A Bayesian network parameter initialization method

Abstract

The present invention belongs to the field of intelligent diagnosis of equipment faults, and specifically relates to a method for initializing Bayesian network parameters. Expert knowledge can only impose large-scale constraints on Bayesian network parameters, and the Bayesian network parameters can only be obtained through manual analysis and continuous calculation, which consumes a lot of time and energy. The present invention includes the following three steps: Step 1: Establishment of a Bayesian network diagnostic model. Step 2: Generation of a simulated fault sample library. Based on the expert knowledge of the equipment, diagnostic rules are formed, and then a simulated "symptom state-fault posterior probability" combination is obtained based on the diagnostic rules to generate a simulated fault sample library. Step 3: Optimization of the conditional probability of the diagnostic model. The present invention obtains the prior knowledge of the diagnostic model from the expert knowledge, and learns the conditional probability parameters of the Bayesian network diagnostic model based on the iterative learning method, and calculates the initialization parameters of the Bayesian network that conform to the existing prior knowledge.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent diagnosis of equipment faults, and in particular relates to a Bayesian network parameter initialization method. Background Art

[0002] The nuclear main pump is a critical component of pressurized water reactor (PWR) nuclear power plants. Accurate and rapid diagnosis of main pump faults is crucial for the safe and efficient operation of nuclear power plants. Bayesian networks, combining graph theory and probability theory, have a strong theoretical foundation. Compared to numerous artificial intelligence methods such as neural networks, support vector machines, and decision trees, Bayesian networks more easily incorporate expert experience and domain knowledge. They offer intuitive and easy-to-understand knowledge representation, powerful uncertainty modeling capabilities, and the ability to mimic the reasoning of the human brain. Therefore, Bayesian network-based fault diagnosis methods have considerable application value in nuclear power plants.

[0003] However, due to insufficient sample data for nuclear main pumps, it is impossible to use statistical methods to calculate the Bayesian network parameters based on the existing fault sample data. The current mainstream approach to learning Bayesian network parameters based on small datasets is to incorporate expert knowledge to compensate for the lack of sample data. This expert knowledge is used to constrain the Bayesian network parameters and thus learn the Bayesian network parameters.

[0004] Expert knowledge can only constrain the parameters of a Bayesian network to a large extent. Determining the parameters of a Bayesian network requires manual analysis and continuous calculation, which consumes a lot of time and effort. Therefore, in order to accurately determine the appropriate initialization parameters of a Bayesian network, the present invention proposes a method for setting the initialization parameters of a Bayesian network based on expert knowledge. Summary of the Invention

[0005] The present invention aims to address the difficulty of setting network parameters for a Bayesian network diagnostic model in the absence of sample data. It proposes a method for initializing Bayesian network parameters based on expert knowledge. This method obtains prior knowledge of the diagnostic model from expert knowledge and uses an iterative learning method to learn the conditional probability parameters of the Bayesian network diagnostic model, calculating the initialization parameters of the Bayesian network that are consistent with the prior knowledge.

[0006] A Bayesian network parameter initialization method includes the following three steps:

[0007] Step 1: Establish a Bayesian network diagnostic model, determine the fault type and symptom type of the equipment to be studied, clarify the symptoms associated with each fault, and preliminarily define the parameters of the diagnostic model, thereby establishing a Bayesian network diagnostic model;

[0008] Step 2: Generate a simulated fault sample library, form diagnostic rules based on the expert knowledge of the equipment, and then obtain a simulated "symptom state-fault posterior probability" combination based on the diagnostic rules to generate a simulated fault sample library;

[0009] Step 3: Optimize the conditional probability of the diagnosis model. Based on the simulated fault sample library, establish a Bayesian network initialization parameter self-learning algorithm to optimize the conditional probability parameters of the diagnosis model.

[0010] The Bayesian network diagnosis model is established in step 1, and its specific steps are as follows: (1) based on the relevant information of the device to be studied, its fault type and symptom type are determined, thereby determining all the fault node sets F and symptom node sets S of the Bayesian network diagnosis model; (2) through expert knowledge analysis of the device to be studied, clarifying the corresponding correlation between each fault node and symptom node in the Bayesian network diagnosis model, establishing the connection line / edge set E between the symptom node and the fault node, thereby establishing the structure of the Bayesian network diagnosis model; (3) combining the expert knowledge of the device to be studied to preliminarily determine the prior probability set B of the fault node and the conditional probability set C of the symptom node, thereby completing the establishment of the Bayesian network diagnosis model.

