Home

manual - KU Leuven

1. Cancel OK Figure 4 3 Tutorial 1 Entering node numbers and coordinates for the creation of the grid file 6 Now you are ready to save the grid file Press OK in the DEFINE EDIT MEASUREMENT GRID window and choose a name and a directory for instance framegrid asc in the tutorial1 di BO TUTORIALS Define Edit measurement grid r Add node to measurement grid Node number 1 5 Coordinates x Izeros 1 5 j add y zeros 1 5 Z 0 2 8 List of nodes Node number Coordinates X Y Z SA Equalaxes V Nodes Remove Rotate3D Edit save figure Cancel oK Figure 4 4 Tutorial 1 Entering multiple node numbers and coordinates at the same time rectory The DEFINE EDIT MEASUREMENT GRID window closes and you return automatically to the MACEC main window In this window the path name of the grid file you just created is now filled in in the GRID FILE command line of the GEOMETRY section Note The grid file is saved in ASCII format so that it can also be created with a text edi tor instead of with the MACEC GUI This facilitates the creation of the grid file when the nodal information is available in ASCII format for instance from Microsoft Excel The grid file is selected by typing its path in the GRID FILE command line of the MACEC main window or by using the SELECT GRID FILE button of the MACEC main
2. Modal Analysis Modal analysis Combine setups Figure 4 8 Tutorial 1 If the measurement data is available in MAT format the sampling frequency must be provided 14 15 in the LABEL field fig 4 9 As the measurement data have the physical meaning of accelerations you don t need to change the DATA TYPE The data are given in m s so you can leave the MEASUREMENT UNITS the SENSITIVITY and the AMPLIFICATION fields to their default values In the same way you can provide the labels for the other 3 channels Afterwards press the OK button fig 4 9 Now the MCSIGNAL object will be saved in a mat file for which you have to provide a proper name like for instance framedata_conv mat You can also specify a directory different from the current working directoy After you have saved the MCSIGNAL object MACEC automatically returns to the main window where the file framedata_conv mat has now been added to the FILE S IN USE section The next step is the actual processing of the measurement signals In order to do so select the framedata_conv mat file in the FILE S IN USE section and press the PROCESS button in the SIGNAL PROCESSING section The PREPROCESS MCSIGNAL OBJECT window opens fig 4 10 You can have a look at the time history and the frequency content of the different signals As the simulated measurement data in this case need no further preprocessing just press the OK button
3. Figure 4 32 Tutorial 2 Loading a GRID file 2 In the same way select the b15_slave asc file from the spice tutorials tutorial2 direc tory using the SELECT SLAVE FILE button in the GEOMETRY section of the MACEC main win dow Afterwards select the b15_surface asc file from the spice tutorials tutorial2 directory using the SELECT BEAM OR SURFACE FILE button in the GEOMETRY section of the MACEC main window 60 TUTORIALS 4 2 4 Processing the measured signals The geometry of the B15 bridge has now been loaded so the signal processing part can start 3 Select the files with the simulated measurement data by pushing the SELECT NEW DATA button in the MACEC main window Choose the files VALA1 1 F32 VALA2 1 F32 VALA3 1 F32 VALA4 1 F32 VALA5 1 F32 VALB1 1 F32 VALB2 1 F32 VALB3 1 F32 VALB4 1 F32 VALB5 1 F32 in the spice tutorials tutorial2 measurements directory The names of these files appear in the FILE S IN USE list in the MACEC main window Select all files and press the CONVERT TO MCSIGNAL button in the SIGNAL PROCESSING section to open the CONVERSION OF THE MEASURED DATA window In the previous tutorial it was indicated how you can convert the measurement data to an MCSIGNAL object using this window so this is not explained in detail here but the sensitivities amplification factors conversion factors labels and units have been saved on beforehand Therefore press the LOAD button fig and select
4. 4 in the MACEC GUI press the MAKE GRID FILE button fig 4 2 MACEC 3 2 aog LEUVEN Geometry Grid file Slave file Beam surface file 088 Signal Processing Convert to mesignal Add DOFs J laa Stochastic Subspace l System Identification Modal Analysis Modal analysis Combine setups 1425 Al Figure 4 2 Tutorial 1 Starting the GUI for making a grid file 5 Now the DEFINE EDIT MEASUREMENT GRID window appears Enter the following node num bers and coordinates and then press the ADD button fig 4 3 OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE 29 Z o NO mT Fw YY waa awae oo o off See es eo SS S eo kN owon N ojn Each added node is automatically plotted in the right figure of the DEFINE EDIT MEASURE MENT GRID window fig 4 3 This enables you to check visually if the node numbers and the corresponding coordinates have been entered correctly If you want to edit or save the figure with node numbers and coordinates press the EDIT SAVE FIGURE button Note it is also possible to add multiple nodes at the same time by using standard MATLAB commands fig 4 4 Define Edit measurement grid Add node to measurement grid Node number 10 Coordinates x5 List of nodes Node number Coordinates X Y Z 0 Equal axes v Rotate3D Edit save figure
5. _ _ _ i Ml label 5X Acceleration m s2 Visualization 40 50 60 Show data from Time s T N o Olsto 81928 an Time Frequency 5 Log x Log Y mn Acceleration m s Hz o Double sided PSD parameters o 10 16 20 25 30 E 40 45 Window type Frequency Hz Ree Preprocessing O Hanning Remove offset v Save Resume Window length Remove ote E L 8182 ponts Apply to Overlap r This channel All channels Save figures OK 0 O Selected channels e g 3 5 8 Figure 4 10 Tutorial 1 Preprocessing the MCSIGNAL object Add channel specifications Select a channel Node and DOF information a Label 2x Data type acc Node Oz O Custom azimuth b elevation o Save Cancel Figure 4 11 Tutorial 1 Coupling between the measurement nodes in the grid file and the measurement channels 38 TUTORIALS 4 1 4 Identification of a linear system model Now you are ready to perform system identification 11 As you have only output data at your disposal the only system identification methods you can use are output only or stochastic system identification methods MACEC contains four of these methods e Nonparametric PSD estimation using the correlogram or periodogram approaches e Reference based data driven stochastic subspace identification SSI data ref e Reference based covarian
6. Complex Mode Indication Function CMIF Frequency Domain Decomposition FDD Mode information Frequency Hz 8 Selected mode shape into Scale channel 1 Y tot Singular value MPC 0 ne o _R 5 o oo o o P A A v t Show real imaginary part Show absolute value angle q Channel 1 1 a 2 2 amp 3 gt E n Channel 2 0 015659 0 0793451 Channel 3 0 061035 0 025343i Channel 4 0 19257 0 08114i Channel 5 0 62598 0 55041 Channel 6 0 44927 0 141331 ani 0 77457 0 22406i Channel 8 0 059747 0 0341i Channel 9 0 15488 0 141521 10 15 frequency Hz Show data from Ol Hz to 24 7154 Hz Y Show CMIF FDD in dB Apply ok Figure 4 42 Tutorial 2 CMIF function for the first measurement of the first setup The selected modes are indicated with red circles 22 23 24 25 If the modes of all 10 setups have been selected we can make use of MACEC s possibility to combine modal information obtained from different setups into one single mode Hereto select VALA1 1_cmif_modes mat and the mode information for the nine other setups in the FILE S IN USE section of the MACEC main window and press the COMBINE SETUPS button in the MODAL ANALYSIS field Save the resulting modes as VAL 1_cmif_modes mat Now select this file in the FILE S IN USE section of the MACEC main window and press the PLOT MODE SHAPES button in the MODAL ANALYSI
7. PSD estimation PSD estimation Correlogram method Number of time lags j zero lag included 1024 Periodogram method Number of data blocks Time window parameter ate standard deviation Calculate and show estimates Resolution info Plot options Show PSD Show correlation 2 Show data in dB Show estimation history Show standard deviation Total number of samples 8192 Window length 1024 samples Frequency resolution 0 097656 Output channel la x Reference 1 10 15 frequency Hz Ce Figure 4 14 Tutorial 1 PSD estimation with the correlogram method PSD estimation PSD estimation Correlogram method Number of time lags 7 zero lag included d Periodogram method Number of data blocks _ 8 Time window parameter l 2 Calculate standard deviations ate and show estimates _ Resolution info Plot options Show PSD O Show correlation Show data in dB Show estimation history 4 Show standard deviation Total number of samples 8192 Window length 512 samples Frequency resolution 0 19531 Output channel la x Reference 1 L 10 15 frequency Hz Ce Figure 4 15 Tutorial 1 PSD estimation with the periodogram method Using SSI data 41 22 Select the file frameda
8. i N Visualization Show data from Olsto 12288 s Autocorrelation PSD Y Log x C Log Y a in o r Double sided PSD parameters 212 Acceleration PSD m s Mal Square acceleration m s2 x 100 150 200 Window type Frequency Hz Rectangular A O Hanning Preprocessing SoS SE Save Resume Window length emesis n 6144 points Apply to Ls Overlap p O This channel 5 All channels Save figures OK 01 Selected channels e g 3 5 8 o Figure 4 35 Tutorial 2 Removing the offset from the signals 7 Now let s have a look at the PSD of both reference accelerations channels 1 and 11 and the force signal channel 12 You can easily notice that the main part of the signal s energy lies between 0 and 100 150Hz However in bridge engineering the frequency range of interest is between 0 and 20Hz In order to perform a data reduction and to facilitate the System Identification let s first apply digital filtering to the signals and then re sample them so that we have now a Nyquist frequency of 25Hz instead of 250Hz Hereto select DECIMAT 112 in the PREPROCESSING section and press APPLY MACEC now asks for the decimation factor an integer by which the number of samples will be divided Choose 10 and press OK fig 4 36 After the decimation press OK and save the processed MCSIGNAL object as VALA1 1_proc mat Repeat the preprocessi
9. to access this function See also MCSIGNAL PLOT 5 1 5 concatenate MCSIGNAL Multi channel time signal unity time 1 s constructor y MCSIGNAL s1 s2 concatenates the time histories of the mcsignals s1 s2 to a single mcsignal The number of channels must be the same for all mcsignal objects The sampling frequency quantity sifactor and labels of y are equal to those of sl s1 s2 mcsignal objects to assemble into 1 mcsignal y resulting mcsignal object See the example master files for info on the usage of the MCSIGNAL class 5 1 6 decimate DECIMATE Decimate a mcsignal y DECIMATE x applies the global function DECIMATE x tdata to the channels of the mcsignal x x mcsignal object y mcsignal object Use y x decimate to access this function See also the global function DECIMATE 5 1 7 delete DELETE Delete channels from a mcsignal y DELETE ich1 x deletes the channels ich1 from the mcsignal x X mcsignal object ich1 Channels to delete Default all channels y mcsignal object Use y x deletefich1 to access this function See also MCSIGNAL SELECT MCSIGNAL ___ ZT 5 1 8 detrend DETREND Detrend a mcsignal y DETREND ich1 x applies the global function DETREND x tdata ichi to the specified channels ichi of the mcsignal x x mcsignal object ichi Channels to detrend Default all channels y mcsignal object Use y x detrend ichi to ac
10. 1 1 What s new in MACEC 3 3 This section highlights the changes in MACEC 3 3 with respect to MACEC 3 2 The major changes with respect to MACEC 3 1 3 0 and 2 0 are listed in sections 1 2 1 3 and 1 4 respectively e The implementation of the covariance driven stochastic subspace identification SSI cov algo rithm has been thoroughly modified resulting in a fast and memory efficient computation of the co variances of the estimated system matrices and modal characteristics e The possibilities to save animations of mode shapes have been extended such that it is now possible to save the animations both on Windows 32 bit and on Windows 64 bit platforms in avi format e A new tutorial has been added with a double aim explaining how MACEC can be run in batch mode and how MACEC functions can be integrated into Matlab scripts and explaining how a roving hammer test can be efficiently processed with MACEC 1 2 What s new in MACEC 3 2 This section highlights the changes in MACEC 3 2 with respect to MACEC 3 1 The major changes with respect to MACEC 3 0 and MACEC 2 0 are listed in sections 1 3 and 1 4 respectively e Modal parameter estimation from identified nonparametric frequency response functions FRFs or positive power spectral densities PSD s has been made possible by adding new functions Qo INTRODUCTION and a new GUI Although this approach yields usually rather rough modal parameter estimates compared to parametr
11. 13 After selecting the stable modes from the stabilization diagram the results can be saved and visualized as detailed in the previous tutorials 4 3 6 Interpretation and conclusions The set modes that you have identified will most probably include the ones that are presented in Fig 1 50 From an inspection of the mode shapes it is clear that they can be characterized by a two digit combination nx ny where nx denotes the number of half wavelengths in the z direction and ny denotes the number of half wavelengths in the y direction Besides the modes that are presented in the figure a few other stable modes may have been selected However their mode shapes cannot be given a clear physical interpretation and these modes do not show up when modal characteristics are numerically computed from a detailed finite element model of the rib stiffened plate This indicates that they additional stable modes are an artefact of the modal analysis process One may therefore conclude that modal testing is often not straightforward even in laboratory conditions and that the results should be carefully analyzed and interpreted BA OOO TUTORIALS 30 9 Hz 1 1 48 5 Hz 2 1 83 0 Hz 3 1 106 Hz 1 2 135 Hz 4 1 143 Hz 3 2 3 0 3 7 3 6 3 0 3 7 3 1 185 Hz 4 2 201 Hz 5 1 210 Hz 1 3 219 Hz 2 3 243 Hz 3 3 245 Hz 5 2 3 3 3 6 3 4 3 0 3 1 3 1 Figure 4 50 Tutorial 3 rib stiffened plate eigenfrequencies damping ratios and mode
12. Label language en or nl Default Default no legend en See also LEGEND Legend location Default Best See also LEGEND Default 0 5 for domain t and f and 1 5 for domain b Margins between the axes and the bounding box in centimeters See NEWFIG for more info Number of XTicks approximately see the global function TICK Default Number of YTicks approximately see the global function TICK Default auto X axis label Default defined using MCSIGNAL LABEL Y axis label Default defined using MCSIGNAL LABEL X axis scaling minimum value Default left side of the plotted curve X axis scaling maximum value auto Default right side of the plotted curve Y axis scaling minimum value Default defined as a function of the plotted curve Y X max abs Y for domain t O for domain f and min Y for domain b Y axis scaling maximum value Default defined as a function of the plotted curve Y X max abs Y for domain t and max Y for domains f and b See also NEWFIG SAVEFIG MCSIGNAL TPLOT MCSIGNAL FPLOT MCSIGNAL BPLOT 9 ooo OVERVIEW OF MACEC FUNCTIONS 5 1 4 bplot BPLOT Plot multi channel signal 1 3 octave band RMS spectrum BPLOT ichi x filename KeyName KeyValue executes the function PLOT b ich1 x filename KeyName KeyValue Use x bplot ich1 filename KeyName KeyValue
13. MODAL ANALYSIS dS allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes allmodes Note if dlambdac vector with minimal relative continuous time eigenvalue distance to a mode of the nearest lower model order df vector with relative eigenfrequency difference w r t the same mode of the nearest lower model order as in allmodes dlambdac dxi vector with relative damping ratio difference w r t the same mode of the nearest lower model order as in allmodes dlambdac Dxi vector with absolute damping ratio difference w r t the same mode of the nearest lower model order as in allmodes dlambdac mac MAC value between the current mode and the same mode of the nearest lower model order as in allmodes df dtrinfd vector with relative deterministic modal transfer infinity norm difference w r t the same mode of the nearest lower model order as in allmodes dlambdac dtrinfs idem but for stochastic infinity norm stdf vector with standard deviations of the eigenfrequencies Hz stdxi vector with standard deviations of the damping ratios stdmr matrix with standard deviations of the real part of the mode shapes stdmi matrix with standard deviations of the imaginary part of the mode shapes stdmmax vector with the maximal standard deviations of the mode shapes cov 3D matrix
14. Preprocessing Decimate Apply to This channel All channels Selected channels e g 35 37 Apply File VALAS 1_convmat Y Channel MIE Visualization Show data from Ole to 12 288 J Time Frequency Reference channel 1 Log x Log Y Window type Rectangular O Hanning Window length Overlap Double sided PSD parameters Preprocessing Delete channel Y Apply to This channel All channels Selected channels e g 3 5 8 JU 63 Figure 4 37 Tutorial 2 Setup 5 deleting channel 6 ADD DOFs button in the SIGNAL PROCESSING section Because the definition of the DOFs has already been treated in the first tutorial section 4 1 3 they have been prepared on beforehand in this case In the ADD CHANNEL SPECIFICATION window press the LOAD button and choose b15_dofs_F1 mat 64 TT TUTORIALS All DOF information is now adjusted Press OK and then YES to save the DOF information Repeat this for the other setups 4 2 5 System identification In MACEC classical experimental modal analysis EMA is possible with nonparametric frequency response function FRF estimation using the classical H estimator 5 and with the deterministic pLSCF method which is a parametric method that starts from a nonparametric FRF description In EMA the influence of the unmeasured ambient
15. _ S S a21 colorind integer equal to 1 if the plot must be in color otherwhise it is in greyscale f_low frequency lower bound f_high frequency higher bound freqscale frequency scale optional psdpsum sum of power spectral densities optional frfsum sum of frequency response functions optional 5 5 System identification 5 5 1 Hlestimate H1ESTIMATE FRF estimation using the H1 estimate hifrf freqscale Hlestimate predat Nblocks windowtype inputs outputs fmaxstr pgbar hifrf hicov freqscale Hlestimate predat Nblocks windowtype inputs outputs fmaxstr pgbar hifrf frf estimate using H1 method row outputs columns frequencies depth inputs hicov 3D matrix of covariances on the H1 estimate row outputs columns frequencies depth inputs freqscale frequency scale predat mcsignal object Nblocks number of blocks to be used in averaging procedure windowtype window type to be used in averaging procedure Valid arguments are rect for a rectangular window and hann for a Hanning window inputs vector with channel input numbers outputs vector with channel output numbers fmaxstr string indicating whether the maximal frequency in hifrf should be the Nyquist frequency fn or the sampling frequency fs pgbar boolean indicating whether a progressbar should be shown 1 or not 0 5 5 2 PSDpos_corr PSDPOS_CORR Estimation of Positive Power Spectral Densities PSD s via the
16. x mcsignal object ichl Channels to apply the window to Default all channels W Window function Must have x N rows and 1 or x nch columns y mcsignal object Use y x window fichi w to access this function See also MCSIGNAL TRIM and the global functions DINTRIMDATA and BUTTERWINDOW 5 2 Conversion 5 2 1 cell_ CELL_ Convert char to cell x cell_ y y a char of size m n x a cell of size m 1 Note white spaces at the ends are trimmed CONVERSION AA OS 5 2 2 fe2ss FE2SS Conversion of a finite element to a state space model A B C D A B C D fe2ss K M Cv Ts fe2ss K M Cv Ts DOF uDOF udDOF uddDOF iDOF A B C D state space matrices If Ts 0 the description is in continuous time If Ts gt 0 the description is in discrete time In the discretization a ZOH assumption is made K M Cv finite element stiffness mass and viscous damping matrices Ts sampling time interval If Ts 0 the resulting description is in continuous time DOF vector with degree of freedom numbers of K M and Cv optional uDOF output displacement degrees of freedom numbers optional udDOF output velocity degrees of freedom numbers optional uddDOF output acceleration degrees of freedom numbers optional iDIF input force degrees of freedom numbers optional 5 2 3 input2mcsignal INPUT2MCSIGNAL This function converts measurement files to objects of the mcsignal class The MCSIGNAL class combines the storage of the time
17. An RMFD description can be estimated from nonparametric FRF data using the MACEC function RMFDCALC see section 5 5 4 One of the parameters that need to be specified by the user is the model order range Please note that the model order of an RMFD model is not equal to that of a state space model the model order of a state space model equals the model order of the corresponding RMFD model multiplied with the number of inputs amounting to 5 in this case Sec 2 2 7 Since the true system order is unknown a wide range of RMFD model orders is chosen here from 2 to 100 in steps of 2 The resulting lines of code read estimate RMFD description using the pLSCF method rmfd RMFDcalc Htot pLSCF 2 2 100 1 nDOFs nDOFs 1 5 f 1 f end 2 Note that the RMFDCALC function also asks for output and input channel numbers these are the fourth and fifth arguments of the function respectively Because the FRF was estimated from different data files dummy numbers are assigned here The outputs are given channel numbers 1 to 56 and the inputs numbers 57 to 61 82 TUTORIALS Tutorial 3 roving hammer test of a rib stiffened plate clear all close all cle DOFs repmat 1 7 1 8 kron 1 8 10 ones 1 7 list of DOF numbers nDOFs length DOFs total number of DOFs Htot zeros nDOFs 5 2918 overall FRF matrix for par 1 nDOFs loop over all hammer tests hDOF DOFs par DOF at which the hammer is applied fi
18. The function calculates the modal phase collinearity of each mode in Psi according to pp 3 4 of R S Pappa K B Elliot and A Schenk A consistent mode indicator for the eigensystem realization algorithm Technical report TM 107607 NASA Hampton VA 1992 y MPHC Psi Psi matrix containing a mode shape in each column y vector containing the modal phase collinearities of the modes in Psi See also MP MPD 5 4 13 mscf MSCF Modal scale factor matrix calculation z mscf x y 116 OVERVIEW OF MACEC FUNCTIONS x y matrices containing mode shapes in each column Z matrix containing the modal scale factors between the columns of x and the columns of y 5 4 14 npmodselect NPMODSELECT Select modes after nonparametric system identification stabmodes stabmodes allmodes freqs stabmodes svals npmodselect allmodes freqs npmodselect allmodes freqs svnums nonparametric allmodes structure structure see anpsd m or cmif m vector containing selected frequency lines structure containing the same fields as allmodes but only at the selected frequency lines vector containing the singular value numbers at the selected frequency lines needed for CMIF FDD only 5 4 15 propmodpar5 PROPMODPARS Modal parameters of a continuous time or discrete time state space model If the model is in discrete time a zero order hold ZOH discretization assumption is used fud xi Phi fud xi Ld Km Gm quan
19. This file now contains 3 variables e PREDAT the mcsignal object with the preprocessed measurement data e NODE_NUM a vector containing the node numbers that correspond to the channels e MEAS_DIR a matrix containing the angles a and 6 that correspond to the channels figure 3 5 Each row corresponds to a channel the first column contains the a values and the second column the P values FILE STRUCTURES AA 9 Figure 3 5 Definition of the direction angles a and Measurement DOFs In the ADD CHANNEL SPECIFICATIONS window of the MACEC GUI it is possible to save the mea surement nodes and measurement directions into a mat file and to load this file later on This is particularly handy if in the same measurement setup different measurements are performed The saved file contains the following variables e NODENUMBERS is a vector containing the node numbers attached to each channel e MEASUREMENT_DIRECTIONS is a matrix containing in each row the a and 8 angles in the first and the second column respectively which determine the measurement direction figure 3 5 System Identification results After you have performed a system identification using the GUI you have to save the identified system information in a mat file State space models If the identified system models are state space models identified with SSI data ref SSI cov ref or CSI ref this mat file contains the following variables e
20. fig 1 10 and save the preprocessed MCSIGNAL object all framedata_proc mat 1 Please note that the SAVE and RESUME buttons do not save the preprocessed MCSIGNAL object to a file but are used to intermediately save the processed data and to resume from the last save respectively 36 TUTORIALS Conversion of the measured data Sensitivities Sensor summary Channel 1 No predefined sensor Label 5x Data type acceleration Dd Measurement units 1 v Volt Sensitivity 1 vims Amplification 1 Das Read sensor file Figure 4 9 Tutorial 1 Conversion of the measurement data to an MCSIGNAL object 16 A last thing to do before the System Identification can start is the the coupling between the mea surement nodes defined in the grid file and the measurement channels Select framedata_proc mat in the MACEC main window and press the ADD DOFSs button Now the ADD CHANNEL SPEC IFICATIONS window opens fig 4 11 For each channel you have to provide the corresponding grid node number and measurement direction Note that the channel label turns out to be a useful feature here If you are ready press SAVE to add the channel information to the mat file with the MCSIGNAL object framedata_proc mat OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE OOOO Preprocess mcsignal object an File framedata_conw mt Y Channel
21. pLSCF 10 1 1 L 1 0 10 20 30 40 50 frequency Hz pLSCF 0 10 20 30 40 50 frequency Hz Figure 6 2 Verification example 1b Element 1 1 of the FRF matrix exact values blue H estimate green and the estimate obtained with the identified RMFD description using deterministic pLSCF red 134 OOOO VERIFICATION EXAMPLES 6 1 3 Example 1c modal time domain response decomposition using SSI data The purpose of this example is to demonstrate how the decomposition of a measured response using a stochastic state space model identified from output only data can be implemented in MACEC For the theoretical background of the decomposition we refer to 7 sec 7 3 First simulate the response in exactly the same way as in section Then identify a stochastic state space model using the SSI data method ii 10 half the number of block rows refs 1 2 reference sensors n 4 system order types cell_ strvcat acc acc define data types labels cell_ strvcat 1A 2A define channel labels predat mcsignal y 1 Ts types 1 labels make an mcsignal object node_num 1 2 define node numbers meas_dir 0 0 0 0 define measurement directions invar ssi_data3 predat tdata ii refs Aid Cid Qid Rid Sid ssi_data3 invar n estimate state space model The prediction error that is the RMS error between the measured response and
22. the resulting mode number of allmodes a value equal to 1 if the mode has not been selected yet otherwise it is equal to 0 a vector containing all selected mode numbers a structure containing all the modes see stable_propmodpar5 for the structure of allmodes the frequency that is sought for the model order that is sought for a vector containing all previously selected mode numbers MP Mean phase calculation according to the Total Least Squares approach y mp Psi MODAL ANALYSIS 1S Ly X mp Psi Psi matrix containing a mode shape in each column y vector containing the mean phases of the modes in Psi in degrees X 2 column matrix containing in each row j coordinates in the complex plane such that y j atan X j 2 X j 1 See also MPD MPHC 5 4 11 mpd MPD Mean Phase Deviation according to the Total Least Squares approach y mpd Psi y mpd Psi weight Psi matrix containing a mode shape in each column y vector containing the mean phase deviations of the modes in Psi in degrees weight weighting factor Valid values are abs and none When abs is selected the absolute values of the mode shape components are used as weighting factors If none is selected all weighting factors equal 1 Defaults to abs Note that if all weights equal zero e g when the MPD of a zero vector is computed y is set to zero See also MP MPHC 5 4 12 mphc MPHC Modal Phase Collinearity
23. vmis Das ue pS Read sensor file 61 Figure 4 33 Tutorial 2 Loading a saved file with sensitivities amplification factors conversion factors labels and units Preprocess mcsignal object File VALA1 1_conv mat Channel il Label R1 Visualization Show data from Dis to Referenc Cl Log x C Log Y Double sided PSD parameters Window type Rectangular O Hanning Window length 6144 points Acceleration PSD m s 2 Hz Square acceleration m s2 6 Time lag s o par E 100 150 200 Frequency Hz Apply to This channel All channels Save figures oK Selected channels e g 3 5 8 Preprocessing Remove offset Y P Figure 4 34 Tutorial 2 Plotting the autocorrelation and power spectral density of a channel s signal 6 When you have a look at the autocorrelation signal of the first channel fig 4 34 you notice that there is an offset on the signals that needs to be removed first Therefore select REMOVE OFFSET in the PREPROCESSING section select ALL CHANNELS and press APPLY fig 4 35 When switching through the channels you now indeed observe both from the autocorrelation and the PSD plots that the constant trend has been removed 62 TUTORIALS Preprocess mcsignal object File VALA1 1_conv mat v N Channel 8 Label Ri o
