Fault detection observer based on finite time disturbance compensation and robust fault detection method based on set membership estimation

Abstract

The invention discloses a fault detection observer based on finite time disturbance compensation and a robust fault detection method based on set membership estimation, and belongs to the field of automatic control. According to the fuzzy system state space model and the multi-target fault detection observer, a dynamic error system based on finite time disturbance compensation is obtained under finite time disturbance compensation, and the dynamic error system comprises a dynamic error system under the fault-free condition and a dynamic error system under the condition that only the influence of a fault signal is considered; the dynamic error system under the fault-free condition enables the residual error to have robustness to disturbance and noise, the dynamic error system only considering the influence of the fault signal enables the residual error to have sensitivity to the fault, the residual error comprises an output observation error, and the effect is that the residual error has robustness to interference and has sensitivity to the fault. Residual signals of robust fault detection can be output more accurately, and the fault detection precision of an existing method can be improved.

Description

Technical Field

[0001] The invention belongs to the field of automatic control and relates to a robust fault detection method based on a fault detection observer and set membership estimation with finite-time disturbance compensation. Background Art

[0002] The safety and reliability of engineering systems, such as aircraft engine control systems, nuclear power systems, and chemical systems, are crucial to their development. If a fault occurs and is not detected promptly, it can lead to mission failure or even more serious consequences. Model-based fault diagnosis methods have demonstrated excellent performance in improving system safety and reliability and have garnered widespread attention from researchers over the past three decades. These methods rely on precise mathematical models of the system, but real-world systems often suffer from modeling errors, unknown interference, and measurement noise, which can affect fault diagnosis effectiveness and result in both false positives and false negatives. Therefore, robustness has become a crucial issue in model-based fault diagnosis.

[0003] Robust fault diagnosis requires not only robustness of the residual signal to interference and noise but also a certain degree of sensitivity to faults. However, existing fault detection methods only consider the robustness of the system to interference and noise, without considering fault sensitivity. The design of the fault detection threshold is also a key and difficult issue in fault detection. Some researchers currently use the maximum value of the threshold over all time periods, which obviously leads to a high degree of conservatism in fault detection. Summary of the Invention

[0004] In one aspect, the present invention aims to solve the problem that the low robustness of the residual generated by the fault detection of the aircraft engine system and the large conservativeness of the threshold affect the speed and accuracy of the fault detection. In order to achieve the above-mentioned purpose, according to some embodiments of the present application, a robust fault detection method based on a fault detection observer and set membership estimation based on finite-time disturbance compensation includes the following steps.

[0005] Establishing a fuzzy system state space model of an aircraft engine, the model including parameters for process disturbances, measurement noise, and actuator faults;

[0006] Establish a multi-objective fault detection observer;

[0007] A dynamic error system based on finite-time disturbance compensation is obtained according to a fuzzy system state space model and a multi-objective fault detection observer. The dynamic error system includes a dynamic error system under a fault-free condition and a dynamic error system under the influence of only a fault signal. The dynamic error system under the fault-free condition makes the residual robust to disturbances and noise. The dynamic error system under the influence of only a fault signal makes the residual sensitive to faults. The residual includes an output observation error.

[0008] Obtaining an observer gain matrix according to the dynamic error system under the fault-free condition and the dynamic error system under the influence of only the fault signal;

[0009] A residual evaluation based on set membership estimation is established according to the observer gain matrix, and whether the system fault occurs or not is determined according to the residual evaluation.

[0010] According to a robust fault detection method based on a finite-time disturbance compensation fault detection observer and set membership estimation in some embodiments of the present application, the fuzzy system state space model:

[0011]

[0012] in:

[0013] x k 、u k 、y k They represent the state vector, process input and measurement output of the system respectively, d k and v k represent process disturbance and measurement noise respectively, f k Indicates sensor failure;

[0014] A i , B i , C i , D i , E i , F i Represent a system matrix known to have suitable dimensions;

[0015] i=1,...,s,μ i (ω k ) weight function, ω k =[ω 1k ,…,ω pk ] represents the premise variable, ω k =[ω 1k ,…,ω pk ] represents p premise variables, M i1 ,…,M ip Denotes the corresponding given set, M im (ω k ) represents M im The premise variable ω mk The level of , s represents the number of subsystems and fuzzy rules;

[0016] According to some embodiments of the present application, a robust fault detection method based on a fault detection observer and set membership estimation based on finite-time disturbance compensation is provided, wherein the multi-objective fault detection observer:

[0017]

[0018] in:

[0019] represents the point estimate of the system state at time k+1, represents the point estimate of the system state at time k, L j represents the gain matrix of the observer.

