A method for equipment fault diagnosability design based on causal matching

Abstract

The present invention relates to a method for designing equipment fault diagnosability based on causal matching, and belongs to the field of system fault diagnosis design. In order to make up for the defects of current equipment in causal diagnosability optimization and design, the method comprises the following steps: Step 1: Establishing a causal matching fault diagnosis model of the equipment system; Step 2: Solving the available minimum consistency relationship set of the causal matching fault diagnosis model in Step 1; Step 3: Solving the minimum consistency relationship set based on the causal matching relationship from the minimum consistency relationship set obtained in Step 2; Step 4: Establishing a diagnosability optimization model based on the minimum consistency relationship set based on the causal matching relationship established in Step 3: Step 5: Solving the diagnosability optimization model established in Step 4. This method improves the fault diagnosis capability of the equipment by optimizing the diagnosability design of the equipment, and promotes the development of the diagnosability of the equipment system to a certain extent.

Description

Technical Field

[0001] The invention relates to an equipment fault diagnosability design method, in particular to an equipment fault diagnosability design method based on causal matching, and belongs to the field of system fault diagnosis design. Background Art

[0002] With the rapid development of science and technology, the complexity of the structure and function of equipment has gradually increased. The complexity of the system's structure and function has greatly increased the probability of its failure, performance degradation and functional failure, and also brought great challenges to the system's fault diagnosis. It is difficult to achieve ideal results by optimizing the design of fault diagnosis algorithms alone. In recent years, the industry has paid more and more attention to improving the system's fault diagnosis capabilities through system diagnosability design. Since the design of the fault diagnosis method is limited by the fault information provided by the system, if the fault information provided by the system itself is insufficient or missing, even the most accurate fault diagnosis algorithm will be of no help. Therefore, it is necessary to start from the source of fault diagnosis and improve the system's fault diagnosis performance.

[0003] Diagnosability refers to the degree to which a fault can be identified with certainty and effectiveness. Among them, "certainty" requires that the fault can be accurately detected and isolated every time a system fault occurs, which essentially emphasizes the ability of the diagnostic system to complete the diagnostic task; "effectively" considers the resource utilization efficiency of the diagnostic system to complete the diagnostic task, that is, it requires the optimization of the resources required to isolate the fault. Diagnosability is an important design feature of the system. Compared with testability, diagnosability fundamentally reflects the system's ability to diagnose faults. A system with good diagnosability can make faults easier to diagnose, help shorten maintenance time, save diagnostic resources, and improve the safety of system operation. It is of great significance to ensure the integrity of the system and the success of the task. Summary of the invention

[0004] The purpose of the present invention is to make up for the defects of current equipment in causal diagnosability optimization and design, and proposes a method for equipment fault diagnosability design based on causal matching. By optimizing the diagnosability design of equipment, the fault diagnosis capability of equipment is improved, which promotes the development of diagnosability of equipment system to a certain extent. The designed causal minimum consistency relationship search algorithm has greatly improved in complexity compared with previous algorithms.

[0005] In order to solve the above problems, the present application is implemented through the following technical solutions:

[0006] A method for designing equipment fault diagnosability based on causal matching is special in that it includes the following steps:

[0007] Step 1: Establish a causal matching fault diagnosis model for the equipment system;

[0008] Step 2: Solve the available minimum consistent relation set of the causal matching fault diagnosis model in step 1;

[0009] Step 3: From the minimum consistency relationship set obtained in step 2, solve the minimum consistency relationship set based on the causal matching relationship;

[0010] Step 4: Establish a diagnosability optimization model based on the minimum consistent relationship set based on the causal matching relationship established in step 3;

[0011] Step 5: Solve the diagnosability optimization model established in step 4.

[0012] Furthermore, the step 1 is as follows: equipment system Using a tuple Indicates that is the set of constraint equations of the equipment system, ; is a set of system internal variables and parameters. ; The variable types in are divided into known variables and unknown variables ,Right now ;

[0013] The structural model of the equipment system is based on a bipartite graph Indicates that is the system edge set: ; The structural model also uses a bipartite graph The correlation matrix A = [ a ij ] Describe: ,

[0014] In the formula: " represents the equation Contains variables ,Right now ; " " represents the equation Does not contain variables ,Right now ;

[0015] A specific behavior pattern is not required All equations are described in:

[0016] make This is a mapping from a set of equations to a set of variables: ,

[0017] make This is a mapping from a set of variables to a set of equations: ,

[0018] because ,make for arrive The mapping of for arrive The system model under a certain behavior mode is expressed as: , the corresponding structural model is: ; Unknown variables The relevant model is ; Here we will The relevant structural model is defined as: ;

[0019] Causality exists in differential equations: ,

[0020] (1) Differential causality: pass The differential of is obtained;

[0021] (2) Integral Causality: pass The points are obtained;

[0022] (3) Mixed causality: and Transform into each other through integration and differentiation operations;

[0023] In order to describe the impact of causality on the diagnosability of the system, let: ,

[0024] in Represents the differential variable in the differential equation Related edges; Represents the difference between non-differentiable variables in differential equations Related edges; express The remaining edges in the system are: .

[0025] Furthermore, the step 2 includes the following specific steps:

[0026] Step 2.1, determine the redundancy of the equipment system and judge whether there is a consistency relationship between the equipment system;

[0027] Step 2.2: Structural model Perform Dulmage-Mendelsohn decomposition to find subsystems with consistent relations;

[0028] Step 2.3, obtain the consistency relation: solve the matching unknown variables through the matching equation, and substitute them into the non-matching equation to obtain the consistency relation of the system.

[0029] Furthermore, the step 2.1 is specifically as follows:

[0030] Given Equipment System , and its structural model is ,make for A mapping of , then: for The structural redundancy of , then the equipment system There is a consistency relationship.