24. 94 a ks evap gy ak pop as an ae ee 94 eu bes Le a Se ee eee bee 94 na ee ene leew ok ae punish be pi paa oe 94 ardid ras ee ee 95 5 1 25 filtfl ee ee eee een 95 pei ghee oe orn oe Ge ee ee ee be ee os 95 tbh hep ays oe os Steck a a en oe a 96 Tbs Gh ae Ss Soa ce ee E eee wade 96 A 424 0644 2 bans eA 4 BORE Reed Od Oo ARS OS 96 neh ae oe Sk oe OA ee ee oe ee ese 96 ihe be een ee ee a et ee ee 97 My wee wee Sak os Ge rates ee ae ee ee ee 98 pe es SRG ode ne es es eee Bee a ee 98 ea is aia de le 98 ie ents oes a ea ee E 98 5 1 36 plo 24 amp oe hed Bcd bSed de bb ees ooo eR GEER ROD SESS 98 se pee a i oes ee ee ee ee 100 ae ety eh ow erence Fh eae ee ele Gees ae ee 100 A A ee 100 o At a Bae 101 rr o ee eee as 101 A AI 101 CONTENTS CASES tee eg ge ee es ee ee Eos ob d 101 pain Baty a ee a ee oie 102 ae ab a HOSA a ERS ark a he ee 102 Lee GP eee a es lee ee ee ee ee ee ae 102 Aen kee oe Ge ee eee eee ae ae en es 102 eee awa es A ee Ea 103 ben eis fh eee og a en es ad 103 Beak ly ona eee oe ee a eda ek a ee ee aa da s 103 Spi sees ee E a ee he 104 Se peas ee adh Sone a ae te 104 Oy bate e ee ee ee a eee 104 A COUP coke cs eras Gs ee Sot Be ae ee Qe oe De Be ee a Se 104 a e ala ae 105 a ico 105 a a az da E 105 5 2 5 A s o eos ee ee a ee Be ee we a D Gee we we ee Ge ee 106 Cen eS Ace eas on eae ade caia ed bees 106 A oa cecy ue oe G 0k ADA Roe be a 106 a eee oe ee 107 Dd Kronpi eed ae ae aa aa eh OE ee Bn a ew ee 8 107 oe Pee
25. Ae ee te oe ee ge eee ee 107 ae ee oe eee nS ee Bee ee eee eee es 107 oh po be oe bo oe oe a ea rca da 107 pe ale ok ee ee a ee 108 e ee 4 4 A ee ee ee 108 be SEG a eee eee a 108 DO Ged Sa oS BE areas Bee e e 108 539 AA 109 o dass a oa 109 A ao 109 A BG a oe Be ee ee 109 54l SANDS EE ee Be a EE a Be aa 109 542 emi oo a 110 Pere eee ee Fe a eee ee eee ees 111 5 44 globmod 2 44 34 442 008544 e208 PA GRA GS Re eH aS ES 112 CONTENTS 5 4 7 mod3D Wain Boas PS hots ote oe ee ee foe Bop ely atte a he he oe os o 5 4 15 propmodpard aoe dete ees A edo ahaa in 5 5 1 Hlestimate a Saeko eae bah ed E 5 5 5 csidatal 5 5 6 identse ie og ba ie eas ee ee 5 5 9 pLSCF4 a ee ee eee Gera ee bee ee ag Oe Rees babe 6_ Verification example 6 1 Example 1 2DOF system 6 1 1 Example la discretizatio 6 1 2 Example 1b pLSCF method 112 113 113 113 114 114 115 115 115 116 116 117 118 120 120 121 121 121 122 122 123 123 124 124 125 125 125 126 127 129 129 130 131 134 VI Reference CONTENTS CMIF CSI CSI ref DOF EMA FDD FRF GUI OMA OMAX pLSCF PP PSD PSD RMFD SSI SSI cov SSL cov ref SSI data SSEdata ref ZOH List of abbreviations complex mode indication function combined deterministic stochastic subspace identification reference based combined deterministic stochastic subspace identific
26. De E S o ai 7 Show real E a ep er o real imaginary pa A Show absolute value angle Stabilization criteria e ad di iad 3 30 o De po w 4 Scale to unit modal mass Frequency 1 E E Y Scale to unit modal displacement Damping 96 sl e ee wf od 4 e e e Channel 1 A yes A eae A 0 36088 0 0257511 Transfer norm 9 50 j Channel 2 Damping ar eT 20 be d 7 0 8823 0 0333671 range opa L 50 D Ed w Channel 3 1 gt t ea 1 Channel 4 e bi 0 85734 0 010582i Ed Ed gi 10 F e w MPC lower bound o 5 ed 4 MP upper bound 30 e MPD upper bound f 90 0 5 10 1 20 25 frequency Hz pe Show data from 0 Hz to 25 Hz _ Show all modes Show only stable modes Show PSD FRFs Calculate Apply Figure oK Figure 4 24 Tutorial 1 Stabilization diagram GUI Repeat the modal analysis with the framedata_ssi_data_ref mat file Now that you know how the PSD sum looks like it is not necessary to plot it on the stabilization diagram Choose for instance the four physical modes at a system order of 16 and save the mode information as framedata_ssi_data_ref_modes mat Select the framedata_ssi_cov mat file in the MACEC main window and press again the MODAL ANALYSIS button The stabilization diagram that is created is very clear and shows only physical modes thanks to the variance calculation fig 4 25 If you move the cursor on a mode the MODE INFORMATION panel shows in addit
27. GS GMS18 trix 1931 GS_GMS18 triy GS_GMS18 triz AC 1932 1932 AC 1933 1933 FORCE_SENSORS manufacturer PCB_208A05 PCB_208C05 PCB_208C05 DISPLACEMENT_SENSORS type no manufacturer micro eps_S601 0 2 micro eps_S601 0 5 micro eps_S601 01 STRAIN_SENSORS type no manufacturer PCB_740B02 302 PCB_740B02 303 PCB_740B02 304 PCB_740B02 VELOCITY_SENSORS no manufacturer SN 11569 20170 25930 sens mV g sens counts g 3774874 3774874 3774874 sens mV 1bf sens V m range mm t sens mV e freq_range Hz ampl_range pk_e 0 5 100000 0 5 100000 0 5 100000 0 5 100000 sens V m s Hino velocity sensors have been defined yet res e Figure 3 1 Example of a sensor definitions file 16 STRUCTURE AND CONVENTIONS OF MACEC Figure 3 2 Example of a grid file Slave files Slaving is a powerful procedure for the visualization of DOFs that are not measured but that can assumed to be related to measured DOFs in a linear way A specific DOF can be slaved to several master DOFs the results are then additive In MACEC the files that contain the definition of the dependent degrees of freedom DOFs are called slave files They can have any name as long as they are of the ASCII type extension asc A slave file is structured as follows e in each row one DOF is coupled to one other DOF e each row has eight columns containing the node number of the master node and th
28. IN USE section of the MACEC main window and press the COMBINE SETUPS button in the MODAL ANALYSIS field Save the resulting modes as VAL 1_CSIref_modes mat Now select this file in the FILE S IN USE section of the MACEC main window and press the PLOT MODE SHAPES button in the MODAL ANALYSIS section to get a look at the different mode shapes You notice that some of them look quite well why others are more noisy due to the small amount of data that was available for the identification As each impact test was repeated 4 times there are 4 measurements per setup If you would repeat the complete modal identification procedure signal processing system identification and modal analysis for the other tests and take the mean value of the modal information obtained for each test at a particular setup you can expect that the results will be more accurate Taking this mean value is not difficult if two files with modal information containing exactly the same DOFs are selected and the COMBINE SETUPS button is pushed the resulting modal data contain the mean values As the previous step is quite time consuming and does not imply new functionalities of MACEC you can just select VAL_CSIref_modes mat which contains the results If you plot these mode shapes the result looks like in fig The quality of the mode shape of mode 2 is less than for the other modes This should not be a surprise since this mode is only weakly excited and it could even not
29. PSD For nonparametric identification the GULnonpar function is called which constructs the window for nonparametric system identification From this window one of the following functions are called x GUI_H1 for FRF estimation x GULPSDp for PSD estimation e MODAL ANALYSIS This section deals with the modal analysis of the identified system models By clicking the MODAL ANALYSIS button one of the following functions is called If parametric system descriptions have been identified the GULstabplot function is called which constructs the window with the stabilization diagram In this window the function GUL psdpfrfsum may be called for the construction of a dialog box for the calculation of the sum of the FRFs or PSD s x If nonparametric system descriptions have been identified the GUI_cmif function is called which constructs the window for modal parameter selection through the peak picking or CMIF FDD methods By clicking the PLOT MODE SHAPES button the GUI_modview function is called which constructs the window for the visualization of the mode shapes 3 5 Logfile and batch run MACEC has the flexibility that its functions can not only be called from the GUI but also from the MATLAB command window or from a MATLAB command m file See chapter 5 for more information about the functions of MACEC that can be called in MATLAB and chapter 6 for examples where MACEC is used in batch mode As soon as you star
30. Specify 1 to revert a channel Can be specified for all channels individually 1 nch or at once 1 1 x Data in actual units For accelerations m s 2 r Conversion rates per channel For accelerations m s 2 V 5 3 Mathematics 5 3 1 Kronpr KRONPR Calculation of the Kronecker product X Kronpr A B A B matrices for which the Kronecker product has to be calculated X the Kronecker product of A and B 5 3 2 blckComp BLCKCOMP Calculation of Block Companion matrix x blckComp A x Resulting Block Companion matrix A 3D matrix comtaining the block colmns of the block Companion matrix the third dimension corresponds to the block row position 5 3 3 blckHank BLCKHANK Calculation of Block Hankel matrix x blckHank C R x Resulting Block Hankel matrix C 3D matrix containing the first block column of the block Hankel matrix the third dimension corresponds to the block row position R 3D matrix containing the last block row of the block Hankel matrix the third dimension corresponds to the block column position 5 3 4 blckToep BLCKTOEP Calculation of Block Toeplitz matrix x blckToep C R 108 OVERVIEW OF MACEC FUNCTIONS x Resulting Block Toeplitz matrix C 3D matrix containing the first block column of the block Toeplitz matrix the third dimension corresponds to the block row position R 3D matrix containing the first block row of the block Toeplitz matrix the third dimension corresponds to the block c
31. X axis label Default defined using MCSIGNAL LABEL Label Y axis label Default defined using MCSIGNAL LABEL gt XMin X axis scaling minimum value Default left side of the plotted curve gt XMax X axis scaling maximum value Default right side of the plotted curve gt YMin Y axis scaling minimum value Default defined as a function of the plotted curve Y X max abs Y for domain t O for domain f and min Y for domain b gt YMax Y axis scaling maximum value Default defined as a function of the plotted curve Y X max abs Y for domain t and max Y for domains f and b See also NEWFIG SAVEFIG MCSIGNAL TPLOT MCSIGNAL FPLOT MCSIGNAL BPLOT 5 1 3 axesplot AXESPLOT Plot multi channel signal in the current axes AXESPLOT domain ichi x filename KeyName KeyValue plots the time history domain t the frequency content continuous Fourier transform domain f or the one third octave band spectrum of the RMS value domain b of the selected channels ichi of the mcsignal x Key options can be specified to fine tune the plot These options are interpreted by the present function and they are passed to the global function NEWFIG which is used to open a new figure window The values of the key options interpreted by the present function may be scalars single strings or vectors cell arrays of strings In the first case the same va
32. are converted to an mcsignal object on which all signal processing operations are performed e system identification for stochastic subspace identification not only the data driven stochastic subspace identi fication SSI data method and its reference based generalization SSI data ref are avail able but also the covariance driven versions SSI cov and SSI cov ref 7 with SSI cov ref it is possible to calculate covariances on the system estimates 14 combined subspace identification is now possible with the combined deterministic stochastic subspace identification CSI and the reference based combined deterministic stochastic subspace identification CSI ref methods 12 the poly reference least squares complex frequency domain pLSCF algorithm also known under its commercial name Polyma H which has become a standard for both experimental and operational modal testing has been added Deterministic and stochastic pLSCF are available the Peak Picking method is no longer supported as simulation studies have shown that it is clearly inferior to the identification methods that are available in the toolbox 8 e modal analysis the stabilization diagram has been extended with a lot of functionalities such as much more stabilization criteria damping range maximum frequency variance modal transfer norm are available the mode shapes are plotted in the complex plane as soon as a pole is picked the stabilization diagram
33. be detected with deterministic pLSCF Modes 4 and 5 are clearly of better quality than the same mode identified with deterministic pLSCF compare with fig 4 44 In all identified modes bending is combined with torsion due to the skewness of the bridge supports with respect to the bridge deck 74 mode 1 1 882Hz 1 22 Van mode 3 3 833Hz 1 35 mode 5 6 196Hz 1 73 mode 7 7 156Hz 2 47 TUTORIALS mode 2 3 026Hz 4 76 mode 4 5 076Hz 1 76 mode 6 6 529Hz 1 87 mode 8 8 938Hz 2 55 Figure 4 46 Tutorial 2 Modes obtained with CSI ref 4 2 7 Conclusions In this tutorial Experimental Modal Analysis with CMIF and deterministic pLSCF identification and Combined Modal Analysis with CSI ref identification were addressed A case study was presented namely the modal analysis of the B15 bridge that overpasses the E19 highway between Brussels and Antwerp Belgium Table 4 6 compares the eigenfrequencies damping ratios modal phase collinearities MPC and mean phases MP obtained with all methods Note that for the CMIF method no modal damping ratios are available and that the modes can not be mass normalized so that the MP is not plotted for this method From the table it can be seen that the MPC values are generally higher for the CSI ref estimates indicating a more accurate mode shape estimate The eigenfrequency estimates for the CMIF and CSI ref methods a
34. can be saved as a Matlab fig file the modes are automatically scaled to unity modal mass if at least one force and one output are measured at the same DOF otherwhise they are scaled to unit modal displacement the animation of mode shapes with surfaces is improved mode shape animations can be saved as avi files LMS PolyMAX is a registered trademark of LMS International A MATLAB TOOLBOX _ S 5 1 5 A Matlab toolbox MACEC is not a stand alone program but a toolbox for use with MATLAB and the Signal Pro cessing Toolbox of MATLAB 1 6 MACEC and SPICE MACEC is a part of the SPICE program but it also runs separately SPICE coordinates the MACEC and SASW programs which both make use of the same preprocessing features 1 7 Development MACEC 1 0 started in 1997 1998 as the Master Thesis project of Bart Van den Branden and Alexan der Laqui re at the Civil Engineering Department of KU Leuven under the supervision of Bart Peeters and prof Guido De Roeck Between 1998 and 2001 the program was improved and extended into version 2 0 by Bart Peeters in the framework his Ph D Thesis 6 Between 2006 and 2011 the program was totally re designed and many new features were added by Edwin Reynders in the framework of his Ph D Thesis and subsequent postdoctoral research resulting in the 3 0 3 1 3 2 an 3 3 versions The mcsignal class was originally created by Mattias Schevenels as a part of of the sigfun toolbox 15 The cl
35. channels selected for identification a vector containing the reference channels selected for identification the vector with frequencies corresponding to the 3rd dimension of H_meas f goes from OHz up to the sampling frequency lower bound of the frequency range of interest upper bound of the frequency range of interest 5 5 5 csi_data CSI_DATA Data driven Reference based Combined Deterministic Stochastic Subspace Identification invar csi_ data F Y ii ref A B C D Q R S csi_data invar n F the Y the input data output data ii half the number of block rows in the Hankel matrix invar a structure which contains the results after QR and SVD n the A B C D the Q R S the order of the identified system system matrices noise covariance matrices 5 5 6 identsel IDENTSEL Select output and input node numbers measurement directions and quantities after system identification node_numout meas_dirout quants_out chan_outin ampl_outin refs node_numout meas_dirout quants_out chan_outin identsel node_num meas_dir quants chanselout chanselin refers vector with the output DOF node numbers matrix with output DOF measurement directions Rows DOFs columns direction angles list of output DOF quantities cell vector containing the output DOF number corresponding to an AA OOOO OVERVIEW OF MACEC FUNCTIONS input DOF If an input has not the quantity force or it does not correspond to ex
36. diagram stabplot allmodes staballmodes stabfdmodes stabfmmodes stabfmodes allmodes staballmodes stabfdmodes stabfmmodes stabfmodes stabonly plotall unstabmodes stabonly plotall colorind f_low f_high freqscale psdpsum frfsum a structure containing all the modes see stable_propmodpar m for the structure of allmodes has the same structure as allmodes but contains only the stable modes contains the modes that have stable frequency and damping for which the damping ratio lies between the upper and lower bounds that have the highest modal transfer norms and for which the modal phase colinearity is higher than the threshold and the mean phase deviation lower than the threshold contains the modes that have stable frequency and mode shape for whith the damping ratio lies between the upper and lower bounds that have the highest modal transfer norms and for which the modal phase colinearity is higher than the threshold and the mean phase deviation lower than the threshold contains the modes that have stable frequency for which the damping ratio lies between the upper and lower bounds that have the highest modal transfer norms and for which the modal phase colinearity is higher than the threshold and the mean phase deviation lower than the threshold integer equal to 1 if only the stable modes need to be plotted integer equal to 1 if also the unstable modes need to be plotted SYSTEM IDENTIFICATION
37. forces is considered as disturbing noise it is removed in the nonparametric FRF estimation Combined vibration testing in MACEC is possible with the data driven reference based Combined deterministic stochastic Subspace Identification CSI ref method It has the advantage that both the measured drop weight force and the unmeasured ambient forces are accounted for Nonparametric FRF estimation 10 Select the VALA1 1_proc mat file in the FILE S IN USE section of the MACEC main window se lect NONPARAMETRIC FOR PEAK PICKING OR CMIF FDD in the SYSTEM IDENTIFICATION field and press APPLY to open the POLY REFERENCE LEAST SQUARES COMPLEX FREQUENCY DOMAIN PLSCF IDENTIFICATION window You can see that MACEC immediately suggests based on the type of data which channels will be considered as inputs and which channels will be outputs and which ANALYSIS TYPE is needed This suggestion is correct so you do not have to change it fig 4 38 Press APPLY in the FRF ESTIMATION field to start the estimation of a non parametric FRF using the H estimator 5 Nonparametric FRF PSD estimation for Peak Picking or CMIF FDD FRF and or PSD estimation Select Channels 7 E Inputs Analysis type Heterministid O stochastic E Ch 1 R1 acc Ch 2 al acc Ch 3 a2 acc ME response function estimation H1 estimator Ch 4 a3 acc Ch 5 a4 acc gt F Ch 6 a5 acc Ch 7 a6 acc Ch 8 a acc Ch 9 a8 acc Ch 10 a9 acc F
38. history of a multi channel signal the sampling frequency and the quantities and units of all channels with a set of methods 1 to determine the signal s metadata in all of its forms sampling frequency time period time step resolution in the frequency domain Nyquist frequency 2 to access the time history and the frequency content of the signal and 3 to perform operations on the signal integrate decimate x input2mcsignal file ext f_sample file a char containing in each row the name of the file that needs to be converted ext a char containing in each row the corresponding file type mat asc ddf msd tdm wav f32 f_sample sampling frequency only needed when at least one of the extentions is equal to asc x 1 x 2 the created mcsignal objects NOTE When the extension equals msd the different files are assumed to be measured simultaneously and they are always combined into a single mcsignal object 5 2 4 modal2ss MODAL2SS Compose a deterministic stochastic or combined 106 OVERVIEW OF MACEC FUNCTIONS deterministic stochastic discrete time state space model from modal parameters A Zero Order Hold ZOH discretization scheme is assumed Lambda Bm Phi D Km modal2ss fud xi Phi Ld Km Ts types Lambda Bm Phi D Km combined deterministic stochastic state space model in decoupled i e modal form In the special case of a purely stochasti
39. matrices A and C Lambda Gm Phi Lambda02 covmod System matrices of the estimated stochastic state space description in decoupled format covmod is SYSTEM IDENTIFICATION _ S 2 a structure containing the covariance matrices for each set of eigenparameters belonging to the same mode This means that the information regarding the covariance between different modes is lost compared to covAC yet the result is more memory efficient especially for large model orders 1 B Peeters and G De Roeck Reference based stochastic subspace identification for output only modal analysis Mechanical Systems and Signal Processing 13 6 855 878 1999 2 E Reynders R Pintelon and G De Roeck Uncertainty bounds on modal parameters obtained from Stochastic Subspace Identification Mechanical Systems and Signal Processing 22 4 948 969 2008 3 M Dhler and L Mevel Efficient multi order uncertainty computation for stochastic subspace identification Mechanical Systems and Signal Processing 38 2 346 366 2013 5 5 13 sysmatcalc SYSMATCALC Calculation of system matrices for increasing system orders This function is used after a stochastic or a combined deterministic stochastic subspace identification sysmat sysmatcalc invar method chanselout chanselin refs calcorders sysmat sysmatcalc invar method chanselout chanselin refs calcorders coupling sysmat structure array containing the A and C system matrices for every po
40. new verification example section 6 1 3 e Minor functionality changes In the GUI it is now possible to change the node number and measurement direction attached to the different channels also after system identification and modal analysis Extra checks have been introduced in order to reduce the risk of human errors when node numbers and measurement directions are defined for different data files at the same time The computation of modal transfer norms has been reprogrammed so that the Systems Control Toolbox of MATLAB is no longer needed for computing them 1 3 What s new in MACEC 3 1 e The functionality of the stabilization diagram has been largely extended If real normal modes are expected a lower limit value for the modal phase collinearity and an upper limit value for the mean phase deviation can be imposed 5 section A 4 5 A lower bound can be imposed on the mean phase of the mode shapes This is helpful when real normal modes are expected after mass normalization If covariance matrices are estimated which is possible for the SSI cov ref subspace iden tification method upper limit values for the standard deviations of the eigenfrequencies damping ratios and mode shapes can be set The change in modal transfer norm between two consecutive model orders can be limited When a mode is pointed to in the stabilization diagram additional information is shown such as the modal phase co
41. nodplot xlims ylims zlims axeq grid_ phase_ view_ mode3 structure array containing mode shape information see function mode3D m modenr number of mode to draw amp amplification factor for the modal displacements complmode equals to 1 if a complex mode must be drawn otherwise 0 plotcolour colour that is used for the plot e g k b linewid line width to use anim_ equals to 1 if the plot is used in an animation path_beam path to beam or surface file path_slave path to slave file empty string if no slaving is required nodplot equals to 1 if node numbers must be drawn otherwise 0 xlims limits of X axis if 0 default values ylims limits of Y axis if 0 default values zlims limits of Z axis if 0 default values axeq equals to 1 if the axes have equal length otherwise 0 grid_ equals to 1 if the grid needs to be plotted otherwise 0 112 OVERVIEW OF MACEC FUNCTIONS phase_ phase to plot view_ view matrix 5 4 4 globmod GLOBMOD combining modal parameters of different setups to one global set of modal characteristics stabglobmodes global_nodes global_dirs globmod stabmodescell node_num meas_dir stabmodescell cell for which each entry contains the modal parameters identified for a single measurement setup Such entry is a structure of the same form as allmodes see stable_propmodpar5 stabglobmodes structure containing the combined modal parameters It has the same form as allmodes see s
42. of a weighted velocity mcsignal according to DIN 4150 2 y DINKBTAU ich1 x applies frequency weighting to the selected channels ichi of the mcsignal x if necessary so delivering a KB mcsignal From this signal the running effective value in mm s is calculated using the global function DINKBTAU x tdata ich1 x F tau x mcsignal object ich1 Channels to apply the operation to Default all channels y mcsignal object Use y x dinkbtaufichi to access this function See also the global function DINKBTAU 5 1 13 disp DISP Display multi channel signal metadata DISP x prints the metadata of the mcsignal x to the console window x mcsignal object 5 1 14 display DISPLAY Display multi channel signal metadata DISPLAY x prints the metadata of the mcsignal x to the console window MATLAB calls this method whenever a mcsignal object is the result of a statement that is not terminated by a semicolon x mcsignal object 5 1 15 domf DOMF Multi channel signal dominant frequency y DOMF x returns the dominant frequency of the mcsignal x x mcsignal object AMCSIGNAL y Sampling frequency Hz Use y x domf to access this function 5 1 16 dt DT Multi channel signal time step y DT x returns the time step of the mcsignal x x mcsignal object y Time step s Use y x dt to access this function 5 1 17 f F Multi channel signal frequency vector y F x returns a vector containing t
43. the file sens F mat in the spice tutorials tutorial2 directory All settings are now automatically adjusted and you can make the conversion to the MCSIGNAL object by pressing the OK button Save the first MCSIGNAL object as VALA1 1_conv mat Save the other MCSIGNAL objects accordingly save the MCSIGNAL object created from the file VALA2 1 F32 as VALA2 1_conv mat etc Note that it was possible to convert the data for all 10 setups at the same time because in each setup the same physical quantities are measured using the same hardware and the same amplification factors In the MACEC main window select the VALA1 1_conv mat file in the FILE S IN USE list and press the PROCESS button in the SIGNAL PROCESSING section to open the PREPROCESS MCSIGNAL OBJECT window Here you can have a look at the raw measurement data and their frequency content or if you change the TIME FREQUENCY setting in the VISUALIZATION section to AUTOCORRELATION PSD at the autocorrelation function and the Power Spectral Density PSD fig 4 34 Also note that the axis labels are automatically adjusted in the right way thanks to the definition of the signal s units during the conversion to an MCSIGNAL object THE B15 BRIDGE Conversion of the measured data Sensitivities Channel 1 No predefined sensor Sensor summary Label 1 Posi acceleration Measurement units 11 1 1 Amplification YI Volt
44. w5 W6 W7 j 0181 1882 083 184 185 186 187 ee Hs 0 20 40 60 80 100 120 tix de La x b c Figure 4 47 Tutorial 3 Rib stiffened plate a as mounted in a transmission opening of the acoustics laboratory of KU Leuven b sketch indicating the geometrical definitions and c sketch indicating the measurement DOFs right An experimental modal analysis has been performed when the stiffened plate was mounted in a trans mission opening between two reverberation rooms of the building acoustics laboratory of KU Leuven see Fig 4 47h A roving hammer test was carried out during which the plate was excited with an impact hammer at 56 different positions and the response of the plate was measured with accelerome ters at 5 fixed positions The measurement locations are defined in Fig 4 47k The fixed accelerometer positions have numbers 31 36 43 54 and 75 The measurement data can be found in the spice tutorials tutorial3 data directory There are 56 data files one for each impact hammer test The file number corresponds to the impact hammer location as defined in Fig 4 47k Again the first thing to do would be to build the geometry in MACEC by creating a grid file and a beam or surface file As this step has already been treated in detail in the first tutorial see section 4 1 2 it is not explained in detail here The grid and surface files have been prepared on beforehand They can be found in the spice tutorials tutoria
45. y x filtfilt ich1 B A to access this function See also MCSIGNAL FILTER and the global function FILTFILT 5 1 26 fplot FPLOT Plot multi channel signal frequency content FPLOT ich1i x filename KeyName KeyValue executes the function PLOT f ich1 x filename KeyName KeyValue Use x fplot ich1 filename KeyName KeyValue to access this function See also MCSIGNAL PLOT 96 OVERVIEW OF MACEC FUNCTIONS 5 1 27 integrate INTEGRATE Integrate a mcsignal y INTEGRATE ich1 x applies the global function INTEGRATE x tdata ich1 x F to the specified channels ichi of the mcsignal x x mcsignal object ichl Channels to integrate Default all channels y mcsignal object Use y x integrate ich1 to access this function See also the global function INTEGRATE 5 1 28 key KEY Extract one key value from a list of key options with unknown length y KEY name default KeyName KeyValue compares the KeyName s with name and returns the following KeyValue If no KeyName matching name is found default is returned name Name of the argument to retrieve the value of default Default argument value y Argument value See also VARARGIN 5 1 29 labels LABELS Multi channel signal label per channel y LABELS x returns a cell array containing strings describing the label for each channel of the mcsignal x
