Diagnostic optimization design method based on structural redundancy sensor configuration

Abstract

The invention relates to a diagnosability optimization design method based on structural redundancy sensor configuration, and belongs to the technical field of fault diagnosis. Comprising the following steps: 1) based on diagnosability qualitative evaluation of structural analysis, finding out a structural sub-model containing a redundancy relationship in a system, establishing a system minimum consistency relationship and a fault sensitive relationship, and qualitatively evaluating fault detection and isolation conditions of the system; 2) minimum consistency relation characteristic analysis: analyzing the characteristics of the MCR from the perspective of DM decomposition and matching, and laying a theoretical foundation for sensor configuration; and 3) based on the diagnosability optimization design of the structural redundancy sensor configuration, finding out a sensor configuration set with the minimum comprehensive cost to maximize the diagnosability of the system. According to the method, a sensor configuration algorithm is designed based on a fault diagnosis principle of structural analysis, and the aim of maximizing the diagnosable performance of the system at the minimum sensor configuration cost is achieved.

Description

Technical Field

[0001] The invention relates to a diagnosability optimization design method based on structural redundant sensor configuration, belonging to the technical field of fault diagnosis. Background Art

[0002] With the continuous development of new materials, electronic integration, machine learning, artificial intelligence and other technologies, drones are developing in the direction of bionics, intelligence, functional diversification, and cluster coordination, showing strong autonomous decision-making and mission planning capabilities, and have been developed to varying degrees in the military, civilian and agricultural fields. With the continuous upgrading of mission levels and working environments, the failure rate of drones is increasing, which also increases the demand for their reliability and safety.

[0003] Structural analysis focuses on obtaining fault information from the system structure model. In the system design stage, diagnosability optimization design based on structural analysis plays an important role in improving system reliability and safety: first, the system has a large degree of design freedom at this time, and the system model can be adjusted and optimized based on diagnosability requirements; second, there is no need to establish a detailed system model, which is advantageous for the diagnosability design of large and complex control systems; third, the use of related tools based on graph theory avoids complex numerical calculations, which is more advantageous than the fault diagnosis method based on analytical models. Wang Zhipeng (Wang Zhipeng, Du Changqing, Hu Jie, et al. Fault diagnosis of 48V mild hybrid system based on structural analysis [J]. Journal of Jiangsu University (Natural Science Edition), 2019, 40 (6): 636-642.) Based on structural analysis, the design of the fault diagnosis system of the 48V mild hybrid system can take into account both the residual design cost and the fault diagnosis requirements. Ding Hua (Ding Hua, Wu Peihong. Fault diagnosis of wire-controlled pedal position sensor based on structural analysis [J]. Electronic Design Engineering, 2021, 29(5): 65-70.) proposed a sensor fault diagnosis strategy for wire-controlled pedal based on structural analysis, and used the system's minimum structural overdetermined design residual to design the diagnostic system, which greatly reduced the design cost of the diagnostic system. Yang Xinhua (Yang Xinhua, Tan Shuiping. EMCVT fault diagnosis and fault-tolerant control based on structural analysis [J]. Journal of Chongqing University of Technology (Natural Science), 2022, 36(8): 134-145.) For the system model of the electromechanical control continuously variable transmission control system, a diagnosability and reconfigurability analysis and design strategy based on structural analysis was proposed, which realized online detection of system faults and active fault-tolerant control. Chen Qi (Chen Qi, Wang Jincheng, Ahmed Q, et al. Model-Based Fault Diagnosis of an Anti-LockBraking System via Structural Analysis[J]. Sensors, 2018, 18(12): 4468.) Based on structural analysis, the key faults of the automobile anti-lock braking system were analyzed, and the fault diagnosis performance of the system was improved through sensor configuration.

[0004] The current research on structural analysis methods mainly has the following problems: First, the existing sensor configuration strategy based on structural analysis lacks relevant theoretical basis and cannot guarantee the maximization of system diagnosability at the minimum cost; second, the diagnosability optimization design based on structural analysis mainly optimizes the cost of the diagnostic system, and most of them lack the optimization of the fault diagnosability itself. Therefore, based on the fault diagnosis principle of structural analysis, this paper designs a sensor configuration algorithm to achieve the purpose of maximizing the system diagnosability performance at the minimum sensor configuration cost. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to provide a diagnosability optimization design method based on structural redundant sensor configuration. Based on the fault diagnosis principle of structural analysis, a sensor configuration algorithm is designed to achieve the purpose of maximizing the diagnosability performance of the system with the minimum sensor configuration cost.

[0006] The diagnosability optimization design method based on structural redundant sensor configuration of the present invention is special in that it includes the following steps:

[0007] Step 1: Qualitative evaluation of diagnosability based on structural analysis

[0008] Find out the structural sub-models containing redundant relations (consistency relations, parity relations) in the system, and establish the sensitive relationship between the system's minimum consistency relation and faults, and qualitatively evaluate the system's fault detection and isolation;

[0009] Step 2: Minimum consistency relation characteristics analysis

[0010] From the perspective of DM decomposition and matching, the characteristics of MCR are analyzed to lay a theoretical foundation for sensor configuration;

[0011] Step 3: Diagnosability optimization design based on structural redundant sensor configuration

[0012] Find the sensor configuration set with the lowest overall cost to maximize the diagnosability of the system.

