Modeling and Troubleshooting with Interventions Applied to an
Contents
1. 1 By To investigate how a repair affects the BN study the exam ple with two components and three observations in Figure 4 Figure 4 a describes the system at time t and the gray node denotes that O is observed In Figure 4 b component 1 is repaired To represent the repair we add a new variable CT dashed that denotes the state of component 1 after the repair Furthermore new variables of and Ox dashed are added to represent the observations related to component 1 after the repair The new component Cr is known to work correctly so evidence is added to this node and mark it with gray The new observations on the other hand have unknown values Fur thermore since the system is paused during troubleshooting the component cr after repair can not cause any new faults in other component nor be affected by any other component Thus even if there is a direct dependency between C and C2 there is no dependency between C7 and Cy Now note that in 3 the probabilities that are computed using the BN are always the probability of an observation o condi tioned on the states of the components after the last repair For the system in Figure 4 for example we may compute the prob ability of any of the observations Ot OF or O2 conditioned on C NF C2 co After the repair of component 1 observe O3 is a request that the planner never will ask and thus the the probability for O3 o3 is not of interest any more Furth2. another approach we begin with the BN describing the system during operation or equally just before troubleshooting begins and update the BN as repairs are performed With the almost two layer structure shown in Figure 1 the probability computations become lore with this approach The details of the computations and updates are presented in Section 4 1 3 5 Assembly Model As mentioned in the beginning of Section 3 an assembly ele ment is a disassemblable part of the vehicle such as the noise shield under the retarder or the oil cooler Each assembly ele ment can be in one of two modes assembled or disassembled We model the relations between assembly elements as a di rected acyclic graph called the assembly graph where each node represents an assembly element To be in the mode assembled all children of the node need to be in the mode assembled and to be in the mode disassembled all parents of the node needs to be in the mode disassembled The assembly state is an assignment of modes to all assembly elements In contrast to the state of the components the assembly state is fully observable 3 6 Modeling Actions When troubleshooting the retarder the mechanic can choose between 70 actions to perform Each action A has a base cost a set of preconditions P and an ordered set of effects E The preconditions are all of the type x where x assembled disassembled and 6 is an assembly element The effects can be to re
3. are measured Figure 5 shows the average of these costs Finding a solution that is guaranteed to be optimal solution requires 620 seconds using a Java imple mentation on a PC but when aborted convergence is reached after 60 seconds aborted optimal 60 80 100 120 140 160 180 abort time Fig 5 The anytime solution at different abort times compared to the optimal solution 6 CONCLUSION Inspired by the application study of the retarder a heavy truck breaking system we have la a decision theoretic ap proach to troubleshooting Focus has been on issues important in real world applications the need for ae the sys tem ue troubleshooting the problem of verifying that the system is fault free and the fact that there are dependencies in between observations and in between components To meet the crucial requirement on short waiting times for the mechanic we have proposed a solution with anytime behavior The solution utilizes the time available to return a best possible troubleshoot ing strategy and converges toward the optimal solution as more time is available We have applied the proposed troubleshooting approach to the retarder and discussed carefully how to model the system and how the troubleshooting is performed There are still several challenging and interesting open ques tions The dependencies in between components and in between faults result in complicated BN structures The BN used he
4. observed the result will be the same until the Gasket on gearbox side C4 is replaced Except that this way of modeling is natural for most of our observations it also prohibit the troubleshooting algorithm from being trapped in cycles where the same observations is made over and over again There may be direct dependencies between observations We assume that all observations that are directly dependent have the same parents This is the case for the two types of dependencies between observations described in Section RS R Gasket Cc 20 Err Oil Oil noise sh Oz 0 L epairOil bun 1 workshop Fig 2 Dependencies are different during operation when ar riving at the workshop and after a repair 3 4 Modeling Repairs Repairs are assumed to be always successful meaning that a component is known to become fault free after repair and that no other faults are introduced during repair However it is not known whether the repair action made the truck fault free since we could have repaired an already fault free component or since we handle multiple faults there may be other components that are still faulty The criterion for ending troubleshooting is that the posterior probability that no fault is present is large enough Either this happens automatically during troubleshooting or it can be verified by performing a verifying observation typically resembling the system and perform a test run Verifica