46. 25 D matlabtoolb spice32 201 1 01 aisource tutorials tutoriall iram 0 CJ Grid file D matlabtoolbispice32 2011 01a source tutorialsitutorialt fram 0 E A Convert to mesignal Add DOFs Signal Processing System Identification ES Subspace x Pu mude aos Modal Analysis Modal analysis Combine setups Figure 4 7 Tutorial 1 Specify a file s name and directory 12 Now the name of this file appears in the FILE S IN USE list in the MACEC main window Click on the filename and press the CONVERT TO MCSIGNAL button in the SIGNAL PROCESSING section A dialog box appears which asks for the sampling frequency fig 4 8 As the sampling frequency is 100 Hz enter 100 and press OK 13 Now a window opens which guides you through the conversion of the measurement data to an MCSIGNAL object Each channel can be labeled for later reference For instance a good label for the first channel is 5X since this channel contains the acceleration measured at node five in the X direction To provide this label fill in 5X OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE A 35 MACEC 3 2 JES Teal File s in use Geometry framedata mat Grid file D imatlabtoolbispice32 2011 01 alsource tutorials tutorialt fram 0 E Slave file 0 10 8 2 Convert to mesignal Add DOFs System Identification Stochastic Subspace Apply
47. 5 0 052 12 117 0 281 15 097 0 493 Table 4 1 Tutorial 1 True eigenfrequencies and estimates obtained from six different methods all in Hz For the SSI cov method the values are shown together with their 20 95 confidence interval The damping ratios listed in table 4 2 correspond less well as could have been expected from a short data record of only 8192 samples This is also reflected in the high relative uncertainty of the damping ratio estimates of the SSI cov method In particular although estimates of the damping ratio of the first mode agree much better than for the other modes the SSI cov uncertainty bound warns us that the accuracy is not better which is confirmed by comparison with the exact value 0 61 0 37 2 26 0 69 3 86 2 55 3 97 3 05 Table 4 2 Tutorial 1 True damping ratios and estimates obtained from six different methods all in of critical For the SSI cov method the values are shown together with their 20 95 confidence interval MACEC offers additional useful validation information When listing the identified modal parameters using the LIST MODES button in the MACEC main window the standard deviations of the mode shape components are listed when available as well as the modal phase collinearity MPC mean phase MP and mean phase deviation MPD values When real normal modes are expected as is the case for the proportionally damped structure considered here the MPC MP a
48. 5 6 node_num meas_dir repmat O 90 maxpar 1 repmat 0 90 5 1 measurement directions quants for par DOFs 31 43 54 36 75 assign node numbers to channels cell maxpar 5 1 measured quantities 1 maxpar quants par acc end for par maxpar 1 maxpar 5 quants par force end node_num meas_dir quants chan_outin ampl_outin refs identsel node_nun meas_dir quants rmfd chanselout rmfd chanselin rmfd refs ROVING HAMMER TESTING OF A RIB STIFFENED PLATE AAA 83 11 After parametric system identification the modal characteristics are selected from a stabilization diagram and this requires significant user interaction Therefore we will switch from batch mode to the MACEC GUI at this stage In order to load the identification results into the MACEC GUI they need to be saved first This is achieved by adding the following line of code to our logfile save tut3_pLSCF mat ampl_outin chan_outin meas_dir node_num gt predat quants refs rmfd P q 4 3 5 Modal analysis after deterministic pLSCF 12 We can now select the modal characteristics in a stabilization diagram In order to do so open the main window of the MACEC GUI load the tut3_pLSCF mat file and press the MODAL ANALYSIS button in the MODAL ANALYSIS field The stabilization diagram that is now constructed is very clear so the stable modes can be easily selected
49. Consequently it can be expected THE B15 BRIDGE OOOO that there is no clear separation between bending and torsion modes but that the vertical modes are a combination of bending and torsion 12 The skew angle of the bridge is 43 4 2 2 Vibration measurements There are three types of dynamic vibration tests II forced ambient and combined In forced vibration testing it is assumed that all forces that are applied to the structure are measured While this method yields very nice results for relatively small mechanical devices tested in laboratory conditions it does not for large bridges because the so called ambient forces like wind or traffic loads can not be measured and not be excluded and large impractical artificial excitation devices are needed to overcome this problem Ambient vibration testing on the other hand is very well suited for bridges because in this type of testing only responses most often accelerations sometimes also displacements velocities or strains at certain points of the structure need to be measured not the forces Finally combined vibration testing consists of ambient vibration testing but on top of the ambient excitation also a forced excitation is applied in order to excite the structure over a broader frequency band and or in order to have scaled mode shapes The crucial difference with forced vibration testing is that the ambient loads are not considered as unwanted noise but as a useful part of the ex
50. F Sampling frequency NOT the Nyquist frequency quantity Text string describing the data type per channel e g volt acc velo disp force If not equal for all channels then provide a cell array containing different text strings sifactor Factor to multiply the stored signal data with as to obtain the Signal in the SI units corresponding to the specified quantity If not equal for all channels then provide a vector labels Text string describing the different channels Defaults to the channel number See the example master files for info on the usage of the MCSIGNAL class 5 1 31 md5 MD5 Generate MCSIGNAL signature using MD5 algorithm y MD5 x accu returns a 512 bit signature identifying all data stored in the mcsignal x tdata F quantity sifactor The tdata is taken into account with the specified accuracy deviations smaller than MAX tdata accu are ignored b MD5 y returns true if the signature of the mcsignal x equals y x mcsignal object accu Accuracy default le 8 y MD5 signature b Boolean Use y x md5 to access this function 98 OVERVIEW OF MACEC FUNCTIONS 5 1 32 n N Multi channel signal length y N_ x returns the number of samples per channel for the mcsignal x x mcsignal object y Number of samples per channel Use y x N to access this function 5 1 33 nch NCH Multi channel signal number of channels y NCH x returns the number of channels fo
51. MA test either A C Q R S or A C G Lambda0 are provided the others are empty For a combined deterministic stochastic state space description obtained from an OMAX test either A B C D Q R S or A B C D G Lamda0 are provided the others are empty driving point locations output numbering If loc equals zero the modes are scaled to unity driving point amplitude reference output numbers sampling period If the state space model is in continuous time Ts equals 0 1 Since Phi is in displacement units an FRF that is synthesized from the modal parameters obtained with propmodpar5b is a force displacement FRF 2 Since both Phi and Gm are rescaled to displacement units a PSD or output correlation sequence synthesized from these are in displacement displacement units ssmodparvar SSMODPARVAR Calculate modal characteristics and their covariances from an identified state space model f xi Phi covfxp trnorm ssmodparvar A C dt ACcov G units xi phi units covfxp quants trnorm A C G ACcov vector of eigenfrequencies vector of corresponding damping ratios matrix of mode shapes each column contains a mode shape normalized to unit maximum displacement or normalized to 1 at the corresponding value in units vector with output numbers that are normalized to 1 each entry corresponds to a mode optional If unit is a scalar the same output number is used for all modes covariance matrix between the eigefreq
52. O 0 0 0 0 0 0 0 predat predats 1 chansel 1 2 3 4 refs 1 invar ssi_data3 predat tdata chansel 30 refs sysmat sysmatcalc invar ssi_data chansel refs 2 2 60 node_num meas_dir quants chan_outin ampl_outin identsel node_num meas_dir predat quantity sysmat chanselout sysmat chanselin allmodes stable_propmodpar5 sysmat predat dt chan_outin ampl_outin quants selnrs modenr yes selnrs modfind allmodes 2 7664 16 selnrs modenr yes selnrs modfind allmodes 7 9459 16 selnrs modenr yes selnrs modfind allmodes 12 135 16 selnrs modenr yes selnrs modfind allmodes 15 1606 16 selnrs stabmodes stabpick allmodes selnrs Figure 3 7 Example of a logfile the determination of the modal characteristics in tutorial 1 with SSEdata ref Chapter 4 Tutorials In this chapter three tutorials are provided that get you acquainted with MACEC The first tutorial concerns an operational modal analysis of a frame structure from simulated data The second tutorial concerns an experimental and a combined modal analysis of a highway bridge from measured data In the third tutorial the batch mode of MACEC is explored for processing data from a roving hammer test in an efficient way 4 1 Operational modal analysis of a frame structure 4 1 1 Introduction As a comparative test between the different ambient system identification methods the simulated ambient data of a
53. OR Multi channel signal SI factor y SIFACTOR x returns the factors to multiply the stored signal data with as to obtain the signal in the SI units corresponding to the channel s quantity x mcsignal object y SI factors Use y x sifactor to access this function 5 1 43 subsref SUBSREF Handle references to the methods of a mcsignal SUBSREF x ref is called by Matlab whenever one of the following commands is encountered x x method ichi x method etc x is conceptually equal to x tdata 102 OVERVIEW OF MACEC FUNCTIONS x abcd ichi results in the execution of the method abcd x ich1 ich0 where ichi is a vector containing the channels specified by the user and ich0 is a vector containing the remaining channels x abcd results in the execution of the method abcd x ich1 ich0 where ich1 is a vector containing all channels and ich0 is an empty vector To take into account the case insensitivity of Windows file names and therefore names of M files the called method is converted to an M file name as follows an underscore _ is inserted right after every capital and every underscore 5 1 44 t T Multi channel signal time vector y T x returns a vector containing the times corresponding to the samples stored in the mcsignal x x mcsignal object y Times s Use y x t to access this function 5 1 45 t T_ Multi channel signal period y T_ x returns the pe
54. PREDAT see the previous paragraph e SYSMAT a MATLAB variable of the STRUCT type with the following fields The system matrices for the different orders For instance for a stochastic state space model of order two that has been estimated with the SSI data method the following matrices are present SYSMAT A_2 SYSMAT C_2 SYSMAT Q_2 SYSMAT R_2 SYSMAT S_2 SYSMAT ORDERS a vector containing the orders of the systems that have been identified SYSMAT CHANSELOUT a vector containing the channel numbers which have been used as outputs in the identification SYSMAT CHANSELIN a vector containing the channel numbers which have been used as inputs in the identification only differs from the empty vector if CSI ref identification has been used e NODE_NUM see the previous paragraph e MEAS_DIR see the previous paragraph 20 STRUCTURE AND CONVENTIONS OF MACEC e QUANTS a cell containing the data type of each channel for instance ACC stands for acceleration e CHAN_OUTIN a vector containing for each input the output number NOT the channel number that has the same DOF If no such output is available the corresponding element of CHAN_OUTIN equals 0 e AMPL_OUTIN a vector containing for each element of CHAN_OUTIN the corresponding sign If for example the input at a certain node was measured in the X direction and the output in the X direction the corresponding element of CHAN_OUTIN equals 1 RMFD
55. S field where you can specify the number of blocks in which the SThe theory behind the SSI data ref algorithm is not explained in this manual The interested reader is referred to for more information The theory behind the SSI cov algorithm is not explained in this manual The interested reader is referred to 7 74 for more information OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE AAA G5 29 30 raw time data will be divided for computing sample covariances of the output correlation matri ces is now enabled The number of blocks should be chosen sufficiently high in order to increase the accuracy of the variance estimation yet low enough to ensure that the different data blocks are still approximately statistically independent from each other If the number of block rows i is already specified MACEC proposes a default value for the NUMBER OF BLOCKS when the ESTIMATE COVARIANCE box is checked Indeed the value for NUMBER OF BLOCKS has been set to 32 In the first instance we can accept this value and press the CALCULATE QR SVD button to start the identification algorithm fig 4 19 Stochastic Subspace Identification Algorithm selection O data driven covariance driven C reterence based OR of data block Hankel matrix SYD of projection matrix Half the number of block rows i Expected system order 3 4 5 Number of blocks 35 m Calculate ES low singular values Remark Thedreti
56. S section to get a look at the different mode shapes You notice that some of them look quite well why others are more noisy due to the small amount of data that was available for the identification As each impact test was repeated 4 times there are 4 measurements per setup If you would repeat the complete modal identification procedure signal processing system identification and modal analysis for the other tests and take the mean value of the modal information obtained for each test at a particular setup you can expect that the results will be more accurate Taking this mean value is not difficult if two files with modal information containing exactly the same DOFs are selected and the COMBINE SETUPS button is pushed the resulting modal data contain the mean values As the previous step is quite time consuming and does not imply new functionalities of MACEC you can just select VAL_cmif_modes mat THE B15 BRIDGE BD which contains the results If you plot these mode shapes the result looks like in fig The quality of the mode shape of mode 3 is less than for the other modes In all identified modes bending is combined with torsion due to the skewness of the bridge supports with respect to the bridge deck e mode 4 6 504Hz mode 5 7 155Hz A ge mode 10 8 947Hz Figure 4 43 Tutorial 2 Eigenfrequencies and mode shapes obtained with CMIF After deterministic pLSCF 26 In the MACEC main window select VALA1 1
57. Ste AA Wisin AA 3 A 1997 2014 KU Leuven Structural Mechanics Section Kasteelpark Arenberg 40 B 3001 Leuven Belgium The software described in this document is distributed under a license agreement The software may be used only under the terms of the license agreement No part of this document may be reproduced in any form by print photoprint microfilm or any other means without written permission from the publisher Contents List of abbreviationg 2 e a a a a a viii rar SEAL SOR erases Bas Kee Sb eae ea ee oe ps ee eee a a ee ee ae e a es bee Ee eee ae re eee a A tee ee ee ee ee ee 1 6 MACEC and SPICH 3 8 a a See oe Sb oe ed PEARS S BRE LS eWeek eg ee nee eh ee een oe SA ee Cees eer ee ree 2 3 Installation of MACHO scsi e oe we p s ae es OO Se A gs 2 4 How to run MACEQ 20 00 02 ee ee oh ee eR eS A PhP be Gye ods pare E e eure ns ae SA or OF OF WwW NN e Ro o o N NNN 3 Structure and conventions of MACEC 11 ASA 11 ee ee ee ee ee ee ee eee 12 a ae oe Sees Be eee an ee ee 13 3 3 1 Measurement data ascii mat ddf msd tdm wav and f32 formats 13 pee wid de es 14 oe aed ener aha weg eae es 14 sd eee er eee ea 17 a eo ee te 22 TE LC CONTENTS 3 5 Logfile and batch run sp sec ka ae a aae en a a e aa E a a i p 24 4 Tutorial 27 e e eee es 27 e e a Sas ae ave ee ene a 27 ae re ee 34 ae eho bee ee ee ae 38 a a ee 47 Aa ea ee ee es ea 51 RN 54 O a oe ee ee eee eee eo 56
58. URE A Ss mode 1 2 77Hz mode 2 7 94Hz 8 8 7 7 6 6 5 5 N 4 N 4 3 3 2 2 1 1 8 4 2 0 2 4 2 0 x X mode 3 12 17Hz mode 4 15 00Hz 8 8 7 7 6 6 5 5 N 4 N 4 3 3 2 2 1 1 0 4 2 0 o 4 2 0 x X Figure 4 27 Tutorial 1 The four modes identified with SSI data eigenfrequencies and mode shapes GA OOO TUTORIALS 4 1 7 Conclusions Table shows the true eigenfrequencies and the corresponding estimates determined with six dif ferent methods Since for the SSI cov method the standard deviations have been estimated the 20 confidence intervals which corresponds to the 95 confidence intervals in the Gaussian case are shown as well The nonparametric estimates obtained with PP and FDD are the least accurate eigenfrequency estimates as expected The values obtained with both methods are exactly the same due to the limited frequency resolution The eigenfrequencies obtained with the different parametric methods correspond very well They all fall inside the 20 confidence bound for the SSI cov estimates The uncertainty of the eigenfrequency of the third and fourth modes which were less well excited as can for instance be seen from the Power Spectral Density function fig 4 10 is somewhat higher than for the other modes This can be seen both from comparing the confidence intervals of the SSI cov estimates as well as from comparing the differences between the different methods 2 766 0 014 7 93
59. _pLSCF mat and press the MODAL ANALYSIS button in the MODAL ANALYSIS field The stabilization diagram that is now constructed is very clear so you can easily pick the nine stable modes at order 80 Note that since it concerns a forced vibration test the modes have been mass normalized 27 After the poles have been selected save them as VALA1 1_pLSCF_modes mat Repeat the pole selection step for all 9 other setups 70 28 29 30 31 TUTORIALS If the poles of all 10 setups have been selected we can make use of MACEC s possibility to combine modal information obtained from different setups into one single mode Hereto select VALA1 1_pLSCF_modes mat and the mode information for the nine other setups in the FILE S IN USE section of the MACEC main window and press the COMBINE SETUPS button in the MODAL ANALYSIS field Save the resulting modes as VAL 1_pLSCF_modes mat You can have a look at the different mode shapes by selecting this file in the FILE S IN USE section of the MACEC main window and pressing the PLOT MODE SHAPES button in the MODAL ANALYSIS section Note that with the pLSCF method more modes could be identified than with CMIF As each impact test was repeated 4 times there are 4 measurements per setup If you would repeat the complete modal identification procedure signal processing system identification and modal analysis for the other tests and take the mean value of the modal information obtained fo
60. a cell containing the measured output quantities covind optional boolean indicating whether or not the complete covariance matrices of the mode shapes are required If covind 1 then allmodes cov is not empty Defaults to 0 normunit optional scalar containing the mode shape output number whos modal displacements are to be normalized to one Is only effective when sysmat contains covariance matrices The structure allmodes has the following fields allmodes f vector with eigenfrequencies Hz allmodes o vector with model orders allmodes xi vector with damping ratios allmodes m matrix with mode shapes in each column m allmodes 1ld matrix with deterministic discrete time modal participation vectors in each column allmodes km matrix with modal Kalman filter vectors in each column not empty when the covariance matrices of the process and measurement noise are available in sysmat allmodes gm matrix with stochastic modal participation vectors in each column not empty when the covariance matrices of the stochastic states at time k 1 and the stochastic outputs at time k are available in sysmat allmodes trinfd vector with deterministic modal transfer infinity norms abs velocity force allmodes trinfs vector with stochastic modal transfer infinity norms velocity allmodes mpc vector with modal phase colinearities allmodes mp vector with mean phases allmodes mpd vector with mean phase deviations
61. actly one output DOF its value in chan_outin equals 0 ampl_outin vector containing the direction info of the corresponding element in chan_outin Equals 1 if the output and input DOF have the same direction otherwise 1 It can also have an intermediate value equal to the cosine of the angle between both directions refs output numbers NOT channels corresponding to the reference channels optional node_num vector with all the node numbers meas_dir matrix with all measurement directions Rows DOFs columns direction angles quants string list of all quantities chanselout vector containing the output channels chanselin vector containing the input channels refers reference output channels only required if refs is asked 5 5 7 makenonpar MAKENONPAR Make a structure containing a nonparametric system description nonpar makenonpar freqscale realscale frf frfcov psdp psdpcov inputs outputs refs freqscale vector with discrete frequency lines where the nonparametric system description is known frf estimated frequency response function data first dimension outputs second dimension inputs third dimension frequency fr cov covariance matrix of the estimated frf data frfcov k contains the covariance matrix of vec_ frf k psdp estimated positive power spectral density data first dimension outputs second dimension reference outputs third dimension frequency psdpcov covariance matrix of the estimated psdp data
62. ade of MACEC 2 0 All sections of the program have been totally re designed and many new features have been added such as e file management MACEC 3 0 creates a Matlab file named logfile m in the MATLAB working directory which contains all commands that the user calls using the GUI This file makes it possible for the user to run MACEC in batch without the GUI INTRODUCTION All files created by the program are in mat format which provides a large data reduction and more transparency for the user Only the gridfiles slavefiles and beam surface files are still in ASCII format as the information needed to create these files is often available as ASCII data MACEC 3 0 makes it much easier to load multiple files In MACEC 3 0 it is possible to import data from NI LabVIEW tdm files and LMS Test Lab wav files Formats that were supported in previous MACEC versions can still be imported e geometry the definition of measurement nodes and connections between these nodes is now graphically supported in the GUI so that you can detect related errors in an early stage surfaces are not longer defined as quadrilaterals but as triangles so that a defined surface is always a plane surface e signal processing MACEC 3 0 makes use of Matlab s Signal Processing Toolbox and of the Matlab toolbox Sigfun that has been developed at the Structural Mechanics Section of KU Leuven 15 the measurement data that serve as input for MACEC
63. al object filename File to save the plot to using the global function SAVEFIG Can be omitted if you do not want to save the plot gt Windowtype In case of a PSD plot the window type has to be specified Valid choises are rectwin and hanning Default rectangular window rectwin 85 86 OVERVIEW OF MACEC FUNCTIONS Windowlength In case of a PSD plot the window length in data points Overlap AddToPlot AxesSize Blank Data gt logx 2 logy 2 Language Legend LegendLoc gt LineWidth Margins gt NXTick NYTick gt XLabel gt YLabel XMin XMax YMin YMazx Color has to be specified Default n_ x In case of a PSD plot the overlap length in data points has to be specified Default 0 Command evaluated after all built in plotting routines as to add elements to the figure e g equal human response curves Size of the axes in centimeters See NEWFIG for more info Do not plot the curve plot only the axes and the labels Value is assigned to the local variable Data which can be used by the AddToPlot command If a cell array is provided the contents of cell i is assigned to the local variable Data when plotting channel i First index of the time interval to plot Default 1 Last index of the time interval to plot Default x N Logarithmic scale for first axis or not Defaul
64. al of 27034 samples are available When dividing the data into 8 blocks there are 3379 samples per block The following command line can then be added to the logfile in order to estimate the FRF H1 f Hlestimate predat 8 rect 1 2 6 fs estimate FRF The third argument indicates that a rectangular window is applied which amounts to no win dowing in this case The fourth argument indicates that the first channel contains the force and the fifth argument indicates that channels 2 to 6 contain the response The last argument ROVING HAMMER TESTING OF A RIB STIFFENED PLATE AA al indicates that the FRF needs to be estimated for all frequencies up to the sampling frequency This is necessary because in a later stage the pLSCF method will be employed for estimating a parametric input output model i e a right matrix fraction description model When peak picking is applied the last argument can be changed into fn in that case FRF is estimated only for frequencies up to the Nyquist frequency 8 The previous procedure can now be employed for estimating the FRF corresponding to each hammer position and for gathering the corresponding estimates into a big overall FRF matrix estimate At this stage the true power of executing MACEC functions in batch mode becomes apparent as only minor modifications to the Matlab script that has been built up so far are necessary for processing all hammer test data files instead of just the s
65. ancel Figure 4 20 Tutorial 1 pLSCF 34 The PSD ESTIMATION window opens fig 4 13 Perform the same actions as in paragraph 20 above fig 4 15 and press OK 8The theory behind the pLSCF or Poly reference Least Squares Complex Frequency Domain algorithm is not explained in this manual The interested reader is referred to 2 for more information OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE AZ 35 36 MACEC returns to the PLSCF IDENTIFICATION window fig 4 20 where the RIGHT MATRIX FRACTION POLYNOMIAL ESTIMATION section has been enabled Since the bandwidth of interest coincides with the available frequency band don t change the default values in the FREQUENCY RANGE fields In the POLYNOMIALS ORDERS field fill in 1 15 and press CALCULATE to start the calculation of Right Matrix Fraction Description RMFD models of orders increasing from 4 to 60 in steps of 4 the system order equals the matrix polynomial order times the number of references and or inputs After the RMFD models have been calculated press OK and save the models in the following mat file framedata_pLSCF mat 4 1 5 Modal analysis of the identified system models For the frame structure under consideration five series of linear system models have now been identified 1 2 3 a nonparametric PSD model stochastic state space models identified with SSI data of orders 2 4 6 60 stochastic state space mod
66. ap In case of a PSD plot the overlap length in data points has to be specified Default 0 AddToPlot Command evaluated after all built in plotting routines as to add elements to the figure e g equal human response curves gt AxesSize Size of the axes in centimeters See NEWFIG for more info Blank Do not plot the curve plot only the axes and the labels Data Value is assigned to the local variable Data which can be used by the AddToPlot command If a cell array is provided the contents of cell i is assigned to the local variable Data when plotting channel i zix First index of the time interval to plot Default 1 2x7 Last index of the time interval to plot Default x N gt logx Logarithmic scale for first axis or not Default 0 logy Logarithmic scale for first axis or not Default O 88 OVERVIEW OF MACEC FUNCTIONS gt Language Label language en or nl Default en Legend Default no legend See also LEGEND LegendLoc Legend location Default Best See also LEGEND LineWidth Default 0 5 for domain t and f and 1 5 for domain b Margins Margins between the axes and the bounding box in centimeters See NEWFIG for more info NXTick Number of XTicks approximately see the global function TICK Default auto NYTick Number of YTicks approximately see the global function TICK Default auto XLabel
67. are of the same order of magnitude as the modal displacement change the AMPLIFICATION field to 1 and press ENTER As the mode shapes are plane shapes in the XZ plane push the VIEW IN THE XZ PLANE button to change the viewpoint as in fig 4 26 46 You can also play an animation of the mode shape by clicking the PLAY button in the ANIMATION 11 section To save the mode shape as a figure press the FIGURE button To save the mode shape since output only measurements were processed the modal displacements have been automatically scaled to unit modal displacement 52 TUTORIALS animation as an avi file press the MOVIE button You can switch between the different modes using the gt and lt buttons or by selecting from the list in the MODE field The mode shapes should look like in fig Mode shape animation a Animation V Equal axes _ Nodes Grid _ Figure ve E Rotate3D C auto tit E Complex modes Slow Fast Color schemes Line Width Amplification Colour d 15 1 4 Figure 4 26 Tutorial 1 Plotting the first mode shape 41 If you want to have a numerical presentation of the identified modal parameters you can just select the appropriate file in the MACEC main window and press the LIST MODES button The text editor opens and all modal information is plotted Using this information tables and have been constructed OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCT
68. ark the REFERENCE BASED box and indicate that the channels with label R1 and R2 for this setup channels 1 and 11 the DOFs of which are common to every setup are the reference channels fig 4 41 18 Then choose 40 as half the number of block rows Y and press the CALCULATE QR SVD button to start the first part of the identification If this is finished choose 2 2 80 The theory behind the CSI ref algorithm is not explained in this manual The interested reader is referred to 12 for more information See for a discussion on the relationship between and the lowest frequency of interest THE B15 BRIDGE AA 7 Combined Deterministic Stochastic Subspace Identification Algorithm selection Select Channels Inputs R1 acc al acc a2 acc QR of data block Hankel matrix SVD of projection matrix 4 a3 acc a4 acc Half the number of block rows i 6 a5 acc 7 ab ace Expected system order 8 a7 pi 9 a8 acc Ch 10 a9 acc Calculate QR SVD how singular values Ch 11 R2 acc h 11 R2 acc Ch 12 for force Ch 12 for force Remark Theoretically the system order equals the number of non zero singular values reference based References e g 2 5 8 1 11 Calculation of system matrices System orders 2 2 Icula Figure 4 41 Tutorial 2 Reference based Combined deterministic stochastic Subspace Identification CSI ref as t