[0011] Step 1: Establishing a Bayesian network diagnosis model. According to Formula 1, the Bayesian network diagnosis model consists of five parts: the fault node set F, the symptom node set S, the edge set E connecting the symptom nodes and the fault nodes, the prior probability set B of the fault nodes, and the conditional probability set C of the symptom nodes:

[0012] BN=(F,S,E,B,C) Formula 1

[0013] The specific meanings of each symbol are as follows:

[0014] BN: represents the fault diagnosis model based on Bayesian network

[0015] F: represents the set of all fault nodes in the diagnosis model, f i represents the i-th fault node, F={f i} i＝1,…,M

[0016] S: represents the set of all symptom nodes in the diagnosis model, s j represents the jth symptom node, S={s j} j＝1,…,N

[0017] E: represents the set of edges connecting each fault node and the associated symptom node, e i,j Indicates that the i-th fault node is associated with the j-th symptom node, E={e i，j} i＝1，…，M；j＝1，…，N

[0018] B: represents the prior probability set of each fault node, b i represents the prior probability of the i-th fault node, B={b i} i＝1，…，M

[0019] C: represents the conditional probability table set of each symptom node, c j The conditional probability table of the j-th symptom node, C = {c j} j＝1，…，N .

[0020] The step 1 of "determining the prior probability set B" specifically includes: combining expert knowledge and fault case sample data to determine the ranking of different fault occurrence probabilities during equipment operation, and then setting the prior probability set B based on the ranking of the fault occurrence probabilities.

[0021] In step 2, a simulated fault sample library is generated. The specific method is: based on the expert knowledge of the equipment, the fault node f is determined. i The associated symptom set S i :

[0022] S i ={s k} k∈[1,N] Formula 2

[0023] Let H(s k ) represents the symptom node s k Current symptom status, H(s k )=0 indicates the symptom node s k The symptom state is not occurred, H(s k )=1 indicates symptom node s k The symptom state is occurrence;

[0024] When S i When there are x (1≤x≤N) symptom nodes in the network, based on the Bayesian network principle S i The state set W is shown in Formula 3, which contains 2 t Combination of symptom states:

[0025]

[0026] Among them, w q Represents the qth symptom state combination in W.

[0027] In step 2, w is determined in turn based on expert knowledge. q The corresponding fault f under the condition i All posterior probabilities Thus establishing the fault f i The simulated sample set g i :

[0028]

[0029] in, Indicates that the symptom state is w q Corresponding fault f i The posterior probability of occurrence is

[0030] Refer to the above to establish the fault f i The simulated sample set g i The simulated sample sets of all faults in the fault sample set F are determined in turn, thereby establishing a simulated fault sample library G, as shown in Formula 5.

[0031] G={g i} i＝1,…,M Formula 5

[0032] Among them, the combination set of all symptom states in the simulated fault sample library G The set of fault posterior probabilities corresponding to each symptom state

[0033] The posterior probability of the fault is divided into three levels: Level 1 indicates that the fault occurs under the symptom state combination conditions, and its posterior probability setting range is greater than or equal to 0.8; Level 2 indicates that it is uncertain whether the fault occurs under the symptom state combination conditions, and its posterior probability setting range is 0.4 to 0.8; Level 3 indicates that the fault does not occur under the symptom state combination conditions, and its posterior probability setting range is less than or equal to 0.4.

[0034] The fault f i When setting the posterior probability, first determine the fault f under various associated symptom state combinations. i The posterior probability of the fault belongs to which level, and then the order of the posterior probability of each fault in the fault node set F is determined in combination with the prior knowledge of the fault, and the posterior probability value of each fault is determined.

[0035] The specific method flow of the optimization of the conditional probability of the diagnostic model in step 3 is as follows: first, a candidate set L(C) of conditional probability tables of the Bayesian network diagnostic model is generated; then, the optimal set C of conditional probability tables of the Bayesian network diagnostic model in L(C) is determined based on the conditional probability optimization algorithm.