5. of the root node corresponds to the current system state The system state of a node m with parent node n is the resulting system state of performing an in Sn and having the outcome Un m In a complete troubleshooting strategy the system state of each leaf node is a goal state A goal state is a system state where the probability that the vehicle is fault free is one The action in such a leaf node is the action that restores the vehicle to a fully assembled state If any leaf node of a troubleshooting strategy is not a goal state it is said to be a partial troubleshooting strategy Expected Cost of Repair The expected cost of repair of a troubleshooting strategy 7 rooted in a node n with system state Sn is denoted ECR m Sn This is the expected cost of reaching any leaf node in mn In a node n the probability of reaching the subtree mm rooted in the child node m is the likelihood In jm Let cost an Sn be the cost of performing an in Sn then the expected cost of repair can be expressed recursively as ECR tn Sn cost Gn Sn by ln mECR Tm Sm mEch n Let II s be the set of all possible complete troubleshooting strategies with the system state s in the root then the complete troubleshooting strategy 7 is an optimal troubleshooting strat egy in s if m argminECR z s 5 mEII s The expected cost of repair of 1 is the minimal expected cost of repair ECR s This strategy can be found by at each encountered non
6. or graphs with cycles Artificial Intelligence 124 1 1 30 2000 a e Lang seth and Finn V Jensen Decision theoretic trou E of coherent systems Reliability Engineering amp System Safety 80 1 49 62 2002 Uri Lerner Ronald Parr Daphne Koller and Gautam Biswas Bayesian Fault Detection and Dia am in Dynamic Sys tems In AAAJJIAAT pages 531 53 Nils J Nilsson Principles Ne Intelligence Morgan Kaufmann San Francisco CA 1980 Xavier Olive Louise Trave Massuyes and Herv Poulard AO variant methods for automatic generation of near optimal di agnosis trees In 74th International Were on Principles of Diagnosis DX 03 pages 169 174 2003 Judea Pearl Causality Cambridge 2000 Marta Vomlelova and Ji Vomlel Troubleshooting NP hardness and solution methods In Proceedings of the Fifth Workshop on Uncertainty Processing WUPES 2000 2000 Hakan Warnquist and Mattias Nyberg A heuristic for near optimal troubleshooting using ao In Proceedings of the 19th International Workshop on Principles of Diagnosis 2008 Philippe Weber Didier Theilliol Christophe Aubrun and Alexandre Evsukoff Increasing Effectiveness of Model based Fault Diagnosis a Dynamic Bayesian Network Design for Decision Making In Proceedings of 6th IFAC Symposium on Fault Detection Supervision and Safety of technical pro cesses pages 109 114 2006 Springer Verlag New
7. In the remainder of this section we describe the different models used a Bayesian network for probability computations an assembly model describing the relations between assembly elements and finally the modeling of actions 3 1 Bayesian Network for Troubleshooting We use a Bayesian network BN to model dependencies in the retarder A BN is a directed acyclic graph where variables are represented by nodes and dependencies are represented by directed edges See for example Jensen 2001 for a reference on BN A BN for troubleshooting consists of two types of variables nodes components and observations Components are de noted C and have the two states No Fault WF and Faulty F Observations are represented by variables Oj and represent observations that can be made e g Air leakage at Proportional valve and Engine warning lamp Observations are typically driver s observations observations made in the workshop D1 agnostic Trouble Codes DTC s generated in the ECU during driving or direct observations of components A direct obser vation is obtained by direct inspection of a component whether it is faulty or not In Figure 1 a BN for the retarder during operation of the system is shown The BN is based on engineers expert knowledge and consists of 22 component nodes denoted C1 C22 and 23 observation nodes denoted O O23 Direct observations of components are not shown in Figure 1 3 2 Practical Issues when Buildi
8. Modeling and Troubleshooting with Interventions Applied to an Auxiliary Truck Braking System Anna Pernestal Hakan Warnquist Mattias Nyberg Dept Electrical PAS eae Link ping tears Sweden e mail fannap matny isy liu se Dept Computer Science Link ping University Sweden email g hakwa ida liu se Abstract We consider computer assisted troubleshooting of complex systems where the objective is to identify the cause of a failure and repair the system at as low expected cost as possible Three main challenges are the need for disassembling the system during troubleshooting the difficulty to verify that the system is fault free and the dependencies in between components and observations We present a method that can return a response anytime which allows us to obtain the best result given the available time The work is based on a case study of an auxiliary braking system of a modern truck We highlight practical issues related to model building and troubleshooting in a real environment Keywords automobile industry decision support systems diagnosis diagnostic inference fault diagnosis probabilistic models 1 INTRODUCTION Modern automotive mechatronic systems are often complex products integrating electronics mechanics and software Due to their intricate architecture and functionality they are often difficult to troubleshoot for a workshop mechanic With com puter aided troubleshooting the cost f
