Aero-engine Sensor Fault Diagnosis Method Based on Multi-objective Fault Detection Observer and Improved LSSVM

Abstract

A method for diagnosing faults in aeroengine sensors based on a multi-objective fault detection observer and improved LSSVM belongs to the field of control. The key points are to establish a mathematical model of an aeroengine control system with model uncertainties, determine a fault detection observer according to the aeroengine control system model; determine an error system according to the fault detection observer; obtain an observer gain matrix according to multi-objective constraint conditions determined by the model uncertainty robustness and fault sensitivity of the error system; obtain a residual robust to model uncertainties according to the fault detection observer; use the obtained robust residual to optimize the kernel function parameters and penalty factors of LSSVM based on the whale algorithm, and establish an optimal aeroengine sensor fault diagnosis model; classify the residual obtained by the fault detection observer according to the diagnosis model, and the effect is that the classification effect for minor faults is good and the accuracy is high.

Description

Technical Field

[0001] The present invention belongs to the field of automatic control, and relates to a fault diagnosis method for sensors of an aero-engine control system. Background Art

[0002] Fault diagnosis technology is widely used in modern aviation systems, such as flight control systems and engine health management systems, etc. An aero-engine is a core component of an aircraft. Once a fault occurs, it is very likely to cause significant casualties and economic losses. Therefore, researching the fault diagnosis technology of aero-engines has great practical significance and economic value. The fault diagnosis method based on an observer is a class of methods for detecting faults. This method mainly constructs an observer of the original system to generate redundant states, subtracts the estimated value from the actual value to obtain a residual, and finally judges whether the system has a fault through effective residual evaluation. When no fault occurs, ideally, the residual should be zero. However, due to the existence of modeling errors, disturbances, and measurement errors, etc., it may result in the residual not being zero even when the system is operating normally, but fluctuating within a certain range. When diagnosing faults, generally a detection threshold is set, and the residual is compared with the threshold to judge whether a fault has occurred. If the residual evaluation function is not within the range of the threshold, it indicates that the system has a fault; if the residual evaluation function is within the range of the threshold, it indicates that the system is operating normally. However, in reality, the amplitude of early faults is very small, and the threshold-based fault diagnosis method usually cannot detect the occurrence of faults. And the support vector machine SVM has been successfully applied to the field of fault diagnosis due to its good classification performance and low requirement for the amount of sample data, and can obtain high-accuracy classification results for minor faults. The original SVM uses the method of solving quadratic programming problems, resulting in a very large amount of calculation. Among them, the least squares support vector machine LSSVM transforms the quadratic programming problem into a linear solution problem, which is not only simple to implement but also has advantages such as high classification and calculation efficiency, and has been widely used. Summary of the Invention

[0003] In order to solve the problem that the current model-based fault diagnosis method is vulnerable to model uncertainty and the fault diagnosis method based on machine learning lacks a suitable sample input, according to some embodiments of the present application, an aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM includes the following steps:

[0004] Establish a mathematical model of an aero-engine control system containing model uncertainty;

[0005] Determine a fault detection observer according to the mathematical model of the aero-engine control system;

[0006] Determine an error system according to the fault detection observer, and the obtained error system includes a first subsystem and a second subsystem;

[0007] Determine multi-objective constraint conditions according to the error system model uncertainty, robustness, and fault sensitivity, and obtain an observer gain matrix according to the multi-objective constraint conditions;

[0008] Obtain a residual that is robust to model uncertainty according to the fault detection observer;

[0009] Initialize the basic parameters of the aero-engine sensor fault diagnosis model based on LSSVM according to the model uncertainty robust residual;

[0010] Optimize the kernel function parameters and penalty factor of the aero-engine sensor fault diagnosis model based on LSSVM using the whale algorithm to obtain an optimal aero-engine sensor fault diagnosis model;

[0011] Classify the faults of the residual obtained by the fault detection observer according to the optimal aero-engine sensor fault diagnosis model to obtain the fault types.

