeceeeeeeseneeaaes 4 14 4 4 13 Appending Input LINES ses a A a aaa ee atat 4 15 4 4 14 Viewing the Current Status of a Command ooccccoconicnnonononcnnnonononnncnnnnnn nono connnconnnnrnnnnon nos 4 15 A A ssanctas datas Sadat pos a A a ec Le eaeasVoeaie avg a E arai 4 15 Using the Graphics Mode User Interface cccccecccecscesseessceesceeeeeseecsceeseceseceseeeseeeaecaecnseeneeeeneeaaes 4 15 4 Howto Get Helpert din cia E a Ada 4 18 45 2 TEO Menus ii ia 4 18 4 5 3 Dialog Boxes and their Contents cceccccsecsseesseeeceeceeeeeeceeseecsseeecseeeeseeeseecseceeeeneeeaes 4 18 4 5 4 The Standard Buttons in a Dialog BoX ccccecccesscceseessceeceesceesseeeeeeeceseeeseecseceeesteseneeeaes 4 20 4 5 5 Entering a Prefixed List
186. ehaviour of the distribution and require a very large number of simulations in order to be estimated accurately Intermediate simulation results NoSim Mean Standard Dev Skewness Kurtosis 100 5 38336E 03 9 867633E 03 0 4084 3 1206 200 4 94207E 03 9 639992E 03 0 1910 2 9822 300 4 97684E 03 9 678793E 03 0 1232 2 9344 400 4 99982E 03 9 648684E 03 0 1564 2 8548 500 4 99812E 03 9 561949E 03 0 1082 2 7310 600 5 17163E 03 9 439078E 03 06 LL23 2 7143 700 4 95297E 03 9 474204E 03 0 0946 2 7041 800 5 00293E 03 9 413223E 03 0 0857 2 7489 900 5 08599E 03 9 295718E 03 0 0955 2 7624 1000 4 96924E 03 9 239695E 03 0 1207 2 7729 The number of lines in the table is controlled by use of the command DEFINE PRESENTATION RESULT INTERMEDIATE SIMULATIONS The table of the empirical distribution function has the following contents Empirical Distribution Fractile Prob 2 188292616E4 1 593654735E4 1 012259806E4 6 582621465E4 4 363203073E4 2 738950028E4 1 270994459E4 2 631476443E4 1 978407038E4 OL o oO 10 DOGO 0 00 0 0 0 WNNR ouog 00DO0O0O0O0O0OOopr GT da EE El El t o WN 0 UU UU UM PB gt H gt o Proban SESAM 3 36 01 OCT 2004 Program version 4 4 4 159150481E 03 0 500 7 121619541E 03 0 600 9 876500914E 03 0 700 1 131511362E 04 0 750 1 319665845E 04 0 800 1 496162676E 04 0 850 1 736876892E 04 0 900 2 045195947E 04 0 950 2 630603369E 04 0
187. ence is a contin uation of a preceding command sequence The single asterisk indicate that B and C may be given any number of times Conclude this sequence by the command END The three dots in the right most column indicate that the command sequence is to be continued by another command sequence B A JC END Proban SESAM 5 2 01 OCT 2004 Program version 4 4 In the example below command A is followed by any number of repetitions of either of the sequences B D and C D Note that a pair of braces is used here merely to define a sequence that may be repeated The braces are not commands themselves B A D fp The characters A B C and D in the examples above represent parameters being line mode COMMANDS written in upper case and numbers written in lower case All numbers may be entered as real or integer values Brackets are used to enclose optional parameters A parameter followed by a signifies a selection of one or more numerical values names or texts from a list of items A parameter followed by a signifies one or more alphanumeric or numerical values of the same type These values are entered as a prefixed list Note Line mode commands are in this chapter presented in upper case including hyphens In graphics mode the commands appear in mixed case and without hyphens Note Graphics mode commands that are irrelevant at a given time
188. ep may be skipped if the model functions are already available in Proban or can be constructed from the functions that are already available by use of the function formula facility when nec essary The third step is to define the model for Proban either interactively or by reading a command input file The input may be verified through print and display Proban 2 2 SESAM 01 OCT 2004 Program version 4 4 The fourth step is to set up and run the analysis The results may be inspected using print and display plot Proban keeps input and results on a reusable database so it is possible to exit and restart the program and still have the model and results available 2 2 Model Definition A Proban model consists of the following objects Variables Events Extreme values Correlations Time derivatives Measured values Model Functions Variables events and functions are referenced by name 2 2 1 Variables Variables are the basic building blocks ofthe Proban model The term covers traditional random variables as well as variables with a constant value A variable may be defined as one of the following types Fixed Distribution Fitted Distribution Function A fixed variable contains a numeric value that is substituted for the variable whenever it is used A distribution variable is assigned one of the distributions that are avallable in Proban Each parameter in the distribution may be defined as a consta
189. ependent identical realisations of the variable Notice that the distribution parameters are kept fixed when the extreme value is taken In case of a gener ated distribution the variables conditioned on serve as distribution parameters 2 2 4 Correlation Correlations are used to model linear dependency between variables Two variables will have a positive trend usually becoming large together and small together if their correlation is positive When the correla tion reaches the maximal value of one they become linearly dependent Conversely the variables have a negative trend one is usually large when the other is small if their correlation is negative and they again become linearly dependent when the correlation reaches the lower limit of 1 Note that two variables may be dependent on each other in a nonlinear way and at the same time have correlation coefficient equal to zero In such a case a more refined modelling is required See Figure 2 1 SESAM Proban Program version 4 4 01 OCT 2004 2 5 Figure 2 1 Correlations and dependencies between variables Correlations can be defined between uni variate variables with type attribute Distribution Fitted distribu tion or Generated In case a variable is a generated distribution the input correlation is the corresponding normal correlation In all other cases the model space basic correlation may be input alternatively Proban accomplishes the correlation of non normal distributio
190. eplaced by its corresponding starting time The calculation of a first passage probability has two steps Firstly the probability that the event is fulfilled at the starting time is calculated Secondly the expected number of crossings is calculated Then these two results are combined by the Poisson formula to give the first passage probability Pre 1 0 p exp fv dt in which f is the reliability index corresponding to the probability that the process is in the failure set at time To V t is the mean crossing rate at time and the integral is taken over the interval 79 7 D If a time variable is present in the model then the time interval is integrated over in order to calculate the time averaged mean crossing rate Time integration is carried out by use of a trapezoidal quadrature The number of quadrature points is specified on input A reduced integration interval may be specified in order to calculate only significant contributions Periodicity in the process may be exploited to further reduce the integration effort Proban SESAM 2 18 01 OCT 2004 Program version 4 4 Proban divides the random variables into two sets Those variables which describe the time dependent sto chastic process constitutes Set A and the remaining random variables constitutes Set B Set A is integrated over to give the first passage probability for the stochastic process conditioned on the values of the variables of Set B The outer integration level avera
191. ersion 4 4 2 3 Probability Analysis Proban supplies several methods for finding the probability of an event and the associated sensitivity results The methods fall into two categories e Analytical methods e Simulation methods The analytical methods include FORM and SORM First and Second Order Reliability Methods These glve approximate results relatively fast but require that the model functions are differentiable twice differ entiable for SORM The accuracy of FORM is usually good for small probabilities The accuracy of SORM is often good over the whole probability range Simulation methods take longer time to run than FORM SORM but do not put similar demands on the model functions and the distribution functions Thus the simulation methods provide analysis tools for mod els other than structural reliability models Within structural reliability simulation methods are used both to verify and to improve a result obtained from a FORM SORM approximation and also to obtain results when FORM SORM cannot be used The features of the different analysis methods are described below 2 3 1 FORM SORM Calculation of the probability of an event may be formulated as a multidimensional integral see also the left part of Figure 2 3 P Event f f x dx Event The variables X are the distribution variables in the model fX x is their joint probability density function and the probability is integrated over the domain of x in which the even
192. es however not pop up auto matically from an iconised state when something is printed 4 5 1 How to Get Help There is a Help menu under the main menu which contains useful on line information Context sensitive help is available through a Help button the F1 button on some computers When an entry in a dialog box e g a text input field or a scrtollable list is active pressing the Help button will often dis play a context sensitive help text in a separate window 4 5 2 Tear Off Menus When using Motif version 1 2 or higher a pulldown menu can be torn off and displayed in a separate win dow This is very useful for accessing commonly used dialog boxes The menu is torn off by clicking on the stipulated line at the top of the menu if no such line is visible the menu cannot be torn off To close the menu select the Close entry in the menu at the upper left corner of the window frame AH Event Figure 4 4 Tear off pulldown menu before and after it is torn off 4 5 3 Dialog Boxes and their Contents A dialog box is used to pass information from the user to Proban Most dialog boxes also present the current defaults and thus may be used to pass information from Proban to the user The typical entries in a dialog box are Input fields Menus and Pushbuttons SESAM Proban Program version 4 4 01 OCT 2004 4 19 An Input field can contain a text a name or a numerical value The Set Plot dialog box contains two input field
193. es in a continuous process analysis NOTES None SESAM Proban Program version 4 4 01 OCT 2004 5 11 ASSIGN CONDITIONING CONDITIONING variable condvar PURPOSE Assign conditioning variable s to a generated distribution variable or to a probability variable PARAMETERS variable The name of a generated distribution variable or probability variable condvar A selection of variables that are kept fixed when the distribution is generated or the probability is calculated NOTES 1 The current conditioning variables are presented as defaults when a generated distribution variable or a probability variable is selected 2 The conditioning assignment to a variable is printed by use of the PRINT VARIABLE command See also CREATE VARIABLE GENERATED CREATE VARIABLE PROBABILITY e PRINT VARIABLE EXAMPLES ASSIGN CONDITIONING GenVar ONLY ABC ASSIGN CONDITIONING PrbVar EXCLUDE Proban 5 12 01 OCT 2004 ASSIGN CONTINUOUS PROCESS SESAM Program version 4 4 CONTINUOUS PROCESS value DURATION time variable NONE value STARTING TIME time variable NONE TIME DERIVATIVE ti me derivative variable process variable NONE PURPOSE Assign duration and starting time to a time variable and assign a variable as the time derivative of a process variable PARAMETERS time variable process variable
194. essesseceseceseeeneeececssecsaeeeeseeceseecseecseceseceaeeeseessecaeceseseeesnsecseseaeens 4 1 4 2 43 4 4 4 5 5 1 4 1 1 Command Line Argument eenei e a a E a eee 4 2 4 1 2 Starting Proban in Graphics Mode cccccccssesscessceeeesceeseceseceseeeeeceseesaeceaecneeseeeenseesaecaeens 4 3 4 1 3 Starting Proban in Line Mode e ec eccecsseeseceseceseeseeeeseceaecneseeeeeeeesaecaaececseeeeneeessecsaeneeeas 4 4 4 1 4 Starting Proban in a Batch Run on ec eccescceseesseeeseeeeceseeeeeseeceseecaaecsecsseeeeeseseeeseeseeseengs 4 5 AS Fillesand Data Satety civic aida dieta RAEE RA dais 4 6 Program Requirements ic sad a E states obesecaciessisahecsaneaasaan sae aA T a a 4 7 ADA ERE CutiOm TI esse A ua caopdon EE A EE 4 7 ADD StOTASE PAC ss eve cveceeesvecesiced A A A a A ti da 4 7 NA NR 4 7 Using the Line Mode User Interface ccccccccscesseesseceseeeeeeeceescensecesecnseesseeesecaeceseeneeseneesaecsaeenseeaes 4 8 AAT Howto get Help cria donna td ideada di eta 4 8 4 42 Command Input Files ai da 4 9 443 Accessing Default Values 0 0 eccccccesceseessecsseeteceeceseeeseeeseceseceseeeeeesaecsaecnseseeeseeeeseeessees 4 9 4 4 4 Abbreviation and Wildcards ccccecccesesssesssesteceeceeceeecescecssensecseeceseecseecseceeesneseneenaes 4 10 4 4 5 Input of a Text or a Name or a Numerical Value cccccecccecseceseceseeeeceseeetseeecneeeseeenes 4 10 4 4 6 Selecting a Single Alternative from a List cccccccccscesecee
195. estpoint PURPOSE Options for NLPQL PARAMETERS search method maxit maximum step length maxfun conv cnsv bestpoint NOTES One of BFGS and STEEPEST DESCENT BFGS generates a quadratic approximation to the function optimised on STEEP EST DESCENT generates a sequential linear approximation and is the more robust method when the gradients have poor numerical quality Maximum number of general iterations gradient evaluations FREE limited by optimisation bounds or VALUE The value is the maximum steplength during one iteration Prevents over shooting Maximum number of function evaluations in line search for step length that improves merit function Kuhn Tucker optimality criterion Test for constraint violation ON DEFAULT uses the square root of conv as test value ON USER uses a user specified val ue as test value OFF skips the constraint value test ON delivers the best point reached during optimisation even if a convergency criterion is not met OFF delivers a point that necessarily fulfils the convergency criteria The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e PRINT ANALYSIS SETTINGS EXAMPLES The following values are default when the program starts up with a new database DEFINE FORM SORM OPTIMIZATION NLPQL BFGS 40 VALUE 5 0 10 0 0001726 ON DEFAULT OFF SESAM Proban Program version 4 4 01 OCT
196. finition Al Al lt 0 0 A2 A2 lt 0 0 A3 A3 lt 0 0 The importance factor print is as follows PRINT RESULT IMPORTANCE FACTORS Probability of A Failure of all A components Analysis method FORM Importance factors Variable Importance Load 82 0 RA2 6 0 RA3 6 0 RA1 6 0 It lists the importance factors in order of magnitude If there are many small importance values they can be cut off from the print by use of the command DEFINE RESULT OPTION IMPORTANCE CUTOFF Proban SESAM 3 14 01 OCT 2004 Program version 4 4 The linearisation point is printed as part of the output from the PRINT RESULT ALL command It looks like this Linearization point number 1 of A Subevent Definition Al Al lt 0 0 A2 A2 lt 0 0 A3 A3 lt 0 0 Variable Type Value Prob RAL Inv Gauss 1 033881161E 02 0 284038 Load Inv Gauss 1 033881089E 02 0 983141 RA2 Inv Gauss 1 033881161E 02 0 284038 RA3 Inv Gauss 1 033881161E 02 0 284038 Al Difference 7 103621499E 06 A2 Difference 7 103621499E 06 A3 Difference 7 103621499E 06 The and indications at the right show if a variable has a load effect or a resistance effect The number of or indicates the strength of the effect The linearisation point has been transformed back to the input space of the variables even though the linearisation actually took place in U space The values of those variables that are not distributions are also shown The
197. floating point number a text a file name or a selection between alternatives dependent on the selected option 1 The default function options can be printed by use of the PRINT FUNCTION DESCRIPTION com mand 2 The function options assigned to a variable are printed by use of the PRINT VARIABLE command 3 The function options assigned to the variables created by this program should not be changed by the user See also e PRINT FUNCTION DESCRIPTION e PRINT VARIABLE EXAMPLES ASSIGN FUNC ASSIGN FUNC ASSIGN FUNC PION 0P7 PION 0P7 PION 0P7 PION FUNCTION F11 POWER 3 TION VARIABLE VAR33 ACCURACY TYPE RELATIVE TION VARIABLE VAR33 ACCURACY VALUE 1 1E 5 Proban SESAM 5 16 01 OCT 2004 Program version 4 4 ASSIGN MEASURED VALUE variable MEASURED VALUE event NONE PURPOSE Assign the measured value to an equality event PARAMETERS event The name of an event of type SINGLE variable The name of the variable which was measured This may be a coordinate in a mul tidimensional variable NONE No measured value is assigned to the selected event NOTES 1 By default no measured variable is assigned to any event except the events describing inspections where a crack is measured to a certain size 2 The measured value assigned to an event is printed by use of the PRINT EVENT command 3 The measured value assignments to the events created by this pr
198. for sensitivity calculation NOTES None SESAM Proban Program version 4 4 01 OCT 2004 5 19 ASSIGN SENSITIVITY CALCULATION INCREMENT value INCREMENT parameter DEFAULT PURPOSE Assign increment to be used for sensitivity calculation PARAMETERS parameter The parameter for which the increment applies This can be a fixed variable the name of a numerical parameter in a distribution variable or the name of a numer ical argument in a function variable value The increment to be used DEFAULT Use the default increment NOTES The specified increment overrides any increment specified by DEFINE ANALYSIS OPTION DIFFEREN TIATION See also e ASSIGN SENSITIVITY CALCULATION VARIABLE EXAMPLES ASSIGN SENSITIVITY CALCULATION INCREMENT P1 1nC ON 0 01 ASSIGN SENSITIVITY CALCULATION INCREMENT P1 1nC OFF Proban SESAM 5 20 01 OCT 2004 Program version 4 4 ASSIGN SENSITIVITY CALCULATION VARIABLE VARIABLE parameter PURPOSE Select a number of parameters for sensitivity calculation PARAMETERS parameter The parameters to be used for sensitivity calculation These can be a fixed variable the name of a numerical parameter in a distribution variable or the name of a nu merical argument in a function variable NOTES 1 The parameters that have previously been selected are presented as the default selection To deassign sensitivity to
199. func tions the basic mathematical and trigonometric functions and a few useful additions to these During an analysis Proban usually needs to take derivatives of the model functions These derivatives may be programmed into the functions in order to enhance performance or may be left out in which case Proban will do the differentiation numerically A programmed model function returns either a single value or a vector value A function created as function formula returns a single value How model functions are programmed and linked into Proban is described in Section 3 10 3 How model functions are created interactively is described in Section 3 10 2 The input model is verified using the PRINT DISPLAY PLOT and RUN DETERMINISTIC ANALYSIS commands Newly programmed model functions can and should be checked using the PRINT FUNCTION command which allows for checks of function values and gradients Some checks cannot be done before the analysis is initialised or run Most of these can be done using the RUN INPUT CHECK command This command will check the consistency of the model but not do the actual run It traps most but not all errors SESAM Proban Program version 4 4 01 OCT 2004 2 7 2 2 8 Generated Distribution Sometimes the maximum or minimum of a number of independent identically distributed realisations of a function G X a of random variables X is required This is facilitated by creating Z as the Generated distri butio
200. g cross terms The response function has two arguments while the approximated function has three arguments CREATE FUNCTION rspfu Response surface RESPONSESURFACE ONLY a x argl b x arg2 appfunc 1 2 a QGroup 1 3 b QGroup 2 Fit linear response surface function to appfunc centred around 1 2 3 with increment for each argument the second argument of appfunc and increment 2 for the third argument of appfunc including cross terms CREATE FUNCTION rspfu Response surface RESPONSESURFACE ONLY a x argl b x arg2 c x arg3 appfunc 1 c L 1 2 b L1 1 3 a L2 1 Proban SESAM 5 56 01 OCT 2004 Program version 4 4 CREATE VARIABLE DISTRIBUTION FITTED DISTRIBUTION FIXED value VARIABLE name desc FUNCTION GENERATED 1d variable PROBABILITY TIME PURPOSE To create a variable PARAMETERS name desc DISTRIBUTION FITTED DISTRIBUTION FIXED value FUNCTION GENERATED 1d variable PROBABILITY TIME Name of the variable to be created This cannot be the name of an existing variable Variable names are matched case insensi tive and can be up to 12 characters long Descriptive text for the variable It can be up to 50 characters long Variable is assigned a distribution See a following page for de tails Variable is assigned a distribution that is fitted to input data See a following page for details
201. g the SAVE RESULT command 3 The results are examined by use of the commands PRINT RESULT or DISPLAY RESULT See also DEFINE DISTRIBUTION SIMULATION SESAM Program version 4 4 DEFINE MEAN VALUE FORM e DEFINE PARAMETER STUDY 01 OCT 2004 e SELECT ANALYSIS METHOD DISTRIBUTION ANALYSIS e SAVE RESULT EXAMPLES RUN DISI RUN DISI RIBUT RIBUT PION ANALYSIS NPV PION ANALYSIS CONDITION ED NPV SINGLI E EVI ENT EXP ENSE Proban gt 100000 5 181 Proban SESAM 5 182 01 OCT 2004 Program version 4 4 RUN INPUT CHECK DISTRIBUTION ANALYSIS INPUT CHECK CONTINUOUS PROCESS ANALYSIS PROBABILITY ANALYSIS PURPOSE Run a check of the input to an analysis PARAMETERS CONTINUOUS PROCESS ANALYSIS Run a check of an analysis of the first passage probability or crossing rate of a variable DISTRIBUTION ANALYSIS Run a check of an analysis of the distribution of a variable PROBABILITY ANALYSIS Run a check of an analysis of the probability of an event pos sibly conditioned on another event NOTES The sub commands are identical in syntax to RUN CONTINUOUS PROCESS ANALYSIS RUN DISTRI BUTION ANALYSIS and RUN PROBABILITY ANALYSIS The only difference is that they only check the input to the analysis they do not run the analysis SESAM Proban Program version 4 4 01 OCT 2004 5 183 RUN PROBABILITY ANALYSIS