[0036] The specific method of generating the candidate set L(C) of the conditional probability table is as follows: when the symptom node s j When associating t fault nodes, according to the Bayesian network principle, the symptom node s j Conditional probability table c j Need to confirm 2 t Conditional probability α k , that is, the conditional probability table cj As shown in Formula 6:

[0037]

[0038] Let the generated conditional probability α k The interval accuracy is δ, and c is generated iteratively j Each conditional probability α k The candidate value set L(α k ), as shown in Formula 7:

[0039]

[0040] Based on α k The candidate value set L(α k ) Determine c j The candidate set L(c j ) as shown in Formula 8:

[0041]

[0042] Among them, α k,p represents the conditional probability α k The value of the set L(α k ), c j,m Indicates c j For the set L(c j ) in the mth candidate conditional probability set;

[0043] Based on the conditional probability table c of each symptom node j The candidate set L(c j ), the conditional probability candidate set L(C) of the Bayesian network diagnosis model is obtained, as shown in Formula 9:

[0044]

[0045] Among them, β n Represents the conditional probability table set C of the nth Bayesian network diagnostic model in L(C).

[0046] The conditional probability optimization process steps in step 3 are as follows:

[0047] (1) Select a conditional probability set β in L(C) n Input into the Bayesian network diagnostic model to form the Bayesian network diagnostic model BN n =(F,S,E,B,C=β n );

[0048] (2) Input all the symptom state combinations L(W) in the fault simulation sample library into the Bayesian network diagnosis model BN in sequence n In the calculation, the actual fault posterior probability set L(Pa n ), as shown in Formula 10

[0049]

[0050] (3) Calculate the actual fault posterior probability set L(Pa n ) and the predicted fault posterior probability set L(P F ) n ; Among them, the error er n The calculation method is to take L(Pa n ) and L(P F ) and square the difference of the posterior probabilities corresponding to each symptom state, and then divide it by the total number of fault posterior probabilities in each posterior probability set

[0051]

[0052] (4) Recording error n And save it in the list L(er n )middle;

[0053] (5) Repeat the above four steps to calculate All errors corresponding to the conditions, Filter out the list L(er n ) minimum value er m , and based on the minimum error er m The subscript m selects the corresponding conditional probability set β from the candidate set L(C) of the conditional probability table m , and obtain the optimal parameters of the Bayesian network diagnosis model. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flow chart of a conditional probability optimization method for Bayesian network parameter optimization based on expert knowledge;

[0055] Figure 2 This is an example diagram of a diagnostic model in an embodiment of a Bayesian network parameter optimization method based on expert knowledge. DETAILED DESCRIPTION

[0056] To provide a clearer understanding of the present invention, the present invention will be further described below using a case study of a main pump bearing failure in a nuclear power plant in conjunction with the accompanying drawings.

[0057] The patent of this invention is a parameter initialization method of Bayesian network based on expert knowledge. The process is as shown in the attached Figure 1As shown, it includes the following three steps:

[0058] Step 1: Establishing a Bayesian network diagnostic model. Determine the fault type and symptom type of the equipment to be studied, identify the symptoms associated with each fault, and preliminarily define the parameters of the diagnostic model to establish the Bayesian network diagnostic model.

[0059] Step 2: Generate a simulated fault sample library. Based on the expert knowledge of the equipment, a diagnostic rule is formed. Then, based on the diagnostic rule, a simulated "symptom state-fault posterior probability" combination is obtained to generate a simulated fault sample library.

[0060] Step 3: Optimization of the conditional probability of the diagnosis model. Based on the simulated fault sample library, a Bayesian network initialization parameter self-learning algorithm is established to optimize the conditional probability parameters of the diagnosis model.

[0061] The specific content of the "Bayesian network diagnosis model" in step 1 can be expressed by formula (1). The Bayesian network diagnosis model consists of five parts: the fault node set F, the symptom node set S, the edge set E connecting the symptom nodes and the fault nodes, the prior probability set B of the fault nodes, and the conditional probability set C of the symptom nodes.

[0062] BN=(F,S,E,B,C) Formula (1)

[0063] The specific meanings of each symbol are as follows:

[0064] BN: represents the fault diagnosis model based on Bayesian network.

[0065] F: represents the set of all fault nodes in the diagnosis model, f i represents the i-th fault node, F={f i} i＝1,…,M .

[0066] S: represents the set of all symptom nodes in the diagnosis model, s j represents the jth symptom node, S={s j} j＝1,…,N .

[0067] E: represents the set of edges connecting each fault node and the associated symptom node, e i,j Indicates that the i-th fault node is associated with the j-th symptom node, E={e i,j} i＝1,…,M；j＝1,…,N .

[0068] B: represents the prior probability set of each fault node, b i represents the prior probability of the i-th fault node, B={b i} i＝1，…，M .