[0012] According to the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, the aero-engine control system model is obtained based on the following method:

[0013] Establish a linearized state-space model of the aero-engine control system and discretize the state-space model;

[0014] Consider disturbance noise and sensor faults to establish an aero-engine control system model with model uncertainty in the presence of sensor faults.

[0015] According to the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, the state-space model of the aero-engine at the ground maximum state is:

[0016]

[0017] where A, B, and C respectively represent the system matrix, control matrix, and output matrix;

[0018] x(t) = [n h n l m f A8] T , u(t) = [m f A8] T ,

[0019] Δx = x - x0, Δu = u - u0, Δy = y - y0, n h 、n l 、mf , A8, respectively represent the high-pressure rotor speed of the engine, the low-pressure rotor speed, the main fuel supply, the throat area of the tail nozzle, the total pressure after the compressor, and the total temperature after the turbine.

[0020] For the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, in the case of sensor faults, the model of the aero-engine control system with model uncertainties is represented by Equation (1):

[0021]

[0022] where is the state vector, is the control input, is the measured output, is the process disturbance, is the measurement noise, is the sensor fault; and respectively represent the n-dimensional and m×n-dimensional Euclidean spaces, and I n represents the n×n-dimensional identity matrix;

[0023] A, B, C, D w , D v and F are known matrices of appropriate dimensions, and ΔA, ΔB, ΔC, and ΔF are parameter uncertainties. ΔA, ΔB, ΔC, and ΔF are unknown but bounded and satisfy

[0024]

[0025] where and are known matrices with all non-negative elements;

[0026] ΔA = M1Δ1N1, ΔB = M2Δ2N2, ΔC = M3Δ3N3, ΔF = M4Δ4N4 (3)

[0027] where M i and N i are known matrices of appropriate dimensions, i = 1, 2, 3, 4, and is an unknown matrix and satisfies

[0028]

[0029] For the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, the fault detection observer is represented by Equation (5):

[0030]

[0031] wherein is the state estimation, is the residual signal, is the observer gain matrix;

[0032] Define the estimation error as Then the error system is represented by Equation (6):

[0033]

[0034] where A c = A - LC, F d = F + ΔF;

[0035] The error system includes a first subsystem and a second subsystem. The first subsystem is represented by Equation (7), and the second subsystem is represented by Equation (8):

[0036]

[0037]

[0038] wherein B f = -Lf d , D x = [D w - LD v ΔA - LΔC ΔB], D y = [0 D v ΔC 0], d k = [w k v k x k u k T .

[0039] For the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, the fault detection observer satisfies the following multi-objective constraint conditions:

[0040]

[0041]

[0042] where λ1 > 0, λ2 > 0, β > 0, 0 < α < 1, k represents the k-th moment, and e0 represents the initial error value;

[0043] The design constraint conditions are transformed into solving the following linear matrix inequality: ​

[0044]

[0045]

[0046]

[0047] where

[0048] n d = n w + n v + n x + n u ,n w ,n v ,n x ,n u represents the dimension of the system matrix;

[0049] Ψ x = Φ x + ∈1N x T N x ;

[0050] Ψ y = Φ y + ∈2N y T N y ;

[0051] Ω = Θ + ∈3V T V;

[0052]

[0053] [[ID=6�]]

[0054]

[0055]

[0056]

[0057]

[0058] where * represents the transpose of the symmetric term, 0 represents the zero matrix of appropriate dimension in a block matrix, <0 indicates that the matrix is negative definite, in the inequality, the scalars 0 < α < 1, γ1 > 0, β > 0 are pre - given constants, P ∈ and are positive definite matrices, is an invertible matrix, the matrix the scalars ∈1 > 0, ∈2 > 0 and ∈3 > 0 are arbitrary scalars, and γ2 > 0 is the parameter to be optimized.

[0059] According to the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, the minimum feasible solution of γ2 satisfying the linear matrix inequalities (11)-(13) is solved according to the YALMIP toolbox in MATLAB, and at the same time, matrices P, Q, G, and W are obtained, and then the optimal observer matrix gain L = G -1 W.

