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Modeling of Fuel Injection System for Troubleshooting

1. The model of the bicycle wheel presented in figure Z earlier can be extended to include the observation nodes and edges between them and the component nodes representing their dependency In figure b d three nodes have been added those are white and represents observation variables Please note that the component variables have been renamed from X to Ci where C stands for component Also note the difference between Cpressure Which models the actual air pressure and Opressure which models the observed pressure All values in the CPTs are guessed by the author from_those values the probabilities for making the observations can be calculated and are presented in table 2 9 P Opressure P Ovubble P Ohote High Low Bubbles No bubbles Hole found No hole found 0 77 0 23 0 234 0 766 0 01 0 99 Table 2 9 This table shows the probabilities for the different modes of the observation variables The probabilities presented in this table are the probabilities to make those observations given no information about the fault modes of the component variables 2 3 4 Inference in Bayesian networks When a model is created it could be used for making diagnosis Using a model for diagnosis requires evidence of its variables and an inference algorithm Evidence is the term for known statistical events for example that C is in the mode m Setting that evidence can be written as Ci my Inference is the
2. 3 Power Combustion stroke diesel fuel is injected with high pressure see fuel injector in fig ure and self ignites due to the high pressure and temperature of the air and the fuel this pushes the piston down with a strong force giving the crankshaft kinetic energy 4 Exhaust stroke the exhaust valve opens and the piston returns to the top of the cylinder pushing the exhaust out and then the cycle restarts at stroke 1 10 9 Figure 2 2 A cross section of a cylinder in a diesel engine 1 Piston 2 intake air 3 intake valve 4 fuel injector 5 exhaust valve 6 exhaust gases 7 cylinder 8 counterweight 9 crankshaft 10 flywheel 11 connecting rod 2 1 2 Fuel injection What makes diesel engines unique is that the fuel self ignites due to the increased heat caused by the compression of the air instead of igniting the fuel with a spark plug used in petrol engines An important part of the diesel engine s combustion process is the fuel injection Injecting the diesel into the cylinders with high pressure leads to a better spread of the diesel particles which increases the efficiency of the combustion 7 Thus the fuel consumption is reduced Another benefit is reduced exhaust gas levels and increased performance of the engine 8 Developing a high pressure fuel injection system is therefore of interest for vehicle manufacturers For further information about fuel injection read the explanatio
3. 13 008 SE ISSN 1653 5715 www kth se
4. process of deriving logical conclusions in this case from statistical data tid Inference and evidence can be studied by looking at the example given in figure 2 6 Since some of the probabilities are conditional This can seam redundant since the sum of P O ind C my P O nind Cj mx 1 0 and P O nind C mx therefore always can be derived from P O ind C mr However this thesis assumes that both probabilities must be specified explicitly 13 2 3 BAXESIAN NETWORKS Alexander Georgii Hemming Cvon P Ohole Crue Crake Hole found Not found Intact 0 1 Punctured 0 10 0 90 P Opressure C pressure C pressure High Low High 0 9 0 1 Low 0 2 0 8 O pressure Obubble P Opubble tube Cualue Ciube C valve Bubbles No bubbles Intact Tightened 0 10 0 90 Intact Leakv 0 60 0 40 Punctured Tightened 0 50 0 50 Punctured Leakv 0 70 0 30 Figure 2 6 The bicycle wheel model updated with observation variables and their CPTs and depend on the mode of Opote setting the evidence Onote holefound affects the probabilities in the model thus the tables must be updated The new values for the probabilitv tables are calculated from the CPTs and the evidence inferred using some inference algorithm Inference can be exact or approximate For large and complex models it is often not possible to use exact inference due to the high time and or space complexitv T
5. 1 1 Problemi formulation 4 4 ss sasama da maaa B ILSNA oR amp e e oe ei eens 1 bf N ei a G bl ae e ander 1 i GPE TE TA ins AAA 2 A 2 3 P1 The diesel enging LL 3 Ia A e 4 A 5 EE RO 6 TEA ta A e 6 IA B a LS i mat 6 i RR READ 7 een 8 2 3 Bayesian networks nenn 9 TE ERREGER ER A g and 9 ab ai ata irae a ae Ae Aca A RA SG 10 Ed Sug f r ge MS ele we oe eee a 12 2 3 4 Inference in Bayesian networks 6 00 13 15 15 15 16 16 19 21 21 21 21 i 23 iy Soh a ada rea Fae eG ee ee 23 eee eer eT eT ee eee Pe ee eee ee ere 23 tet A ee RR a ed eee ee ee 24 rg Get Ee A a 24 pit Seen re OE 27 CONTENTS Alexander Georgii Hemming Cvon enerating the modell cia a a a Da a a e a e a E 29 Noisv Or Nodes III Result 37 39 del iii ea A a a h ir aA aT 39 O 1 1 Test one expert interview 2 nooo e e a e e e a 39 1 2 Test two case studied aa a a a a a a 40 43 43 44 44 47 51 53 55 Part I Introduction Chapter 1 Background It has become difficult for mechanics to troubleshoot a faulty truck due to the increasing complexitv of its svstems Trucks are nowadavs composed of several complex svstems containing components sensors computers and connections between them Troubleshooting refers to the act of determining which component is faultv and performing an action in order to mend this fault Identifving the fault is not trivial since the svstems
6. CB 74 1 C20 Inlet Metering Valve IMV Controls fuel amount into Co1 8 633 EMF 1 8 SC 72 8 CB 21 2 TV 4 3 Continued on next page 1Probability that component C is faulty expressed in o 21f the fuel gets cold the risk of parrafin clogging increasesd dramatically 25 4 3 THE MODEL Alexander Georgii Hemming Cvon Continued Component variable Description P F Fault modes Ca Pressure Filter PF Fine meshed particle separation filter 4 428 EMF 47 4 WP 50 2 SC 1 2 IV 1 1 C22 Pressure Sensor Measures the pressure 9 644 WP 100 0 C23 Safety Valve SV Opens if pressure gets too high in Co1 2 287 WP 65 0 CB 27 6 EMF 7 0 SC 0 5 C24 Suction Filter SF Coarse meshed water separation filter 8 888 EMF 47 8 EF 6 6 SC 22 1 FL 23 5 C25 Venturi Housing Venturi on Co3 creates suction for C24 9 260 AL 39 9 FL 23 9 WP 26 6 SC 9 6 Co6 face gt HPC High pressure pipe from Co to Cor 7 325 CB 72 0 EMF 9 5 EF 18 4 Cor facc gt HPCha High pressure pipe from Co1 to Cos 1 755 WP 79 7 SC 20 3 Cog facc gt HPC 3 High pressure pipe from Co to Cog 8 133 EMF 6 8 AL 24 2 WP 35 4 TV 33 6 C29 acc gt HPC High pressure pipe from Co to Cio 0 927 EF 55 3 AL 44 7 C30 acc gt HPC s High pressure pipe from Co to C11 5 739 SC 14 3 EF 85 7 C31 facc gt HPC s Hig
7. O47 FL 66 81 SC 33 19 Table 5 2 Table with the result from the case studies using EPIS BN as inference algorithm with 100 iterations maximum in GeNIe But the values differed much between runs so each case was run 100 times each for a total of 100 x 100 10000 iterations The average value for those 10000 iterations is displayed in the rightmost column From the table we can deduce two important things 1 Using EPIS BN 10000 iterations as inference algorithm generated similar result as the exact inference algorithm 9 12 vs 10 and 45 89 vs 44 2 For each case the correct fault mode was diagnosed as the most likely fault mode i e if both fault mode m m are diagnosed then P m O na gt gt P m Oina if m is the correct diagnosis where gt gt was defined as P m Oina 2P m Oina 5When an MPC of 4 was tested no result could be obtained for the last test case The reason for this is probably that four parents were too many for the inference algorithm 42 Chapter 6 Conclusion 6 1 Discussion The model presented in this thesis correctly mimics the behavior of the XPI system It is also compatible with the project provider s research The program yED to GeNle developed by the author and the method used for modeling can be reused to generate models of other systems this will hopefully be helpful for the provider of the project The data on which the a priori CPTs are created only measures the n
8. a mechanic then the model should make the same diagnosis Continue reading more about the behavior of the model in section Correctness of the model 5 1 The model must be represented or implemented in a computer program somehow so that it is possible to interact with it The model presented in this thesis has been represented in a graphical network program called GeNIe pl The model can not be created in GeNIe manually since it is way to much work due to the complexity of the model instead it is generated by a program developed and presented in this thesis This model generating program can be reused for modeling of other systems given that the necessary data files are available and on the correct format described in section Limits in GeNIe 4 4 2 1 1 2 Thesis delimitations The work presented in this thesis will hopefully be useful for other systems than the XPl svstems How ever the thesis will be limited to modeling the XPI system only This model will have some restrictions The XPl system is in fact used in three different engine types the 9 13 and 16 liter engines The 9 and the 13 liter versions does however differ very little in ways of design and functionality The 16 liter version has a slightly different configuration then the other two The XPl svstem being modeled in this thesis is the 13 liter version although the difference between it and the 9 liter version is very smallH 1 2 Thesis Outline First necessary theory
9. computer with 33 more memory was tested still no evidence on non indicating and with MPC 2 using that computer values could be obtained for every test case except the last one The solution to this was to use an approximate inference algorithm There were a variety of algorithms to chose between e Relevance based decomposition Polytree e EPIS sampling e AIS sampling Logic sampling e Backward sampling e Likelihood sampling e Selfimportance The algorithm chosen was a sampling algorithm called Evidence Pre propagation Importance Sampling Algorithm EPIS BN EPIS BN_was used since it is considered to be the current state of the art for sampling in Bayesian networks For an overview of inference algorithms please see b3 and bg Read more about stochastic sampling algorithms here 41 5 1 CORRECTNESS OF THE MODEL Alexander Georgii Hemming Cvon Using EPIS BN inference instead of the exact inference algorithm we could obtain results for everv test case when MPC was set to 2 on the 8gb RAM computer with all the correct evidence set non indicating mode on all observation nodes not in O na CV Mmaz Oind P milOina Coo Electrical fault Oo1 02 O04 O24_32 EF 100 C23 Fuel leakage Opo1 04 O33 FL 56 21 Coz Cracked or broken Oo1 02 O04 O33 FL 9 12 CB 45 89 Ci3 Fuel leakage Oo1 04 O33 FL 26 1 CB 7 72 Cr Fuel leakage Op1 04 Oo7 08 O12 O24 033