[0013] Preferably, the specific steps of step 1 are:

[0014] 1.1 Structural Model

[0015] The structural model of the system is a bipartite graph. Indicated by, where E is the system constraint equation, V is the system internal variable, is the system edge set:

[0016]

[0017] The structural model of the system is a bipartite graph. The association matrix A = [a ij ] to describe:

[0018]

[0019] Given a mapping Q:2 E →2 V :

[0020]

[0021] Given mapping R:2 V →2 E :

[0022]

[0023] The variable V can be subdivided into system state variables X, known variables Z, and system faults F. Therefore, the mapping Q is further defined as: Q X :2 E →2 X , Q Z :2 E →2 Z , Q F :2 E →2 F ; The mapping R is further defined as: R X :2 X →2 E , R Z :2 Z →2 E , R F :2 F →2 E ;

[0024] Structural analysis is mainly aimed at models related to the unknown variables X of the system, that is, For ease of description, Expressed as

[0025] 1.2 Fault diagnosis principle based on structural analysis

[0026] The structural model of the known system M is make but:

[0027]

[0028] is the structural redundancy of M, |·| represents the cardinality of the set, that is, the number of elements in the set. Then M has a consistency relation;

[0029] 1.2.1Dulmage-Mendelsohn (DM) decomposition

[0030] DM decomposition is to , find the subsystem M′=(E′,X′)∈M so that Converted to upper triangular form, after decomposition, the corresponding structure diagram Divided into: Structural under-stator diagram Structural positive subgraph Structural superstator diagram And the structure is positive subgraph G 0 It is further divided into a group of Hall elements: G1, G2, ..., G n , and each Hall element G i are all structurally positive; the system M is divided into: structurally underdetermined subsystems M - =(E - ,X - ), and |E - |<|X - |; Structure positive stator subsystem M 0 =(E 0 ,X 0 ), and |E 0 |=|X 0 |; Structural superstator system M + =(E + ,X + ), and |E + |>|X + |; Therefore, That is, the consistency relation of the system exists in the structural overdetermined subsystem M + In the above formula, +, 0, and - are used as operators to obtain the system's structural overdetermined, structural positively determined, and structurally underdetermined respectively;

[0031] Based on DM decomposition, formula (5) is further expressed as:

[0032]

[0033] Because |E + |>|X + |, therefore exist:

[0034]

[0035] The set of equations of the system M = (E, V) A consistency relationship (CR) is formed if and only if E r =E + ;

[0036] like and Then E r Constitute a consistent relationship;

[0037] A consistency relation CR is a minimum consistency relation (MCR) if and only if there is no Let CR′ be a consistency relation, and

[0038] A fault f in a system M = (E, V) is structurally detectable if and only if:

[0039] e f ∈E + (8) Among them, e f represents the equations affected by the fault;

[0040] Fault f in system M = (E, V) i It can be combined with f j Isolated if and only if:

[0041]

[0042] Structural isolability and structural detectability can be transformed into each other. Let NF represent the no-fault mode, then equation (8) can be written as:

[0043] e f ∈(E\e NF ) + (10) make Then formula (9) is written as:

[0044]

[0045] 1.2.2 Matching

[0046] Known systems Define a mapping for the edge and mapping That is: p E (a) = e, p V (a) = x.

[0047] Known For the system The edge of The system is matched if and only if:

[0048]

[0049] is a maximum matching if and only if It is not a match;

[0050] is a complete match if and only if or when The match is a complete match of the column; when The match is a complete match of the line; when The match when is a perfect match;

[0051] According to the matching characteristics, the mapping p E and p X Expanded to the mapping π E :N→2 E and the mapping π X :N→2 X ,for satisfy:

[0052]

[0053] Then, match satisfy:

[0054]

[0055] 1.3 Qualitative analysis of diagnosability

[0056] The minimum set of consistent relations of the known system M is: MCRs = {MCR1, MCR2, ..., MCR m}, the system fault set is: F = {f1,f2,…,f n}, establish the fault feature matrix FSM = [fm ij ] n×m :

[0057]

[0058] Establish the fault isolation matrix FIM = [f ij ] n×n :

[0059]

[0060] Based on FSM and FIM, the fault detection rate (FDR) of system M can be obtained as:

[0061]

[0062] where or(fm i·) represents the logical OR operation between the i-th row data of the FSM, and the fault isolation rate (FIR) is:

[0063]

[0064] Preferably, the specific steps of step 2 are:

[0065] E′ is a minimal consistency relation if and only if the system (E′,Q X (E′)) has a column-by-column match E′=(E′) + ,and

[0066] Known The columns of MCR are fully matched. The relationship between equations and variables in MCR is:

[0067]

[0068] Assumptions is the matching relationship of the system M=(E,X), if but There is a consistency relationship; if but Constitute the minimum consistency relationship;

[0069] Known structure positive subgraph G 0 The Hall element is G0 = {G1, G2, ..., G n},but:

[0070]

[0071] Given that G0 = {G1, G2, ..., G n} is the positive part of the system structure G 0 If the sensor y is added to measure G i The unknown variable x in i ∈π X (G i ), that is, the system adds the constraint equation e:y=x i .but Constitute the minimum consistency relationship.