[0031] Furthermore, the step 2.2 is specifically as follows:

[0032] The structural model established in step 1 Perform Dulmage-Mendelsohn decomposition to transform the bipartite graph of the structural model into an upper triangular form. The specific results are as follows:

[0033] Equipment System Divided into 3 subsystems: Structural underdetermined subsystem , ; Structural positive subsystem , ; Structural superstator system , ;because , , , so the consistency relation exists in the structural superdetermined subsystem middle;

[0034] The corresponding structural model Decomposed into three subgraphs: Structural underdetermined subgraph , structural positive subgraph , Structural Super Stator Diagram ; Structural positive part There is a set of Hall elements: , and each Hall element is structurally positive;

[0035] The redundancy of the equipment system structure is further expressed as: ; For equipment system , if and only if ,and When Constitute a consistency relation CR if and only if , the consistency relation CR is the minimum consistency relation .

[0036] Furthermore, the step 2.3 is specifically as follows:

[0037] Step 2.3.1: Find the maximum matching set of the equipment system , the specific steps are as follows:

[0038] A1. Initial value setting: Maximum matching set is an empty set, ;

[0039] B1. Update the maximum matching set: for the system structure model The edge set No. Strip Edge , the edge Merge with the current maximum matching set to form the latest maximum matching set;

[0040] C1. Obtain a new system structure model: Replace the current system structure model with the equation and unknown variables The relevant edges are deleted to obtain a new system structure model;

[0041] D1. Edge set judgment: The edge set of the system structure model obtained in step C1 Make a judgment, if is not an empty set, then execute steps B1 to D1. is an empty set, then Strip Edge The maximum matching set determined is the maximum matching set in step B1, Execute steps B1 to D1 for each edge in the edge set until each edge in the edge set has executed steps B1 and D1;

[0042] E1. Obtain the maximum matching set: After removing the same matches from the maximum matching set obtained in step D, obtain the final maximum matching set ;

[0043] The definition of matching in the algorithm is as follows:

[0044] Structural model of the system ,in , define the mapping and mapping ,

[0045] Given system ,match for Subset of ,and: ,

[0046] If and only if , ,and When it is not a match, is the maximum matching,

[0047] Matching Sets It is only partially ordered, and the number of maximum matches is generally greater than 1;

[0048] Pair Mapping and To expand: , ,

[0049] Matching relationship satisfy: , ,

[0050] Where: The cardinality of the set is the number of elements in the set;

[0051] Step 2.3.2, solving the column complete matching of the equipment system according to the maximum matching set obtained in step 2.3.1;

[0052] For step 2.3.1, the maximum matching set The Maximum matching Perform column full match condition judgment, if , then the maximum match is a column complete match, and it is placed in the column complete match set In; if , then for Maximum matching Perform column full match condition judgment until the maximum matching set is found The maximum matching of all After judging, get the column complete match set ;

[0053] Step 2.3.3: According to the column complete match obtained in step 2.3.2, solve the minimum consistency relation set available for the equipment system :

[0054] A2. Initial value setting: minimum consistent relationship set is an empty set, ;

[0055] B2. Get the column complete match set Each column in the of Related equations: System equations Remove the match Medium Equation Every equation except , do the following: ,

[0056] Where: represent Zhongyu The corresponding set of equations is, for arrive The mapping of

[0057] C2, determine the value obtained in step B2 Is it a minimum consistency relationship: Determine the current Whether the judgment condition is met, if it is met , then it is the minimum consistency relationship; if it does not meet the requirements, continue to add equations until the judgment condition is met. , then, in determining Is it available?

[0058] Where: For The corresponding set of unknown variables;

[0059] D2. Determine whether the minimum consistency relation is available: For the minimum consistency relation obtained in step C2, when Delete the current , otherwise the minimum consistent relation set , , execute step B2 to step D2;

[0060] E2. Obtain the minimum available set of consistent relations : After removing the identical matches from the minimum consistent relationship set obtained in step D2, the final available minimum consistent relationship set is obtained. .

[0061] Furthermore, step 3 specifically includes the following steps: determining the minimum available consistent relationship set Each The causality, according to The causality is classified to obtain the minimum consistency relationship set based on the causal matching relationship:

[0062] Remove any equation After the system For positive system , positive system Hall element obtained after DM decomposition The only perfect match relationship exists in the Hall element:

[0063] If and only if its Hall element There is a perfect match : , positive system is integral causal; if and only if its Hall component There is a perfect match : , , positive system is differentially causal; if and only if there is a perfect match , so that The Hall component is a differential causal, positive definite system It is a mixture of cause and effect;

[0064] in, represent Zhongyu A collection of related equations; Representatives will And its corresponding edges are sequentially from the structure diagram The structure subgraph after deletion;

[0065] Representatives will And its corresponding edges are sequentially from the structure diagram The structure subgraph after deletion; Representing structural subgraph ;

[0066] For the minimum consistent relation set In Every equation in , Remove one equation and the remaining part is structurally positive; The structure is positive and there is a perfect match. The set of Hall components can be obtained by structural decomposition. , for each Hall element , determine each Hall element Causality:

[0067] like The dimension of is greater than 1, , and its matching edges Belongs to, integral edge and differential edge , then the Hall element It is mixed causality, represented by 'mix', i.e. , For Hall element The edge set of The dimension of is greater than 1, , and its matching edges belong , then it is non-causal, represented by 'none', that is, ;

[0068] like The dimension of is equal to 1, , and its matching edges belong , then it is differential causality, represented by 'der', that is, ;

[0069] like The dimension of is equal to 1, , and its matching edges belong , then it is an integral causal relationship, represented by 'int', that is ;

[0070] like The dimension of is equal to 1, , and its matching edges belong , then it is non-causal, represented by 'none', that is, ;

[0071] like In addition to non-causal relationships, it only contains integral causality, then the is integral causality, all integral causality Composition Integral Causality ;

[0072] like In addition to non-causal relationships, it only contains differential causation, then the is differential causation, all differential causation Compositional differential causality ; Otherwise, it is mixed causality, all mixed causal Composition of mixed causality .