69. ased on the data type of the channels in this case accelerations only 33 The pLSCF identification algorithm is a frequency domain algorithm and therefore the first step of the algorithm is for the stochastic case the estimation of the matrix of Positive Power Spectral Densities PSD Before starting the PSD estimation you should first select which outputs will be used for the identification in the SELECT CHANNELS section As all channels contain valid output data they should all be selected in the OUTPUTS column Please note that also here MACEC automatically suggests the right choice depending on the data type of each channel For the pLSCF algorithm it is also possible to work with reference channels but we will not make use of this possibility now Therefore fill in 1 4 in the REFERENCES field of the POSITIVE POWER SPECTRAL DENSITY ESTIMATION so that all channels are selected as reference channels and press APPLY fig 4 20 Poly reference Least Squares Complex frequency Domein pLSCF Identification E 3 FRF and or PSD estimation Select Channels Inputs 1 5X acc 2 4X acc 3X acc 2X acc Analysis type O deterministic stochastic FRF estimation H1 estimator eRe Tete Positive Power Spectral Density estimation References e g 3 5 7 h a Right Matrix Fraction Polynomial estimation Frequency range Hzto Polynomial orders v C
70. ass was later incorporated into the MACEC toolbox instead of the sigfun toolbox Edwin Reynders Leuven July 9 2014 INTRODUCTION Chapter 2 Getting started 2 1 MACEC and MATLAB Before you can run MACEC on your computer you need to have a compatible MATLAB version installed MACEC 3 3 has been tested on MATLAB 8 2 0 R2013b Important In contrast to MACEC 2 0 and older the 3 3 version requires that you have the Signal Processing Toolbox of MATLAB installed 2 2 Operating system and hardware requirements MACEC can be used on the Windows operating system only Both the 32 bit and the 64 bit versions are supported 2 3 Installation of MACEC The installation of MACEC consists of the following steps 1 Install MATLAB on your computer 2 Copy the spice33 2014 07a and sigfun 2008 10a folders to your hard disc for instance to the directory C Program Files MATLAB R2013b toolbox 3 Move your license file named splicense mat to the license subdirectory of spice33 2014 07a 4 Start MATLAB 5 In the main window of MATLAB choose FILE gt SET PATH Then click ADD WITH SUB FOLDERS and specify the spice33 2014 07a and sigfun 2008 10a directories or simply C Program Files MATLAB R2013b toolbox Then click SAVE and then CLOSE 8S GETTING STARTED 2 4 How to run MACEC After the installation of MACEC has been completed first specify the directory you want to work in by changing the CURRENT DIRECTORY field in t
71. assumption during discretization on the identified modal parameters The assumption should only have an influence on the modal scaling factors not on the eigenfrequencies damping ratios and unscaled mode shapes 10 The Matlab source code of this example can be found in the file Example1a m in the examples directory In MACEC the system is defined and converted to a discrete time state space model with the following commands note that a sampling frequency of 100Hz is chosen M 2 0 0 2 mass matrix Cv 5 2 2 5 damping matrix K 6000 2000 2000 6000 stiffness matrix Ts 1 100 sampling period A B C D fe2ss K M Cv Ts 1 01 2 01 0 0J 1 01 2 01 1 01 2 01 discrete time ss model The modal parameters are computed as follows quants cell_ strvcat acc acc Y define the output quantities f_ud xi phi quantsnew L propmodpar5 A B C D 01 01 01 1 1 Ts quants 1 2 1 11 01 compute the modal parameters The corresponding continuous time modal parameters are obtained from Ac Bc Cc Dc fe2ss K M Cv Ts 1 01 2 011 1 J 1 01 2 01 1 01 2 01 continuous time ss model quants cell_ strvcat acc acc define the output quantities f_ud_c xi_c phi_c quantsnew Lc propmodparb Ac Bc Cc Dc 1 1 1 1 1 0 quants 1 2 1 11 01 compute the modal parameters It can be verified that the eigenfrequencies and damping ratios obtained before and after discret
72. at all DOFs of interest Taking the transpose results in the reciprocal FRF H w Heomp w 4 5 4 iw A J 4 6 J from which the natural frequencies damping ratios and full mode shapes of interest can be identified using e g the peak picking or pLSCF methods as detailed in the previous tutorial see section 4 2 5 ROVING HAMMER TESTING OF A RIB STIFFENED PLATE OOOO 4 3 2 Rib stiffened plate The structure that is considered in this tutorial consists of a base plate made of polymethyl metacrylate PMMA to which 11 steel L30 stiffeners are attached see Fig 4 47 The base plate has a width of Ly 1 25m a height of Ly 1 5m and a thickness of tp 15mm The steel L shaped stiffeners have an outer leg length of Ls 30mm and a thickness of ts 3mm The center to center spacing between the stiffeners is dx 100mm the distance between a vertical edge of the plate and a vertical edge of the closest stiffener is az 110mm and the distance between a horizontal edge of the plate and the closest end section of a stiffener is ay 52 5mm The stiffeners are both glued to the base plate over their entire length and additionally screwed to the base plate at four points I 2 23 4 5 m6 m7 100 81 82 63 84 85 86 87 41 m2 m3 m4 m5 mo m7 Ly gt 61 62 63 64 m5 66 67 50 gt 4 61 62 63 64 65 66 167 wi 72 w3 W4
73. ation degree of freedom experimental modal analysis frequency domain decomposition frequency response function graphical user interface operational modal analysis operational modal analysis with exogenous inputs poly reference least squares complex frequency domain peak picking power spectral density positive power spectral density right matrix fraction description stochastic subspace identification covariance driven stochastic subspace identification reference based covariance driven stochastic subspace identification data driven stochastic subspace identification reference based data driven stochastic subspace identification zero order hold viii Chapter 1 Introduction Welcome to MACEC a program dedicated to modal analysis Modal analysis of structures consists of three distinct steps data collection system identification and determination of the modal characteristics eigenfrequencies damping ratios mode shapes and modal scaling factors MACEC is a powerful tool that deals with every step in the modal analysis procedure except for the data collection The inputs to the program are raw measurement data MACEC offers extensive functionalities for the visualization and processing of the data the identification of system models and the determination and visualization of the structure s modal characteristics The program disposes of a graphical user interface GUI which makes it very intuitive and easy to handle
74. atrix x vec_ X X a matrix of sizem x n x a vector of size mn x 1 5 3 11 vecuns VECUNS unselect from vector y vecuns x ind x vector from which some elements are unselected ind the element numbers of x which have to be unselected not the elements themselves y x without ind 5 4 Modal analysis 5 4 1 anpsd ANPSD Calculate Averaged Normalized Power Spectral Density from Positive Power Spectral Density data and related operational deflection shape ODS information allmodes anpsd nonpar quants allmodes anpsd freqs psdp ref quants allmodes a structure containing the operational deflection shape ODS 110 OVERVIEW OF MACEC FUNCTIONS information Allmodes contains the following fields allmodes anpsd averaged normalized power spectral density function size 1 x n_f with n_f the number of frequency lines y is equal to the weighted mean of the Power Spectral Densities of the reference outputs allmodes f vector with corresponding frequencies Hz allmodes m matrix with operational deflection shapes in its columns m For a particular frequency the corresponding ODS is computed as the column containing the largest element of the PSD matrix allmodes mpc vector with modal phase colinearities of the ODSs allmodes mpd vector with mean phase deviations of the ODSs allmodes wscheme string containing mode schaling information Equals to unit since the ODSs have been scaled to unit modal displacemen
75. c at bwk dot kuleuven dot be 2 7 Note for SPICE users MACEC s part of the SPICE program which contains besides MACEC also the SASW module for Spectral Analysis of Surface Waves You can start the SPICE program simply by typing spice in the Command Window of Matlab and then press ENTER SPICE first starts the MACEC module If you have a license for SASW you can easily switch to the SASW module by making use of the SASW button at the top of the SPICE main window ln SPICE 3 0 and newer the tools for vibration analysis in the build environment are no longer available They are now part of Sigfun the signal Processing toolbox of the Structural Mechanics Section of KU Leuven When purchasing MACEC you also obtain Sigfun Please consult the Sigfun user s guide for more information 10 GETTING STARTED Chapter 3 Structure and conventions of MACEC By reading this chapter you will become familiar with the structure of the MACEC program and its main conventions regarding variable formats file formats and visualization and you will learn how to use the logfile 3 1 Program structure MACEC is a part of the SPICE MATLAB toolbox and it makes use of another MATLAB toolbox developed at the Structural Mechanics Section of KU Leuven SIGFUN The MATLAB toolboxes are a set of MATLAB functions that serve a specific purpose e SPICE contains functions that allow the user to identify a mathematical system model from measured data sys
76. c state space model Bm and D are empty In the special case of a purely deterministic state space model Km is empty fud vector with undamped eigenfrequencies xi vector with modal damping ratios units of critical Phi matrix with mode shapes Ld matrix with deterministic modal participation vectors Km vector with Kalman filter in modal form Ts samping period units s types vector with output data types 5 2 5 rmfd2ss RMFD255 Conversion of a Right Matrix Fraction Description model to a frequency domain state space model i e a state space model with complex matrices A B C D rmfd2ss Ap Bp Ap Bp 3D matrices containing the matrix polynomials of the rmfd description 3rd dimension polynomial order A B C D complex matrices of the equivalent state space description 5 2 6 rmfd2sysmat RMFD2SYSMAT convert structure of identified Right Matrix Fraction Description models to an equivalent structure of State Space models sysmat rmfd2sysmat rmfd rmfd structure of identified RMFD models sysmat structure of SS models 5 2 7 volt2x VOLT2X Convert data from Volts to actual units x r VOLT2X volt sens amp db direction volt Data in Volt sens Sensitivities For accelerations V m s 2 amp Amplification factors Can be in dB MATHEMATICS 107 db 1 if amp is in dB 0 otherwise Can be specified for all channels individually 1 nch or at once 1 1 direction Defaults to 1 for every channel
77. called beam or surface files depending on the type of connection you want for the visualization 3Since beams and surfaces are only used for the visualization they are not numbered FILE STRUCTURES Y Figure 3 3 Example of a slave file If you want the nodes to be connected by lines you need a beam file If you want the nodes to be connected by triangles you need a surface file Beam or surface files can have any name and are of the ASCII type extension asc A beam or surface file is structured as follows e each row contains the definition of a beam connection or a surface connection e each row contains the numbers of the two nodes that are connected by a beam or the numbers of the three nodes that are connected by a triangle Beams and surfaces can also be combined In this case beams should be treated as surfaces for which the last node number equals zero Example Figure 3 4 shows a small beam file The nodes 1 and 2 2 and 3 3 and 4 and 4 and 5 are connected by a beam AeA WwW N o e Ww N Figure 3 4 Example of a beam file 3 3 4 All GUI files mat format If an experimental operational or combined modal analysis is performed with the MACEC GUI you need to save the data after some operations in a mat file If you have saved the data the name of the new mat file appears in the FILE S IN USE section of the MACEC main window figure B I You can proceed further by clicking on the name of the fil
78. caly the system order equals the number of non zero singular values Calculation of system matrices f System orders 2 2 ulate Figure 4 19 Tutorial 1 Covariance driven SSI If you have a look at the singular values of the block Toeplitz matrix of covariance matrices you can draw the same conclusions as for the SSI data identification Therefore choose 2 2 60 as system order range and press the CALCULATE button System orders between 2 and 60 are now calculated in increasing steps of 2 After the calculation is finished press the OK button and save the identified systems in a mat file for instance framedata_ssi_cov mat MACEC now returns to the main window where the file has been added to the FILE S IN USE section 46 TT TUTORIALS using operational pLSCF 31 Select the file framedata_proc mat in the File s in use section of the MACEC main window change the identification method in the SYSTEM IDENTIFICATION section to PLSCF and press APPLY The PLSCF IDENTIFICATION window appears fig 2 20 5t 32 The pLSCF algorithm is suitable for experimental or operational modal analysis which corre sponds to a deterministic or stochastic system identification respectively As the data of the frame structure are output only data the ANALYSIS TYPE in the FRF AND OR PSD ESTIMA TION section should be set to STOCHASTIC Please note that MACEC automatically suggests the right ANALYSIS TYPE b
79. ce driven stochastic subspace identification SSI cov ref e Operational poly reference least squares complex frequency domain identification pLSCF The purpose of this section is to make you acquainted with these different methods which have each there own advantages and disadvantages using nonparametric PSD estimation 17 18 19 Select the file framedata_proc mat in the File s in use section of the MACEC main window change the identification method in the SYSTEM IDENTIFICATION section to NONPARAMETRIC FOR PEAK PICKING OR CMIF FDD and press APPLY The NONPARAMETRIC FRF PSD ESTIMATION FOR PEAK PICKING OR CMIF FDD window appears As the data of the frame structure are output only the ANALYSIS TYPE should be set to STOCHASTIC Please note that MACEC automatically suggests the right ANALYSIS TYPE based on the data type of the channels in this case accelerations only The system model that will be identified is a Positive Power Spectral Density PSD matrix at discrete frequency lines The Positive Power Spectral Densitiy By w between two channels X and Y is defined as the Fourier transform of the positive lags of the cross correlation function rxy t between these two channels 2 Co oO S y w rta f rxy eat oo 0 where u t is the unit step function equal to zero for negative values of t and equal to one for positive values of t Before starting the PSD estimation you should first select which outp
80. celeration m s o Acceleration m s Hz 0 5 10 15 20 25 30 0 50 100 150 200 250 300 350 400 Time s Frequency Hz a b Acceleration m s o Acceleration m s Hz 0 5 10 15 20 25 30 0 50 100 150 200 250 300 350 400 Time s Frequency Hz c d Figure 4 48 Tutorial 3 Rib stiffened plate a c time history and b d Fourier amplitude spectrum of the third channel of the first measurement setup a b after removing the DC component and re sampling and c d after additional high pass filtering with a cut on frequency of 10 Hz MACEC function H1ESTIMATE see section 5 5 1 Because the H estimator relies on an av eraging process the input and output time data are divided into a number of blocks of equal length When choosing the number of blocks a trade off needs to be made a small number of blocks may result in significant variance errors on the FRF estimate due to insufficient averaging while a large number of blocks may result in significant bias errors due to leakage Sec 5 2 2 A crude rule of thumb would be to choose the number of data blocks such that the number of samples in one data block is not smaller than 2000 5000 samples The total number of data samples available in the predat variable can be obtained by executing the following command in the Matlab main window predat N A tot
81. cess this function See also the global function DETREND 5 1 9 df DF Multi channel signal frequency resolution y DF x returns the frequency resolution of the mcsignal x x mcsignal object y Frequency resolution Hz Use y x df to access this function 5 1 10 dinkb DINKB Frequency weighting of a velocity mcsignal according to DIN 4150 2 y DINKB ich1 x multiplies the frequency content of the specified channels ichi of the mcsignal x with the weighting function obtained by the global function DINWEIGHT The sifactor of the specified channels is set to 1 1000 as to obtain a signal in mm s x mcsignal object ichl Channels to apply the weighting to Default all channels y mcsignal object Use y x dinkb ich1 to access this function See also the global function DINWEIGHT 5 1 11 dinkbf DINKBF Running effective value of a weighted velocity mcsignal according to DIN 4150 2 y DINKBF ich1 x applies frequency weighting to the selected channels ichi of the mcsignal x if necessary so delivering a KB mcsignal From this signal the running effective value in mm s is calculated using the global function DINKBF x tdata ich1 x F OQ OVERVIEW OF MACEC FUNCTIONS x mcsignal object ichl Channels to apply the operation to Default all channels y mcsignal object Use y x dinkbf ichi to access this function See also the global function DINKBF 5 1 12 dinkbtau DINKBTAU Running effective value
82. citation Consequently the amplitude of the artificial forces can be small compared to the amplitude of the ambient forces 13 Combined vibration testing has raised interest only recently because it requires special system identification methods One of these methods is the CSI ref method 12 which is incorporated into the MACEC software On the B15 bridge both an ambient and a combined vibration test were performed For the combined test a falling weight mass 120kg drop height 1m was used as an artificial measured force and the bridge was not closed to the road traffic The system could be installed on the sidewalk thus minimizing any disruption of traffic fig 4 30 Figure 4 30 Tutorial 2 B15 bridge drop weight setup The response of the bridge at selected points was measured only in the vertical direction using ac celerometers types PCB type 393A 393A03 393C and Schaevitz A spectrum analyser type Ono Sokki was used to control the measurement on site Fig shows the experimental setup In order not to disrupt the traffic on the bridge the impact weight and the accelerometers were placed on the sidewalk and bicycle lane The vertical accelerations at a total of 86 points 43 points per side were measured fig 4 31 For the combined test the falling weight was placed at node 25 At the Antwerp side of the bridge the vibration measurements were divided into 10 setups each 58 TUTORIALS B 15 A 77
83. containing in allmodes cov k the covariance matrix of allmodes f k allmodes xi k real allmodes m k imag allmodes m k wscheme string containing mode schaling information If equal to unit the mode shapes have been scaled to unit modal displacement If equal to mass the mode shapes have been scaled to unity modal mass quants cell containing the physical units of each mode shape component refquants cell containing the physical units of each reference output conj boolean indicating whether for a particular mode another mode with complex conjugate eigenvalue has also been identified If so only the mode with positive eigenfrequency is listed in allmodes some quantities e g standard deviations are not available the corresponding parts of allmodes are empty 120 5 4 18 stabpick OVERVIEW OF MACEC FUNCTIONS STABPICK Pick selected modes out of a structure named allmodes stabmodes stabmodes allmodes selnrs crit 5 4 19 stabplot stabpick allmodes selnrs crit a structure containing the selected modes see stable_propmodpar m for the structure of stabmodes a structure containing all the modes see stable_propmodpar m for the structure of allmodes a vector containing the selected mode numbers the criterium according to which the poles are sorted Defaults to ascend Other possibility trnorm in decending order of modal transfer norm STABPLOT plot stabilization
84. correlogram method psdp freqscale cor timescale PSDpos_corr predat Nlags outputs refs fmaxstr dart psdp positive power spectrum estimate row outputs columns frequencies depth inputs cor corresponding correlations OVERVIEW OF MACEC FUNCTIONS freqscale frequency scale predat mcsignal object Nlags number of time lags to be used zero lag included Nlags equals the total number of positive frequency points outputs vector with channel output numbers refs vector with reference channel output numbers fmaxstr string indicating whether the maximal frequency in psdp should be the Nyquist frequency fn or the sampling frequency fs optional defaults to fn dart artificial damping in of critical optional defauts to 0 5 5 3 PSDpos_per PSDPOS_PER Estimation of Positive Power Spectral Densities PSD s using the periodogram approach psdp freqscale PSDpos_per predat Nblocks outputs refs m fmaxstr psdp freqscale cor timescale PSDpos_per predat Nblocks outputs refs m fmaxstr psdp freqscale cor timescale psdpcov PSDpos_per predat Nblocks outputs refs m fmaxstr psdp positive power spectrum estimate row outputs columns frequencies depth inputs psdpcov 3D matrix of covariances on psdp row outputs columns reference outputs depth frequencies freqscale frequency scale timescale time scale cor 3D matrix of correlation functions without applyin
85. csignal s channels not only the selected channels ich1 have to be provided domain ichi x filename gt AddToPlot gt AxesSize Blank Data Language Legend gt LegendLoc gt LineWidth Margins NXTick NYTick gt XLabel gt YLabel XMin XMax gt YMin gt t to plot time history f to plot frequency content or b to plot the one thirds octave band spectrum of the RMS value Channels to plot Default all channels mcsignal object File to save the plot to using the global function SAVEFIG Can be omitted if you do not want to save the plot Command evaluated after all built in plotting routines as to add elements to the figure e g equal human response curves Size of the axes in centimeters See NEWFIG for more info Do not plot the curve plot only the axes and the labels Value is assigned to the local variable Data which can be used by the AddToPlot command If a cell array is provided the contents of cell i is assigned to the local variable Data when plotting channel i First index of the time interval to plot Default 1 Last index of the time interval to plot Default x N Label language en or nl Default Default no legend See also LEGEND Legend location Default Best See also LEGEND Default 0 5 for domain t and f and 1 5 for domain b Margins between the axes and th
86. cts of the MCSIGNAL type For a good understanding of terminology it is important to make the distinction between system identification and modal analysis Experimental operational or combined modal analysis as defined in the literature consists of three distinct steps 1 collection of the data and preprocessing 2 system identification 3 determination of the modal characteristics from the identified system model modal analysis So the term modal analysis is defined at two different levels i the whole process of obtaining modal characteristics from measurements steps 1 2 and 3 and ii the determination of the modal characteristics from the identified system model step 3 This often causes confusion which some times results in mixing up system identification with modal analysis of level ii especially when the difference is subtle for instance when modal characteristics are determined directly from a nonpara metric frequency response function FRF identified from data Therefore the MACEC toolbox clearly differentiates between system identification and modal analysis of level ii both in the function definitions and in the GUI 3 2 Variable formats MACEC makes use of standard MATLAB variable formats as DOUBLE CHAR STRUCT etc Consult the MATLAB help for more information In addition MACEC also allows the user to create MCSIGNAL multi channel signal variables which are from a programming point of view objects o
87. d then taking the discrete Fourier transform For larger time lag values there are less data points available for averaging which makes that the correlation estimates are less ac curate This can also be verified for this case Select the SHOW CORRELATION option in the PLOT OPTIONS part leave all other settings to their default values and press CALCULATE AND SHOW ESTIMATES fig 4 13 From the plot you can see that the value of the autocorrelation estimate decreases between the time lags of 0 and 12s as expected However when the lag is larger than 12s the estimates increase again which indicates their inaccuracy Therefore fill in 1024 for the NUMBER OF TIME LAGS and press CALCULATE AND SHOW ESTIMATES If you select now Show PSD in PLOT OPTIONS you notice that the new estimate is much smoother than the previous one After unchecking the SHOW ESTIMATION HISTORY box fig 4 14 is obtained It should be kept in mind that for short data sequences the number of useful correlations might be low and leakage errors might become important 5 The periodogram method calculates the PSD by dividing the available raw time data into Np blocks doubling the length of each block by adding zeros taking the Fourier transform for each block multiplying for each frequency all outputs with the Hermitian transpose of the reference outputs and averaging the result over all blocks 2 Note that in this way the number of blocks is an upper bound for t
88. dal2ss 5 4 7 mod3D MOD3D calculate 3D mode shapes mode3 mod3D mod_sel node_num meas_dir grid mode3 a structure array consisting of the grid of the 3D mode shapes mode3 grid and the x y and z components of the different mode shapes mode3 x mode3 y and mode3 z mod_sel a matrix of measured mode shapes node_num a vector with node numbers meas_dir a matrix with the measurement directions grid the measurement grid 5 4 8 modeselect MODESELECT select modes from allmodes that mach the stabilization criteria stabmodes modeselect allmodes df dxi dm dampco damplco trnormco dmtn maxfrstd maxdmpstd maxmodstd mpclb mpub mpdub stabmodes stabfdmodes stabfmmodes stabfmodes unstabmodes selectedmodes modeselect allmodes df dxi dm dampco damplco trnormco dmtn maxfrstd maxdmpstd maxmodstd mpclb mpub mpdub stabmodes has the same structure as allmodes but contains only the stable modes stabfdmodes contains the modes that have stable frequency and damping but no stable mode shape for whith the damping ratio lies between the upper and lower bounds and that have the highest modal transfer norms stabfmmodes contains the modes that have stable frequency and mode shape but no stable damping for whith the damping ratio lies between the upper and lower bounds and that have the highest modal transfer norms 114 stabfmodes unstabmodes OVERVIEW OF MACEC FUNCTIONS contains the modes that have stable frequency bu
89. e relax the TRANSFER NORM criterion to 75 and press APPLY The stabilization diagram now consists of clear vertical lines between 0 and 10Hz but it is still hard to interpret between 10 and 25Hz fig 4 45 This can be explained from the sum of the FRFs that is plotted on top of the stabilization diagram in fig above 10Hz many modes are present that are probably not well excited The most important peaks in the FRF sum are situated around 13 and 16 5Hz which corresponds to modes 9 and 10 from fig 4 44 Although it is also possible to pick these modes from the stabilization diagram obtained after CSI ref identification it is a time consuming task due to the unclear stabilization Therefore we confine ourselves here to the modes between 0 and 10Hz of oye 70 TOD i gd SMV GY 60 ff as J fy AS 50t R E Ones ee ee model order S a 30 ES 20 ES S pa k Y ae S 10 KY 1 0 5 10 15 20 25 frequency Hz Figure 4 45 Tutorial 2 Stabilization diagram constructed from state space systems identified with CSI ref first setup first measurement default stabilization criteria denotes a stable mode v a stable frequency and mode shape d a stable frequency and damping and f a stable frequency The selected modes are indicated with red circles 32 In the frequency range between 0 and 10Hz one can easily find the eight stable modes indicated in table Note that within a c
90. e Power Spectral Density estimation Ch 11 R2 Spock References e g 3 5 7 El Cancel Figure 4 38 Tutorial 2 Deterministic nonparametric system identification 11 In the FRF ESTIMATION H1 METHOD window you have to specify a number of data blocks first As the total number of samples available is small and the minimal number of 2 blocks is automatically suggested by MACEC you don t have to change anything Just press the CALCULATE AND SHOW ESTIMATES button to start the H1 estimation If this is finished you THE B15 BRIDGE AAA 5 12 13 can see from the RESOLUTION INFO panel that the frequency resolution is quite course 0 1626Hz fig 1 39 FRF estimation H1 method H1 estimation parameters Output channel 1 v Input channel Number of data blocks Window type rectangular O Hanning Calculate and show estimates J Plot options M Show data in dB Y Show standard deviation FRF m s2 N Hz m Resolution into Total number of samples 615 Window length 307 samples Frequency resolution 0 1626 Hz 10 15 frequency Hz Figure 4 39 Tutorial 2 H FRF estimation for pLSCF identification After pressing OK MACEC returns to the NONPARAMETRIC FRF PSD ESTIMATION FOR PEAK PICKING OR CMIF FDD window In this window press OK and save the models in the following mat file VALA1 1_nonpar Repeat t