202. ge of the paper Thus if a plot produced by Proban is imported into a document and is intended to be presented with text as in this manual it will most likely be oriented in the wrong direction Proban SESAM 3 72 01 OCT 2004 Program version 4 4 Some word processors cannot rotate such a picture If you have this problem use the following procedure instead 1 Write the plot file in SESAM NEUTRAL format 2 Use the program PLTCNV_EXT which is delivered with Proban to convert it to another format The input to PLTCNV_EXT will be SCALE 0 9 OUTPUT FILE NAME lt the proper file name gt lt input_file gt PLO lt output_format gt EXIT The scale command is necessary for conversion to Postscript files but may not be needed otherwise For the list of proper output formats run PLTCNV_EXT interactively Postscript is PSCR For documents maintained on a PC the CGM or HPGL 7550 format may be more suitable than Postscript the latter format is e g recognised by MS Word when renamed to have a HGL suffix However if such a file is written when running VMS it cannot be imported directly into a PC document because of file format differences between VMS and DOS In this case it is better to write a file in SESAM NEUTRAL format and then use PLTCNV_EXT to convert it as above using HP70 as the output format During this conver sion the SCALE command is not needed and NO ROTATE should be used instead Please note that it is necessary to
203. ges this first passage probability over the variables of Set B The implied nested optimization employs the optimization criteria defined for nested reliability analysis see above If a random variable which is not a time dependent stochastic process is to be integrated at the inner integra tion level then this is achieved by pushing the variable to the inner level 2 6 Crossing Rate Analysis The rate v of a continuous stochastic process crossing into a failure set at time is calculated as a parallel system sensitivity measure employing the FORM method The continuous stochastic process is modelled as explained for first passage probability calculation If a time variable is present in the model then the time interval is averaged over in order to calculate the time averaged mean crossing rate Time integration is carried out by use of a trapezoidal quadrature The number of quadrature points is specified on input A reduced integration interval may be specified in order to calculate only significant contributions Periodicity in the process may be exploited to further reduce the integration effort Proban divides the random variables into two sets Those variables which describe the time dependent sto chastic process constitutes Set A and the remaining random variables constitutes Set B Set A is integrated over to give the time averaged mean crossing rate for the stochastic process conditioned on the values of the variables of Set
204. ghts The input data will be sorted in order of increasing observation values Observed values of the random variable to which a distribution is fitted The input data will be sorted in order of increasing ob servation values Fit the distribution to the results of a probability or distribution analysis Simulation results will be fitted and stored as OB SERVATIONS after being grouped into weighted interval data if many samples exist Mean value based FORM results will be fitted and stored as CUMULATIVE data with equal weights on all points Probability results from a parameter study will be fit ted if possible and stored as CUMULATIVE data with equal weights on all points In the case of a parameter study of a dis tribution analysis the result for the first parameter value is used The input data are sampled values of the variable and first mo ments fit is used The name of the result for which the distribution is to be fitted 1 The existing values are presented as defaults whenever this is possible 2 The RESULT option can be useful for substituting a variable requiring lengthy computation time with a fitted distribution 3 The variable may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command 4 The distribution function and density values may be printed by use of the PRINT DISTRIBUTION com mand 5 The moments of the distribution are calculated and printed if possible by use of the P
205. he SCREEN or to a FILE Set the prefix and name of the print file The prefix and name are concatenated The suffix of the file will be LIS Set the page orientation for the print file See note 2 below The print page is 132 characters wide The print page is 80 characters wide Set number of lines in one screen page to nlines The purpose of this is to be able to pause the printout at the correct time when printing to SCREEN in a line mode run 1 The print DESTINATION is reset to SCREEN each time Proban starts up even if it is on an existing database 2 The following figure illustrates the print layout Proban SESAM 5 216 01 OCT 2004 Program version 4 4 A4 paper PORTRAIT LANDSCAPE Figure 5 2 Setting PORTRAIT and LANDSCAPE print page orientation See also SET DISPLAY DESTINATION e PLOT EXAMPLES The following is default when the program starts with a new database SET PRINT DESTINATION SCREEN SET PLOT FILE same prefix and name as the database and journal file SET PLOT PAGE ORIENTATION LANDSCAPE SET SCREEN HEIGHT 24 On VMS Proban sets the correct height El SESAM Proban Program version 4 4 01 OCT 2004 A 1 APPENDIX A PROBAN LINK IN FUNCTIONS AND DISTRIBUTION A1 Implementing New Model Functions into Proban How to program new model functions is described in Section 3 10 1 and Section 3 10 3 A1 1 Unix Proban comes with a Makefile which
206. he currently selected plot file PARAMETERS None NOTES 1 The plot file and format is specified by use of the SET PLOT command 2 Note that the command does not actually write the display as seen on the screen to file it re executes the DISPLAY command taking any changed settings into account 3 This command is not available from the menu bar in graphics mode Use FILE PLOT instead or use the graphics pick mode See also e DISPLAY e SET PLOT EXAMPLES PLOT Proban 5 132 PRINT SESAM 01 OCT 2004 Program version 4 4 ANALYSIS SETTINGS CORRELATION DISTRIBUTION EVENT PRINT FUNCTION PARAMETER STUDY RESULT STARTING POINT VARIABLE PURPOSE To present input data and results graphically PARAMETERS ANALYSIS SETTINGS CORRELATION DISTRIBUTION EVENT FUNCTION PARAMETER STUDY PLAN INSPECTION RESULT STARTING POINT VARIABLE NOTES Print all analysis settings related to probability and distribution analysis Print all correlations assigned to a selection of variables Print the distribution and density functions of a variable Print information about a selection of events Print information about a function or a function value deriva tive Print the assigned parameter study Print an inspection plan Print an analysis result Print the starting point assignment for a selection of events Print information about a sel
207. he result is Variable 1 Variable 2 Input Basic El E2 Basic 0 7500 Normalized 0 7537 SESAM Proban Program version 4 4 01 OCT 2004 3 9 Note that the normalised correlation is also printed 3 2 2 Display and Plot The DISPLAY command is used to view data graphically The PLOT command is used to send the last dis play to a file Displays are by default sent to the screen The operation of such a display window depends on the device used The display device is set by use of the SET DISPLAY DEVICE command If a display to screen is attempted to an incorrect device the terminal window will most likely be filled with strange characters and it may be necessary to issue a few lt Return gt s in order to get back to the main prompt A display may also be directed to a file The display destination and the plot file name are controlled by the commands SET DISPLAY DESTINATION and SET PLOT FILE respectively The last display may be sent to the current plot file even if the current display destination is to the screen by issuing the PLOT command This command will actually process the last display again and send it to the file it will not just take a copy of the previous display This implies that if any display settings or other input has been changed the plot file version may be different from the display that was shown on the screen Several plot file formats are available See the description of the SET PLOT command
208. he user to enter the model file name more information in Section 4 1 2 through the following prompt Database file prefix Database file name Proban No extension should be given since this file has a predetermined extension For NT and UNIX installations this is mod The file name Proban i e Proban mod is offered as a default Database File Status OLD NEW If the Proban database file already exists the default OLD should be given If the database is to be created the answer is NEW See also Section 4 1 2 Note that if at least one of PREFIX NAME or STATUS is specified as a command line argument the prompts for these values will be ignored and the value s that are not specified will be given defaults This start up has opened a new database file called Proban mod and a new journal file called Proban jnl If the file specification is incorrect Proban will reissue the prompt for the database file prefix Typing a double dot during the start up phase will abort the program The facilities that are available in line mode are described in Section 4 4 To exit the program type the EXIT command This will close all files and exit the program 4 1 4 Starting Proban in a Batch Run Using command line arguments see Section 4 1 1 is the simplest way to execute Proban in batch If proban is the command that executes the program the command to run test_in jnl in batch could be proban NAME TEST STAT NEW INT
209. her without intervening spaces to keep accepting defaults as long as they are presented or until the command is complete The semicolon must be preceded by a blank space if it is not the first item on the command line However several semicolons may follow each other without intervening spaces semicolon Please note that an empty line in a command input file will not be interpreted as a default The colon and semicolon may be written into a command input file A colon or semicolon is never logged on the journal file Instead the substituted default values are logged 4 4 4 Abbreviation and Wildcards Proban offers two methods to short cut selection of elements in a list Abbreviation and the use of wild cards Alternatives up to hyphens can be abbreviated as long as the abbreviation is unique Thus SUB LEVEL INTEGRATION may be abbreviated to any of SU S L I S LEV as long as the abbreviation is unique among the alternatives presented Wildcards consist of the following two characters Table 4 5 Wildcard characters pe substitutes for any number of characters including no characters amp substitutes for any one character It must match exactly one character As an example y amp amp amp matches xabyccl and xy111 but not xaby11 Abbreviation and wildcards may not be mixed in the same matching expression 4 4 5 Input of a Text or a Name or a Numerical Value Numerical values can b
210. hod FORM Importance factors Variable Importance Load 74 0 RB 22 8 RC 2 0 RA3 0 4 RA1 0 4 RA2 0 4 The importance factors reveal that it would pay to reduce the uncertainty on the resistance of RB and that the uncertainty in the other resistance is insignificant However the really significant contribution comes from the uncertainty in the load Using the estimate in Section 2 8 it can be predicted that if the standard deviation on RB is removed the lower bound reliability index will change to 2 3261 V 1 0 228 2 6474 while the upper bound reliability index will change to 2 6572 If RB is changed to a fixed variable with value 120 and the analysis is run again the result gives the following bounds on the reliability index 2 6541 lt B lt 2 6645 so in this case the prediction was quite good When analysing equality events i e an event of the type B 0 the results are different Such events do not generate probabilities The probability of an equality event is always zero when the distributions are continuous Instead what is calculated is the derivative of the probability with respect to the right hand side of the equality event s In case the analysis is of a single equality event the result is the value of the density function for the random variable that is used to define the event calculated at the right hand side threshold value for the event Equality events cannot be used in analyses that require calculatio
211. iate results form a parameter study cannot be selected separately They will be printed in the order in which the parameter study was performed See also DEFINE ANALYSIS OPTION INTERMEDIATE RESULTS DEFINE ANALYSIS OPTION GENERATED DISTRIBUTION INTERMEDIATE RESULTS e SELECT RESULT e SET TITLE EXAMPLES PRINT RESULT INTERMEDIATE RESULTS SESAM Proban Program version 4 4 01 OCT 2004 5 157 PRINT RESULT PARAMETER STUDY IMPORTANCE FACTOR MAIN RESULT PARAMETER STUDY PURPOSE Print results as a function of the parameter in a parameter study PARAMETERS IMPORTANCE FACTOR Print importance factors as a function of the parameter MAIN RESULT Print one or more main results as a function of the parameter NOTES None Proban SESAM 5 158 01 OCT 2004 Program version 4 4 PRINT RESULT PARAMETER STUDY IMPORTANCE FACTOR IMPORTANCE FACTOR impname PURPOSE Print importance factors as a function of the parameter in a parameter study PARAMETERS impname A selection of importance factor names The segment named Other in the pie chart representation is not used here All available importance factor names can be selected NOTES See also DISPLAY RESULT PARAMETER STUDY IMPORTANCE FACTOR PRINT RESULT IMPORTANCE FACTORS e SELECT RESULT e SET TITLE EXAMPLES PRINT RESULT PARAMETER STUDY IMPORTANCE FACTOR ONLY Depth ImpGroup 1 PRINT RESULT
212. ibrary Then compile USRINI USRDDI and the distribution DDI routine e g XXXDDI and possibly other routines that are needed by the new DDI routine and place the object codes in the USER library 6 ink the USER library into Proban using the link command file or makefile delivered with Proban The procedure for doing this is installation dependent and is described in the installation guide 7 Check the distribution by use of the PRINT DISTRIBUTION command The HIGH RESOLUTION print option will print warnings if the DDI routine seems to give wrong results Also try giving some extreme tail values using the FRACTILE and PROBABILITY options Proban SESAM 3 60 01 OCT 2004 Program version 4 4 3 10 Model Functions The library of model functions are divided into sublibraries also called function libraries This subdivision is used in order to group functions into logically coherent groups and to be able to mask off temporarily some of the functions see the command SELECT FUNCTION LIBRARY All functions and sublibraries are named and are referenced by name in Proban At the top of the hierarchy resides a routine that must have the name FUNCLB This routine is called by Proban when it needs information from a model function or sublibrary FUNCLB then calls a number of sublibrary routines and each of these controls a number of model functions FUNCLB ae Sx Re rate a o N A ee So y BN SUBLIB SUBLIB SUBLIB
213. ibutions New functions Proban SESAM 1 4 01 OCT 2004 Program version 4 4 SESAM Proban Program version 4 4 01 OCT 2004 2 1 2 FEATURES OF PROBAN 2 1 General Description The overall scope of Proban is to be a practical software tool for probabilistic analysis Proban has a flexible input module allowing for definition of simple models as well as sophisticated models with complicated dependencies Proban also has a number of calculation methods available giving a wide range of results on probabilities crossing rates distributions and sensitivities This chapter goes through features of Proban in the order in which they would normally be used during a Proban analysis The first step in a Proban analysis is to define the question s to be answered and the model that is going to provide the answers The questions that Proban can answer are typically e What is the probability that a given event happens e What is the first passage probability of a stochastic process in a given time e What is the crossing rate of stochastic process out of a given domain at a specified time e What is the mean standard deviation skewness or kurtosis of a given variable e What is the distribution of a given variable e How much will this result change if an input parameter or value is changed by a given amount The second step in a Proban analysis is to define the necessary model functions and code them and link them to Proban This st
214. ibutions to the sample by creating variables with type attribute Fitted Dis tribution see Section 3 9 2 SESAM Proban Program version 4 4 01 OCT 2004 2 25 2 7 3 Mean Value Based FORM Mean value based FORM is often an unreliable method and the only reason for including it in Proban is that it is fast It allows estimation of distributions that cannot be simulated because of extreme computation times Another useful application of the method is to quickly identify the range of a distribution The principle of Mean value based FORM is to estimate the distribution from the FORM approximation of the limit state level surface through the origin of U space If g 0 is the value at the origin the probability that g u lt g 0 is estimated as 0 5 using FORM the reliability index B is 0 Shooting out in the direction of the U space gradient at the origin the function value at points along the gradient direction are related to the distance reliability index from the origin and f is in turn related to the corresponding probability B The error made can be small and can be very large It depends on the angular difference between the gradi ent at the origin and the direction to the correct design point u in Figure 2 17 SS g u gu g u 9 0 Figure 2 17 Mean value based FORM In extreme cases Mean value based FORM may give an estimated distribution function that is not increas ing everywhere so the method must be used
215. ide At the same place there is an example routine USRINI TST showing how the TST distribution is implemented 3 Program the DDI routine for the distribution e g named XXXDDI This routine calculates the density function distribution function and complementary distribution function from a fractile in the distribu tion Proban is delivered with an example called TSTDDI that should be used as a template for the rou tine The location of this routine is specified in the installation guide Proban requires good accuracy in the tail of the distribution and may call the DDI routine with extreme tail values Please be aware of this and take special note of the possibility of an overflow e g in the exp function if a tail value is extreme 4 The DDI routine is activated through the routine USRDDI USRDDI must be modified by inserting a call to the DDI routine for the distribution See the documentation in USRDDI itself for further clarification Proban is delivered with a USRDDI routine that does not call any user defined distributions The location of USRDDI is described in the installation guide At the same place there is an example routine USRDDI TST showing how the TST distribution is implemented 5 Proban is delivered with an object library called USER The location of the library is described in the installation guide This library contains the user defined distributions it is delivered with only USRINI and USRDDI Take a copy of this l
216. if a line with only an is found There may be one or more blank spaces between and the file name Read lt p gt lines of the named file from the top Reading will stop if an error is filename lt n gt found or if a line with only an is found There may be one or more blank y spaces between and the file name Continue reading the presently open file Reading will stop if an error is found or at the end of the file or if a line with only an is found a lt n gt Continue reading the presently open file Reading will stop if an error is found or if a line with only an is found Close the last opened command input file There cannot be any blank space j between and the dots Show the name and status of the currently open command input file s 4 4 3 Accessing Default Values Proban will in many cases supply a default value when input is requested The default will be presented in An example Proban SESAM 4 10 01 OCT 2004 Program version 4 4 DEFINE ANALYSIS OPTION PARAMETER STUDY Run Parameter Study Analysis ON The default may be accepted using one of the following methods Table 4 4 Input of default value s lt Return gt i e an empty input line to accept the current default to accept the current default The colon must be preceded by a blank if it is not colon the first item on the command line However several colons may follow each ot
217. in line mode specify INTERFACE LINE as a command line argument see Section 4 1 1 After a short while a heading similar to the one shown below is echoed on the screen provided that NOHEADER was not specified on the command line KKKKKK KKKKKKKK k k k k kk KKKKKKK KkKKKKKK kk k k k k KKKKKKKK KKKKKK KKKKKK KKKKKKKK k k k k k k kk KKKKKKKKKK KKKKKKKKK Kk k k k k KKKKKKKK KKKKKK KKKKKK KKKKKKKK K k Kk k k KKKKKKK KKKKKKK k k K k kK KKKKKK KK KKKKKK KKKKKK KKKKKKKK kk kK k k KKAXKKKKKkAk KKKKKKKKKK Kk k kk K KKKKKKKKK KkKKKKK KK kk KKK KKK KKKKKKKKKKKKK kk k k k k k k k k k k k k k k kK k k K k k k k k k k K k k k k k k k k k kk k k k k KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK SESAM Proban Program version 4 4 01 OCT 2004 4 5 PROBAN Probabilistic analysis system KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KK KKK Marketing and Support by DNV Sesam Program id 4 2 01 Computer DEC 3000 Model 400 Release date 11 JAN 1996 Impl update Access time 11 JAN 1996 15 06 55 Operating system VMS V6 1 User id OLES CPU id 0858461026 Installation DNVS GRID Copyright DET NORSKE VERITAS SESAM AS P O Box 300 N 1322 Hovik Norway Proban then invites t
