A method and system for evaluating failure diagnosability of a fuzzy system

Abstract

The application discloses a fault diagnosability evaluation method and system of a fuzzy system, and the method comprises the following steps: determining a control system according to an application scene; generating an output equation of defuzzification based on a T-S fuzzy model and the control system; constructing an equivalent system based on the output equation; and analyzing in the equivalent system in combination with a preset fault diagnosability metric to quantize diagnosability capability. The system comprises a scene setting module, a defuzzification module, an equivalent module and a quantization module. By using the application, fault diagnosability evaluation of a nonlinear system in engineering application is realized. The application can be widely applied to the field of fault diagnosability analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fault diagnosability analysis, in particular to a fault diagnosability evaluation method and system of fuzzy system. BACKGROUND

[0002] With the progress of industrial technology, the function structure of control system is increasingly complex, and the demand for its safety and reliability is higher and higher. Reducing the risk of failure can effectively improve the service life of the system and ensure the safety and operation quality of the system. Many researchers improve the fault diagnosis ability by designing fault diagnosis algorithm, such as designing a diagnosis algorithm with high precision or strong applicability. However, with the complexity of the control system, the design of the diagnosis algorithm is becoming more and more difficult, and at the same time, considering that the diagnosis algorithm needs to be designed on the premise that the fault can be diagnosed, therefore, simply improving the fault diagnosis algorithm cannot fundamentally improve the fault diagnosis ability of the system.

[0003] Fault diagnosability is a property that characterizes the diagnosis ability of the system, which can determine whether the fault can be diagnosed and the difficulty of diagnosing the fault. At present, some solutions have been proposed for the fault diagnosability analysis problem of control system, but the existing solutions are only applicable to linear systems, however, the application system in actual engineering is usually complex, mostly nonlinear. SUMMARY

[0004] Therefore, in order to solve the technical problem that the existing fault diagnosability analysis method is mostly only applicable to linear systems and cannot be directly applied to the application system in actual engineering, the present application proposes a fault diagnosability evaluation method of fuzzy system, which comprises the following steps:

[0005] determining the control system according to the application scenario;

[0006] establishing the defuzzification output equation of the control system based on the T-S fuzzy model;

[0007] constructing an equivalent system based on the output equation;

[0008] In the equivalent system, the pre-set fault diagnosability metric is combined for analysis, and the diagnosability ability is quantified.

[0009] In some embodiments, the defuzzification output equation is expressed as follows:

[0010]

[0011] wherein A(k), B u (k), B f (k), B v (k), C(k), D u(k), D f (k) and D w (k) respectively represent corresponding system matrices, x(k) represents the kth system state, u(k) represents the kth system input, y(k) represents the kth system output, f(k) represents the kth fault vector, v(k) represents the first type of noise, and w(k) represents the second type of noise. Different fuzzy rules can be established according to different system matrices, and different systems can be described through the above equations, such as aircraft systems and robot systems described by nonlinear systems.

[0012] In some embodiments, the equivalent system is represented as follows:

[0013] y s -Uu s = Hx(k-s+1) + Ff s +Ee s

[0014] wherein y s , u s , f s , and e s represent corresponding vectors with s as the sliding window length; U, H, F, and E represent corresponding transformation matrices.

[0015] In some embodiments, the step of analyzing, in the equivalent system, in combination with a preset fault diagnosability metric to quantify the diagnosability capability specifically includes:

[0016] In the equivalent system, the definitions of fault isolability and detectability are given by using residuals and residual sets.

[0017] The diagnosability capability is quantified based on the preset fault diagnosability metric.

[0018] In some embodiments, the calculation formula of the diagnosability metric is represented as follows:

[0019]

[0020] M i , 0 = ||Γ.F i θ i || 2

[0021] wherein M i，j represents an isolability index, M i，0 represents a detectability index, F i represents a set of all possible types of faults f i , θ i represents a time series, Γ · represents an invertible matrix, and (Γ · Fj + represents Γ · F j pseudo-inverse matrix.