[0069] C: represents the conditional probability table set of each symptom node, c j The conditional probability table of the j-th symptom node, C = {c j} j＝1，…，N .

[0070] The specific approach to establishing the Bayesian network diagnostic model in step 1 is as follows: Based on the relevant information about the device under study, determine its fault type and symptom type, thereby determining the set of all fault nodes F and symptom nodes S in the Bayesian network diagnostic model. Furthermore, through expert knowledge analysis of the device under study, the corresponding relationships between each fault node and symptom node in the Bayesian network diagnostic model are clarified, and the set of lines / edges E connecting symptom nodes to fault nodes is established, thereby establishing the structure of the Bayesian network diagnostic model. Furthermore, combined with expert knowledge of the device, the prior probability set B of the fault node and the conditional probability set C of the symptom node are preliminarily determined, thus completing the establishment of the Bayesian network diagnostic model.

[0071] The specific approach to "determining the prior probability set B" in step 1 is: combining expert knowledge and fault case sample data to determine the ranking of the probabilities of different faults occurring during equipment operation, and then setting the prior probability set B based on the ranking of the fault probabilities.

[0072] The specific approach of "generating a simulated fault sample library" in step 2 is to determine the fault node f based on the expert knowledge of the device. i The associated symptom set S i :

[0073] S i ={s k} k∈[1，N] Formula (2)

[0074] Let H(s k ) represents the symptom node s k Current symptom status, H(s k )=0 indicates the symptom node s k The symptom state is not occurred, H(s k )=1 indicates symptom node s k The symptom state is occurrence.

[0075] When S i When there are x (1≤x≤N) symptom nodes in the network, based on the Bayesian network principle S i The state set W is shown in formula (2), which contains 2 t A combination of symptom states.

[0076]

[0077] Among them, wq represents the qth symptom state combination in W. For example, when q=1, When q=2 t hour,

[0078] Determine w in turn based on expert knowledge q The corresponding fault f under the condition i All posterior probabilities Thus establishing the fault f i The simulated sample set g i :

[0079]

[0080] in, Indicates that the symptom state is w q Corresponding fault f i The posterior probability of occurrence is

[0081] Refer to the above to establish the fault f i The simulated sample set g i The simulated sample sets of all faults in the fault sample set F are determined in sequence, thereby establishing a simulated fault sample library G, as shown in formula (5).

[0082] G={g i} i＝1,…,M Formula (5)

[0083] Among them, the combination set of all symptom states in the simulated fault sample library G The set of fault posterior probabilities corresponding to each symptom state

[0084] Among them, in order to facilitate the establishment of the simulation fault library, it is advisable to divide the posterior probability of the fault into three levels: Level 1 indicates that the fault occurs under the condition of the symptom state combination, and its posterior probability setting range is greater than or equal to 0.8; Level 2 indicates that it is uncertain whether the fault occurs under the condition of the symptom state combination, and its posterior probability setting range is 0.4~0.8; Level 3 indicates that the fault does not occur under the condition of the symptom state combination, and its posterior probability setting range is less than or equal to 0.4. i The posterior probability of the fault f is determined first when various associated symptom state combinations are combined. i The posterior probability of the fault belongs to which level, and then the order of the posterior probability of each fault in the fault node set F is determined in combination with the prior knowledge of the fault, and the posterior probability value of each fault is determined.

[0085] Among them, the specific method flow of "optimization of the conditional probability of the diagnostic model" in step 3 is: first, generate a candidate set L(C) of conditional probability tables of the Bayesian network diagnostic model; then determine the optimal set C of conditional probability tables of the Bayesian network diagnostic model in L(C) based on the conditional probability optimization algorithm.

[0086] The specific method of "generating the candidate set L(C) of the conditional probability table" in step 3 is as follows: when the symptom node s j When associating t fault nodes, according to the Bayesian network principle, the symptom node s j Conditional probability table c j Need to confirm 2 t Conditional probability α k , that is, the conditional probability table c j As shown in formula (6).

[0087]

[0088] Let the generated conditional probability α k The interval accuracy is δ, and c is generated iteratively j Each conditional probability α k The candidate value set L(α k ), as shown in formula (7).

[0089]

[0090] For example, when δ = 0.01,

[0091] Based on α k The candidate value set L(α k ) can determine c j The candidate set L(c j ) as shown in formula (8).

[0092]

[0093] Among them, α k,p represents the conditional probability α k The value of the set L(α k ), c j,m Indicates c j For the set L(c j ) is the set of m-th candidate conditional probabilities.