9. Table 1 It starts out with a search graph and a partial solution consisting only of the root OR node Until the root node is marked solved an unsolved leaf node in the partial solution is chosen by findUnsolvedLeaf and expanded b expandNode When expanding this node a succeeding AN node is created for every applicable action each with succeeding OR nodes for each possible outcome of these actions Starting from the expanded node and backtracking toward the root the currently best solution is revised in reviseSolution while root is unsolveddo nextNode findUnsolvedLeaf expandNode nextNode reviseSolution nextNode end while Table 1 The AO algorithm A node is marked solved if all succeeding nodes are solved The nodes in the solution are assigned costs in accordance with Proposition where unsolved leafs receive an estimated cost given by a heuristic function h As soon as the root node becomes solved we have a complete solution This solution is optimal if the heuristic function is admissible i e for a node n labeled with the system state sn h n lt ECR sn Nilsson 1980 In the current work the heuristics presented in Warnquist and Nyberg 2008 are used to find optimal and suboptimal solutions are used Anytime Properties Finding optimal troubleshooting for a problem as large as the model of the retarder can be very time consuming Whenever desired by the user the search can be aborted and the currently best p
10. artial solution is returned When this happens the algorithm stops expanding nodes and sets the costs in the unsolved leafs to a upper bound and revises the solution 5 APPLICATION The troubleshooting system described above is implemented and applied to the problem of repairing a heavy truck with a faulty retarder In the implementation the diagnoser is set to disregard diag noses where four or more components are faulty This is done to keep the size of the belief state manageable and is reason able since the probability for several simultaneous faults in the retarder is typically very small In the action planner the size of the belief state is further reduced by only keeping the k most probable diagnoses This method of keeping down the size of the belief state works for our model of he retarder but it is not feasible for larger systems In those cases methods as the one presented in Lerner et al 2000 can be used where the diagnoser collapses similar diagnoses into one To test the troubleshooting system we inject faults in the model of the retarder and simulate the troubleshooting process The time required to find an optimal solution varies greatly depend ing on the initial observations generated by the fault To avoid long waiting times the user can abort the search and perform a suboptimal action instead For a randomly generated test the optimal the optimal expected cost of repair and the ECR when aborted at different times
11. ations and repairs are evidence General Idea The main idea is to use a Bayesian network BN to answer queries in the probability computations How ever as discussed in Section 3 1 repairs change dependencies in the BN and therefore the BN 5 must be updated as repairs are performed during troubleshooting Let 6 denote the BN at time t When troubleshooting begins at time t 1 we initialize the BN to one describing the system during operation For the retarder this BN is shown in Figure 1 and for the small example in Figure 2 it is represented by the leftmost section As repairs are performed we update the BN from 5 to By_1 Let ct cj ch be the component states at time t We have that 1 P c le1z 1 P e e1 1 1 meaning that observations and repairs made at times 1 t 1 do not change the states of the components from time t 1 to time t To simplify notation we omit subscript t on the components when referring to the components in 5 Below we explain how the belief state and then BN are updated as observation and repair events are obtained We do not con sider assemble disassemble events since they do not affect the belief state Observation event First let the event at time t be an observa tion e oj We can then by using 1 update the belief state bt recursively as P o j e 1 4 1 01 1 c b c P clei 1 0 4 _ D Pert where pe is a normalization constant in
12. c The update procedure presented above do not give a BN that describes the current system correctly meaning that we can not pose arbitrary queries However it guarantees the correct answers to the particular queries of the type 3 that we need for our computations Furthermore it tracks and illustrates how dependency relations change in between components during troubleshooting 4 2 Action Planner The task of the action planner is to suggest the next action To decide which action this is the action planner searches for a troubleshooting strategy that if executed to end yields a minimal expected cost of repair given the current system state The time spent calculating a complete troubleshooting strategy would affect the total cost of repair if the mechanic is actively waiting for a response Therefore if required the action planner will terminate early and return the currently most promising partial troubleshooting strategy Troubleshooting Strategies A troubleshooting strategy 7 is a rooted tree in which each node n is associated with an action ay and a system state s The system state consists of the assembly state in node n the events performed at the path to n and the belief state in n sn dn ein bn Associated to each outgoing edge from n to a child node m in the troubleshooting strategy is a possible outcome of an Un m and the likelihood ln m Of having the outcome uy When an is performed in sn The system state