91. e and by subsequently pressing a command button in the MACEC main window Please note that the mat file is not loaded in the memory until you press a command button A powerful possibility of MACEC is that you can also create these mat files without the GUI and then use the GUI in a next step by adding the file to the FILE S IN USE section of the GUI main window with the SELECT NEW DATA button figure 1 7 However in this case it is important that the variables stored in the mat files have the right names types and dimensions 18 STRUCTURE AND CONVENTIONS OF MACEC Converted measurement data After you have converted the measurement data in ddf asc tdm wav mat or f32 format to an MCSIGNAL object using the GUI you are required to save this MCSIGNAL object in a mat file This mat file contains only one variable namely the MCSIGNAL object which has the name CNVDAT from converted data Conversion factors In the CONVERSION OF THE MEASURED DATA window of the MACEC GUI it is possible to save the conversion factors separately into a mat file and to load this file later on This is particularly handy if the measurements are performed in several setups for which the number of channels and the sensors are identical The saved file contains the following variables e LABELS a cell which contains the labels given to each channel e TYPE a vector containing the information about the data type If an eleme
92. e bounding box in centimeters See NEWFIG for more info Number of XTicks approximately see the global function TICK Default Number of YTicks approximately see the global function TICK Default X axis label Default defined using MCSIGNAL LABEL Y axis label Default defined using MCSIGNAL LABEL X axis scaling minimum value Default left side of the plotted curve X axis scaling maximum value Default right side of the plotted curve Y axis scaling minimum value Default defined as a function of the plotted curve Y X max abs Y for domain t O for domain f and min Y for domain b en auto auto 100 OVERVIEW OF MACEC FUNCTIONS gt YMax Y axis scaling maximum value Default defined as a function of the plotted curve Y X max abs Y for domain t and max Y for domains f and b See also NEWFIG SAVEFIG MCSIGNAL TPLOT MCSIGNAL FPLOT MCSIGNAL BPLOT 5 1 37 quantity QUANTITY Multi channel signal data type per channel y QUANTITY x returns a cell array containing strings describing the data type for each channel of the mcsignal x x mcsignal object y Cell array containing data type describing strings e g volt Use y x quantity to access this function 5 1 38 resample RESAMPLE Resample a mcsignal y RESAMPLE x P applies the global function RESAMPLE x tdata P x F to the channels of the mcsignal thus setting the sampling frequenc
93. e master DOF direction in X Y Z coordinates followed by the node number of the slave node and the slave DOF amplified direction in X Y Z coordinates respectively Example Figure 3 3 shows a small slave file containing the definitions of 4 slave DOFs e In the first row the deformation in the X direction of node 7 is coupled to the deformation in the X direction of node 2 The amplification factor is 1 e In the second row the deformation in the X direction of node 8 is coupled to the deformation in the X direction of node 3 The amplification factor is 0 5 so that the amplitude of the 8X DOF is half that of the 3X DOF e In the third row the deformation in the X direction of node 8 is coupled to the deformation in the X direction of node 4 The amplification factor is 0 5 so that the amplitude of the 8X DOF is half that of the 4X DOF Because the 8X DOF was also coupled to the 3X DOF the amplitude of the 8X DOF is the mean of 3X and 4X e In the fourth row the deformation in the X direction of node 6 is coupled to the deformation in the X direction of node 2 The amplification factor is 0 so that node 6 does not move This trick can in general be used for the visualization of DOFs that are not measured but that can from the geometry of the problem be supposed to have nearly zero amplitude Beam surface files In MACEC the files that contain the definition of the connections between the measurement nodes are
94. ee hae bie od Gees se es eee ee 56 i A Bee ened ad 57 Ee ee ne eR enter eek a 60 snap BA GP oe od ecg as Rs ee ee 64 Ca Oa beak eee eae eh ea Bees ae 67 bone fee be Ge oe ee ee ee eke 74 4 3 1 Roving hammer testing a a 76 43 2 Rib stiffened plate 77 4 3 3 Processing the measured signals into an FRF matrix 78 4 3 4 System identification using the pLSCF method 81 4 3 5 Modal analysis after deterministic pLSCF 2200 83 4 3 6 Interpretation and conclusiong 0000 a ee 83 5 Overview of MACEC functions 85 che aaa eae hand a oe eee ee ee eee se 85 DLL axesACPSDplot vaca wb vs hb Oa ge ee ed we eh EM eA 85 5 1 2 axesCPSDFRFCOHplot 0 o 87 A E o 20 4 4 4 24 444460 4S ne Pa PE eae eR Ee a es 88 bo Have ene Sere oh a bee ee oe ee Ge a 90 jlo concatenatd 40s ae e ER EO ee eR ee we ee ee 90 5 1 6 decimate scs os a ba Sc eA Ree SRS OE SEER SoS SHE EAE ES ES 90 DL delete sia 6 Pa a d bee Be of ee a ee we ee we ee 90 CONTENTS OI a Rees oe eee ee es a 91 Wea te othe obo Gee eee eee ee 91 bebe dee A 91 a G8 poms aes a ee ee eee bee ee ee ee 91 5 1 12 dinkbtad 2 0 0 0 0 ee eee eee eee 92 ae ee a ee ee a Se 92 eta ae eh ee Sh ese A ek ee one ee ted 92 a ee Be ee oe ee ee eee eon ees 92 boon a oe Be a ee ee 93 a ae ete ee 93 bh a oe pe a ee ee ee ee ee eae 93 A Ale wae area o Ged b Reece Recs Ge Se ne Bee Fk a Ae 93 pi need es A
95. els identified with SSI data ref of orders 2 4 6 30 stochastic state space models identified with SSI cov of orders 2 4 6 60 right matrix fraction description models identified with operational pLSCF of orders 4 8 12 60 The next step in the experimental determination of the modal parameters of the structure is the modal analysis of the identified system models For each of the four series of parametric models a stabilization diagram will be calculated and from this diagram we will select the stable physical system modes that we are looking for But first we will identify the modal parameters in a more intuitive but rather rough way starting from the identified nonparametric PSD model using nonparametric techniques 37 Select the framedata_nonpar mat file in the FILE S IN USE section of the MACEC main window and press the MODAL ANALYSIS button in the MODAL ANALYSIS section You are asked to select a modal analysis method Choose PEAK PICKING The averaged normalized power spectral density ANPSD is then computed and plotted in an interactive window Since in this case the modal parameters are well separated they can be estimated by picking the peaks in the ANPSD plot fig 4 21 Note that after a peak has been selected the corresponding mode shape is listed and plotted in the complex plane After the modes have been selected press OK and save the mode information as The theory behind the peak Pic
96. equency f_low lower bound of the frequency range of interest f_up upper bound of the frequency range of interest 5 5 10 ss2mss SS2MSS Conversion of a state space description into its modal form Lambda Cm ss2mss A C Lambda Bm Cm D ss2mss A B C D Lambda Cm Qm R Sm ss2mss A C Q R S Lambda Bm Cm D Qm R Sm ss2mss A B C D Q R S Lambda Bm Cm Dm the state space description in modal form Lambda is a diagonal matrix Qm R Sm the state space noise covariance matrices in modal form A B C D the original state space matrices Q R S the original state space noise covariance matrices 5 5 11 ssi_data3 SSI_DATA3 Data driven Reference based Stochastic Subspace Identification invar ssi_data3 Y ii ref algorithm 126 OVERVIEW OF MACEC FUNCTIONS A C Q R S ssi_data3 invar n Y the output data ii half the number of block rows in the Hankel matrix ref column matrix containing the reference sensors algorithm optional string containing the desired algorithm PC UPC or CVA Default UPC invar results after QR and SVD n the order of the identified system A C the identified state space matrices Q R S the identified state space covariance matrices 5 5 12 ssicov SSICOV calculates the system matrices A C Gref and LambdaOref from measured outputs y only using reference based stochastic subspace idenficiation SSI cov ref 1 The computation is done in two commands t
97. ethod yields strongly consistent system estimates while the pLSCF results in slightly inconsistent estimates On the other hand using deterministic pLSCF some higher modes could easily be detected due to the very clear stabilization diagram while with CSI ref this operation would be troublesome due to the unclear stabilization diagram So one can conclude that deterministic pLSCF and CSI ref complete each other well The CMIF method is suited for quick rough estimates but it should be applied with care since modes that are less well excited may be missed The fact that pLSCF results in biased damping ratio estimates has been demonstrated through numerical simulation studies see e g L1 76 TT TUTORIALS 4 3 Roving hammer testing of a rib stiffened plate In this tutorial the capabilities of using MACEC in batch mode are explored The objective is to identify modal characteristics from roving hammer test data 4 3 1 Roving hammer testing In a roving hammer test dynamic reciprocity is employed so as to reduce the total time of testing Us ing the dynamic or Betti Rayleigh reciprocity theorem it can be shown that the frequency response function H w between structural displacement outputs and force inputs decomposes as H w rene GP iv jo 4 1 iw A where A denotes the continuous time eigenvalue of mode j the corresponding mode shape vector and q the corresponding modal scaling factor The parts of the
98. f the Control Systems Toolbox of MATLAB EXAMPLE 1 2DOF SYSTEM __ 185 fud xi Phi quants Ld Km Gm refquants propmodpar5 Aid Cid Qid Rid Sid 1 Ts types 1 refs compute the modal parameters Lambda Bm Phi D Km modal2ss fud xi Phi Ld Km Ts types ym mdtime y Lambda Phi Km newfig 10 10 hi subplot 4 1 1 plot y 1 set gca xlim 0 500 ylim 5 1 1 h2 subplot 4 1 2 plot squeeze ym 1 1 set gca xlim 0 500 ylim 5 1 1 h3 subplot 4 1 3 plot squeeze ym 1 2 set gca xlim 0 500 ylim 5 1 1 h4 subplot 4 1 4 plot y 1 squeeze ym 1 1 ym 1 2 set gca xlim 0 500 ylim 5 1 1 xlabel h4 time s ylabel h1 signal m s 2 ylabel h2 mode 1 m s 2 ylabel h3 mode 2 m s 2 ylabel h4 error m s 2 signal m s 0 100 200 300 400 500 mode 1 m s 0 100 200 300 400 500 mode 2 m s o error m s o 0 100 200 300 400 500 time s Figure 6 3 Verification example 1c modal time domain response decomposition from an output only state space model identified with SSI data 136 OOOO VERIFICATION EXAMPLES References 10 11 12 H Akaike Stochastic theory of minimal realization IEEE Transactions on Automatic Control 19 6 667 674 1974 B Cauberghe Applied frequency domain system identifica
99. f the MCSIGNAL class The philosophy behind MCSIGNAL objects is that they contain all information about the measured data in one single MATLAB variable Therefore MCSIGNAL objects have the following properties e NCH is the number of channels used in the measurement e N is the number of samples measured e Fis the sampling frequency in Hz e DF is the frequency resolution in Hz e T is the total measurement duration in s e DT is the sampling period time resolution in s e QUANTITY is a cell containing the measured quantities of each channel for instance acc stands for acceleration e SIFACTOR contains the factor which links the measurement units to SI units for instance if the measured data for a particular channel are accelerations and the sifactor equals 10 the units are mm s e LABELS is a cell containing the labels of each channel FILE STRUCTURES da The properties of an MCSIGNAL object are accessible in two ways in dot notation or as a command For instance if you want to know the sampling frequency of an MCSIGNAL object named CNVDAT you can use the MATLAB commandd cnvdat F or f cnudat Objects of the mcsignal type are defined with the mcsignal command For more information about this command and for an overview of all functions that can be performed on objects of the MCSIGNAL type please consult section 3 3 File structures 3 3 1 Measurement data ascii mat ddf msd tdm wav and f32 forma
100. ference Least Squares Complex frequency Domein pLSCF Identification FRF and or PSD estimation Select Channels Analysis type deterministic stochastic ee ES Ch 1 R1 acc FRF estimation H1 estimator pl Ch 4 a3 acc j Ch 5 a4 acc Ch 6 a5 acc Ch 7 a6 acc Positive Power Spectral Density estimation Ch 8 a7 acc Ch 9 a8 acc a8 e References e g 3 5 7 Ch 10 a9 acc C 0 Ch 12 for force Right Matrix Fraction Polynomial estimation Frequency range Hz to Polynomial orders Figure 4 40 Tutorial 2 Deterministic pLSCF 2 2 100 Since there s only one input the polynomial order range equals the system order range If the identification is ready press OK and save the identified system matrices as VALA1 1_pLSCF mat 16 Repeat the identification step for the other setups You can have a look at the logfile_pLSCF m file in the tutorial2 section in order to have an idea on how this can be performed in a batch run i e without using the GUI CSI ref 17 Select the VALA1 1_proc mat file in the FILE S IN USE section of the MACEC main window select COMBINED SUBSPACE in the SYSTEM IDENTIFICATION field and press APPLY to open the COMBINED DETERMINISTIC STOCHASTIC SUBSPACE IDENTIFICATION window 4 At the right you can see that MACEC immediately suggests which channels have to be considered as inputs and which channels are outputs based on the data type In the ALGORITHM SELECTION field m
101. g the time window row outputs columns reference outputs depth time steps predat mcsignal object Nblocks number of blocks to be used in averaging procedure outputs vector with channel output numbers refs vector with reference channel output numbers m time window parameter if N is the total number of samples and Nw is the length of the time window m N Nw fmaxstr string indicating whether the maximal frequency in psdp should be the Nyquist frequency fn or the sampling frequency fs optional defaults to fn 5 5 4 RMFDcalc RMFDCALC Calculation of Right Matrix Fraction Description Polynomial This function is used after a non parametric preprocessing step during frequency domain system identification rmfd rmfdcalc H_meas method orders chanselout chanselin refs freqscale f_low f_high SYSTEM IDENTIFICATION S 123 rmfd H_meas method chanselout chanselin refs freqscale f_low f_up a structure array containing the A and B matrix polynomial coefficients for the given system orders a 3D array containing FRF PSD or combined FRF PSD matrices for each frequency The 3rd dimension is the frequency dimension describes the system identification method to be used If the Poly reference Least Squares Complex Frequency Domain method has to be used method equals pLSCF a vector containing the output channels selected for identification a vector containing the input
102. gures are indicated by white rectangles the files that are created from or interact with a GUI figure are indicated by grey ellipses A OOOO STRUCTURE AND CONVENTIONS OF MACEC x If a time window needs to be applied during signal processing the GULtimewind function which constructs a dialog window is called by the signal processing window With the App DOFs button the GUL spec function is called which constructs the window for the specification of the measurement DOF s e SYSTEM IDENTIFICATION In this section the user specifies which system identification method he or she wishes to use Depending on the method chosen different windows are opened For all stochastic subspace identification methods SSI data SSI data ref SSI cov SSI cov ref the GULssi function is called which constructs the window for SSI For all combined subspace identification methods CSI and CSI ref the GUI_csi function is called which constructs the window for CSI For all pLSCF methods Deterministic pLSCF and Operational pLSCF the GUI_pLSCF function is called which constructs the window for pLSCF identification Because an identified non parametric system model is needed for pLSCF from this window one of the following functions is called x GUI_H1 constructs the window for the estimation of a non parametric FRF H esti mator GULPSDp constructs the window for the estimation of a non parametric Positive Power Spectral Density
103. he MACEC main window press the CREATE BEAM OR SURFACE FILE button A new window entitled DEFINE EDIT BEAMS OR SURFACES appears MACEC offers two alternatives for the visualization of the link information between the mea surement points e beams which are defined by two node numbers lines e surfaces which are defined by three node numbers triangles As the structure under study is a frame structure beams are the natural choice for the visual ization Again MACEC offers the possibility to accelerate the definition of the beams by using MATLAB vector notation To connect the nodes at the left columns of the frame structure enter 1 4 in the NODE 1 field and 2 5 in the NODE 2 field If you then click the ADD button the defined beams are added to the list at the left bottom and to the figure at the right Now follow the same procedure for connecting the right columns and the horizontal beams of the frame structure The result should look like in fig OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE A Ss Define Edit beams or surfaces Add beam or surface to list Connected nodes Node1 2 5 Node 2 7 10 Node 3 9 for surfaces only List of beams or surfaces Node number Coordinates X Y Z Equalaxes Vv Cancel Figure 4 6 Tutorial 1 Creation of links between the measurement point
104. he MATLAB main window Now you can start the GUI of MACEC simply by typing macec in the Command Window of Matlab and then press ENTER MACEC starts up and the main window of MACEC appears gy macec po Sim LEUVEN File s in use Geometry aa a 08 VE Oo OBO a Signal Processing Convertto mesignal Process Add DOFs System Identification Stochastic Subspace E Modal Analysis Modalanalysis Combine setups Plot mode shapes Listmodes Figure 2 1 The main window of MACEC You can also call individual MACEC functions see chapter 4 from the Matlab Command Window or by running a Matlab m file 2 5 Help and support This manual provides the main user support for MACEC It also contains tutorials which clarify the use of the MACEC GUI Furthermore detailed help for the individual MATLAB functions of MACEC is available from this manual chapter 5 as well as examples of the use of these functions in batch mode chapter 6 Important Please note that for MACEC no help desk or individual support is available The manual and the MATLAB help should provide sufficient user support BUG REPORTS DD 2 6 Bug reports MACEC has been extensively tested and validated However it might be possible that you still encounter bugs If so please report them by email to mace
105. he first command should only be called once when several system descriptions with different model orders are identified from the same data e g for constructing a stabilization diagram The covariance matrix of the estimation errors can be optionally computed according to the algorithm of 2 3 The implementation of this covariance estimation procedure is much more memory efficient when compared to previous editions of MACEC but this procedure may require most of the CPU time needed to run SSICOV invar ssicov Y ii refs invar ssicov Y ii refs Nb invar ssicov invar n_max A G C Lambda02 ssicov invar n A G C Lambda02 covAC ssicov invar n Lambda Gm Phi Lambda02 covmod ssicov invar n decoupled Y Matrix containing the output vectors as its columns ii Number of block rows in the block Hankel matrix refs vector containing the reference outputs row number of Y optional all outputs are reference outputs by default Nb Number of blocks in the covariance estimation process optional equals to min 500 j by default with N the number of samples minus 2 ii If N equals 1 the covariances of the system matrices are not estimated invar Structure containing intermediate identification results that are can be used at different model orders n A G C Lambda02 System matrices of the estimated stochastic state space description covAC Complete statistical covariance matrix of the estimated stochastic state space
106. he first positive frequencies corresponding to the FFT of the data stored in the mcsignal x x mcsignal object y Frequencies Hz Use y x f to access this function See also MCSIGNAL F2 MCSIGNAL FFTFREQ 5 1 18 f2 F2 Multi channel signal frequency vector y F2 x returns a vector containing the frequencies corresponding to the FFT of the data stored in the mcsignal x up to the Nyquist frequency x mcsignal object y Frequencies Hz Use y x f2 to access this function See also MCSIGNAL F MCSIGNAL FDATA2 5 1 19 f F_ Multi channel signal sampling frequency y F_ x returns the sampling frequency NOT the Nyquist frequency of the mcsignal x x mcsignal object y Sampling frequency Hz 93 A OOOO OVERVIEW OF MACEC FUNCTIONS Use y x F to access this function 5 1 20 fn F_N_ Multi channel signal Nyquist frequency y F_N_ x returns the Nyquist frequency of the mcsignal x x mcsignal object y Nyquist frequency Hz Use y x FN to access this function 5 1 21 fdata FDATA Multi channel signal frequency content y FDATA x returns the frequency content of the mcsignal x obtained by calling Matlab FFT which is a DFT An approximation of the continuous Fourier transform can be obtained by dividing y by the sampling frequency x mcsignal object y Frequency content Use y x fdata to access this function See also MCSIGNAL FDATA2 5 1 22 fdata2 FDATA Multi channel sig
107. he identification step for the other setups You can have a look at the logfile_cmif m file in the tutorial2 section in order to have an idea on how this can be performed in a batch run i e without using the GUI deterministic pLSCF 14 15 Select the VALA1 1_proc mat file in the FILE S IN USE section of the MACEC main win dow select PLSCF in the SYSTEM IDENTIFICATION field and press APPLY to open the POLy REFERENCE LEAST SQUARES COMPLEX FREQUENCY DOMAIN PLSCF IDENTIFICATION win dow You can see that MACEC immediately suggests based on the type of data which channels will be considered as inputs and which channels will be outputs and which ANALYSIS TYPE is needed This suggestion is correct so you do not have to change it Press APPLY in the FRF ESTIMATION field fig 4 40 to start the estimation of a non parametric FRF using the H estimator 5 Follow exactly the same steps as in paragraph 11 from the previous section After pressing OK MACEC returns to the POLY REFERENCE LEAST SQUARES COMPLEX FRE QUENCY DOMAIN PLSCF IDENTIFICATION window where it is now possible to calculate the system matrices of a Right Matrix Fraction Description RMFD model using the pLSCF algo rithm Since the bandwidth of interest coincides with the available frequency band don t change the default values in the FREQUENCY RANGE fields In the POLYNOMIAL ORDERS field fill in 66 TUTORIALS Poly re
108. he model orders to be calculated and press CALCULATE This calculation might take several minutes If the system matrices have been calculated press OK and save them as VALA1 1_CSIref mat 19 Repeat this identification step for the other setups 4 2 6 Modal Analysis With the Complex Mode Indication Function 20 In the MACEC main window select VALA1 1_nonpar mat and press the MODAL ANALYSIS button in the MODAL ANALYSIS field The complex mode indication function CMIF is computed and plotted fig 4 42 Since only one input the drop weight was used in the test the CMIF consists of one singular value only and as such properly identifying closely spaced modes is not possible As noted before the short measurement duration results in a very coarse frequency resolution Since for this bridge it is expected that the mass normalized mode shapes are purely real no double modes no localized dampers the selected modes should have a high modal phase collinearity MPC value and a low mean phase deviation MPD value By inspecting the CMIF by moving the cursor over it it can be verified that only two peaks have an MPC value larger than 0 9 Select the peaks as indicated in fig the other peaks will not be present in all setups or will yield very poor modal parameter estimates in some setups 21 After the poles have been selected save them as VALA1 1_CMIF_modes mat Repeat the mode selection step for all 9 other setups 68 TUTORIALS
109. he rank of the PSD matrix In order to reduce the variance error of the perdiodogram estimate one can take the inverse Fourier Transform of it apply a time window to the resulting correlation estimate and take the Fourier transform again p 58 This approach usually yields much better results than taking an excessive number of averages resulting in short data blocks and as a consequence large leakage errors However it results in biased estimates for the modal participation factors which need only to be compensated for when the contributions of the different modes to the PSD is of interest 2 40 TUTORIALS PSD estimation Sse Hotel Output channel 1 Reference 15 4 Correlogram method Periodogram method Number of time lags M Zags Number of data blocks zero lag included y Time window parameter Corrlation m s m s Plot options Resolution info O Show PSD Total number of samples 8192 Window length 4096 samples ORS aah tie ctl Frequency resolution 0 024414 Show estimation history time s gt ime s Show standard deviation Figure 4 13 Tutorial 1 Autocorrelation estimation before PSD estimation In the PERIODOGRAM METHOD section the user has to provide two values the number of blocks that the raw time data will be divided in and the time window parameter m which equals the ratio between the length of one block N
110. i channel signal in the current axes AXESCPSDFRFCOHPLOT domain refch ich1 x filename KeyName KeyValue plots the cross power spectral density domain cpsd the frequency response function domain frf or the coherence function domain coh of the mcsignal x Key options can be specified to fine tune the plot These options are interpreted by the present function and they are passed to the global function NEWFIG which is used to open a new figure window The values of the key options interpreted by the present function may be scalars single strings or vectors cell arrays of strings In the first case the same value is employed for all channels while in the second case values for all of the mcsignal s channels not only the selected channels ich1 have to be provided domain gt cpsd to plot cross power spectral density frf to plot frequency response function and coh to plot coherence function refch Reference channel ichl Channels to plot Default all channels x mcsignal object filename File to save the plot to using the global function SAVEFIG Can be omitted if you do not want to save the plot Windowtype In case of a PSD plot the window type has to be specified Valid choises are rectwin and hamning Default rectangular window rectwin Windowlength In case of a PSD plot the window length in data points has to be specified Default n_ x Overl
111. ic system identification 8 10 it is physically very intuitive and therefore mainly suited for getting a first quick idea of the structural modes before performing a more detailed analysis or for educational purposes Two methods are supported Peak Picking PP where the modal characteristics are identified by selecting the peaks of the averaged normalized power spectral density function which is easily computed from an identified PSD function This technique is only available for output only data Complex Mode Indication Function CMIF where peaks of the singular values of the iden tified FRF matrix as a function of frequency are selected for estimating the modal char acteristics 16 When applied to output only data the singular values of the PSD matrix computed as the sum of the identified PSD matrix and its transpose are used the method is then sometimes also referred to as Frequency Domain Decomposition FDD Please note that modal damping ratios are not provided for these methods as nonparametric damping ratio estimation is not reliable e Data import from GeoSIG Miniseed msd files is now supported Multiple files coming from simultaneous measurements on different stations can be imported at once and they are auto matically synchronized e New functions have been added so as to support time domain modal response decomposition from an identified output only model The use of these functions is illustrated in a
112. ied modal parameters with the exact values obtained in section 6 1 1 after ZOH discretization with the same sampling frequency The estimates are not exact despite the fact that the data are purely deterministic It can be verified that increasing the number of samples N increases the accuracy of the modal parameter estimates decreasing this number decreases the accuracy fua 7 1176 10 0658 7 1486 10 0337 fos an a mm 0 4963 0 05153 0 4930 0 07167 0 4961 0 05722 0 5014 0 06182 0 4963 0 05153 0 4930 0 07167 0 4883 0 04177 0 4843 0 08032 Table 6 2 Verification example 1b undamped eigenfrequencies fuq damping ratios and mode shapes exact values vs the estimates obtained with deterministic pLSCF Figure compares the exact frequency response function FRF as found in 5 p A1 30 with the H estimate and the FRF that is computed with the identified RMFD description The corresponding Matlab code can be found below compute FRFs p 11 2 pixfreqscale Laplace variables nf length freqscale number of frequency lines used in the plot frf_ex zeros 2 2 nf initialize the matrix with exact FRFs z exp Ts p 4 z variables frf_rmfd zeros 2 2 nf initialize the matrix with FRFs estimated from the rmfd description Ar2 rmfd A_2 3 Ari rmfd A_2 2 ArO rmfd A_2 1 define the A matrices of the right matrix fractio