[0060] According to the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, obtaining the residuals robust to model uncertainties according to the fault detection observer includes setting two labels, namely the normal state and the fault state, for each sensor of the aero-engine sensor control system. There are a total of 2n y labels in the entire aero-engine control system, and the label numbers increase sequentially from 1, 2,..., 2n y one by one, and the fault detection observer generates residuals with a known data volume for the corresponding state labels of each sensor.

[0061] According to the aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, the initial LSSVM basic parameter aero-engine sensor fault diagnosis model, a recognition model is established from the normal input-output space of the aero-engine control system model, and its function expression and constraint conditions are:

[0062]

[0063]

[0064] where ω is the weight vector, γ is the penalty factor, is the non-linear mapping function that maps the data in the original feature space to a high-dimensional space, x k is the input vector, e k is the slack variable, b is the bias variable, and n is the total number of samples;

[0065] Through Lagrange function Lagrange optimization, the expression is:

[0066]

[0067] where α k is the Lagrange multiplier. According to the KKT conditions, the partial derivatives of ω, b, e k , α k in formula (15) are obtained and made equal to 0, and the variables ω and e k are eliminated, and a non-linear optimization problem is transformed into a linear solution problem. The specific formula is as follows:

[0068]

[0069] where \(P = [1,\ldots,1]\) T , \(A = [\alpha_1,\ldots,\alpha\) k T , \(Y = [y_1,\ldots,y\) k T , and \(I\) is the identity matrix;

[0070] The least squares support vector machine LSSVM model is:

[0071]

[0072]

[0073] where \(y\) out (x) is the predicted output of the model, \(K(x,x\) k ) is the Gaussian radial basis kernel function selected in the present invention, \(x\) is a certain fixed data in the training data, and \(x\) k is the \(k\)-th data in the training data;

[0074] The optimal aeroengine sensor fault diagnosis model is obtained by optimizing the penalty factor \(\gamma\) and the kernel function parameter \(\sigma\) of the least squares support vector machine LSSVM model based on the whale optimization algorithm WOA, and the classification accuracy is used as the fitness function; 2 where the specific steps of the whale optimization algorithm WOA for optimizing the LSSVM penalty factor \(\gamma\), the kernel function parameter \(\sigma\)

[0075] and generating the optimal model are as follows: 2

[0076] (6) Initialize the population size, the maximum number of iterations, the number of variables, and the upper and lower limits of the variables of the whale algorithm;

[0077] (7) Randomly initialize the positions of the whale swarm;

[0078] (8) Calculate the corresponding fitness values of each individual in the population and sort them, select the optimal solution as the current global optimal solution, and update the positions according to formulas (19)-(26);

[0079] Assume that the current optimal candidate solution is the target position of the humpback whale prey. The whales that do not belong to the current optimal candidate solution position will continuously update their positions and try to approach the target position. The mathematical expression for position update is:

[0080] \(D = |CX\) * (t)-X(t)| (19)

[0081] \(X(t + 1)=X\)​​* (t)-AD (20)

[0082] A = 2ar1 - a (21)

[0083] C = 2r2 (22)

[0084]

[0085] where t is the current iteration number, t max is the maximum iteration number, X * (t) is the position vector of the current optimal solution, X(t) is the position vector of the current solution, A and C are the convergence coefficient vector and the oscillation coefficient vector respectively, the value of a linearly decreases from 2 to 0 as t increases, and r1 and r2 are random vectors within [0, 1];

[0086] The hunting methods of humpback whales include the shrinking and encircling prey mechanism and the spiral position update mechanism. The probability of choosing each of the two hunting methods is 50%. Humpback whales update their own positions through the two hunting methods, and the mathematical expression for position update is:

[0087]

[0088] where D ′ = |X * (t) - X(t)| is the distance between the i-th whale and the prey, d is a constant defining the spiral shape, l is a random number within [-1, 1], and p is a random number within [0, 1];

[0089] When hunting prey, humpback whales randomly search for prey instead of using the currently found best target position to update the current target position. The mathematical expression for position update is:

[0090] D = |CX rand (t) - X(t)| (25)

[0091] X(t + 1) = X rand (t) - AD (26)