[0073] Furthermore, the step 4 includes the following specific steps:

[0074] Step 4.1: Calculate the system failure matrix under different causal conditions ;

[0075] Step 4.2: Calculate the system fault isolation matrix under different causal conditions ;

[0076] Step 4.3: Based on integral , Differentiation ,mix Dimension , establish the corresponding optimization vector : ;

[0077] Step 4.4: Obtain the diagnosability optimization model and constraints.

[0078] Furthermore, the step 4.1 is specifically as follows: for the minimum consistency relationship set under different causal conditions obtained in step 2 And the system's fault set , for system failure Every failure in , the minimum set of consistent relations for the system Every minimal consistency relation , make the following judgment: If , then it means Ability to diagnose faults , then the fault feature matrix ,

[0079] like , then it means Unable to diagnose fault , then the fault feature matrix ,

[0080] Get the fault feature matrix , used to indicate a fault Relationship with consistency The logical mapping relationship is: FSM = [ fr ij ] m × n ,

[0081] Where: .

[0082] Furthermore, the step 4.2 is specifically as follows:

[0083] Step 4.2.1. Calculate the fault feature matrix in step 4.1 The dimension of , where m is the number of rows and n is the number of columns;

[0084] Step 4.2.2: Define the Fault Isolation Matrix is an m*m dimensional identity matrix with all elements being 1;

[0085] Step 4.2.3: Obtain the fault isolation matrix :For the fault feature matrix For each column of ,but , indicating the fault With failure Phase isolation, obtain the fault isolation matrix .

[0086] Furthermore, the step 4.4 is specifically as follows:

[0087] The diagnosability optimization model is: , ,

[0088] For the preferred The price of The minimum number, , For the preferred The corresponding fault isolation matrix.

[0089] Furthermore, the step 5 uses the gray wolf optimization algorithm to solve the model of step 4, as follows:

[0090] Step 5.1: Population initialization, including population size N=500 and maximum number of iterations ,parameter , , ;

[0091] Step 5.2: Based on The range of the gray wolf is randomly initialized. ;

[0092] Step 5.3: If the gray wolf individual Satisfy the conditions , then based on Calculate the fitness value of each wolf, otherwise the gray wolf individual The fitness value is infinite. Secondly, according to the fitness value, find Wolf, Wolf, Wolf;

[0093] Step 5.4: Update the gray wolf individual according to the position update formula location;

[0094] Step 5.5: Update parameters , , ;

[0095] Step 5.6: Determine whether the maximum number of iterations has been reached. If so, the algorithm stops and returns The value of is taken as the optimal solution; otherwise, return to step 5.4.

[0096] The present application discloses a diagnosability optimization design method based on causal matching and the Gray Wolf optimization algorithm, which can improve the reliability and diagnosability of the equipment control system; a consistency relationship search algorithm based on causal matching and availability can overcome the problem of difficulty in searching for system redundant sub-models; a diagnosability optimization design method based on the Gray Wolf optimization algorithm takes into account both the system diagnosability requirements and the consistency relationship design costs.

[0097] This application is based on the structural analysis method, establishes a structural model of the system, fully considers the design process of the consistency relationship and the causal relationship between dynamic variables, and designs algorithms for solving the maximum matching, complete matching and causal matching of the system; in order to facilitate the analysis of the causal diagnosability of the system, a minimum causal consistency relationship search algorithm is designed; the complexity of the algorithm is at the polynomial level, which is a significant improvement over the previous exponential level algorithms; fully considers the impact of causal relationships on the diagnosability of the system, and designs an algorithm for analyzing the causal diagnosability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 is a flow chart of the present invention;

[0099] Figure 2 It is the calculation flow chart of differential causal consistency relationship;

[0100] Figure 3 It is the calculation flow chart of integral causal consistency relationship;

[0101] Figure 4 M 1 The causal structural model of

[0102] Figure 5 M 1 DM decomposition diagram;

[0103] Figure 6 It is the differential causal matching relationship diagram of the positive definite system;

[0104] Figure 7 It is the integral causal matching diagram of the positive definite system;

[0105] Figure 8 This is the mixed causal matching relationship diagram for a positive definite system. DETAILED DESCRIPTION

[0106] The following is a specific implementation of the present invention with reference to the accompanying drawings to further illustrate the composition of the present invention.

[0107] Example 1. Figure 1 A method for equipment fault diagnosability design based on causal matching is shown in Figure 1 As shown, the following steps are included:

[0108] Step 1: Establish a causal matching fault diagnosis model for the equipment system;

[0109] Step 2: Solve the available minimum consistent relation set of the causal matching fault diagnosis model in step 1;

[0110] Step 3: From the minimum consistency relationship set obtained in step 2, solve the minimum consistency relationship set based on the causal matching relationship;

[0111] Step 4: Establish a diagnosability optimization model based on the minimum consistent relationship set based on the causal matching relationship established in step 3;

[0112] Step 5: Solve the diagnosability optimization model established in step 4.