13. ch Graph All possible choices of actions can be rep resented as an AND OR graph with alternating layers of OR nodes and AND nodes The OR nodes are labeled with system states and correspond to decision points where different actions can be chosen The AND nodes correspond to chance nodes where the outcomes of the last action will decide the next OR node Each different choice successing AND node to the OR nodes is a solution to the AND OR graph If the leaf nodes in a solution are all goal states the solution is complete otherwise it is partial There is a one to one correspondence between a solution and a troubleshooting strategy Vomlelova and Vomlel 2000 so a complete solution correspond to a complete trou bleshooting strategy and partial solution correspond to a partial troubleshooting strategies The size of the AND OR graph is highly exponential but by using heuristic search algorithms such as AO Nilsson 1980 not the entire graph needs to be explored to find an optimal solution Since observations are modeled such that they cannot be re peated and repairs always are successful the search graph is acyclic when only applicable actions are considered If we wish to relax any of these assumptions the search graph may become cyclic However there are variants of the AO algorithm such as the CFC rey algorithm that can treat cyclic graphs Jim nez and Torras 2000 Algorithm The main parts of the AO algorithm are shown in
14. dependent of c and by_1 is the belief state at the previous time step To determine the third term in 2 P oj c e1 4 1 3 we use the BN 6 Due to the almost two layer structure of the BN this probability is often easily computed In particular in where O has no direct dependencies to other components it is simply the conditional probability for the observation O that can be directly found in By Fig 4 Schematic picture of the change of the BN when repair ing component C4 Repair Now let the new event be the repair of component i Repairing a component means that we force the component to be fault free by intervention rather than observing it as being fault free Therefore it is not sufficient to only add the evidence Ci NF to the BN The difference between interventions and observations is carefully discussed in Pearl 2000 Using the nomenclature from Pearl 2000 we write do C NF to denote repair of component 7 After a repair we update the belief state as b c P clei 1 do C NF if c F if c NF 4 n j j Fh and F 0 bate b1 where 1 This means that c and are the same assignments of component states except for component j which is faulty in and fault free in c by the condition in 4 Updating the BN When the event is an observation depen dencies between nodes in the BN are not affected and we keep the current BN Bi
15. e of the assembly elements its cost and its effects An effect is either an observation a repair or a mode change of an assembly element and generates a request to the mechanic gt N E er y X v F F oo gt a X y S S 3 s X Re we ro s LA a Ri g aL x se S gL S K s s ne S S s amp y g Ka g x gt e g gt x a g g o v oa g 3 S gt x A LP ise FA N Ss ai lt S d e S X E S S SF SF eg all NSl SF SF CF S SF FY S amp S SY S S PT MF WM FT PF FX XQ SF PF KF LF STF KF KF ST FF Ke QS SESS BEPRN q Ia ISS TASS Y SSE SSS Oo SOF RSS SPSS cS a AANS LLA SSS ISSS AS SR lt SS KK lt S n a PR NIYII gt 5 A xw g Ra S Q fod Ba v v 5 ad Ra Ne N gt gt P amp RO amp i amp RS SS X x Ry s os D Pa amp s Aa sl amp K g x S s s S s Fo amp g s lt sF S gt gt Fe S 3S SS lt gt X K Q Y j x S g D a S s I oe Kii S 3 FY So amp eS ee SF s SS SF SM we S S amp F F S a Cg S e y P F OS RS N A O A SK V x ye g xX eS ES SS FM Oo Ss Ss S S oe SS S S ve SS oe ST LO 9 Fig 1 A Bayesian network for the retarder In the paper we use capital letters for variables and lower case letters for their values e g C c Vectors are written in bold face For probability distributions we write P c to denote the probability that C c For variables in all kinds of graphs pa X denotes the parents of X and ch X denotes the children of X
16. ermore probabilities of the type 3 are conditioned on the complete vector of component states Therefore no old observations will be of interest unless they are direct causes of the new observations By the assumptions on the observations in Section 3 3 only observations that have the same parents are allowed to have direct dependency relations Thus there is always a new copy of the observations that are children or parents of an observation of a component after repair This leads to that there are nodes in BN 4 b that will never be used In Figure 4 c nodes and dependencies that will be used in computations after the repair of component 1 are marked with bold lines Since we always consider queries of the kind 3 we can safely remove the nodes that are not used in future computations Re moving these unused nodes from Figure 4 c gives Figure 4 d Now if in Figure 4 d we rename the nodes Cy OF and OF to C1 O1 and O3 we obtain the BN 5 to be used for next evidence Instead of introducing new nodes for variables deleting old nodes and updating node names as in Figure 4 we can sum marize the BN updating in the following four steps taken when a repair of component 2 is performed i Update the belief state with the repair action C NF according to 4 ii Add evidence C NF iii Remove edges between C and all other components both incoming and outgoing iv Remove evidence from all observations O ch
