# Study on Fault Diagnosis Method and Application of Automobile Power Supply Based on Fault Tree-Bayesian Network

Authors: Chunhua Zhang; Wen Fang; Baopeng Zhao; Zhen Xie; Changning Hu; Hongzhuan Wen; Tao Zhong
Journal: Security and Communication Networks
 (2022)

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## Abstract

Among various fault types of automotive power faults, power supply UB + faults have the most complex relationship between fault signs and fault points and are difficult to diagnose. So this paper proposes a Bayesian network fault diagnosis model of automobile power supply based on fault tree. Firstly, based on the in-depth analysis of the principle of automobile power supply fault, the UB + fault tree model is constructed. The fuzzy Bayesian network model of UB + fault is constructed through the mapping relationship between fault tree and Bayesian network. Then, the prior probability of UB + fault points are obtained according to the five-year fault dataset of FAW Volkswagen Reck system, and the relevant conditional probabilities are determined by fuzzy set theory due to the lack of data and the uncertainty in expert scoring. Finally, the relevant fault point probability values are determined according to the Bayesian network inference algorithm in the case of single or parallel UB + fault sign occurring, and the fault diagnosis sequence is guided, further improving fault diagnosis efficiency.


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## Body

## 1. Introduction

The vehicle power supply system is a fundamental part of the vehicle structure, and is also the basis for the proper operation. All types of vehicle electronics are inseparable from the power supply. The rapid development of automotive electronics and equipment has brought more comfort and convenience to car user. Meanwhile, automobile power supply systems are becoming more complex and UB + faults are becoming more difficult to monitor. As power supply is a prerequisite for the normal operation of a vehicle, when a total vehicle failure occurs, there is very limited reference information to draw from and few aids to collect information, making it even more difficult to diagnose power supply failures quickly and accurately, so research into methods for diagnosing vehicle power supply failures is of great significance for efficient maintenance and safe operation of vehicles.Machine learning is a popular direction for research in various fields in recent years, and fault diagnosis through machine learning-related algorithms is also a hot spot for current research. In the literature [1], a fault diagnosis method based on convolutional neural network was proposed. In the literature [2], an improved BP neural network algorithm for automotive engine fault diagnosis was proposed. Bayesian network models are also a hot direction currently applied to fault diagnosis. The literature [3] summarizes four types of fault diagnosis applicable to the application of Bayesian networks, which provides a normative framework for the application of Bayesian networks in fault diagnosis. In the literature [4–6], the application of fault tree and Bayesian network algorithm in the field of fault diagnosis of medical equipment and large mechanical equipment is proposed. In the literature [7–9], a method of constructing Bayesian network for automotive fault diagnosis by combining expert knowledge and a large amount of data statistics is proposed. In the literature [10–12], the fault tree model was established by analyzing the fault distribution characteristics from three aspects: overall fault, fault type and high-frequency fault causation, and the posterior probability of each fault was estimated by using Bayesian network. In the literature [13, 14], a modeling method of Bayesian network model was proposed, which can accurately and effectively carry out the fault prediction of complex equipment. In recent years, based on fault trees and fuzzy calculations have been gradually applied to the fault diagnosis of complex equipment. In literature [15, 16], a fault factor preference method is proposed by fuzzy calculation of fault importance. In literature [17], a fault diagnosis model for complex equipment based on fuzzy Bayesian networks is proposed. This paper focuses on the fault factors of the automotive power start power supply system, establishes a fault tree, which is then transformed into a Bayesian network, and uses fuzzy set theory methods to determine the probability of occurrence of fault points, providing a new idea for the diagnosis of automotive power start power supply faults.


## 2. Fault Tree Analysis of Automotive Power Supply System

### 2.1. Fault Principle Analysis of Automobile Power Supply System

This paper analyzes the power supply mechanism based on the Volkswagen MAGOTAN B7 model and the starter control circuit (as shown in Figure1). After the driver steps on the brake pedal and presses the ignition switch, the engine control unit (J623) will check the vehicle real-time data. It mainly includes the electronic steering column locking device control unit (J764), the electronic ignition switch (D9) and P/N signals, etc. When all start conditions are met, J623 controls the grounding circuit of the 50 power supply relay (J682) and power supply relay 2 (J710). At this time, the two relay coils of J682 and J710 are energized and the switch is closed. The power supply line is connected between the starter and the battery. The starter circuit is connected and starts to work, thereby providing the initial power source for the engine to start.Figure 1
Logic diagram of automobile power supply system.According to the summary and induction of fault characteristics of engine power supply system, the main causes of engine power supply system fault are component fault and line fault. This section makes a detailed analysis of the faults that lead to the starter not working, and combs the causal logic relationship, so as to provide a basis for the construction of fault tree of engine power supply system.