[0072] Preferably, the specific steps of step 3 are:

[0073] 3.1 Sensor configuration based on detectability

[0074] If we add a sensor y to measure the unknown variable x k , that is, add the measurement equation e:y=xk ,but is MCR; let F i =Q F (π E (G i )),but F i is detectable. By configuring the sensor is detectable, then the remaining fault F i \f is also detectable; if F i is detectable, then for because So f j Also detectable; through sensor configuration π X (G i ) makes is detectable, then Fault j Also detectable; measured by sensor configuration Any unknown variable in F i The fault is detectable;

[0075] Based on the sorting relationship of the Hall components, sort the faults related to the Hall components: if G i ≤G j , then F i ≤F j ,make like Then all faults in the positive part of the system structure are detectable;

[0076] Given that G0 = {G1, G2, ..., G n} is the positive part M of the system structure 0 The Hall element set, for Fault F i =Q F (π E (G i )) is detectable if and only if

[0077] Design a sensor configuration algorithm based on detectability Algorithm 1: The input of the algorithm is M 0 , the output is to satisfy M 0 The sensor configuration set S with maximum detectability of faults D , the algorithm is called SensorDetectability, and Algorithm 1 can be further expressed as S D =SensorDetectability(M 0 ), the specific steps are as follows:

[0078] Step 1: Based on formula (26), 0 The Hall components {G1, G2, ..., G n} to sort

[0079] Step 2: Sort the faults of the Hall components to obtain the maximum fault set F of the system m ;

[0080] Step 3: For F m Every maximum fault set F k , find its sensor configuration D(F k );

[0081] Step 4: For the sensor configuration set D(F k ), find the minimum collision set S of the sensor configuration set D .

[0082] 3.2 Sensor Configuration Based on Isolatability

[0083] e f ∈E + , that is, E + The faults in are all detectable. Then the fault f can achieve its maximum isolability; in special cases, In Q F ((E\e f ) 0 ) fault, based on Algorithm 1, by adding the measurement equation E S , so that That is, f and f k is structurally isolable, equivalent to f k in((E\e f ) 0 ∪E S ) + is structurally detectable; in special cases, That is, f and f j appears in the same equation, Therefore, it is further shown that the two cannot be isolated from each other; but f cannot be isolated from F ((E\e f ) - ) in the fault phase isolation; due to M + The structural decomposition after removing any equations may only contain positive and overdetermined parts, but not underdetermined parts. F ((E\e f ) -) does not exist, and its structural detectability does not need to be considered;

[0084] M + =(E + ,X + ) is the positive part of the system structure, then can achieve its maximum isolability if and only if

[0085] Design a sensor configuration algorithm based on isolability Algorithm 2: The input of the algorithm is M + , the output is to satisfy M + The sensor configuration set S with maximum isolability of faults I , the algorithm is called SensorIsolability, and Algorithm 2 can be further expressed as S I =SensorIsolability(M + ), the specific steps are as follows:

[0086] Step 1: M + Each fault f i Find the sensor configuration that satisfies its maximum isolation

[0087] Step 2: For each faulty sensor configuration set D obtained in step 1 f (i) Find the minimum collision set S of the sensor configuration set I .

[0088] 3.3 Sensor configuration based on diagnosability

[0089] Diagnosability can be divided into detectability and isolability. Based on Algorithm 1 and Algorithm 2, a sensor configuration algorithm based on diagnosability, Algorithm 3, is designed to ensure that the system achieves maximum diagnosability and isolability. The basic principle of Algorithm 3 is: first, through Algorithm 1, all system faults are measurable; second, based on Algorithm 2, the system faults are guaranteed to achieve their maximum isolability.

[0090] Design a sensor configuration algorithm based on diagnosability, Algorithm 3: The input of the algorithm is the system M = (E, X), and the output is the sensor configuration set S that satisfies the maximum diagnosability of faults in the system M = (E, X). The algorithm is called SensorDiagnosis. Further, Algorithm 3 can be expressed as S = SensorDiagnosis (M = (E, X)). The specific steps are as follows:

[0091] Step 1: Obtain the structural positive part M that satisfies the system M = (E, X) 0 The maximum detectable sensor configuration set S D =SensorDetectability(M 0 );

[0092] Step 2: S D Each sensor configuration S i , find the sensor configuration that satisfies the maximum isolability of the system at this time and in, Represents a multiset S i and S j and between;

[0093] Step 3: Delete the same sensor configurations in S to obtain the sensor configuration set that ultimately satisfies the maximum diagnosability of the system. S .