[0020] According to some embodiments of the present application, a robust fault detection method based on a finite-time disturbance-compensated fault detection observer and set membership estimation, the dynamic error system without disturbance compensation:

[0021]

[0022] The dynamic error system based on finite time disturbance compensation:

[0023]

[0024] in:

[0025] e k represents the estimation error of the state; r k represents the output observation error, represents an estimate of the measured output, represents the disturbance estimation error, Denotes the disturbance d k Estimate of , Υ(μ) represents the matrix function, represents the finite-time disturbance compensator, The ratio g / q∈(0,1), g, q are odd numbers, and T represents transpose;

[0026]

[0027] According to a robust fault detection method based on a finite-time disturbance compensation fault detection observer and set membership estimation in some embodiments of the present application, a dynamic error system is divided into two systems;

[0028] Dynamic error system under fault-free conditions:

[0029]

[0030] Consider only the dynamic error system under the influence of fault signals:

[0031]

[0032] represents the disturbance estimation error, d represents the superscript of the residual in the dynamic error system under fault-free conditions, and f represents the superscript of the residual in the dynamic error system under the influence of only the fault signal;

[0033] It represents the state observation error of the dynamic error system under fault-free conditions;

[0034] It represents the state observation error of the dynamic error system considering only the influence of the fault signal;

[0035] represents the output observation error of the dynamic error system under fault-free conditions;

[0036] It represents the output observation error of the dynamic error system considering only the influence of the fault signal.

[0037] in:

[0038] (i) The dynamic error system under fault-free conditions satisfies the conditions ‖‖ represents the norm, ‖‖ ∞ represents the infinite norm, γ1, γ2, α, and P represent the parameters that satisfy the linear matrix inequality conditions. represents the system disturbance under fault-free conditions, and v represents the measurement noise of the system;

[0039] (ii) Considering only the dynamic error system under the influence of the fault signal, the system satisfies the condition represents the transfer function of the dynamic error system input considering only the influence of the fault signal, η represents the parameter that satisfies the linear matrix inequality condition, θ represents the system failure frequency;

[0040] According to a robust fault detection method based on a fault detection observer and set membership estimation with finite-time disturbance compensation in some embodiments of the present application, the observer gain matrix Parameters τ1, τ2, α, G, W, N j , η, δ, K, W′, Q satisfy the following linear matrix inequality conditions:

[0041]

[0042] in,

[0043] L j =G -1 N j ,j=1,...,s

[0044] Ω′ 41 =GA(μ)-N(μ)C(μ)

[0045] Ω′ 42 =-N(μ)D(μ)

[0046] Ω′ 43 =GE(μ)

[0047] Ω′ 44 =WGG T

[0048] N(μ)=GL(μ)

[0049] Ψ′ 11 =W′-(2cosθ l )QC T (μ)C(μ)+He(δ(GA(μ)-N(μ)C(μ)))

[0050] Ψ′ 21 =K(GA(μ)-N(μ)C(μ))-δ(N(μ)F(μ)) T -F(μ) T C(μ)

[0051]

[0052] Ψ′ 31 =GA(μ)-N(μ)C(μ)-δG T +Q

[0053] Ψ′ 32 =-N(μ)F(μ)-G T K T

[0054] Ψ′ 33 =-W′-GG T

[0055] in:

[0056] τ1 represents a given scalar and has no actual physical meaning;

[0057] τ2 represents a given scalar and has no actual physical meaning;

[0058] α represents a given scalar and has no actual physical meaning;

[0059] W represents a positive definite matrix and has no actual physical meaning;

[0060] G represents a matrix and has no actual physical meaning;

[0061] N j Represents a matrix and has no actual physical meaning;

[0062] I represents the identity matrix with appropriate dimensions;

[0063] He means that for a matrix W, we define

[0064] -1 indicates the inverse of the matrix;

[0065] η represents a given scalar and has no actual physical meaning;

[0066] δ represents a given scalar and has no actual physical meaning;