[0092] where X rand (t) is a randomly selected position vector in the current population. When |A| ≥ 1, the humpback whale will abandon approaching the current optimal position and conduct a random search. When |A| < 1, the humpback whale will use the position vector of the current optimal solution to update the position vector of the current solution, and switch between the shrinking and encircling mechanism and the spiral position update mechanism according to the value of p. Finally, when the maximum iteration number is reached, the algorithm terminates;

[0093] (9) Repeat step (3) until the current iteration number is equal to the maximum iteration number, and output the position with the best fitness and the two parameters γ and σ of the least squares support vector machine (LSSVM) model. 2 ;

[0094] (10) Substitute the optimized penalty factor γ and kernel function parameter σ 2 obtained by optimization into the least squares support vector machine (LSSVM) model, and import the training data for training to obtain the optimal aeroengine sensor fault diagnosis model.

[0095] According to the aeroengine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to some embodiments of the present application, according to the optimal aeroengine sensor fault diagnosis model, classify the residuals obtained by the fault detection observer to obtain the fault type, including inputting the residuals obtained by the fault detection observer into the optimized aeroengine sensor fault diagnosis model for fault diagnosis, and classifying the residuals under different sensor fault modes of the aeroengine. Specifically: by setting two labels, the normal state and the fault state, for each sensor of the aeroengine control system, the normal state label of the first sensor is 1, and the fault state label is 2, the normal state label of the second sensor is 3, and the fault state label is 4. The normal state label of the i-th sensor is 2i - 1, and the fault state label is 2i + 1. The entire aeroengine control system has 2n y labels, and the label numbers increase sequentially from 1, 2,..., 2n y one by one. If the residual label number corresponding to each sensor is odd, then each sensor is working normally; otherwise, there is a sensor failure. Among them, the sensor fault location strategy is specifically

[0096]

[0097] where l is the number corresponding to the fault label, and S is the number of the corresponding faulty sensor.

[0098] Advantageous effects: The present invention mainly relates to an aeroengine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM, which can generate robust residuals in real time and perform multi-fault classification on them, realizing the function of fault diagnosis. Description of the Drawings

[0099] Figure 1 is the flow chart of the embodiment of the present invention.

[0100] Figure 2 is the flow chart of the whale optimization algorithm.

[0101] Figure 3This is a comparison chart of the fitness effects of three algorithms, namely WOA-LSSVM, GA-LSSVM, and PSO-LSSVM, for the data of the sensor full-fault model in the present invention.

[0102] Figure 4 This is a comparison chart of the fitness effects of three algorithms, namely WOA-LSSVM, GA-LSSVM, and PSO-LSSVM, for the data of the sensor partial-fault model in the present invention.

[0103] Figure 5 This is a classification chart of the test data of WOA-LSSVM for the data of the sensor full-fault model in the present invention.

[0104] Figure 6 This is a classification chart of the test data of WOA-LSSVM for the data of the sensor partial-fault model in the present invention. Detailed implementation manners

[0105] Next, the embodiments of the present application will be described in detail with reference to the accompanying drawings. The examples of the embodiments are shown in the drawings. As Figure 1 shown, the present invention proposes an aero-engine sensor fault diagnosis method using a multi-objective fault detection observer and an improved LSSVM, including the following steps:

[0106] Step 1: Establish a linearized model for the aero-engine control system, and considering the disturbance noise and sensor faults, the following form of the system can be obtained:

[0107]

[0108] Where is the state vector, is the control input, is the measured output, is the process disturbance, is the measurement noise, is the sensor fault; and respectively represent the n-dimensional and m×n-dimensional Euclidean spaces, and I n represents the n×n-dimensional identity matrix;

[0109] A, B, C, D w , D v and F are known matrices of appropriate dimensions. ΔA, ΔB, ΔC, and ΔF are parameter uncertainties, which are unknown but bounded and satisfy

[0110]

[0111] Where and is a matrix with all non - negative elements, and ≤ holds for each element. Additionally, considering the structural characteristics of parameter uncertainties, ΔA, ΔB, ΔC, and ΔF need to satisfy

[0112] ΔA = M1Δ1N1, ΔB = M2Δ2N2, ΔC = M3Δ3N3, ΔF = M4Δ4N4 (3)

[0113] where M i and N i (i = 1, 2, 3, 4) are known matrices of appropriate dimensions, and and are unknown matrices and satisfy

[0114]

[0115] Step 2: Design a fault detection observer for the above - mentioned system so that the resulting residual signal is robust to disturbances, noise, and parameter uncertainties, and at the same time is sufficiently sensitive to faults. The specific fault detection observer used is:

[0116]

[0117] where is the state estimate, is the residual signal, is the observer gain matrix to be designed.