[0094] The present invention discloses a diagnosability optimization design method based on structural redundant sensor configuration. Based on the system structure model, a sensor configuration algorithm is designed to seek the minimum sensor configuration set that satisfies the maximum diagnosability of the system. First, for the faults of the positive part of the system structure, Algorithm 1 is designed to seek the minimum sensor configuration set that satisfies the maximum detectability of the system; secondly, for the faults of the overdetermined part of the structure, Algorithm 2 is designed to seek the minimum sensor configuration set that satisfies the maximum isolatability of the system; finally, based on Algorithm 1 and Algorithm 2, Algorithm 3 is designed to seek the minimum sensor configuration set that satisfies the maximum diagnosability of the system. The existing sensor configuration strategy based on structural analysis lacks relevant theoretical basis and cannot guarantee the maximization of system diagnosability at the minimum cost; secondly, the diagnosability optimization design based on structural analysis mainly optimizes the cost of the diagnostic system, and most of them lack the optimization of the fault diagnosability itself. Therefore, based on the fault diagnosis principle of structural analysis, this paper designs a sensor configuration algorithm to achieve the purpose of maximizing the diagnosability performance of the system with the minimum sensor configuration cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 : It is the decomposition diagram of DM of the present invention. DETAILED DESCRIPTION

[0096] Example 1

[0097] This embodiment describes in detail a diagnosability optimization design method based on structural redundant sensor configuration of the present invention. The processing flow of the present invention is described in detail below:

[0098] Step 1: Qualitative evaluation of diagnosability based on structural analysis

[0099] The basic principle of structural analysis is to find the structural sub-models that contain redundant relations (consistency relations, odd-even relations) in the system. The system M can be represented by a tuple (E, V), where E is the system constraint equation and V is the internal variable of the system.

[0100] 1.1 Structural Model

[0101] Compared with the analytical model of the system, its structural model focuses on E and V The logical mapping relationship between them.

[0102] Definition 1 (Bipartite Graph) The structural model of the system can be represented by a bipartite graph. Indicates. is the system edge set:

[0103]

[0104] Definition 2 (Incidence Matrix) The structural model of the system can be represented by a bipartite graph The association matrix A = [a ij ] to describe:

[0105]

[0106] When modeling a specific behavior of a system M, not all equations in E are needed. Given a mapping Q:2 E →2 V :

[0107]

[0108] Given mapping R:2 V →2 E :

[0109]

[0110] Depending on the nature of the variables, the mapping Q can be further defined as: X :2 E →2 X , Q Z :2 E →2 Z , Q F :2 E →2 F ; The mapping R can be further defined as: R X :2 X →2 E , R Z :2 Z →2E , R F :2 F →2 E .

[0111] Structural analysis is mainly aimed at models related to the unknown variables X of the system, that is, For ease of description, It can be expressed as:

[0112] 1.2 Fault diagnosis principle based on structural analysis

[0113] Structural analysis mainly uses Dulmage-Mendelsohn (DM) decomposition and matching to find the structural sub-models that contain consistent relationships in the system.

[0114] Definition 3 (Structural Redundancy) The structural model of the known system M is make but:

[0115]

[0116] is the structural redundancy of M. Among them, |·| represents the cardinality of the set, that is, the number of elements in the set. Then M has a consistency relation.

[0117] 1.2.1Dulmage-Mendelsohn decomposition

[0118] Based on the Dulmage-Mendelsohn (DM) decomposition, we can , find the subsystem M′=(E′,X′)∈M so that like Figure 1 As shown, based on DM decomposition, Convert to upper triangle form. Figure 1 In the correlation matrix shown in , the blank part is 0, and the gray part is 0 or 1. After DM decomposition, the corresponding structure diagram Divided into: Structural under-stator diagram Structural positive subgraph Structural superstator diagram And the structure is positive subgraph G 0 It can be further divided into a group of Hall components: G1, G2, …, G n , and each Hall element G i are all structurally positive. The system M can be divided into: structurally underdetermined subsystems M - =(E - ,X - ), and |E - |<|X -|; Structure positive stator subsystem M 0 =(E 0 ,X 0 ), and |E 0 |=|X 0 |; Structural superstator system M + =(E + ,X + ), and |E + |>|X + |. Therefore, That is, the consistency relation of the system exists in the structural overdetermined subsystem M + In order to simplify the definition, +, 0, and - are regarded as operators for obtaining the system's structural overdetermined, structural positively determined, and structurally underdetermined, respectively.

[0119] Based on DM decomposition, formula (5) can be further expressed as:

[0120]

[0121] Because |E + |>|X + |, therefore exist:

[0122]

[0123] Definition 4 (Consistency relation) The set of equations of a system M = (E, V) is called A consistency relationship (CR) is formed if and only if E r =E + .

[0124] Lemma 1: If and Then it constitutes a consistency relationship.

[0125] Lemma 1 shows that E + There may be multiple consistency relations in .

[0126] Definition 5 (Minimum Consistency Relationship) A consistency relation CR is called a minimum consistency relation (MCR) if and only if there is no Let CR′ be a consistency relation, and

[0127] Definition 6 (Structural Detectability) A fault f in a system M = (E, V) is structurally detectable if and only if:

[0128] e f ∈E+ (8) Among them, e f Represents the equation affected by the fault.