[0094] Based on the conditional probability table c of each symptom node j The candidate set L(c j), we can get the conditional probability candidate set L(C) of the Bayesian network diagnosis model, as shown in formula (9).

[0095]

[0096] Among them, β n Represents the conditional probability table set C of the nth Bayesian network diagnostic model in L(C).

[0097] The process of conditional probability optimization in step 3 is as shown in the attached Figure 1 As shown, the process steps are:

[0098] (1) Select a conditional probability set β in L(C) n Input into the Bayesian network diagnostic model to form the Bayesian network diagnostic model BN n =(F,S,E,B,C=β n ).

[0099] (2) Input all the symptom state combinations L(W) in the fault simulation sample library into the Bayesian network diagnosis model BN in sequence n In the calculation, the actual fault posterior probability set L(Pa n ), as shown in formula (10).

[0100]

[0101] (3) Calculate the actual fault posterior probability set L(Pa n ) and the predicted fault posterior probability set L(P F ) n .

[0102] Among them, the error er n The calculation method is to take L(Pa n ) and L(P F ) is calculated by taking the difference of the posterior probabilities corresponding to each symptom state and squaring them, and then dividing them by the total number of fault posterior probabilities in each posterior probability set.

[0103]

[0104] (4) Recording error n And save it in the list L(er n )middle.

[0105] (5) Repeat the above four steps to calculate All errors corresponding to the conditions, Filter out the list L(er n ) minimum value er m , and based on the minimum error er mThe subscript m selects the corresponding conditional probability set β from the candidate set L(C) of the conditional probability table m , and obtain the optimal parameters of the Bayesian network diagnosis model.

[0106] The specific embodiments are as follows:

[0107] The specific implementation steps of the method for calculating the initialization parameters of the Bayesian network include the following three steps:

[0108] Step 1: Establish a Bayesian network diagnostic model

[0109] Based on the expert knowledge of the main pump, it is known that when the guide bearing on the main pump motor fails, its bearing temperature exceeds the alarm threshold, and the spectrum analysis of the motor shaft vibration can be performed to observe the characteristic frequency of bearing friction, that is, the vibration waveform has a "clipping" phenomenon, and the motor shaft vibration 1, 2, 3, and 4 times the frequency increases. Similarly, when the main pump main thrust bearing fails, there are signs of "motor shaft vibration with bearing friction characteristics" and "main thrust bearing temperature exceeds the threshold." Therefore, the establishment of the auxiliary Figure 2 The Bayesian network diagnostic model shown.

[0110] Based on the above main pump bearing diagnosis rules, a Bayesian network diagnosis model is established as shown in formula (1). In which, the fault node set F = {f1, f2}, the symptom node set S = {s1, s2, s3}, and the edge set connecting the symptom node and the fault node E = {e 1，1 , e 1，2 , e 2，2 ,e 2，3 The specific meanings of the fault node codes and symptom node codes are shown in Table 1. The symptom status of each symptom node is a binary variable, with 0 and 1 indicating that the symptom has not occurred and has occurred, respectively.

[0111] Table 1 Specific meaning of each code

[0112]

[0113] Since main pump bearing failures are rare and lacking in case studies, we can set the prior probability of the motor guide bearing failure, which occurs less frequently, to 0.1. For main thrust bearing failures, which occur more frequently and are affected by the main pump axial force and are related to primary circuit parameters, the prior probability can be set to 0.15. Therefore, the set of prior probabilities for fault occurrence is B = {0.1, 0.15}.

[0114] Step 2: Create a simulation sample library

[0115] Based on the association between the faulty node and the symptom node in step 1, we know that the associated symptom set S1 for faulty node f1 = {s1, s2}. The state variables of symptom nodes s1 and s2 are both binary variables. Therefore, the symptom state set W for associated symptom set S1 = {(0, 0), (0, 1), (1, 0), (1, 1)}.

[0116] There are two possible causes for the "bearing temperature exceeds the threshold" symptom: 1. Excessive lubricant oil temperature, causing the bearing temperature to exceed the threshold when lubricating the bearing; 2. Bearing damage, resulting in wear and heat, causes the bearing temperature to exceed the threshold. Symptom s2 occurs when a bearing exhibits wear failure. Therefore, the simultaneous occurrence of symptoms s1 and s2 indicates the occurrence of fault f1. The presence of only one symptom does not guarantee the occurrence of fault f1. The absence of both symptoms indicates that fault f1 has not occurred.