[0067] K represents a matrix and has no actual physical meaning;

[0068] W′ represents a matrix, W′ T =W′, no actual physical meaning;

[0069] Q represents a positive definite matrix and has no actual physical meaning;

[0070] θ l Indicates the fault frequency in the low-frequency domain of the system,

[0071] Θ l represents the given fault frequency domain;

[0072] According to a robust fault detection method based on a finite-time disturbance compensation fault detection observer and set membership estimation in some embodiments of the present application, when the aero-engine system sensor is fault-free, r is obtained according to the dynamic error system under fault-free conditions. k A set member estimate By performing reachable set analysis on the dynamic error system, we can obtain the following reachable set of the dynamic error system:

[0073]

[0074] in:

[0075] Formula (11) and formula (12) are and r k The reachable set of represents the set of system state errors at time k-1, represents a generator matrix, Represents the system disturbance under fault-free conditions A collection of represents a generator matrix, represents the set of system state errors at time k, Represents a generator matrix, <0,H v > represents the set of system measurement noise, H v represents a generator matrix, in ‖‖1 represents the 1-norm, represents a given matrix, s represents the number of subsystems and fuzzy rules, represents a generator matrix, Represents the generator matrix The nth row component of ;

[0076] The residual r is obtained k The interval estimate of , r(k) represents the lower bound of the residual, Indicates the upper bound of the residual, when the system has no faults Once the obtained residual r(k) exceeds the interval, the system fails.

[0077] Beneficial effects of the present invention: The detection of the present invention fully considers the impact of the change rate of disturbance on residual fluctuations, and combines the finite-time disturbance compensation technology with the multi-objective fault detection observer. This integration makes the residual robust in the case of interference, while maintaining sensitivity to faults, and can more accurately output the residual signal of robust fault detection. The fault detection accuracy of the existing method can be improved, and it is not easy to have false alarms or missed alarms. The present invention combines the fault detection observer based on finite-time disturbance compensation with set membership estimation and applies it to the residual generation and residual evaluation of aircraft engine fault detection. First, using the fault detection observer based on finite-time disturbance compensation, the change rate of disturbance is taken into account in the residual generation, which improves the stability of the residual signal. Then, in order to improve the recognition of the residual signal in the fault detection process, the residual signal generation under multi-objective optimization is realized, so that it satisfies both the interference attenuation index and the finite frequency domain H - Performance Metrics. Finally, the residual signal is evaluated using a set membership estimation method based on adaptive zonotopes, which produces an accurate dynamic threshold for fault detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 Flow chart of the detection method;

[0079] Figure 2 is the rank diagram of the antecedent variable;

[0080] Figure 3 An estimated map of the disturbance set for the present invention;

[0081] Figure 4 The residual r1 and threshold diagram of the sudden fault of the aircraft engine sensor under the method proposed by the present invention;

[0082] Figure 5 The residual r2 and threshold diagram of the sudden fault of the aircraft engine sensor under the method proposed by the present invention;

[0083] Figure 6 The residual r1 and threshold diagram of sudden failure of aircraft engine sensor under the existing method;

[0084] Figure 7 The residual r2 and threshold diagram of sudden failure of aircraft engine sensor under the existing method;

[0085] Figure 8 Residual and threshold diagrams for sudden faults in aircraft engine sensors using existing methods. DETAILED DESCRIPTION

[0086] The embodiments of the present application are described in detail below with reference to the accompanying drawings. Examples of the embodiments are shown in the accompanying drawings. The present application provides a robust fault detection method based on a fault detection observer and set membership estimation based on finite-time disturbance compensation, which is used to solve the problems of low robustness of residual generation, low fault sensitivity and large threshold conservatism of fault detection in aircraft engine systems, which affect the fault detection speed and accuracy.

[0087] The robust fault detection method based on a finite-time disturbance-compensated fault detection observer and set membership estimation described in this embodiment generally includes the following steps:

[0088] Establish the fuzzy model state space equation.

[0089] Solve the fault detection observer gain under multi-objective optimization.

[0090] The generated residual information is subjected to reachable set analysis, and the fault detection threshold is generated using set membership estimation for residual evaluation.