17. goal state choose an action a such that the expected cost of repair becomes minimal Proposition 1 Minimal Expected Cost of Repair Let n be the root node of a troubleshooting strategy with the action an and the system state sn Then the minimal expected cost of repair in Sp is ECR sn min cost an Sn 5 ln mECR sm an mEch n Applicable Actions Not all actions need to be considered when deciding candidates to be included in the optimal trou bleshooting strategy We only need to consider actions that can affect the belief state part of the system state These actions are applicable actions Applicable actions in a system state must be actions that repair faults with a marginalized probability greater than zero or makes observations that are causally dependent on such a fault Composite Actions The preconditions are not considered when finding applicable actions This is not needed since as stated in Section 3 6 there exists exactly one action that assem bles or disassembles each assembly element This means that there is a unique way to fulfill all preconditions A composite action is created by combining actions that fulfill the non fulfilled preconditions of the original applicable action The cost preconditions and effects of these actions are added to the cost preconditions and effects of the original action This allows us to ignore all preconditions and focus on the desired effects without losing optimality Sear
18. ith the system and complicates the probability computations further see e g Pearl 2000 Third not all parts of the retarder can be reached without first disas sembling other parts of the system This means that the level of disassembly and the extra time required for disassembly and assembly actions needs to be considered in the solution During troubleshooting the aim is to guide the mechanic by finding the next repair or observation such that the expected repair cost is minimized Here the troubleshooting problem is formulated as a decision theoretic problem The troubleshoot ing system consists of an action planner and a diagnoser In the diagnoser probabilities for combinations of faults are com puted using a BN Supported by Scania CV AB IVSS and Vinnova VICT In the planner the probabilities are used to solve a general search problem in an AND OR graph An optimal solution is guaranteed if sufficient computing time is allowed Since total repair time is crucial and longer waiting times for the mechanic is generally not acceptable the time to find the solution i e the next action for the mechanic is crucial Therefore we emphasize on the anytime behavior of the proposed solution That is the proposed solution quickly computes an action leading to an acceptable repair cost and also that for every additional computation time allowed the expected repair cost is considerably reduced by optimizing the choice of the next ac
19. mponents at different times illustrates that components do not change unless repaired The arcs between observations mean that we can only perform an observation once as described in Section 3 3 After repairing a component its related observations can be performed again Sometimes the observations need a test drive in practice We assume that time time scale for faults to affect observations is short in relation to the time for a component to affect other components to be faulty Therefore we can still use our assumption that no new faults appear during troubleshooting In Breese and Heckerman 1996 probability updates with in terventions are handled using so called persistence networks where mapping nodes are used to track dependency changes In Langseth and Jensen 2002 computing probabilities with interventions are avoided since it is assumed possible to al ways verify the consequence of the repair Another attractive 1 This assumption can be relaxed in the framework but may lead to non optimal troubleshooting Troubleshooting system Action Planner Diagnoser mechanic Fig 3 The troubleshooting system approach in diagnosis is to utilize Dynamic Bayesian Network DBN see e g Weber et al 2006 However in our settings interventions the change of causality and the fact that an obser vation is the same until one of its parents is repaired complicates the application of DBN In the current work we take a