218. ine the parameters in the distribution called input sequences e g a normal distribution may be defined through the mean and standard deviation or through the mean and coefficient of variation The available distributions and input sequences are listed in Section 3 9 1 It is also possible to add user defined distributions A multidimensional variable is defined as a multidimensional distribution or as a multidimensional func tion These can be referenced directly when a multidimensional value is required but more often the one dimensional coordinates are used Coordinates in a multidimensional distribution variable are referenced by adding the coordinate number to the variable name after a hyphen Coordinates in a multidimensional function variable are referenced similarly but by adding the function coordinate name instead of the coordinate number The following example illustrates these naming conventions by using a Network function This function has been programmed as a multidimensional function in Proban The names of the function coordinates are Path1 Path2 Path3 and Longest CREATE VARIABLE X DISTRIBUTION Multi Normal 7 lt parameters gt CREATE VARIABLE F FUNCTION Network X 1 X 2 X 3 X 4 X 5 X 6 X 7 RUN DISTRIBUTION ANALYSIS F Pathl 2 2 2 Events Calculation and examination of probability is often the goal of a Proban analysis The probability is associ ated with an event in the input model for exa
219. inomial N Probab Number Probability Number gt 1 0 lt Probability lt 1 Non integer Number is replaced by nearest integer Burr M C K Low M C K Lower Bound M gt Lower Bound C gt 0 K gt 0 Chi square Mean Low Mean Lower Bound DoF Low Deg of Freed Lower bound Mean gt Lower Bound Deg of Freed gt 0 Exponential Mean Low Mean Lower Bound Rate Low Rate Lower bound Mean gt Lower Bound Rate gt 0 Gamma Mean StD Low Mean Stand Dev Lower Bound Mean Cov Low Mean Coef of Var Lower Bound K Lambda Low K Lambda Lower Bound Mean gt Lower Bound Mean Coef of Var gt 0 Proban 3 54 Gen Gamma Gen Pareto Gumbel Hermit Secon Hermit Trans Inv Gauss Lognormal Long Higgins Maxwell Al B C Low Alpha gt 0 C gt 0 Sig KsiP Low Mean StD Mean Cov Alpha Moments Central Mom Moments Central Mom Mean StD Low Mean Cov Low Ksi Lamb Low Mean StD Low Mean Cov Low Sigma Mu Low NCycle Delta Mean Low Theta Low SESAM 01 OCT 2004 Program version 4 4 Stand Dev gt 0 Coef of Var gt 0 K gt 0 Lambda gt 0 Alpha B C Lower Bound Sigma KsiP Low Sigma gt 0 KsiP gt 0 Mean Stand Dev Mean Coef of Var Alpha B Mean Coef of Var gt 0 Stand Dev gt 0 Coef of Var gt 0 Alpha gt 0 Mean Stand Dev Skewness Kurtosis Mean Variance Third C Mom Fourth C Mom Stand Dev gt 0 Kurtosis gt 0 Variance gt 0 Fourth C Mom gt 0 8 9 Kurtosis gt
220. ion incre ments are defined for the outer integration level and the inner integration level separately 2 5 First Passage Probability Analysis A first passage probability is the probability that a continuous stochastic process initially is in the failure set defined by an event plus the probability that it starts in the safe set and enters the failure set at least once within a specified time interval This is shown in Figure 2 11 for the process X t with starting time 75 0 and duration D gt t SESAM Proban Program version 4 4 01 OCT 2004 2 17 X2 X2 failure set x 0 x t H aD x 0 safe set gt X4 gt Xy starting point in failure set starting point in safe set Figure 2 11 First Passage Probability The continuous stochastic process is modelled by assignment of a time derivative process variable to the process variable The time interval is modelled with starting time T and duration D When a variable with type attribute time is a part of the model 7 and D must be attached to this variable or be defined as defaults If no time varia ble is present in the model only the default duration is required The starting time and the duration may be modelled as random variables Notice that if an ordinary probability analysis not first passage probability analysis is carried out on a model which includes a stochastic process then the time derivative variables are neglected and the time var iable is r
221. ion of the multinormal probability fails In this case the design point s have been found and the linearisation completed but the resulting failure set is of a form so that the probability content of the set cannot be calculated It might help in this case to change the convergence criterion to a smaller value using the same command as above There is also the possibility that the event used in the analysis has probability zero or one because of a prob lem in the model In these cases the model does not provide a limit state surface and therefore no design point Proban SESAM 3 74 01 OCT 2004 Program version 4 4 SESAM Proban Program version 4 4 01 OCT 2004 4 1 4 EXECUTION OF PROBAN Proban may be run in three different modes e In interactive line mode using only character based input The line mode facilities are described in Sec tion 4 4 In interactive graphics mode with menus and dialog boxes where input may be given using a mouse as well as the keyboard The interactive graphics mode facilities are described in Section 4 5 but in addi tion this mode also gives access to the line mode facilities It requires a work station or an X terminal running the OSF MOTIF window system In batch mode which uses the line mode syntax and facilities The start up of Proban in the three different modes is described in Section 4 1 This section also describes the files that Proban uses The program requirements and limitations
222. isplayed with a logarithmic X or Y axis SESAM Program version 4 4 4 The empirical distribution function is calculated as F Xi 1 n 1 when n simulations were com pleted and the sample points have been ordered as x 1 X 2 X n See also DISPLAY DISTRIBUTION e PRINT RESULT e SELECT RESULT SET EXAMPLE DISPLAY R DISPLAY R ESULT ESULT DISI DIST RIBUT RIBUT TION ONLY Empirical Normal Fit TION ONLY Mean V FORM DISTRIBUTION D ENSITY SESAM Proban Program version 4 4 01 OCT 2004 5 121 DISPLAY RESULT IMPORTANCE FACTORS IMPORTANCE FACTORS valuel value2 PURPOSE Display importance factors PARAMETERS value 1 This input is only required if the selected result is a parameter study valuel is then a selection of the first parameter values for which the study was run The particular results from the analysis using the selected value s will be displayed value2 This input is only required if the selected result is a two parameter study Value2 is then a selection of the second parameter values for which the study was run The particular results from the analysis using the selected value s will be displayed NOTES 1 The importance factors are displayed as a pie chart 2 All importance factor values less than a user definable limit are grouped into one segment labelled Other see DEFINE PRESENTATION RESULT
223. ity of a loss in Example 3 2 The following commands will simulate this probability Proban messages are also shown S R ELECT ANALYSIS M UN PROBABILITY ANALYSIS SINGLE EV ETHOD PROBABILITY ANALYSIS MONT ENT NPV lt 0 E CARLO SIMULATION Starting Probability Analysis of NPV lt 0 0 Proban SESAM 3 20 01 OCT 2004 Program version 4 4 Starting Monte Carlo simulation Stopping after 1000 simulations or 60 0 CPUsec Simulations completed 250 Simulations completed 500 Simulations completed 750 Simulations completed 1000 Number of simulations 1000 Number in intersection event 330 Estimated probability 3 3000E 01 Standard dev of Probability 1 4869E 02 Coeff of Var of Probability 0 045 Estimated Reliability index 0 4399 The accuracy here was quite good a coefficient of variation of about 5 Note that the stop criteria 60 seconds or 1000 simulations are shown It is also possible to demand a stop if a required coefficient of var iation has been reached The stop criteria is manipulated using the command DEFINE PROBABILITY SIMULATION MONTE CARLO A summary of the results may be printed PRINT RESULT SUMMARY Probability of NPV lt 0 0 Net Present Value Analysis method Monte Carlo simulation Final results after 1000 simulations Estimate Stand Dev C of V 90 confidence interv Probability 3 300E 01 1 487E 02 0 045 3 05
224. ivatives with other argu ments QName Q followed by name Quadratic approximation including cross terms for arguments that have the same group Name Q alone is treated as a group Increment to be used with the fit 1 An argument name consists of maximum 12 alphanumeric characters and _ The first character must be alphabetic 2 An argument description consists of maximum 50 characters 3 Point argname method and increment are comma separated See also e CREATE FUNCTION RESPONSESURFACE DISPLAY FUNCTION Proban SESAM 5 32 01 OCT 2004 Program version 4 4 PRINT FUNCTION PRINT RESPONSESURFACE RENAME FUNCTION EXAMPLES Change a quadratic response surface function to appfunc centred around 1 2 3 with increment 1 for the second argument of appfunc and increment 2 for the third argument of appfunc including cross terms The response function has two arguments while the approximated function has three arguments CHANGE FUNCTION rspfu Response surface RESPONSESURFACE ONLY a x argi b x arg2 appfunc 1 2 a QGroup 1 3 b QGroup 2 Change linear response surface function to appfunc centred around 1 2 3 with increment 1 for each argu ment the second argument of appfunc and increment 2 for the third argument of appfunc including cross terms CHANGE FUNCTION rspfu Response surface RESPONSESURFACE ONLY a x argi b x arg2 c x arg3 J appfunc 1 c L 1 2 b L1 1 3 a
225. ix must be positive definite Mean Stand Dev Mean Coef of Var Mean Coef of Var gt 0 Stand Dev gt 0 Coef of Var gt 0 Mean Lower Bound Sigma Lower bound Mean gt Lower Bound Sigma gt 0 Mean Scale Scale gt 0 Mean Mean Lower Bound Theta Lower bound Mean gt Lower Bound Theta gt 0 Deg of Freed Mean Lower Bound Most Likely Upper Bound Lower Bound Mean Upper Bound Lower Bound Most Likely Upper Bound Mean must be within middle third of interval Mu Sigma Lower Bound Upper Bound Mu Coef of Var Lower Bound Upper Bound Mu Coef of Var gt 0 Sigma gt 0 Coef of Var gt 0 Lower Bound lt Upper Bound Lower Bound Upper Bound Mean Lower Bound Proban 3 56 Mean StD Mean Cov Weibull Mean StD Low Mean Cov Low Delt Bet Low Alp Beta Low 3 9 2 Distribution Fitting SESAM 01 OCT 2004 Program version 4 4 Mean Stand Dev Mean Coef of Var Stand Dev gt 0 Mean Coef of Var gt 0 Coef of Var gt 0 Lower Bound lt Upper Bound Mean gt Lower Bound Mean Stand Dev Lower Bound Mean Coef of Var Lower Bound Delta Beta Lower Bound Alpha Beta Lower Bound Mean gt Lower Bound Mean Coef of Var gt 0 Beta gt 0 Stand Dev gt 0 Coef of Var gt 0 Delta gt 0 Alpha gt 0 A Proban distribution result can be fitted to distributions in the Proban Distributions Library As an exam ple the distribution of NPV in Example 3 2 can be fitted to a normal distribution
226. lar result from the analysis using the selected value will be displayed This input is only required if the selected result is a two param eter study Value2 is then one of the second parameter values for which the study was run The particular result from the anal ysis using the selected value will be displayed A selection of one dimensional distribution variables with nu merical or fixed parameters or of results The following results may be available Empirical The empirical distribution from a simulation Mean V FORM The distribution calculated in a Mean value based FORM analysis Display the density function for the selected variable s For an empirical distribution a histogram is drawn see also SET GRAPH HISTOGRAM It is not possible to display the densi ty for a Mean V FORM result Display the distribution function for the selected variable s Display the complementary distribution function for the select ed variable s 1 The distribution and density functions are calculated within a range of three standard deviations on each side of the mean 2 When a distribution simulation is selected and no parameter study was performed two variables are fit ted to the estimated moments a Hermite transformation distribution using four moments and a Normal distribution using two moments These are available in the variables named Hermite Fit and Normal Fit Proban 5 120 01 OCT 2004 3 A histogram cannot be d
227. lculated with the value of variables in the model for lt event gt as arguments The selection of variables is made by using the command ASSIGN CONDITIONING See also CREATE VARIABLE e COPY VARIABLE RENAME VARIABLE PRINT VARIABLE e ASSIGN CONDITIONING EXAMPLES CHANGE VARIABLE P EVENT PROBABILITY RELIABILITY INDEX EVENAM Proban SESAM 5 44 01 OCT 2004 Program version 4 4 COPY EVENT EVENT from to PURPOSE To copy one event to another PARAMETERS from Name of the event to be copied to Name of the new event This cannot be the name of an existing event NOTES Only the basic contents of the event i e those defined in CREATE are copied Assignments are not copied See also e CHANGE EVENT e CREATE EVENT e DELETE EVENT e RENAME EVENT e PRINT EVENT DISPLAY EVENT ASSIGN MEASURED VALUE e ASSIGN STARTING POINT EXAMPLES COPY EVENT Moment 1 Moment 2 SESAM Program version 4 4 COPY VARIABLE VARIABLE from to PURPOSE To copy one variable to another PARAMETERS from to 01 OCT 2004 The name of the variable to be copied Proban 5 45 The name of the new variable This cannot be the name of an existing variable NOTES Only the basic contents of the event i e those defined in CREATE are copied Assignments are not copied See also CHANGE VARIABLE CREATE VARI
228. le may contain more than one plot 3 There is two ways of generating a plot By use of the PLOT command By use of SET DISPLAY DESTINATION FILE followed by a DISPLAY command 1 The CGM plot format is well suited for export of Proban plots to word processors such as Word FrameMaker and DecWrite You may transfer CGM files from one Operating System to another just make sure to use the binary option when transferring the file with FTP or another protocol 2 Proban creates a new file each time you plot with the CGM format Therefore you must specify a new name with each plot command Otherwise you will overwrite the previous one In Proban you may give a new plot file name with the command SET PLOT FILE lt prefix gt lt name gt See also SET DISPLAY DESTINATION PLOT EXAMPLES The following is default when the program starts with a new database SET PLOT COLOUR ON SET PLOT FILE same prefix and name as the database and journal file SET PLOT FORMAT SESAM NEUTRAL SET PAGE SIZE A4 SESAM Proban Program version 4 4 01 OCT 2004 5 215 SET PRINT FILE DESTINATION SCREEN FILE prefix name LANDSCAPE PAGE ORIENTATION PORTRAIT SCREEN HEIGHT nlines PURPOSE To set print characteristics PARAMETERS DESTINATION FILE prefix name PAGE ORIENTATION LANDSCAPE PORTRAIT SCREEN HEIGHT nlines NOTES Set the destination of the printed output to t
229. logical functions and the Misc library contains some functions that are generally useful These routines are useful building blocks from which many model functions can be built The following is a list of the print of the contents of the three libraries NumArg is the number of arguments in the function If the number of arguments is specified as Input it means that the function does not have a fixed number of arguments Examples of this are the Sum and the Product functions Math Function Dimen NArg NOp Description Abs ArcCos Deg ArcCos Rad ArcSin Deg ArcSin Rad ArcTan Deg ArcTan Rad Cos Degrees Cos Radians Absolute value ArcCosinus returning a value in ArcCosinus returning a value in 0 pi ArcSinus returning a value in ArcSinus returning a value in pi 2 pi 2 ArcTangens returning a value in 90 90 ArcTangens returning a value in pi 2 pi 2 Cosinus of an argument in degrees 0 360 Cosinus of an argument in radians Cosh Hyperbolic cosinus exp x exp x 2 Exp Exponential function Fraction 1 Fraction part of a number Indicator EQ 2 Indicator 1 if X1 X2 0 otherwise Indicator GE 2 Indicator 1 if Xl gt X2 0 otherwise Indicator GT 2 Indicator 1 if X1 gt X2 0 otherwise Indicator LE 2 Indicator 1 if X1 lt X2 0 otherwise Indicator LT 2 Indicator 1 if X1 lt X2 0 otherwise Integer Strip away decimal part of
230. lue of all distribution variables as basis excepting the specified modifications the median will be used if the mean cannot be calculated se the median value 50 fractile of all distributions as basis excepting the specified modifications Input of values that are to overwrite values specified elsewhere Name is a one di mensional variable of distribution type and value is either a single numerical value or fracxx the fractile at xx probability level followed by a numerical value The frac is case insensitive Notice the preceding hyphen Calculate the limit state value of an event The limit state value is left hand side right hand side for a single event minimum of all subevent values for an intersec tion maximum of all subevent values for a union Conditional events cannot be used here The name of the event for which an analysis is made SESAM Proban Program version 4 4 01 OCT 2004 5 179 STARTING POINT Use the starting point for the event if assigned If no starting point is assigned the default starting point is used USPACE ORIGIN Calculate the value at the U space origin identical to the median values NOTES 1 The result is stored under the name LastAnalysis and is overwritten the next time an analysis is per formed unless saved under another name using the SAVE RESULT command 2 The results are examined by use of the commands PRINT RESULT or DISPLAY RESULT See also ASSIGN STARTING POIN
231. ly hit this content a few times and it will get a result that is dif ferent from the others each time it does so This illustrates the weakness of basing a simulation upon an approximated result The strength of doing this lies in the calculation speed when the FORM approximation is sound The number of lines in the table is controlled by use of the command DEFINE RESULT OPTION INTER MEDIATE RESULTS It is possible to print and display the sample of correction values using the commands PRINT RESULT SAMPLE and DISPLAY RESULT DISTRIBUTION These commands and the results are described in Sec tion 3 6 1 The simulation may be restarted from the previous result by using the command RUN RESTART The stop criteria may be changed before the run is restarted This is useful e g for estimating the time a simulation need to run in order to produce a required accuracy on the result or for continuing a simulation that did not produce the desired accuracy A conditional probability analysis 1s split into two analysis The first for the intersection event and the sec ond for the conditioning event The sample cannot be printed in this case 3 4 First Passage Probability and Results 3 4 1 Definition of a Stochastic Process for Calculation of First Passage Probability A stochastic process is defined by assigning a random variable as the time derivative process of another ran dom variable Typically X and XDOT The variables X and XDOT must be variable
232. mal Inverse of Std Normal Inverse of Std Normal Inverse of Std Normal Exponential distribution Gamma distribution Inverse of Std Normal Gen Gamma distribution Inverse of Std Normal Gumbel distribution Inverse of Std Normal Hermit secon distribution Inverse of Std Normal Hermit trans distribution Inverse of Std Normal Inv Gauss distribution Inverse of Std Normal Lognormal distribution Inverse of Std Normal Long Higgins distribution Inverse of Std Normal Maxwell distribution Inverse of Std Normal Onesi Normal distribution Inverse of Std Normal Oval distribution Inverse of Std Normal Rayleigh distribution Inverse of Std Normal Student t distribution Inverse of Std Normal Triangle distribution Inverse of Std Normal Trunc Normal distribution Inverse of Std Normal Weibull distribution Inverse of Std Normal Beta distribution Standard Normal fractile Burr distribution Standard Normal fractile Chi square distribution distribution Exponential Standard Normal fractile Standard Normal fractile Gamma distribution Gen Gamma distribution Gumbel distribution Hermit secon distribution Standard Normal fractile Standard Normal fractile Standard Normal fractile Standard Normal fractil SESAM Program version 4 4 U Hermit t U Inv Gaus U Lognorma U Long Hig U Maxwell U Onesi No U Oval U Rayleigh
233. manager could be more certain about his income from this project he would reduce his probability of a loss It is not nearly as important to control the uncertainty on the expenses The importance factors may also be displayed in a pie chart The following commands generate a plot file with the importance factor plot without generating a screen display SET DISPLAY DESTINATION FILE DISPLAY RESULT IMPORTANCE FACTORS The PLOT command could have been used after the display instead of setting the display destination to file Proban SESAM 3 24 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Importance Factors NPV lt 0 0 Net Present Value Figure 3 4 Importance factors for probability of loss in Example 3 2 The sensitivity factors are shown in three tables One for the probability one for the reliability index and one for the logarithm of the probability The tables have the same layout The table for the probability is Parametric sensitivity result for Probability 0 29648506009 Variable Type Parameter Value dProb dPar SD deri Measure TE Triangle Mean 7 500E 04 3 571E 05 2 76E 06 2 68E 01 El Lognormal Mean 5 000E 03 3 372E 05 2 77E 06 1 69E 02 12 Triangle Mean 5 000E 04 3 291E 05 2 56E 06 1 65E 01 E2 Lognormal Mean 1 000E 04 3 059E 05 2 50E 06 3 06E 02 Normal Mean 1 000E 04 3 060E 05 2 50E 06 3 06E 02 Note that the table includes a standard deviation SD de
234. mand 3 The results are examined by use of the commands PRINT RESULT or DISPLAY RESULT 4 Variables with type attribute PROBABILITY cannot be used in a crossing rate analysis See also DEFINE ANALYSIS OPTION DEFINE FORM SORM DEFINE PARAMETER STUDY SELECT ANALYSIS METHOD FIRST PASSAGE PROBABILITY ANALYSIS e SAVE RESULT SESAM Proban Program version 4 4 01 OCT 2004 5 177 e PRINT RESULT e DISPLAY RESULT EXAMPLES RUN CONTINUOUS PROCESS ANALYSIS FIRST PASSAGE PROBABILITY FP_Ev RUN CONTINUOUS PROCESS ANALYSIS FIRST PASSAGE PROBABILITY SINGLE EVENT FP Var gt 50 Proban 5 178 SESAM 01 OCT 2004 Program version 4 4 RUN DETERMINISTIC ANA LYSIS DETERMINISTIC ANALYSIS MEAN VALUE MEDIAN VALUE VARIABLE variable MEAN BASED MODIFIED name value MEDIAN BASED STARTING POINT EVENT event USPACE ORIGIN PURPOSE Run a deterministic analysis PARAMETERS VARIABLE variable MEAN VALUE MEDIAN VALUE MODIFIED MEAN BASED MEDIAN BASED name value EVENT event Calculate the value of a variable The name of the variable for which the analysis is made U U mean cannot be calculated U U U se the mean value of all distribution variables the median will be used if the se the median value 50 fractile of all distributions se the mean or median as basis se the mean va