### 2.2. Establishment of Fault Tree of Automobile Power Starting Power Supply System

Fault tree is a method to describe the logical relationship of various events in the system with the tree view of causality. The method consists of logic gates, input events and output events. The logic gate represents the logical judgment whether the result is caused by one cause or multiple causes, the input event represents the cause, and the output event represents the result. There is a strong hierarchical relationship between the structures of automobile starting power supply system. This set of causal logic tree diagram can intuitively and effectively analyze the complex composition structure of the system. Now we invite two experts in automobile fault diagnosis technology and two national technical experts in automobile maintenance to sort out the logical relationship between the faults of automobile power supply system, as shown in Figure2.Figure 2
Fault tree of automobile power supply system.There are many subphenomena of vehicle system fault. For example, press the remote control to unlock the vehicle, and the double flashing light does not light up. After inserting the key, the key cannot be pulled out. Turn on the ignition switch, the middle display screen does not display, the steering column does not unlock, the steering column can unlock but not lock, the radio does not work, and the instrument does not light up. Display of various fault indicators after the instrument is normally lit. Start the engine and the engine makes a clicking sound. The starter cannot be turned again after turning once, etc., during the troubleshooting process, the technical experts will quickly lock down the nonworking parts based on one or more combinations of subphenomenon (fuse, relay, ECU, sensor, and actuator), so as to quickly narrow the fault diagnosis range, finally find the fault point Combined with multimeter (circuit fault or component fault).Fuse (SC10)-relay (J682) line break as an example for troubleshooting. First of all, when the driver starts the engine, he finds that the starter does not rotate, turns on the ignition switch, the instrument display is normal, and the steering column can be unlocked and locked normally. Use a multimeter to measure that the voltage of T1v section of the starter is 0V in the starting gear (normally it should be the battery voltage). It is known that the battery does not supply power to the starter in the starting gear. Search from the battery section, connect the relay detection tee test line, measure the terminal voltage of J710-87# (5#) to be 0V in the starting gear, and measure the terminal voltage of J710-30# (3#) to be 0V in the starting gear. Then look for the battery section, measure the terminal voltage of J682-87# (5#) to be 0V in the starting gear, and measure the terminal voltage of J682-30# (3#) to be the battery voltage in the starting gear. At this point, it can be known that the J682 relay does not supply power to the J710 relay, but the J682 has power input. It can be seen that the J682 relay is faulty, but it is necessary to continue to check whether the J682 coil is working normally. After turning on the ignition switch, use a multimeter to measure the J682 relay 1#. The terminal voltage is 0V. Looking at the circuit diagram, it is known that J682-1# is powered by the SC10 fuse, and the voltage on both sides of the SC10 fuse is the power supply voltage. At this time, it can be basically concluded that there is an open circuit in the line from SC10 fuse to J682-1# terminal. However, in order to further confirm the fault, it is necessary to turn off the ignition switch, disconnect the negative cable of battery (when the multimeter uses resistance gear for measurement, it can’t be measured with points), and measure the resistance of the line from SC10 fuse to J682-1# terminal as infinity. At this time, it can be determined that the fault point is the open circuit between SC10 fuse and J682-1# terminal.


## 2.1. Fault Principle Analysis of Automobile Power Supply System

This paper analyzes the power supply mechanism based on the Volkswagen MAGOTAN B7 model and the starter control circuit (as shown in Figure1). After the driver steps on the brake pedal and presses the ignition switch, the engine control unit (J623) will check the vehicle real-time data. It mainly includes the electronic steering column locking device control unit (J764), the electronic ignition switch (D9) and P/N signals, etc. When all start conditions are met, J623 controls the grounding circuit of the 50 power supply relay (J682) and power supply relay 2 (J710). At this time, the two relay coils of J682 and J710 are energized and the switch is closed. The power supply line is connected between the starter and the battery. The starter circuit is connected and starts to work, thereby providing the initial power source for the engine to start.Figure 1
Logic diagram of automobile power supply system.According to the summary and induction of fault characteristics of engine power supply system, the main causes of engine power supply system fault are component fault and line fault. This section makes a detailed analysis of the faults that lead to the starter not working, and combs the causal logic relationship, so as to provide a basis for the construction of fault tree of engine power supply system.


## 2.2. Establishment of Fault Tree of Automobile Power Starting Power Supply System

Fault tree is a method to describe the logical relationship of various events in the system with the tree view of causality. The method consists of logic gates, input events and output events. The logic gate represents the logical judgment whether the result is caused by one cause or multiple causes, the input event represents the cause, and the output event represents the result. There is a strong hierarchical relationship between the structures of automobile starting power supply system. This set of causal logic tree diagram can intuitively and effectively analyze the complex composition structure of the system. Now we invite two experts in automobile fault diagnosis technology and two national technical experts in automobile maintenance to sort out the logical relationship between the faults of automobile power supply system, as shown in Figure2.Figure 2
Fault tree of automobile power supply system.There are many subphenomena of vehicle system fault. For example, press the remote control to unlock the vehicle, and the double flashing light does not light up. After inserting the key, the key cannot be pulled out. Turn on the ignition switch, the middle display screen does not display, the steering column does not unlock, the steering column can unlock but not lock, the radio does not work, and the instrument does not light up. Display of various fault indicators after the instrument is normally lit. Start the engine and the engine makes a clicking sound. The starter cannot be turned again after turning once, etc., during the troubleshooting process, the technical experts will quickly lock down the nonworking parts based on one or more combinations of subphenomenon (fuse, relay, ECU, sensor, and actuator), so as to quickly narrow the fault diagnosis range, finally find the fault point Combined with multimeter (circuit fault or component fault).Fuse (SC10)-relay (J682) line break as an example for troubleshooting. First of all, when the driver starts the engine, he finds that the starter does not rotate, turns on the ignition switch, the instrument display is normal, and the steering column can be unlocked and locked normally. Use a multimeter to measure that the voltage of T1v section of the starter is 0V in the starting gear (normally it should be the battery voltage). It is known that the battery does not supply power to the starter in the starting gear. Search from the battery section, connect the relay detection tee test line, measure the terminal voltage of J710-87# (5#) to be 0V in the starting gear, and measure the terminal voltage of J710-30# (3#) to be 0V in the starting gear. Then look for the battery section, measure the terminal voltage of J682-87# (5#) to be 0V in the starting gear, and measure the terminal voltage of J682-30# (3#) to be the battery voltage in the starting gear. At this point, it can be known that the J682 relay does not supply power to the J710 relay, but the J682 has power input. It can be seen that the J682 relay is faulty, but it is necessary to continue to check whether the J682 coil is working normally. After turning on the ignition switch, use a multimeter to measure the J682 relay 1#. The terminal voltage is 0V. Looking at the circuit diagram, it is known that J682-1# is powered by the SC10 fuse, and the voltage on both sides of the SC10 fuse is the power supply voltage. At this time, it can be basically concluded that there is an open circuit in the line from SC10 fuse to J682-1# terminal. However, in order to further confirm the fault, it is necessary to turn off the ignition switch, disconnect the negative cable of battery (when the multimeter uses resistance gear for measurement, it can’t be measured with points), and measure the resistance of the line from SC10 fuse to J682-1# terminal as infinity. At this time, it can be determined that the fault point is the open circuit between SC10 fuse and J682-1# terminal.