[0118] Define the estimation error as Then, from (1) and (5), the following error system can be obtained:

[0119]

[0120] where A c = A - LC, F d = F + ΔF.

[0121] To more conveniently analyze the disturbance robustness and fault sensitivity, the error system (6) is split into the following two subsystems:

[0122]

[0123]

[0124] where B f = - LF d , D x = [D w - LD v ΔA - LΔCΔB], D y = [0 D vΔC0], d k = [w k v k x k u k T 。

[0125] Step 3: To make the resulting residual signal robust to interference, noise, and parameter uncertainties, while maintaining sufficient sensitivity to faults, the design of the multi-objective fault detection observer requires the system to satisfy the following conditions, specifically:

[0126]

[0127]

[0128] where γ1 > 0, γ2 > 0, β > 0, 0 < α < 1, k represents the k-th moment, and e0 represents the initial error value.

[0129] The above multi-objective constraint conditions can be transformed into solving the following linear matrix inequality:

[0130]

[0131]

[0132]

[0133] where n d = n w + n v + n x + n u ,n w ,n v ,n x ,n u represents the dimension of the system matrix, which has no specific value and is related to the selection of the simulation model.

[0134] Ψ x = Φ x + ∈1N x T N x ;

[0135] Ψ y = Φ y + ∈2N y T N y ;

[0136] Ω = Θ + ∈3V T V;

[0137]

[0138] n y represents the dimension of the system matrix, without a specific numerical value, related to the selection of the simulation model;

[0139]

[0140]

[0141] n f represents the dimension of the fault matrix, without a specific numerical value, related to the selection of the simulation model;

[0142]

[0143]

[0144] where * represents the transpose of the symmetric term, 0 represents a zero matrix of appropriate dimension in a block matrix, <0 indicates that the matrix is negative definite, and for the inequality, the scalars 0 < α < 1, γ1 > 0, β > 0 are constants given in advance. and are positive definite matrices, is an invertible matrix, the matrix The scalars ∈1 > 0, ∈2 > 0, and ∈3 > 0 are arbitrary scalars, γ2 > 0 is a parameter to be optimized, and the minimum feasible solution of γ2 satisfying the linear matrix inequalities (11)-(13) can be obtained based on the YALMIP toolbox in MATLAB. At the same time, matrices P, Q, G, and W can be obtained, and then the optimal observer matrix gain L = G -1 W.

[0145] Step 4: Obtain and classify the robust residuals according to the fault detection observer. By setting two labels, the normal state and the fault state, for each sensor in the aero-engine sensor control system, there are a total of 2n y labels for the entire control system, and the label numbers increase sequentially from 1, 2,..., 2n y one by one. Finally, the fault detection observer generates residuals of a known data volume for each sensor corresponding state label, and a known number of samples are randomly selected as training samples in each label, and the remaining samples are used as test samples. At the same time, to improve the accuracy and convergence speed of model training, the above samples need to be normalized.

[0146] Step 5: Based on the initial LSSVM basic parameter aero-engine sensor fault diagnosis model, establish an identification model from the normal input-output space of the aero-engine control system model, and its functional expression and constraint conditions are:

[0147]

[0148]

[0149] where ω is the weight vector, γ is the penalty factor, is a non-linear mapping function that maps the data in the original feature space to a high-dimensional space, x k is the input vector, e k is the slack variable, b is the bias variable, and n is the total number of samples.