20. nd assemble d disassemble The mechanic returns the outcome of the request The outcome of a request is called an event and is either that C is repaired the values O o of the observation or that they system is assembled disassembled To be able to determine the next action the planner creates a conditional plan of actions called a troubleshooting strategy and uses the diagnoser to predict the outcome of future actions The diagnoser uses the BN to compute the probability distribu tion over possible combinations of component states given all events The probability distribution over the component states is called the belief state If an assignment of component states to all components has probability larger than zero is called a diagnosis 4 1 Diagnoser The planner sends the previous belief state i e the probability distribution b P c e1 _1 and the ordered set e1 4 e1 e of events up to and including the last event to the diagnoser The diagnoser determines the current belief state by41 As described in Section 3 6 an action can lead to a sequence of requests and thus a sequence of events In the diagnoser events are handled recursively and it is sufficient to study the probability updates for one event at the time We use the convention that a time step is taken after each new evidence In accordance with e g Jensen 2001 we call an assignment of a variable in the BN an evidence Events concerning observ
21. ng BN for Troubleshooting In most cases components are parents to observations How ever there are deviations from this structure which complicates the troubleshooting task Components There are several ways to choose the compo nents in the BN The maximum size of components are sets of parts of the retarder that always are repaired together also called minimal repairable unit Choosing larger components may lead to that more parts than necessary are replaced during troubleshooting Choosing smaller sets of parts of the retarder as components in the BN is possible but gives worse perfor mance in the troubleshooting algorithm and may give more parameters that need to be determined in CPT s Here we choose components to be minimal repairable units Furthermore we allow several components to be faulty at the same time Driver or Mechanic Observations concerning the perfor mance of the vehicle for example the braking torque can be obtained by asking the driver or by letting the mechanic per form a test drive In general the answer from the mechanic is less uncertain but is often obtained at a higher cost since it is more expensive to let the mechanic perform a test drive than interviewing the driver The driver s answers can only be obtained at the beginning of troubleshooting It may be the case that the driver s answers bias the mechanic For example if the driver complains about uncontrollable braking torque it is reasonable
22. or troubleshooting and repair can be reduced and less experienced mechanics can be supported during their work Inspired by an application study of an auxiliary heavy truck breaking system called the retarder we develop a novel de cision theoretic approach to troubleshooting The objective is to find a sequence of repairs and observations that leads to a fault free truck at lowest expected cost Earlier application studies typically consider electronic systems such as printers and electronic control units Heckerman et al 1995 Langseth and Jensen 2002 Olive et al 2003 In comparison with these earlier application studies the automotive mechatronic system considered here imply that the solution to the trou bleshooting problem needs to take a number of additional issues into account First in automotive mechatronic systems it is not as straight forward to determine whether a repair have solved the problem In the previous works it is assumed that after each repair it is verified whether the system is fault free or not Such a veri fication is often expensive in automotive mechatronic systems and therefore it is not presumed in the present work This means that we need to compute probabilities after interventions i e af ter changing the system with the repairs Second automotive mechatronic applications typically contains dependencies in between faults that arise during operation These dependencies change when intervening w
23. pair a component C repair C to ob serve the value of an observation O in the Bayesian network observe Q or to assemble or dissassemble an assembly ele ment 6 assemble d or disassemble 6d For each component C there is at least one action with the effect repair C and for each observation O in the BN there is at least one action with the effect observe O For each assembly element 6 there is exactly one action with the effect assemble 0 and exactly one action with the effect disassemble 0 For example the action Replace Oil Pressure Sensor A7 has base cost cost A7 175 preconditions P A7 4 disassembled dg disassembled and effect E A7 repair C7 Actions can have more than one effect e g when the mechanic removes the noise shield the observation Oil on noise shield O25 will be made even if this was not the reason for removing the noise shield Therefore the ac tion Remove noise shield Agz is modeled with the effects E A62 disassemble dz observe Oo5 4 TROUBLESHOOTING SYSTEM The troubleshooting system consists of two subsystems the di agnoser and the action planner see Figure 3 The actionplanner determines the next action so that the expected cost of repairing the vehicle becomes as low as possible and the suggests the request caused by that action to the mechanic As described in Section 3 requests are operations to be applied to the truck such as repair C observe O a