[0129] Definition 7 (Structural Isolatability) The fault f in the system M = (E, V) is i It can be combined with f j Isolated if and only if:

[0130]

[0131] Structural isolability and structural detectability can be transformed into each other. Let NF represent the no-fault mode, then equation (8) can be written as:

[0132] e f ∈(E\e NF ) + (10)

[0133] make Then formula (9) can be written as:

[0134]

[0135] 1.2.2 Matching

[0136] The consistency-based fault principle states that: by solving the matching unknown variables through the matching equations, and bringing them into the non-matching equations (redundant equations), the consistency relationship of the system is obtained. In structural analysis, matching only focuses on the matching relationship between equations and unknown variables, and has nothing to do with the algebraic elimination between equations. Known system Define a mapping for the edge and mapping That is: p E (a) = e, p V (a) = x.

[0137] Definition 8 (Matching) Known For the system The edge of The system is matched if and only if:

[0138]

[0139] Definition 9 (maximum matching) is called is a maximum matching if and only if Not a match.

[0140] Definition 10 (Complete Match) is a complete match if and only if or when The match is a complete match of the column; when The match is a complete match of the line; when The match is perfect.

[0141] Based on Definition 8, we know that the matching set N of the system is only partially ordered, and the number of maximum matching is not unique. According to the matching characteristics, the mapping p E and p X Expanded to the mapping π E :N→2 E and the mapping π X :N→2 X .for satisfy:

[0142]

[0143] Then, match satisfy:

[0144]

[0145] like Figure 1 As shown, due to |E - |<|X - |, so M - There is a row-matching relationship in |E 0 |=|X 0 |, M 0 There is a perfect matching relationship in the Hall element G i is structurally positive definite, so G i There is a perfect matching relationship in |E + |>|X + |, so M + There is a column-to-column matching relationship in . It can be seen that the column-to-column matching relationship is closely related to the consistency relationship.

[0146] 1.3 Qualitative analysis of diagnosability

[0147] The minimum set of consistent relations of the known system M is: MCRs = {MCR1, MCR2, ..., MCR m}, the system fault set is: F = {f1,f2,…,f n}. Based on Definition 6, establish the fault feature matrix FSM = [fm ij ] n×m :

[0148]

[0149] Based on Definition 7, the fault isolation matrix FIM = [f ij ] n×n :

[0150]

[0151] Based on FSM and FIM, the fault detection rate (FDR) of system M can be obtained as:

[0152]

[0153] where or(fm i· ) represents the logical OR operation between the i-th row data of the FSM.

[0154] The fault isolation rate (FIR) is:

[0155]

[0156] Step 2: Minimum consistency relation characteristics analysis

[0157] Mainly from the perspective of DM decomposition and matching, the characteristics of MCR are analyzed to lay a theoretical foundation for subsequent research.

[0158] Theorem 1E′ is a minimal consistency relation if and only if the system (E′,Q X (E′)) has a column-by-column match E′=(E′) + ,and prove:

[0159] Sufficiency. Since the system (E′,Q X (E′)) There is a column-by-column match therefore Since E′=(E′) + ,so:

[0160]

[0161] Based on Definition 4 and Definition 5, we can see that E′ is the minimum consistency relation.

[0162] Necessity. If E′ is the minimum consistency relation, then E′=(E′) + and That is (E′,Q X The number of equations in (E′) is one more than the number of unknown variables. So All have e i =R X (x i ),e j =R X (x j ) corresponds to it, and e i ≠ej .Right now There exists an ordered pair (e i ,x i ), forming a set and Satisfy p E (a1)≠p E (a2)∧p E (a1)≠p X (a2). For the system (E′,Q X (E′)) is the maximum matching. Therefore The column is fully matched. so:

[0163]

[0164] Theorem 1 gives the structural decomposition and matching characteristics of MCR, which links the structural overdetermined characteristics and column complete matching relationship in MCR. is the column complete matching relationship of MCR. Based on Theorem 1, the relationship between equations and variables in MCR is:

[0165]

[0166] Lemma 2 Assumption is the matching relationship of the system M=(E,X), if but

[0167] There is a consistency relationship. but Constitute the minimum consistency relationship.

[0168] Proof: If but but:

[0169]

[0170] Therefore, There is a consistency relationship. Based on equation (6) and equation (25), if but Constitute the minimum consistency relationship.

[0171] Lemma 2 gives the consistency relation obtained by using the system matching relation and the redundant equation. However, Lemma 2 weakens the constraints of the system structure characteristics and the selection of redundant equations. This lays the foundation for the construction of the consistency relation. DM decomposition shows that the consistency relation only exists in the structural overdetermined part M of the system. + . System structure positive part M 0, there is only a perfect matching relationship, so there is no consistency relationship. Therefore, M can be constructed by sensor configuration 0 In order to facilitate description, the variables of the Hall component matching are sorted based on their membership. 0 The Hall element is G0 = {G1, G2, ..., G n}.but:

[0172]

[0173] Lemma 3 Given G0 = {G1, G2, ..., G n} is the positive part of the system structure G 0 If sensor y is added to measure G i The unknown variable x in i ∈π X (G i ), that is, the system adds the constraint equation e:y=x i .but Constitute the minimum consistency relationship.