[0117] Based on the above diagnostic rules and the posterior probability level settings, the posterior probability of fault f1 occurring under each symptom state is determined. For example, when the symptom states of symptom nodes s1 and s2 are both 1, the posterior probability of fault f1 occurring is set to 0.90 based on the diagnostic rules, i.e., v4 = ((1, 1), 0.90).

[0118] By the same token, we can obtain v1 = ((0, 0), 0.02), v2 = ((0, 1), 0.05), and v3 = ((1, 0), 0.90).

[0119] Therefore, the specific content of the simulation sample set g1 of fault f1 is shown in Table 2.

[0120] Table 2 Motor upper guide bearing fault simulation sample library g1

[0121]

[0122] Referring to the steps of establishing the simulation sample set g1, the simulation sample set g2 of the fault f2 is determined. The specific content is shown in Table 3.

[0123] Table 3 Main thrust bearing fault simulation sample library g2

[0124]

[0125] The simulated fault sample library G of the entire Bayesian network diagnosis model is determined based on g1 and g2, and its specific content is shown in Table 4.

[0126] Among them, the combination set of all symptom states in the simulated fault sample library G

[0127] L(W)={(0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1)},

[0128] The set of posterior probabilities of each fault occurring corresponding to each symptom state

[0129] L(P F ) = {(0.02, 0.02), (0.02, 0.6), (0.05, 0.1), (0.05, 0.9), (0.48, 0.02), (0.48, 0.6), (0.9, 0.1), (0.9, 0.9)

[0130] Table 4 Simulated fault sample library G of the diagnosis model

[0131]

[0132] Step 3: Conditional probability optimization of the diagnostic model.

[0133] First, a candidate set of conditional probability tables for the diagnostic model is generated. Since symptom node s1 is associated with a faulty node, according to the Bayesian network principle, the conditional probability table c1 for symptom node s1 is shown in Table 5. Two conditional probabilities α1 and α2 need to be determined, i.e., c1 = {α1, α2}.

[0134] Table 5 Conditional probability table c1 of sign s1

[0135]

[0136] In Table 5, H(f1) = 0 indicates that fault f1 has not occurred, and H(f1) = 1 indicates that fault f1 has occurred. P(H(s1) = 0 | H(f1)) represents the conditional probability that symptom s1 does not occur under the corresponding fault state, and P(H(s1) = 1 | H(f1)) represents the conditional probability that symptom s1 occurs under the corresponding fault state.

[0137] For example, when generating the conditional probability α k When the interval precision is δ = 0.01, according to formula (7), each conditional probability α in c1 is k The set of candidate values

[0138] Since the range of conditional probabilities α1 and α2 belongs to L(α k ), according to formula (8), we can get the candidate set of c1 L(c1) = {(0, 0), (0.1, 0), …, (1, 0.99), (1, 1)}. Similarly, we can get the candidate sets L(c2) and L(c3) of the conditional probability tables c2 and c3.

[0139] By combining various conditional probabilities in L(c1), L(c2) and L(c3), we can obtain the conditional probability candidate set L(C) = {[(0,0),(0,0,0,0),(0,0)],…} = {β n} n＝1,2,… .

[0140] Based on the conditional probability candidate set L(C) of the diagnosis model, the method for learning the optimal conditional probability of the Bayesian network diagnosis model includes the following four steps.

[0141] (1) When β n =[(0.03, 0.92),(0.05, 0.8, 0.8, 0.9),(0.03, 0.92)], the conditional probability table of each symptom node can be derived according to formula (9), and its specific content is: c1 = (0.03, 0.92), c2 = (0.05, 0.8, 0.8, 0.9), c3 = (0.03, 0.92). The conditional probability tables c1, c2 and c3 are input into the Bayesian network to form the Bayesian network diagnosis model BN n =(F,S,E,B,C=β n )

[0142] (2) Then all the symptom state combinations L(W) in the fault simulation sample library are input into the Bayesian network diagnosis model BN in sequence. z In the actual situation, the posterior probability set of the fault occurrence corresponding to each symptom state is calculated The specific calculation results are shown in Table 6.

[0143] Table 6 Bayesian network diagnosis model BN n Calculation results

[0144]

[0145]

[0146] (3) Calculate the actual fault posterior probability set L(Pa n ) and the predicted fault posterior probability set L(P F ) z According to formula (11), the sum of squares of the difference between the posterior probabilities of faults f1 and f2 under the same symptom conditions in Table 4 and Table 6 is calculated to obtain the error er z .