[0150] The Lagrange function can solve the above optimization problem, and the specific expression is:

[0151]

[0152] where α k is the Lagrange multiplier. According to the KKT conditions, taking partial derivatives of ω, b, e k , α k in formula (15) and setting them to 0, and eliminating the variables ω and e k , a non-linear optimization problem can be transformed into a linear solution problem. The specific formula is as follows:

[0153]

[0154] where P = [1,..., 1] T , A = [α1,..., α k T , Y = [y1,..., y k T , and I is the identity matrix.

[0155] The least squares support vector machine LSSVM is an improvement on the principle of the support vector machine SVM, with characteristics such as fast solution speed and strong generalization ability. The specific model is:

[0156]

[0157]

[0158] where y out (x) is the predicted output of the model, K(x, x k ) is the Gaussian radial basis kernel function selected in the present invention, x is a certain fixed data in the training data, and x k is the k-th data in the training data.

[0159] ​​Step 6: According to the fitness function and the optimal aero-engine sensor model, using the classification accuracy as the fitness function and applying the Whale Optimization Algorithm (WOA) to optimize the penalty factor γ and the kernel function parameter σ of the LSSVM model 2 for optimization.

[0160] The Whale Optimization Algorithm (WOA) is a new meta-heuristic optimization algorithm that simulates the bubble-net hunting behavior of humpback whales in nature. The predation behavior of whales mainly consists of the following three parts:

[0161] I. Encircling Prey

[0162] Humpback whales identify different positions of prey and encircle them. The WOA algorithm assumes that the current optimal candidate solution is the target prey position or the position closest to the optimal target prey position. Then, other individuals will continuously update their positions, attempting to approach the target position. The mathematical expression for position update is:

[0163] D = |CX * (t) - X(t)| (19)

[0164] X(t + 1) = X * (t) - AD (20)

[0165] A = 2ar1 - a (21)

[0166] C = 2r2 (22)

[0167]

[0168] where t is the current iteration number, t max is the maximum iteration number, X * (t) is the position vector of the current optimal solution, X(t) is the position vector of the current solution, A and C are the convergence coefficient vector and the swing coefficient vector respectively, the value of a linearly decreases from 2 to 0 as t increases, and r1 and r2 are random vectors within [0, 1].

[0169] II. Bubble Attack

[0170] Humpback whales have two attack methods to choose from during the attack phase, namely the shrinking encircling prey mechanism and the spiral position update mechanism. The probability of choosing each of the two attack methods is 50%. Update their own positions through the two methods. The mathematical expression for position update is:

[0171]

[0172] where D ′ = |X *(t) - X(t)| represents the distance between the i-th whale and the prey, d is a constant defining the spiral shape, l is a random number within [-1, 1], and p is a random number within [0, 1].

[0173] III. Search and predation

[0174] When the humpback whale preys on its prey, it randomly searches for the prey instead of using the currently found best target position to update the current target position. To avoid falling into the local optimum problem, the algorithm performs a global search. The mathematical expression for position update is:

[0175] D = |CX rand (t) - X(t)| (25)

[0176] X(t + 1) = X rand (t) - AD (26)

[0177] where X rand (t) is a randomly selected position vector in the current population. When |A| ≥ 1, the humpback whale will abandon approaching the current optimal position and perform a random search. When |A| < 1, the humpback whale will use the position vector of the current optimal solution to update the position vector of the current solution. And according to the value of p, the algorithm can switch between the shrinking encirclement mechanism and the spiral position update mechanism. Finally, when the maximum number of iterations is reached, the algorithm terminates.

[0178] WOA optimizes the penalty factor γ and kernel function parameter σ of LSSVM 2 and the specific steps to generate the optimal model are as follows:

[0179] (1) Initialize the population size, maximum number of iterations, number of variables, and upper and lower limits of variables of the whale algorithm.

[0180] (2) Randomly initialize the positions of the whale group.

[0181] (3) Calculate the corresponding fitness values of each individual in the population and sort them, select the optimal solution as the current global optimal solution, and perform position update according to formulas (19) - (26).

[0182] (4) Repeat step (3) until the current number of iterations is equal to the maximum number of iterations, and output the position with the best fitness and the two LSSVM parameters γ and σ 2 .