235. meter value 6 Present the results as a function of the parameter using PRINT RESULT PARAMETER STUDY and DISPLAY RESULT PARAMETER STUDY and or present the individual analysis results using PRINT RESULT and DISPLAY RESULT If the next analysis is to be done without using the parameter study there are two options available DEFINE ANALYSIS OPTION PARAMETER STUDY OFF temporarily disabling the parameter study and ASSIGN PARAMETER STUDY lt current parameter gt EXCLUDE removing the assignment When a parameter study has been run the main results and importance factors if available can be printed and displayed as a function of the parameter The available main results are listed in Section 2 10 As an example consider Example 3 2 described in Section 3 1 The manager wishes to investigate the connection between the Net Present Value of the project and the required rate of return Two parameter studies are done One for the distribution of the NPV and one for the probability of a loss The parameter study for r in the range from 1 to 15 is assigned as follows Proban 3 42 EFINE Defined par 4 0E 02 5 0 0 15 01 OCT 2004 PARAMETER STUDY r GROUP 0 01 0 15 0 01 ameter study for r using the values 1 0E 02 2 0 E 02 6 0E 02 7 0 E 02 8 0 E 02 9 01 For this analysis no parametric sensitivity values are required ASSIGN S Deassigned Deassigned Deassigned Deassign
236. method See DEFINE RFCRC The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e PRINT ANALYSIS SETTINGS EXAMPLE The following values are default when the program starts up with a new database EFINE ANALYSIS OPTION GENERAT 1 0E 6 1 0E 10 ED DISTRIBUTION INTERMEDIATE RESULTS NONE EFINE ANALYSIS OPTION GENERA EFINE ANALYSIS OPTION GENERAT 0 1 72633D 7 0 0 eon EFINE ANALYSIS OPTION GENERAT 1 72633D 7 ED DISTRIBUTION DIFFERENTIATION 1 0E 6 1 0E 3 1 0E ED DISTRIBUTION FRACTILE FROM PROBABILITY UNMIN 40 ED DISTRIBUTION PROBABILITY FROM FRACTILE SQP 40 10 SESAM Program version 4 4 01 OCT 2004 Proban 5 75 DEFINE ANALYSIS OPTION NESTED ANALYSIS NESTED ANALYSIS GLOBAL DIFFERENTIATION uspacel uspace2 relative absolute limit SYSTEM ANALYTICAL GLOBAL GRADIENT CALCULATION ONEWAY INCREMENTATION SYSTEM TWOWAY INCREMENTATION GLOBAL U SPACE BOUNDS VALUE SYSTEM NONE GLOBAL LOW INTERMEDIATE RESULTS MEDIUM SYSTEM EXCESSIVE PURPOSE Define analysis options for usage of nested analyses PARAMETERS GLOBAL SYSTEM DIFFERENTIATION uspacel uspace2 relative absolute limit Outer level of a nested analysis Inner level of a ne
237. ming mode Comments are prefixed by the percent sign Everything from the percent sign to the end of the line is treated as a comment A comment need not be the first item on a line Example 4 3 CREATE VARIABLE Time TIMESIn seconds This is a comment 4 5 Using the Graphics Mode User Interface The Proban graphics environment offers a main window with the following parts from top to bottom e Title bar This is the name of the program that is being run e Main menu This menu gives access to all the commands of Proban e Short cut buttons The first three toggles command input mode on and off reads a command input file and closes a command input file This last button is only active when a command input file is open The last three buttons will cut copy and paste texts to and from the text input areas of Proban e Message area This is used to show messages to the user plus commands that have been typed into the command input line as well as those that have been read from command input files Command input line This line contains the prompt for line mode input showing the default when this is available followed by a field which is used to type line mode commands All facilities that are described in Section 4 4 are available through this line Proban SESAM 4 16 01 OCT 2004 Program version 4 4 me PROBAN 4 3 03 fx File Function amable Process Event Analysis Result Options Help User id E CPU id
238. mmand see also the description there This number controls when prompts are issued as described above as well as the insertion of inter mediate headers in a table when the table scrolls out of the screen Some of the print tables used for model verification are shown below The following table shows the print of a distribution variable PRINT VARIABLE RAl Type Name Dim Parameter Value Sens Distribution Inv Gauss 1 Mean 110 0 Off Coef of Var 0 1 off Lower Bound 0 0 off Calculated parameters Stand Dev 11 0 Skewness 0 3 Kurtosis 3 15 Median 109 453185 Proban 3 8 01 OCT 2004 SESAM Program version 4 4 Note that those moments that are not given as input will be calculated and printed when this is possible This is the print of a function variable PRINT VARIABLE Al Variable l A1 Failure criterion for component A1 Type Name Dim Parameter Value Function Difference 1 Additive Arg RA1 Subtract Arg Load This it the print of the system event in Example 3 1 PRINT EVENT System System Event type Subevent Subtype Contents Union A Intersection 3 sub events B Single B lt 0 0 Cc Single C lt 0 0 Other event types are printed similarly The correlation between the two expenses in Example 3 2 is printed with the command PRINT CORRELATION INCLUDE Because it is the only correlation that has been defined no other correlation will be printed T
239. mpany owner estimates that he can have income from selling computer time the following two years of respectively NOK 75000 and NOK 50000 He further estimates that the maintenance costs will be respectively NOK 5000 and 10000 in the two years and assumes that after two years it will be difficult to sell computer time It is estimated that the computer then will be sold at NOK 10000 The customers will run the computer themselves via termi nals so the company s cost of running the computer is negligible There is no other use of the computer Inflation is assumed to be negligible The company requires a minimum 10 percent rate of return on its investments The Net Present Value can be expressed as NPV Cp 1 E N 0 9 0 ry where Cy is the initial investment J is the income in year i E is the expense in year i S is the scrap value and r is the required rate of return The variables are assigned the following distributions Table 3 2 Example NPV Variables Variable Type Parameter Value CO Fixed 100000 r Fixed 0 1 Il Triangle distribution Lower 60000 Mean 75000 Upper 90000 D Triangle distribution Lower 30000 Mean 50000 Upper 70000 SESAM Program version 4 4 Proban 01 OCT 2004 3 5 Table 3 2 Example NPV Variables El Lognormal distribution Mean 5000 Stdv 1000 Low 0 E2 Lognormal distribution Mean 10000 Stdv 2000 Low 0 S Normal distribution M
240. mple the event that a Net Present value is negative or the event that at least one of three components in a series system fail There are four different types of events in Proban Single A single event is the event that a value of a variable is less than equal to or greater than a numerical threshold value The single event is the basic event in Proban Intersection An intersection event is an intersection of other events i e it is fulfilled only when all subevents are fulfilled All events except conditioned events may be subevents in an intersection Proban SESAM 2 4 01 OCT 2004 Program version 4 4 Union A union event is a union of other events i e it is fulfilled if at least one of the sub events is fulfilled All events except conditioned events may be subevents in a un ion Conditioned A conditioned event facilitates analysis of conditional probability It has two sub events the event that is conditioned and the event condition on All events except conditioned events may be used to define a conditioned event As with variables this provides for a great flexibility in definition of events Unions and intersections can be built on top of each other freely defining a complex network of events if required 2 2 3 Extreme Values A uni variate random variable with one of the type attributes Distribution Fitted distribution and Gener ated can have its definition replaced by the maximum or minimum of an integer number of ind
241. n a large number of functions and or not be relevant to the current problem See also e CHANGE VARIABLE e PRINT VARIABLE PRINT FUNCTION e SELECT FUNCTION LIBRARY e ASSIGN WAVE DIRECTION PROBABILITY CHANGE WAVE STATISTICS PRINT WAVE STATISTICS e ASSIGN MODEL FACTOR SCATTER DISTRIBUTION e ASSIGN MODEL FACTOR WAVE SPECTRUM SHAPE e ASSIGN MODEL FACTOR WAVE SPREADING e ASSIGN UNCERTAINTY VALUE Proban SESAM 5 66 01 OCT 2004 Program version 4 4 EXAMPLES CREATE VARIABLE Total Durati Total duration of project FUNCTION Sum EXCLUDE Path 1 CREATE VARIABLE Diff1 FUNCTION Difference Resist Load4 SESAM Proban Program version 4 4 01 OCT 2004 5 67 CREATE VARIABLE PROBABILITY RELIABILITY INDEX PROBABILITY PROBABILITY event LOG PROBABILITY PURPOSE To create a variable to have the probability of an event as value PARAMETERS RELIABILITY INDEX Reliability index corresponding to the probability of event PROBABILITY Probability of event LOG PROBABILITY Natural logarithm of the probability of event event Name of an existing event NOTES 1 Event must not be a conditional event or contain equality events 2 Event must be calculable by using FORM 3 The probability of event may be calculated with the value of variables in the model for event as argu ments The selection of variables is made by using the command ASSIGN CONDITIONING
242. n of G conditioning Z on a and assigning the appropriate extreme value to Z X2 G x a Z F Z3 Zo 24 G X a Z Figure 2 2 Generated Distribution Distribution of level surfaces Geometrically the Generated distribution is the distribution Fz of level surfaces z G X a of the corre sponding function of random variables The vector a is the current realisation of variables conditioned on Three points on the distribution are shown in Figure 2 2 The Probabilities and fractiles of a generated distri bution are approximated by pointwise application of the FORM method Because the random variables X are integrated out in the calculation process the random variable Z is uncorrelated with other variables unless such correlation is explicitly defined Dependency on other variables is modelled through the varia bles conditioned on An arbitrary number of generated distributions can be defined Random variables having generated distributions can be correlated with other distribution variables It is not possible to include a generated distribution or a probability variable in the vector X above since those variables introduce an extra level of optimization Calculations of fractile from probability and probability from fractile generally require different optimiza tion algorithms Optimization criteria and differentiation increments are defined separately for the generated distribution Proban SESAM 2 8 01 OCT 2004 Program v
243. n of bounds involves a probability variable or a time dependent stochastic process Equality events mostly come up in analyses involving inspection and updating where a quantity is observed to be equal to some value In this situation however the variable which keeps the measurement information must be assigned to the equality event since the corresponding conditional probability is calculated from sensitivity factors with respect to the measured value The two examples Fatigue crack growth and Creep in concrete from the example manual 3 contain analyses of inspection and updating using equality events However in order to document the results consider the follow hypothetical example CHANGE EVENT B SINGLE B 0 Proban 3 18 RUN PROBABILITY ANALYSIS Simple Starting Probabil Starting FORM cal lculation Starting linearization of Union of FORM Derivative of Probability Al B C Linearization completed Calculating importance factors 01 OCT 2004 lity Analysis of Simple 1 48788E 0 The print is similar to the print that has been described previously 5 SESAM Program version 4 4 Conditional probability calculation is straightforward to execute This will be demonstrated using Example 3 2 To calculate the probability P NPV lt 0 I gt 70000 P NPV lt 0A T gt 70000 P 1 gt 70000 using FORM SORM Proban first finds the intersection probability in the n
244. name of an existing one dimensional variable Please note that the name of a variable cannot be abbreviated here NOTES 1 The existing values are presented as defaults whenever this is possible 2 The variables that are created by this program should not be changed by the user 3 The selection of functions presented is determined by the current selection of sub libraries see SELECT FUNCTION LIBRARY This is because some libraries may contain a large number of functions and or not be relevant to the current problem See also CREATE VARIABLE PRINT VARIABLE PRINT FUNCTION e SELECT FUNCTION LIBRARY EXAMPLES CHANGE VARIABLE Total Durati FUNCTION Sum EXCLUDE Path 1 CHANGE VARIABLE Diff1 FUNCTION Difference Resist5 Load4 SESAM Proban Program version 4 4 01 OCT 2004 5 43 CHANGE VARIABLE PROBABILITY RELIABILITY INDEX PROBABILITY PROBABILITY event LOG PROBABILITY PURPOSE To change a variable to have the probability of an event as value PARAMETERS RELIABILITY INDEX The reliability index corresponding to the probability of event PROBABILITY The probability of event LOG PROBABILITY The natural logarithm of the probability of event event The name of an existing event NOTES 1 lt event gt must not be a conditional event or contain equality events 2 lt event gt must be calculable by using FORM 3 The probability of lt event gt may be ca
245. nction formula s to be deleted NOTES Deletion cannot be undone The only way to undo a deletion is to edit the command s generating the deleted object from the journal file and then read the command input file into the program again See also e CREATE FUNCTION e CHANGE FUNCTION e RENAME FUNCTION DISPLAY FUNCTION e PRINT FUNCTION EXAMPLES DELETE FUNCTION SYMFUN Proban 5 110 DELETE RESULT RESULT name PURPOSE Delete one or more results PARAMETERS name NOTES Name s of the result s to be deleted SESAM Program version 4 4 1 Deletion cannot be undone The only way to undo a deletion is to edit the command s generating the deleted object from the journal file and then read the command input file into the program again 2 Those results created by this program should not be deleted by the user See also e RUN PROBABILITY ANALYSIS e RUN DISTRIBUTION ANALYSIS e SAVE RESULT DISPLAY RESULT e PRINT RESULT EXAMPLES DELETE RESULT Prob SESAM Proban Program version 4 4 01 OCT 2004 5 111 DELETE VARIABLE VARIABLE name PURPOSE Delete one or more variables PARAMETERS name Name s of the variable s to be deleted NOTES 1 Deletion cannot be undone The only way to undo a deletion is to edit the command s generating the deleted object from the journal file and then read the command input file into
246. nd 3 The simulation will run until any one of the stop criteria has been met 4 Sensitivity calculation is not possible with this analysis method See also e PRINT ANALYSIS SETTINGS SELECT ANALYSIS METHOD PROBABILITY ANALYSIS EXAMPLES The following values are default when the program starts up with a new database SESAM Proban Program version 4 4 01 OCT 2004 5 99 DEFINE PROBABILITY ANALYSIS DESIGN POINT COEFFICIENT OF VARIATION 0 DEFINE PROBABILITY ANALYSIS DESIGN POINT CPU TIME 60 EFINE PROBABILITY ANALYSIS DESIGN POINT SIMULATIONS 1000 J Proban 5 100 01 OCT 2004 SESAM Program version 4 4 DEFINE PROBABILITY SIMULATION DIRECTIONAL COEFFICIENT OF VARIATION cov CPU TIME cpu DEFAULT RANDOM DIRECTION METHOD ORTHOGONAL 1 ORTHOGONAL 2 ORTHOGONAL 3 DIRECTIONAL RISKY AND FAST SEARCH MEDIUM SAFE SAFE AND SLOW TOS PROBABILITY probvalue STANDARD NORMAL argvalue STEP LENGTH length SIMULATIONS nsim RESET PURPOSE Define analysis options for directional simulation of a probability PARAMETERS COEFFICIENT OF VARIATION cov CPU TIME cpu METHOD DEFAULT The simulations will stop if the coefficient of variation of the simulated result becomes lower than or equal to cov To disable this stop criterion set cov to 0 The cov must be non negative The simulations will stop when the cpu time in s
247. ne analysis options for Monte Carlo simulation of a probability PARAMETERS COEFFICIENT OF VARIATION cov The simulations will stop if the coefficient of variation of the CPU TIME cpu SIMULATIONS nsim RESET NOTES simulated result becomes lower than or equal to lt cov gt To dis able this stop criterion set cov to 0 cov must be non negative The simulations will stop when the cpu time cpu in seconds has been exceeded The check is performed after each simula tion is completed To disable this stop criterion set cpu to 0 cpu must be non negative The simulation will stop after nsim simulations has been com pleted nsim must be a positive whole number Reset all values and options to the default values used when in itialising a new database 1 The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command 2 The simulation will run until any one of the stop criteria has been met 3 Sensitivity calculation is not possible with this analysis method See also PRINT ANALYSIS SETTINGS SELECT ANALYSIS METHOD PROBABILITY ANALYSIS EXAMPLES The following values are default when the program starts up with a new database DI DI EFINE PROBABILITY ANALYSIS MONTE CARLO COEFFICIENT OF VARIATION 0 EFINE PROBABILITY ANALYSIS MONTE CARLO CPU TIME 60 Proban SESAM 5 104 01 OCT 2004 Program version 4 4 DEFINE PROBABILITY ANALYSIS MONTE CARLO SIMULATIONS
248. ne mode command input area If the main window is iconised all the open dialog boxes disappear into the icon They pop up again when the main window is popped up In addition to this the graphics environment consists of e Pulldown menus These are pulled down from the items in the main menu They are activated by clicking on an item in the main menu with the left mouse button or by holding the left mouse button down on an item in the main menu Similarly some of the items in a pulldown menu may have a sub menu sliding sidewards from the parent menu To select an item in a pulldown menu click on it or drag the mouse pointer to the item and release the button Proban SESAM 4 18 01 OCT 2004 Program version 4 4 e Dialog boxes Much of the user interaction will happen through dialog boxes Those items in the pull down menus that have three dots following the item label all open a dialog box when selected The dia log box is described more fully in Section 4 5 3 Print window After the first Print command has been issued a print window will pop up This is a scrol lable window that contains all the output from the Print command that is directed to the screen The window has a limited buffer so if a single print command generates excessive amounts of print some of it may disappear out of the top of the window The print window may be iconised separately from the main window It is possible to print inside an iconised print window It do
249. ng print Variable Type Parameter Value StdNormal Normal Mean 0 000000000E 00 Stand Dev 1 000000000E 00 Fractile Distr Compl Density 3 090232306E 00 0 001000 0 999000 3 367090077E 03 2 326347874E 00 0 010000 0 990000 2 665214220E 02 1 644853627E 00 0 050000 0 950000 1 031356404E 01 1 281551566E 00 0 100000 0 900000 1 754983319E 01 1 036433389E 00 0 150000 0 850000 2 331587753E 01 8 416212336E 01 0 200000 0 800000 2 799619204E 01 6 744897502E 01 0 250000 0 750000 3 177765727E 01 5 244005127E 01 0 300000 0 700000 3 476926142E 01 2 533471031E 01 0 400000 0 600000 3 863425335E 01 5 293868432E 14 0 500000 0 500000 3 989422804E 01 2 533471031E 01 0 600000 0 400000 3 863425335E 01 5 244005127E 01 0 700000 0 300000 3 476926142E 01 6 744897502E 01 0 750000 0 250000 3 177765727E 01 8 416212336E 01 0 800000 0 200000 2 799619204E 01 1 036433389E 00 0 850000 0 150000 2 331587753E 01 1 281551566E 00 0 900000 0 100000 1 754983319E 01 1 644853627E 00 0 950000 0 050000 1 031356404E 01 2 326347874E 00 0 990000 0 010000 2 665214220E 02 Proban 5 138 PRINT EVENT EVENT name PURPOSE Print information about one or more events PARAMETERS name NOTES Name s of event s to be printed SESAM Program version 4 4 The printout contains information about the event data including all assignments except starting point See also
250. ns by transforming the variables to standard normal variables as described in Section 2 3 1 before defining the correlation the usual way between the standard normal variables This yields the Nataf distribution model which is the natural generalisation of the Multi Normal distribution to correlation of non normal random variables The Nataf distribution model may define a valid range of a basic correlation coefficient as a b with a and b strictly less than 1 Illegal basic correlation indicates that non linear dependency is present in the model and that this is not captured by the Nataf distribution model Correlation of normal random variables can also be input by use of a Multi Normal distribution This is a multidimensional distribution with normal marginal distributions and a full correlation matrix Notice that creating dependencies between variables will introduce correlation As an example if both A and B are functions of C and C is a random variable A and B will be dependent and most likely also corre lated This provides a means to model statistical dependency that is not captured by the Nataf model 2 2 5 Time Derivatives A continuous stochastic process is modelled through variables which represent the stochastic process and their corresponding time derivatives A process variable and its corresponding time derivative variable are both random variables with the same dimension and with type attributes Distribution Fitted distributi
251. nsists of maximum 50 characters 3 The text value integrator may be an attribute of more than one function parameter See also e CREATE FUNCTION INTEGRAL DISPLAY FUNCTION Proban SESAM 5 30 01 OCT 2004 Program version 4 4 e PRINT FUNCTION e RENAME FUNCTION EXAMPLES Change integration of c x from x a to x b to c c a b x x from x a to x b CHANGE FUNCTION cplusx Integrate c c atb x x from x a to x b INTEGRAL ONLY a x lower b x upper c additive parameter Sum ONLY c c a b Integrator In tegrator Romberg a b 0 000001 SESAM Program version 4 4 Proban 01 OCT 2004 5 31 CHANGE FUNCTION RESPONSESURFACE RESPONSESURFACE argname argdesc function point argname method increment PURPOSE To change a response surface function PARAMETERS argname argdesc function point argname method increment NOTES Matrix of argument names and corresponding argument descriptions At least one argument must be defined Name of function to be approximated Centre of approximations Argument name This approximated function argument becomes the argument ar gname of the approximation Function fit method to be used L or L1 Linear approximation based on positive incrementation L2 Linear approximation based on two way incrementation D Quadratic diagonal approximation No cross der