## 3. Fault Diagnosis of Fuzzy Bayesian Network Based on Fault Tree Analysis

Bayesian network is a directed acyclic graph based on probabilistic reasoning, it is represented by the symbol B (G, P), where G represents the structure of random variable nodes, that is Bayesian network topology.P represents the probability of directed edges, which is described by conditional probability [14]. Bayesian network can analyze the dependence and correlation strength through the joint probability distribution of variable set, which is suitable for the reasoning of uncertain fault problems in automobile starting power supply system [16]. In the transformation from fault tree to Bayesian network, each event of fault tree corresponds to each node in Bayesian network, and logic gate is transformed into directed edge and conditional probability of Bayesian network. In the transformation between fault tree and traditional Bayesian network, the conditional probability is determined according to the setting of logic gate; in the transformation between fault tree and fuzzy Bayesian network, the conditional probability is no longer determined according to the setting of logic gate. Rather, there is a vague probability.According to literature [18], the specific steps of transforming fault tree into fuzzy Bayesian network are as follows:Step 1: the basic event, intermediate event and top event of the fault tree corresponding to the fault layer node, symptom layer node and state layer node of the fuzzy Bayesian network, respectively. The repeated events in the fault tree are combined into one node.Step 2: convert the logic gates in the fault tree into the directed edges of the fuzzy Bayesian network, and determine the relationship of logic gates between nodes.Step 3: the probability of occurrence of basic events in fault tree is replaced by the prior probability of fault layer nodes in Bayesian network.Step 4: the degree of influence between events in the fault tree are expressed as a conditional probability in a fuzzy Bayesian network.Table 1
Interpretation of Bayesian network nodes.
Node codeNode nameStatus valueState descriptionμ31Access and start permission button01NormalAbnormalμ32Central control unit for comfort/convenience systems01NormalAbnormalμ33Engine control unit01NormalAbnormalμ34Electronic steering column locking device control unit01NormalAbnormalμ35Starting relay 101NormalAbnormalμ36Starting relay 201NormalAbnormalμ3715 relay01NormalAbnormalμ38Data bus diagnostic interface control unit01NormalAbnormalμ39Gear signal01NormalAbnormalμ21Press the remote control to unlock, and the double flashing light does not light up01NormalAbnormalμ22Parking lights do not work01NormalAbnormalμ23Turn on the ignition switch, the meter does not light up01NormalAbnormalμ24Turn on the ignition switch, the middle display does not work01NormalAbnormalμ25Turn on the ignition, steering column unlocked01NormalAbnormalμ26Insert the key, the key cannot be pulled out01NormalAbnormalμ27Brake pedal lamp does not work01NormalAbnormalμ28EPC light does not work01NormalAbnormalμ29The gear indicator flashes01NormalAbnormalμ210ESP normally on01NormalAbnormalμ211Abnormal noise of throttle01NormalAbnormalμ212Fan normally turns01NormalAbnormalμ213The starter rattles when starting01NormalAbnormalμ214The starter cannot be started again after being started once01NormalAbnormalμ215Engine fault light is delayed01NormalAbnormalμ216EPC, engine fault light flashing01NormalAbnormalμ217The instrument display is normal01NormalAbnormalμ218The instrument displays antitheft activation01NormalAbnormalμ219The steering column can be locked and unlocked normally01NormalAbnormalμ220The steering column can be unlocked but not locked01NormalAbnormalμ221The instrument shows that the direction lock is abnormal01NormalAbnormalμ222All fault lights on the instrument are on01NormalAbnormalμ223The instrument shows that the gear is not in the P/N gear01NormalAbnormal


### 3.1. Establishment of Fuzzy Bayesian Network for Automobile Power Supply System

According to Figure2, the above number of failures and fuzzy Bayesian network transformation steps, the generated fuzzy Bayesian network model of the vehicle engine fault power supply system is shown in Figure 3.Figure 3
Fuzzy Bayesian network for engine power supply system fault.


### 3.2. Determining the Fault Model Parameters of the Vehicle Power Supply System

Firstly, the five-year failure dataset of the FAW Volkswagen ReCK system was used as the a priori probability for this model based on each failure rate statistic, as shown in Tables1 and 2.Table 2
A priori probability of failure of FAW Volkswagen vehicles in the last five years.
StateFault typeμ31μ32μ33μ34μ35μ36μ37μ38μ3900.96750.99420.99310.99360.97550.97540.98410.99810.998810.03250.00580.00690.00640.02450.02460.01590.00190.0012The automotive engine power supply system is a complex piece of equipment, and there are many uncertainties about failures during operation. This paper takes advantage of the extensive experience of experts and adopts the Delphi method to determine the conditional probability of Bayesian networks. In order to improve the credibility of expert experience, this paper uses a fuzzy set theory approach in the process of determining the conditional probabilities of Bayesian networks. Specific methods are as follows:(1)
Determine the rubric set: the rubric grade set is indicated byA. A = A1,A2,…,An,Akk=1,2,…,n is the k rubric level. This paper sets out 10 rubric levels to assess the probability of a faulty node occurring. Namely, A = A1,A2,A3,A4,A5,A6,A7,A8,A9,A10. The possibility of occurrence is reduced at once. Then set the range of values of A1,A2,A3,A4,A5,A6,A7,A8,A9,A10. This can be set in turn as (100%, 90%), (90%, 80%), (80%, 70%), (70%, 60%), (60%, 50%), (50%, 40%), (40%, 30%), (30%, 20%), (20%, 10%), (10%, 0%). For ease of calculation, the probability values are taken as A1=0.95, A2=0.85, A3=0.75, A4=0.65, A5=0.55, A6=0.45, A7=0.35, A8=0.25, A9=0.15, A10=0.05.(2)
Determining affiliation: affiliation is the number of evaluation values given by experts in each index of the comment set based on the established fuzzy comment set. The affiliation of each node failure occurrence in a Bayesian network is denoted byrijk, rijk=μAkuij represents the affiliation of the k rubric level occurring at node uij. The affiliation of each node failure nonoccurrence is denoted by an ri¯j¯k, ri¯j¯k=μAkuij¯ represents the affiliation of the kth rubric level that does not occur at the node uij. And both cases of point uij occurrence and nonoccurrence are possible, it is denoted by rijk.(3)
Determine the evaluation value: the evaluation value of node occurrence probability is represented byPuij:(1)Puij=∑k=15rijkAk∑k=15rijk.The evaluation value of joint probability between nodes is expressed byPui′j′,uij:(2)Pui′j′,uij=∑k=15rijkvAk∑k=15rijk.The correlation strength between nodes, that is, the evaluation value of conditional probability is expressed byPui′j′/uij:(3)Pui′j′uij=∑k=15ri′j′/ijk′Ak∑k=15ri′j′/ijk′.According to the above methods, 12 senior engineers and national technical experts in automobile maintenance are invited to evaluate the association relationship between nodes in the fuzzy Bayesian network of automobile engine power supply system fault. The evaluation results are summarized as follows (Table3):Table 3
Summary of expert evaluation.
Event probabilityProbability %100∼9090∼8080∼7070∼6060∼5050∼4040∼3030∼2020∼1010∼0Pu31=1,u23=1,u24=1,u25=00034500000Pu31=1,u23=1,u24=0,u25=10024600000Pu31=1,u23=1,u24=0,u25=00000000372Pu31=1,u23=0,u24=1,u25=10245100000Pu31=1,u23=0,u24=1,u25=00000008310Pu31=1,u23=0,u24=0,u25=10000016320Pu32=1,u21=1,u23=0,u24=0,u25=0,u26=01254000000Pu32=1,u21=1,u23=1,u24=0,u25=0,u26=00144300000Pu32=1,u21=1,u23=0,u24=1,u25=0,u26=00253200000Pu32=1,u21=1,u23=0,u24=0,u25=1,u26=02431200000Pu32=1,u21=1,u23=0,u24=0,u25=0,u26=10143400000Pu32=1,u21=1,u23=1,u24=1,u25=0,u26=00053400000⋯⋯Pu32=1,u21=0,u23=1,u24=1,u25=1,u26=00000002226Pu32=1,u21=0,u23=1,u24=0,u25=1,u26=10000001416Pu32=1,u21=0,u23=1,u24=1,u25=0,u26=10000001416Pu32=1,u21=0,u23=1,u24=1,u25=1,u26=10000001326Pu32=1,u21=0,u23=0,u24=1,u25=1,u26=10000001236Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=000000000111Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=100000001110Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=00000001119Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=10000000129⋯⋯Pu39=1,u220=1,u222=1,u223=010110000000Pu39=1,u220=1,u222=0,u223=111100000000Pu39=1,u220=1,u222=0,u223=00000034230Pu39=1,u220=0,u222=1,u223=111100000000Pu39=1,u220=0,u222=1,u223=011100000000Pu39=1,u220=0,u222=0,u223=111100000000