10. expert The verification process is explained in detail in chapter Verifying the X PI model bl 17 3 2 METHODS FOR VERIFVING THE MODEL Alexander Georgii Hemming Cyon 18 Part II System Modeling Chapter 4 Modeling the X Pl svstem In this chapter the theorv learned in chapter b and chapter Methodolog E will be applied on the data creating the model of the XPI system 4 1 About the XPI system The purpose of the XPI system is to supply the engine with the right amount of fuel at the right time and with high pressure It increases the diesel injection pressure to around 2000 bar The system consists of pumps pipes filters and nozzles amongst other components The purpose of this section is to give an explanation of how the system works so that the reader has a fundamental understanding of the system in prior to the modeling of it 4 1 1 Components Some of the components in the XPI system are presented in figure The description of the XPI system in section The route of the fuel in the engind 1 1 3 will refer to the components presented in the list below using the components index in parenthesis 4 1 2 The route of the fuel in the engine This section explains the route of the fuel in the XPI system giving the reader an insight on how the system works Fuel is sucked from the fuel tank by the feed pump 22 The fuel enters through connection 1 and gets drawn through the suction filter 21 into the engin
11. function in the table for node OR and analogously for OR2 and that O has a similar OR function but has a set FPR 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cyon 34 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cyon 4 4 3 The complete model N X m Xl W Ss K X WN HY Y N N AD lq N jil LEA A 1 i i 1 7 fl V ji f 4 Figure 4 6 This is the complete model with an FPR of 4 The nodes on the left side are component nodes and on the right side observation nodes The two layers of nodes in between the component and the observation nodes are the intermediate nodes Many of the intermediate nodes are stacked the are placed on top of each other The reason for this is that Y2G places the intermediate nodes depending of the components nodes this results in the same placement of intermediate nodes for observation nodes that have a similiar set of component nodes as parents 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cyon 36 Part III Result Chapter 5 Verifying the XPI model An important part of the modeling of a system is to be able to evaulate the model There are several ways to evaluate a model the evauluation done in this section is a verification that tries to determine if the model is correct 5 1 Correctness of the model By correctness we mean if
12. http en wikipedia org wiki Two stroke_engine 2012 Ac cessed online 2012 11 22 Future and Potential of Diesel Injection Systems Springer Verlag 2002 V Hariharana and R K Vijayakumar Effect of injection pressure on diesel engine performance with sea lemon oil Indian Journal of Science and Technology 2001 Accessed online 2012 07 01 F Dekking C Kraaikamp and H Lopuha A Modern Introduction To Probability And Statistics New York USA Springer 2009 G Simon Discrete random variables tech rep Stern School of Business 2007 Accessed online 2012 06 27 Wikipedia Conditional probability http en wikipedia org wiki Conditional_ 2012 Accessed online 2012 11 08 F V Jensen and T D Nielsen Bayesian Networks and Decision Graphs Springer Verlag 2007 A Nicholson O Woodberry and C Twardy The native fish bayesian networks tech rep Bayesian Intelligence 2010 Accessed online 2012 06 21 Wikipedia Inference http en wikipedia org wiki Inference 2012 Accessed online 2012 11 20 47 Alexander Georgii Hemming Cvon 15 S Thrun W Burgard and D Fox Robotics Intelligent Robotics and Autonomous Agents Series 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Mit Press 2005 B G Marcot J D Steventon G D Sutherland and R K Mccann Guidelines f
13. named electrical fault for each component potentially generating multiple electrical DTCs The data consists of number of warranty claims per component This constitutes the fault frequency data needed to create the a priori probabilities for each component variable in the model The probabilities are created by dividing the fault frequencies with the size of the truck population examined denoted POP Choosing POP as the denominator results in that the a priori probabilities will be the probabilities that a certain component is faulty given that we take any truck t POP randomly from the street and examining it Determining the denominator is not a trivial task since it affects the whole model the problem of choosing the denominator is known as the reference class problemP1 and is a classic statistical problem Instead of POP the denominator could have been the set of all trucks that have been to service or only trucks that have been to service because of known faults Some of the components have no reported warranty claims this would result in probability P C Faulty 0 Vi S where S is a set of components with zero reported claims In other words the model would say that it is impossible for the components in S to be faulty which is a dangerous assumption and would limit the model dramaticallyB To solve this problem we use a common method to handle zero probability entries called add one smoothing also called Laplace smooth
14. needed to understand this thesis is explained the reader will be introduced to how a diesel engine works in section The diesel engine e calculus of probabilitv in section of probability z and what Bayesian networks are in section Bayesian networks 2 3 Section B about modeling techniq followed by a short introduction to the model evaluation about e process in im ethods for verifying the model After that the XPl model is presented and thoroughly explained followed by the verification of the model The thesis ends with a conclusion and discussion about the results in chapter I The primary difference is that the 13 liter version has one cylinder more Chapter 2 Theory The purpose of this section is to introduce the reader to the fundamental theory necessary to understand the thesis Two major fields are presented firstly the reader is introduced to the basics of a diesel engine and fuel injection An insight of how a diesel engine works is important because the sole purpose of this thesis is to model the fuel injection system in such an engine Secondly a presentation of statistics is given since XPI will be modeled using a statistical model therefore it is important to have basic knowledge of the theory of statistics and calculus of probabilitv A various number of concepts and their notation is presented for the reader s convenience a summary of the notation can be found in appendix B 2 1 The diese
15. node O in table E for an example If an observation node O originally had gt M PC parents two levels of intermediate nodes are needed The first layer closest to the component nodes will be LNONs with FRP or zero the second layer consists of plain OR nodes without FPR and with the bottom layer of observation nodes modeled as LNONs with the set FPR and the OR function characteristic If O had gt MPC parents the same thing applies only that a third layer of intermediate OR nodes are inserted before the layer of observation nodes Please see figure z for an example graph prior to the Y2G conversion The result of the conversion is shown in figure 4 5 An observation node with gt MPC parents forms together with its parents a big tre 4 Those observation nodes O with an pa O lt MPC forms small trees Please note that it is only the big trees in which extra nodes are inserted The number of layers of extra nodes for the big trees is calculated by logurpc pac Ri 1 Where logmpc is the maximum parent count logarithm and R is the root of big tree T an observation node that is Tn fact it is only adviced against but the author never got the model to work with more than 20 parents on a computer with a dual core 2 5 GHz CPU and 6GB DDR3 RAM TInverted trees where the root is the observation node and the component nodes are the leaves 31 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cvon
16. shape the cylinders constitute when having them in two planes rows almost perpendicular to each other forming a V shape please see figure bil 1In contrast to the traditional engine fueled by petrol 2 1 THE DIESEL ENGINE Alexander Georgii Hemming Cyon Figure 2 1 This figure shows the V shaped configuration of the cylinders Pistons move up and down in the cylinder the movement of the pistons causes the crankshaft to move creating mechanical energy 1 Piston 2 connecting rod 3 fivwheel 4 intake and exhaust valve 5 cylinder 6 counterweight 2 1 1 The combustion process The combustion process is classicallv either a two or four stroke step cycle Both the two and the four stroke cycle is used in diesel engines The two stroke was more popular before when emission control was not as strict The two stroke engine is cheap to produce repair and rebuild it is light weight but has poor exhaust emission features Today the four stroke is most common 6 Here follows a simple explanation of the combustion process of the four stroke cycle 1 Intake stroke the piston moves down towards the bottom of the cvlinder which reduces the cylinder s air pressure This sucks air into the cylinder through the air valve please see intake air in figure bd 2 Compression stroke the piston rises thus increasing the air pressure and temperature in the 4 2 1 THE DIESEL ENGINE Alexander Georgii Hemming Cyon cylinder
17. the model of the XPI system is realistic if it behaves correctly The verification of the XPI model consists of two separate tests 5 1 1 Test one expert interview The first case study was an expert interview with an engineer at Scania who has several years of experience with troubleshooting the XPl svstem For the system to be viewed as correct two requirements has to be met Requirement one The first step of the evaluation was studying different cases together with the XPI expert and letting him judge whether or not the model behaves correctly By behave correctly we mean that the model represents the real system by behaving reasonably much similar to the real system Prior to the interview with the expert some formal definition of a realistic model had to be done So the following requirement was defined Definition 5 1 1 Realistic model P C faultylO reatity gt gt 0 P C faultylO mode gt gt 0 VC where P O C gt 0 In other words a model is realistic if for every observation O examined the probability P C faulty O ind gt gt 0 in the model if it is in reality for all C that can cause O In total 12 observation variables where examined namely Op1 Oo3 Oo7 033 030 Oog Oss O29 O24 O26 O32 Oo2 The expert confirmed that the model was realistic according to definition definition bid Not only did he confirm the correctness of the model but was also impressed that the model could confi
18. Co Accumulator acc Thick high pressure pipe fuel rail 5 539 EMF 100 0 Co2 Feed Pump FP Sucks fuel from fuel tank 0 005 FL 67 4 CB 32 6 Coz Filter Housing Case for C24 and C21 5 368 FL 60 2 IV 26 1 EF 1 1 WP 12 7 Cor Fuel Heater Heats the fuel A 3 296 IV 38 0 WP 41 7 EF 10 1 FL 10 2 Cos Fuel Manifold FM Manifold for return excess fuel 9 496 WP 30 6 EMF 47 8 EF 21 6 Cos Hand Pump Hand pump used for fault diagnosis 7 027 SC 50 5 IV 49 5 Cor HPC Connector between C26 and Cia 4 315 IV 98 0 WP 1 4 CB 0 2 AL 0 3 Cos HPCa Connector between C27 and Cis 3 291 CB 33 4 AL 52 6 SC 3 5 WP 10 5 Coo HPC3 Connector between C2g and Che 4 452 EF 15 8 IV 57 8 FL 18 4 AL 8 0 Cio HPC Connector between C29 and C47 3 819 IV 66 6 EF 10 9 EMF 18 6 SC 4 0 Cu HPC Connector between Cso and Cis 6 983 AL 1 6 EF 4 3 IV 82 1 CB 12 0 Ci HPCs Connector between C3 and Cig 0 801 IV 38 6 EF 6 7 WP 52 1 EMF 2 6 C3 High Pressure Pump HPP Increases pressure to max 3000 bar 9 804 TV 100 0 Cia Injectori Injects fuel into cylinder 1 0 510 FL 25 9 CB 74 1 Cs Injectora Injects fuel into cvlinder 2 0 510 FL 25 9 CB 74 1 Cie Injectors Injects fuel into cylinder 3 0 510 FL 25 9 CB 74 1 Ci7 Injectora Injects fuel into cylinder 4 0 510 FL 25 9 CB 74 1 Cis Injectors Injects fuel into cylinder 5 0 510 FL 25 9 CB 74 1 Cig Injectors Injects fuel into cylinder 6 0 510 FL 25 9