113. igital counts F a force sensor D a displacement sensor S a strain sensor and V a velocity sensor For accelerometers the sensitivity is defined in mV g or counts g for force sensors in mV 1bf for displacement sensors in V m for strain sensors in mV e and for velocity sensors in V m s Comments may be used but need to be put between two symbols An example of a sensor definitions file is shown in fig 3 3 3 Geometry definitions ASCIT format All files that deal with the geometry of the measurement setup need to be of the ASCII type See the subsections below for the definitions of specific geometry related files Grid files In MACEC the files that contain the definition of the measurement nodes are called grid files They can have any name as long as they are of the ASCII type extension asc A grid file is structured as follows e each row contains the definition of a measurement node e each row has four columns containing the node numbel and its X Y Z coordinates in any units Example Figure shows a small grid file containing the definitions of 4 nodes Node 1 has coordinates 0 0 0 node 2 is situated at 3 0 0 node 3 at 0 3 0 and node 4 at 3 3 0 2Only positive nonzero integers are allowed as node numbers FILE STRUCTURES ACCELEROMETERS manufacturer PCB_393A03 PCB_393A03 PCB_393A03 PCB_393A03 PCB_393B04 PCB_393B04 PCB_393B04 PCB_393B04 manufacturer AC 1931
114. ilization diagram is created fig 4 24 Notice that thanks to the preset values for the stabilization criteria the diagram looks very clear 40 Now tick the SHow PSD FRFs checkbox and press CALCULATE A small window opens fig 4 23 Leave all settings to their default values and press OK The sum of all Positive Power Spectral Densities is now calculated and MACEC returns to the stabilization diagram If l For well separated modes as in this case only the highest singular value should be considered For closely spaced modes however the other singular values should be considered as well The theory behind the CMIF FDD method is not explained in this manual The interested reader is referred to for more information OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE AD Complex Mode Indication Function CMIF Frequency Domain Decomposition FDD Mode information Frequency Hz 14 844 Selected mode shape info Scale channel Singular value 0 465 MPC 1 000 MPD 0 00 Show real imaginary part O Show absolute value angle v ES gt 5 5 a te e Channel 1 0 44562 Channel 2 1 Channel 3 0 90974 Channel 4 0 50891 20 25 30 35 40 frequency Hz v Show data from O Hz to 49 8047 Hz Show CMIFIFDD in dB Apply oK Figure 4 22 Tutorial 1 Selection of modes by Frequency Domain Decomposition you then press APPLY the PSD sum i
115. imension frequency MODAL ANALYSIS 111 allmodes mpc matrix with modal phase colinearities of the ODSs 1st dimension singular value 2nd dimension frequency vector with mean phase deviations of the ODSs 1st dimension singular value 2nd dimension frequency allmodes mpd allmodes wscheme string containing mode schaling information Equals to unit unit modal displacement scaling matrix with deterministic discrete time modal participation vectors in each column allmodes quants cell containing the physical quantities of each mode shape component allmodes ld nonpar structure containing a system description identified using nonparametric system identification freqs frequency lines for which the PSDP has been estimated psdp positive power spectral density matrix size n_o x n_ref x n_f with n_ref the number of reference outputs quants a cell containing the measured output quantities loc driving point locations output numbering If loc equals zero the modes are scaled to unity ampl driving point amplitude Note the PSD is computed by taking the sum of the provided PSD function and its complex conjugate for each frequency line Note damping ratios are not computed since the half power bandwidth method for computing damping ratios is inaccurate 5 4 3 drawmodes DRAWMODES Plot a mode in the current axes drawmodes mode3 modenr amp complmode plotcolour linewid anim_ gridfile path_beam path_slave
116. ingle file that has been processed so far Basically a for loop needs to be written around the current script together with a few related changes resulting in the Matlab script of Fig 4 49 The only additional difficulty is caused by the fact that not all test data sequences have the same length so an additional signal processing step is necessary to ensure that all partial FRF estimates have the same number of frequency lines This has been achieved by adding the following command line predat trim predat 1 116736 apply time window The effect is that for each test a time window is applied such that only the first 116736 samples are retained As a result there are 2918 frequency lines in the overall FRF matrix estimate 4 3 4 System identification using the pLSCF method After estimating the overall FRF matrix using the nonparametric Aj estimator the modal character istics of interest could be obtained immediately using the peak picking or CMIF approach However parametric system identification generally yields much more accurate results 11 and therefore an additional parametric system identification step is performed here The pLSCF method is employed for fitting a parametric right matrix fraction description or RMFD model to the nonparametric FRF data System identification with the pLSCF method using the MACEC GUI has already been treated in the two previous tutorials In this tutorial the batch mode of MACEC is explored 9
117. ion criteria except for the damping mode shape and damping and mode shape differences respectively e Leave the damping range and the number of highest modal transfer norms unaltered e Change the modal phase collinearity lower bound to 0 e Leave the mean phase and mean phase deviation upper bounds to their default value If you then press APPLY the stabilization diagram still shows only the four physical modes although the only restrictive criterion is the damping range fig 4 25 But there is a price to pay the linear least squares estimate for the RMFD model obtained with pLSCF is not statistically consistent when the transfer function has poles 9 pp 199 200 In practice this means that the pLSCF estimate does not converge to the noiseless solution even if a very large number of data points is available However we will see that this bias is in general quite small After the physical modes have been selected for instance at a model order of 48 save the mode information as framedata_pLSCF_modes mat 4 1 6 Results 45 The results of the Operational Modal Analysis can be viewed in graphical and numerical repre sentation Let s start with the graphical one Select the framedata_ssi_data_modes mat file in the MACEC main window and press the PLOT MODE SHAPES button in the MODAL ANALYSIS field The MODE SHAPE ANIMATION window now opens and the first mode is plotted Since the dimensions of the structure under test
118. ion to other information the standard deviations of the eigenfrequency and damping ratio estimates as well as the maximum standard deviations of any of the real and imaginary mode shape components Select the four different stable modes for instance at a model order of 34 and save the mode information as framedata_ssi_cov_modes mat For the last modal analysis select the framedata_pLSCF mat file in the MACEC main window and press again the MODAL ANALYSIS button The stabilization diagram looks very clear as the pLSCF method forces mathematical modes that arise due to an over estimation of the model order to have negative damping You can convince yourself of this property by setting the following values for the stabilization criteria e Set the differences in eigenfrequency damping ratio mode shape and modal transfer norm between two consecutive model orders to 100 100 100 and 5000 respectively OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE OOOO Dl 60 60 p P o o e 50 v0 000 a e 9 6 e 3 40 340 0 e e z 5 l D 0 eo e E 30 3 30 o D o e a a a 20 gS 20 e 2 e e y o 6 e 10 10 v y v 0 5 10 15 20 25 0 5 10 15 20 25 frequency Hz frequency Hz Figure 4 25 Tutorial 1 Stabilization diagram for the SSI cov left and pLSCF right algorithms denotes a stable mode and v d and f a mode which satisfies all stabilizat
119. ise which is present in the data the identified system description contains 3The suggested value of i is calculated by multiplying the expected system order with the factor 8 and dividing the result by the number of reference channels Please note that in MACEC 2 0 a factor 6 was used instead of 8 Due to the increased computation power and memory since the development of MACEC 2 0 it was possible to increase this factor for standard use in the MACEC 3 0 and later versions Please consult I2 for a discussion on how the choice of i is connected to the relationship between the Nyquist frequency and the lowest frequency of interest OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE 4B 500 450P 400 350 300 250 1 singular value 200 y 1501 1001 50 H 0 20 40 60 80 100 Figure 4 17 Tutorial 1 Data driven SSI singular values both system and noise dynamics A common approach in modal analysis is then to over specify the model order such that the true system modes also called physical modes are separated from the noise modes also called mathematical modes This separation is performed manually in a stabilization diagram see further To create the stabilization diagram models of increasing order need to be identified From fig one knows that the maximal possible system order equals 120 However as the physical modes should stabilize from a model order between 8 and 12 we choose
120. ization are equal The mode shapes are also equal up to a scaling factor The mass normalized mode shapes however are not equal due to the ZOH assumption Table 6 1 below shows one of the mode shapes obtained for different sampling frequencies EXAMPLE 1 2DOF SYSTEM __ S S 3 it fo 1 50 1 100 1 1000 1 100000 0 5001 0 00427 0 4822 0 10547 0 4963 0 05152 0 5001 0 00142 0 5001 0 00412 0 5001 0 00427 0 4822 0 10547 0 4963 0 05152 0 5001 0 00142 0 5001 0 00412 Table 6 1 Verification example la mode shape of mode 1 at 7 1176Hz obtained from discretization with a ZOH assumption for different sampling periods T 6 1 2 Example 1b pLSCF method The purpose of this example is to check the performance of the deterministic pLSCF method for experimental modal analysis Hereto the system is discretized at a sampling frequency of 100Hz and a sequence of inputs uz and outputs yx is simulated the inputs are taken as random Gaussian sequences The corresponding Matlab code reads M 2 0 0 2 mass matrix Cv 5 2 2 5 damping matrix K 6000 2000 2000 6000 stiffness matrix Ts 1 100 sampling period A B C D fe2ss K M Cv Ts 1 01 2 011 1 J 1 01 2 01 1 01 2 01 discrete time ss model N 8192 number of samples randn state 0 ensure repeatability u randn 2 N Gaussian random input y zeros 2 N y 1 Dtu 1 initialization of outp
121. king method is not explained in this manual The interested reader is referred to e g for more information 48 TT TUTORIALS Peak Picking m Mode information Frequency Hz 14 844 Selected mode shape info Scale channel ANPSD 0 066 MPC Show real imaginary part O Show absolute value angle a a a v a T E 3 E 5 D ao 2 5 gt Ea Channel 1 0 40365 0 05095i Channel 2 0 87368 0 0049801 Channel 3 1 Channel 4 0 64097 0 028773i 20 25 30 35 40 frequency Hz v Show data from 0l Hz to 49 8047 Hz Show ANPSD in dB Apply oK Figure 4 21 Tutorial 1 Selection of modes by Peak Picking framedata_peakpick_modes mat 38 Now repeat the modal analysis with the framedata_nonpar mat file but select FDD as modal analysis method The singular values of the PSD matrix obtained by adding the estimated PSD and its complex conjugate are then computed and plotted in an interactive window The modal parameters can be estimated by picking the peaks in the highest singular value s fig 4 22 After the modes have been selected press OK and save the mode information as framedata_fdd_modes mat using the stabilization diagram 39 Select the framedata_ssi_data mat file in the FILE S IN USE section of the MACEC main window and press the MODAL ANALYSIS button in the MODAL ANALYSIS section The modal parameters are calculated automatically and a stab
122. l3 calculations directory T8 OOO TUTORIALS 4 3 3 Processing the measured signals into an FRF matrix 1 The measurement data can be loaded into Matlab using the MACEC GUI as detailed in the pre vious tutorials However in the present tutorial we will achieve this without the GUI by using MACEC in batch mode First we create a blank Matlab script by clicking on New Script in the Matlab main window Save this script file in the spice tutorials tutorial3 calculations directory as logfile_tutorial3 m and create a header for the logfile e g Tutorial 3 roving hammer test of a rib stiffened plate clear all clc clear the Matlab memory and command window 2 Then we load the measurement data of the first hammer test into Matlab From section 5 2 3 of this manual it is clear that this can be achieved with the INPUT2MCSIGNAL function of MACEC Let us add the following line of code to our logfile x input2mcsignal data Ex11 DDF ddf 1 load the measurement data The resulting variable X is a cell of MCSIGNAL objects In this case there is only a single MCSIGNAL object in the cell because only a single measurement file was converted Therefore we can redefine x x x11 redefine x as an mcsignal object instead of a cell 3 The measurement data have now been converted into an MCSIGNAL object yet they still need to be converted from electrical potential to force and acceleration units Furthermore the type
123. le data Ex num2str hDOF DDF current data file x input2mcsignal file ddf load the measurement data x11 redefine x as an mcsignal object instead of a cell sens 0 0019806 0 010503 0 010003 0 0096465 0 010697 0 0096975 sensor sensitivities ampl ones 6 1 amplification factors db zeros 6 1 are not in dB types cell_ strvcat force acc acc acc acc acc data types labels cell_ strvcat hammer s1 s2 s3 s4 s5 channel labels predat volt2xa x sens ampl db types labels signal conversion predat trim predat 1 116736 apply time window predat detrend predat constant remove DC component predat decimate predat 5 resample b a butter 4 0 024414 high define high pass filter predat filtfilt 1 6 predat b a apply the filter H1 f Hiestimate predat 8 rect 1 2 6 fs estimate FRF Htot par H1 apply reciprocity switch inputs and outputs Figure 4 49 Tutorial 3 Matlab script making use of MACEC functions in batch for processing 56 roving hammer test files into a big overall FRF matrix estimate 10 Before advancing to the modal analysis stage node numbers measurement directions and mea surement quantities need to be attached to the different channels This can be achieved with the MACEC function IDENTSEL see section 5
124. linear time invariant frame structure with four degrees of freedom are analyzed in this tutorial The objective is to perform an operational modal analysis using the different OMA methods that are available in MACEC The data contain the horizontal acceleration response at each floor of the structure to a stationary Gaussian white noise vector excitation fig 4 1 simulated in MATLAB with a simple mass spring damper model using MACEC functions The file with which the data have been generated is named framedata_generation m It can be found in the tuturial1 directory The structure is proportionally damped VILLA 4 t VILL gt Y t Figure 4 1 Tutorial 1 Frame structure The simulated data are characterized by the following specifications 27 28 TUTORIALS e Four measurement channels contain four different horizontal acceleration signals e The data consist of 8192 time samples obtained at a sampling frequency of 100 Hz 4 1 2 Building the geometry The first thing to do is to construct the grid of measurement nodes and to connect them into a beam model of the structure for visualization This consists of the following steps 1 Start MATLAB 2 Change the MATLAB working directory to the directory you want to run the tutorial in for instance C Program Files MATLAB R2010b toolbox spice tutorials tutoriall 3 In the Command Window of MATLAB type macec and then press ENTER Now the MACEC GUI appears
125. llinearity the mean phase deviation the mean phase and the damping and mode shape standard deviations when available WHAT S NEW IN MACEC 3 0 33 When a mode is selected in the stabilization diagram the mode shape is plotted in the complex plane For mass normalized mode shapes it is possible to plot them as such or using the unit modal displacement weighting scheme Identified and selected modal characteristics are now clustered as fields of a single Matlab STRUCT variable This choice enhances the flexibility of MACEC when used in batch mode and it allows for more compact function calls It affects most MACEC functions in which modal characteristics are involved These functions have been adapted accordingly e When combining modal characteristics from different setups reference sensors are no longer required if the mode shapes are mass normalized e The function for computing the modal assurance criterion MAC values has been completely re programmed so as to make it much faster In MACEC 3 0 the square root of the MAC value was computed instead of the MAC value itself this bug has been removed e A new section has been added to the manual containing verification examples These examples serve two purposes i demonstrating how the MACEC functions which are explained in chapter can be employed directly without the GUI and ii verifying the performance of MACEC by comparing the obtained results with analytical so
126. lly system orders that impossible so system orders higher than 30 are not considered Save the identified systems as framedata_ssi_data_ref mat Stochastic Subspace Identification Algorithm selection data driven O covariance driven reference based References e g 2 5 8 1 2X acc QR of data block Hankel matrix SYD of projection matrix Half the number of block rows i Expected system order timate covariance Number of blocks Calculate QR SYD Remark Theoretically the system order equals the number of non zero singular values Calculation of system matrices System orders 2 2 Figure 4 18 Tutorial 1 Reference based data driven SSI using SSI cov 27 28 Select the file framedata_proc mat in the FILE S IN USE section of the MACEC main window don t change the identification method in the SYSTEM IDENTIFICATION section and press AP PLY The STOCHASTIC SUBSPACE IDENTIFICATION window appears Change the ALGORITHM SELECTION to COVARIANCE DRIVEN As for the SSI data analyses choose 30 as the value for half the number of block rows An advantage of SSI cov over SSI data is that for SSI cov the variances of the identified system parameters system matrices poles eigenfrequencies damping ratios mode shapes can be esti mated I4 B In order to activate the variance computation check the ESTIMATE COVARIANCES box The NUMBER OF BLOCK
127. lue is employed for all channels while in the second case values for all of the mcsignal s channels not only the selected channels ich1 have to be provided domain gt t to plot time history f to plot frequency content or b to plot the one thirds octave band spectrum of the RMS value ichl Channels to plot Default all channels AMCSIGNAL x filename gt AddToPlot gt AxesSize Blank Data gt logx 2 logy 2 Language Legend gt LegendLoc gt LineWidth gt Margins NXTick NYTick gt XLabel gt YLabel XMin XMax gt YMin gt YMax 89 mcsignal object File to save the plot to using the global function SAVEFIG Can be omitted if you do not want to save the plot Command evaluated after all built in plotting routines as to add elements to the figure e g equal human response curves Size of the axes in centimeters See NEWFIG for more info Do not plot the curve plot only the axes and the labels Value is assigned to the local variable Data which can be used by the AddToPlot command If a cell array is provided the contents of cell i is assigned to the local variable Data when plotting channel i First index of the time interval to plot Default 1 Last index of the time interval to plot Default x N Logarithmic scale for first axis or not Default 0 Logarithmic scale for first axis or not Default 0
128. lutions or benchmark results reported in the literature The MACEC function propmodpar4 m has been extended so as to allow the computation of the modal characteristics of a continuous time state space model e The format of the sensor definitions files has been changed and the selection of displacement strain and velocity sensors from the file is now supported in the GUI See section for more information and an example 1 4 What s new in MACEC 3 0 MACEC 3 0 can be used for Experimental Operational and Combined Modal Analysis of structures in contrast to previous versions of MACEC which only dealt with Operational Modal Analysis In Experimental modal analysis EMA the structure is excited by one or several measured forces the response of the structure to these forces is recorded and the modal characteristics are extracted from the input output data In Operational Modal Analysis OMA only the responses are recorded and the modal characteristics are extracted from output only data Because the forces are not measured an extra assumption is needed in all existing OMA procedures it is assumed that the unmeasured inputs can be mathematically described as white noise When a modal test is performed in operational conditions and when in addition to the operational excitation one or several measured artificial forces are applied it is called an OMAX test Operational Modal Analysis with eXogenous inputs 4 MACEC 3 0 is a major upgr
129. mcsignal command see section 5 1 e Measurement data that are available in mat MATLAB binary format can be converted to an MCSIGNAL object with the mcsignal command see section 5 1 e Measurement data that are available in 32 format can be converted to an MCSIGNAL object with the GUI or the input2mcsignal command see section 5 2 3 The 32 format has been used at the Civil Engineering Department of KU Leuven to convert measurement data that were available in ASCII format to a binary format in order to save disk space Please note that these commands are case sensitive MA OO STRUCTURE AND CONVENTIONS OF MACEC 3 3 2 Sensor definitions ASCII format If you use the CONVERSION OF THE MEASURED DATA window of the MACEC GUI it is possible to load a file containing sensor definitions for the conversion of the measurement data This file should be of ASCII format Five types of sensors can be defined accelerometers force sensors displacement sensors strain sensors and velocity sensors Each sensor is defined on a single row A sensor definition consists of 5 or more columns which contain from left to right e the sensor type e the sensor number e the manufacturer type e the serial number e the sensitivity e extra columns may be added but they are not used by MACEC The sensor type is a string A denotes an accelerometer with raw measurements in Volt AC an ac celerometer with raw measurements in d
130. mode shape vector corresponding to the output and input DOFs are denoted as and je respectively The decomposition also holds for the force acceleration FRF when q is redefined Suppose now that a limited number of accelerometers and a hammer are available for modal testing and that the mode shapes need to be identified in a large number of DOFs The dynamic reciprocity principle can then be employed to achieve this in an elegant way as follows First the accelerometers are fixed to the structure at those DOFs where normally the loads would be applied Then a forced vibration test is performed in which the hammer force is applied at the first mode shape DOF of interest From the recorded force acceleration data a first FRF denoted by Hj is estimated Subsequently the test is repeated but with the hammer force applied at the second mode shape DOF of interest resulting in a second FRF denoted by H By further repeating the test each time roving the hammer additional FRFs are obtained Note that roving the hammer from one DOF to another usually requires a minimal effort the time in between two tests is often negligible compared to the duration of a test Since all FRFs that are obtained from a roving hammer test have the same output DOFs but different input DOFs they can be combined as follows Heomb w EN H Hh 4 2 tby oia a ial a e 4 3 Lo Ay at e 4 4 lw A where denotes the full mode shape vector
131. models If the identified system models are right matrix fraction description RMFD models identified with Deterministic pLSCF Operational pLSCF or Combined pLSCF the mat file contains the following variables e PREDAT e RMFD a MATLAB variable of the STRUCT type with the following fields The system matrices for the different orders For instance for an RMFD model of order two the following matrices are present RMFD A_2 and RMFD B_2 RMFD ORDERS a vector containing the orders of the systems that have been identified RMFD CHANSELOUT a vector containing the channel numbers which have been used as outputs in the identification RMFD CHANSELIN a vector containing the channel numbers which have been used as inputs in the identification equals the empty vector if Operational pLSCF identification has been used RMFD REFS a vector containing the channel numbers which have been used as reference outputs in the identification equals the empty vector if Deterministic pLSCF identification has been used RMFD H_MEAS a 3D matrix containing the estimated FRF s or PSD s that have been used as inputs for the pLSCF algorithm The rows correspond to the output channels the columns to the input channels or the reference output channels and the depth to the frequency points e NODE_NUM e MEAS_DIR e QUANTS e CHAN_OUTIN e AMPL_OUTIN e REFS a vector containing the output numbers NOT the output channel numbers the
132. n C reference based OR of data block Hankel matrix SYD of projection matrix Half the number of block rows i Expected system order 8 30 arial Number of blocks E Calculate Ki SVD ng lu Remark Th oretically the system order equals the number of non zero singular values Calculation of system matrices System orders 22 te A Figure 4 16 Tutorial 1 Data driven SSI After the QR and SVD steps of the SSI algorithm have been performed the real system order can be estimated by looking at the singular values calculated from the SVD step For noiseless data the system order equals the number of nonzero singular values For noisy data the noise causes some singular values to be different of zero However their values are usually very low After pressing the SHOW SINGULAR VALUES button a standard MATLAB figure appears which shows the singular values in decreasing order of magnitude fig 4 17 As can be seen from the figure the first eight singular values are clearly larger than the other ones which indicates that a model order of 8 could be able to describe the system dynamics quite well The other singular values are not exactly zero but it can be seen that choosing a model order higher than 20 scarcely influences the dynamics of the identified system We know that the true system order equals 8 However from the above discussion it is clear that due to the no
133. n 2009 E Reynders System identification methods for operational modal analysis review and com parison Archives of Computational Methods in Engineering 19 1 51 124 2012 E Reynders and G De Roeck Reference based combined deterministic stochastic subspace iden tification for experimental and operational modal analysis Mechanical Systems and Signal Pro cessing 22 3 617 637 2008 E Reynders D Degrauwe G De Roeck F Magalh es and E Caetano Combined experimental operational modal testing of footbridges ASCE Journal of Engineering Mechanics 136 6 687 696 2010 E Reynders R Pintelon and G De Roeck Uncertainty bounds on modal parameters obtained from Stochastic Subspace Identification Mechanical Systems and Signal Processing 22 4 948 969 2008 137 138 REFERENCES 15 M Schevenels SIGFUN a MATLAB toolbox for signal processing in civil engineering Technical Report BWM 2006 02 Department of Civil Engineering KU Leuven February 2006 16 C Y Shih Y G Tsuei R J Allemang and D Brown Complex mode indicator function and its applications to spatial domain parameter estimation Mechanical Systems and Signal Processing 2 4 367 377 1988 17 P Van Overschee and B De Moor Subspace identification for linear systems Kluwer Academic Publishers Dordrecht The Netherlands 1996
134. n description Br2 rmfd B_2 3 Bri rmfd B_2 2 BrO rmfd B_2 1 define the B matrices of the right matrix fraction description for par i nf frf_ex par 2 p par 2 5 p par 6000 p par 2000 p par 2000 2 p par 2 4 p par 6000 2 p par 7 2 4 p par 6000 2 p par 2 5 p par 6000 p par 2000 72 frf_ex par frf_ex par p par 2 compute the exact frf matrix frf_rmfd par Br2 z par 2 Br1 z par Br0 Ar2 z par 2 Ar1 z par Ar0 compute the synthesized frf matrix using the EXAMPLE 1 2DOF SYSTEM __ gt 133 identified RMFD description end frf_ex end 2 1 end conj frf_ex end 2 1 1 create figure newfig 10 12 subplot 2 1 1 semilogy freqscale abs squeeze frf_ex 1 1 freqscale abs squeeze hifrf 1 1 freqscale abs squeeze frf_rmfd 1 1 xlabel frequency Hz ylabel abs FRF m N xlim 0 50 legend exact H1 pLSCF location southeast title Exact and estimated FRFs fontsize 14 subplot 2 1 2 plot freqscale angle squeeze frf_ex 1 1 freqscale angle squeeze hifrf 1 1 freqscale angle squeeze frf_rmfd 1 1 xlabel frequency Hz ylabel angle FRF rad xlim 0 50 legend exact H1 pLSCF location southeast Exact and estimated FRFs 107 exact
135. nal frequency content y FDATA2 x returns the frequency content of the mcsignal x up to the Nyquist frequency obtained by calling Matlab FFT which is a DFT An approximation of the continuous Fourier transform can be obtained by dividing y by the sampling frequency x mcsignal object y Frequency content Use y x fdata2 to access this function See also MCSIGNAL FDATA MCSIGNAL F2 5 1 23 fftfreq FFTFREQ Multi channel signal frequency vector y FFTFREQ x returns a vector containing the frequencies corresponding to the FFT of the data stored in the mcsignal x Conceptually y 0 df F 2 F 2 df 0 MCSIGNAL ___ 5 x mcsignal object y Frequencies Hz Use y x fftfreq to access this function See also MCSIGNAL F and the global function FFTFREQ 5 1 24 filter FILTER Filter a mcsignal y FILTER ich1 x B A applies the global function FILTER B A x tdata ichl to the specified channels ich1 of the mcsignal x x mcsignal object icht Channels to filter Default all channels y mcsignal object Use y x filterfichi B A to access this function See also MCSIGNAL FILTFILT and the global function FILTER 5 1 25 filtfilt FILTFILT Filter a mcsignal y FILTFILT ich1 x B A applies the global function FILTFILT B A x tdata ich1 to the specified channels ich1 of the mcsignal x x mcsignal object ich1 Channels to filter Default all channels y mcsignal object Use