### 3.3. Fuzzy Bayesian Network Inference Fault Diagnosis of Automotive Power Supply System

Fuzzy Bayesian network uses topological structure and probability value to represent the qualitative and quantitative knowledge of the model, respectively, so as to process the observation information and implement uncertainty reasoning. The essence of fuzzy Bayesian network reasoning is the process of probability calculation. The topology structure of fuzzy Bayesian network is combined with fuzzy conditional probability table effectively, and the probability of required nodes is calculated by knowing the value of nodes. According to the fault model parameters shown above, the Bayesian network inference calculation is performed. The fuzzy diagnosis reasoning is carried out by the fault symptom layeru2j to obtain the probability of the relevant fault point of the fault factor layer u3j when the symptom occurs. The fault probability vector is formed according to the probability value to guide the maintenance and troubleshooting sequence, and then determine the fault source.The specific reasoning process is illustrated by taking the node in Figure3 as an example. Assuming that the different combinations of failure symptom layer nodes u23, u24, u25 cause the probability of failure factor layer node u31 to occur as(4)Pu31u23=Pu31,u23Pu23=∑k=15r31/23k′Ak∑k=15r31/23k′=∑k=15r31/23kAk/∑k=15r31/23k∑k=15r31/23kAk/∑k=15r31/23k,(5)Pu31=∑u2¯3¯,u2¯4¯,u2¯5¯Pu2¯3¯,u2¯4¯,u2¯5¯,u31=∑k=15r23kAk∑k=15r23k=∑u2¯3¯,u2¯4¯∑k=15r2¯3¯2¯4¯2¯5¯31Ak∑k=15r2¯3¯2¯4¯2¯5¯31k.In fuzzy Bayesian networks, the state of a node is only related to the value of its parent node. Figure2 the joint distribution of random variables in the model is(6)Pu2¯3¯,u2¯4¯,u2¯5¯,u31=T=∏i,jPui¯j¯aui¯j¯,where, aui¯j¯ represents the parent node set of node ui¯j¯. From Equation (6), Equation (5) can be simplified to(7)Pu31|u23=∑u2¯3¯,u2¯4¯u2¯5¯Pu3¯1¯Pu2¯3¯|u31Pu2¯4¯|u31Pu2¯5¯|u31Pu25|u24=∑k=15r31/23k′Ak∑k=15r31/23k′=∑u2¯3¯,u2¯4¯,u2¯5¯∑k=15r31kAk∑k=15r31k∑k=15r23/31k′Ak∑k=15r23/31k′∑k=15r24/31k′Ak∑k=15r24/31k′∑k=15r23/2324k′Ak∑k=15r23/2324k′,(8)Pu31=∑u2¯3¯,u2¯4¯u2¯5¯Pu3¯1¯Pu2¯3¯|u11Pu2¯4¯|u11Pu2¯5¯|u11Pu25|u24=∑k=15r31/23k′Ak∑k=15r31/23k′=∑u2¯3¯,u2¯4¯,u2¯5¯∑k=15r31kAk∑k=15r31k∑k=15r23/31k′Ak∑k=15r23/31k′∑k=15r24/31k′Ak∑k=15r24/31k′∑k=15r23/2324k′Ak∑k=15r23/2324k′.In the above reasoning process, The process from formula (4) to formula (8) is causal reasoning, that is, the probability of the occurrence of the target event is calculated according to the known cause P=u11 conditional probability, based on this, the probability of occurrence of the relevant fault point is inferred when the fault symptom occurs, and the calculated probability value is shown in the following Table 4.Table 4
Conditional probability table of fuzzy Bayesian network.
Fault symptomFault pointCorrelation strength (conditional probability)u23u24u25u31Pu31=1|u23=1,u24=1,u25=1=1Pu31=0|u23=1,u24=1,u25=1=0Pu31=1|u23=1,u24=1,u25=0=0.6333Pu31=0|u23=1,u24=1,u25=0=0.3667Pu31=1|u23=1,u24=0,u25=1=0.6167Pu31=0|u23=1,u24=0,u25=1=0.3833Pu31=1|u23=1,u24=0,u25=1=0.1583Pu31=0|u23=1,u24=0,u25=0=0.8417Pu31=1|u23=0,u24=1,u25=1=0.7083Pu31=0|u23=0,u24=1,u25=1=0.2917Pu31=1|u23=0,u24=1,u25=0=0.3083Pu31=0|u23=0,u24=1,u25=0=0.6917Pu31=1|u23=0,u24=0,u25=1=0.3Pu31=0|u23=0,u24=0,u25=1=0.7Pu31=1|u23=0,u24=0,u25=0=0Pu31=0|u23=0,u24=0,u25=0=1u21u23u24u25u26u32Pu32=1|u21=1,u23=0,u24=1,u25=1,u26=1=1Pu32=0|u21=1,u23=1,u24=1,u25=1,u26=1=0Pu32=1|u21=1,u23=0,u24=0,u25=0,u26=0=0.75Pu32=0|u21=1,u23=0,u24=0,u25=0,u26=0=0.25Pu32=1|u21=1,u23=1,u24=0,u25=0,u26=0=0.67Pu32=0|u21=1,u23=1,u24=0,u25=0,u26=0=0.325Pu32=1|u21=1,u23=0,u24=1,u25=0,u26=0=0.71Pu32=0|u21=1,u23=0,u24=1,u25=0,u26=0=0.291Pu32=1|u21=1,u23=0,u24=0,u25=1,u26=0=0.77Pu32=0|u21=1,u23=0,u24=0,u25=1,u26=0=0.225Pu32=1|u21=1,u23=0,u24=0,u25=0,u26=1=0.66