252. nt The ab solute increment is used if the absolute value of the parameter is less than limit It must be positive Define analysis options for use of generated distributions See a following page Determines if the gradients that have been programmed into the model functions are used ANALYTICAL or if one way u du or two way u du and u du incrementation is used to determine the gradient NUMERICAL is obsolete but points to one way incrementation Initialises the u space optimisation upper bounds to Value and the u space lower bounds to Value Controls if importance factors are calculated ON OFF During an analysis intermediate results may be stored on the database and possibly written to the screen This is mainly in order to facilitate debugging of the probabilistic model Controls if gradient values are shown during the analysis Controls the amount of intermediate results to be generated The possible alternatives are NONE LOW MEDIUM EX CESSIVE Controls if point values e g values of variables forming single events are shown during the analysis SESAM Program version 4 4 SHOW DURING ANALYSIS NESTED ANALYSIS PARAMETER STUDY SEEDS DEFAULT RANDOM seed1 seed2 eed3 SENSITIVITY NOTES Proban 01 OCT 2004 5 71 Controls whether the immediate results will be shown on the screen during the analysis run Please take care as excessive amounts of output may be generated Define analysis op
253. nt value or be assigned an existing random variable A fitted distribution variable is assigned one of the distribu tions that are available in Proban by use of distribution fit on observations on fractiles on the results ofa Proban distribution analysis or on the results of a Proban parameter study on prob ability A function variable is assigned one of the functions that are available in Proban The function is either created interactively or coded and linked into Proban Each argument in the function may be defined as a constant value or be assigned an existing random variable SESAM Proban Program version 4 4 01 OCT 2004 2 3 Generated A generated distribution variable is assigned the distribution defined by another random variable as its distribution type The distribution type may be conditioned on values of variables in the definition of the other random variable Probability A probability variable is assigned the probability of an event possibly in terms of the corresponding reliability index or log probability The probability may be conditioned on the values of selected variables in the event model Time A time variable is the time parameter of a time dependent sto chastic process It permits time to be an explicit parameter of a probabilistic model A great flexibility is obtained in that a variable can be used as argument or parameter in another variable Most distributions in Proban allow for several ways to def
254. ntegrand Value can be a numerical value or an input argument name argname Text value integrator Case insensitive The text value integrator is inserted in order to identify the single integration variable Integration method to be used One of ROMBERG SIMPSON or TRAPEZOI DAL Lower bound for integrator Must be a numerical value or an argument name ar gname Upper bound for integrator Must be a numerical value or an argument name ar gname Relative precision in result of integration 1 An argument name consists of maximum 12 alphanumeric characters and _ The first character must be alphabetic 2 An argument description consists of maximum 50 characters 3 The text value integrator may be an attribute of more than one function parameter See also e CHANGE FUNCTION INTEGRAL e DISPLAY FUNCTION SESAM Proban Program version 4 4 01 OCT 2004 5 53 e PRINT FUNCTION e RENAME FUNCTION EXAMPLES Integrate c x from x a to x b CREATE FUNCTION cplusx Integrate c x from from a to b INTEGRAL ONLY a x lower b x upper c additive parameter SUM ONLY c Integrator Romberg a b 0 000001 Proban 5 54 SESAM 01 OCT 2004 Program version 4 4 CREATE FUNCTION RESPONSESURFACE RESPONSESURFACE argname argdesc function point argname method increment PURPOSE To cre
255. o avoid averaging both the duration assigned to Time and the default value must be turned off The following commands assures that the crossing rate is averaged over duration ASSIGN CONTINUOUS PROCESS STARTING TIME Time 1000 ASSIGN CONTINUOUS PROCESS DURATION Time 10800 The following commands assures that the crossing rate is calculated at time 5000 ASSIGN CONTINUOUS PROCESS STARTING TIME Time 5000 ASSIGN CONTINUOUS PROCESS DURATION Time NONE DEFINE CONTINUOUS PROCESS DURATION NONE The crossing rate calculation is invoked by the command RUN CONTINUOUS PROCESS ANALYSIS CROSSING RATE Notice that Proban sets up the FORM analysis required to solve the problem If the model involves a distri bution variable not assigned a time derivative or assigned as a time derivative then Proban sets up a nested FORM analysis and the options for nested FORM analysis applies When a time variable is present in the model and a duration is specified then time is integrated over by use of a trapezoidal rule The integration is by default over the duration taken from the starting point This inter val may be reduced in order to capture the significant part of the time interval DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS INTEGRATION INTERVAL 9000 10800 The number of points in the quadrature may be manipulated by the command DEFINE CONTINUOUS PROCESS ANALYSIS OPTIONS POINTS IN QUADRATURE 20
256. odel and results It has the extension mod The JOURNAL file is used to keep a log of most of the commands that are accepted during a Proban ses sion If an existing OLD database is opened the journal will be appended to the corresponding old journal file if this exists The journal file has the extension jn The COMMAND INPUT file is used to read commands and data into Proban The usage of command input files is described in Table 4 4 2 The default extension of a command input file is jnl but this default is not used if another extension is specified The PRINT file is used to keep output from the PRINT command when the print destination is set to FILE The extension of the print file is lis The print file name and settings is specified using the command SET PRINT It is possible to use more than one print file during the same Proban session but only one can be open at a time The PLOT file is used to keep output from the PLOT command and from the DISPLAY command when the display destination is set to file The plot file name and settings is specified using the command SET PLOT SESAM Proban Program version 4 4 01 OCT 2004 4 7 The extension of the plot file depends on the plot format used If the SESAM neutral format is used the extension is plo Several other formats are available including Postscript with extension PS It is pos sible to use more than one plot file during the same Pro
257. ogram should not be changed by the user See also PRINT EVENT EXAMPLES ASSIGN MEASURED VALUE FindCrack am SESAM Program version 4 4 01 OCT 2004 ASSIGN OPTIMISATION BOUNDS Proban 5 17 OPTIMISATION BOUNDS variable MODEL SPACE lower upper U SPACE OFF OFF PURPOSE Assign bounds on variables to be used in FORM SORM optimization PARAMETERS variable MODEL SPACE U SPACE lower upper OFF NOTES Name of variable to which the bounds are assigned This is a one dimensional distribution variable or a generated distribu tion variable Bounds are specified in model space physical input values Bounds are specified in the transformed normal space Value of the lower bound Value of the upper bound The default bound is used The optimization bounds assigned to a variable are printed by use of the PRINT VARIABLE command See also e PRINT VARIABLE EXAMPLES ASSIGN OPTIMISAT ASSIGN OPTIMISAT PION BOUNDS Load U SPACE 20 20 PION BOUNDS Amplitude MODEL SPACE 0 OFF Proban SESAM 5 18 01 OCT 2004 Program version 4 4 ASSIGN SENSITIVITY CALCULATION INCREMENT VARIABLE SENSITIVITY CALCULATION PURPOSE Assign sensitivity calculation parameters and increments PARAMETERS INCREMENT Assign increment value to be used for sensitivity calculation VARIABLE Select parameters
258. ole system fails if either B1 fails or C1 fails or all three A components fail This can be modelled as a union of these three subevents The system with no redundancy in A is modelled similarly This is entered into Proban with the following commands CREATE EVENT LOOP Al Failure of component Al SINGLE Al lt 0 0 A2 Failure of component A2 SINGLE A2 lt 0 0 Proban SESAM 3 4 01 OCT 2004 Program version 4 4 A3 Failure of component A3 SINGLE A3 lt 0 0 B Failure of component B SINGLE B lt 0 0 C Failure of component C SINGLE Cc lt 0 0 A Failure of all A components INTERSECTION A System Failure of the system UNION ONLY A BC Simple Failure with no redundancy in A UNION ONLY Al BC END The analysis is treated in the following sections However the following commands may be used in an inter active session to create the necessary results and print them Note that the summary results given with the runs will answer questions a and b RUN PROBABILITY ANALYSIS System PRINT RESULT IMPORTANCE FACTORS RUN PROBABILITY ANALYSIS Simple These commands will run the currently selected probability analysis which by default is a FORM analysis Another analysis method may be selected by use of the SELECT ANALYSIS METHOD PROBABILITY ANALYSIS command Example 3 2 Economical Investment A small company is offered a used computer at the cost of NOK 100000 The co
259. on or Generated The mean value of a time derivative variable must be zero Proban SESAM 2 6 01 OCT 2004 Program version 4 4 A continuous stochastic process can be viewed as a particle which moves continuously in time see Figure 2 11 2 2 6 Measured Values A variable may model the measurement of a physical quantity e g the depth of a crack in a beam subjected to fatigue loading One may wish to calculate the reliability of the beam conditioned on the information obtained by the measurement A single equality event models the event that the crack has grown to the measured depth and the measured value variable models the uncertainty of the measurement It is necessary to attach the measured value variable to the single equality event in order to calculate a cor rect conditional probability since the calculation depends on this relation The attachment is specified on input 2 2 7 Model Functions Most of the complexity of the model to be analysed is hidden inside the model function A model function can be coded by the user and linked into Proban or be created interactively as a function formula In many cases the set of built in functions together with the function formula facility will be sufficient to build the required model Because of the flexibility Proban offers for definition of variables a basic set of functions provides building blocks from which a great many models can be built Proban is delivered with the basic arithmetic
260. ondence D u probval The search method steps out in the u space in search for zero points until the probability of the remaining line becomes Proban SESAM 5 102 01 OCT 2004 Program version 4 4 negligible as specified by the search limit Starting from u 0 the next step iS Unext Ucurrent length SIMULATIONS nsim The simulation will stop after nsim simulations has been com pleted nsim must be a positive whole number RESET Reset all values and options to the default values used when in itialising a new database NOTES 1 The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command 2 The simulation will run until any one of the stop criteria has been met See also PRINT ANALYSIS SETTINGS SELECT ANALYSIS METHOD PROBABILITY ANALYSIS EXAMPLES The following values are default when the program starts up with a new database DEFINE PROBABILITY ANALYSIS DIRECTIONAL COEFFICIENT OF VARIATION 0 EFINE PROBABILITY ANALYSIS DIRECTIONAL CPU TIME 60 EFINE PROBABILITY ANALYSIS DIRECTIONAL METHOD DEFAULT EFINE PROBABILITY ANALYSIS DIRECTIONAL SEARCH MEDIUM SAFE EFINE PROBABILITY ANALYSIS DIRECTIONAL SIMULATIONS 50 D D D D SESAM Proban Program version 4 4 01 OCT 2004 5 103 DEFINE PROBABILITY SIMULATION MONTE CARLO COEFFICIENT OF VARIATION cov CPU TIME cpu MONTE CARLO SIMULATIONS nsim RESET PURPOSE Defi
261. ottier allas 3 9 Probability Analysis and Results cccccccsccssececeessessecseceeecseeeescecsaenseceseesseeesecsaeceseseeeeeaeeaenaeenes 3 11 3 3 1 FORM SORM uuu cece cecesscccesssccesssceccsssecceuscececuseccesassececasseceeaueccnsaueseneasscensaeeeeneaseeensaas 3 12 3 3 2 Monte Carlo Simulation ccccsscscccoccsvsecscccessessssceccovssssssccecessesssteccescoesesesecescessens 3 19 3 3 3 Directional SiMUl ET ATO id acia 3 22 3 3 4 Axis Orthogonal Simulation cecccccescesseeseeeseeeeceeceeeeeeeeseecsseeeecseeceseeeeececseeeseeseaes 3 25 First Passage Probability and Results 0 ccccccsccsscescessecsseesseseceseeeseecseecseceseeneseseesaecnaecneeeeeeenes 3 27 3 4 1 Definition of a Stochastic Process for Calculation of First Passage Probability 3 27 Crossing Rate and Results iii id tacita 3 29 3 5 1 Definition of a Stochastic Process for Calculation of Crossing Rate o ooonocnncnincnionconnons 3 29 Distribution Analysis and Results cccccccesesscescessecseceseceeeeeseeeseeeseceeeeeeecesecssesseeseeeeseecsaeeneeneeeaes 3 30 3 6 1 Monte Carlo and Latin Hypercube Simulation oooconicnnnnoninnninnconnnonncnnnonnnrnncconoconarnannnos 3 30 3 6 2 Mean Value Based FORM occcccnnnnnonononinnnnnnnnonccnnnananononoconanannonocoronananonononronnnanononerininanns 3 38 Deterministic Analysis and Results c cccscccscesscesseesecseceseceeeeescenseceseceeeeeseessecaaeceseseneeeaeeaecneeags 3 40 Parameter
262. owed in line mode including reading another command input file To read in a command input file type an followed by the file name To read parts of the file specify the number of lines to read after the file name If the file name does not have a suffix i e a dot and the follow ing part Proban adds jnl to the name Proban may have more than one command input file open at one time i e you may reference a command input file from within another command input file It will always read each file sequential finishing the last opened file first To get a list of the currently open files type The last opened command input file may be closed explicitly by typing the followed by two dots When a command input file is being read the lines read are echoed on the screen and logged on the journal file Programming expressions are logged as comments and the resulting values are logged as part of the command The command itself is not logged on the journal file If an error is found in a command input file Proban stops reading the file and skips the remaining part of the line where the error was found Proban will also stop reading of a command input file if it finds a line containing only an The commands used to manipulate command input files are summarised below Table 4 3 Manipulation of command input files Read the named file from the top Reading will stop is an error if found or at filename the end of the file or
263. pecified in line mode input after SAMPLE any specified fractiles or probabilities are kept as defaults Otherwise the default set of fractiles and probabilities is empty SESAM Proban Program version 4 4 01 OCT 2004 5 161 See also PRINT DISTRIBUTION e SET TITLE EXAMPLES PRINT RESULT SAMPLE FRACTILE ONLY 0 5 0 6 Generates the following print f Network Planning Example Distribution of Network Longest Duration of all paths through the network Analysis method Latin Hypercube simulation 5 5 5 5 SAMPLED DISTRIBUTION CALCULATED FRACTILES Fractile Distr Compl 6 791248101E 01 5 000000000E 01 5 000000000E 01 6 899417939E 01 6 000000000E 01 4 000000000E 01 Proban SESAM 5 162 01 OCT 2004 Program version 4 4 PRINT RESULT SENSITIVITY SENSITIVITY valuel value2 coordinate PURPOSE Print the parametric sensitivity values for the selected result PARAMETERS valuel This input is only required if the selected result is a parameter study Valuel is then a selection of the first parameter values for which the study was run The particular results from the analysis using the selected value s will be printed value2 This input is only required if the selected result is a two parameter study Value2 is then a selection of the second parameter values for which the study was run The particular results from the an
264. probability column shows the probability cor responding to the fractile at the linearisation point for each distribution variable e g 103 39 is the 98 3 fractile in the distribution for the load The V space point may also be added to this table by use of the com mand DEFINE RESULT OPTION V SPACE POINT The V space point is the fractile in the standard nor mal distribution that corresponds to the probability value A SORM analysis of the system without redundancy in component A and including a sensitivity analysis on all parameters can be done as follows SELECT ANALYSIS METHOD PROBABILITY ANALYSIS SORM PARABOLIC DEFINE ANALYSIS OPTION SENSITIVITY ALL RUN PROBABILITY ANALYSIS Simple The message appearing while the analysis is running is Starting Probability Analysis of Simple Starting SORM calculation Starting linearization of Union of Al B C Linearization completed Calculating importance factors and 10 parametric sensitivity values SORM Reliability index T9131 SORM Probability 2 78657E 02 SESAM Proban Program version 4 4 01 OCT 2004 3 15 Note that this is a large intersection It will therefore produce one linearisation point for each subevents component The print of the linearisations PRINT RESULT ALL is not shown here Note also that Proban does not simultaneously provide FORM and SORM results for a large intersection It does so for any other geometry Note
265. r study facility A parameter study can be assigned to any fixed variable or to any parameter in a distribution or argument in a function that has a numerical value A number of values are specified When the parameter study is used an analysis will be done for each of the specified values The main results and importance factors may be presented as a function of the parameter Each of the indi vidual analyses may also be examined independently The following main results may be printed and displayed plotted as a function of the parameter Main results for FORM SORM not including equality event s or bounds Prob FORM First Passage Probability calculated by FORM Beta FORM Reliability against first passage index calculated by FORM Log10P FORM Logl0 first passage probability calculated by FORM Prob SORM Probability calculated by SORM Beta SORM Reliability index calculated by SORM Log10P SORM Log10 of probability calculated by SORM Crossing rate FORM Crossing rate calculated by FORM Main results for FORM SORM using bounds but not including equality event s Prob Lower Lower bound of probability Prob Upper Upper bound of probability Beta Lower Lower bound of reliability index Beta Upper Upper bound of reliability index Proban 2 28 Prob Lower Prob Upper SESAM 01 OCT 2004 Program version 4 4 Lower bound of logl10 probability Upper bound of log10 probability Main results for FORM SORM including equality event
266. rd dev of Probability 2 9661E 03 Coeff of Var of Probability 0 010 Estimated Reliability index 0 5183 The simulation requires a FORM analysis to run hence the FORM result The sensitivity analysis applies to the FORM result not to the simulation The multiplicative correction to the FORM probability is stmulated by default To change to the additive correction use the command DEFINE PROBABILITY SIMULATION AXIS ORTHOGONAL DENSITY STANDARD NORMAL As can be seen the correction is small in this case The stop criteria for the simulation are manipulated using the command DEFINE PROBABILITY SIMU LATION AXIS ORTHOGONAL It is possible to demand a stop if a required coefficient of variation has been reached This command is also used to define the search method The summary print looks like this PRINT RESULT SUMMARY Probability of NPV lt 0 0 l Net Present Value Analysis method Axis Orthogonal simulation Final results after 50 simulations Estimate Stand Dev C of V 90 confidence interv Correction 1 034E 00 1 015E 02 0 010 1 017E 00 1 051E 00 Probability 3 021E 01 2 966E 03 0 010 2 973E 01 3 070E 01 Beta 0 5183 0 5043 0 5323 Log10 Prob 5 198E 01 5 269E 01 5 128E 01 It includes a line showing the results for the simulated correction value The standard deviation of the prob ability is derived from the standard deviation of the correction not from a sample of prob
267. re inactive initially If ON such constraints are attempted linearised If OFF they are not linearised Controls how the probability is calculated through the multi normal distribution The SQP option is the most accurate The CRUDE option should only be used if the SQP option fails Selection of the optimization algorithm Currently only one al gorithm is available Outer level in a nested analysis Inner level in a nested analysis Selection of the optimization algorithm Currently only one al gorithm is available Sequential quadratic programming The maximal number of iterations allowed The maximal number of steps in one search direction Convergence criterion Sequential quadratic programming Extended options set See DEFINE NLPQL Robusted Rackwitz Fiessler method See DEFINE RFCRC Response surface method See DEFINE RSM Controls the method used to calculate parametric sensitivities and importance factors ANALYTICAL calculation is exact for the FORM result but requires a number of differentiations AS YMPTOTIC calculation is quick but not as accurate The sec ond order derivations using the ANALYTICAL calculation may be done ONE WAY or TWO WAY to gain accuracy Controls the usage of the starting point in the FORM SORM optimization In a parameter study it applies to the first analy sis as well as any other analysis where the previous solution is not used The starting point can be either ASS