[0091] In some specific examples, the present invention combines a fault detection observer based on finite-time disturbance compensation with set membership estimation and applies it to residual generation and residual evaluation in aircraft engine fault detection. This can improve the stability of the residual signal, reduce the conservatism of the fault detection threshold, and improve the speed and accuracy of fault detection.

[0092] Specifically, Figure 1 The flow chart of the detection method is as follows: Figure 1 As shown, the detection method includes the following steps:

[0093] S1. Establishing a fuzzy system state space model for an aircraft engine includes the following steps:

[0094] like Figure 1 As shown in Figure 2, considering that the system is affected by disturbances and noise and actuator failure occurs, the state space of the fuzzy system can be written as follows:

[0095]

[0096] where: x k represents the state vector of the system, A i represents a known matrix of suitable dimensions, u k represents the process input vector of the system, B i represents a known matrix of suitable dimensions, d k represents the process disturbance, E i represents a known matrix of suitable dimensions, y k represents the measured output of the system, C i represents a known matrix of suitable dimensions, v k represents the measurement noise, D i represents a known system matrix of suitable dimensions, f k represents the sensor fault, F i represents a known system matrix of suitable dimensions.

[0097] S1.1 To establish the state observer, the state-space model of the aeroengine fuzzy system is represented as:

[0098]

[0099] where:

[0100] x k represents the state vector of the system, A i represents a known matrix of suitable dimensions, u k represents the process input vector of the system, B i represents a known matrix of suitable dimensions, d k represents the process disturbance, E i represents a known matrix of suitable dimensions, y k represents the measured output of the system, C i represents a known matrix of suitable dimensions, v k represents the measurement noise, D i represents a known system matrix of suitable dimensions, f k represents the sensor fault, F i represents a known system matrix of suitable dimensions.

[0101] i = 1,..., s, μ i (ω k ) represents the weight function, ω k = [ω 1k ,..., ω pk ] represents the premise variables, ω 1k ,..., ω pk represents p premise variables, M i1,…,M ip Denotes the corresponding given set, M im (ω k ) represents M im The premise variable ω mk The level of , s represents the number of subsystems and fuzzy rules.

[0102] S2. Obtain the dynamic error system, including

[0103] S2.1: Establishing Fault Detection Observer (FDO): The multi-objective Fault Detection Observer (FDO) is expressed by formula (3):

[0104]

[0105] in:

[0106] represents the point estimate of the system state at time k+1, represents the point estimate of the system state at time k, L j represents the gain matrix of the observer.

[0107] S2.2: Using the fault detection observer (FDO) for the state space model (hereinafter referred to as the fuzzy model) of the aircraft engine fuzzy system expressed by formula (2) obtained in step S1.1, the dynamic error system for disturbance-free compensation is obtained. That is, by combining formula (2) and formula (3), the dynamic error system for disturbance-free compensation is obtained as:

[0108]

[0109] With the help of the finite-time disturbance compensator, the dynamic error system based on finite-time disturbance compensation is obtained as follows:

[0110]

[0111] in:

[0112] e k represents the estimation error of the state; r k represents the output observation error, x k represents the state vector of the system, represents a point estimate of the system state, y k represents the measured output of the system, represents the estimate of the measured output, A i Represents a matrix with known suitable dimensions, E i represents a matrix with known suitable dimensions, d k represents the process disturbance, L j represents the observer gain matrix, Ci Represents a matrix with known suitable dimensions, u k represents the process input vector of the system, B i Represents a matrix with known suitable dimensions, y k represents the measured output of the system, v k represents the measurement noise, D i Denotes a system matrix known to have suitable dimensions, f k Indicates sensor failure, F i represents a system matrix known to have suitable dimensions. h i (θ k ) represents the weight function, θ k represents the premise variable;

[0113] represents the disturbance estimation error, represents the disturbance d k Estimate of , γ(μ) represents the matrix function, represents the finite-time disturbance compensator, M(μ)=[D(μ)-A(μ)D(μ)], the ratio g / q∈(0,1), g,q are odd numbers, T represents transpose;

[0114]

[0115] S2.3: To meet the multi-objective optimization design problem, the dynamic error system formulation based on finite-time disturbance compensation is divided into two cases;

[0116] Dynamic error system under fault-free conditions:

[0117]

[0118] Consider only the dynamic error system under the influence of fault signals:

[0119]

[0120] in, represents the disturbance estimation error, d represents the superscript of the residual in the dynamic error system under fault-free conditions, and f represents the superscript of the residual in the dynamic error system under the influence of only the fault signal. represents the dynamic error system state observation error under fault-free conditions, It represents the state observation error of the dynamic error system considering only the influence of the fault signal, represents the output observation error of the dynamic error system under fault-free conditions, It represents the output observation error of the dynamic error system considering only the influence of the fault signal.