Pu32=0|u21=1,u23=0,u24=0,u25=0,u26=1=0.333Pu32=1|u21=1,u23=1,u24=1,u25=0,u26=0=0.658Pu32=0|u21=1,u23=1,u24=1,u25=0,u26=0=0.341Pu32=1|u21=0,u23=1,u24=1,u25=1,u26=0=0.15Pu32=0|u21=0,u23=1,u24=1,u25=1,u26=0=0.85Pu32=1|u21=0,u23=1,u24=0,u25=1,u26=1=0.15Pu32=0|u21=0,u23=1,u24=0,u25=1,u26=1=0.85Pu32=1|u21=0,u23=1,u24=1,u25=0,u26=1=0.15Pu32=0,u21=0,u23=1,u24=1,u25=0,u26=1=0.85Pu32=1|u21=0,u23=1,u24=1,u25=1,u26=1=0.141Pu32=0|u21=0,u23=1,u24=1,u25=1,u26=1=0.858Pu32=1|u21=0,u23=0,u24=1,u25=1,u26=1=0.866Pu32=0|u21=0,u23=0,u24=1,u25=1,u26=1=0.866Pu32=1|u21=0,u23=0,u24=0,u25=0,u26=0=0Pu32=0|u21=0,u23=0,u24=0,u25=0,u26=0=1u27u28u29u210u211u212u213u215u216u217u33Pu33=1|u27=1,u28=1,u29=1,u210=1,u211=1,u212=1,u213=1,u215=1,u216=1,u217=1=1Pu33=0|u27=1,u28=1,u29=1,u210=1,u211=1,u212=1,u213=1,u215=1,u216=1,u217=1=0Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=0=0.0583Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=0=0.9417Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=1=0.0750Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=1=0.925Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=0=0.1000Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=0=0.9Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=1=0.833Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=1=0.9167u23u24u25u214u217u34Pu34=1|u23=1,u24=0,u25=0,u214=0,u217=0=0.9083Pu34=0|u23=1,u24=0,u25=0,u214=0,u217=0=0.0917Pu34=1|u23=1,u24=1,u25=0,u214=0,u217=0=0.9000Pu34=0|u23=1,u24=1,u25=0,u214=0,u217=0=0.100Pu34=1|u23=1,u24=0,u25=1,u214=0,u217=0=0.8917Pu34=0|u23=1,u24=0,u25=1,u214=0,u217=0=0.1083Pu34=1|u23=1,u24=0,u25=0,u214=1,u217=0=0.8833Pu34=0|u23=1,u24=0,u25=0,u214=1,u217=0=0.1167Pu34=1|u23=1,u24=0,u25=0,u214=0,u217=1=0.9167Pu34=0|u23=1,u24=0,u25=0,u214=0,u217=1=0.0833u217u218u35Pu35=1|u217=1,u218=1=1Pu35=0|u217=1,u218=1=0Pu35=1|u217=0,u218=1=0.0583Pu35=1|u217=0,u218=1=0.9417Pu35=1|u217=1,u218=0=0.9417Pu35=0|u217=1,u218=0=0.0583Pu35=1|u217=0,u218=0=0Pu35=0|u217=0,u218=0=1u217u218u36Pu36=1|u217=1,u218=1=1Pu36=0|u217=1,u218=1=0Pu36=1|u217=0,u218=1=0.0583Pu36=0|u217=0,u218=1=0.9417Pu36=1|u217=1,u218=0=9417Pu36=0|u217=1,u218=0=0.0583Pu36=1|u217=0,u218=0=0Pu36=0|u217=0,u218=0=1u23u219u37Pu37=1|u23=1,u219=1=1Pu37=0|u23=1,u219=1=0Pu37=1|u23=0,u219=1=0.1167Pu37=0|u23=0,u219=1=0.8833Pu37=1|u23=1,u219=0=0.8833Pu37=0|u23=1,u219=0=0.1167Pu37=1|u23=0,u219=0=0Pu37=0|u23=0,u219=0=1u22u221u38Pu38=1|u22=1,u221=1=1Pu38=0|u22=1,u221=1=0Pu38=1|u22=0,u221=1=0.9000Pu38=0|u22=0,u221=1=0.1Pu38=1|u22=1,u221=0=0.1000Pu37=0|u22=1,u221=0=0.9Pu38=1|v2=0,u221=0=0Pu37=0|u22=0,u221=0=1u220u222u223u39Pu39=1|u220=1,u222=0,u223=1=0.9250Pu39=0|u220=1,u222=1,u223=0=0.075Pu39=1|u220=1,u222=0,u223=1=0.9417Pu39=0|u220=1,u222=0,u223=1=0.0583Pu39=1|u220=1,u222=0,u223=0=0.3083Pu39=0|u220=1,u222=0,u223=0=0.6917Pu39=1|u220=0,u222=1,u223=1=0.9417Pu39=0|u220=0,u222=1,u223=1=0.0583Pu39=1|u220=0,u222=1,u223=0=0.9417Pu39=0|u220=0,u222=1,u223=0=0.0583Fault diagnosis is carried out according to a single fault symptom. The process is as follows: assuming that the fault symptomu24 occurs, the fault probability of the corresponding fault points u31, u32 and u34 is (0.3083, 0.85 and 0.2917) in turn. According to the maximum a posteriori probability judgment logic, it is determined that u32 is the predicted fault point after the fault symptom u24 occurs.The process of fault diagnosis based on multiple fault symptoms is as follows: assuming that the fault symptomsu23 and u24 occur, the fault probability of corresponding fault points u32 and u34 is (0.3417 and 0.9) in turn. According to the maximum a posteriori probability judgment logic, u34 is the predicted fault point after the fault symptoms u23 and u24 occur.According to the last process, it can be inferred to the reasoning diagnosis of fault point when other fault symptoms appear in combination.