136. nd MPD values OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE A 55 should equal 1 0 and 0 respectively Table compares the MPD values for all methods All values are very close to 0 the limit value for real normal modes Sstdata SSEdata ra ISGP 1 0 1 0 0 1 0 1 0 0 0 4 Table 4 3 Tutorial 1 Mean phase deviation MPD in degrees for the mode shapes obtained from six different methods 56 TUTORIALS 4 2 The B15 bridge 4 2 1 Introduction In this tutorial experimental data obtained on a large civil engineering structure are analyzed The objective is to extract the modal characteristics from operational data that contain forced excitation using the EMA and OMAX methods that are available in MACEC The structure under test is the B15 bridge which crosses the E19 highway that connects Brussels and Antwerp Belgium The bridge is located between the villages of Peutie and Perk fig 4 28 Figure 4 28 Tutorial 2 View on the B15 bridge A schematic side view of the bridge and the deck cross section are shown in fig The B15 bridge built in 1971 is a three span box girder bridge with an overall length of 124 6m 35 8 53 0 35 8m The box girder is 9 4m wide and varies in height between 1 0 and 2 5m Including the two traffic lanes it reaches a width of 13 0m Figure 4 29 Tutorial 2 B15 bridge side view and cross section An important feature of the B15 bridge is that it is skew symmetric
137. ng steps for the other setups In the fifth setup the sixth channel should be removed in the sixth setup the eighth channel and in the seventh setup the third channel In order to do so select DELETE CHANNEL in the PREPROCESSING part of the PREPROCESS MCSIGNAL OBJECT window select the right channel press APPLY and confirm your choice fig 4 37 Note that you can process several MCSIGNAL objects at the same time by selecting more than one object in the MACEC main window however not all signal processing operation are allowed then on the individual MCSIGNAL objects 9 To end the preprocessing the measured DOFs have to be defined for each channel Select the VALA1 1_proc mat file in the FILE S IN USE section of the MACEC main window and press the 1 DECIMATE is a standard function from the Signal Processing Toolbox of MATLAB For more information about this function consult the MATLAB help or the MATLAB documentation THE B15 BRIDGE Preprocess mesignal object r Channel File VALA1 1_conv mat oy 8 Label R1 Visualization Show data from Olsto 12288 5 Autocorrelation PSD Reference channel 1 Log x C Log Y Double sided PSD parameters Window type Rectangular O Hanning Window length 6144 Overlap 0 Acceleration PSD ms Hz Square acceleration m s decimation f E o o 100 150 Frequency Hz
138. nnel can be easily achieved with the following commands which make use of the AXESPLOT function of MACEC see section 5 1 3 figure axesplot t 3 predat figure axesplot f 3 predat logy 1 The results are shown in Fig and Fig 4 48 b Note that the correct units and axis labels are immediately applied It can be noted that a low frequency drift distorts the signal Therefore the following command lines are added to the logfile resulting in a high pass filtering of the data with a cut on frequency of 10 Hz 409 6 Hz x 0 024414 b a butter 4 0 024414 high define high pass filter predat filtfilt 1 6 predat b a apply the filter The time history and Fourier amplitude spectrum of the third channel after high pass filtering can be plotted again in the same way as before the results are shown in Fig 4 48b and Fig 4 48H respectively The influence of the high pass filter is clearly visible 7 After completing the signal preprocessing stage an FRF can be estimated from the processed data using the nonparametric Hy eto This estimator has been implemented into the 16Tn the present application this amounts to a cutoff frequency of 327 68 Hz See TT Sec 5 2 2 for a detailed description and an extensive discussion of the H estimator In MACEC the periodogram variant has been implemented as it enables to estimate the variance errors of the FRF estimates 80 OA TUTORIALS Ac
139. nt equals 1 the corresponding data type is acceleration if 2 a displacement if 3 a force if 4 a strain and if 5 a velocity e NUMBER a vector containing in each element the row number of the sensor definition file see section 3 3 2 that is associated with a channel e SENSITIVITIES a vector containing the conversion factor of each channel s sensor e AMPLIFICATIONS a vector containing the amplification factors for each channel e DB a vector of which an element equals 1 if the corresponding conversion factor is in deciBel dB otherwise it is 0 e FACTORS a vector containing the information about the measurement units If the data is measured in kiloVolt or 10 digital counts the corresponding element in factors equals 1 if it is Volt or digital counts it equals 2 if it is miliVolt it equals 3 and if it is microVolt it equals 4 Processed measurement data After you have processed an MCSIGNAL object using the GUI you need to save this adapted MCSIGNAL object in a mat file This mat file contains only one variable namely the processed MCSIGNAL object which has the name PREDAT from preprocessed data After processing you can specify the node numbers and measurement directions that are associated with a certain channel If you use the GUI for this you are asked if the specifications should be saved or not If you choose to save them they are added to the mat file that already contains the preprocessed data
140. of data force or acceleration needs to be defined for each measurement channel and labels need to be assigned to the different measurement channels As this conversion will be performed for an MCSIGNAL object we need one of the MACEC functions that are listed in section to achieve this After inspecting the different functions available it is clear that the VOLT2XA function is needed here A correct use of the function results in the following Matlab code see section 5 1 50 for more details on the VOLT2XA function sens 0 0019806 0 010503 0 010003 0 0096465 0 010697 0 0096975 sensor sensitivities ampl ones 6 1 amplification factors db zeros 6 1 are not in dB types cell_ strvcat force acc acc acc acc acc data types labels cell_ strvcat hammer si s2 s3 s4 s5 channel labels predat volt2xa x sens ampl db types labels signal conversion 4 The next stage is preprocessing these converted data The preprocessing steps all involve op erations on the PREDAT variable which is an MCSIGNAL object Therefore all preprocessing operations will involve MACEC functions that are listed in section 5 1 For example by adding the following command to the logfile and running the logfile again the static or DC component is removed from the data ROVING HAMMER TESTING OF A RIB STIFFENED PLATE AAA predat detrend p
141. ol ern oe A a 13 00m T _ ANTWERPEN 80m T Tom 4 70m 180m 21 B 3 A al ye T _BRUSS EL 5 A Figure 4 31 Tutorial 2 B15 bridge measurement setup consisting of 11 Degrees Of Freedom DOFs measurements Table 4 4 indicates which DOFs were measured in which setup The force was of course only measured in the combined test setup DOFs measured 25Az 14z 64z 114z 164z 21Az 264z 314z 364z 414z 7Bz 254 fz 25Az 2Az TAz 12Az 174z 22Az 27Az 32Az 37Az 42Az 7Bz 25Afz 25Az 3Az 8Az 13Az 184z 23Az 28Az 33Az 384z 43Az 7Bz 25Afz 25Az 4Az 9Az 144z 194z 24Az 294z 344z 394z 43Az 7Bz 25Afz 25Az 5Az 104z 15Az 20Az 25Az 30Az 35Az 40Az 434z 7Bz 25Afz 25Az 1Bz 6Bz 11Bz 16Bz 21Bz 26Bz 31Bz 36Bz 41Bz 7Bz 25Afz 25Az 2Bz 7Bz 12Bz 17Bz 22Bz 27Bz 32Bz 37Bz 42Bz 7Bz 25Afz 25Az 3Bz 8Bz 13Bz 18Bz 23Bz 28Bz 33Bz 38Bz 43Bz 7Bz 25Afz 25Az 4Bz 9Bz 14Bz 19Bz 24Bz 29Bz 34Bz 39Bz 43Bz 7Bz 25Afz setup 1 2 3 4 5 6 7 8 9 10 25Az 5Bz 10Bz 15Bz 20Bz 25Bz 30Bz 35Bz 40Bz 43Bz 7Bz 25Afz Table 4 4 Tutorial 2 B15 bridge measurement setups and corresponding DOFs For the ambient vibration sessions the ambient excitation was provided by the traffic underneath and on top of the bridge During peak hours the B15 bridge has intensive traffic making this vibration source the main cause of excitation The total acquisition time for one outp
142. olumn of stable modes the estimates with the highest MP or MPC values are selected The mode at 3 113Hz could not be identified using deterministic pLSCF simply because it was not present in the stabilization diagram Another remarkable difference can be noticed at 3 825Hz although at this frequency only one stable mode appeared in the pLSCF stabilization diagram from the CSI ref stabilization diagram we notice that in reality two very closely spaced modes are present around this frequency For example in fig 4 45 at a model order of 60 we have a stable pole at 3 709Hz damping ratio of 4 2 and one at THE B15 BRIDGE AAA f Hz 1 877 3 119 3 830 5 072 6 181 6 513 7 150 8 957 ea 14 0 a aa e as 20 an mito a pe e o o e e e Table 4 5 Tutorial 2 Eigenfrequencies and damping ratios for setup 1 determined using CSI ref 33 34 30 36 37 3 825Hz damping ratio of 1 3 However we advise not to select the pole at 3 709Hz because it will show up in most but not all setups After the poles have been selected save them as VALA1 1_CSIref_modes mat Repeat the pole selection step for all 9 other setups If the poles of all 10 setups have been selected we can make use of MACEC s possibility to combine modal information obtained from different setups into one single mode In order to do this select VALA1 1_CSIref_modes mat and the mode information for the nine other setups in the FILE S
143. olumn position 5 3 5 blckVec BLCKVEC Calculation of Block Vector x blckVec Y ta Resulting Block Vector Y 3D matrix containing the block elements of the block Vector the third dimension corresponds to the block number 5 3 6 cov_ COV_ Calculation of sample covariance matrix Y cov_ X X anm x 1 x n matrix containing m variables and n observations Y the sample covariance matrix of X 5 3 7 eiglr EIGLR calculation of eigenvalues and left and right eigenvectors of a matrix L X Y eiglr A diagonal matrix with eigenvalues corresponding right eigenvectors corresponding left eigenvectors the matrix for which the eigenvalue problem needs to be solved gt lt es one has X L X A and Y conj L Y A 5 3 8 key KEY Extract one key value from a list of key options with unknown length y KEY nmame default KeyName KeyValue compares the KeyName s with name and returns the following KeyValue If no KeyName matching name is found default is returned name Name of the argument to retrieve the value of MODAL ANALYSIS S 109 default Default argument value y Argument value See also VARARGIN 5 3 9 re_ RE_ Stacking the real part of a matrix on top of the imaginary part y re_ x X complex matrix may also be purely real or purely imaginary of size m X n y real matrix of size 2m x n 5 3 10 vec_ VEC_ Vectorization of a m
144. on diagram of the GUI after parametric system identification or from a nonparametric ANPSD CMIF FDD plot after nonparametric system identification you are required to save them in a mat file This file contains the following variables e STABMODES a MATLAB variable of the STRUCT type with the following fields STABMODES F a vector containing the eigenfrequencies STABMODES O a vector containing the model orders STABMODES XI a vector containing the damping ratios STABMODES M a matrix containing the mode shapes in each column STABMODES MTN a vector containing the modal transfer norms STABMODES MP a vector containing the mean phases STABMODES MPC a vector containing the modal phase collinearities STABMODES MPD a vector containing the mean phase deviations STABMODES WSCHEME a string that indicates whether the mode shapes are mass normal ized mass or scaled to unit modal displacement unit IA STRUCTURE AND CONVENTIONS OF MACEC STABMODES QUANTS a cell containing the physical quantities corresponding to each mode shape component STABMODES STDF a vector containing the standard deviations of the eigenfrequencies STABMODES STDXI a vector containing the standard deviations of the damping ratios STABMODES STDMR a matrix containing the standard deviations of the real parts of the mode shapes in each column STABMODES STDMI a matrix containing the standard deviations of the imaginar
145. or constructing or editing the grid file GULslave constructs the window for constructing or editing the slave file GUI_beam constructs the window for constructing or editing the beam or surface file e SIGNAL PROCESSING This section deals with the construction of an mcsignal object With the CONVERT TO MCSIGNAL button the GUI_CONVERT function is called which constructs the window for the conversion of the measurement data to the CNVDAT MCSIGNAL object With the PROCESS button the GUI_PREP function is called which constructs the window for signal processing x If the standard MATLAB function filtfilt needs to be called during signal processing the signal processing window calls the GULfltfilt function which constructs a dialog window for the FILTFILT operation GRAPHICAL USER INTERFACE Signal processing Raw time data ddf asc f32 wav tdm Conversion factors mat GUI_convert Conversion factors mat GUI_integrate GUI_proc GUI_filtfilt GUI_timewind Raw mcsignal object mat Processed mcsignal GUI object mat Measured DOFs mat System identification af f GUI_PSDp l System des cription mat 23 GUI_grid a grid file asc GUI slave slave file asc GUI beam beam surface file asc Modal Analysis GUI stabplot GUI _psdpfrfsum GUI_cmif Modal para meters mat GUI_modview Figure 3 6 GUI structure of MACEC The GUI fi
146. psdpcov k contains the covariance matrix of vec_ psdp k inputs input numbers outputs output numbers refs reference output numbers 5 5 8 modalmr MODALMR Modal model reduction of a state space model Ar Cr modalmr A C poles Ar Br Cr Dr modalmr A B C D poles Ar Cr Qr Rr Sr modalmr A C Q R S poles Ar Br Cr D Qr R Sr modalmr A B C D Q R S poles A B C D system matrices in the original state space description Q R S noise covariance matrices in the original state space SYSTEM IDENTIFICATION AA ds description poles a vector with the poles which are RETAINED All system poles that are not in this matrix will be eliminated Ar Br Cr Dr system matrices in the reduced state space description Qr Rr Sr noise covariance matrices in the reduced state space description 5 5 9 pLSCF4 pLSCF4 Poly Reference Least Squares Complex Frequency Domain system p LSCF identification No frequency weighting is applied A B pLSCF4 H n f f_low f_up A B the right matrix fraction description matrices resulting from the identification The third dimension corresponds to the exponent of the z minus 1 H the measured transfer function matrix at different frequencies 3rd dimension H may also contain positive power spectral densities PSD s or a combination of FRFs and PSD s n the required system order f the vector with frequencies corresponding to the 3rd dimension of H f goes from OHz up to the sampling fr
147. r each test at a particular setup you can expect that the results will be more accurate Taking this mean value is not difficult if two files with modal information containing exactly the same DOFs are selected and the COMBINE SETUPS button is pushed the resulting modal data contain the mean values As the previous step is quite time consuming and does not imply new functionalities of MACEC you can just select VAL_pLSCF_modes mat which contains the results If you plot these mode shapes the result looks like in fig 4 44 The quality of the mode shapes of modes 4 and 9 is less than for the other modes In all identified modes bending is combined with torsion due to the skewness of the bridge supports with respect to the bridge deck THE B15 BRIDGE 222 a mode 1 1 884Hz 0 89 mode 3 3 830Hz 1 14 mode 4 5 081Hz 0 59 mode 5 6 182Hz 1 31 mode 6 6 525Hz 1 74 mode 7 7 154Hz 2 36 X mode 8 8 933Hz 2 23 mode 9 13 266Hz 2 29 mode 10 16 713Hz 2 29 Figure 4 44 Tutorial 2 Eigenfrequencies damping ratios and mode shapes obtained with determin istic pLSCF 72 TUTORIALS After CSI ref 31 In the MACEC main window select VALA1 1_CSIref mat and press the MODAL ANALYSIS button in the MODAL ANALYSIS field The stabilization diagram that is now constructed is clear but looks incomplete indicating that the default stabilization criteria are too strict Therefor
148. r the mcsignal x x mcsignal object y Number of channels Use y x nch to access this function 5 1 34 noelec NOELEC Remove specified frequency components from a mcsignal y NOELEC ich1 x applies the global function NOELEC x tdata ich1 x F to the specified channels ichi of the mcsignal x x mcsignal object ich1 Channels to remove frequency components from Default all channels y mcsignal object Use y x noelec ichi to access this function See also the global function NOELEC 5 1 35 numel NUMEL Function called before subsref to determine the number of outputs n NUMEL always returns 1 5 1 36 plot PLOT Plot multi channel signal PLOT domain ich1 x filename KeyName KeyValue plots the time history domain t the frequency content continuous Fourier transform domain f or the one third octave band spectrum of the RMS value domain b of the selected channels ichi of the mcsignal x Key options can be specified to fine tune the plot These options are interpreted by AMCSIGNAL 99 the present function and they are passed to the global function NEWFIG which is used to open a new figure window The values of the key options interpreted by the present function may be scalars single strings or vectors cell arrays of strings In the first case the same value is employed for all channels while in the second case values for all of the m
149. re very close but the damping ratios for the pLSCF method are THE B15 BRIDGE OOOO CMIF pLSCF A CSI ref 4 Jue epa ue Jue 1 0 Juro mode nr MO Table 4 6 Tutorial 2 Modes identified with deterministic pLSCF and CSI ref eigenfrequencies damping ratios modal phase collinearities MPC and mean phases MP E o systematically smaller this is probably because the damping ratio estimates of pLSCF are biased With the CMIF method only a limited number of modes could be estimated and the eigenfrequency estimates are rather poor due to the rather coarse frequency resolution 0 163Hz The MP values are very low for the first mode indicating that the imaginary part of the mass normalized mode shape is close to zero For the higher modes the MP values differ between both methods Using CSI ref it was possible to obtain more accurate information about modes that were less well excited by the drop weight forces modes 2 and 3 than with deterministic pLSCF This is probably due to two reasons 1 Deterministic pLSCF is a deterministic system identification method so the resulting modal analysis type is EMA while CSI ref is a combined deterministic stochastic system identification method so the resulting modal analysis type is OMAX As an OMAX analysis does not consider ambient excitation as noise but as valuable excitation it is capable to detect modes that are not well excited by the measured forces 2 The CSI ref m
150. redat constant remove DC component 5 The data have been sampled at 4096 Hz as can be verified by executing the following command in the Matlab main window predat F However the frequency range of interest in this analysis is 0 300 Hz In order to concentrate the analysis on the frequency range of interest we will re sample the data at a rate which is five times lower resulting in a new sampling frequency of 4096 5 819 2 Hz and a new Nyquist frequency of 409 6 Hz This can be achieved with the DECIMATE function see section 5 1 6 This function employs an eighth order low pass Chebychev Type I filter with a cutoff frequency of 0 8 times the new Nyquist frequency in both the forward and reverse directions to remove all phase distortion before re sampling the data The function is applied by adding the following command to the logfile predat decimate predat 5 resample 6 At any stage of data processing it is a good practice to look at the data in both the time and frequency domain in order to detect any anomalies or to verify the effect of a signal processing step In this case the data have been checked at the time of acquisition yet it is a good idea to perform a final check before going to the system identification stage MACEC has powerful functions for plotting data that are related to an MCSIGNAL object For example plotting the time history and the amplitude of the related Fourier transform of the third cha
151. riod of the mcsignal x X mcsignal object y Period s Use y x T to access this function 5 1 46 tdata TDATA Multi channel signal time history y TDATA x returns the time history of the mcsignal x x mcsignal object y Time history Use y x TDATA to access this function 5 1 47 tplot TPLOT Plot multi channel time history TPLOT ichi x filename KeyName KeyValue executes the function AMCSIGNAL 103 PLOT t ich1 x filename KeyName KeyValue Use x tplot ichi filename KeyName KeyValue to access this function See also MCSIGNAL PLOT 5 1 48 trim WINDOW Restrict an mcsignal to a certain range of samples y WINDOW x s_1 s_u selects the signals from sample s_1 and s_u and mcsignal object lower sample number upper sample number mcsignal object 5 1 49 volt2x VOLT2X Convert multi channel signal from Volt to actual units y VOLT2XC ich1 x sensnr applies the global function VOLT2X x tdata ich1 S to the specified channels ich1 of the mcsignal x The sensitivities S and the quantities to convert to result from the global function SENSITIVITY sensnr x ich1 sensnr y Use y mcsignal object Channels to convert Default all channels Sensor numbers specified in one of the files sensors bwm txt and sensors other txt which should be located in the Matlab path mcsignal object x volt2x ichi sensnr
152. s added to the diagram to help you select the physical modes Since the four lines of stable modes and the peaks in the PSD sum all lie below 25 Hz show only the data in the 0 25 Hz bandwidth by filling out the relevant fields at the bottom and pressing APPLY Choose for instance the four stable modes at model order 52 by clicking on the modes in the diagram After each mode has been clicked the corresponding mode shape is plotted in the complex plane at the right hand side of the stabilization diagram fig 4 24 This can be used as a tool to check the signature of each mode PSDp FRF settings Show the sum of all PSDp s C Show the sum of all FRF s Number of data blocks block length 4096 Calculate block length Cancel OK N Figure 4 23 Tutorial 1 Calculation of Positive Power Spectral Densities for the stabilization diagram 41 After the modes have been selected press OK and save the mode information as framedata_ssi_data_modes mat 50 42 43 44 TUTORIALS Mode information 60 oe F lt fF ee A gt Selected mode shape info Frequency Hz 14 996 ES oo e ft w gt Damping 9 4 1 ES em w Scale channel 1 M tot Order 52 p Bey p p MEN 8 er e E 50F Ed EA 4 Be Ed di De e g R MPC 0 998 i sas ed ji pe Ea E E T Y e P of Mean phase 1 1 40b ES EN row g 7 MPD E 1 1 e e A Ed
153. s for visualization 10 Now you are ready to save the beam file Press OK in the DEFINE EDIT BEAMS OR SURFACES GRID window and choose a name and a directory for instance framebeam asc in the tutorial1 directory The DEFINE EDIT BEAMS OR SURFACES GRID window closes and you return au tomatically to the MACEC main window In this window the path name of the beam file you just created is now filled in in the BEAM SURFACE FILE command line of the GEOMETRY section Note The beam file is saved in ASCII format so that it can also be created with a text ed itor instead of with the MACEC GUI This facilitates the creation of the beam file when the slaving information is available in ASCII format for instance from Microsoft Excel The beam file is selected by typing its path in the BEAM SURFACE FILE command line of the MACEC main window or by using the SELECT BEAM OR SURFACE FILE button of the MACEC main window A AO TUTORIALS 4 1 3 Processing the measured signals The geometry of the frame structure is now defined so the signal processing part can start 11 First select the file with the simulated measurement data by pushing the SELECT NEW DATA button in the MACEC main window fig 4 7 Choose the file framedata mat in the tuturial1 directory MACEC 3 2 DE AQUA LEUVEN Aa S Ff Select new data Geometry A Slave file D matlabtoolbispice32 2011 01 aisourcetutorials tutorialt fram 0 2 Beam surface file 14
154. shapes obtained with deterministic pLSCF Chapter 5 Overview of MACEC functions In this chapter all individual functions of the MACEC program are described This enables you to e use the logfile and to detect possible errors in it e run separate MACEC functions in batch The functions are grouped in sections according to the different subdirectories in the spice32 directory Within each subdirectory the functions are described in alphabetical order 5 1 Omcsignal 5 1 1 axesACPSDplot AXESACPSDPLOT Plot multi channel signal in the current axes AXESACPSDPLOT domain ichi x filename KeyName KeyValue plots the autocorrelation domain ac or the power spectral density domain psd using Welch s method of the selected channels ich1 of the mcsignal x Key options can be specified to fine tune the plot These options are interpreted by the present function and they are passed to the global function NEWFIG which is used to open a new figure window The values of the key options interpreted by the present function may be scalars single strings or vectors cell arrays of strings In the first case the same value is employed for all channels while in the second case values for all of the mcsignal s channels not only the selected channels ichi have to be provided domain ac to plot autocorrelation f to plot power spectral density ichl Channels to plot Default all channels x mcsign
155. ssible even system order invar structure array containing the R factor from the QR decomposition the U matrix and the singular values from the SVD and the new order of the channels differs from the old order if the reference based SSI was used chanselout vector containing the output channels selected for identification chanselin vector containing the input channels selected for identification refs vector containing the output reference channels method describes the system identification method used If the ssi_data method was used method equals ssi_data If the ssi_cov method was used method equals ssi_cov If the csi_data method was used method equals csi_data calcorders vector containing the model orders to be calculated coupling optional string indicating whether or not the full covariance matrix between all system matrix elements should be computed This option is only effective when method gt ssi_cov When coupling decoupled the identified system matrices are in decopuled modal form and the covariance between estimates belonging to different modes is not computed 128 OVERVIEW OF MACEC FUNCTIONS Chapter 6 Verification examples In this chapter full examples are provided where MACEC is used in batch mode They have two purposes i to demonstrate how the MACEC functions which are explained in chapter B can be employed directly without the GUI and ii to
156. t allmodes quants cell containing the physical quantities of each ODS component nonpar structure containing a system description identified using nonparametric system identification freqs frequency lines for which the PSDP has been estimated psdp positive power spectral density matrix size n_o x n_ref x n_f with n_ref the number of reference outputs ref vector with reference output numbers quants a cell containing the measured output quantities Note in order to avoid negative values of the estimated ANPSD the so called positive realness problem the function returns the magnitude of the estimated ANPSD Note damping ratios are not computed since the half power bandwidth method for computing damping ratios is inaccurate 5 4 2 cmif CMIF Calculate the Complex Mode Indication Function CMIF also referred to as Frequency Domain Decomposition FDD and related modal information from Frequency Response Function FRF input output or Positive Power Spectral Density PSD output only data allmodes cmif nonpar quants allmodes cmif freqs frf quants loc ampl allmodes cmif freqs psdp quants allmodes a structure containing the modal information Allmodes contains the following fields allmodes f vector with frequency lines Hz allmodes s matrix with corresponding FRF PSD singular values second dimension frequency allmodes m 3D matrix with corresponding mode shapes 2nd dimension singular value 3rd d
157. t 0 Logarithmic scale for first axis or not Default 0 Label language en or nl Default Default no legend See also LEGEND Legend location Default Best See also LEGEND Default 0 5 for domain t and f and 1 5 for domain b Margins between the axes and the bounding box in centimeters See NEWFIG for more info Number of XTicks approximately see the global function TICK Default auto Number of YTicks approximately see the global function TICK Default auto X axis label Default defined using MCSIGNAL LABEL Y axis label Default defined using MCSIGNAL LABEL X axis scaling minimum value Default left side of the plotted curve X axis scaling maximum value Default right side of the plotted curve Y axis scaling minimum value Default defined as a function of the plotted curve Y X max abs Y for domain t O for domain f and min Y for domain b Y axis scaling maximum value Default defined as a function of the plotted curve Y X max abs Y for domain t and max Y for domains f and b Color of the plot Default b blue Other valid parameters g green r red c cyan m magenta y yellow k black and w white en MCSIGNAL ___ gR See also NEWFIG SAVEFIG MCSIGNAL TPLOT MCSIGNAL FPLOT MCSIGNAL BPLOT 5 1 2 axesCPSDFRFCOHplot AXESCPSDFRFCOHPLOT Plot mult
158. t no stable mode shape or damping for whith the damping ratio lies between the upper and lower bounds and that have the highest modal transfer norms contains the unstable modes selectedmodes contains the modes that have stable frequency allmodes df dxi dm dampco damplco trnormco dmtn maxfrstd maxdmpstd maxmodstd mpclb mpub mpdub for whith the damping ratio lies between the upper and lower bounds and that have the highest modal transfer norms a structure containing all the modes see stable_propmodpar5 for the structure of allmodes frequency stabilization criterium damping ratio stabilization criterium mode shape stabilization criterium damping ratio upper bound damping ratio lower bound if for a certain model order the modes are ordered in descending modal transfer norm only the first trnormco modes are stable modal transfer norm stabilization criterium upper bound on the standard deviation of the frequency upper bound on the standard deviation of the damping ratio upper bound on the standard deviation on any real or imaginary component of the mode shape lower bound on the modal phase collinearity upper bound on the mean phase upper bound on the mean phase deviation 5 4 9 modfind MODFIND Find for a certain order the mode number in allmodes that is closest to a given frequency modenr yes selnrs_new allmodes frequency order selnrs_old 5 4 10 mp