19. Modeling of Fuel Injection Svstem for Troubleshooting ALEXANDER GEORGII HEMMING CVON 4 ES KTH 3 VETENSKAP 9 OCH KONST p IV KTH Computer Science and Communication Master of Science Thesis Stockholm Sweden 2013 Modeling of Fuel Injection Svstem for Troubleshooting ALEXANDER GEORGII HEMMING CYON DD221X Master s Thesis in Computer Science 30 ECTS credits Degree Progr in Computer Science and Engineering 300 credits Master Programme in Computer Science 120 credits Royal Institute of Technology year 2013 Supervisor at CSC was Johan Karlander Examiner was Anders Lansner TRITA CSC E 2013 008 ISRN KTH CSC E 13 008 SE ISSN 1653 5715 Royal Institute of Technology School of Computer Science and Communication KTH CSC SE 100 44 Stockholm Sweden URL www kth se csc Abstract With the technology progressing further making heavy duty vehicles more complex more computerized it becomes necessarv to update the troubleshooting process of such vehicles From the vehicles computers diagnosis trouble codes can be extracted informing the mechanic about the health of the vehicle Using those codes together with physical observations as input for a diagnosing software the software can give educated troubleshooting advice to the mechanic Such diagnosing software requires a model of the vehicle or one of its system which mimics the behavior of the real one If there would be a one to one correspondence between o
20. P C mo NF P Pi AS AICC Parent Co 7 Ci State mo NF mo NF FPR ind Po 0 P FPR Figure 4 4 Graph G before the conversion made by Y2G See appendix 6 for pseudocode of the algorithm that makes the graph conversion In order to create the probability tables for each node Y2G needs data with probabilities a priori conditinal and FPR but also data with list of fault modes for each component node and optionally a name for each node The data is declared in separate XML files that is passed as input to Y2G along with the yED graph 81t is convenient to use an index as unique identifier for each node as shown in this thesis Co and Oo etc and then declare a name for each node that can be displayed in GeNle 32 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cyon P C Z SS MA a ko Parent Ci Ca State mo NF mo NF FPR ind Po 0 P 0 0 OR Ni ind nind Na ind nind ind nind ind 1 1 1 0 nind 0 0 0 1 Parent OR OR State ind nind ind nind FPR ind 1 0 1 0 FPR nind 0 1 0 1 FPR Figure 4 5 The same graph G after the conversion made by Y2G with maximum parent count set to 2 Note that the FPR in the table for Ni and analogously for Na N3 Na is set to zero Also note the OR
21. This affected the model a lot especially the grouping and splitting It is very difficult to understand how it affected the model The injectors was modeled individually although each injector have the same part number and the fault count data for the injector part was divided by six This may have been a bad modeling decision One of the biggest challenges when developing this model was the format in which the data was accessible It was desired to start the modeling process by looking at the real system and how it functions as described in section d Knowing how the XPl system functions the next step was to identify the key component and include them as component variables in the model But the description of the system was an abstraction of how the real system really functions There was already a gap between the system and its description this gap may have widened the gap between the system and the model This poses a problem for the creation of the a priori probability tables The reason for this is that some components actually are composed of a set of smaller parts Thus there were no fault count 43 6 2 FUTURE WORK Alexander Georgii Hemming Cvon for those components but for the parts instead Some of those parts were used in several components making it impossible to use the fault counts for those parts If part p can be found in component C and C2 should the number of reported faults for p be added merged to Ci or C2 or eq
22. and delimitations A model is in its essence a description of something real therefore disregarding how detailed the model is there will always be some aspects and characteristics of the reality that the model will not cover We can call this incongruence a gap There will be a gap between the behavior of the real XPI system and the model presented in chapter 4 Closing this gap requires a vastly detailed and complex model This is not always wanted since it is difficult to get an overview of the system making it hard to understand Limiting the scope of the model is not only convenient but also necessary since it gets unmanageable to make calculations on it otherwise due to the large search space 4 2 1 Assumptions To make the modeling of the XPl svstem feasible some assumptions have to be made otherwise the model will be too complex Assumption 1 Components are independent The component variables are independent and faults occur independently This is a strong assumption Assumption 2 All components can be faulty Even though some components have a fault count of zero in the warranty claims they have a non zero pr ili i in the model this is an effect obabilitv of being faulty i of the additive smoothing mentioned in section Analyzing and formatting the data 8 1 2 4 2 2 Delimitations The XPLI system is a dynamic system that has been developed during several years More importantly it is still in development Th
23. are so complex The mechanics identifies a fault bv analvzing diagnosis trouble codes DTC generated bv the sensors in the trucks svstem but also bv doing phvsical observations It is therefore desirable to help the mechanics with the troubleshooting process one way of doing so is to model the truck s systems with a statistical model that behaves like the real system A certain fault in one of the truck s svstems can lead to multiple DTCs and the same DTC can be derived from different faults This makes fault determination non deterministic and therefore we cannot model the svstem with a deterministic model Instead we represent the system s behavior with a statistical model so that given some observations we believe with a certain probability that a certain component is faulty Since it is difficult for mechanics to identify the faulty component a quick solution would be to replace for example the whole engine instead of a small part of the engine Isolating the fault and only doing repairs or replacements of faulty components costs less than changing whole systems in terms of material cost but might cost more in terms of time Because of the strong correlation between time and money a reparation system needs to weigh material cost against time cost In this master thesis a model of one of the truck s system is modeled the eXtreme high Pressure fuel Injection system XPI This model will hopefully serve two purposes to help XPI experts
24. bservations and diagnosis the model would be completely accurate However no such one to one correspondence exists This makes the system non deterministic therefore the model has to be constructed using another approach This master thesis presents a statistical model of a fuel injection system called XPI The XPlI svstem is modeled using a statistical model called a Bayesian network which is a convenient way to model a non deterministic system The purpose of this model is to be able to make diagnosis of the XPl svstem but also to ease the understanding of the dependency between components and faults in the XPI system The model is also used to evaluate detectability and isolability of faults in the XPI system Sammanfattning Modellering av br nslesystem f r fels kning D teknologins utveckling g r tunga fordon mer komplexa mer datorberoende blir det n dv ndigt att modernisera fels kning av dessa fordon Fr n fordonens datorer kan felkoder avl sas Dessa felkoder med delar mekanikern om fordonets skick Felkoderna i kombination med fysiska observationer kan anv ndas som indata till en diagnostiseringsmjukvara som kan f rse mekanikerna med kvalificerade fels knings r d En s dan diagnostiseringsmjukvara kr ver en modell av fordonet eller ett delsystem av det vilken modellerar beteendet av det riktiga systemet Om det skulle finnas en ett till ett mappning mellan obser vationer och diagnoser skulle modellen ha fullst ndig
25. bytes number and float is represented as a 32 bit 4 bytes number 4Equals 256 GiB Bd 5Called Noisy MAX nodes in GeNle 29 44 GENERATING THE MODEL Alexander Georgii Hemming Cyon File Help Select paths to YED file graphml Models yED XPI_model graphml Browse fault mode data file XML Models Node data fault_mode_data xml Browse Component node data file XML Models Node data component_data xml Browse edge probability data file XML Models Node data edge_data xml Browse genie target file xdsl Models GeNie models XPl_converted xdsl Browse observation data file XML Models Node data observation_data xml Browse Options Y Import component node names _ Display component node names M Import observation node names _ Display observation node names M Use node margin M Display nodes as barcharts M Generate genie cases Coordinate offset X Coordinate offset Y 4 Max parent count Convert 0 3 Height margin yED to GeNIE version 1 0 8 Decimal precision Developed by Alexander Cyon at Scania Figure 4 3 Screenshot of the Y2G programs window a FPR close to zero since it makes the model even more non deterministic and would lead to incorrect diagnosis Even though a low FPR value is wanted it makes the model more powerful since it allows the model to catch casual dependencies that are outside the m
26. curred but it is not possible that A occurs at the same time thus A and B are independent As mentioned earlier the whole probability space must sum up to 1 0 which it does 0 52 0 04 0 10 0 34 1 0 Image curtsy of Wikipedia Li 2 3 Bayesian networks A Bayesian network BN is a graphical model that explains dependencies and the joint probability distributions between stochastic variables A BN can be used as a statistical model of a system be it an environmental technical or economical system This thesis will use the definition of BNs given in E Definition 2 3 1 Bayesian network A Bayesian network is a triple B X E 0 where X is a set of stochastic variables and E is a set of directed edges between the stochastic variables such that X E is a directed acyclic graph The set contains parameters that define the conditional probabilities P X pa X where pa X are the parents of X in the graph In the graph that constitutes the BN the stochastic variables are represented as nodes in this thesis the nodes are drawn as circles An edge between two nodes is drawn as a directed arrow 2 3 1 Small Bayesian network model This section introduces the reader to modeling using a BN A simple model will be presented with the goal of easing the understanding of how BNs are used to model real world objects systems and scenarios A BN model of a bicycle wheel describes the fault probabilities and depend