[0121] According to the scheme, the system is divided into two cases: one case makes the residual robust to disturbance and noise, and the other case makes the residual sensitive to fault.

[0122] S3. The dynamic error system obtained in step S2 and represented by formula (5) is divided into two systems, represented by formula (6) and formula (7) respectively. In this step S3, the observer gain matrix that satisfies the multi-objective optimization problem is obtained:

[0123] The designed FDO gain matrix needs to make the dynamic error system meet the conditions of being robust to disturbances and noise and sensitive to faults:

[0124] (i) The dynamic error system under fault-free conditions satisfies the conditions ‖‖ represents the norm, ‖‖ ∞ represents the infinite norm, γ1, γ2, α, and P represent the parameters that satisfy the linear matrix inequality conditions. represents the system disturbance under fault-free conditions, and v represents the measurement noise of the system;

[0125] (ii) Considering only the dynamic error system under the influence of the fault signal, the system satisfies the condition represents the transfer function of the dynamic error system input considering only the influence of the fault signal, η represents the parameter that satisfies the linear matrix inequality condition, θ represents the system failure frequency;

[0126] (iii) The FDO gain matrices obtained in (i) and (ii) are jointly solved to achieve multi-objective optimization design, so that the obtained observer gain matrix is ​​both robust to disturbances and noise and sensitive to faults.

[0127] Designed observer gain matrix Parameters τ1, τ2, α, G, W, N j , η, δ, K, W′, Q need to satisfy the following linear matrix inequality conditions:

[0128]

[0129] in,

[0130] L j =G -1 N j ,j=1,...,s

[0131] Ω′ 41 =GA(μ)-N(μ)C(μ)

[0132] Ω′ 42 =-N(μ)D(μ)

[0133] Ω′ 43 =GE(μ)

[0134] Ω′ 44 =WGG T

[0135] N(μ)=GL(μ)

[0136] Ψ′ 11 =W′-(2cosθ l )QC T (μ)C(μ)+He(δ(GA(μ)-N(μ)C(μ)))

[0137] Ψ′ 21 =K(GA(μ)-N(μ)C(μ))-δ(N(μ)F(μ)) T -F(μ) T C(μ)

[0138]

[0139] Ψ′ 31 =GA(μ)-N(μ)C(μ)-δG T +Q

[0140] Ψ′ 32 =-N(μ)F(μ)-G T K T

[0141] Ψ′ 33 =-W′-GG T

[0142] Among them: τ1 represents a given scalar, which has no actual physical meaning, τ2 represents a given scalar, which has no actual physical meaning, α represents a given scalar, which has no actual physical meaning, W represents a positive definite matrix, which has no actual physical meaning, G represents a matrix, which has no actual physical meaning, N j Represents a matrix, which has no actual physical meaning, I represents the identity matrix with appropriate dimensions, He represents that for a matrix P, the definition -1 represents the inverse of the matrix, η represents a given scalar, which has no actual physical meaning, δ represents a given scalar, which has no actual physical meaning, K represents a matrix, which has no actual physical meaning, W′ represents a matrix, W′ T =W′, which has no actual physical meaning, Q represents a positive definite matrix, which has no actual physical meaning, θ l Indicates the fault frequency in the low-frequency domain of the system, Θ l Represents the given fault frequency domain.