[0022] In some embodiments, the fault isolability and detectability are defined as follows:

[0023] In the equivalent system, a sliding window length is selected;

[0024] If the time series is θ i , the fault f i is separable, and there is only one residual β i such that where β i and R i represent the residual and the residual set under the influence of the fault f i , respectively;

[0025] If the time series is θ i , the fault f i is detectable, and there is only one residual β i such that where R0 represents the residual set under the fault-free condition;

[0026] The application also provides a fault diagnosability evaluation system for a fuzzy system, the system comprising:

[0027] A scene setting module is configured to determine a control system according to an application scenario;

[0028] A defuzzification module is configured to generate a defuzzified output equation based on a T-S fuzzy model and the control system;

[0029] An equivalent module is configured to construct an equivalent system based on the output equation;

[0030] A quantification module is configured to analyze the fault diagnosability capacity in the equivalent system in combination with a preset fault diagnosability metric.

[0031] Based on the above scheme, the application provides a fault diagnosability evaluation method and system for a fuzzy system, which is based on a T-S fuzzy model to approximate a nonlinear system, and further provides a fault diagnosability evaluation method for a fuzzy system; further, the fault separability and detectability defined based on the statistical distribution information of the residual are used for analysis and evaluation, and the fault diagnosability metric constructed based on the Mahalanobis distance is used for analysis and evaluation, thereby providing a basis for fault diagnosability evaluation of a nonlinear system in engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is a step flowchart of a fault diagnosability evaluation method for a fuzzy system.​

[0033] Figure 2 is a flow chart of an embodiment of the present application using a T-S fuzzy model to approximate a nonlinear system;

[0034] Figure 3 is a flow chart of an embodiment of the present application to quantify the diagnosability of a fuzzy system;

[0035] Figure 4 is a structural block diagram of a fault diagnosability evaluation system of a fuzzy system of the present application. DETAILED DESCRIPTION

[0036] It is noted that the T-S (Tagaki-Sugeno) fuzzy model provides a theoretical basis for approximating complex nonlinear systems, and therefore developing a quantitative fault evaluation of a fuzzy system plays an important role in ensuring the reliability and performance of complex engineering systems.

[0037] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of the present application.

[0038] It should be noted that, for the convenience of description, only the parts related to the present application are shown in the drawings. The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0039] It should be understood that the "system", "device", "unit" and / or "module" used in the present application is a method for distinguishing different components, elements, parts, portions or assemblies at different levels. However, if other words can achieve the same purpose, the words can be replaced by other expressions.

[0040] As shown in the present application and claims, unless the context clearly indicates otherwise, the words "one", "a", "an" and / or "the" do not refer to the singular, but can also include the plural. Generally, the terms "comprise" and "include" only indicate the inclusion of the steps and elements explicitly identified, and these steps and elements do not constitute an exclusive list, and the method or device can also include other steps or elements. The element defined by the phrase "comprising a" does not exclude the presence of additional identical elements in the process, method, product or device comprising the element.

[0041] In the description of the embodiments of the present application, "multiple" refers to two or more than two. The following terms "first", "second" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features.

[0042] In addition, flowcharts are used in the present application to illustrate the operations performed by the system according to the embodiments of the present application. It should be understood that the preceding or subsequent operations are not necessarily performed in sequence. On the contrary, each step can be processed in reverse order or simultaneously. Meanwhile, other operations can be added to these processes, or one or more steps of operations can be removed from these processes.

[0043] Reference Figure 1 The flowchart of an optional example of the fault diagnosability evaluation method of the fuzzy system proposed in the present application can be applied to a computer device. The fault diagnosability evaluation method proposed in the present embodiment can include but is not limited to the following steps:

[0044] Step S1, determining a control system according to an application scenario;

[0045] Step S2, establishing a defuzzification output equation of the control system based on a T-S fuzzy model;

[0046] Step S3, constructing an equivalent system based on the output equation;

[0047] Step S4, in the equivalent system, combining a pre-set fault diagnosability measure for analysis, and quantifying the diagnosability capability.