268. resent Value Distribution of NPV j 1 l Net Present Value Analysis method Monte Carlo simulation Proban SESAM 3 34 01 OCT 2004 Program version 4 4 Final results after 1000 simulations Mean 4 96924E 03 Skewness 1 20695E 01 Standard Dev 9 23969E 03 Kurtosis 2 77288E 00 The print of sensitivity results contains four tables similar to the table presented for directional simulation There is one table with sensitivity values for each of the four moments PRINT RESULT SENSITIVITY Parametric sensitivity result for Mean 4969 2439404 Variable Type Parameter Value dMean dPar Measure 11 Triangle Mean 7 500E 04 9 292E 01 6 97E 03 El Lognormal Mean 5 000E 03 9 082E 01 4 54E 02 I2 Triangle Mean 5 000E 04 8 174E 01 4 09E 03 E2 Lognorma Mean 1 000E 04 8 272E 01 8 27E 02 S Normal Mean 1 000E 04 8 264E 01 8 26E 02 Parametric sensitivity result for Standard Deviation 9239 6947365 Variable Type Parameter Value dStDv dPar Measure 11 Triangle Mean 7 500E 04 1 142E 02 8 56E 01 E Lognormal Mean 5 000E 03 2 365E 04 1 18E 01 I2 Triangle Mean 5 000E 04 1 401E 02 7 00E 01 E2 Lognormal Mean 1 000E 04 1 372E 03 1 37E 00 S Normal Mean 1 000E 04 1 834E 15 1 83E 12 Parametric sensitivity result for Skewness 0 112069534213 Variable Type Parameter Value dSkew dPar Measure 11 Triangle Mean 7 500E 04
269. ri of dProb dPar because the sensitivity value is a simulated value The other entries are described in Section 3 3 1 SESAM Proban Program version 4 4 01 OCT 2004 3 25 The PRINT RESULT ALL command generates a print of the summary intermediate simulation results importance factors and sensitivity results The intermediate result table is identical to the table presented in the description of Monte Carlo simulation in Section 3 3 2 It is possible to print and display the sample of probabilities using the commands PRINT RESULT SAM PLE and DISPLAY RESULT DISTRIBUTION These commands and the results are described in Section 3 6 1 A conditional probability is calculated just like any other probability The analysis will be slower because Proban needs to calculate both the intersection event probability and the conditioning event probability The resulting probability is a division of the estimates of the intersection probability and the conditioning proba bility For this reason there is no sample of independent and identically distributed conditional probabilities and therefore the PRINT RESULT SAMPLE command is not in effect in this case The simulation may be restarted from the previous result by using the command RUN RESTART The stop criteria may be changed before the run is restarted This is useful e g for estimating the time a simulation will run in order to produce a required accuracy on the result or for continuing a simulation
270. rnatives in the matrix Use LIST to see the rows in the matrix 4 4 9 Setting and Clearing Loops in a Command When a command is completed then Proban by default goes back to the main command level If a com mand is to be repeated many times in slightly different versions 1t may be desirable to go back to an inter mediate command level rather than to the main command level This is accomplished by typing LOOP when the intermediate command level to be repeated from is entered The loop is ended by typing END at the command level repeated from or by aborting the command by using the double dot Example 4 2 DEFINE CONTINUOUS PROCESS LOOP ANALYSIS OPTION etc Proban SESAM 4 14 01 OCT 2004 Program version 4 4 DURATION etc STARTING TIME etc END 4 4 10 Inserting a Command into Another Command It is possible to insert a command at any point while in command mode not in programming mode This is done by simply typing the main prompt followed by the inserted command Proban will finish the new command and then return to the command level in the previous command where the new command was inserted This is useful e g for catching up on settings or definitions that was forgotten while inside a PRINT or DIS PLAY command or for printing out objects to see what they contain The following examples illustrate this DISPLAY FUNCTION DIFFERENCE PRINT FUNCTION DESCRIPTION DIFFERENCE ete
271. roban 2 20 01 OCT 2004 SESAM PROBAN 4 3 03 De JUN 2000 15 41 Mean Value Measure of location Mean of x_1 2 0 Mean of X_2 0 0 Mean of x_3 2 0 Denstty functton 0 4 Density 0 5 0 2 Variable x_i ak x_2 O x_3 SESAM PROBAN 4 3 03 07 JUN 2000 13 36 Mean Value Measure of location Mean of x_1 2 0 Mean of X_2 0 0 Mean of x 3 2 0 Distribution function Distribution Variable A x_i e E EA O x3 Figure 2 12 Illustration of Mean SESAM Program version 4 4 SESAM Program version 4 4 01 OCT 2004 SESAM PROBAN 4 3 03 D7 JUN 2000 14 18 Standard deviation Measure of uncertainty Std of x_1 0 8 Std of X_2 1 0 Std of x 3 1 5 Denstty function Density Variable A x_i e Be O x3 SESAM PROBAN 4 353 03 D7 JUN 2000 14 18 Standard deviation Measure of uncertainty Sid OF xat DO Sle of X2 1 0 Std of x_5 1 5 Distribution function Distribution Variable x_i E D xS Figure 2 13 Illustration of Standard Deviation Proban 2 21 Proban 2 22 01 OCT 2004 SESAM PROBAN 4 3 03 21 NOV 2000 13 25 Skewness Measure of symmetry Skewness of x_4 1 0 Skewness of x 3 1 0 Density function Dens ity 0 4 0 5 0 3 Skewness of x_2 0 0 Var table x_i n x2 O x_3 SESAM PROBAN 4 3 03
272. rrection Conf Corr Up Upper confidence bound for Correction Prob FORM Probability calculated by FORM Beta FORM Reliability index calculated by FORM Log10P FORM Log10 Prob FORM Main results for Monte Carlo and Latin hypercube simulation of a distribution Mean The sample mean Conf Mean Lo Lower confidence bound for Mean Conf Mean Up Upper confidence bound for Mean Standard Dev The standard deviation of the sample Skewness The skewness of the sample Kurtosis The kurtosis of the sample Main results for Deterministic analysis Value of lt event name gt or of lt variable name gt 2 11 Presentation of Results During the analysis Proban displays a short history and summary of the analysis After an analysis is com pleted the results are stored in the database The results may then be printed and or displayed at will Print files and plot files may be generated Proban provides different levels of print reaching from a very short summary to a complete listing of all relevant results In addition many different plots are possible For first passage probability analysis importance factors may be displayed as pie charts For distribution analysis the estimated Mean value based FORM or simulated distribution may be dis played together with any other distribution A simulated distribution may be presented as a histogram or as a cumulative distribution After a parameter study has been completed the main results and the importanc
273. rrent selection of sub libraries see SELECT FUNCTION LIBRARY This is because some libraries may contain a large number of functions and or not be relevant to the current problem See also e SELECT FUNCTION LIBRARY PRINT FUNCTION LIBRARY SET TITLE EXAMPLES PRINT FUNCTION DESCRIPTION Difference Generates the following print Difference Difference X1 X2 The function belongs to sublibrary Misc First and second order derivatives are implemented Name Description Arguments Additive Arg Additive argument Subtract Arg Subtractive argument Proban 5 142 PRINT FUNCTION FORMULA FORMULA name PURPOSE Print a description of a selection of function formulas PARAMETERS name NOTES Name s of the function formula s to be printed SESAM Program version 4 4 Prints the name description argument list calculation scheme and definition of a function formula See also CREATE FUNCTION FORMULA CHANGE FUNCTION FORMULA DELETE FUNCTION FORMULA RENAME FUNCTION FORMULA SET TITLE SESAM Proban Program version 4 4 01 OCT 2004 5 143 EXAMPLES PRINT FUNCTION FORMULA SYMFUN Generates the following print SYMFUN Symbolic Function Gradients must be calculated numerically Name DescriptionValue Index 2 arg AVL B Arg BV2 Operator OperandsResult er yr vaya Formula A B Proban 5 144 01 OCT 2004 PRINT F
274. s the file prefix and the file name description To type into the field place the pointer in the field and press down the left mouse button In some input fields the text can be longer than the width of the field as shown in the dialog box The text will then scroll if typed beyond the width of the input field Menus come in four different types Togglebuttons Radio boxes Option menus and Scrollable lists Selecting in a menu may cause considerable changes in the layout of the dialog box This will depend on the dialog box in use A Togglebutton is a button that has two states On and Off One example is given in the Set Plot box where the Colour button is Off To switch the status of the button place the pointer on the button and press down the left mouse button A Radio box is a collection of togglebuttons where only one button can be active All buttons are visible on the screen simultaneously An example is the Type buttons in the Display Distribution dialog box To select a button place the pointer on the button or on its corresponding label and press down the left mouse button An Option menu is similar to a radio box in that it presents a number of alternatives of which only one can be active It is however operated differently To display the menu place the pointer on the button showing the active alternative and press down the left mouse button To select an alternative from the menu place the pointer on the alternative and press do
275. s a tool for general purpose probabilistic analysis The main objective of Proban is to provide a variety of methods aimed at different types of probabilistic analysis This includes probability analysis of events distribution analysis first passage probability analysis and crossing rate analysis Proban can deal with a broad class of probabilistic and statistical problems encountered in for example engineering and economies Proban allows efficient modelling of random variables and events On line definition of functions is availa ble Proban may be run in batch mode from a tty terminal or from a graphics work station using a modern graphics interface The same command interface is supported in all modes and commands generated in the graphics mode are logged and can be read into the program in the line input mode during a later run Proban supports a database that contains the input model and results as well as a journal file that stores a record of all actions done during a program session Proban is ideally suited to structural reliability analysis It may often be convenient to use loads body motions or stresses computed by other modules in the SESAM system as input to the reliability analysis This manual is valid from Proban Version 4 4 SESAM Program version 4 4 Proban 1 2 01 OCT 2004 the SESAM System m Proban 1 2 Manager NISSHJOAdLSOd SISVIVNV TV INGIWNOUIANG E INISSADONAA Ad WVdD0ud
276. s used The normalised gradient a of g u at u 0 is approximated from the first response surface The smalles values of ai2 are summed up S until the zero limit is reached the next contri bution violates the limit The corresponding ui variables are kept constant at zero value during the iterations The final reli ability index is multiplied by the omission factor 1 1 S 1 2 SESAM Proban Program version 4 4 01 OCT 2004 5 87 NOTES The response surface method fits a linear or a partly quadratic function to a set of points experiments The design point is found for the zero surface implied by the response function A new set of experiments is generated around this point The new information and possibly previous experiments are used to gener ate a new resonse function This is repeated until convergency The method is restricted to a single event The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e PRINT ANALYSIS SETTINGS EXAMPLES The following values are default when the program starts up with a new database DEFINE FORM SORM OPTIMIZATION RSM LINQUADIAG RADIUSCONTR 40 0 01 0 5 TWOWAY 0 1 3 001 0 01 Proban SESAM 5 88 01 OCT 2004 Program version 4 4 DEFINE MEAN VALUE FORM POINTS number LOWER PR OBABILITY lower UPPER PROBABILITY upper MEAN VALUE FORM GRADIENT ONE THREE RESET PURPOS
277. s with type attribute Distribution Fitted Distribution or Generated distribution The assignment of XDOT as the time derivative of X is done with the command ASSIGN CONTINUOUS PROCESS TIME DERIVATIVES X XDOT The variable XDOT must have zero expectation If no time variable is present in the model then the duration of the process is input by the command Proban SESAM 3 28 01 OCT 2004 Program version 4 4 DEFINE CONTINUOUS PROCESS DURATION 10800 The duration is 10800 If a time variable Time is present in the model then the starting point and duration assigned to this variable is used CREATE VARIABLE Time Time variable TIME ASSIGN CONTINUOUS PROCESS STARTING TIME Time 1000 ASSIGN CONTINUOUS PROCESS DURATION Time 10800 If assignment of starting time or duration is not explicitly done for Time then the default values are used DEFINE CONTINUOUS PROCESS STARTING TIME 1000 DEFINE CONTINUOUS PROCESS DURATION 10800 The above defined and assigned values may be undefined or unassigned in which case Proban issues an error message The first passage probability calculation is invoked by the command RUN CONTINUOUS PROCESS ANALYSIS FIRST PASSAGE PROBABILITY Notice that Proban sets up the nested reliability analysis required to solve the problem However in order to manipulate differentiation options and convergence criteria for optimization algorithms the user
278. sed to dump dis play output to nowhere Set the size and position of the display window when using a workstation device This command will only be taken into ac count if issued prior to any DISPLAY command Otherwise the settings will not be valid until the user has exited from Proban and entered again Please note that the window can be re sized using the mouse under X Windows Position of left display window border Position of right display window border Position of bottom display window border Position of top display window border SESAM Proban Program version 4 4 01 OCT 2004 5 197 100 screen border top A A workstation window bottom O 0 left right 120 Figure 5 1 Setting the initial size of a workstation window NOTES 1 The destination is always set to SCREEN when the program starts up also with an existing database 2 The DUMMY device is useful for effectively disabling all DISPLAY commands in a command input file when the displays themselves are not needed See also DISPLAY e PLOT EXAMPLES The following is default when the program starts with a new database SET DISPLAY COLOUR ON Proban SESAM 5 198 01 OCT 2004 Program version 4 4 ET DISPLAY DESTINATION SCREEN SET DISPLAY WORKSTATION WINDOW lt To be completed gt The default DEVICE depends on the computer system SESAM Program version 4 4 SET DRAWING Proban 01 OCT 2004 5 199 CHARACTER TY P
279. set plot file characteristics PARAMETERS HISTOGRAM Set options for display of a histogram LINE OPTIONS Set the options controlling how lines are drawn and marked PIE CHART Set options for display of a pie chart XAXIS ATTRIBUTES Set the options controlling the drawing and scale of the x axis YAXIS ATTRIBUTES Set the options controlling the drawing and scale of the y axis ZAXIS ATTRIBUTES Set the options controlling the drawing and scale of the z axis NOTES All sub commands and data are fully explained subsequently as each command is described in detail Proban SESAM 5 202 01 OCT 2004 Program version 4 4 SET GRAPH HISTOGRAM COLUMNS ncol HATCHED HISTOGRAM FILLING HOLLOW SOLID PURPOSE Set options controlling display of a histogram PARAMETERS COLUMNS ncol Set the number ncol of columns in the histogram FILLING The columns in the histogram can be filled with a HATCHED pattern or not filled at all HOLLOW or be filled with a SOLID pattern NOTES 1 To present a smooth histogram the number of columns should be about 1 10 of the sample size or smaller 2 When running the program on a black and white screen it the it usually a good idea to change the default SOLID filling to a HOLLOW or HATCHED See also DISPLAY RESULT DISTRIBUTION PLOT EXAMPLES The following is default when the program starts with a new database S S GRAPH HISTOGRAM COLUMNS 20 GRAPH HISTOG
280. sity values may be printed by use of the PRINT DISTRIBUTION com mand The moments of the distribution are calculated and printed if possible by use of the PRINT VARIA BLE command The distribution itself may be displayed using DISPLAY DISTRIBUTION The accuracy of the fit may be examined using DISPLAY FITTED DISTRIBUTION See also CREATE VARIABLE DISPLAY DISTRIBUTION DISPLAY FITTED DISTRIBUTION PRINT VARIABLE PRINT DISTRIBUTION ASSIGN EXTREME VALUE EXAMPLES CHANGE VARIABLE X DISTRIBUTION Spline 1Dim 0 10 UNWEIGHTED ONLY 1 0 0 5 3 0 0 25 5 0 0 5 7 0 0 7 8 0 0 9 9 0 0 95 HIGH UNIMODAL SEE ALSO SESAM Proban Program version 4 4 01 OCT 2004 5 39 CHANGE VARIABLE FITTED DISTRIBUTION FITTED DISTRIBUTION distribution input seq parameter WEIGHTED Fractile Probability Weight CUMULATIVE UNWEIGHTED Fractile Probability WEIGHTED Observation Weight 1 OBSERVATIONS UNWEIGHTED Observation OBSERVATION WEIGHTED Observation Weight a MOMENTFIT UNWEIGHTED Observation RESULT result name RESULT MOMENTFIT result name PURPOSE To change a variable to be fitted to a distribution or to change a fitted distribution already assigned PARAMETERS distribution input seq parameter CUMULATIVE WEIGHTED UNWEIGHTED Fractile Probability Weight Fractile Probability
281. sted analysis Define differentiation increments for use in optimization on outer or inner level of a nested analysis The differentiation increment in U space to be used for first or der derivatives It must be positive Used during FORM SORM optimization The differentiation increment in U space used to be used for calculation of second order derivatives It must be positive Relative parameter increment It must be positive Absolute parameter increment It must be positive Limit for application of relative parameter increment The ab solute increment is used if the absolute value of the parameter is less than limit It must be positive Proban 5 76 GRADIENT CALCULATION U SPACE BOUNDS INTERMEDIATE RESULTS NOTES SESAM 01 OCT 2004 Program version 4 4 Determines if the gradients that have been programmed into the model functions are used ANALYTICAL or if one way u du or two way u du and u du incrementation is used to determine the gradient Initialises the selected level u space optimisation upper bounds to Value and the u space lower bounds to Value Controls the amount of intermediate results to be generated on outer and inner level of a nested analysis The possible alterna tives are NONE LOW MEDIUM EXCESSIVE The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command EXAMPLE The following values are default when the program starts up with a new database
282. stop when a certain coefficient of variation has been reached 2 4 Nested FORM Analysis The nested FORM analysis is invoked when a model contains a probability variable or when a model con tains both a continuous stochastic process and at least one other distribution variable Proban SESAM 2 16 01 OCT 2004 Program version 4 4 g x Ax lt 0 AX D PO P X P g lt 0 V g2 lt 0 V g3 lt 0 Figure 2 10 Nested reliability analysis The outer integration level is a design point search for the single event which contains the probability varia ble Variables conditioned on are integrated on the outer level together with variables not contained in the event of the probability variable The inner integration level calculates the log probability or reliability index of the event of the probability variable The result is calculated given the current values of variables conditioned on Figure 2 10 shows a nested FORM analysis resulting from a single event model which involves a probabil ity variable the probability variable itself being the probability of a union event of single events The outer loop event is always a single event model Proban checks for inconsistencies in the separation between outer integration level and inner integration level resulting from inconsistent selection of conditioning variables The calculation method available is FORM on both levels Optimization options and differentiat
283. stribution Distribution function Onesi Normal distribution Distribution function Oval distribution Distribution function Rayleigh distribution Distribution function Student t distribution Distribution function Triangle distribution Distribution function Trunc Normal distribution Distribution function Weibull distribution Distribution function Beta distribution Inverse distribution fct Inv Beta Oro Ww a UY 0 Y MY Y Ys 01 01 AY UT a Y Y 0 O S oP Y Y Y Y a UY UY s S 01 01 Y OB WW OU oOo0oO0DOD0DOOO0OO00O00O00O00O00O0O0O0O0O0O0O0O0O0O0O0O00O0O0O0O0O0000000000O000O00O0O0O0o0O0Oo0Oo0o0Oo0oOoOo0o0o0o0Oo0o0Oo0OoooOo Proban 3 64 nv Burr nv Chi squa nv Exponent nv Gamma nv Gen Gamm nv Gumbel nv Hermit s nv Hermit t nv Inv Gaus nv Lognorma nv Long Hig nv Maxwell nv Normal nv Onesi No nv Oval nv Rayleigh nv Student HHHHHHHHHHHHHHHHH Function w 0 W w Y YU id S T YN AY OP WwW a O0OoO0O0OO0O00O00O00O0O0O0O0O0O0oOoOoo Oo 01 OCT 2004 Burr distribution Chi square distribution SESAM Program version 4 4 Inverse distribution fct Inverse distribution fct Inverse distribution fct Exponential Inv Gauss Lognormal distribution Gamma distribution Gen Gamma distribu Gumbel distributio Hermit secon dis Hermit trans dis distribu distribu Long Higgins dis Ny tribu tribu tribu Inverse distribution fct tion Inverse distribution fct Inverse
284. stribution of NPV from the previous section SET DRAWING FONT SIZE RELATIVE 1 5 DISPLAY RESULT DISTRIBUTION ONLY Mean V FORM Original Fit DISTRIBUTION Proban SESAM 3 40 01 OCT 2004 Program version 4 4 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Mean Value FORM calc for NPV Net Present Value Distribution function Distribution 7 pat y o T T l 30000 20000 10000 0 10000 20000 30000 o Variable A M W FORM result for NPV Original Fit Figure 3 8 Mean value based FORM distribution for NPV with Hermite fit In this case the mean value based FORM result is quite accurate This is not necessarily the case 3 7 Deterministic Analysis and Results It is often helpful to calculate the value of a variable or an event function at a specified point in order to ver ify the formulation of a stochastic model In Proban this is achieved through the RUN DETERMINISTIC ANALYSIS command The following command calculates the value of the variable x at the mean of the random variables in the model RUN DETERMINISTIC ANALYSIS VARIABLE X MEAN VALUE The following command calculates the value of the variable at a point modified from the mean RUN DETERMINISTIC ANALYSIS VARIABLE X MODIFIED MEAN BASED and then entering the modifications The analysis of a variable can also be median based SESAM Proban Program version 4 4 01 OCT 2004 3 4