[0143] S4. Use the observer gain matrix obtained in step S3 to establish the residual evaluation based on set membership estimation:

[0144] The dynamic error system under fault-free conditions is formula (6). According to the dynamic error system at this time, r k A set member estimate At this time there must be By performing reachable set analysis on the dynamic error system, we can get:

[0145]

[0146] Where: Formula (11) and Formula (12) are and r k The reachable set of represents the set of system state errors at time k-1, represents a generator matrix, Represents the system disturbance under fault-free conditions A collection of represents a generator matrix, represents the set of system state errors at time k, Represents a generator matrix, <0,H v > represents the set of system measurement noise, H v represents a generator matrix, in ‖‖1 represents the 1-norm, represents a given matrix, s represents the number of subsystems and fuzzy rules, represents a generator matrix, Represents the generator matrix The nth row component of ;

[0147] The residual r is obtained k The interval estimate of , r(k) represents the lower bound of the residual, Indicates the upper bound of the residual, when the system has no faults Once the obtained residual r(k) exceeds the interval, the system fails;

[0148] The proposed fault detection method can be expressed as:

[0149]

[0150] According to the proposed solution, the present invention uses set membership estimation on an error system that does not contain faults to generate a fault detection threshold. This allows detection of a fault if the residual signal exceeds the fault detection threshold when a fault occurs, signaling a system fault. Using the set membership method, the residual interval boundaries are used as the fault detection threshold, creating a natural residual estimation method. Furthermore, the threshold generated by the set membership method is dynamic, significantly reducing the conservatism of fault diagnosis.

[0151] According to the scheme, formula (2) of the present invention enables the present invention to apply an observer based on finite-time disturbance compensation to compensate for disturbances. In formula (5) containing the residual, the effects of disturbances, noise, and sensor faults are considered. Therefore, the dynamic error system is divided into the dynamic error system formula (6) under fault-free conditions and the dynamic error system formula (7) under the influence of only the fault signal. Further, according to the design goals of residual robustness and fault sensitivity, the observer gain is obtained by solving linear matrix inequalities (8) and (9) using MATLAB, and a residual signal that is sensitive to faults and robust to interference and noise is obtained. Then, based on the obtained residual, the dynamic interval estimation of the residual in the fault-free state is obtained through the set membership estimation design process of formulas (11) and (12), and the interval boundary of the residual is used as the dynamic threshold for fault detection.

[0152] According to the detection method, a simulation experiment of aircraft engine system fault detection is carried out to verify that the continuous aircraft engine mathematical model is modeled using the TS fuzzy model to simulate the characteristics of the aircraft engine system in the ground idle state. The sampling time interval T s =0.025s, the model structure is as follows:

[0153] Rule 1: If H = 0 km, Ma = 0, and the high-pressure turbine relative conversion speed n 2cor =88%, then

[0154]

[0155] Rule 2: If H = 0 km, Ma = 0, and the high-pressure turbine relative conversion speed n 2cor =92%, then

[0156]

[0157]

[0158] Rule 3: If H = 0 km, Ma = 0, and the high-pressure turbine relative conversion speed n 2cor =96%, then

[0159]

[0160] Rule 4: If H = 0 km, Ma = 0, and the high-pressure turbine relative conversion speed n 2co =100%, then

[0161]

[0162] Select the premise variable ω k =n 2cor ,like Figure 2 As shown, the hierarchy of the premise variables is described as follows:

[0163] when

[0164] When k =ω i ,M i (ω k )=1,

[0165] Otherwise M i (ω k )=0,

[0166] In particular, ω1, ω2, ω3, and ω4 are 88%, 92%, 96%, and 100%, respectively.

[0167] when

[0168] Consider the following grade sensor failure:

[0169]

[0170] The initial state is x0 = [0.01 0.01] T , the disturbance is d k =0.26sin(0.2(k-1)), the noise is a bounded random signal |v k |≤[0.1 0.1] T , the low frequency range is Θ l ={|θ l |≤π / 4}, parameter δ=0.9, parameter α=0.1, parameter K=-7I.

[0171] By solving the multi-objective optimization problem, the gain matrix and parameters of the fault detection observer can be obtained as follows:

[0172]

[0173]

[0174] τ1=3.6214, τ2=3.6108, η=0.227.

[0175] The parameters of the finite-time disturbance compensator are:

[0176] Y1=diag(4.28,4.28), g=9, q=11.

[0177] The perturbation estimation results are as follows Figure 3 As shown, the perturbed estimation results are applied to residual generation and residual evaluation.