[0048] In some feasible embodiments, the step S1 specifically includes:

[0049] The process of approximating a nonlinear dynamic model by using a T-S fuzzy model is shown in Figure 2 Specifically, the fuzzy rules in the T-S fuzzy model are as follows:

[0050] Rule 1: IF z1(k) is M l1 AND z2(k) is M l2 ...AND z n (k) is M ln , THEN

[0051]

[0052] where z m (k), m = 1, 2,..., n are premise variables, M lm is the lth rule under zm (k) corresponding fuzzy sets, r is the number of fuzzy rules; is the time variable; are the system state, system input, system output and fault vector, respectively; and denote the noise, which are independent and identically distributed Gaussian vectors with zero mean and symmetric positive definite covariance matrix Λ v and Λ w ; A l , C l , are system matrices with corresponding dimensions. Different fuzzy rules can be established according to different system matrices, and then different systems can be described by the above equations, such as aircraft systems, robot systems, etc. described by nonlinear systems.

[0053] The defuzzification can obtain the following system:

[0054]

[0055] where the system matrices are respectively:

[0056]

[0057]

[0058] membership function where z(k) = [z1(k), z2(k),..., z n (k)] T , and in addition, for any k, W l (z(k)) ≥ 0, (l = 1, 2,..., r),

[0059] The output equation of the defuzzification is quantified for the diagnosability capability, and the implementation process is shown in Figure 3 .

[0060] In some possible embodiments, the step S3 specifically comprises:

[0061] Considering the sliding window length s, the following vector is defined:

[0062] y s = (y T (k-s+1), y T (k-s+2),..., y T (k)) T ,

[0063] u s = (u T (k-s+1), u T (k-s+2),..., u T (k)) T ,

[0064] f s = (f T (k-s+1), f T (k-s+2),..., f T (k)) T ,

[0065] e s = (v T (k-s+1),..., v T (k), w T (k-s+1),..., w T (k)) T ,

[0066] where Based on the above equation, the equivalent equation of the output equation in the S2 step is obtained as follows:

[0067] y s = Uu s = Hx(k-s+1) + Ff s + Ee s

[0068] where the specific form of the matrix is as follows:

[0069]

[0070] U1= C(k-1)A(k-2)...A(k-s+2)B u (k-s+1),

[0071] U2= C(k-1)A(k-2)...A(k-s+3)B u (k-s+2),

[0072] U3= C(k)A(k-1)...A(k-s+2)B u (k-s+1),

[0073] U4= C(k)A(k-1)...A(k-s+3)B u (k-s+2),

[0074]

[0075] The specific form of the matrix F can be obtained by Df 、B f Replace D in the matrix U accordingly u 、B u Representation; Matrix E=(E v E w ) and E v Can be 0, B v Replace D in the matrix U accordingly u 、B u Indicates that E w =diag(D w (k-s+1),...,D w (k)).

[0076] In some feasible embodiments, step S4 specifically includes:

[0077] In order to perform fault diagnosability analysis, the following three assumptions are given.

[0078] Assumption 1: In the equivalent system, the matrix ( HE ) is of full rank.

[0079] Assumption 2: In the fault-free mode, when τ≤k-s+1, the mean μ of the system state vector x(τ) is x(τ) and the covariance matrix Σ x(τ) is known.

[0080] Assumption 3: In the defuzzified output equation, when τ≤k-s+1, the fault vector f(τ)=0.

[0081] S4.1. In the equivalent system, using residuals and residual sets, define fault isolability and detectability.

[0082] The fault time series is defined as follows:

[0083]

[0084] in is the fault vector f at time The i-th element of i=1,...,l y , In addition, when i = 0, θ0≡0 indicates a no-fault mode. Considering only a single fault mode, since the dynamic behavior of the system (5) obeys a Gaussian random distribution, that is, Its statistical information mean vector μ · and the covariance matrix Σ · The specific calculation method is as follows:

[0085]

[0086] Among them Fi is the column of matrix F corresponding to θ i is the covariance matrix of vector es.