[0113] Furthermore, the step 1 is as follows: equipment system Using a tuple Indicates that is the set of constraint equations of the equipment system, ; is a set of system internal variables and parameters. ; The variable types in are divided into known variables and unknown variables ,Right now ;

[0114] The structural model of the equipment system is based on a bipartite graph Indicates that is the system edge set: ,

[0115] The structural model also uses a bipartite graph The correlation matrix A = [ a ij ] Describe: ,

[0116] In the formula: " represents the equation Contains variables ,Right now ; " " represents the equation Does not contain variables ,Right now ;

[0117] A specific behavior pattern is not required All equations are described in:

[0118] make This is a mapping from a set of equations to a set of variables: ,

[0119] make This is a mapping from a set of variables to a set of equations: ,

[0120] because ,make: for arrive The mapping of for arrive The mapping of

[0121] The system model under a certain behavior mode is expressed as: , the corresponding structural model is: ;

[0122] Unknown variables Related Models ; Here we will The relevant structural model is defined as: ;

[0123] Causality exists in differential equations: ,

[0124] (1) Differential causality: pass The differential of is obtained;

[0125] (2) Integral Causality: pass The points are obtained;

[0126] (3) Mixed causality: and Transform into each other through integration and differentiation operations;

[0127] In order to describe the impact of causality on the diagnosability of the system, let: ,

[0128] in: Represents the differential variable in the differential equation Related edges; Represents the difference between non-differentiable variables in differential equations Related edges; express The remaining edges in the system are: .

[0129] Furthermore, the step 2 includes the following specific steps:

[0130] Step 2.1, determine the redundancy of the equipment system and judge whether there is a consistency relationship between the equipment system;

[0131] Step 2.2: Structural model Perform Dulmage-Mendelsohn decomposition to find subsystems with consistent relations;

[0132] Step 2.3, obtain the consistency relation: solve the matching unknown variables through the matching equation, and substitute them into the non-matching equation to obtain the consistency relation of the system.

[0133] Furthermore, the step 2.1 is specifically as follows:

[0134] Given Equipment System , and its structural model is ,make for A mapping of , then: for The structural redundancy of , then the equipment system There is a consistency relationship.

[0135] Furthermore, the step 2.2 is specifically as follows:

[0136] The structural model established in step 1 Perform Dulmage-Mendelsohn decomposition to transform the bipartite graph of the structural model into an upper triangular form. The specific results are as follows:

[0137] Equipment System Divided into 3 subsystems: Structural underdetermined subsystem , ; Structural positive subsystem , ; Structural superstator system , ;because , , , so the consistency relation exists in the structural superdetermined subsystem middle;

[0138] The corresponding structural model Decomposed into three subgraphs: Structural underdetermined subgraph , structural positive subgraph , Structural Super Stator Diagram ; Structural positive part There is a set of Hall elements: , and each Hall element is structurally positive;

[0139] The redundancy of the equipment system structure is further expressed as: ; For equipment system , if and only if ,and When Constitute a consistency relation CR if and only if , the consistency relation CR is the minimum consistency relation .

[0140] Furthermore, the step 2.3 is specifically as follows:

[0141] Step 2.3.1: Find the maximum matching set of the equipment system , the specific steps are as follows:

[0142] A1. Initial value setting: Maximum matching set is an empty set, ;

[0143] B1. Update the maximum matching set: for the system structure model The edge set No. Strip Edge , the edge Merge with the current maximum matching set to form the latest maximum matching set;

[0144] C1. Obtain a new system structure model: Replace the current system structure model with the equation and unknown variables The relevant edges are deleted to obtain a new system structure model;

[0145] D1. Edge set judgment: The edge set of the system structure model obtained in step C1 Make a judgment, if is not an empty set, then execute steps B1 to D1. is an empty set, then Strip Edge The maximum matching set determined is the maximum matching set in step B1, Execute steps B to D1 for each edge in the edge set until each edge in the edge set has executed steps B1 and D1;

[0146] E1. Obtain the maximum matching set: After removing the same matches from the maximum matching set obtained in step D, obtain the final maximum matching set ;

[0147] The definition of matching in the algorithm is as follows:

[0148] Structural model of the system ,in , define the mapping and mapping ,

[0149] Given system ,match for Subset of ,and: ,

[0150] If and only if , ,and When it is not a match, is the maximum matching,

[0151] Matching Sets It is only partially ordered, and the number of maximum matches is generally greater than 1;

[0152] Pair Mapping and To expand: , ,

[0153] Matching relationship satisfy: , ,

[0154] Where: The cardinality of the set is the number of elements in the set;

[0155] Step 2.3.2, solving the column complete matching of the equipment system according to the maximum matching set obtained in step 2.3.1;

[0156] For step 2.3.1, the maximum matching set The Maximum matching Perform column full match condition judgment, if , then the maximum match is a column complete match, and it is placed in the column complete match set In; if , then for Maximum matching Perform column full match condition judgment until the maximum matching set is found The maximum matching of all After judging, get the column complete match set ;

[0157] Step 2.3.3: According to the column complete match obtained in step 2.3.2, solve the minimum consistency relation set available for the equipment system :

[0158] A2. Initial value setting: minimum consistent relationship set is an empty set, ;

[0159] B2. Get the column complete match set Each column in the of Related equations: System equations Remove the match Medium Equation Every equation except , do the following: ,

[0160] Where: represent Zhongyu The corresponding set of equations is, for arrive The mapping of

[0161] C2, determine the value obtained in step B2 Is it a minimum consistency relationship: Determine the current Whether the judgment condition is met, if it is met , then it is the minimum consistency relationship; if it does not meet the requirements, continue to add equations until the judgment condition is met. , then, in determining Is it available?