[0178] Furthermore, in order to demonstrate the significant performance and superiority of the proposed method in fault detection, the present invention comprehensively compares the detection method of the above embodiment with the existing method. The existing method only regards the control of the entire nonlinear system as a fuzzy approximation of the control of multiple local linear systems, and does not compensate for the interference. The existing method uses the same system parameters as the proposed method and applies the same reachable set analysis method, but the existing method does not have finite-time disturbance compensation and does not have a dynamic fault detection threshold generated by set membership estimation. The present invention uses a finite-time disturbance compensator through formulas (3) and (4) to reduce the impact of interference on fault detection. The present invention combines finite-time disturbance compensation with set membership estimation, so the "design state feedback control law" is improved to "dynamic fault detection threshold generated by set membership estimation", solves the multi-objective optimization problem, and obtains the observer gain matrix:

[0179]

[0180] Figures 4-8 Shows the simulation results, residuals, and threshold references generated by reachable set analysis Figures 4-7 As shown, from Figure 4 and Figure 5 It can be seen that the residual signal fluctuates within a range of no more than ±0.02 when there is no fault, which indicates that it is less affected by interference and noise. Figure 4 and Figure 5 The residual signal in fluctuates greatly when there is no fault, reaching a maximum of 0.04, indicating poor robustness. Figure 4 and Figure 5 It can be seen that when a fault occurs in the system, the residual signal changes to about 0.03, which is significantly different from the residual signal when there is no fault, indicating that the sensitivity to faults is better. Figure 6 and Figure 7 As can be seen from the figure, when a sudden fault occurs in the system, the residual signal does not change significantly, making it difficult to accurately diagnose the fault. Therefore, the residual generated by the proposed method is not only smaller but also more stable due to the proposed finite-time disturbance compensator and multi-objective optimization. Furthermore, the proposed method is highly robust to interference and noise.

[0181] In terms of fault detection threshold, compared with Figure 6 and Figure 7The fault detection threshold under the existing method is less conservative, so the fault can be detected quickly and accurately. Figure 6 and Figure 7 as well as Figure 8 As shown in the figure, it can be seen that the residuals obtained by the existing method fluctuate greatly. Under the influence of interference and noise, this will lead to a more conservative threshold. At the same time, when the amplitude of the fault signal is masked by interference and noise, it is easy to cause missed alarms or false alarms, thereby reducing the fault detection rate.

[0182] From the above simulation experiment analysis, it can be seen that the present invention realizes robust fault detection based on finite-time disturbance compensation fault detection observer and set membership estimation, which has obvious advantages over existing methods.

[0183] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A robust fault detection method based on a finite-time disturbance-compensated fault detection observer and set membership estimation, characterized in that: Includes the following steps Establishing a fuzzy system state space model of an aircraft engine, the model including parameters for process disturbances, measurement noise, and actuator faults; Establish a multi-objective fault detection observer; A dynamic error system based on finite-time disturbance compensation is obtained according to a fuzzy system state space model and a multi-objective fault detection observer. The dynamic error system includes a dynamic error system under a fault-free condition and a dynamic error system under the influence of only a fault signal. The dynamic error system under the fault-free condition makes the residual robust to disturbances and noise. The dynamic error system under the influence of only a fault signal makes the residual sensitive to faults. The residual includes an output observation error. Obtaining an observer gain matrix according to the dynamic error system under the fault-free condition and the dynamic error system under the influence of only the fault signal; A residual evaluation based on set membership estimation is established according to the observer gain matrix, and whether the system fault occurs or not is determined according to the residual evaluation.

2. The robust fault detection method based on a finite-time disturbance compensation fault detection observer and set membership estimation according to claim 1, characterized in that: The state space model of the fuzzy system: in: x k 、u k 、y k They represent the state vector, process input and measurement output of the system respectively, d k and v k represent process disturbance and measurement noise respectively, f k Indicates sensor failure; A i , B i , C i , D i , E i , F i Represent a system matrix known to have suitable dimensions; μ i (ω k ) represents the weight function, ω k =[ω 1k ,…,ω pk ] represents the premise variable, ω 1k ,…,ω pk represents p premise variables, M i1 ,…,M ip Denotes the corresponding given set, M i, (ω k ) represents M im The premise variable ω mk The level of , s represents the number of subsystems and fuzzy rules.

3. The robust fault detection method based on finite-time disturbance compensation fault detection observer and set membership estimation according to claim 2, characterized in that: The multi-objective fault detection observer: in: represents the point estimate of the system state at time k+1, represents the point estimate of the system state at time k, L j represents the gain matrix of the observer.