[0087] To define fault isolability and detectability, first define the residual:

[0088] β = Hx(k-s+1) + Ff s +Ee s

[0089] β i = Hx(k-s+1) + F i θ i +Ee s

[0090] where β i is the residual under the influence of fault f i . Let F i denote the set of all possible types of faults f i , and further define the corresponding residual set as:

[0091] R i = {β i |f i ∈ F i}

[0092] and R0 = {Hx(k-s+1) + Ee s |f i ≡ 0} represents the residual set under the fault-free mode.

[0093] Give the definition of fault isolability and detectability:

[0094] For the equivalent system, select the sliding window length s, and given the time series θ i , the fault f i can be separated from the fault mode F j if and only if there is a residual β i such that In addition, given the time series θ i , the fault f i is detectable if and only if there is a residual β i such that

[0095] S4.2, based on the preset fault diagnosability metric to quantify the diagnosability ability.

[0096] Specifically, based on the Mahalanobis distance, establish the fault diagnosability metric, in order to realize the quantitative evaluation of fault diagnosability, introduce the Mahalanobis distance:

[0097] ​

[0098] in and ∑α are the corresponding mean and covariance matrices respectively. Then, based on the Mahalanobis distance, a fault diagnosability metric is established.

[0099] Fault diagnosability measurement: For the equivalent system, select the sliding window length s and set the given time series to θ i Fault f i From the failure mode F j The diagnosability measure for separation is defined as:

[0100]

[0101] In particular, the detection of a given time series is θ i Fault f i The diagnosability measure is defined as M i，0 , where M i，0 Replace R in the above formula with R0 j Income.

[0102] Setting: For the equivalent system, select the sliding window length s, given the time series θ i Fault f i From the failure mode F j Separation, if and only if M i，j > 0. In addition, given the time series θ i Fault f i is detectable if and only if M i，0 >0.

[0103] For the equivalent system, select the sliding window length s and set the given time series to θ i Fault f i From the failure mode F j The diagnosability measure for separation is:

[0104]

[0105] And detect the given time series as θ i Fault f i The diagnosability measure is

[0106] M i , 0=||Γ.F i θ i || 2

[0107] in Γ · is a reversible matrix that satisfies ∑ ·is given by (6), and the pseudo-inverse matrix of Γ·F j ) + denotes the pseudo-inverse matrix of Γ·F j .

[0108] It is proved that the fault diagnosability measure can be further calculated as

[0109]

[0110] According to the Cholesky decomposition, we have Then the above equation can be written as

[0111]

[0112] The explicit solution is

[0113]

[0114] In addition, if θ,≡0, then from (12) we have M i , 0=||Γ·F i θ i || 2 .

[0115] The quantitative analysis of fault diagnosability is performed by calculating the result, specifically, calculating the index M i，j or M i，0 The larger the numerical value is, the easier it is to separate the fault f i from the fault mode F j or the easier it is to detect the fault f i .

[0116] In step S4, the fuzzy system diagnosability capability quantification flowchart is implemented, which is referred to Figure 3 .

[0117] As shown in Figure 4 , a fault diagnosability evaluation system of a fuzzy system comprises:

[0118] A scene setting module is configured to determine a control system according to an application scenario;

[0119] A defuzzification module is configured to generate a defuzzified output equation based on a T-S fuzzy model and the control system;

[0120] An equivalence module is configured to construct an equivalent system based on the output equation;

[0121] A quantification module is configured to analyze a preset fault diagnosability measure in the equivalent system and quantify the diagnosability capability.

[0122] The contents in the method embodiments are applicable to the system embodiments, the system embodiments specifically implement the functions same as the method embodiments, and achieve the beneficial effects same as the method embodiments.