[0174] Proof: Based on DM decomposition, we know that since G 0 The perfect matching relationship exists in its Hall component, that is, therefore There is a perfect match between . Based on Lemma 2, we know that There is a consistency relationship. so but and That does not exist So that E″ constitutes a consistency relation. Based on Definition 5, we can see that E′ is the minimum consistency relation.

[0175] For the underdetermined part of the structure, due to Therefore, if we want to increase the structural redundancy through sensor configuration, the cost is huge. - |-|E - The larger | is, the more expensive the sensor configuration is. However, in real systems, there are very few systems with underdetermined structures, so they are not considered here.

[0176] Step 3: Diagnosability optimization design based on structural redundant sensor configuration

[0177] Based on Lemma 3, we know that sensor configuration is the basis for the existence of system structural redundancy. Therefore, the structural redundancy of the system can be increased through sensor configuration, thereby achieving the purpose of optimizing the diagnosability of the system. Since the cost of system sensor configuration is huge, this section mainly finds the minimum sensor configuration set to maximize the diagnosability of the system. In the actual equipment control system design, in order to ensure that the system state is controllable and observable, there is generally no structural underdetermined part. Therefore, the sensor configuration of the structural underdetermined part is not considered here.

[0178] 3.1 Sensor configuration based on detectability

[0179] Based on Definition 6, we know that the fault in the overdetermined structure can be detected. Therefore, the sensor configuration based on detectability is mainly oriented to the positive part of the structure. Assume that the system state is observable. Based on Lemma 3, we know that If we add a sensor y to measure the unknown variable x k , that is, add the measurement equation e:y=x k ,but is MCR. For the convenience of description, all sensors are represented by unknown variables. Let F i =Q F (π E (G i )),but Based on Definition 6, we know that F i is detectable. Therefore, the detectability of faults in the same Hall element is equivalent. That is, by configuring the sensor is detectable, then the remaining fault F i \f is also detectable. Furthermore, if F i is detectable, then for because So f j Therefore, if the sensor is configured with π X (G i ) makes is detectable, then Fault j It is also detectable. Therefore, the sensor configuration is used to measure Any unknown variable in F i The faults in G are detectable. This also further shows that only a part of the faults need to be detectable. Therefore, based on the sorting relationship of the Hall components, the faults related to the Hall components are sorted: if G i ≤G j , then F i ≤F j .make like Then all faults in the positive part of the system structure are detectable.

[0180] Theorem 2 Given G0 = {G1, G2, ..., G n} is the positive part M of the system structure 0 A collection of Hall components. Fault F i =Q F (π E (G i )) is detectable if and only if

[0181] Proof: Sufficiency. If Based on Lemma 3, D(F k ) for any unknown variable x k , that is, increase the measurement equation but For MCR. Then F k All faults in the f j ∈Q F (π E (G j )), Right now Its faults are all detectable. Therefore, if F m If all faults in G are detectable, then 0 All faults in the system are detectable.

[0182] Necessity. F i =Q F (π E (G i )) are all detectable, which implies

[0183] Based on Theorem 2, a detectability-based sensor configuration algorithm Algorithm 1 is designed.

[0184]

[0185] Algorithm 1 returns the value that can be implemented in G 0 The minimum set of sensors S whose faults can be detected D .

[0186] 3.2 Sensor Configuration Based on Isolatability

[0187] Known e f ∈E + , that is, E+ All faults in are detectable. Based on Definition 7, if Then fault f can achieve its maximum isolability. At this time, f cannot be compared with F ((E\e f ) - ) is isolated from the fault phase. However, F ((E\e f ) 0 ) fault, based on Algorithm 1, it can be solved by adding the measurement equation E S , so that That is, f and f k is structurally isolable, equivalent to f k in(E\e f ) 0 ∪E S ) + is structurally detectable. In special cases, That is, f and f j appears in the same equation, This further shows that the two cannot be isolated from each other. + The structural decomposition after removing any equations may only contain positive and overdetermined parts, but not underdetermined parts. F (E\e f ) - ) does not exist and its structural detectability does not need to be considered.

[0188] Theorem 3M + =(E + ,X + ) is the positive part of the system structure, then can achieve its maximum isolability if and only if

[0189] Proof: Sufficiency. If for Let its sensor configuration equation be but is structurally overdetermined. Therefore therefore The fault in is structurally detectable, which is equivalent to Faults in f i is structurally isolable. The faults in are themselves structurally detectable, so f i It is also structurally isolable. Therefore, if f iTo achieve maximum isolation. Necessity. It can achieve its maximum isolability. Based on Definition 7, it is necessary to ensure The faults in are structurally detectable. The faults in are detectable by themselves and are not considered here. Based on Theorem 2, if It can guarantee is structurally detectable.

[0190] Based on Theorem 3, the isolatable sensor configuration algorithm Algorithm 2 is designed.