## 3.1. Establishment of Fuzzy Bayesian Network for Automobile Power Supply System

According to Figure2, the above number of failures and fuzzy Bayesian network transformation steps, the generated fuzzy Bayesian network model of the vehicle engine fault power supply system is shown in Figure 3.Figure 3
Fuzzy Bayesian network for engine power supply system fault.


## 3.2. Determining the Fault Model Parameters of the Vehicle Power Supply System

Firstly, the five-year failure dataset of the FAW Volkswagen ReCK system was used as the a priori probability for this model based on each failure rate statistic, as shown in Tables1 and 2.Table 2
A priori probability of failure of FAW Volkswagen vehicles in the last five years.
StateFault typeμ31μ32μ33μ34μ35μ36μ37μ38μ3900.96750.99420.99310.99360.97550.97540.98410.99810.998810.03250.00580.00690.00640.02450.02460.01590.00190.0012The automotive engine power supply system is a complex piece of equipment, and there are many uncertainties about failures during operation. This paper takes advantage of the extensive experience of experts and adopts the Delphi method to determine the conditional probability of Bayesian networks. In order to improve the credibility of expert experience, this paper uses a fuzzy set theory approach in the process of determining the conditional probabilities of Bayesian networks. Specific methods are as follows:(1)
Determine the rubric set: the rubric grade set is indicated byA. A = A1,A2,…,An,Akk=1,2,…,n is the k rubric level. This paper sets out 10 rubric levels to assess the probability of a faulty node occurring. Namely, A = A1,A2,A3,A4,A5,A6,A7,A8,A9,A10. The possibility of occurrence is reduced at once. Then set the range of values of A1,A2,A3,A4,A5,A6,A7,A8,A9,A10. This can be set in turn as (100%, 90%), (90%, 80%), (80%, 70%), (70%, 60%), (60%, 50%), (50%, 40%), (40%, 30%), (30%, 20%), (20%, 10%), (10%, 0%). For ease of calculation, the probability values are taken as A1=0.95, A2=0.85, A3=0.75, A4=0.65, A5=0.55, A6=0.45, A7=0.35, A8=0.25, A9=0.15, A10=0.05.(2)
Determining affiliation: affiliation is the number of evaluation values given by experts in each index of the comment set based on the established fuzzy comment set. The affiliation of each node failure occurrence in a Bayesian network is denoted byrijk, rijk=μAkuij represents the affiliation of the k rubric level occurring at node uij. The affiliation of each node failure nonoccurrence is denoted by an ri¯j¯k, ri¯j¯k=μAkuij¯ represents the affiliation of the kth rubric level that does not occur at the node uij. And both cases of point uij occurrence and nonoccurrence are possible, it is denoted by rijk.(3)
Determine the evaluation value: the evaluation value of node occurrence probability is represented byPuij:(1)Puij=∑k=15rijkAk∑k=15rijk.The evaluation value of joint probability between nodes is expressed byPui′j′,uij:(2)Pui′j′,uij=∑k=15rijkvAk∑k=15rijk.The correlation strength between nodes, that is, the evaluation value of conditional probability is expressed byPui′j′/uij:(3)Pui′j′uij=∑k=15ri′j′/ijk′Ak∑k=15ri′j′/ijk′.According to the above methods, 12 senior engineers and national technical experts in automobile maintenance are invited to evaluate the association relationship between nodes in the fuzzy Bayesian network of automobile engine power supply system fault. The evaluation results are summarized as follows (Table3):Table 3
Summary of expert evaluation.
Event probabilityProbability %100∼9090∼8080∼7070∼6060∼5050∼4040∼3030∼2020∼1010∼0Pu31=1,u23=1,u24=1,u25=00034500000Pu31=1,u23=1,u24=0,u25=10024600000Pu31=1,u23=1,u24=0,u25=00000000372Pu31=1,u23=0,u24=1,u25=10245100000Pu31=1,u23=0,u24=1,u25=00000008310Pu31=1,u23=0,u24=0,u25=10000016320Pu32=1,u21=1,u23=0,u24=0,u25=0,u26=01254000000Pu32=1,u21=1,u23=1,u24=0,u25=0,u26=00144300000Pu32=1,u21=1,u23=0,u24=1,u25=0,u26=00253200000Pu32=1,u21=1,u23=0,u24=0,u25=1,u26=02431200000Pu32=1,u21=1,u23=0,u24=0,u25=0,u26=10143400000Pu32=1,u21=1,u23=1,u24=1,u25=0,u26=00053400000⋯⋯Pu32=1,u21=0,u23=1,u24=1,u25=1,u26=00000002226Pu32=1,u21=0,u23=1,u24=0,u25=1,u26=10000001416Pu32=1,u21=0,u23=1,u24=1,u25=0,u26=10000001416Pu32=1,u21=0,u23=1,u24=1,u25=1,u26=10000001326Pu32=1,u21=0,u23=0,u24=1,u25=1,u26=10000001236Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=000000000111Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=100000001110Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=00000001119Pu33=1,u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=10000000129⋯⋯Pu39=1,u220=1,u222=1,u223=010110000000Pu39=1,u220=1,u222=0,u223=111100000000Pu39=1,u220=1,u222=0,u223=00000034230Pu39=1,u220=0,u222=1,u223=111100000000Pu39=1,u220=0,u222=1,u223=011100000000Pu39=1,u220=0,u222=0,u223=111100000000