27. d how bright it is outside Let the stochastic variable X ime represent the hour of the day and Xsuntignt represent the brightness outside Xtime and Xsuntignt are said to be dependent since it is brighter during the day and darker during the night If two variables or more are not dependent then they are said to be independent Let Xcoin be the same variable as declared in table 2 1 Xgunlight and X ojn are typically independent and so is X jme and Xcoin 2 2 BASIC CALCULUS OF PROBABILITV Alexander Georgii Hemming Cvon Definition 2 2 1 Independence Two stochastic variables X and Y are independent if and only if for all values x of X and all values y of Y the following equality holds P X x Y y P X x P Y y Definition 2 2 2 Dependence Two stochastic variables are said to be dependent if they are not independent Thus for all values x of X and all values y of Y the following inequality holds P X x Y y P X x P Y y This means that knowing the value of one of them affects the probability of the other 2 2 3 Joint probability distribution Joint probability distribution describes the probability of two stochastic variables X Y having some values simultaneously i e P X x Y y This can be denoted with a shorter version P x y There is also another common notation let A denote the event that X x and B that Y y then P AN B denotes that A and B occurs at the same t
28. e groups the probabilities wre the Xpressure variable Where the value in 2 3 3 Observation variables To identify which of the system s components is faulty and make a diagnosis observations has to be made on the faulty system It can either be a physical observation made by the mechanic or DTCs provided by the XPI system s computer system called engine management system EMS In the bicycle wheel example such observations can be examination of the tube and the valve with the purpose of determining if the tube is punctuated and whether the valve is tightened or not Definition 2 3 3 Observation variable An observation variable is a stochastic variable An observation variable OV can only have two different modes either indicating ind or non indicating nind Edges are directed from CVs to OVs An OV may have multiple edges to it i e multiple component nodes as parents As mentioned pa O denotes the parent list for the observation variable Oj i e a list of CVs M C denotes the set of fault modes of the component variable C then there is a conditional probability that parent to O C is in the mode mz P O ind C Mr VC pa O Vm M C pac C Thus there is a CPT for each OV with II j 0 parents to O The factor 2 comes from that each of OVs O s modes ind nind must have a conditional 1 2xM C VO pa O where pa C is the number of 3A type of electronic contr
29. e management system EMS with cooler 24 via the fuel hose 2 The fuel is drawn from the EMS 24 and its cooler to the feed pump 22 via the fuel hose 3 The feed pump increases the fuel pressure to between 9 and 12 bar and via the fuel pipe 4 forces the fuel through the pressure filter 6 From the pressure filter the fuel flows via the fuel pipe 5 into the fuel inlet metering valve IMV 19 fitted on the high pressure pump HPP 23 The IMV controls the amount of fuel that flows into the HPP and is controlled by he EMS The HPP increases the pressure dramatically from previous 9 to 12 bar to a maximum of 3000 bar Via a high pressure pipe 7 the fuel continues to the accumulator 14 21 4 1 ABOUT THE XPI SYSTEM Alexander Georgii Hemming Cyon 8 9 10 7 13 14 15 in Be C zo 0 nt a mi U Figure 4 1 Drawing of the XPl svstem with the major components indexed A high pressure fuel pipe B low pressure pipe hose C pipe for return fuel 1 pipe from fuel tank 2 hose to EMS cooler 3 hose to feed pump 4 pipe to pressure filter 5 pipe to IMV 6 pressure filter 7 pipe to accumulator 8 pipe to high pressure connector 9 safety valve 10 pipe to fuel manifold 11 pipe to fuel tank 12 HPC 13 injector 14 accumulator 15 pressure sensor 16 fuel manifold 17 bleed nibble 18 overflow valve 19 IMV 20 hand pump 21 suction filter 22 feed p
30. e version of the system being modeled in this thesis is called generation 57 and is installed in the heavy duty vehicles being used on the market today The model presented in this chapter will thus only model the components faults and observations taken from the S7 XPLI system therefore ignoring all the updates improvements that has been made on the XPl svstem since The CPTs used in the XPI model are based on statistical data derived from technical reports on vehicles during the one year warranty period sent from workshops from the whole global market Customers are experiencing different problems e g due to their local whether conditions such as temperature and humidity another important factor is i quality of the diesel In Sweden the diesel is very clean almost free from water and with low paraffin4 concentrations However if a vehicle is fueled with diesel with high paraffin concentrations in a country in southern Europe and enters Sweden during the winter the paraffin often deposits into paraffin wax clogging the fuel filters Markets all over the world are different and in order to get a feasible and applicable model global workshop data will be used Most of the pipes in the XPl svstem will be included in the model These components represents the pipes themselves but also the connection in both ends Hoses are treated as pipes Paraffin is a hvdrocarbon compound found in diesel that can take a solid wax form if the temperature is b
31. elow 37 degrees Celsius 23 4 3 THE MODEL Alexander Georgii Hemming Cvon The XPlI system is not independent of other systems the healthiness of its components may be affected by other systems in the vehicle but it is also affected by environmental factors The fuel filters can easily get clogged due to paraffin As mentioned above the fuel clogs if the fuel has a bad qualitv i e high paraffin level in the diesel in combination with low temperatures These factors as well as the other svstems or parts of svstems in the vehicle will not be included in this model The reason for this is to trv to limit the fault detection of the svstem to its components Since the model is suppose to reflect the realitv it can be modeled with the same limits and crassness as the realitv has In the troubleshooting manual the mechanic is often instructed to replace whole parts of the XPl svstem consisting of several components instead of identifving the individual component in that part E g if the suction filter is broken both that component and the pressure filter is replaced since these components are connected and installed as a single part therefore it is not necessarv to model everv single part in the XPl svstem instead the model will sometimes use one single component to represent part of the XPI system 4 3 The model The data that the model is based on is sensitive to Scania thus the data presented in this thesis are fictive All values i
32. encies between the wheels components A bicycle wheel consists of a metal rim with spokes a tube and a tire The tube can be faulty i e some sharp pointy object can penetrate the tire and punctuate it Holes on the tube affects its air pressure the air pressure depends on the tube This means that the believed state mode of the air pressure depends on the information about the mode of the tube Mounted on the tube is an air valve which may be leaking air 2 3 BAYESIAN NETWORKS Alexander Georgii Hemming Cyon lt 2 1 3 N PIA INN Figure 2 4 Overview of a bicycle wheels components 1 tube 2 tire 3 rim 4 hub 5 spoke 6 air valve O 2 3 2 Component variables We would somehow like to represent the mode of the parts of the wheel in a model or to be specific the belevied mode This is done by representing them as stochastical variables Definition 2 3 2 Component variable A component variable is a stochastic variable The values that a component variable CV holds are called fault modes Each CV have at least two fault modes one of them is the non faulty NF which means that the component that the CV represents models is working correctly Each CV have at least one faulty mode with some specific name e g Electrical fault if the component that the CV models contains some electric circuit Let M C denote the set of all possible fault modes for some component variable C As shown in table each pos
33. erably very low and in the best case scenario it is zero All observation nodes in the XPI model is modeled as Leaky Noisy Or Nodes otherwise it would not be possible to create the model in GeNle In fact all observation nodes are LNONS initially but some of them are modeled a bit differently as presented in section Limits in GeNIe 4 4 2 4 4 2 Limits in GeNIe In order to create the model in GeNle not only is it necessary to model observation nodes as LNONS it is also required that no LNON has more than 20 parents Even when an LNON has more than around 13 15 parents GeNle performs sluggish inference can take several seconds Since observation node Op1 has 36 parents the graph had to be altered so that the parent count is reduced One of Y2G s primary functions is that it reduces the number of parents for all nodes in the graph to Max parent count MPC which is a number chosen bv the user see figure ha Y2G creates extra nodes intermediate nodes between the component and the observation nodes The intermediate nodes being children to component nodes are modeled as LNONs with an FPR of zero The observation nodes are modeled as LNON with the real often non zero FPR However instead of conditional probabilities P O ind C mi the LNON has a probability table that creates an OR function The OR function sets the observation node to indicating if any of its parents are indicating otherwise non indicating see table of
34. etter to include more removing some or grouping some component variables together The injectors component variables Ci4 19 could for example be modeled as a single component since their fault frequency was grouped together and then split in six equal probabilities to be modeled as six different components The model could have modeled the dependency between fuel quality temperature in the country and the fuel filters C21 and C4 Other smoothing techniques than add one smoothing could be used to solve zero probability diagnosis as mentioned in section Analyzing and formatting the data b 1 2 In fact this has not been investigated at all The model generating program Y2G programmed during this thesis maybe extended to have more dy namic input It could e g be convenient to be able to enter the FPRs for the observations in the program instead of having to declaring them in XML files or enter names for the nodes 6 3 Final words Modeling a system as complex as XPI is difficult The model never gets better than the that it is based on and the data used for the XPI model presented in this thesis is very noisy It was however showed during the verification process that the model seamed to behave correct The model was also able to confirm a theory that the expert of the XPl svstem have had for some time It is easy to understand how Bayesian networks are used for modeling but it is hard to judge how data manipulation and modeling deci
35. h pressure pipe from Co to C12 1 857 AL 12 0 EF 51 8 WP 36 1 C32 EMSC gt FP Low pressure pipe from the EMS cooler to 8 252 AL 80 5 SC 19 5 Coz C33 FM Fueltank Return fuel Pipe from Cos to fuel tank 7 572 SC 70 1 EMF 29 9 Cr FP gt PF LP from Coz to Ca 4 158 WP 9 7 EF 19 6 EMF 4 8 CB 65 9 C35 Fuel Tank SF Return fuel Pipe from C24 to C24 7 896 EMF 71 8 FL 17 8 CB 10 4 C35 HPP acc HP pipe from C13 to Co1 2 659 AL 100 0 Car PF gt IMV Low pressure pipe from C21 to Cao 1 905 IV 12 3 CB 60 4 EMF 27 3 C33 SV FM Return fuel Pipe from C23 to Cos 5 159 FL 5 9 AL 51 3 EMF 42 7 Table 4 2 Table with overview of all the component variables in the XPl model Please note that all 26 4 3 THE MODEL Alexander Georgii Hemming Cvon values in this table are fictive A B means low pressure pipe between A and B A gt B means high pressure pipe between A and B A B means pipe between A and B for return fuel 4 3 2 Observation Variables The observation variables can be classified into two different categories DTCs taken from the EMS called Diagnosis Trouble Codes DTC and physical observations The physical observations may have been made by the truck driver prior to entering the workshop or by the mechanic during service Such observations can be for example e Something smell differently than usual maybe burnt e Some abnormal