[0191]

[0192] 3.3 Sensor configuration based on diagnosability

[0193] Diagnosability can be divided into detectability and isolability. Based on Algorithm 1 and Algorithm 2, this section designs a sensor configuration algorithm based on diagnosability, Algorithm 3, to ensure that the system achieves its maximum diagnosability and isolability. The basic principle of Algorithm 3 is: first, through Algorithm 1, ensure that all system faults are measurable; second, based on Algorithm 2, ensure that the system faults achieve their maximum isolability. The algorithm may involve the union of multiple sets. Let Represents the union of multisets A and B.

[0194] For example

[0195]

[0196] This embodiment designs a sensor configuration algorithm based on the fault diagnosis principle of structural analysis to achieve the purpose of maximizing the diagnosable performance of the system with the minimum sensor configuration cost.

Claims

1. A diagnosability optimization design method based on structural redundant sensor configuration, characterized in that The following steps are involved: Step 1: Qualitative evaluation of diagnosability based on structural analysis Find out the structural sub-models that contain redundant relationships in the system, and establish the sensitive relationship between the system's minimum consistency relationship and faults, and qualitatively evaluate the system's fault detection and isolation; Step 2: Minimum consistency relation characteristics analysis From the perspective of DM decomposition and matching, the characteristics of MCR are analyzed to lay a theoretical foundation for sensor configuration; Step 3: Diagnosability optimization design based on structural redundant sensor configuration Find the sensor configuration set with the lowest overall cost to maximize the diagnosability of the system.

2. A diagnosability optimization design method based on structural redundant sensor configuration according to claim 1, characterized in that The specific steps of step 1 are: 1.1 Structural Model The structural model of the system is a bipartite graph Indicated by, where E is the system constraint equation, V is the system internal variable, is the system edge set: The structural model of the system is a bipartite graph. The association matrix A = [a ij ] to describe: Given a mapping Q:2 E →2 V : Given mapping R:2 V →2 E : The variable V can be subdivided into system state variables X, known variables Z, and system faults F. Therefore, the mapping Q is further defined as: Q X :2 E →2 X , Q Z :2 E →2 Z , Q F :2 E →2 F ; The mapping R is defined as: R X :2 X →2 E , R Z :2 Z →2 E , R F :2 F →2 E ; Structural analysis is mainly aimed at models related to the unknown variables X of the system, that is, Expressed as 1.2 Fault diagnosis principle based on structural analysis The structural model of the known system M is make but: is the structural redundancy of M, |·| represents the cardinality of the set, that is, the number of elements in the set. Then M has a consistency relation; 1.2.1 DM decomposition DM decomposition is to , find the subsystem M′=(E′,X′)∈M so that Converted to upper triangular form, the corresponding structure diagram Divided into: Structural under-stator diagram Structural positive subgraph Structural superstator diagram And the structure positive stator graph G0 is further divided into a group of Hall components: G1, G2, ..., G n , and each Hall element Gi is structurally positive; the system M is divided into: structurally underdetermined subsystem M - =(E - ,X - ), and |E - |<|X - |; Structure positive stator subsystem M 0 =(E 0 ,X 0 ), and |E 0 |=|X 0 |; Structural superstator system M + =(E + ,X + ), and |E + |>|X + |; Therefore, That is, the consistency relation of the system exists in the structural overdetermined subsystem M + In the above formula, +, 0, and - are used as operators to obtain the system's structural overdetermined, structural positively determined, and structurally underdetermined respectively; Based on DM decomposition, formula (5) is further expressed as: Because |E + |>|X + |, therefore exist: The set of equations of the system M = (E, V) The consistency relation CR is formed if and only if E r =E + ; like and Then E r Constitute a consistent relationship; A consistency relation CR is a minimal consistency relation MCR if and only if there does not exist Let CR′ be a consistency relation, and A fault f in a system M = (E, V) is structurally detectable if and only if: and f ∈E + (8) Among them, e f represents the equations affected by the fault; Fault f in system M = (E, V) i is with f j Isolated if and only if: Structural isolability and structural detectability can be transformed into each other. Let NF represent the no-fault mode, then equation (8) can be written as: And f ∈(E\e NF ) + (10) make Then formula (9) is written as: 1.2.2 Matching Known systems For the edge, define the mapping p E : and the mapping p X : That is: p E (a) = e, p V (a) = x; Known For the system The edge of The system is matched if and only if: is a maximum matching if and only if It is not a match; is a complete match if and only if or when The match is a complete match of the column; when The match is a complete match of the line; when The match when is a perfect match; According to the matching characteristics, the mapping p E and p X Expanded to the mapping π E :N→2 E and the mapping π X :N→2 X ,for satisfy: Then, match satisfy: 1.3 Qualitative analysis of diagnosability The minimum set of consistent relations of the known system M is: MCRs = {MCR1, MCR2, ..., MCR m }, the system fault set is: F = {f1,f2,...,f n }, establish the fault feature matrix FSM = [fm ij ] n×m : Establish the fault isolation matrix FIM = [f ij ] n×n : Based on FSM and FIM, the fault detection rate FDR of system M can be obtained as: where or(fm i. ) represents the logical OR operation between the i-th row data of FSM, and the fault isolation rate FIR is:

3. A diagnosability optimization design method based on structural redundant sensor configuration according to claim 1, characterized in that The specific steps of step 2 are: E′ is a minimal consistency relation if and only if the system (E′,Q X (E′)) has a column-by-column match E′=(E′) + ,and Known The columns of MCR are fully matched. The relationship between equations and variables in MCR is: Assumptions is the matching relationship of the system M=(E,X), if but There is a consistency relationship; if but Constitute the minimum consistency relationship; Known structure positive subgraph G 0 The Hall element is G0 = {G1, G2, ..., G n },but: Given that G0 = {G1, G2, ..., G n } is the positive part of the system structure G 0 If the sensor y is added to measure G i The unknown variable x in i ∈π X (G i ), that is, the system adds the constraint equation e:y=x i ,but Constitute the minimum consistency relationship.