[0183] (5) Substitute the optimized penalty factor γ and kernel function parameter σ 2 into LSSVM and import the training data for training to obtain the optimal model.

[0184] Step 7: Perform fault diagnosis by inputting the residuals obtained from the fault detection observer into the optimized aviation engine sensor fault diagnosis model, and classify the residuals under different sensor fault modes of the aviation engine. Specifically:

[0185] It is known that two labels, the normal state label and the fault state label, are set for each sensor in the aviation engine sensor control system. For example, the normal state label of the first sensor is 1, and the fault state label is 2. The normal state label of the second sensor is 3, and the fault state label is 4. That is, the entire control system has a total of 2n y labels, and the label numbers increase sequentially from 1, 2, …, 2n y one by one.

[0186] If the residual label number corresponding to each sensor is odd, it indicates that the corresponding sensor is working normally; otherwise, the sensor has a fault. The sensor fault location strategy is specifically

[0187]

[0188] where l is the number corresponding to the fault label, and S is the number of the corresponding faulty sensor.

[0189] According to the above solution, the present invention proposes an aviation engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM for a class of aviation engine control system sensors. Based on the fault detection observer, a robust residual signal is obtained, making the residual signal robust to unknown disturbances and sensitive to faults at the same time. Based on the improved LSSVM, the obtained residuals are classified for faults, and it has a high classification accuracy for minor faults. Finally, the fault diagnosis function is realized.

[0190] In a specific embodiment, the specific embodiment of the present invention is described through an aviation engine model. In this example, the present invention details the specific model and model parameters. In this specific example, the aviation engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM specifically includes the following steps:

[0191] Step 1: Establish a linearized model for the aviation engine control system and construct a fault detection unit;

[0192] Considering a certain turbofan engine as the research object, the state space model of this type of engine at the maximum state on the ground (H = 0 km, Ma = 0) is:

[0193]

[0194]

[0195]

[0196]

[0197] where \(x(t)=[n h n l m f A8] T and \(u(t)=[m f A8] T and \(\Delta x = x - x_0\), \(\Delta u = u - u_0\), \(\Delta y = y - y_0\). \(n h and \(n l and \(m f and \(A8 are the high-pressure rotor speed, low-pressure rotor speed, main fuel supply, throat area of the tail pipe, total pressure after the compressor, and total temperature after the turbine of the engine respectively. \(A\), \(B\), and \(C\) are the system matrix, control matrix, and output matrix respectively.

[0198] Discretizing the continuous model (1) and considering the disturbance noise and sensor faults, we can obtain a system in the following form:

[0199]

[0200] where and are the state vector, control input, and measured output respectively. and are the process disturbance and measurement noise respectively, is the sensor fault. \(A\), \(B\), \(C\), \(D w and \(D v and \(F\) are known matrices of appropriate dimensions. \(\Delta A\), \(\Delta B\), \(\Delta C\), and \(\Delta F\) are parameter uncertainties, which are unknown but bounded and satisfy

[0201]

[0202] where and are known matrices with all non-negative elements, and \(\leq\) holds for each element. Additionally, we also need to consider the structural characteristics of the parameter uncertainties. \(\Delta A\), \(\Delta B\), \(\Delta C\), and \(\Delta F\) satisfy

[0203] \(\Delta A = M_1\Delta_1N_1\), \(\Delta B = M_2\Delta_2N_2\), \(\Delta C = M_3\Delta_3N_3\), \(\Delta F = M_4\Delta_4N_4\ (4)

[0204] where \(M i and \(N i \((i = 1,2,3,4)\) are known matrices of appropriate dimensions, and and is an unknown matrix and satisfies

[0205]

[0206] Step 2: Use the discrete Euler one-step method for the state-space equation (1) of a certain turbofan engine model in Step 1, with a sampling time of 0.1 s, and transform it into a discrete model in the form of (2). The corresponding parameter matrices are as follows:

[0207]

[0208] D w = 0.2I4, D v = 0.2I4, F = I4;

[0209]

[0210]

[0211] Δ1 = Δ2 = 0.8I2, Δ3 = Δ4 = 0.8I4, The disturbance w k and the noise v k satisfy white noise with an amplitude of 0.02.