36. he model presented in this thesis is too complex for exact inference hence an approximate method will be used There is no room for an explanation of how inference work in this thesis For a comprehensive introduction to approximate inference algorithms see Ill 14 Chapter 3 Methodologv In this chapter the methodology used in the thesis will be presented and motivated 3 1 Methods for modeling The model presented in this thesis uses Bayesian networks The main reason why XPI is modeled using BN is that the XPl system is non deterministic and therefore it is suitable to use a BN due to their statistical nature Fault counts for each component are available from which we can calculate the a priori probabilities The set of fault modes for each component are also provided Furthermore BNs are typically well suited for modeling when you have system experts available that can describe the system and help understanding the data 16 Using BNs have been shown to be a convenient methodology for modeling complex system such as ecosystems 17 Another reason why BN was used is that the provider of the project have worked with BN in his licentiate thesisjil Since this thesis is closelv related to the supervisor s work it was natural to use BNs too 3 1 1 Creating the model The model will be presented in the modeling program GeNI eb GeNle is used to create BNs and enables to interact with the model by setting evidence i e setting a
37. he world Unfortunately the data is not formated on any standard format the data have been saved on different formats by different people The reason for this is partially that the data is reported in by mechanics who have no insight in statistics and partially because the mechanics have not been instructed well enough on how they should report the data or that they simple have been ignoring any instructions This results in noisy data For example a mechanic may report that component C is faulty and having the fault mode Leakage when the true fault mode of C actually was cracked or broken CB which led to the symptom named Leakage this results in an incorrect internal fault mode distribution between the fault modes of C therefore certain fault modes has been grouped together The fault modes for the pipes have been changed the mode CB_has been merged into fuel leakage FL since this probably is what the mechanics who reported it meant The fault frequency for the fault mode CB has been merged into electrical fault EF for the component pressure sensor C22 since it probably is what the mechanics meant Some DTCs that are very similar have been grouped together since they are caused by the same fault mode For example some components can lead to multiple DTCs that are caused by electrical faults where the DTCs could be named short circuit to ground and short circuit to battery those DTCs has been merged into one single observation variable
38. hough the values in this table are nothing but calculation based on the original values in figure it is one of the most relevant tables from which we can conclude that the probability that the air pressure in the tube is high is 0 8142 given no information about the condition of the system 11 2 3 BAXESIAN NETWORKS Alexander Georgii Hemming Cvon X pressure X tube X valve P X pressure A iubes X valve High Intact Tightened 0 684 High Intact Leaky 0 126 High Punctuated Tightened 0 004 High Punctuated Leaky 0 0002 Low Intact Tightened 0 036 Low Intact Leaky 0 054 Low Punctuated Tightened 0 076 Low Punctuated Leaky 0 0198 Table 2 6 CPT over different combination of the modes of the three stochastic variables The rightmost column shows the probability for the triple Xpressure Xtube Xvalve The probability in the first row is calculated by P Intact P Tightened P High Intact Tightened 0 9 0 8 0 95 0 684 And the last row is calculated by P Punctuated P Leaky P Low Punctuated Leaky 0 1 x 0 2 x 0 99 0 0198 etc P X pressure X tube X valve P High P Low 0 8142 0 1858 the left column is the sum if the first four rows in table 2 6 are P High P High Intact Tightened P High Intact Leaky P High Punctuated Tightened P High Punctuated Leaky 0 684 0 126 0 004 0 0002 0 8142 and P Low is calculated analogously with the four last rows Table 2 7 This tabl
39. ime however the former notation is the one used in this thesis Let us demonstrate with a simple example Let Xeyen True False be a stochastic variable denoting whether a die throw results in an even number or not let Xjow True False denote whether the value is low number 1 2 or 3 or not It is trivial to see that P Xeven True 3 and P Xiow True 3 respectively Xeven and Xjow are dependent since P Xeven T P Xiow T Ya but P Xeven T Xiow T 1 6 The joint probability distribution for the combination of those variables is shown in table 8 3 Xeven Xiow P Xeven Xlow True True 1 6 True False 1 3 False True 1 3 False False 1 6 Table 2 3 The joint probability table for two stochastic variables The combination of P Xeven True Xiow True yields that the number must be even and either number 1 2 or 3 The only number that fulfills those criteria is the number 2 i e only one number of six fulfills those criteria which yields a probability of 5 P Xeven True Xlow False yields an even number in the range 4 6 which is either 1 number 4 or 6 Two possible outcomes out of six gives the probability 3 The joint probability for two independent variables are the product of their individual probability P A B P A P B Note the important difference when A and B are dependent which yields the inequality P A B P A P B The example presented above shows joint probability
40. ing 22 It has been shown that there are more effective techniques than add one smoothing 23 however this method meets our needs and is very simple to use For a further reading about smoothing methods please bis 3 2 Methods for verifying the model The use of BNs for modeling have steadily increased during the last decades thanks to their suitability for modeling using statistics But few models are verified or validated 16 p 3064 The difference between validation and verification might be hard to distinguish but here is a good definition 3Taken from Scania s statistics program 4This has been done for components C07 C12 C14 C19 C20 C23 C27 C32 C33 C36 C38 which all are component variables presented in table h 2 5Since the model only could behave according to how the XPl svstems in the truck population that the data is taken from have been behaved 16 3 2 METHODS FOR VERIFVING THE MODEL Alexander Georgii Hemming Cvon Validation Are we building the right system Verification Are we building the system right This thesis will perform a verification of the model and not a validation The verification techniques used in this thesis is case based evaluation 27 p 284 In fact two different case studies will be performed one of them supervised i e an expert of the XPl svstem will be present and give his expert opinion on each case result The second is unsupervised without the presence of an XPl
41. ion variables grows exponentially Since some edges in the XPI model have many parents GeNle would have to handle very big CPTs Oo for example has 36 parents Modeling Oy as an ordinary observation node would lead to a CPT with 286 6 8 1010 probabilities Each probability is represented as a decimal_number taking up at least four bytes of memory This would take up a total of 2 x 4 byte 275 GB of memory just for the CPT of Oo1 Thus it is necessary to use some other type of node fre probability table does not grow exponentially one such node is the Leaky Noisy OR Node LNON 2 presented in 31 Definition 4 4 1 Leaky Noisy OR Node A Leaky Noisy OR Node LNON is a node with two modes for example indicating and non indicating It can be set to indicating by any of its parent nodes with the probabilitv P independently of the other parents The probability that an LNON O is indicating is P indC 1 P ind C NF where C is the set of parent nodes to O Giec The LNON not only has a slower growth of its CPTs but also a behavior wanted by most models including the XPI model 83 The behavior the LNONs allow is the possibility that the node is in mode indicating even though none of its parents are faulty The probability of such false negative indications is called the false positive rate FPR It his highly desirable for a system and thus its model to have 3Double in Java is represented as a 64 bit 8
42. ition Englewood Cliffs NJ Prentice Hall 2000 S Easterbrook The difference between verification and validation http www easterbrook ca steve p 2030 2012 Accessed online 2012 06 29 K Korb and A Nicholson Bayesian Artificial Intelligence Chapman and Hall 1 ed sep 2003 J Rintanen Complexity of planning with partial observability in Proceedings of the 14th In ternational Conference on Automated Planning ICAPS 04 pp 345 354 2004 Accessed online 2012 06 21 Wikipedia Paraffin http en wikipedia org wiki Paraffin 2012 Accessed online 2012 11 13 Wikipedia Gibibyte http en wikipedia org wiki Gibibyte 2012 Accessed online 2012 11 13 M Henrion Practical issues in constructing a bayes belief network in Proceedings of the Third Conference Annual Conference on Uncertainty in Artificial Intelligence UAI 87 Corvallis Ore gon pp 132 139 AUAI Press 1987 A Onisko M J Druzdzel and H Wasyluk Learning bayesian network parameters from small data sets application of noisy or gates Int J Approx Reasoning vol 27 no 2 pp 165 182 2001 M Krysander Design and Analysis of Diagnosis Systems Using Structural Methods PhD thesis Link pings universitet June 2006 F van Harmelen V Lifschitz and B Porter Handbook of Knowledge Representation San Diego USA Elsevier Science 2007 48 Alexander Georgii Hemming Cyon 35 M Hen
43. l engine This section will explain how a diesel engine works without the requirement of anv prior knowledge of engines A diesel engine is a combustion engine fueled by dieseld When introduced they were workhorse engines i e powering heavy duty vehicles such as trucks tractors buses and trains B Today nearly 70 of the automobiles on the Swedish market are powered by diesel engines 4 The corresponding number for Europe overall is 50 and in the global market it is predicted to be 12 globally by 2018 5 A combustion engine converts chemical energy in fuel to mechanical energy by burning the fuel which causes motion The combustion which takes place in the engines cylinders creates a small and controlled explosion which pushes the piston in the cylinder down giving it kinetic energy The movement of the piston transfers force to the crankshaft making it rotate Such a combustion takes place in every cylinder in the engine The more cylinders the more mechanical energy the engine creates The volume of the cylinders also affects the power the bigger the more powerful and more fuel consuming For an illustration of the cylinders see figure 2 1 In light to medium duty engines such as cars and small trucks the most common cylinder configuration is the inline six cylinder also called straight six engine In heavy duty engines such as trucks and buses the V6 and V8 cylinder configuration is typically used The V describes the