## 3.3. Fuzzy Bayesian Network Inference Fault Diagnosis of Automotive Power Supply System

Fuzzy Bayesian network uses topological structure and probability value to represent the qualitative and quantitative knowledge of the model, respectively, so as to process the observation information and implement uncertainty reasoning. The essence of fuzzy Bayesian network reasoning is the process of probability calculation. The topology structure of fuzzy Bayesian network is combined with fuzzy conditional probability table effectively, and the probability of required nodes is calculated by knowing the value of nodes. According to the fault model parameters shown above, the Bayesian network inference calculation is performed. The fuzzy diagnosis reasoning is carried out by the fault symptom layeru2j to obtain the probability of the relevant fault point of the fault factor layer u3j when the symptom occurs. The fault probability vector is formed according to the probability value to guide the maintenance and troubleshooting sequence, and then determine the fault source.The specific reasoning process is illustrated by taking the node in Figure3 as an example. Assuming that the different combinations of failure symptom layer nodes u23, u24, u25 cause the probability of failure factor layer node u31 to occur as(4)Pu31u23=Pu31,u23Pu23=∑k=15r31/23k′Ak∑k=15r31/23k′=∑k=15r31/23kAk/∑k=15r31/23k∑k=15r31/23kAk/∑k=15r31/23k,(5)Pu31=∑u2¯3¯,u2¯4¯,u2¯5¯Pu2¯3¯,u2¯4¯,u2¯5¯,u31=∑k=15r23kAk∑k=15r23k=∑u2¯3¯,u2¯4¯∑k=15r2¯3¯2¯4¯2¯5¯31Ak∑k=15r2¯3¯2¯4¯2¯5¯31k.In fuzzy Bayesian networks, the state of a node is only related to the value of its parent node. Figure2 the joint distribution of random variables in the model is(6)Pu2¯3¯,u2¯4¯,u2¯5¯,u31=T=∏i,jPui¯j¯aui¯j¯,where, aui¯j¯ represents the parent node set of node ui¯j¯. From Equation (6), Equation (5) can be simplified to(7)Pu31|u23=∑u2¯3¯,u2¯4¯u2¯5¯Pu3¯1¯Pu2¯3¯|u31Pu2¯4¯|u31Pu2¯5¯|u31Pu25|u24=∑k=15r31/23k′Ak∑k=15r31/23k′=∑u2¯3¯,u2¯4¯,u2¯5¯∑k=15r31kAk∑k=15r31k∑k=15r23/31k′Ak∑k=15r23/31k′∑k=15r24/31k′Ak∑k=15r24/31k′∑k=15r23/2324k′Ak∑k=15r23/2324k′,(8)Pu31=∑u2¯3¯,u2¯4¯u2¯5¯Pu3¯1¯Pu2¯3¯|u11Pu2¯4¯|u11Pu2¯5¯|u11Pu25|u24=∑k=15r31/23k′Ak∑k=15r31/23k′=∑u2¯3¯,u2¯4¯,u2¯5¯∑k=15r31kAk∑k=15r31k∑k=15r23/31k′Ak∑k=15r23/31k′∑k=15r24/31k′Ak∑k=15r24/31k′∑k=15r23/2324k′Ak∑k=15r23/2324k′.In the above reasoning process, The process from formula (4) to formula (8) is causal reasoning, that is, the probability of the occurrence of the target event is calculated according to the known cause P=u11 conditional probability, based on this, the probability of occurrence of the relevant fault point is inferred when the fault symptom occurs, and the calculated probability value is shown in the following Table 4.Table 4
Conditional probability table of fuzzy Bayesian network.
Fault symptomFault pointCorrelation strength (conditional probability)u23u24u25u31Pu31=1|u23=1,u24=1,u25=1=1Pu31=0|u23=1,u24=1,u25=1=0Pu31=1|u23=1,u24=1,u25=0=0.6333Pu31=0|u23=1,u24=1,u25=0=0.3667Pu31=1|u23=1,u24=0,u25=1=0.6167Pu31=0|u23=1,u24=0,u25=1=0.3833Pu31=1|u23=1,u24=0,u25=1=0.1583Pu31=0|u23=1,u24=0,u25=0=0.8417Pu31=1|u23=0,u24=1,u25=1=0.7083Pu31=0|u23=0,u24=1,u25=1=0.2917Pu31=1|u23=0,u24=1,u25=0=0.3083Pu31=0|u23=0,u24=1,u25=0=0.6917Pu31=1|u23=0,u24=0,u25=1=0.3Pu31=0|u23=0,u24=0,u25=1=0.7Pu31=1|u23=0,u24=0,u25=0=0Pu31=0|u23=0,u24=0,u25=0=1u21u23u24u25u26u32Pu32=1|u21=1,u23=0,u24=1,u25=1,u26=1=1Pu32=0|u21=1,u23=1,u24=1,u25=1,u26=1=0Pu32=1|u21=1,u23=0,u24=0,u25=0,u26=0=0.75Pu32=0|u21=1,u23=0,u24=0,u25=0,u26=0=0.25Pu32=1|u21=1,u23=1,u24=0,u25=0,u26=0=0.67Pu32=0|u21=1,u23=1,u24=0,u25=0,u26=0=0.325Pu32=1|u21=1,u23=0,u24=1,u25=0,u26=0=0.71Pu32=0|u21=1,u23=0,u24=1,u25=0,u26=0=0.291Pu32=1|u21=1,u23=0,u24=0,u25=1,u26=0=0.77Pu32=0|u21=1,u23=0,u24=0,u25=1,u26=0=0.225Pu32=1|u21=1,u23=0,u24=0,u25=0,u26=1=0.66Pu32=0|u21=1,u23=0,u24=0,u25=0,u26=1=0.333Pu32=1|u21=1,u23=1,u24=1,u25=0,u26=0=0.658Pu32=0|u21=1,u23=1,u24=1,u25=0,u26=0=0.341Pu32=1|u21=0,u23=1,u24=1,u25=1,u26=0=0.15Pu32=0|u21=0,u23=1,u24=1,u25=1,u26=0=0.85Pu32=1|u21=0,u23=1,u24=0,u25=1,u26=1=0.15Pu32=0|u21=0,u23=1,u24=0,u25=1,u26=1=0.85Pu32=1|u21=0,u23=1,u24=1,u25=0,u26=1=0.15Pu32=0,u21=0,u23=1,u24=1,u25=0,u26=1=0.85Pu32=1|u21=0,u23=1,u24=1,u25=1,u26=1=0.141Pu32=0|u21=0,u23=1,u24=1,u25=1,u26=1=0.858Pu32=1|u21=0,u23=0,u24=1,u25=1,u26=1=0.866Pu32=0|u21=0,u23=0,u24=1,u25=1,u26=1=