159. t the MACEC GUI a MATLAB command file named logfile m is created in the MATLAB working directory When you perform certain operations in the GUI this logfile is automatically filled with the proper commands Such a logfile has three advantages LOGFILE AND BATCH RUN AA 25 1 It leaves you a blueprint of the operations performed in the GUI which enables you to detect possible errors 2 It enables you to recalculate everything without the need to perform all interactive operations again 3 It gives you an example of how to perform a modal analysis by MACEC without the GUI Example Figure 3 7 shows the logfile used for the determination of the modal characteristics in tutorial 1 with the SSI data ref identification algorithm The logfile was automatically created by MACEC 26 OOOO STRUCTURE AND CONVENTIONS OF MACEC MACEC version 3 3 Copyright KU Leuven Structural Mechanics Section Edwin Reynders macec bwk kuleuven be gridfile framegrid asc slavefile frameslave asc beamfile framebeam asc file strvcat framedata mat ext strvcat mat x input2mcsignal file ext 100 sens 1 1 1 1 ampl 1 1 1 1 0 0 0 0 types cell_ strvcat acc acc acc acc labels cell_ strvcat 1 2 3 4 for par 1 1 cnvdats par volt2xa x par sens ampl db types labels end predats cnvdats node_num 5 4 3 2 meas_dir
160. ta_proc mat in the FILE S IN USE section of the MACEC main window don t change the identification method in the SYSTEM IDENTIFICATION section and press APPLY Now the STOCHASTIC SUBSPACE IDENTIFICATION window appears Leave the ALGORITHM SELECTION on DATA DRIVEN In the EXPECTED SYSTEM ORDER field you have to specify the theoretical order of the system description that you need This order equals two times the expected number of modes that are present in the data As the frame structure is a 4 DOF structure the expected system order equals 2 4 8 Now press the gt gt button and notice that MACEC proposes the number 2The theory behind the SSI data algorithm is not explained in this manual The interested reader is referred to n 77 for more information 42 23 24 TUTORIALS as half the number of block rows in the SSI data algorithnil However this proposed value can be viewed as a minimal value for i in the SSI data algorithm since it is known that higher values of 7 usually yield more accurate system estimated Furthermore it offers the possibility to choose higher stabilization orders in the stabilization diagram So choose 30 as the value for and press the CALCULATE QR SVD button to start the construction of the Hankel matrix of measurement data and the QR and SVD steps of the SSI algorithm fig 4 16 Stochastic Subspace Identification Algorithm selection data driven O covariance drive
161. table_propmodparb The following fields however are not present o mtn df dxi mac dmtn stdf stdxi stdmr stdmi stdmmax cov and quants node_num meas_dir three dimensional matrices containing in each depth level the node numbers and measurement directions for each setup When the number of outputs is different amongst different setups the order of setups should be changed such that the setup with the largest number of outputs Remarks 1 Unity modal mass scaling is possible if the mode shapes of all setups are scaled in this way Otherwise the global mode shapes are scaled to unit modal displacement 2 If all setups contain exactly the same DOFs the mode shapes are averaged See also stable_propmodpar5 5 4 5 mac MAC Modal Assurance criterion matrix calculation z mac x z mac x y x y matrices containing mode shapes in each column Zi if y is not specified z is the mac matrix of x If y is specified z contains the MAC values between the modes in x and the modes in y MODAL ANALYSIS 1218 5 4 6 mdtime MDTIME Time domain modal decomposition of a measured output only signal ym z mdtime y Lambda Phi Km ym 3D matrix first dimension output number second dimension mode number third dimension time y matrix with measured outputs Lambda Phi Km stochastic state space matrices in decoupled i e modal form See also mo
162. tem identification to perform a modal analysis with the identified system description and to perform a spectral analysis of surface waves from measured data e SIGFUN contains functions that are useful for the processing of measured signals If you take a look at the functions that are available in the SPICE toolbox you notice that they are divided into several maps e GUI contains all functions that are needed to run the SPICE MACEC graphical user interface e conversion contains all functions that deal with the conversions between data types for instance the conversion from measured data in ASCII format to a MATLAB mesignal object e mathematics contains all mathematical functions that are useful in system identification but not available in MATLAB for instance for constructing a block Hankel matrix e modal analysis contains all functions that can be used for the modal analysis of an identified system model for instance for determining the modal characteristics of an identified Right Matrix Fraction Description model e sasw contains all functions related to spectral analysis of surface waves e system identification contains functions that can be used for system identification for in stance Reference based Combined Deterministic Stochastic Subspace Identification CSI ref e dummy contains the functions for objects of the DUMMY type 11 O OOO STRUCTURE AND CONVENTIONS OF MACEC e Omcsignal contains the functions for obje
163. the response predicted by the identified model can be computed as follow Sigmaid dlyap Aid Qid state correlation Gid Aid Sigmaid Cid Sid state output correlation Lambda0id Cid Sigmaid Cid Rid zero lag correlation Pid dare Aid Cid Qid Rid Sid eye size A 1 Solve Riccati eq Kid Aid Pid Cid Sid Rid Cid Pid Cid Kalman filter ypred O y z zeros size Aid for par 1 N simulate response with identified forward innovation model z parti Aid Kid Cid z par Kidx y par ypred par Cid z par end prerr zeros 2 1 for par 1 2 compute prediction errors prerr par sqrt sum y par ypred par 72 sum y par 72 100 end The computed prediction error is around 42 for both channels Although this might be surprising it can be verified that this prediction error can not be reduced noticeably by increasing the data length The Kalman filter yields optimal linear one step ahead predictions 12 and 40 is the best this filter performs for this system As can be expected much lower prediction errors have been reported for more lightly damped systems 7 sec 8 3 The time domain decomposition of the measured response can be computed from only 3 MACEC functions The following Matlab code illustrates this and shows at ones how the decomposed signal can be plotted as in fig Note that for solving the Riccati equation use is made o
164. then press the ADD button The coupled DOFs are now added to the list at the left bottom fig 4 5 To plot also the nodes with zero displacement fill in 32 TUTORIALS 2 as MASTER NODE choose X as MASTER DOF fill in 1 6 in the SLAVE NODE field and choose X as SLAVE DOF In the AMPLITUDE field fill in 0 and then press the ADD button Now you are ready to save the slave file Press OK in the DEFINE EDIT SLAVE DOFS window and choose a name and a directory for instance frameslave asc in the tutorial1 directory The DEFINE EDIT SLAVE DOFs window closes and you return automatically to the MACEC main window In this window the path name of the slave file you just created is now filled in in the SLAVE FILE command line of the GEOMETRY section Note The slave file is saved in ASCII format so that it can also be created with a text ed itor instead of with the MACEC GUI This facilitates the creation of the slave file when the slaving information is available in ASCII format for instance from Microsoft Excel The slave file is selected by typing its path in the SLAVE FILE command line of the MACEC main window or by using the SELECT SLAVE FILE button of the MACEC main window Now that the measurement grid has been defined and the necessary DOF s have been coupled in a slave file the only geometrical information that is missing are the links between the measurement points They are only defined for visualization purposes In t
165. tion in the field of experimental and operational modal analysis PhD thesis Vrije Universiteit Brussel 2004 M Dohler and L Mevel Efficient multi order uncertainty computation for stochastic subspace identification Mechanical Systems and Signal Processing 38 2 346 366 2013 P Guillaume T De Troyer C Devriendt and G De Sitter OMAX a combined experimental operational modal analysis approach In P Sas and M De Munck editors Proceedings of ISMA2006 International Conference on Noise and Vibration Engineering pages 2985 2996 Leu ven Belgium September 2006 W Heylen S Lammens and P Sas Modal analysis theory and testing Department of Mechanical Engineering Katholieke Universiteit Leuven Leuven Belgium 1997 B Peeters System identification and damage detection in civil engineering PhD thesis Depart ment of Civil Engineering KU Leuven 2000 B Peeters and G De Roeck Reference based stochastic subspace identification for output only modal analysis Mechanical Systems and Signal Processing 13 6 855 878 1999 B Peeters and G De Roeck Stochastic system identification for operational modal analysis A review ASME Journal of Dynamic Systems Measurement and Control 123 4 659 667 2001 R Pintelon and J Schoukens System Identification IEEE Press New York NY 2001 E Reynders System identification and modal analysis in structural mechanics PhD thesis Department of Civil Engineering KU Leuve
166. to access this function See also the global functions VOLT2X and SENSITIVITY 5 1 50 volt2xa VOLT2XA Convert multi channel signal from Volt to actual units y VOLT2XA x applies the global function VOLT2X x tdata to all channels of the mcsignal x X sens amp db quantity label mcsignal object Sensitivities For accelerations V m s 2 Amplification factors Can be in dB 1 if amp is in dB 0 otherwise Text string describing the data type per channel e g volt acc velo disp force Label defining the channel e g 5z 104 OVERVIEW OF MACEC FUNCTIONS y mcsignal object See also the local function VOLT2X and the global function VOLT2X 5 1 51 weight WEIGHT Apply frequency weighting to a mcsignal y WEIGHT ich1 x H multiplies the frequency content of the specified channels ichi of the mcsignal x with the weighting function H Use FFTFREQ to obtain the frequencies to use for the definition of H x mcsignal object ichl Channels to weight Default all channels H Weighting function y mcsignal object Use y x weight ich1 H to access this function See also MCSIGNAL FFTFREQ 5 1 52 window WINDOW Apply a time window to a mcsignal y WINDOW ich1 x w multiplies the selected channels of the mcsignal x with the corresponding channels of the window function w If w only contains a single channel then this one is used for all selected channels of x
167. to construct the stabilization diagram only up to a model order of 60 So in the SYSTEM ORDERS field fill in 2 2 60 and press the CALCULATE button System orders between 2 and 60 are now calculated in increasing steps of 2 25 After the calculation is finished press the OK button and save the identified system matrices in a mat file for instance framedata_ssi_data mat MACEC now returns to the main window where the file has been added to the FILE S IN USE section using SSI data ref 26 In the previous section you have used the classical version of the SSI algorithm as described in 17 However a faster reference based version of this algorithm has been developed by Peeters and De Roeck 7 which is also more accurate if the channels with the highest SNR 5In general the maximum possible system order equals which equals 30 in this case multiplied by the number of reference channels in this case equal to all 4 channels 44 OOO TUTORIALS are selected as the reference channeld To see if there is a noticeable difference with the classic version repeat the SSJ identification again but now mark the REFERENCE BASED checkbox in the STOCHASTIC SUBSPACE IDENTIFICATION window and indicate that the first channel which contains the horizontal displacement at the top is the only reference channel fig 4 18 Note that system orders between 2 and 30 are now calculated in increasing steps of 2 MACEC ignores automatica
168. ts MACEC contains several functions to load measurement data from external files into MATLAB and to convert these data to an mcsignal object see section 3 2 e Measurement data that were stored during the data acquisition using DASYLAB software are available in ddf format They can be converted to an MCSIGNAL object with the GUI the input2mcsignal command see section 5 2 3 or the mcsignal command see section 5 1 e Measurement data that were stored during the data acquisition in GeoSIG measurement stations are available in msd Miniseed format They can be converted to an MCSIGNAL object with the GUI the input2mesignal command see section or SIGFUN s readmsd and MACEC s mesignal commands see section 5 1 e Measurement data that were stored during the data acquisition using LabVIEW software are available in tdm format They can be converted to an MCSIGNAL object with the GUI the input2mesignal command see section 5 2 3 or the mcsignal command see section 5 1 e Measurement data that were stored during the data acquisition using Test Lab software are available in wav format They can be converted to an MCSIGNAL object with the GUI the input2mcsignal command see section 5 2 3 or the mcsignal command see section 5 1 e Measurement data that are available in asc format ASCII type can be converted to an MCSIGNAL object with the GUI the input2mcsignal command see section 5 2 3 or the
169. ts quants Phi quants Ld Km Gm refquants propmodpar5 A B C D Q R S G Lambda0 Ts quants loc ampl refs matrix containing in each column a mode shape scaled to the mass matrix if the input location is specified in displacement units row vector with the corresponding undamped frequencies row vector with the corresponding damping ratios in matrix containing in each column the corresponding discrete time deterministic modal participation vector matrix containing in each column the corresponding modal Kalman filter vector only computed when the Control Systems Toolbox is available matrix containing in each column the corresponding discrete time stochastic participation vector although the elements of Phi are re scaled to displacement units the elements of Gm are not this s cell containing the output quantities Valid arguments are acc accelerations velo velocities disp displacements and strain strains Since the output quantities are redefined to modal displacements or modal strains is both an input and an output argument refquants cell containing the reference output quantities MODAL ANALYSIS OOO 17 A B C D Q R S G Lambda0 state space system matrices For a loc ampl refs Ts Notes 5 4 16 deterministic state space description obtained from an EMA test only A B C D are provided and the others are empty For a stochastic state space description obtained from an O
170. uency damping ratio and mode shape of a single mode syntax covixp k Cov f k xi k re_ phi k where Cov is a function that takes the covariance of a vector cell containing the output quantities Valid arguments are acc accelerations velo velocities disp displacements and strain strains Since the output quantities are redefined to mode shape quantities in ssmodparvar quants is both an input and an output argument vector with modal transfer infinity norm values identified system matrices covariance matrix of the identified matrices This can be the full 118 OVERVIEW OF MACEC FUNCTIONS covariance matrix Cov vec_ A vec_ C or when the system description is in decoupled or modal form ACcov can be a cell containing the covariance matrices for each decoupled system dt the sampling period 5 4 17 stable_propmodpar5 STABLE_PROPMODPARS Computing all the modes of a sequence of discrete time state space models allmodes stable_propmodpar5 sysmat Ts chan_outin ampl_outin quants covind allmodes a structure containing the mode information sysmat structure containing all identified system matrices Ts sampling period chan_outin vector containing for each input the corresponding output DOF channel If an input corresponds to no output DOF the value equals zero ampl_outin vector containing for each input the weighting factor needed for unity modal mass weighting quants
171. ut only setup measurement was approximately 5 minutes at a sampling rate of 200Hz For the combined vibration measurements in which also the impact force was used and measured the sampling frequency was chosen to be as high as 500Hz to capture the short time transient signals of the impact in full detail The measurement duration was about 12s THE B15 BRIDGE AA Z 9 4 2 3 Building the geometry 1 The first thing to do would be to construct the grid of measurement nodes and to connect them into a surface model of the structure for visualization Because the GEOMETRY part of the MACEC main window has already been treated in detail in the previous tutorial section 4 1 2 the construction of the grid and the surface files is not explained in detail here but the files have been prepared on beforehand You can simply load the b15_grid asc file from the spice tutorials tutorial2 directory using the SELECT GRID FILE button in the GEOMETRY section of the MACEC main window fig 4 32 If you want you can have a look at the defined measurement nodes by using the EDIT GRID FILE button which is located next to the SELECT GRID FILE button MACEC 3 2 BEE LEUVEN X Grid file Slave file Beam surface file Geometry i Signal Processing Convert to mesignal Add DOFs Stochastic Subspace v Apply l System Identification Modal Analysis Modal analysis Combine setups
172. uts x zeros 4 N for par 2 N x par A x par 1 Bx u par 1 y par C x par D u par end With the simulated data a nonparametric FRF estimate is computed first using the H approach 5 then a right matrix fraction description RMFD model is computed using the pLSCF algorithm the RMFD model is converted to a state space model and then the modal parameters are computed types cell_ strvcat force force acc acc define data types labels cell_ strvcat 1F 2F 1A 2A define channel labels predat mcsignal u y 1 Ts types 1 labels make an mcsignal object with the simulated data node_num 1 2 1 2 define node numbers for each channel meas_dir 0 0 0 0 0 0 0 0 define measurement directions for each channel hifrf hicov freqscale Hlestimate predat 4 rect 1 2 3 4 fs estimate FRFs rmfd RMFDcalc hifrf pLSCF 2 3 4 1 2 freqscale 0 50 estimate a right matrix fraction description of 3 order 2 exact order 132 OOOO VERIFICATION EXAMPLES node_num meas_dir quants chan_outin ampl_outin refs identsel node_num meas_dir predat quantity rmfd chanselout rmfd chanselin rmfd refs sysmat rmfd2sysmat rmfd convert to a state space model modes stable_propmodpar5 sysmat predat dt chan_outin ampl_outin quants compute the modal parameters Table compares the identif
173. uts will be used for the identification in the SELECT CHANNELS section As all channels contain valid output data they should all be selected in the OUTPUTS column Please note that also here MACEC automatically suggests the right choice depending on the data type of each channel It is also possible to work with reference channels but we will not make use of this possibility now Therefore fill in 1 4 in the REFERENCES field of the POSITIVE POWER SPECTRAL DENSITY CORRELOGRAM ESTI MATION so that all channels are selected as reference channels and press APPLY fig 4 12 The PSD ESTIMATION window opens fig 4 13 The user has the choice between two different methods for the estimation of the positive power spectral densities the correlogram and the periodogram method OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE 88 20 Nonparametric FRF PSD estimation for Peak Picking or CMIF FDD FRF and or PSD estimation Select Channels Analysis type deterministic stochastic noas 1 5X acc ch 1 5X acc 4X acc 2 4X acc 3 3X acc th 3 3X acc response function estimation H1 estimator 4 2 acc 4 2 acc References e g 3 5 7 z Positive Power Spectral Density estimation Figure 4 12 Tutorial 1 Nonparametric PSD estimation The correlogram method calculates the PSD by first estimating the correlation function through averaging an
174. verify the performance of MACEC by comparing the obtained results with analytical solutions or benchmark results reported in the literature So far only one example is provided More examples will follow in future editions of this manual 6 1 Example 1 2DOF system p gt u t gt u t yi t gt Y2 t k po k2 A k3 VW LW Ne mi ma i i 1 Cj fy IS Ca C C3 Figure 6 1 Verification example 1 2DOF structure In this example a system with two degrees of freedom DOFs and proportional damping is simulated fig 6 1 It is used as an example in the classic textbook on modal testing by Heylen et al 5 section A 1 4 2 The masses dampers and stiffnesses have the following values e m ma 2kg DN m s Ca 2 e cq c3 3 AE e k k3 4000 k 2000 With these values the mass stiffness and damping matrices are computed as My 0 2 0 M kg 0 ma 0 2 129 130 OOOO VERIFICATION EXAMPLES C Cy cg C2 5 2 N C2 C2 C3 2 5 m s ee k 6000 2000 N ky kitka 2000 6000 The system has two inputs u1 t and u2 t which are the horizontal forces applied to the masses m and ma respectively There are two outputs y t and yo t which are the horizontal accelerations of the masses m and ma respectively 6 1 1 Example la discretization The purpose of this example is to check the influence of the Zero Order Hold ZOH
175. window Because only the horizontal accelerations at one side of the frame structure have been simulated a slaving procedure is needed to define the mode shapes at the other side of the frame Therefore click the MAKE SLAVE FILE button in the MACEC main window The DEFINE EDIT SLAVE DOFs window now appears fig 4 5 At the right the nodes defined in the grid file are shown for your convenience How should the DOFs be linked It can be assumed that the horizontal beams of the frame structure are very rigid in the horizontal direction Furthermore nodes 1 and 6 are not measured but it can be assumed that they have zero displacement Therefore the following DOF s should be coupled OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE al Define Edit slave DOFs r Define slave DOFs Master node 2 Master DOF X OY OZ Slave node 1 6 Slaye DOF Ox OY OZ Amplitude F r List of master slave DOFs Master node DOF X Y Z Slave node DOF Equal axes Rotate3D Cancel slave node 7 8 9 10 1 6 These DOFs can be coupled one by one or alternatively at once using MATLAB vector notation We will follow the second alternative as it is more convenient here In the MASTER NODE field fill in 2 5 As the MASTER DOF choose X In the SLAVE NODE field fill in 7 10 As the SLAVE DOF choose also X In the AMPLITUDE field fill in 1 and
176. x mcsignal object y Cell array containing label describing strings e g 12z Use y x labels to access this function 5 1 30 mesignal MCSIGNAL Multi channel time signal unity time 1 s constructor y MCSIGNAL s1 s2 assembles the mcsignals s1 s2 to a single mcsignal y MCSIGNAL ddffile quantity sifactor labels creates a mcsignal containing the data in the specified DasyLab DDF file Quantity defaults to volt and sifactor defaults to 1 MCSIGNAL ___ ONT y MCSIGNAL tdmfile quantity sifactor labels creates a mcsignal containing the data in the specified LabVIEW TDM file Quantity defaults to volt and sifactor defaults to 1 y MCSIGNAL wavfile quantity sifactor labels creates a mcsignal containing the data in the specified Test Lab WAV file Quantity defaults to volt and sifactor defaults to 1 y MCSIGNAL ascfile F quantity sifactor labels creates a mcsignal containing the data in the specified ASCII file Sifactor defaults to 1 y MCSIGNAL x F quantity sifactor labels creates a mcsignal containing the data in the specified matrix x Columns are interpreted as channels Sifactor defaults to 1 s1 s2 mcsignal objects to assemble into 1 mcsignal ddffile DasyLab DDF file name ascfile Name of an ASCII file containing a multi channel time signal Columns are interpreted as channels x Matrix containing a multi channel time signal Columns are interpreted as channels
177. y are in RMFD REFS which have been used as reference outputs in the identification FILE STRUCTURES 2 Nonparametric model Ifthe identified system model is a nonparametric frequency response func tion FRF or positive power spectral density PSD the mat file contains the following variables e NONPAR a MATLAB variable of the STRUCT type with the following fields NONPAR FREQSCALE a vector containing the frequency points of the nonparametric model NONPAR FRF a 3D matrix containing the estimated FRF s The rows correspond to the output channels the columns to the input channels and the depth to the frequency points This field can be empty NONPAR PSDP a 3D matrix containing the estimated PSD t s The rows correspond to the output channels the columns to the reference output channels and the depth to the frequency points This field can be empty NONPAR CHANSELOUT a vector containing the channel numbers which have been used as outputs in the identification NONPAR CHANSELIN a vector containing the channel numbers which have been used as inputs in the identification This field can be empty NONPAR REFS a vector containing the channel numbers which have been used as reference outputs in the identification This field can be empty e NODE_NUM e MEAS_DIR e QUANTS e CHAN_OUTIN e AMPL_OUTIN Modal Analysis results After you have selected the proper modal characteristics in the stabilizati
178. y of x to P y RESAMPLE x P Q applies the global function RESAMPLE x tdata P Q to the channels of the mcsignal x x mcsignal object y mcsignal object Use y x resample P or x resample P Q to access this function See also the global function RESAMPLE 5 1 39 select SELECT Delete channels from a mcsignal y SELECT ich1 x deletes the channels ich0 from the mcsignal x Only the channels ichi are kept x mcsignal object ichl Channels to keep y mcsignal object Use y x select fichi to access this function See also MCSIGNAL DELETE Q MCSIGNAL AAA o 5 1 40 setn_ SETN_ Set number of samples of mcsignal y SETN x N truncates the mcsignal x if it is longer than N samples and pads is with zeros otherwise x mcsignal object N number of samples y mcsignal object Use y x setN N to access this function 5 1 41 setsifactor SETSIFACTOR Convert mcsignal units y SETSIFACTOR ich1 x sifactor sets the SI factor more info see MCSIGNAL of the selected channels to the specified value E g to convert an acceleration signal x from m s 2 to g use y SETSIFACTOR ich1 x 9 81 x mcsignal object ichl Channels to convert Default all channels sifactor New SI factor e g 9 81 for the conversion from m s 2 to g If not equal for all channels then pass a vector y mcsignal object Use y x setsifactor ichi sifactor to access this function 5 1 42 sifactor SIFACT
179. y parts of the mode shapes in each column STABMODES STDMMAX a vector containing the maximum standard deviations of a real or imaginary part of the mode shapes Please note that depending on the system identification method that has been employed some of these fields may not be available e NODE_NUM see the previous paragraph e MEAS_DIR see the previous paragraph 3 4 Graphical User Interface MACEC s Graphical User Interface GUI is constructed around one main window divided into dif ferent sections In each section a specific part of the modal analysis process is dealt with mostly by clicking buttons which call other windows In this section you can find a schematic overview of how the different GUI windows are called Fig provides an overview of the GUI structure of MACEC and also indicates the interaction between the GUI figures and the files that are created from or interact with the GUI The MACEC main window figure 2 1 which is constructed by calling the GULmain function consists of the following sections e FILE S IN USE In this section no other MACEC windows are called It just consists of a list of files that are used in MACEC and buttons to select new files to quit the main window etc e GEOMETRY This section deals with the definition and the editing of grid slave or beam surface files Depending on the button used the following MACEC functions will be called GUL grid constructs the window f
180. z and the length of the rectangular time window used for the noise reduction Nw m Na As the total number of time samples we have at our disposal is 8192 this can be verified from the RESOLUTION INFO box at the left bottom choose 8 as the NUMBER OF DATA BLOCKS so that each block will contain 1024 samples To appreciate the effect of the TIME WINDOW PARAMETER first leave it to its default value 1 check CALCULATE STANDARD DEVIATIONS and SHOW STANDARD DEVIATION press CALCULATE AND SHOW ESTIMATES and uncheck SHOW ESTIMATION HISTORY The estimated PSD curve is now shown in blue and the estimated standard deviation is shown in grey Now change the TIME WINDOW PARAMETER to 2 and press again CALCULATE AND SHOW ESTIMATES Now you see that the PSD curve is much smoother than for m 1 which indicates that the noise level has been seriously reduced fig 4 15 This is also reflected in the estimated standard deviation which has decreased However there s a price to pay the frequency resolution has increased with a factor 2 to 0 2 Hz this can be verified from the RESOLUTION INFO box at the left bottom Therefore do not increase m any further but press OK fig 4 15 The last PSD estimate is passed to the NONPARAMETRIC FRF PSD ESTIMATION FOR PEAK PICKING OR CMIF FDD window 21 In this window press OK and save the models in the following mat file framedata_nonpar mat OPERATIONAL MODAL ANALYSIS OF A FRAME STRUCTURE

manual - KU Leuven

Contents

Download Pdf Manuals

Related Search

Related Contents