44. n of the XPI system in section About the X PI system d 5 2 2 BASIC CALCULUS OF PROBABILITV Alexander Georgii Hemming Cvon 2 2 Basic calculus of probability Here follows a very brief repetition on basic probability concepts and calculation readers with a clear understanding of calculus of probability can either skim through this section or continue reading sec tion Bayesian networks For a comprehensive introduction to statistics and probability see 9 2 2 1 Stochastic variables A stochastic variable also called random variable is a variable whose value is not fixed instead its value is described by a probability distribution Stochastic variables are denoted with capital letters Let the stochastic variable X oin represent the outcome of a flip of a coin If we assume the outcome to be completely random the probability of the side facing up is equally distributed between heads and tails The probability that stochastic variable for example Xcoin has a certain value is written P Xeoin heads 0 5 Stochastic variable values are often presented as probability tables see ead Note that the probabilities must sum up to 1 0 P Xeoin heads P Xcoin tails 0 5 0 5 Table 2 1 The probability table for the stochastic variable X oin A stochastic variable can have more than two possible outcomes See table for the probability dis tribution of a die throw here the stochastic variable Xq e has si
45. n tables and the model is fictive However the result and conclusion is based on the original data 4 3 1 Component Variables Deciding which components to include in the model is not an easy task and it is one of the factors that affects the model the most Figure shows the most important components in the XPLsystem but not all The model will include those components together with some other ones In table 4 2 all component variables in the XPI model are re If a component is working correctly it is said to be non faulty NF this mode is left out in table The different fault modes for the components are presented in table la Abbreviation Fault mode IV imbalance or vibration FL fuel leakage CB cracked or broken EF electrical fault SC stuck or clogged WP wrong pressure EMF emission fault AL air leakage Table 4 1 A table presenting the possible fault modes for the component nodes Please note that all values in table are fictive randomly generated since the real values are sensitive for Scania s business Since the data is_fictive the fault mode list for the components may seem strange or illogical If the reasoning in section 1 seams illogical because of inconsistency with the data it is because the conclusion is based on the original data 24 4 3 THE MODEL Alexander Georgii Hemming Cvon Component variable Description P rji Fault modes
46. node to a certain mode after which the model is updated and presents the different diagnoses conditional probabilities given the evidence However it would be intractable to create this model manually due to its size and the aa of some of its nodes Furthermore there is no feature that allows automatic placement of the nodes in order to make the graph planat4 if possible or rearrange the nodes positions such that a minimum number of edges intersects The graph will therefore be made in a graph making program called yED bo which has the wanted feature of node rearrangement Please observe that the yED model only contains the graph used in the BN model it has no probability data This introduces the need of converting the yED model to a GeNIe model and somehow insert the probability data The author of this thesis developed a Java program called yED to GeNle or Y2G for short Y2G takes a yED graph together with XML data files as input and outputs a GeNIe model Continue reading about Y2G in section Generating the model id 1The cardinality is the number of neighboring nodes i e the number of parent or child nodes for some node 2A planar graph is a graph were no edges intersect other than in the endpoint of a node 15 3 2 METHODS FOR VERIFVING THE MODEL Alexander Georgii Hemming Cvon 3 1 2 Analyzing and formatting the data The data used in the creation of the a priori probabilities comes from service workshops all over t
47. odel e g components outside the XPI system which could affect it as mentioned in section Delimitations 12 3 The growth rate of a noisy node QO is N 1 2 3 2M C O 2 2MmasN O MmasN j 0 Where N pa O and Mmaz is the maximum fault mode count of all parent nodes The set of fault modes for each parent node includes the mode non indicating The reason for the factor two is that each conditional probability in the CPT explicitly must define the probability of both the mode indicating and non indicating The reason for the constant two is that LNON has an FPR for the mode indicating and 30 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cyon its complement for non indicating See table hd for an example of the CPT of an LNON note that the parents of an observation variable does not need to have the same amount of fault modes but as stated in definition b 3 4 all component variables have at least two modes one of which is the NF mode Parent Co1 Coa State mo mi NF mo mi ma NF FPR ind Po P 0 Po Ps Pi 0 FPR nind Py Pi 1 P Ps P 1 FPR Table 4 4 The CPT of a noisy observation node O where m is some fault mode and P is some probability preferably high since it is the probability of O indicating a fault given that some if its parents Co and Coa are faulty F PR is the probability of O indicating a fault even though none of its parents are faulty this value is pref
48. of two stochastic variables however it is possible to calculate the joint probability of a set of stochastic variables X The calculation of the joint probability distribution of a set of stochastic variables is the product of the probability for each individual variables 7 2 2 BASIC CALCULUS OF PROBABILITV Alexander Georgii Hemming Cvon in the set or expressed mathematicallv II P X if X X is independent Xex N 1 l 2 1 P X Mz X if X EX is dependent 0 j 0 I P X P Xo T0 we XN 1 ZN 1 2 2 4 Conditional probability Conditional probability expresses the probability of some event A given the knowledge that some other event B is known to have occurred and is denoted as P A B The conditional probability can be calculated according to definition 2 2 3 Definition 2 2 3 Conditional probability The conditional probability between the stochastic variables A and B is expressed by the following equation P A B E where P B gt 0 and P A B is the probability that A and B occurs simultaneously joint probability If A and B are independent then P A B P A i e knowing that B has occurred does not change the probability of A Since the two stochastic variables in section Joint probability distribution 2 2 3 are dependent we can illustrate conditional probability using them Knowing the value of either Xiow or Xeven affects the probability of the other one Given Xeven T
49. ol unit ECU 12 2 3 BAXESIAN NETWORKS Alexander Georgii Hemming Cvon probability The number of probabilities can be generalized to the asymptotic upper bound O 2M O M Where C pac O and M max M C VC pa O In other words the maximum fault mode probability of O s parents raised to the power of the parent count for that OV In other words the size of the CPT grows exceptionally which is an unwanted complexity The exponential growth of CPTs for OVs explained in definition is visualized in table kd In section eee Y it is shown that the exponential growth poses a big problem for the XPlI model as a solution to this another representation of observation variables is presented with a probability table that has polynomial growth Co1 mo NF Co2 mo NF mo NF Co3 mo m3 NF mo m3 NF mo m3 NF mo m3 NF ind Pi Po Ps Py Ps Pe Pr Ps Po Pio Pi Pa nind Pi P P P Ps Pe P Pg Po Po Pu Pi Table 2 8 This is an example of a CPT for an observation variable with three parents note that the fault modes m for a row belongs to the component variable written in the leftmost column The probabilities P are numbers between zero and one and P denotes the complementary probabilities i e 1 P Note that Co1 02 have two fault modes mo and NF and Cog has three thus the number of probabilities are 2 2 2 3 24 O 32 000
50. omponents Oi7 DTC Inj 6 leaking cyl giving incorrect power 9 C20 C32 Qis DTC Inj 1 electrical fault 4 O19 DTC Inj 2 electrical fault or Og DTC Inj 3 electrical fault Osi DTC Inj 4 electrical fault Oz2 DTC Inj 5 electrical fault O33 DTC Inj 6 electrical fault QJQJQJQJQEJAPRQRJEAEJRAJRQJPJAJRJRA o Oas DTC Inj 1 over or under fueling 4 C20 O25 DTC Inj 2 over or under fueling 5 C20 Ox DTC Inj 3 over or under fueling 6 Co0 Oar DTC Inj 4 over or under fueling 7 C20 O28 DTC Inj 5 over or under fueling 8 C20 Oa9 DTC Inj 6 over or under fueling 9 C20 O30 DTC IMV electrical fault C30 O3 DTC IMV has one or several faults C30 Oz2 DTC Plausible leakage in the IMV C20 C37 0O33 DTC Safety valve tripped accumulator pressure above 2800 bar Leakage 0O34 Visual Fuel leakage on pipe between H PCi and accumulator C36 Os Visual Fuel leakage on pipe between H PC and accumulator C37 O36 Visual Fuel leakage on pipe between H PC and accumulator Co O37 Visual Fuel leakage on pipe between H PC and accumulator C39 Oss Visual Fuel leakage on pipe between H PC and accumulator C30 O39 Visual Fuel leakage on pipe between H PC and accumulator C31 O40 Visual Fuel leakage on pipe between EMS coole
51. or developing and updating bayesian belief networks applied to ecological modeling and conservation Canadian Journal of Forest Research vol 36 pp 3063 3074 dec 2006 F Crome M Thomas and L Moore A novel bayesian approach to assessing impacts of rain forest logging Ecological Applications vol 6 no 4 pp 1104 1123 1996 Y Cohen Bayesian estimation of clutch size for scientific and management purposes Journal of Wildlife Management vol 52 no 4 pp 787 793 1988 T C Haas Partial validation of bavesian belief network advisorv systems Artificial Intelligence Applications vol 5 pp 59 71 1991 y Works yed graph editor http www vworks com en products ved about html 2012 Ac cessed online 2012 11 08 Wikipedia Reference class problem http en wikipedia org wiki Reference_class_ 2012 Accessed online 2012 10 10 C D Manning P Raghavan and H Schiitze Introduction to Information Retrieval New York NY USA Cambridge University Press 2008 F C Stanley and J Goodman An empirical study of smoothing techniques for language modeling tech rep Harvard University and Cambridge 1998 C D Manning and H Schiitze Foundations of Statistical Natural Language Processing Cambridge MA MIT Press 1999 D Jurafsky and J H Martin Speech and Language Processing An Introduction to Natural Language Processing Computational Linguistics and Speech Recogn
52. precision Dessv rre finns det ingen s dan ett till ett mappning Modellen m ste s ledes konstrueras med en annan metod Detta examensarbete presenterar en statistisk modell av ett br nslesystem kallat XPI Denna typ av statistiska modell kallas f r ett Baye sianskt n tverk som r l mpligt att anv nda vid modellering av icke deterministiska system Syftet med denna modell r att den ska kunna diagnostisera XPI systemet samt underl tta f rst else f r beroendet mellan komponenter och fel Modellen kan ocks anv ndas f r att utv rdera urskiljbarhet och isolerbarhet hos fel i XPI systemet Alexander Georgii Hemming Cvon Acknowledgement H kan Warnquist XSNS for guidance and feedback Johan Karlander KTH for vour input Anders Lanser KTH for help and feedback on the report Johan Svensson YQN for giving be detailed information about the XPl svstem and feedback about mv model Jonas Biteus YSNS for showing me around at Scania and showing me engines and the XPl svstem physically Joe Mohs NMKB for giving me detailed information about XPI Mikael kerfelt YSNB for giving me the basic knowledge of the components and faults of the XPI system Frida Larsson TIKAB contractor for doing the illustrations of the engine and cylinders Isabella Chowra my wonderful girlfriend for help with graphics Alexander Georgii Hemming Cvon Contents I Introductio 1