[0162] Where: For The corresponding set of unknown variables;

[0163] D2. Determine whether the minimum consistency relation is available: For the minimum consistency relation obtained in step C2, when Delete the current , otherwise the minimum consistent relation set , , execute step B2 to step D2;

[0164] Consistent detectability: Failure is detectable if and only if: ;

[0165] Consistent Isolatability: Failures Can be used with Isolate if and only if: ;

[0166] From the perspective of consistent detectability and consistent isolability: It is helpful for fault isolation analysis; however, there are some It does not contain fault information, constructing the operator To judge Availability: ;

[0167] E2. Obtain the minimum available set of consistent relations : After removing the identical matches from the minimum consistent relationship set obtained in step D2, the final available minimum consistent relationship set is obtained. .

[0168] Furthermore, step 3 specifically includes the following steps: determining the minimum available consistent relationship set Each The causality, according to The causality is classified to obtain the minimum consistency relationship set based on the causal matching relationship:

[0169] Remove any equation After the system For positive system , positive system Hall element obtained after DM decomposition The only perfect match relationship exists in the Hall element:

[0170] If and only if its Hall element There is a perfect match : , positive system It is integral cause and effect;

[0171] If and only if its Hall element There is a perfect match : , , positive system It is differential causal;

[0172] If and only if there is a perfect matching , so that The Hall component is a differential causal, positive definite system It is a mixture of cause and effect;

[0173] in: represent Zhongyu A collection of related equations; Representatives will And its corresponding edges are sequentially from the structure diagram The structure subgraph after deletion;

[0174] Representatives will And its corresponding edges are sequentially from the structure diagram The structure subgraph after deletion; Representing structural subgraph ;

[0175] For the minimum consistent relation set In Every equation in , Remove one equation and the remaining part is structurally positive;

[0176] The structure is positive and there is a perfect match. The set of Hall components can be obtained by structural decomposition. , for each Hall element , determine each Hall element Causality:

[0177] like The dimension of is greater than 1, , and its matching edges Belongs to, integral edge and differential edge , then the Hall element It is mixed causality, represented by 'mix', i.e. , For Hall element The edge set of

[0178] like The dimension of is greater than 1, , and its matching edges belong , then it is non-causal, represented by 'none', that is, ;

[0179] like The dimension of is equal to 1, , and its matching edges belong , then it is differential causality, represented by 'der', that is, ;

[0180] like The dimension of is equal to 1, , and its matching edges belong , then it is an integral causal relationship, represented by 'int', that is ;

[0181] like The dimension of is equal to 1, , and its matching edges belong , then it is non-causal, represented by 'none', that is, ;

[0182] like In addition to non-causal relationships, it only contains integral causality, then the is integral causality, all integral causality Composition Integral Causality ;

[0183] like In addition to non-causal relationships, it only contains differential causation, then the is differential causation, all differential causation Compositional differential causality ; Otherwise, it is mixed causality, all mixed causal Composition of mixed causality .

[0184] Furthermore, the step 4 includes the following specific steps:

[0185] Step 4.1: Calculate the system failure matrix under different causal conditions ;

[0186] Step 4.2: Calculate the system fault isolation matrix under different causal conditions ;

[0187] Step 4.3: Based on integral , Differentiation ,mix Dimension , establish the corresponding optimization vector : ;

[0188] Step 4.4: Obtain the diagnosability optimization model and constraints.

[0189] Furthermore, the step 4.1 is specifically as follows:

[0190] For the minimum consistent relation set under different causal conditions obtained in step 2 And the system's fault set , for system failure Every failure in , the minimum set of consistent relations for the system Every minimal consistency relation , make the following judgment:

[0191] like , then it means Ability to diagnose faults , then the fault feature matrix ,

[0192] like , then it means Unable to diagnose fault , then the fault feature matrix ,

[0193] Get the fault feature matrix , used to indicate a fault Relationship with consistency The logical mapping relationship is: FSM = [ fr ij ] m × n ,

[0194] Where: .

[0195] Furthermore, the step 4.2 is specifically as follows:

[0196] Step 4.2.1. Calculate the fault feature matrix in step 4.1 The dimension of , where m is the number of rows and n is the number of columns;

[0197] Step 4.2.2: Define the Fault Isolation Matrix is an m*m dimensional identity matrix with all elements being 1;

[0198] Step 4.2.3: Obtain the fault isolation matrix :For the fault feature matrix For each column of ,but , indicating the fault With failure Phase isolation, obtain the fault isolation matrix .

[0199] Furthermore, the step 4.5 is specifically as follows:

[0200] The diagnosability optimization model is: , ,

[0201] For the preferred The price of The minimum number, , For the preferred The corresponding fault isolation matrix.

[0202] Furthermore, the step 5 uses the grey wolf optimization algorithm to solve the model of step 4.

[0203] The specific contents of the Gray Wolf optimization algorithm are as follows:

[0204] As a social animal, the gray wolf mainly hunts by tracking, chasing, encircling, harassing, etc. The GWO algorithm is a new type of bionic intelligent optimization algorithm. The GWO algorithm achieves the purpose of algorithm optimization by imitating the social hierarchy and hunting behavior of the gray wolf.

[0205] Gray wolves in nature are top predators that live in groups. Usually, each group consists of 5 to 12 wolves, and there is a strict hierarchy between them. Wolves in the gray wolf family can be divided into four categories according to their social status from high to low. Wolf, Wolf, Wolf and Wolf. The wolf is at the top of the social hierarchy, also known as the "alpha wolf". It is the high ruler and manager of the wolf pack, responsible for deciding the time, place and tactics of the wolf pack's hunting. Wolf, equivalent to the deputy leader of the alpha wolf, if the alpha wolf dies, it is responsible for continuing to lead the wolf pack. The wolf is mainly responsible for reconnaissance, sentinel and guarding. As a wolf, it must obey other dominant wolves in the pack.

[0206] In the GWO algorithm, in order to construct the social hierarchy of gray wolves, the solution with the best fitness value, the second best solution and the third generation solution in the gray wolf population are regarded as Wolf, Wolf, Wolf, the remaining solutions are considered Wolf. Then by Wolf, Wolf, The wolf is responsible for leading, The wolf follows Wolf, Wolf, Wolves are optimized for hunting by searching for prey, surrounding it, and attacking it.