[0147]

[0148] (4) Referring to the previous three steps, calculate the nThe error er corresponding to the remaining elements in the conditional probability candidate set L(C) n According to all the error results, the error er z =0.004 is the minimum value among all errors. Therefore, the optimal value of the conditional probability table of this diagnostic model is β z =[(0.03,0.92),(0.05,0.8,0.8,0.9),(0.03,0.92)] corresponding to c1, c2 and c3.

Claims

1. A Bayesian network parameter initialization method, characterized by: It includes the following three steps: Step 1: Establish a Bayesian network diagnostic model, determine the fault type and symptom type of the equipment to be studied, clarify the symptoms associated with each fault, and preliminarily define the parameters of the diagnostic model, thereby establishing a Bayesian network diagnostic model; Step 2: Generate a simulated fault sample library G. Based on the expert knowledge of the equipment, form diagnostic rules. Then, based on the diagnostic rules, obtain a simulated "symptom state - fault posterior probability" combination to generate a simulated fault sample library. Step 3: Optimize the conditional probability of the diagnosis model. Based on the simulated fault sample library, establish a Bayesian network initialization parameter self-learning algorithm to optimize the conditional probability parameters of the diagnosis model. The conditional probability optimization process steps are as follows: (1) Select a conditional probability set β in L(C) n Input into the Bayesian network diagnostic model to form the Bayesian network diagnostic model BN n =(F,S,E,B,C=β n ); Where L(C) is the conditional probability candidate set of the Bayesian network diagnosis model. The conditional probability candidate set of each symptom node is iteratively generated with an interval accuracy of δ. F represents the set of all fault nodes in the diagnosis model, S represents the set of all symptom nodes in the diagnosis model, E represents the set of connecting edges between each fault node and the associated symptom node, B represents the set of prior probabilities of each fault node, and C represents the set of conditional probability tables of each symptom node. (2) Input all the symptom state combinations L(W) in the fault simulation sample library into the Bayesian network diagnosis model BN in sequence n In the calculation, the actual fault posterior probability set L(Pa n ): Where N is the total number of symptom nodes; (3) Calculate the actual fault posterior probability set L(Pa n ) and the predicted fault posterior probability set L(P F ) n ; Among them, the error er n The calculation method is to take L(Pa n ) and L(P F ) in the posterior probability corresponding to each symptom state, calculate the difference and square it, and then divide it by the total number of fault posterior probabilities in each posterior probability set; (4) Recording error n And save it in the list L(er n )middle; (5) Repeat the above four steps to calculate All errors corresponding to the conditions, Filter out the list L(er n ) minimum value er m , and based on the minimum error er m The subscript m selects the corresponding conditional probability set β from the candidate set L(C) of the conditional probability table m , and obtain the optimal parameters of the Bayesian network diagnosis model.

2. A Bayesian network parameter initialization method according to claim 1, characterized in that: The Bayesian network diagnosis model is established in step 1, and its specific steps are as follows: (1) according to the relevant information of the device to be studied, the fault type and symptom type are determined, thereby determining all the fault node sets F and symptom node sets S of the Bayesian network diagnosis model; (2) Through expert knowledge analysis of the equipment under study, the corresponding relationship between each fault node and symptom node in the Bayesian network diagnosis model is clarified, and the connection line / edge set E between the symptom node and the fault node is established, thereby establishing the structure of the Bayesian network diagnosis model; (3) Combined with the expert knowledge of the equipment, the prior probability set B of the fault node and the conditional probability set C of the symptom node are preliminarily determined, thereby completing the establishment of the Bayesian network diagnosis model.

3. A Bayesian network parameter initialization method according to claim 1, characterized in that: Step 1: Establish a Bayesian network diagnosis model. According to formula 1, the Bayesian network diagnosis model consists of five parts: the fault node set F, the symptom node set S, the edge set E connecting the symptom node and the fault node, the prior probability set B of the fault node, and the conditional probability set C of the symptom node. composition: BN=(F,S,E,B,C) Formula 1 The specific meanings of each symbol are as follows: BN: represents the fault diagnosis model based on Bayesian network F: represents the set of all fault nodes in the diagnosis model, f i represents the i-th fault node, F={f i } i＝1,…,M S: represents the set of all symptom nodes in the diagnosis model, s j represents the jth symptom node, S={s j } j＝1,…,N E: represents the set of edges connecting each fault node and the associated symptom node, e i,j Indicates that the i-th fault node is associated with the j-th symptom node, E={e i,j } i＝1,…,M；j＝1,…,N B: represents the prior probability set of each fault node, b i represents the prior probability of the i-th fault node, B={b i } i＝1,…,M C: represents the conditional probability table set of each symptom node, c j The conditional probability table of the j-th symptom node, C = {c j } j＝1,…,N .