53. r and FP C32 Our Visual Fuel leakage on pipe between FM and fuel tank C33 O42 Visual Fuel leakage on pipe between FP and PF C34 Qas Visual Fuel leakage on pipe between fuel tank and SF C35 O44 Visual Fuel leakage on pipe between HPP and acc C36 Continued on next page 28 4 4 GENERATING THE MODEL Alexander Georgii Hemming Cyon Continued OV Type Description Components Qas Visual Fuel leakage on pipe between PF and IMV C37 Qas Visual Fuel leakage on pipe between SV and FM C38 O47 Visual Black smoke from exhaust pipe Could be leaking injector Ci4 19 Table 4 3 Table with the observation variables their identifier type and a short description of each component In the rightmost column is a list of component variables that the observation variable is dependent on Leakage can be caused by any of the following components Co1 03 Co5 06 Cis 21 C23 Ca5_ 38 Leakage HP part can be caused by any of the following components Co1 Cor 19 C23 C26 31 C6 4 4 Generating the model The model was generated using the program called Y2G developed during this thesis as described earlier section Creating the model B 1 1 V2G has a graphical user interface where the user can enter paths to models and data files and make enter some optional settings please see figure 4 3 4 4 1 Leakv Noisv Or Nodes As explained in definition the CPTs for observat
54. re presented in the tables next to the nodes in figure The table next to variable Xpressure is its CPT P Xtube P X valve Intact Punctured Tightened Leaky 0 9 0 1 0 8 0 2 P X pressure X tube X valve X tube X valve High Low Intact Tightened 0 95 0 05 Intact Leaky 0 70 0 30 Punctured Tightened 0 05 0 95 Punctured Leaky 0 01 0 99 Figure 2 5 A small BN describing conditional probabilities of certain faults on a bicycle wheel The BN model of the bicycle wheel consists of the nodes with their a priori probabilities represent ing components the arcs representing dependency and the CP T For a comprehensive introduction to modeling using BN see The a priori probabilities are typically calculated from data but please note that the values in this bicycle wheel example are nothing but guessed values More importantly the values in the CPT of X pressure are also guessed and can not be calculated given the a priori probabilities of its parents Given the tables in figure 2 5 we can calculate the probabilities of all possible scenarios triples Xpressure Xtube X valve in the wheel model The calculated probabilities are presented in table bd From table bd we can derive the total probability for high low air pressure by adding the four different combination which results in high and low air pressure respectively which is done and presented in table 2 7 Even t
55. rion and M Morgan Uncertainty A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis Cambridge University Press 1992 36 Huang and A Darwiche Inference in belief networks A procedural guide International Journal of Approximate Reasoning vol 15 pp 225 263 1996 37 R D Shachter and M A Peot Simulation approaches to general probabilistic inference on belief networks in Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence UAI 89 Amsterdam The Netherlands The Netherlands pp 221 234 North Holland Publishing Co 1990 49 Alexander Georgii Hemming Cvon 50 Appendix A Acronyms LNON XPI Air leakage Bavesian Network Cracked or broken Component variable Conditional Probabilitv Table Diagnosis Trouble Code Electric Control Unit Electrical fault Engine Management Svstem Evidence Pre propagation Importance Sampling Fuel leakage False positive rate High Pressure High Pressure Connector High Pressure Pump Inlet Metering Valve Leakv noisv OR node Maximum parent count Observation variable Non faultv Stuck or clogged Extreme High Pressure Fuel Injection l Alexander Georgii Hemming Cvon 52 Appendix B Notation Here follows a list of the most fundamental notation used in this thesis X A stochastic variable X A set of stochastic variables pa X List of parent nodes to X pa X Size of parent list
56. rm 39 5 1 CORRECTNESS OF THE MODEL Alexander Georgii Hemming Cyon that the qo probability P C29 O29 was significantly higher than P C1g O29 as he already had suspectedH Requirement two The second part of the test was to determine that the model suggests the components in the right order The expert agreed that the model did so In the model the observation Oo was set to indicating the go then proposed the correct set of components to be faulty in an order the expert thought was likely 5 1 2 Test two case studies The model was also evaluated to see that the correct observation variable was indicating for a certain fault on a certain component and that the correct fault mode for the same component was diagnosed when setting the same observation variables to indicating Here follows two measurements of how well the model diagnoses have been defined 83 Definition 5 1 2 Isolable A fault mode mi is isolable from another fault mode m if there exists some observation O such that m is diagnosis but m is not Vi j mi m M O Definition 5 1 3 Detectable A fault mode m is detectable in a model if m is isolable from the mode NF in the model The five most relevant components were studied the components with the highest a priori probability to be faulty that is Those were C20 C23 Coa C13 C148 For each of those five components it was investigated whether or not their most likel
57. rue the probability distribution of Xjow changes Since there are only one even number in the range 1 3 namely number 2 knowing Xeyen True makes it twice as probable that Xiow false since there are two numbers in the range 4 6 that are even namely number 4 and 6 Let T denote True the conditional probability P Xiow T Xeven T is calculated as follows P Xiow T Xeven T _ 1 6 u 2 1 P Xeven T Y 6 3 2 P Xow T Xeven T Conditional probability can comprehensibly be visualized using venn diagrams see figure ka A table of conditional probabilities are called conditional probabilitv table CPT the CPT for the variables in table are presented in table 2 4 Xiow Xeven P XiowlXeven P Xevenl Xiow True True 1 3 1 3 True l False 2 3 2 3 False True 2 3 2 3 False False 1 3 1 3 Table 2 4 The CPT for the two dependant stochastic variables Xjoy and Xeven Note that P Xiow X even P X even X1ow since they are symmetrical 2 3 BAXESIAN NETWORKS Alexander Georgii Hemming Cvon Figure 2 3 Venn diagram for illustrating conditional probability Q is the whole probability space P Q 1 0 A and B _3 are stochastic variables representing events The unconditional probability P A 0 3 0 1 0 12 0 52 and the conditional probabilities are P A B 1 P A B2 rg oo al 0 75 and P A B3 0 The last conditional probability is zero because it is known that B3 has oc
58. s thesis may very well be the first formal measurement of this 3In fact one can say that the top 10 most relevant components was studied since C14 is injector 1 and injector 2 6 are symmetrical with this component Sometimes several components are diagnosed and several of those components fault modes making the probabilities pretty low for each fault mode why 0 10 is a rather high value representing some kind of certainty 40 5 1 CORRECTNESS OF THE MODEL Alexander Georgii Hemming Cvon CV Mmaz Oind P m Oina Cao Electrical fault Oo1 02 O04 Oz24 32 EF 100 C23 Fuel leakage Oo1 04 O33 GeNle error Coz Cracked or broken Oo1 02 Ooa O33 FL 10 CB 44 Cis Fuel leakage O01 04 O33 GeNle error Cia Fuel leakage O01 04 Dor 08 O12 O24 033 O47 GeNle error Table 5 1 Table with the result from the case studies GeNle error means that no result could be obtained because GeNle could not update the belief network due to too high complexity The value of MPC was set to all values in the range 2 10 as an attempt to solve this however it did not matter The second column shows the fault mode with the highest probability The third column shows the set of observation variables having P indicating C mi gt thresholdos when the evidence Ci Mmaz Was set The rightmost column shows the diagnoses made by the model when OVs in O na was set to indicating Furthermore another
59. sible fault mode must have a probability and the sum of all modes must be 1 0 This can be expressed formally as follows each mode M C 1 m M C must have some probability such that P C m 1 0 where MAC is the size of i 0 M C i e the number of possible fault modes of C In the wheel we model three of its components Xhole holds information whether there is any hole on the tube or not Xyawe describes if the air valve is tightened or leaking and Xpressure describes the 20ne could claim that it is an oxymoron to call the mode non faulty a fault mode 10 2 3 BAXESIAN NETWORKS Alexander Georgii Hemming Cvon air pressure in the tube An overview of the variables used in the BN model of the bicycle wheel is given in table 2 5 Note that the non fault mode has been given a more specific name for the sake of comprehensibility Variable Non faulty mode Faulty mode X tube Intact Punctured Xyalie Tightened Leaky Xpressure High Low Table 2 5 This table shows the three component variables in the BN model of the bicycle wheel The non faulty mode has been given a more specific name for the sake of comprehensibility Let X pressure depend on Xhole and Xvalve but the two latter be independent of each other Xnoie and X value have so called a priori probabilities which expresses the probability for each fault modes given no information about the system The a priori probabilities a
60. sions affects the behavior of the model There is plenty of room for improvements of the model primary choosing the conditional probabilities for the observation variables in a better way preferably 44 6 3 FINAL WORDS Alexander Georgii Hemming Cvon together with an XPI expert The work presented in this master thesis will hopefullv be of use for further research about computer assisted troubleshooting 45 6 3 FINAL WORDS Alexander Georgii Hemming Cvon 46 Chapter 7 Bibliographv 10 11 12 13 14 H Warnquist Computer Assisted Troubleshooting for Efficient Off board Diagnosis PhD thesis Link ping Universitet 2011 Accessed online 2012 06 20 T Loboda and M Voortman Genie and smile http genie sis pitt edu 2012 Accessed online 2012 11 01 U D of Energy Just the basics Diesel engine tech rep Office of Energy Efficiency and Renewable Energy 2003 Accessed online 2012 06 29 O Adlercreutz N ra sju av tio bilar en diesel http www teknikensvarld se 2012 05 02 30924 nara sju av tio bilar en diesel 2012 Accessed online 2012 06 29 R Martin Clean diesel vehicles to represent more than 12 percent of global light dut vehicle sales by 2018 http www pikeresearch com newsroom clean diesel vehicles to represent more than 12 percent of global light duty vehicle sales by 2018 2012 Ac cessed online 2012 06 29 Wikipedia Two stroke engine
61. sound e Vibrations made by the engine e Something is visible wrong maybe a pipe is leaking fuel DTCs are either indicating or non indicating The observation variables for the XPl model is presented in table ka OV Type Description Components Oo DTC Accumulator pressure too low Leakage Cor 12 C24 Ov DTC Accumulator pressure too high Leakage Oo3 DTC Accumulator pressure too low due to leakage in the HP part Leakage in HP part Ova DTC Accumulator pressure is excessively high Leakage Oo DTC Pressure sensor faulty C22 Oos DTC Pressure sensor electrical fault C22 Oo7 DTC Engine over speed possible leakage from injectors C14 19 Oos DTC Particulate filter too hot possible leakage inj Cia4 19 Ov DTC Injectors 4 6 electrical fault Ci7 19 Oio DTC Injectors 1 3 electrical fault C1416 O1 DTC Injection error injectors 1 3 Ci4 16 O12 DTC Inj 1 leaking cyl giving incorrect power Cha C20 C32 O 3 DTC Inj 2 leaking cyl giving incorrect power C15 C20 C32 O 4 DTC Inj 3 leaking cyl giving incorrect power Ci6 C20 C32 Oi5 DTC Inj 4 leaking cyl giving incorrect power Ci7 C20 C32 Oig DTC Inj 5 leaking cyl giving incorrect power Cis C20 C32 Continued on next page 27 4 3 THE MODEL Alexander Georgii Hemming Cvon Continued OV Type Description C