0.866Pu32=1|u21=0,u23=0,u24=0,u25=0,u26=0=0Pu32=0|u21=0,u23=0,u24=0,u25=0,u26=0=1u27u28u29u210u211u212u213u215u216u217u33Pu33=1|u27=1,u28=1,u29=1,u210=1,u211=1,u212=1,u213=1,u215=1,u216=1,u217=1=1Pu33=0|u27=1,u28=1,u29=1,u210=1,u211=1,u212=1,u213=1,u215=1,u216=1,u217=1=0Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=0=0.0583Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=0=0.9417Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=1=0.0750Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=0,u217=1=0.925Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=0=0.1000Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=0=0.9Pu33=1|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=1=0.833Pu33=0|u27=1,u28=0,u29=0,u210=0,u211=0,u212=0,u213=0,u215=0,u216=1,u217=1=0.9167u23u24u25u214u217u34Pu34=1|u23=1,u24=0,u25=0,u214=0,u217=0=0.9083Pu34=0|u23=1,u24=0,u25=0,u214=0,u217=0=0.0917Pu34=1|u23=1,u24=1,u25=0,u214=0,u217=0=0.9000Pu34=0|u23=1,u24=1,u25=0,u214=0,u217=0=0.100Pu34=1|u23=1,u24=0,u25=1,u214=0,u217=0=0.8917Pu34=0|u23=1,u24=0,u25=1,u214=0,u217=0=0.1083Pu34=1|u23=1,u24=0,u25=0,u214=1,u217=0=0.8833Pu34=0|u23=1,u24=0,u25=0,u214=1,u217=0=0.1167Pu34=1|u23=1,u24=0,u25=0,u214=0,u217=1=0.9167Pu34=0|u23=1,u24=0,u25=0,u214=0,u217=1=0.0833u217u218u35Pu35=1|u217=1,u218=1=1Pu35=0|u217=1,u218=1=0Pu35=1|u217=0,u218=1=0.0583Pu35=1|u217=0,u218=1=0.9417Pu35=1|u217=1,u218=0=0.9417Pu35=0|u217=1,u218=0=0.0583Pu35=1|u217=0,u218=0=0Pu35=0|u217=0,u218=0=1u217u218u36Pu36=1|u217=1,u218=1=1Pu36=0|u217=1,u218=1=0Pu36=1|u217=0,u218=1=0.0583Pu36=0|u217=0,u218=1=0.9417Pu36=1|u217=1,u218=0=9417Pu36=0|u217=1,u218=0=0.0583Pu36=1|u217=0,u218=0=0Pu36=0|u217=0,u218=0=1u23u219u37Pu37=1|u23=1,u219=1=1Pu37=0|u23=1,u219=1=0Pu37=1|u23=0,u219=1=0.1167Pu37=0|u23=0,u219=1=0.8833Pu37=1|u23=1,u219=0=0.8833Pu37=0|u23=1,u219=0=0.1167Pu37=1|u23=0,u219=0=0Pu37=0|u23=0,u219=0=1u22u221u38Pu38=1|u22=1,u221=1=1Pu38=0|u22=1,u221=1=0Pu38=1|u22=0,u221=1=0.9000Pu38=0|u22=0,u221=1=0.1Pu38=1|u22=1,u221=0=0.1000Pu37=0|u22=1,u221=0=0.9Pu38=1|v2=0,u221=0=0Pu37=0|u22=0,u221=0=1u220u222u223u39Pu39=1|u220=1,u222=0,u223=1=0.9250Pu39=0|u220=1,u222=1,u223=0=0.075Pu39=1|u220=1,u222=0,u223=1=0.9417Pu39=0|u220=1,u222=0,u223=1=0.0583Pu39=1|u220=1,u222=0,u223=0=0.3083Pu39=0|u220=1,u222=0,u223=0=0.6917Pu39=1|u220=0,u222=1,u223=1=0.9417Pu39=0|u220=0,u222=1,u223=1=0.0583Pu39=1|u220=0,u222=1,u223=0=0.9417Pu39=0|u220=0,u222=1,u223=0=0.0583Fault diagnosis is carried out according to a single fault symptom. The process is as follows: assuming that the fault symptomu24 occurs, the fault probability of the corresponding fault points u31, u32 and u34 is (0.3083, 0.85 and 0.2917) in turn. According to the maximum a posteriori probability judgment logic, it is determined that u32 is the predicted fault point after the fault symptom u24 occurs.The process of fault diagnosis based on multiple fault symptoms is as follows: assuming that the fault symptomsu23 and u24 occur, the fault probability of corresponding fault points u32 and u34 is (0.3417 and 0.9) in turn. According to the maximum a posteriori probability judgment logic, u34 is the predicted fault point after the fault symptoms u23 and u24 occur.According to the last process, it can be inferred to the reasoning diagnosis of fault point when other fault symptoms appear in combination.


## 4. Conclusion

This paper constructs a logical diagnosis model of automobile power supply, which is used for the rapid diagnosis method of single fault and multiple fault modes of automobile engine. Firstly, the automobile power supply fault tree is established according to the experience of four automobile fault diagnosis experts, and the Bayesian network model is established. Then, the a priori probability value of the fault point is obtained through the data of FAW Volkswagen’s Rick system, and the relevant conditional probability is determined by the method of Fuzzy set theory. Finally, the probability value of the relevant fault point when the corresponding fault symptom appears is calculated. At the same time, the fault tree established in this paper can provide a reference for making maintenance plan for vehicle power supply fault, and the calculation results of Bayesian network can provide a basis for fault diagnosis sequence.



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*Source: 4046966-2022-05-12.xml*