4. A Bayesian network parameter initialization method according to claim 2, characterized in that: The step 1 of "determining a priori probability set B" specifically includes: combining expert knowledge and fault case sample data to determine the ranking of different fault occurrence probabilities during equipment operation, and then setting the priori probability set B based on the ranking of the fault occurrence probabilities.

5. A Bayesian network parameter initialization method according to claim 2, characterized in that: In step 2, a simulated fault sample library is generated. The specific method is: based on the expert knowledge of the equipment, the fault node f is determined. i The associated symptom set S i : S i ={s k } k∈[1,N] Formula 2 Let H(s k ) represents the symptom node s k Current symptom status, H(s k )=0 indicates the symptom node s k The symptom state is not occurred, H(s k )=1 indicates symptom node s k The symptom state is occurrence; When S i When there are x (1≤x≤N) symptom nodes in the network, based on the Bayesian network principle S i The state set W is shown in Formula 3, which contains 2 x Combination of symptom states: Among them, w q Represents the qth symptom state combination in W.

6. A Bayesian network parameter initialization method according to claim 5, characterized in that: In step 2, w is determined in turn based on expert knowledge. q The corresponding fault f under the condition i All posterior probabilities Thus establishing the fault f i The simulated sample set g i : in, Indicates that the symptom state is w q Corresponding fault f i The posterior probability of occurrence is Refer to the above to establish the fault f i The simulated sample set g i The simulated sample sets of all faults in the fault sample set F are determined in turn, thereby establishing a simulated fault sample library G, as shown in Formula 5. G={g i } i＝1,…,M Formula 5 Among them, the combination set of all symptom states in the simulated fault sample library G The set of fault posterior probabilities corresponding to each symptom state 7. A Bayesian network parameter initialization method according to claim 6, characterized in that: The posterior probability of the fault is divided into three levels: Level 1 indicates that the fault occurs under the symptom state combination conditions, and its posterior probability setting range is greater than or equal to 0.8; Level 2 indicates that it is uncertain whether the fault occurs under the symptom state combination conditions, and its posterior probability setting range is 0.4 to 0.8; Level 3 indicates that the fault does not occur under the symptom state combination conditions, and its posterior probability setting range is less than or equal to 0.

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8. A Bayesian network parameter initialization method according to claim 7, characterized in that: The fault f i When setting the posterior probability, first determine the fault f under various associated symptom state combinations. i The posterior probability of the fault belongs to which level, and then the order of the posterior probability of each fault in the fault node set F is determined in combination with the prior knowledge of the fault, and the posterior probability value of each fault is determined.

9. A Bayesian network parameter initialization method according to claim 7, characterized in that: The specific method flow of the optimization of the conditional probability of the diagnostic model in step 3 is as follows: first, a candidate set L(C) of conditional probability tables of the Bayesian network diagnostic model is generated; then, the optimal set C of conditional probability tables of the Bayesian network diagnostic model in L(C) is determined based on the conditional probability optimization algorithm.

10. A Bayesian network parameter initialization method according to claim 9, characterized in that: The specific method of generating the candidate set L(C) of the conditional probability table is as follows: when the symptom node s j When associating t fault nodes, according to the Bayesian network principle, the symptom node s j Conditional probability table c j Need to confirm 2 t Conditional probability α k , that is, the conditional probability table c j As shown in Formula 6: Let the generated conditional probability α k The interval accuracy is δ, and c is generated iteratively j Each conditional probability α k The candidate value set L(α k ), as shown in Formula 7: Based on α k The candidate value set L(α k ) Determine c j The candidate set L(c j ) as shown in Formula 8: Among them, α k,p represents the conditional probability α k The value of the set L(α k ), c j,m Indicates c j For the set L(c j ) in the mth candidate conditional probability set; Based on the conditional probability table c of each symptom node j The candidate set L(c j ), the conditional probability candidate set L(C) of the Bayesian network diagnosis model is obtained, as shown in Formula 9: Among them, β n Represents the conditional probability table set C of the nth Bayesian network diagnostic model in L(C).

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