285. sult NOTES None SESAM Program version 4 4 SESAM Proban Program version 4 4 01 OCT 2004 5 187 SAVE RESULT RESULT name desc PURPOSE Save a result under a name PARAMETERS name Name of the result This cannot be the name of an existing result Result names are matched case insensitive and can not be longer than 12 characters desc Descriptive text for the result It can be up to 50 characters long NOTES 1 Only results from RUN DETERMINISTIC ANALYSIS RUN PROBABILITY ANALYSIS and RUN DISTRIBUTION ANALYSIS can be saved using this command These results are by default stored under the name LastAnalysis and will be overwritten by the next analysis if they are not saved 2 The results created by this program should not be modified by the user See also RUN DISTRIBUTION ANALYSIS e RUN PROBABILITY ANALYSIS DELETE RESULT e RENAME RESULT DISPLAY RESULT e PRINT RESULT EXAMPLES SAVE RESULT Fail 444S SORM Failure of joint 444 Proban SESAM 5 188 01 OCT 2004 Program version 4 4 SELECT ANALYSIS METHOD SELECT FUNCTION LIBRARY RESULT PURPOSE Select objects or methods for use in other commands PARAMETERS ANALYSIS METHOD Select a method for use in probability and distribution analysis FUNCTION LIBRARY Select the function libraries to be available in other commands RESULT Select the result to be used for presentation PR
286. svcssccssescecsenensesecessessesnces 2 13 2 3 4 Axis Orthogonal Simulation ccccceecesseeseeeeeeeceeceeeeeeeesaecsaeeeecseeceseecsececseeeseeenaes 2 14 Nested FORM Aaly SiS cozcs sy eget created lege cea lehated lnk ose boncecatosiey Sab A aa id diz 2 15 First Passage Probability Analysis cccceccccsseessessecesseeseeeseeeseceseseeeeeeeeesecsaecaaeceeseeeeseeeeeesaeeseees 2 16 Crossing Rate Analia dino 2 18 Distribution Anal sia a ca 2 18 2 7 1 Monte Carlo Simulation ocnconccncconnnnnnononecinonananonocncnnannanonorononnnnnn nano cn nana a anaie 2 18 2 7 2 Latin Hypercube Simulation oonccnnncnonononnnonononnnnnonnncnnnnnnnonn cono ron nn nora nn rrnnrrnnr corran nino 2 24 2 7 3 Mean Value Based FORM ccccccccccccesessccccecessssscsscccsesesseeecesceesessesscsecessssassesceseensasees 2 25 Sensitivity Resulta anita iran iia 2 25 2 9 2 10 2 11 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 4 1 Determimistic Anal si tt ti EA Aaa CAES 2 27 Parameter Md atencion E a ae ia e R E aR E a o IRA nerds cai 2 27 Presentation Of RR E A E E E E E ER EE E E 2 29 USER S GUIDE TO PROBAN ccccsssscsccccccccssssssccccsccesccscesessscsccesccscesesssccccescescesens 3 1 Howto Doan Analysis rasie e ee ae TE EEEE dt aa EEEREN Tera 3 1 Presentation of Model Data and ResultS oooooccccnnononancninonanananacoconannnnnnarononnnnononccncannnaneconanannna 3 6 3 2 1 SA ad A O 3 7 3 2 2 Display and Pl
287. system com mand Everything on the input line after the exclamation mark is sent to the operating system The following example taking from a run on a Unix computer will list all journal files on current directory lls JNL The command below spawns a sub process on a Unix system and must be terminated by use of the com mand exit SESAM Proban Program version 4 4 01 OCT 2004 4 15 Ish The facility is very useful for obtaining directory listings editing files e g input files spawning into the operating system to do more complicated tasks etc The facility is also available from the command input line in graphics mode but when used here the output from the operating system will appear in the terminal window from which Proban was started 4 4 13 Appending Input Lines After receiving an input line Proban processes the input unless told otherwise The way to suspend processing of an input line is to type a backslash as the last character in the line Proban then issues the append prompt gt gt 4 4 14 Viewing the Current Status of a Command Some commands are long and it may be difficult to keep track of what has actually been given as input In other cases where commands have been inserted it may be useful to see what the current command s actu ally look like to Proban This is achieved by use of the command 4 4 15 Comments A comment may be typed anywhere in a command while in command mode not in program
288. t is a union of other events i e it is fulfilled when at least one subevent is fulfilled Selection of events forming either an intersection of union These cannot be conditioned events Event is a simple in equality Name of the one dimensional variable that is forming the left hand side if the in equality One of lt less than equal gt greater than Numerical right hand side of the single event Proban 5 48 01 OCT 2004 e COPY EVENT RENAME EVENT DELETE EVENT DISPLAY EVENT PRINT EVENT e ASSIGN STARTING POINT e ASSIGN MEASURED VALUE EXAMPLES CREATE EVENT Loss Negative net present value NPV lt 0 ERS ECTION CREATE EVENT Nol Crack2 Both inspections INT CREATE EVENT Fail Cond Failure given nofind Crack2 the n find SESAM Program version 4 4 ONLY NoCrack 1 Crack2 CONDITION ED Failure Nol SESAM Proban Program version 4 4 01 OCT 2004 5 49 CREATE FUNCTION FORMULA FUNCTION name desc INTEGRAL RESPONSESURFACE PURPOSE To create a function PARAMETERS name desc FORMULA INTEGRAL RESPONSESURFACE NOTES None Name of the function This name must be unique among functions and no longer than 12 characters Names are matched case insensitive Descriptive text associated with the function formula Create a function formula Create an integration function
289. t occurs The FORM and SORM methods have been developed with the purpose of approximating this integral This is accomplished by approximating the surface at the boundary of the area where the event is fulfilled in such a way that the integration can be done over the approximated area The trick to do this is twofold e First the random variables X are transformed into independent standard normal variables U e Secondly the area where the event is fulfilled is approximated by an area bounded by hyperplanes FORM or a second order surface SORM Theoretical results for integration of the standard normal density over such areas can then be applied In order to understand the FORM SORM method it is necessary to describe the transformation into the standard normal spaces called V space and U space first The description here is not theoretically com plete During an analysis Proban always operates in a transformed space where all variables are independent and have standard normal distributions It is possible in theory to map any distribution into such a space using a one to one transformation Proban first maps those input variables that are defined as distributions to SESAM Proban Program version 4 4 01 OCT 2004 2 9 standard normal variables in the so called V space These standard variables may still be correlated if corre lations have been assigned See Section 2 2 4 The coordinates in V space correspond to variables in the
290. t that they are non negative VANISH Both tail values of a FREE fit must be zero NOTES 1 Ifthe spline will not fit try relaxing the demands on accuracy or check if any of the points have been specified wrongly 2 The variable may be assigned an extreme type distribution by using the ASSIGN EXTREME VALUE command 3 The distribution function and density values may be printed by use of the PRINT DISTRIBUTION com mand 4 The moments of the distribution are calculated and printed if possible by use of the PRINT VARIA BLE command 5 The distribution itself may be displayed using DISPLAY DISTRIBUTION The accuracy of the fit may be examined using DISPLAY FITTED DISTRIBUTION See also e CHANGE VARIABLE DISPLAY DISTRIBUTION PRINT VARIABLE DISPLAY FITTED DISTRIBUTION PRINT DISTRIBUTION ASSIGN CORRELATION e ASSIGN EXTREME VALUE EXAMPLES CREATE VARIABLE X DISTRIBUTION Spline 1Dim 0 10 UNWEIGHTED ONLY 1 0 0 5 3 0 0 25 5 0 0 5 7 0 0 7 8 0 0 9 9 0 0 95 HIGH UNIMODAL Proban 5 62 SESAM 01 OCT 2004 Program version 4 4 CREATE VARIABLE FITTED DISTRIBUTION FITTED DIS distributi out ter TRIBUTION istribution input seq parameter WEIGHTED fractile probability weight CUMULATIVE UNWEIGHTED fractile probability WEIGHTED observation weight pe OBSERVATIONS UNWEIGHTED o
291. tabase DISPLAY DISTRIBUTION EXCLUDE B will display all distributions except those with names starting with B 4 4 8 Entering a Vector or a Matrix of Values The syntax for entering a vector or a matrix of values is an extension of the syntax for selecting values from a list In this case there is no fixed list to select from Instead the items are inserted and manipulated as the vector matrix is entered The term vector is used for the case where the input is one dimensional The term matrix is used for the case where the input is multidimensional Like a vector is built up from single items a matrix is built from rows There cannot be an unequal number of items in two different columns of a matrix The input of a vector matrix is consists of one or more operations If more than one operation is required as 1t most likely will be they must be enclosed in parentheses SESAM Proban Program version 4 4 01 OCT 2004 4 13 The syntax of one operation is lt row gt refers to a single value in a vector or to a row in a matrix Table 4 7 Entering a vector of matrix of values Include the specified lt row gt as the last row Set the default status to INCLUDE lt row gt PEE ESO Until the status is changed rows that are entered will be added at the end Exclude the specified lt row gt Set the default status to EXCLUDE The next EXCLUDE lt row gt row s that are entered will also be excluded until the defa
292. that Proban informs about how many parametric sensitivity values it calculates The sensitivity results are presented in three tables one for the reliability index one for the probability and one for the logarithm of the probability The tables are similar In this case the table for the reliability index is Parametric sensitivity result for Beta 1 9131294288 Variable Type Parameter Value dBeta dPar Measure RA1 Inv Gauss ean 100E 02 4 384E 02 0 48220 Coef of Var 000E 01 6 803E 00 0 06803 Lower Bound 0 000E 00 2 354E 04 Undefined Load Inv Gauss ean 8 000E 01 6 555E 02 0 52437 Stand Dev 000E 01 1 112E 01 0 11124 Lower Bound 0 000E 00 5 525E 04 Undefined RB Normal ean 1 200E 02 1 036E 02 0 12429 Coef of Var 1 000E 01 3 025E 00 0 03025 RC Normal ean L 300E 02 2 241E 03 0 02913 Coef of Var L 000E 01 9 421E 01 0 00942 The table lists the variable name and type and each parameter name and value Then follows the sensitivity value dBeta dPar and finally when possible the sensitivity measure The measure is defined in Section 2 8 In this case it shows the estimated change in B given a 10 increase in the parameter The sensitivity meas ure shows at a glance that the mean of the Load and the mean of RA1 are the two most important parame ters The analysis of the total system using SORM without parametric sensitivity analysis is produced as follows DEFINE ANALYSIS OPTION SENSITI
293. that did not pro duce a sufficient accuracy 3 3 4 Axis Orthogonal Simulation Axis orthogonal simulation is used to estimate a correction to the FORM probability The correction may be additive or multiplicative depending on the type of sampling density used It is not possible to simulate importance factors or parametric sensitivities by use of axis orthogonal simula tion Consider again the probability of a loss in Example 3 2 The following commands will simulate this proba bility using axis orthogonal simulation the messages given by Proban are also shown SELECT ANALYSIS METHOD PROBABILITY ANALYSIS AXIS ORTHOGONAL SIMULATION RUN PROBABILITY ANALYSIS SINGLE EVENT NPV lt 0 Starting Probability Analysis of NPV lt 0 0 Starting FORM calculation Starting linearization of Single event NPV lt 0 0 Linearization completed Calculating importance factors and 5 parametric sensitivity values FORM Reliability index 0 5470 FORM Probability 2 92197E 01 Starting Axis orthogonal simulation Stopping after 50 simulations or 60 0 CPUsec 12 simulations completed 24 simulations completed 36 simulations completed Proban SESAM 3 26 01 OCT 2004 Program version 4 4 48 simulations completed Number of simulations 50 Estimated Correction 1 0340E 00 Standard dev of Correction 1 0151E 02 Coeff of Var of Correction 0 010 Ww Estimated Probability 0213E 01 Standa
294. that the default status is Old Type in the file prefix and name and select the proper status then press the OK button or type lt Return gt Pressing the Cancel button will abort the session If the file specification is somehow in error Proban will give an error message and keep the start up dialog box open for a new file specification If the file specification is correct Proban will open the database file with extension MOD and a journal file with the same prefix and name but with extension jnl Proban can now be operated as described in Section 4 5 Using the Graphics Mode User Interface SESAM Program version 4 4 Proban 4 4 01 OCT 2004 a PROBAN 4 3 03 File Function Variable Proce Midas Ea Please specify the Database File Biel ES ttrt rt RES REE HEEEEEER see Name Proban EXAEARRATAR ne OK ee ES AAA weet Status E New Peres oo KEEKEEK KEKE at O Old nk nk ek nt EEES rr ERRATA corea A e t EEES aE Figure 4 1 The program start up dialog box To exit the program choose the Exit option under the File menu Proban will then close all open files and terminate execution 4 1 3 Starting Proban in Line Mode A line mode session will not give access to the interactive graphics mode capabilities The program runs in the terminal window and commands are typed on the input line To start Proban
295. the following print Power Function Argument Value Numerical Argument Value 4 000000000E 00 Exponent 3 000000000E 00 Function Power 6 400000000E 01 Gradient Power Value 4 800000000E 01 4 804801600E 01 Power Exponent 8 872283911E 01 8 890758910E 01 Proban SESAM 5 146 01 OCT 2004 Program version 4 4 PRINT FUNCTION LIBRARY LIBRARY name PURPOSE Print a description of a selection of function libraries PARAMETERS name Name s of the function libraries to be printed NOTES See also e SELECT FUNCTION LIBRARY e PRINT FUNCTION DESCRIPTION EXAMPLES PRINT FUNCTION LIBRARY Misc Generates the following print Misc Function Dimen NArg NOp Description Difference 1 2 O Difference X1 X2 Division 1 2 0 Division X1 X2 Identity 1 1 O Identity f x x Linear Comb 1 Input O Linear combination x1 x2 x3 x4 Log Diff 1 2 0O Difference Log X1 Log X2 Maximum 1 Input O Maximum of any number of variables Minimum Input O Minimum of any number of variables Polynom 1 4 O Polynomium of degree 1 Polynom 2 5 0 Polynomium of degree 2 Polynom 3 6 O Polynomium of degree 3 Polynom 4 1 7 O Polynomium of degree 4 Polynom N 1 Input O Polynomium N X X0 C0 Sum of Ci X X0 i Power Diff 1 3 O Difference X1 X3 X2 X3 Product 1 Input 0 Product of any number of variables SignPo
296. the list Prefixing the question mark with a text lt text gt will show all items in the list matching lt text gt The input text may be typed in upper case or lower case Proban disregards the case of the text when com parison is made The input text used to make the selection is not logged on the journal file Instead the selected value is logged as it is presented in the list 4 4 7 Selecting Several Alternatives from a List In some cases a list of items is presented from which one or more items can be selected An example is the DISPLAY DISTRIBUTION command where a number of names may be selected for display In this selection both wildcards and abbreviation may be used but not inside the same text The syntax for the selection allows for more flexibility than in the single selection case because it may be of interest to keep modifying the selection for some time before accepting it The selection process consists of one or more selection operations each of which follow the syntax described below If more than one opera tion is required to complete the selection the selection must be enclosed in parentheses Proban SESAM 4 12 01 OCT 2004 Program version 4 4 The syntax for a single selection operation is Table 4 6 Selection of several alternatives from a list Include the item s matching lt text gt in the selection Set the default status to INCLUDE lt text gt INCLUDE Any items specified after this will
297. the program again 2 Ifadeleted variable is used in a single event the single event is also deleted See also e CREATE VARIABLE CHANGE VARIABLE e COPY VARIABLE e RENAME VARIABLE DISPLAY VARIABLE e PRINT VARIABLE EXAMPLES DELETE VARIABLE X Proban SESAM 5 112 01 OCT 2004 Program version 4 4 DISPLAY DISTRIBUTION EVENT DISPLAY FUNCTION FITTED DISTRIBUTION RESULT PURPOSE To present input data and results graphically PARAMETERS DISTRIBUTION Display the distribution of random variable s EVENT Display an event FUNCTION Display a model function FITTED DISTRIBUTION Display a fitted the distribution with input data RESULT Display an analysis result NOTES Display of results will only be available when the results exist SESAM Proban Program version 4 4 01 OCT 2004 5 113 DISPLAY DISTRIBUTION DENSITY DISTRIBUTION univar DISTRIBUTION COMPLEMENTARY DISTRIBUTION PURPOSE Display distribution and density functions for existing variables PARAMETERS univar A selection of one dimensional distribution variables with nu merical or fixed parameters DENSITY Display the density function for the selected variable s DISTRIBUTION Display the distribution function for the selected variable s COMPLEMENTARY DISTRIBUTION Display the complementary distribution function for the select ed variable s NOTES
298. tion that returns one value and does not calculate derivatives FUNC11 DOC is used for a function that returns one value and provides first order derivatives FUNC12 DOC is used for a function that returns one value and provides first and second order deriva tives FUNCNO DOC is used for a function that returns a vector value and does not calculate derivatives FUNCN1 DOC is used for a function that returns a vector value and provides first order derivatives FUNCN2 DOC is used for a function that returns a vector value and provides first and second order de rivatives 2 Insert call to the function into a sublibrary It may be necessary or desirable to create a new sublibrary first Use the template SUBLIB DOC or a copy of an existing sublibrary routine to do this Remember to change the value specifying the number of functions in the sublibrary 3 Add a call to the new sublibrary to FUNCLB if a new sublibrary was created If not this step can be skipped Remember to change value specifying the number of sublibraries in FUNCLB 4 Compile all new and modified routines and update the object library with the object modules 5 Link Proban using the link command procedure or makefile that is delivered with Proban Specify the location of your private function object library in the command 6 Check the function value and gradients by use of the PRINT FUNCTION VALUE and PRINT FUNC TION GRADIENT commands It is important that the func
299. tion value and especially the gradients are somehow checked When programming model functions 1t is usually a good idea to separate each part of the model into differ ent functions in order to gain more flexibility in the modelling and analysis As an example consider the model function b f E E ANS K x y SESAM Proban Program version 4 4 01 OCT 2004 3 71 The immediate approach is to code the difference f g as one function However it is much better to code f as a function in itself and model g using the already available Product function Modelling f and g separately gives the following advantages e Itis easy to reformulate the problem e g to log f log g using the Log Diff function instead of the Difference function If f g had been coded as one function such a remodelling would require repro gramming and subsequent re linking It becomes possible to examine the behaviour of and g separately e g look at their distributions e The individual functions may be reused in other modelling situations 3 10 4 Compatibility with Proban Version 2 LIBLIM Proban can use the existing LIBLIM routines without any changes However it is not possible to use the new facilities without converting the function to the new format The only slight conversion problem is that the names of function arguments will be truncated from 25 to 12 characters and hyphens are inserted instead of blank spaces in the names betw
300. tions for use of probability variables See a following page Controls if an assigned parameter study is actually performed Controls specification of seeds for the pseudo random number generator The generator requires three integer seeds If two otherwise identical simulations are started with the same seeds they will produce the same results The default seeds are 699570728 398267609 1044576128 These are mostly useful for testing reproduction of results The seeds are generated randomly from the date and time This works quite well and is recommended for most simulations A direct specification of the three integer seeds Controls the extent of the parametric sensitivity calculation does not control importance factor calculation May be used to override the assignments done by the ASSIGN SENSITIVI TY CALCULATION command The possible alternatives are ALL calculate all SELECTED calculate assigned values or NONE The current analysis settings may be printed by use of the PRINT ANALYSIS SETTINGS command See also e e e EXAMPLE PRINT ANALYSIS SETTINGS DEFINE PARAMETER STUDY ASSIGN SENSITIVITY CALCULATION The following values are default when the program starts up with a new database DEFINE ANALYSIS OPTION DEFINE ANALYSIS OPTION DEFINE ANALYSIS OPTION DEFINE ANALYSIS OPTION DEFINE ANALYSIS OPTION DEFINE ANALYSIS OPTION DEFINE ANALYSIS OPTION DEFINE ANAL