[0207] In the D-dimensional search space, assume that the population consists of N gray wolves. . Define The position of the gray wolf is , indicating the The position of the wolf in D-dimensional space. Define the historical optimal solution of the gray wolf group as Wolf, the suboptimal solution is Wolf, the third best solution is Wolf, other meanings are Wolf.

[0208] The process of the gray wolf approaching and surrounding its prey is reflected in the algorithm as the process of the gray wolf approaching the optimal solution. The position update formula of the gray wolf is: ,

[0209] Where: is the current iteration number; For the location of prey. is the encirclement step length; and They are: , ,

[0210] Where: , They are Random numbers in the interval; is the convergence factor, which changes with the number of iterations, that is: ,

[0211] Where: and are the current number of iterations and the maximum number of iterations respectively.

[0212] The position update formula of each type of gray wolf is: , ,

[0213] Where: express , and The weight coefficient of

[0214] ,

[0215] Where: Represents the fitness value of gray wolf j.

[0216] The gray wolf optimization algorithm of this application is as follows:

[0217] Step 5.1: Population initialization, including population size N=500 and maximum number of iterations ,parameter , , ;

[0218] Step 5.2: Based on The range of the gray wolf is randomly initialized. ;

[0219] Step 5.3: If the gray wolf individual Satisfy the conditions , then based on Calculate the fitness value of each wolf, otherwise the gray wolf individual The fitness value is infinite. Secondly, according to the fitness value, find Wolf, Wolf, Wolf;

[0220] Step 5.4: Update the gray wolf individual according to the position update formula location;

[0221] Step 5.5: Update parameters , , ;

[0222] Step 5.6: Determine whether the maximum number of iterations has been reached. If so, the algorithm stops and returns The value of is taken as the optimal solution; otherwise, return to step 5.4.

[0223] Example 2. This example uses the system model Take some steps of the method in Example 1 as an example to further illustrate.

[0224] Step 1: Establish a causal matching fault diagnosis model for equipment systems for: ,

[0225] in , , , , , is the system failure; the causal structure model is expressed as , its structural model is as follows Figure 4 As shown in Figure 2. The consistency relation mainly focuses on solving the unknown variables of the system.

[0226] Therefore, the diagnosability analysis based on structural analysis is mainly oriented towards the model ,like Figure 4 The blue part.

[0227] Figure 4 The shaded part is "0 or 1", and the blank part is "0". Based on DM decomposition, Divided into 3 subsystems: Structural underdetermined subsystem , , ; Structural positive subsystem , , ; Structural superstator system , , Therefore, the consistency relation exists in the structurally superdetermined subsystem middle. Decomposed into three subgraphs: Structural underdetermined subgraph , structural positive subgraph , Structural Super Stator Diagram . Structural positive part There is a set of Hall elements: , and each Hall element is structurally positive.

[0228] To simplify the definition, and As a structural decomposition operation to obtain the system structure is overdetermined and the structure is positive. For example, the system After DM decomposition, we can get: .

[0229] The calculation process of the consistency relationship is as follows: based on the redundant sub-model, a part of the equations is selected to solve the unknown variables; secondly, based on the redundant equations, a consistency check is performed. Figure 2 , Figure 3 The calculation flow chart of the consistency relationship is shown in FIG. Figure 2 It can be seen that , pass , Calculated; Dynamic variables , pass , Differentiate and finally pass Get the consistency relation : ,

[0230] because and Appear in middle, Appear in In, when , , When any fault occurs, ;otherwise, ;

[0231] from As can be seen from the calculation process, the dynamic variable , The solution of only requires differential operation, so Also called differential causal consistency.

[0232] from Figure 3 It can be seen that the consistency relationship and The equations involved are the same, but the order in which the unknown variables are calculated is different. pass Calculated; , , Apply the equations in turn , , get. , A differential loop is formed, and the differential loop can be broken by an integrator, that is: , in order to facilitate the description of the order Finally, based on Get the consistency relation: ,from It can be seen from the calculation process that the solution of unknown variables only involves integral causality. Therefore, It is called integral causal consistency.

[0233] In order to describe the impact of causality on system diagnosability, let: ,

[0234] Where: Represents the differential variable in the differential equation Related edges; Represents the difference between non-differentiable variables in differential equations Related edges; express The remaining edges.

[0235] Consistency Relationship and , expressed as . Assume that the same fault will not appear in different equations. If the equation There is a fault in , then define it as: .Pick The structural subgraph of , ,

[0236] available The maximum matching set is: , , , . From the returned results, we can see that the maximum match is not unique.

[0237] For structural subgraphs The columns that get the system fully matched are: .

[0238] get The minimum set of consistent relations available for: , , , , , , , , , , ;

[0239] Determine the minimum set of consistent relations available Each The causality, according to The causality of the system is classified .

[0240] For ease of description, we get of The serial number indicates: =[1,2,4,5,8,11]; =[1,2,3,5,6,7,9]; =MCRs.

[0241] For example The fault equation is: , , . The fault is detectable, that is, if , then the fault is detectable. It also contains a smaller consistency relation, namely , .

[0242] Once a matching relationship is determined, the equation endpoints and variable endpoints of the structural model will be removed accordingly, and the algorithm will terminate when there are no edges that can be matched.

[0243] and Belong to the same , but the causal relationship is different. The causal difference in the computation of the consistency relation depends on:

[0244] (1) Which equation is used as the redundant equation and as the equation for finally calculating the consistency relation;

[0245] (2) Determine the use The columns in the are matched exactly to solve for the unknown variables.