[0123] A fault diagnosability evaluation device of a fuzzy system

[0124] At least one processor;

[0125] At least one memory for storing at least one program;

[0126] When the at least one program is executed by the at least one processor, the at least one processor implements the fault diagnosability evaluation method of the fuzzy system.

[0127] The contents in the method embodiments are applicable to the device embodiments, the device embodiments specifically implement the functions same as the method embodiments, and achieve the beneficial effects same as the method embodiments.

[0128] A storage medium, wherein the storage medium stores processor-executable instructions, and the processor-executable instructions, when executed by a processor, are used to implement the fault diagnosability evaluation method of the fuzzy system.

[0129] The contents in the method embodiments are applicable to the storage medium embodiments, the storage medium embodiments specifically implement the functions same as the method embodiments, and achieve the beneficial effects same as the method embodiments.

[0130] The above is a specific description of the preferred embodiments of the application, but the application is not limited to the embodiments, and those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the application, and these equivalent modifications or replacements are all included in the scope defined by the claims of the application.

Claims

1. A method for evaluating fault diagnosability of a fuzzy system, characterized in that: The following steps are involved: Determine the control system based on the application scenario; Based on the TS fuzzy model, the defuzzified output equation of the control system is established; Based on the output equation, construct an equivalent system; In the equivalent system, a preset fault diagnosability metric is combined for analysis to quantify the diagnosability capability; The step of analyzing and quantifying the diagnosability capability in the equivalent system in combination with a preset fault diagnosability metric specifically includes: In the equivalent system, the definitions of fault isolability and detectability are given using residuals and residual sets. Quantifying diagnosability capabilities based on pre-set fault diagnosability metrics; The calculation formula of the diagnosability metric is expressed as follows: M i,0 =||C · F i i i || 2 Among them, M i,j Represents the isolation index, M i,0 Denotes the detectability index, F i Indicates fault f i The set of all possible types, θ i represents the time series, Γ · represents the reversible matrix, (Γ · F j ) + Represents Γ · F j The pseudo-inverse matrix, F j Indicates the failure mode; M i,j or M i,0 The larger the value, the easier it is to i From the failure mode F j Separation or easier to detect fault f i ; The definitions of fault isolability and detectability are as follows: In the equivalent system, the sliding window length is selected; If the time series is θ i Fault f i is separable, there is only one residual β i Make Among them, β i and R i Respectively represent the fault f i residuals and residual sets under influence; If the time series is θ i Fault f i is detectable, there is only one residual β i Make Among them, R0 represents the residual set in the case of no fault.

2. The method for evaluating fault diagnosability of a fuzzy system according to claim 1, characterized in that: The output equation of the defuzzification is expressed as follows: Among them, A(k), B u (k), B f (k), B v (k), C(k), D u (k), D f (k) and D w (k) represents the corresponding system matrix, x(k) represents the kth system state, u(k) represents the kth system input, y(k) represents the kth system output, f(k) represents the kth fault vector, v(k) represents the first type of noise, and w(k) represents the second type of noise.

3. The method for evaluating fault diagnosability of a fuzzy system according to claim 1, characterized in that: The equivalent system is expressed as follows: and s -Uu s =Hx(k-s+1)+Ff s +Ee s Among them, y s 、u s 、f s 、e s represents the corresponding vector with s as the sliding window length; U, H, F and E represent the corresponding transformation matrices.

4. A fault diagnosability evaluation system for a fuzzy system, characterized in that: A method for evaluating fault diagnosability of a fuzzy system according to claim 1, comprising: A scenario setting module is used to determine the control system according to the application scenario; A defuzzification module generates a defuzzified output equation based on the TS fuzzy model and the control system; An equivalent module constructs an equivalent system based on the output equation; The quantification module performs analysis in the equivalent system in combination with a preset fault diagnosability metric to quantify the diagnosability capability.

5. A device for evaluating the fault diagnosability of a fuzzy system, characterized in that: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the fault diagnosability evaluation method for a fuzzy system as described in any one of claims 1 to 3.

Images