301. treme type distribution by using the ASSIGN EXTREME VALUE command 3 The distribution function and density values may be printed by use of the PRINT DISTRIBUTION com mand 4 The moments of the distribution are calculated if possible and printed by use of the PRINT VARIA BLE command 5 The distributions are listed in SESAM User s Manual Proban Distributions See also CREATE VARIABLE e DISPLAY DISTRIBUTION PRINT VARIABLE PRINT DISTRIBUTION Proban SESAM 5 36 01 OCT 2004 Program version 4 4 e ASSIGN EXTREME VALUE EXAMPLES CHANGE VARIABLE X DISTRIBUTION Normal Mean CoV 22 0 2 CHANGE VARIABLE Y DISTRIBUTION Normal Mean Std X 3 1 SESAM Proban Program version 4 4 01 OCT 2004 5 37 CHANGE VARIABLE DISTRIBUTION SPLINE 1DIM UNWEIGHTED fractile probability SPLINE 1DIM lower upper WEIGHTED fractile probability weight HIGH EQUAL MEDIUM FREE FREE VANISH LOW UNIMODAL PURPOSE To change a variable to have a fitted distribution based on splines or to change a spline distribution already assigned PARAMETERS lower The lower bound of the distribution upper The upper bound of the distribution UNWEIGHTED Do not apply user defined weights to the spline fit WEIGHTED Apply user defined weights to the input points in the spline fit fractile probability fractile probability weighted HIGH
302. ts a distribution function to a set of input points Also a number of the continuous distributions can be used to fit data generated by Proban by use of maximum likelihood fits or least square fits Section 3 9 1 describes the distributions that are available in Proban Section 3 9 2 gives an example of distribution fitting of a continuous distribution to Proban generated data SESAM Program version 4 4 Proban 01 OCT 2004 3 53 In addition to these it is possible to specify user defined distributions How this is done is described in Sec tion 3 9 3 3 9 1 List of Distributions The following table lists all distributions in Proban except the spline distribution see the command CRE ATE VARIABLE DISTRIBUTION SPLINE 1DIM for an explanation of this With each distribution is listed the input sequences the parameters in each input sequence and the restrictions that apply to the parameters The distributions are documented in the SESAM User s Manual Proban Distributions Distribution Input sequence Parameters Beta Mean StD Lim Mean Stand Dev Lower Bound Upper Bound Mean Cov Lim Mean Coef of Var Lower Bound Upper Bound R T Lim R T Lower Bound Upper Bound R S Lim R S Lower Bound Upper Bound Low MostL Up Lower Bound Most Likely Upper Bound Lower Bound lt Mean lt Upper Bound Mean Coef of Var gt 0 Stand Dev gt 0 Coef of Var gt 0 R gt 0 S gt 0 T gt R Lower Bound lt Most Likely lt Upper Bound B
303. turssnadeyabaeitenientegsbanstarsnagddiedssanahages 5 188 SELECT ANALYSIS METHOD arion na ad aa a a a E RNE Ai 5 189 SELECT FUNC TION LIBRARY Y aoisi icaro dioe iape tanii aaeoa teanas ai aana Eaa ati 5 192 SELECTRESUL eect esane a EPI EaR EEA E A ROE E A A eaea 5 193 SE Terse a a E A E A a E rd 5 194 SEICOMPANY NAME vorpal aen rE E E E AA E E A 5 195 SET DISPLAY oao a a a E A E S 5 196 SELDRA WING A E T AE AA 5 199 SETORA P Hirra vals AO E E NA 5 201 SETGRAPH HISTOGRAM Sada dt E E EE EE 5 202 SETIGRAPH LINE OPTION Sc renerne e eta liliana E a aa aer ea E EEAS S 5 203 SET GRAPH PIB CHA Riis sscctiscsseedsssestontoussticerdevaenuscstapecbas stents EEEa pA aaaea aN AE aa A ESEE A 5 205 SET GRAPH XAXIS ATTRIBUTE Sisseton ennaa R A i aa e anaE 5 207 SET GRAPH YAXIS ATTRIBUTES iien anie eaaa aaaea aa a a a a 5 209 SET GRAPH ZAXIS ATTRIBUTES netic codssierisseseudeesetcsneonedeesvasieostondeusdendensdaaccstavacserssseoegie 5 211 SELLO a ara to ot 5 213 SEPIA a o 5 215 APPENDIX A PROBAN LINK IN FUNCTIONS AND DISTRIBUTION A 1 A 1 Implementing New Model Functions into ProbanN oconcoinnnionoconnconnnononancnn nono nonnnonnncnnconncconncnnncnnos A 1 ATT A A AT A 1 A A cba ertadets A 1 A1 3 Implementing New Distributions into Proban ccecccesccesseeseeeseesseceteeeeeeeeeeaeceeneenees A 2 SESAM Proban Program version 4 4 01 OCT 2004 1 1 1 INTRODUCTION 1 1 Proban Probabilistic Analysis Program Proban i
304. ty An example of a small intersection is being analysed is shown in Figure 2 9 The method cannot be applied to large intersection geometries SESAM Proban Program version 4 4 01 OCT 2004 2 15 z A failure set me gu 0 Vg Pcorrection D v D v 2 V qt il Safe set u u space Figure 2 9 Axis Orthogonal simulation The simulation consists of sampling points on the hyperplane that is perpendicular to the limit state sur face and then finding the correction to the failure probability along a line perpendicular to the hyperplane and originating from the sampled point There are two ways to sample points on the hyperplane A standard normal density may be used or a condi tioned sampling density taking the shape of the limit state surface into account may be used The standard normal sampling density will give a simulated additive correction to the FORM probability while the condi tioned density will give a multiplicative correction to the FORM probability As in Directional simulation a nonlinear equation must be solved in order to find the point s where the fail ure surface intersects the sampled search direction Three search methods are supplied giving different trade off between safety and speed The length of an Axis Orthogonal simulation my be controlled by defining the maximal number of simula tions by restricting the time to be used or by demanding a
305. ty incorporates variables as signed as adjusted simulation density in a sam pling of probability The sampling adjustment is for the standard normal u space variables and is restricted to normal random variables SESAM Proban Program version 4 4 01 OCT 2004 5 191 NOTES 1 The current analysis selection may be printed by use of the PRINT ANALYSIS SETTINGS command 2 Both a probability and a distribution analysis method is selected at the same time See also PRINT ANALYSIS SETTINGS DEFINE ANALYSIS OPTIONS DEFINE CONTINUOUS PROCESS DEFINE DISTRIBUTION SIMULATION DEFINE MEAN VALUE FORM DEFINE DISTRIBUTION SIMULATION DEFINE PROBABILITY SIMULATION e RUN PROBABILITY ANALYSIS e RUN CONTINUOUS PROCESS ANALYSIS e RUN DISTRIBUTION ANALYSIS e ASSIGN SIMULATION DENSITY EXAMPLES The following values are default when the program starts up with a new database SELECT ANALYSIS M SELECT ANALYSIS M THOD PROBABILITY ANALYSIS FORM THOD DISTRIBUTION ANALYSIS MONTE CARLO SIMULATION a a Proban SESAM 5 192 01 OCT 2004 Program version 4 4 SELECT FUNCTION LIBRARY FUNCTION LIBRARY name PURPOSE Select one or more function libraries in order to limit the selection of functions presented in other com mands PARAMETERS name A selection of function library names NOTES 1 This command serves to mask off some function libraries temporarily This
306. ulation X SPACE is used to calculate the x space model space values of all variables used in the definition of the specified event Those values that are not specified in the command are set to their median value before calculation Get a main result a sensitivity factor or a design point value MAIN RESULT is used to access any one main result The re sult name lt mresname gt can be any of those allowed in the PRINT RESULT PARAMETER STUDY command SENSITIVITY is used to access any one sensitivity value the derivative of target with respect to one parameter DESIGN POINT is used to access the value of lt variable gt in the design point for single event lt sevent gt The value is re turned in either X V or U SPACE The inters input is need ed if a calculation of bounds was performed Name of event Matrix of variables and their corresponding x space values Matrix of variables and their corresponding u space values Proban 5 128 mresname target parameter inters variable sevent NOTES SESAM 01 OCT 2004 Program version 4 4 Main result name Depends on the analysis type For example Beta FORM Depends on the analysis type In a probability analysis the tar gets are Beta Probability and Log10 Prob and in a distribu tion analysis the target names are Mean Standard Dev Skewness and Kurtosis Name of parameter Index of intersection if event is a union for exampl
307. ult is presented here The main commands are ASSIGN CREATE etc These are described in Chapter 5 When moving inside a command the prompt will change and a default may be presented Different items on the command line are separated by blank spaces except if it is text that is protected inside quotes In special cases the blank space may be left out Such cases are documented in the sections below Proban does not require line breaks anywhere Thus several commands can be typed into the same com mand input line In the following input typed by the user is shown in bold face while prompts given by Proban are shown as ordinary text 4 4 1 How to get Help Context sensitive help is available in command mode at any time using any of these methods Table 4 2 How to get help in line mode Type to get a brief description of what Proban is expecting right now during a selection between alternatives to see all the alternatives that match Type lt text gt ae ae YP lt text gt lt text gt may contain wildcards or be an abbreviation Type to get a more descriptive help text showing how to proceed There is also a HELP menu under the main menu giving on line access to the items that are described here SESAM Proban Program version 4 4 01 OCT 2004 4 9 4 4 2 Command Input Files Line mode commands may be read from a file as well as typed directly into Proban Such a file may contain any syntax that is all
308. ult status is changed Wildcards may be used to specify lt row gt All matching rows will be excluded Include only lt row gt in the matrix clearing any previous contents first Set the ONLY lt row gt default status to INCLUDE Until the status is changed rows that are entered will be added at the end Insert lt row2 gt before lt row1 gt Set the default status to INSERT BEFORE INSERT BEFORE Until the status is changed rows will be keep being inserted before lt row1 gt lt row1 gt lt row2 gt immediately after the last row entered Wildcards may be used to specify lt row1 gt provided that one row is matched uniquely Overwrite lt row1 gt with lt row2 gt Set the default status to OVERWRITE The next row s that are entered will continue overwriting until the default status is changed scrolling down as they do so When the last row has been overwritten the default status is changed to INCLUDE Wildcards may be used to specify lt row1 gt provided that one row is matched uniquely OVERWRITE lt row l gt lt row2 gt LIST List the contents of the matrix Insert Exclude or overwrite using lt row gt depending on the default status The TOWA initial default status is INCLUDE When a default vector matrix is being presented or if the left parenthesis has been typed as input Proban presents the right parenthesis as default A single question mark will show the possible alte
309. umerator then the probability in the denominator and finally divides to get the conditional probability Importance factors and parametric sensitivity values may be calculated with a conditional probability In this case the importance factors and the sensitivity values with respect to the mean values is calculated ASSIGN SENSITIVITY CALCULATION VARIABLE ONLY Mean Assigned Assigned Assigned Assigned Assigned RUN PROBABILITY ANALYSIS CONDITION se se se se se nsitivity calculation to the Mean nsitivity calculation to the Mean nsitivity calculation to the Mean nsitivity calculation to the Mean nsitivity calculation to the Mean ED SINGLE EV SINGLE EVENT Starting Probability Analysis of NPV lt 0 0 The Triang The Triang le density for variabl le density for variabl le Il is not le 12 is not of of of of of I1 A El E2 Il 12 S ENT NPV lt 0 gt 70000 given 11 gt 70000 0 differentiabl differentiabl le everywhere le everywhere WARNING The model does not fulfil the differentiability requirements of the selected analysis As a consequence the analysis may not work or the may be wrong results particularly sensitivities Analysing intersection event in conditional Starting SORM calculation calculation SESAM 0 1 OCT 2004 Proban Program version 4 4 Starting lineariza
310. utions to the sample by creating variables with type attribute Fitted Dis tribution see Section 3 9 2 2 7 2 Latin Hypercube Simulation Latin hypercube simulation is a refinement of Monte Carlo simulation designed to be used in cases where the calculation of a sample point is time consuming The sample points are spread out over the sample space in a systematic way in order to cover the space as well as possible with a few points The technique is illus trated in Figure 2 16 Each axis is divided into a number of intervals the number of intervals being equal to the number of sample points Each of these intervals has the same probability content One coordinate is sampled from each inter val on each axis and the coordinates are combined into sample points in the sample space in such a way that each coordinate is used exactly once This ensures a spread of the points over the sample space The target value is calculated in each of these points and these values are then treated as an ordinary sam ple as described in Section 2 7 1 above u space Figure 2 16 Latin hypercube simulation Proban fits if possible a Hermite transformation distribution to the sample using the estimates of the first four moments This is stored in a variable called Hermite Fit Proban will also fit a normal distribution using the estimated mean and standard deviation This is stored in a variable called Normal Fit It is also possible to fit other distr
311. ve whole number The extreme distribution is the maximum of n_max independ ent identically distributed variables with the distribution that was input when the selected variable was created changed n_max must be a positive whole number No extreme type distribution is used for this variable 2 The extreme value assignment is printed by use of the PRINT VARIABLE command See also e PRINT VARIABLE EXAMPLES ASSIGN EXTREME VALUE Amp ASSIGN EXTREME VALUE Amp itude MAX OF N 5 itude NONE SESAM Program version 4 4 Proban 01 OCT 2004 5 15 ASSIGN FUNCTION OPTION FUNCTION function FUNCTION OPTION option value VARIABLE variable PURPOSE Assign input that is not of random nature to a model function PARAMETERS FUNCTION function VARIABLE variable option value NOTES Assign the value directly to a function In this case it is applied to all variables cre ated by use of the function until changed again Name of the function to which the value is assigned Assign the value to a variable that is based on a model function This assignment affects only the selected variable not any other variables based on the same func tion Name of the variable to which the value is assigned The option to be defined The range of available options varies from function to function The value of the option This will be either a whole number a
312. wDiff 1 3 0 Sign X1 Abs X1 X3 Sign X2 Abs X2 X3 Sum 1 Input O Sum of any number of variables SESAM Proban Program version 4 4 01 OCT 2004 5 147 PRINT FUNCTION RESPONSESURFACE RESPONSESURFACE name PURPOSE Print description of a selection of response surface functions PARAMETERS name Name s of the response surface function s to be printed NOTES Prints the name description argument list and definition of a response surface function See also e CREATE FUNCTION RESPONSESURFACE CHANGE FUNCTION RESPONSESURFACE e DELETE FUNCTION e RENAME FUNCTION e SET TITLE Proban SESAM 5 148 01 OCT 2004 Program version 4 4 EXAMPLES PRINT FUNCTION FORMULA SYMFUN Generates the following print SYMFUN Symbolic Function Gradients must be calculated numerically Name DescriptionValue Index _ Arg AVL B Arg BV2 Operator OperandsResult A o Formula A B SESAM Proban Program version 4 4 01 OCT 2004 5 149 PRINT FUNCTION VALUE VALUE function SINGLE POINT dim argument PURPOSE Calculate and print the value of a function PARAMETERS function Name of the function to be printed SINGLE POINT The value is to be calculated in a single point dim The dimension of the value calculated by the function Is not required as input if the dimension is fixed argument The arguments of the function NOTES 1
313. ween the original distribution and the updated distribution SET TITLE Updating of NPV distribution Income after first year gt 70000 DISPLAY RESULT DISTRIBUTION ONLY Original Fit Updated Fit DISTRIBUTION Proban 3 38 Distribution 01 OCT 2004 SESAM PROBAN 4 3 03 22 JUN 2000 16 38 Updating of NPV distribution Income after first year gt 70000 Distribution function a SESAM Program version 4 4 o T T 30000 20000 10000 0 Variable 2 Original Fit Updated Fit T 10000 1 20000 30000 Figure 3 7 Comparison between original and updated distribution of NPV The income still has the same upper limit so the upper limit of the distribution has not been changed Instead the centre and lower tail is shifted so that the probability of a loss now is about 0 2 3 6 2 Mean Value Based FORM The mean value based FORM method gives an estimate of the distribution function of a variable The options for the method are controlled by the command DEFINE MEAN VALUE FORM see the explana tion of this command The default options will usually suffice Sensitivity calculation and conditional distribution analysis cannot be done using the mean value based FORM method Running this method on the Net Present Value of Example 3 2 using the default options gives the following messages from Proban SEL ECT ANALYSIS MI EAN VALU E FORM ETHOD
314. well as the dimension and function value SESAM Proban Program version 4 4 01 OCT 2004 5 117 See also e DEFINE PRESENTATION FUNCTION PRINT FUNCTION ASSIGN FUNCTION OPTION e SET GRAPH EXAMPLES DISPLAY FUNCTION Power 0 0 2 34 ONE ARG Value 7 0 DISPLAY FUNCTION Power 0 0 1 0 TWO ARG Value 5 0 Exponent 3 0 SURFACE Proban SESAM 5 118 01 OCT 2004 Program version 4 4 DISPLAY RESULT DISTRIBUTION RESULT IMPORTANCE FACTORS PARAMETER STUDY PURPOSE Display results generated by Proban graphically PARAMETERS DISTRIBUTION Display the result of a distribution analysis IMPORTANCE FACTORS Display the importance factors resulting from a probability analysis PARAMETER STUDY Display results as a function of the parameters in a parameter study NOTES None SESAM Program version 4 4 Proban 01 OCT 2004 5 119 DISPLAY RESULT DISTRIBUTION DENSITY DISTRIBUTION value1 value2 var coordi DISTRIBUTION nate result COMPLEMENTARY DISTRIBUTION PURPOSE Display distribution and density functions for existing variables and for results PARAMETERS valuel value2 univar coordinate result DENSITY DISTRIBUTION COMPLEMENTARY DISTRIBUTION NOTES This input is only required if the selected result is a parameter study Value is then one of the first parameter values for which the study was run The particu
315. wn the left mouse button Alternatively display the menu but keep the mouse button down Then move the pointer through the menu to the selected alternative and then release the mouse button The Type menu of the Variable dialog box is an example of an option menu A Scrollable list is a list of alternatives that is presented in a scrollable box Such a menu is used in order to save space or because the items in the list cannot be predicted before the menu used A scrollable list is either a single selection list or a multiple selection list Use the scrollbar to manoeuvre through the list In a single selection list place the pointer on the desired alternative and press down the left mouse button In a multiple selection list place the pointer on the first desired alternative and press down the left mouse button and keep it down Then drag the pointer through the list and release the button when the selection is ready To modify an existing selection in a multiple selection list hold the Control key down and make a selection as described above The alternatives selected this way then reverse their selection status Selected values are marked by highlighting The Distribution list in the Create Variable dialog box is an example of a single selection scrollable list The Function list in the Print Function Description dialog box is an example of a multiple selection scrollable list Proban SESAM 4 20 01 OCT 2004 Program version 4 4 Plot Options
316. write one plot only to each plot file that is to be imported into a word proc essor 3 11 2 If the Required Plot Format is not Available If the plot format required by your printer plotter is not available in the SET PLOT FORMAT command you can try the following 1 Write the plot file in SESAM NEUTRAL format 2 Use the program PLTCNV_EXT which is delivered with Proban to convert it to another format This program includes several formats that are not available in Proban However the extra formats are not tested and supported as well as the formats included in Proban itself 3 11 3 Problems with Convergence During FORM SORM Analysis In some cases the calculation of reliability index using FORM or SORM fails There are basically two things that can go wrong 1 The search for the design point s fails In this case Proban will display a message stating that the linearisation of the design point has failed The Kuhn Tucker convergence criterion KTO can be monitored by using the commands DEFINE ANALYSIS OPTION INTERMEDIATE PRINT LEVEL SESAM Proban Program version 4 4 01 OCT 2004 3 73 DEFINE ANALYSIS OPTION NESTED ANALYSIS INTERMEDIATE PRINT GLOBAL DEFINE ANALYSIS OPTION NESTED ANALYSIS INTERMEDIATE PRINT SYSTEM and inspect the development of the KTO Very often it converges initially to a small value and then do not get further This is most often caused by lack of numerical precision in the calculation of functions
317. xit conv range incrementation initial increment reduction factor minimum increment zero limit PURPOSE Options for RSM PARAMETERS method contribution maxit conv range incrementation initial increment reduction factor minimum increment zero limit One of LINEAR LINQUADIAG and LINQUA LINEAR ap proximates the function with a linear surface LINQUADIAG includes the diagonal terms of a quadratic approximation LIN QUA estimates a full quadratic approximation LASTPOINT means that only the last point is used for function approximation RADIUSCONTR means that experiments gen erated around a point that is closer than range to the current it eration point contributes to the response surface generation It contributes only if the incremnt used at that point is also less than range Maximum number of general iterations response surface ap proximations Optimality criterion When the u space distance between two successive iterates is less than conv the iteration stops As described above contribution ONEWAY or TWOWAY One way means that an experiment is defined at ut delta TWOWAY means that an experiment is also defined at u delta delta at the starting point for the iterations delta is divided by the reduction factor once for each new iter ate The minimum delta If the reduction yields a value less than this value the minimum value i

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