[0246] use As a redundant equation; use As a redundant equation. and The DM decomposition results of the matching relationship adopted are as follows Figure 6 and Figure 7 As shown:

[0247] 'int', 'der', and 'mix' represent integral, differential, and mixed causal, respectively. Remove any equation After the system The Hall component obtained after the DM decomposition of the positive system is unique. And, the perfect matching relationship exists in the Hall element. For example Figure 6 The Hall components of the positive system shown in the figure after DM decomposition are: , , , The Hall element corresponds to The columns are exactly matched This also explains Figure 2 middle The calculation order of . Figure 6 It can be seen contains only differential causal matching relations, so It is differential causation. Figure 7 The Hall components of the positive system shown are: , , . It shows that in solving for unknown variables and When it appeared Figure 3 The differential loop shown. Integral causality can break the differential loop, so in In the calculation process, the integral causal relationship is adopted, that is, the column matching relationship adopted is: That is, adopt As The perfect match of is to use integral causality to calculate unknown variables, so It is integral causal.

Claims

1. A method for designing equipment fault diagnosability based on causal matching, characterized in that: The following steps are involved: Step 1: Establish a causal matching fault diagnosis model for the equipment system: Equipment System Using a tuple Indicates that is the set of constraint equations of the equipment system, ; is a set of system internal variables and parameters. ; The variable types in are divided into known variables and unknown variables ,Right now ; The structural model of the equipment system is based on a bipartite graph Indicates that is the system edge set: , The structural model also uses a bipartite graph The correlation matrix Describe: , Where: " represents the equation Contains variables ,Right now ;" " represents the equation Does not contain variables ,Right now ; A specific behavior pattern is not required All equations are described in: make This is a mapping from a set of equations to a set of variables: , make This is a mapping from a set of variables to a set of equations: , because ,make: for arrive The mapping of for arrive The mapping of The system model under a certain behavior mode is expressed as: , the corresponding structural model is: ; Unknown variables Related Models ; Here we will The relevant structural model is defined as: ; Causality exists in differential equations: , (1) Differential causality: pass The differential of is obtained; (2) Integral causality: pass The points are obtained; (3) Mixed causality: and Transform into each other through integration and differentiation operations; make: , in: Represents the differential variable in the differential equation Related edges; Represents the difference between non-differentiable variables in differential equations Related edges; express The remaining edges in the system; the causal structure model of the system is ; Step 2: Solve the available minimum consistent relationship set of the causal matching fault diagnosis model in step 1, including the following specific steps: Step 2.1, determine the redundancy of the equipment system and judge whether there is a consistency relationship between the equipment system; Step 2.2: Structural model Perform Dulmage-Mendelsohn decomposition to find subsystems with consistent relations; Step 2.3, obtain the consistency relation: solve the matching unknown variables through the matching equation, and bring them into the non-matching equation to obtain the consistency relation of the system; Step 3: From the minimum consistency relationship set obtained in step 2, solve the minimum consistency relationship set based on the causal matching relationship, including the following steps: Determine the minimum set of consistent relations available Each The causality, according to The causality is classified to obtain the minimum consistency relationship set based on the causal matching relationship: Remove any equation After the system For positive system , positive system Hall element obtained after DM decomposition The only perfect match relationship exists in the Hall element: If and only if its Hall element There is a perfect match : , positive system It is integral cause and effect; If and only if its Hall element There is a perfect match : , , positive system It is differential causal; If and only if there is a perfect matching , so that The Hall component is a differential causal, positive definite system It is a mixture of cause and effect; in, represent Zhongyu A collection of related equations; Representatives will And its corresponding edges are sequentially from the structure diagram The structure subgraph after deletion; Representatives will And its corresponding edges are sequentially from the structure diagram The structure subgraph after deletion; Representing structural subgraph ; For the minimum consistent relation set In Every equation in , Remove one equation and the remaining part is structurally positive; The structure is positive and there is a perfect match. The set of Hall components can be obtained by structural decomposition. , for each Hall element , determine each Hall element Causality: like The dimension of is greater than 1, , and its matching edges Belongs to, integral edge and differential edge , then the Hall element It is mixed causality, represented by 'mix', i.e. , For Hall element The edge set of ,; like The dimension of is greater than 1, , and its matching edges belong , then it is non-causal, represented by 'none', that is, ; like The dimension of is equal to 1, , and its matching edges belong , then it is differential causality, represented by 'der', that is, ; like The dimension of is equal to 1, , and its matching edges belong , then it is an integral causal relationship, represented by 'int', that is ; like The dimension of is equal to 1, , and its matching edges belong , then it is non-causal, represented by 'none', that is, ; like In addition to non-causal relationships, it only contains integral causality, then the is integral causality, all integral causality Composition Integral Causality ; like In addition to non-causal relationships, it only contains differential causation, then the is differential causation, all differential causation Compositional differential causality ; Otherwise, it is mixed causality, all mixed causal Composition of mixed causality ; Step 4: Establish a diagnosability optimization model based on the minimum consistency relationship set based on the causal matching relationship established in step 3, including the following specific steps: Step 4.1: Calculate the system failure matrix under different causal conditions ; Step 4.2: Calculate the system fault isolation matrix under different causal conditions ; Step 4.3: Based on integral , Differentiation ,mix Dimension , establish the corresponding optimization vector : ; Step 4.4, obtaining the diagnosability optimization model and constraint conditions; Step 5: Solve the diagnosability optimization model established in step 4.

2. The equipment fault diagnosability design method based on causal matching according to claim 1 is characterized in that: The step 2.1 is as follows: Given Equipment System , and its structural model is ,make for A mapping of , then: for The structural redundancy of like , then the equipment system There is a consistency relationship.