4. The robust fault detection method based on a finite-time disturbance compensation fault detection observer and set membership estimation according to claim 3, characterized in that: Dynamic error system without disturbance compensation: The dynamic error system based on finite time disturbance compensation: in: e k represents the estimation error of the state; r k represents the output observation error, represents an estimate of the measured output, represents the disturbance estimation error, represents the disturbance d k Estimate of , Υ(μ) represents the matrix function, represents the finite-time disturbance compensator, M(μ)=[D(μ)-A(μ)D(μ)], the ratio g / q∈(0,1), g,q are odd numbers, T represents transpose; 5. The robust fault detection method based on finite-time disturbance compensation fault detection observer and set membership estimation according to claim 4, characterized in that: The dynamic error system is divided into two types of systems; Dynamic error system under fault-free conditions: Consider only the dynamic error system under the influence of fault signals: represents the disturbance estimation error, d represents the superscript of the residual in the dynamic error system under fault-free conditions, and f represents the superscript of the residual in the dynamic error system under the influence of only the fault signal; It represents the state observation error of the dynamic error system under fault-free conditions; It represents the state observation error of the dynamic error system considering only the influence of the fault signal; represents the output observation error of the dynamic error system under fault-free conditions; It represents the output observation error of the dynamic error system considering only the influence of the fault signal; in: (i) The dynamic error system under fault-free conditions satisfies the conditions ‖‖ represents the norm, ‖‖ ∞ represents the infinite norm, τ1, τ2, α, and P represent the parameters that satisfy the linear matrix inequality conditions. represents the system disturbance under fault-free conditions, and v represents the measurement noise of the system; (ii) Considering only the dynamic error system under the influence of the fault signal, the system satisfies the condition represents the transfer function of the dynamic error system input considering only the fault signal, ε>0, η represents the parameter that satisfies the linear matrix inequality condition, Indicates the frequency of system failures.

6. The robust fault detection method based on finite-time disturbance compensation fault detection observer and set membership estimation according to claim 5, characterized in that: Observer gain matrix Parameters τ1, τ2, α, G, W, N j , η, δ, K, W′, Q satisfy the following linear matrix inequality conditions: in, L j =G -1 N j ,j=1,...,s Oh' 41 =GA(μ)-N(μ)C(μ) Oh' 42 =-N(μ)D(μ) Ω′ 43 =GE(μ) Oh' 44 =WGG T N(μ)=GL(μ) P′ 21 =K(GA(μ)-N(μ)C(μ))-δ(N(μ)F(μ)) T -F(μ) T C(μ) P′ 31 =GA(μ)-N(μ)C(μ)-δG T +Q P′ 32 =-N(μ)F(μ)-G T K T P′ 33 =-W′-GG T in: τ1 represents a given scalar; τ2 represents a given scalar; α represents a given scalar; W represents a positive definite matrix; G represents a matrix; N j represents a matrix; I represents the identity matrix with appropriate dimensions; He represents a matrix P, and defines He(P) = P T +P; -1 indicates the inverse of the matrix; η represents a given scalar; δ represents a given scalar; K represents a matrix; W′ represents a matrix, W ′T =W′; Q represents a positive definite matrix; Indicates the fault frequency in the low-frequency domain of the system, Θ l Represents the given fault frequency domain.

7. The robust fault detection method based on finite-time disturbance compensation fault detection observer and set membership estimation according to claim 6, characterized in that: When the aero-engine system sensor has no fault, the dynamic error system under the fault-free condition can be used to obtain r k A set member estimate By performing reachable set analysis on the dynamic error system, we can obtain the following reachable set of the dynamic error system: in: Formula (11) and formula (12) are and r k The reachable set of represents the set of system state errors at time k-1, represents a generator matrix, Represents the system disturbance under fault-free conditions A collection of represents a generator matrix, represents the set of system state errors at time k, Represents a generator matrix, <0,H v > represents the set of system measurement noise, H v represents a generator matrix, in ‖‖1 represents the 1-norm, represents a given matrix, s represents the number of subsystems and fuzzy rules, represents a generator matrix, Represents the generator matrix The nth row component of ; The residual r is obtained k The interval estimate of , r(k) represents the lower bound of the residual, Indicates the upper bound of the residual, when the system has no faults Once the obtained residual r(k) exceeds the interval, the system fails.

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