62. tLayer layers b graphH eight get HeightO fGraph rootCount rootLayer size b number of extra layers this includes layers of Noisy OR nodes extraLayerCount ceil logM rootCount 1 gt MAX PARENT COUNT logarithm height Per Layer graphHeight extraLayerCount 1 return getLayersRecursive postionData layers rootLayer end function function GETLAYERSRECURSIVE heightPerLayer yCoordinateNextNode layers parentLayer parentCount parentLayer gt Base case for the recursion if parentCount lt MAX PARENT COUNT then return layers end if newLayer 0 nodeT ype null if parentLayer nodeT ype rootN ode then nodeT ype NOISY else nodeType OR end if newLayer NodeCount ceil parentCount MAX_PARENT_COUNT getLayerInfo getLayerIn fo parentLayer leftmostNode getLayer In fo getLe ftmost N ode xCoordinateFirstNodeInLayer leftmost Node get X Coordinate widthO f PreviousLayer getLayerInfo getWidth width Per Node widthO f PreviousLayer newLayer NodeCount 1 aCoordinateNextNode xCoordinateFirstNodelnLayer width Per N ode for 1 newLayer NodeCount do newNode newN ode type xCoordinateNextNode yCoordinateN ext Node newLayer U newN ode xCoordinateN extNode widthPer N ode end for layers U newLayer yCoordinateN extN ode height Per Layer return getLayersRecursive height Per Layer yCoordinateN ext N ode layers new Layer end function 57 TRITA CSC E 2013 008 ISRN KTH CSC E
63. to X M X List of fault modes of X MAX Size of fault mode list 53 Alexander Georgii Hemming Cvon 54 Appendix C Pseudocode Alexander Georgii Hemming Cvon function GENERATEINTERMEDIATENODES bigTrees get BigTrees for all tree bigT rees do leaf tree getLeaf nodeLayers getLayers tree get Roots lower Layer f upper Layer tree get Roots for all nodeLayer nodeLayers do lower Layer nodeLayer countU pper Layer s 0 countLower Layer s 0 child ower Layer get N ode count Lower Layer for all parent upperLayer do if child noisyNode then b Let child be the new child of node parent instead of leaf Copy probabilities and fault modes changeParent parent leaf child end if child addParent parent countU pper Layer if countUpper Layer MAX PARENT COUNT then countU pper Layer lt 0 count Lower Layer if countLowerLayer lt lowerLayer size then child lower Layer get N ode count Lower Layer end if end if end for upper Layer lower Layer end for gt Add bottom layer as parents to leaf node for all parent lower Layer do lea f addParent parent end for end for end function function GETBIGTREES bigTrees 0 for all node nodesWithTooManyParents do tree setO fTrees nodeWithTooManyParents leaf tree leaf leaf purgeParentList bigT rees U tree end for return bigTrees end function 56 Alexander Georgii Hemming Cvon function GETLAYERS roo
64. to understand the system even further as well as to help the supervisor of this thesis H kan Warnquist in his research of automated troubleshooting using mathematical models 1 1 Problem formulation 1 1 1 Goal The purpose of this master thesis is to develop a statistical model of one of Scania s systems called XPI The XPl svstem has not been modeled as thoroughly before hence the thesis s main contribution is to in a correct and accurate manner model this system Where great difficulty lies within defining correct and accurate as well as fulfilling those definitions In other words the model s behavior should mirror that of the real system s More specifically if the XPI system would indicate a certain DTC or physical 1 1 2 THESIS OUTLINE Alexander Georgii Hemming Cyon User Troubleshooter System information System information Diagnoser System to mn diagnoses a i likelihoods troubleshoot Potential ae eee Planner I Performed Recommended actions actions i Figure 1 1 The concept of a troubleshooting framework in this thesis only the diagnoser will be developed The system to troubleshoot is the XPI system the user could for example be a mechanic the system information consists of DTCs and physical observations Image found in L event for a certain fault then so should the model If a set of observations the size of the set could be one would lead to a fault diagnosis bv
65. ually divided between both2 The fault counts for those parts were not merged into the fault count for those components making the imprecise fault counts even more imprecise Some of the weaknesses and in the XPl svstem may already have been fixed since the version of XPI modeled is outdated bv a couple of vears Hoses were treated as pipes which might have been a bad modeling decision since they may behave differently than pipes The decisions made for all challenging problems above mentioned has affected the behavior of the model and probably not always in the best of ways It is difficult maybe impossible to judge which decision is the right one though 6 2 Future work In this section suggestions for how to continue the work is presented Those suggestions includes both improvements on the work presented but also new features and studies Even though the verification of the model presented in chapter Verifying the X PI model 8 showed that the model behaves correctly it is likely that it can be improved The biggest reason to believe this is that all the conditional probabilities and the false positive rates were set by the author together with the supervisor i e no expert of the XPl svstems were consulted during this process due to limited resources It is likely that the model will be even more accurate if those probabilities were set by an XPI expert The components included in the model might be changed maybe it is b
66. umber of times component C has been replaced nothing else It is important to understand that this does not necessarily mean that C has been faulty that amount of times The mechanic that has chosen to replace C may have done so due to the simple fact that they have been instructed to maybe because it is cheap and simple to replace C and that it may fix the problem It has become clear during interviews with experts of the XPl svstem that the pressure sensor C22 is one example of such a component When a DTC that indicates abnormal fuel pressure is observed the standard procedure have during a long time been to replace the pressure sensor first even though it seldom is the culprit Thus the model presented in this thesis is based on data derived from the incorrect fault diagnosis done in the workshops during 2010 and 2011 The assumptions and delimitations regarding the model may also have affected the model Assumption lil is a particularly strong assumption that may be true for some components and false for others Since the fuel passes through the system in linear manner first C then C etc it is quite possible that if C becomes faulty the risk of Cj becomes faulty increases For example if the fuel heater Coa is faulty the risk that the suction filter C24 or the pressure filter C21 clogs is increased In section Analyzing and formatting the data 6 1 9 the data was analyzed and manipulated foremost data was grouped and split
67. ump 23 HPP 24 EMS with cooler A high pressure pipe 8 connects the accumulator to each high pressure connector HPC 12 bringing fuel to the injectors 13 When the solenoid valve in the injector is supplied with voltage the injector opens and fuel is injected into the cylinder Since the XPl svstem operates with high fuel pressure it is important that the fuel is free from water because water leads to corrosion of the components The system tolerance is tight and damaged compo nents could cause the system to not function properly To prevent this water is separated from the fuel in the suction filter 21 If a fault that results in too high pressure occurs the safety valve 9 on the accumulator opens and the fuel is returned to the HPP via the pipe 10 The threshold for this safety procedure is gt 3000 bar and drops the pressure to 1000 bar the safety valve continues to regulate the pressure so that a pressure in the range 700 1300 bar is maintained Excess fuel from the injectors flows from the fuel manifold 16 back to the fuel tank via the pipe 11 The route of the fuel is summarized in figure ME 1A type of electromagnet 42 MODEL ASSUMPTIONS AND DELIMITATIONS Alexander Georgii Hemming Cvon Fuel tank Water Pressure Fuel particle Pressure to Injected in wen separation to 12 bar filtering 3000 bar cylinders Figure 4 2 A summary of what happens in the XPl svstem 4 2 Model assumptions
68. x different values yet again with equal probabilities which they do not have to be Please note that the notation used in table 2 2 has been simplified from P Xaie 1 to P 1 The latter is often used in the literature and will for convenience be used in this thesis o p 3 P 1 PO PB P 4 P 5 P 6 1 6 1 6 1 6 1 6 1 6 1 6 Table 2 2 The probability table for the stochastic variable X qie In both the coin flipping and the die example we have seen probabilitv distributions where the values are discrete However sometimes it is needed or it is convenient to have a continuous probabilitv distribution Since the values are continuous thev can no longer be presented in a table instead a probabilitv function is used The values of both Xcoin and Xqie can be represented with trivial probability functions for example P Xcoin i 5 1 lt i lt 6 When handling multiple stochastic variables it is convenient to express them as a list or a set of stochastic variables A set of stochastic variables is denoted in capital bold font For example let X X1 X2 Xn n N denote a series of die throws where X X denotes the i th die throw 2 2 2 Dependence and independence Stochastic variables can be related by some dependency meaning that knowing the value of one of them affects the probability distribution of the other An example of such dependence could be between the hour of the day an
69. y fault mode Mmar was isolable or not This was done in GeNle by setting the evidence that C was in fault mode Mmax and all other components to the mode non faulty After all the evidence was set it was noted which OVs had the probability P indicating C m gt threshold p s where thresholdors 0 99 those OVs are denoted Oina The value 0 99 was chosen to represent certainty Then the evidence on C was cleared and all the observations in Oina was set to indicating and all other OVs to non indicating After all the evidence was set it was noted whether or not P mfi JOina gt thresholdcomp Where thresholdcomp 0 10 which was chosen to represent certainty E The model used for the results in the table below had an MPC set to 4 Since the model only could handle the first case study due to high complexity the case studies had to be altered The model was too complex for an exact inference algorithm to be able to compute the conditional probabilities probably because some nodes have a lot of parents The alterations done was that the evidence non indicating was removed for all observation nodes not in Oina However this did not help 1The troubleshooting guide available for mechanics today states the reversed which the expert suspected was incorrect now this could be verified by the model 2There is no more precise answer than that since there is no formal way of determining the truth The XPl model presented in thi

Modeling of Fuel Injection System for Troubleshooting

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