3. The equipment fault diagnosability design method based on causal matching according to claim 1 or 2, characterized in that: The step 2.2 is specifically as follows: The structural model established in step 1 Perform Dulmage-Mendelsohn decomposition to transform the bipartite graph of the structural model into an upper triangular form. The specific results are as follows; Equipment System Divided into 3 subsystems: Structural underdetermined subsystem , ; Structural positive subsystem , ; Structural superstator system , ;because , , , so the consistency relation exists in the structural superdetermined subsystem middle; The corresponding structural model Decomposed into three subgraphs: Structural underdetermined subgraph , structural positive subgraph , Structural Super Stator Diagram ; Structural positive part There is a set of Hall elements: , and each Hall element is structurally positive; The redundancy of the equipment system structure is further expressed as: ; For equipment system , if and only if ,and When Constitute the consistency relation CR; If and only if , the consistency relation CR is the minimum consistency relation .

4. The equipment fault diagnosability design method based on causal matching according to claim 3 is characterized in that: The step 2.3 is as follows: Step 2.3.1: Find the maximum matching set of the equipment system , the specific steps are as follows: A1. Initial value setting: Maximum matching set is an empty set, ; B1. Update the maximum matching set: for the system structure model The edge set No. Strip Edge , the edge Merge with the current maximum matching set to form the latest maximum matching set; C1. Obtain a new system structure model: Replace the current system structure model with the equation and unknown variables The relevant edges are deleted to obtain a new system structure model; D1. Edge set judgment: The edge set of the system structure model obtained in step C1 Make a judgment, if is not an empty set, then execute steps B1 to D1. is an empty set, then Strip Edge The maximum matching set determined is the maximum matching set in step B1, Execute steps B1 to D1 for each edge in the edge set until each edge in the edge set has executed steps B1 and D1; E1. Obtain the maximum matching set: After removing the same matches from the maximum matching set obtained in step D, obtain the final maximum matching set ; The definition of matching in the algorithm is as follows: Structural model of the system ,in , define the mapping and mapping , Given system ,match for Subset of ,and: , If and only if , ,and When it is not a match, is the maximum matching, Matching Sets It is only partially ordered, and the number of maximum matches is generally greater than 1; Pair Mapping and To expand: , , Matching relationship satisfy: , , Where: The cardinality of the set is the number of elements in the set; Step 2.3.2, solving the column complete matching of the equipment system according to the maximum matching set obtained in step 2.3.1; For step 2.3.1, the maximum matching set The Maximum matching Perform column full match condition judgment, if , then the maximum match is a column complete match, and it is placed in the column complete match set In; if , then for Maximum matching Perform column full match condition judgment until the maximum matching set is found The maximum matching of all After judging, get the column complete match set ; Step 2.3.3: According to the column complete match obtained in step 2.3.2, solve the minimum consistency relation set available for the equipment system : A2. Initial value setting: minimum consistent relationship set is an empty set, ; B2. Get the column complete match set Each column in the of Related equations: System equations Remove the match Medium Equation Every equation except , do the following: , where: represent Zhongyu The corresponding set of equations is, for arrive The mapping of C2, determine the value obtained in step B2 Is it a minimum consistency relation? Determine the current Whether the judgment condition is met, if it is met , then it is the minimum consistency relationship; if it does not meet the requirements, continue to add equations until the judgment condition is met. , then, in determining Is it available? Where: For The corresponding set of unknown variables; D2. Determine whether the minimum consistency relation is available: For the minimum consistency relation obtained in step C2, when Delete the current , otherwise the minimum consistent relation set , , execute step B2 to step D2; E2. Obtain the minimum available set of consistent relations : After removing the identical matches from the minimum consistent relationship set obtained in step D2, the final available minimum consistent relationship set is obtained. .

5. The equipment fault diagnosability design method based on causal matching according to claim 3 is characterized by: The step 4.1 is specifically as follows: For the minimum consistent relation set under different causal conditions obtained in step 2 And the system's fault set , for system failure Every failure in , the minimum set of consistent relations for the system Every minimal consistency relation , make the following judgment: like , then it means Ability to diagnose faults , then the fault feature matrix , like , then it means Unable to diagnose fault , then the fault feature matrix , Get the fault feature matrix , used to indicate a fault Relationship with consistency The logical mapping relationship is: , Where: , The step 4.2 is specifically as follows: Step 4.2.

1. Calculate the fault feature matrix in step 4.1 The dimension of , where m is the number of rows and n is the number of columns; Step 4.2.2: Define the Fault Isolation Matrix is an m*m dimensional identity matrix with all elements being 1; Step 4.2.3: Obtain the fault isolation matrix :For the fault feature matrix For each column of ,but , indicating the fault With failure Phase isolation, obtain the fault isolation matrix ; The step 4.4 is as follows: The diagnosability optimization model is: , , For the preferred The price of The minimum number, , For the preferred The corresponding fault isolation matrix.

6. The equipment fault diagnosability design method based on causal matching according to claim 3 is characterized by: The step 5 uses the gray wolf optimization algorithm to solve the model of step 4, as follows: Step 5.1: Population initialization, including population size N=500 and maximum number of iterations ,parameter , , ; Step 5.2: Based on The range of the gray wolf is randomly initialized. ; Step 5.3: If the gray wolf individual Satisfy the conditions , then based on Calculate the fitness value of each wolf, otherwise the gray wolf individual The fitness value is infinite. Secondly, according to the fitness value, find Wolf, Wolf, Wolf; Step 5.4: Update the gray wolf individual according to the position update formula location; Step 5.5: Update parameters , , ; Step 5.6: Determine whether the maximum number of iterations has been reached. If so, the algorithm stops and returns The value of is taken as the optimal solution; otherwise, return to step 5.4.

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