24. re is still fairly simple and in our future work we will investigate how interventions can be modeled in even more general BNs The results from simulations with noisy parameters show that parameters may deviate a little from their nominal values but in our future work we will also ask us whether deviations in certain parameters have larger impact on the result than others Other interesting open questions are how to determine parame ters in the BN Furthermore one challenge is the dimension of the belief state which increases exponential with the number of components We are currently working on methods for focus ing on the most probable diagnoses in the diagnoser without risking to loose diagnoses with small probabilities in the first time steps The results presented are promising and show that computer aided troubleshooting can be applied to complex mechatronic systems such as the retarder We look forward to extend our algorithm to troubleshoot even larger systems REFERENCES John S Breese and David Heckerman Decision theoretic troubleshooting A framework for repair and experiment In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence 1996 David Heckerman John S Breese and Koos Rommelse Decision theoretic troubleshooting Communications of the ACM 38 3 49 57 1995 Finn V Jensen Bayesian Networks York 2001 P Jim nez and C Torras An efficient algorithm for searching implicit and
25. that the mechanic will be influenced and observe the same symptom with higher probability This case is modeled as a dependency between the observation nodes see O4 and O3 in Figure for an example Several Observations of Same Component Some components can be observed at several places for example the cable be tween the retarder and the ECU can be observed both at the ECU O19 and at the retarder O29 They are two different obser vations since they need two different assembly states However there is a dependency between the two observations since if the cable is found broken at the ECU it is less likely to be damaged at the retarder also Perception In some observations there may be uncertainties For example the observation Leakage air tube O14 can be mistaken for Leakage air valves O15 We model this by adding dependencies from both components tube and valve package that can be mistaken for We give these observations three possible values Sure Ambiguous and No leakage 3 3 Modeling Observations An observation is an indicator of faults in a subset of the components which are modeled as parents to the observation node There may be false indicators as well as missed faults When an observation is performed evidence is added to the corresponding node The value of an observed observation is assumed to be the same until at least one of its parent components is repaired For example if Oil on cooler Og is
26. tion We begin by presenting the retarder system and discussing modeling issues in Sections 2 and 3 We then present the troubleshooting system in Section 4 before summing up with application results in Section 5 2 THE RETARDER The retarder is an auxiliary hydraulic braking system that al lows braking of the truck without applying the conventional brakes It consists of a mechanical system and a hydraulical sys tem and is controlled by an electronic control unit ECU The retarder generates breaking torque by letting oil flow through a rotor driven by the propeller axle causing friction The kinetic energy is thereby converted into thermal energy in the oil that is cooled off by the truck s cooling system At full effect and high rpm the retarder can generate as much torque as the engine The retarder which is a representative system of heavy duty trucks is difficult to troubleshoot due to its complexity and the combination of both mechanical hydraulical and electronical components 3 MODELING FOR TROUBLESHOOTING The retarder is a set of components which may be faulty or fault free and which can be repaired During troubleshooting the retarder often must be assembled or disassembled For example to replace the oil pressure sensor the retarder oil needs to be drained and the oil cooler needs to be removed Each such disassemblable part is called an assembly element An action is variable defined by its requirements on the stat
27. tion is often expensive and it can not be assumed that verification is made after each repair Faults can only appear during operation of the system During troubleshooting the system is paused and no new faults can appear This also means that causal dependencies between faults are different during operation and at the workshop This in combination with the fact that we not presume verification after repair force us to handle interventions in the BN This is further illustrated in the following example Consider the causal graph in Figure 2 which describes a sub part of the retarder In Figure 2 nodes represent observations components and repairs and edges denote causal dependen cies In the retarder a faulty Oil Cig may cause the Radial Gasket at gearbox C9 to brake during operation When the truck arrives at the workshop the observation Erroneous Oil O21 will change our opinion about in the Radial Gasket at gearbox However after replacing Oil repair of C19 there is no longer any dependency between the Oil and the Radial Gasket until the retarder has been run again In Figure 2 the three different sections represent different situations The leftmost section denoted trun shows dependencies during operation the middle section tworkshop shows dependencies when the truck has just arrived to the workshop and the rightmost section trepairoitt Shows dependencies after repair of Cig In the peut dependencies between co
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