4. A diagnosability optimization design method based on structural redundant sensor configuration according to claim 1, characterized in that The specific steps of step 3 are: 3.1 Sensor configuration based on detectability If we add sensor y to measure the unknown variable x k , that is, add the measurement equation e:y=x k ,but is MCR; let F i =Q F (π E (G i )),but F i is detectable, through the sensor configuration is detectable, then the remaining fault F i \f is also detectable; if F i is detectable, then for because So f j Also detectable; through sensor configuration π X (G i ) makes is detectable, then Fault j Also detectable; measured by sensor configuration Any unknown variable in F i The fault is detectable; Based on the sorting relationship of the Hall components, sort the faults related to the Hall components: if G i ≤G j , then F i ≤F j ,make like Then all faults in the positive part of the system structure are detectable; Given that G0 = {G1, G2, ..., G n } is the positive part M of the system structure 0 The Hall element set, for Fault F i =Q F (π E (G i )) is detectable if and only if Design a sensor configuration algorithm based on detectability Algorithm 1: The input of the algorithm is M 0 , the output is to satisfy M 0 The sensor configuration set S with maximum detectability of faults D , the algorithm is called SensorDetectability, and Algorithm 1 is further expressed as SD = SensorDetectability (M 0 ), the specific steps are as follows: Step 1: Based on formula (26), 0 The Hall components {G1, G2, ..., G n } to sort Step 2: Sort the faults of the Hall components to obtain the maximum fault set F of the system m ; Step 3: For F m Every maximum fault set F k , find its sensor configuration D(F k ); Step 4: For the sensor configuration set D(F k ), find the minimum collision set S of the sensor configuration set D ; 3.2 Sensor Configuration Based on Isolatability e f ∈E + , that is, E + The faults in are all detectable. Then the fault f can achieve its maximum isolability; in special cases, In Q F ((E\e f ) 0 ) fault, based on Algorithm 1, by adding the measurement equation E S , so that That is, f and f k is structurally isolatable, equivalent to f k in((E\e f ) 0 ∪E S ) + is structurally detectable; in special cases, That is, f and f j appears in the same equation, Therefore, it is further shown that the two cannot be isolated from each other; but f cannot be isolated from F ((E\e f ) - ) in the fault phase isolation; due to M + The structural decomposition after removing any equations may only contain the positive and overdetermined parts of the structure, but not the underdetermined parts of the structure. F ((E\e f ) - ) does not exist, and its structural detectability does not need to be considered; M + =(E + ,X + ) is the positive part of the system structure, then can achieve its maximum isolability if and only if Design a sensor configuration algorithm based on isolability Algorithm 2: The input of the algorithm is M + , the output is to satisfy M + The sensor configuration set S with maximum isolability of faults I , the algorithm is called SensorIsolability, and Algorithm 2 is further represented by S I =SensorIsolability(M + ), the specific steps are as follows: Step 1: M + Each fault in fi requires a sensor configuration that satisfies its maximum isolability Step 2: For each faulty sensor configuration set D obtained in step 1 f (i) Find the minimum collision set S of the sensor configuration set I ; 3.3 Sensor configuration based on diagnosability Diagnosability can be divided into detectability and isolability. Based on Algorithm 1 and Algorithm 2, a sensor configuration algorithm based on diagnosability, Algorithm 3, is designed to ensure that the system achieves maximum diagnosability and isolability. The basic principle of Algorithm 3 is: first, through Algorithm 1, all system faults are measurable; second, based on Algorithm 2, the system faults are guaranteed to achieve their maximum isolability performance; Design a sensor configuration algorithm based on diagnosability, Algorithm 3: The input of the algorithm is the system M = (E, X), and the output is the sensor configuration set S that satisfies the maximum diagnosability of faults in the system M = (E, X). The algorithm is called SensorDiagnosis. Further, Algorithm 3 can be expressed as S = SensorDiagnosis (M = (E, X)). The specific steps are as follows: Step 1: Obtain the structural positive part M that satisfies the system M = (E, X) 0 The maximum detectable sensor configuration set S D =Sensor Detectability)M 0 ); Step 2: S D Each sensor configuration S i , find the sensor configuration that satisfies the maximum isolability of the system at this time and in, Represents a multiset S i and S j and between; Step 3: Delete S The same sensor configuration in the system is used to obtain the sensor configuration set that ultimately satisfies the maximum diagnosability of the system. S .

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