[0212] Assume that the small-amplitude full-failure of the introduced sensor is f(k) = [0.02 0.03 0.05 0.03] T .

[0213] Assume that the small-amplitude partial-failure of the introduced sensor is f(k) = [0.00 0.03 0.00 0.03] T .

[0214] Step 3: Design a fault detection observer for the above system to make the resulting residual signal robust to disturbances, noise, and parameter uncertainties, and at the same time be sufficiently sensitive to faults. Use the following fault detection observer:

[0215]

[0216] where is the state estimate, is the residual signal, is the observer gain matrix to be designed.

[0217] Define the estimation error as Then, from (2) and (6), the following error system can be obtained:

[0218]

[0219] where A c = A - LC, Fd = F + ΔF.

[0220] To more conveniently analyze the disturbance robustness and fault sensitivity, the error system (7) is split into the following two subsystems:

[0221]

[0222]

[0223] where B f = -LF d , D x = [D w - LD v ΔA - LΔC ΔB], D y = [0 D v ΔC 0], d k = [w k v k x k u k T .

[0224] Design the observer parameters such that the system needs to satisfy the following conditions:

[0225]

[0226]

[0227] where γ1 > 0, γ2 > 0, β > 0, 0 < α < 1, The above design constraint conditions can be transformed into solving the following linear matrix inequality:

[0228]

[0229]

[0230]

[0231] where

[0232] n d = n w + n v + n x + n u n w , n v , n x , n u represents the dimension of the system matrix;

[0233] Ψ x = Φ x + ∈1N x ​T N x ;

[0234] Ψ y = Φ y + ∈2N y T N y ;

[0235] Ω = Θ + ∈3V T V;

[0236]

[0237] n y represents the dimension of the system matrix;

[0238]

[0239]

[0240]

[0241]

[0242] where * represents the transpose of the symmetric term, 0 represents the zero matrix of appropriate dimension in a block matrix, <0 indicates that the matrix is negative definite, and the scalars 0 < α < 1, γ1 > 0, β > 0 are pre-given constants, and are positive definite matrices, is an invertible matrix, the matrix The scalars ∈1 > 0, ∈2 > 0 and ∈3 > 0 are arbitrary scalars, γ2 > 0 is the parameter to be optimized, and the minimum feasible solution of γ2 that satisfies the linear matrix inequalities (12)-(14) can be obtained based on the YALMIP toolbox in MATLAB. At the same time, the matrices P, Q, G, and W can be obtained, and then the optimal observer matrix gain L = G -1 W.

[0243] Let α = 0.5, γ1 = 2, β = 3.5. Solving the inequalities (12), (13), and (14) can obtain the observer gain matrix L as:

[0244]

[0245] Step 4: Based on the conditions in Steps 2 and 3, there are four sensors, resulting in eight classification labels. Labels 1 and 2 correspond to the high-pressure rotor speed sensor. Label 1 indicates that the sensor is functioning properly, while label 2 indicates that the sensor is faulty. The meanings of the remaining labels are similar. Thirty samples are collected for each label, each containing 100 data points, for both complete and partial sensor failure. Thirteen of the 30 samples for each label are randomly selected as training samples, and the remaining 17 are used as test samples. To improve model training accuracy and convergence speed, these samples are normalized.

[0246] Step 5: Initialize the parameters of the whale optimization algorithm and the basic parameters of LSSVM. The population size of the whale optimization algorithm is 30, and the maximum number of iterations is 100. Since LSSVM needs to optimize the penalty factor γ and the kernel function parameter σ 2 , that is, the number of optimization variables is 2, the upper limit value is 5000, and the lower limit value is 0.01.

[0247] The identification model is established from the normal input and output space of the aircraft engine control system model. Its function expression and constraints are as follows:

[0248]

[0249]

[0250] Where ω is the weight vector, γ is the penalty factor, It is a nonlinear mapping function that maps the data of the original feature space to a high-dimensional space, x k is the input vector, e k is the slack variable, b is the bias variable, and n is the total number of samples.

[0251] The Lagrange function can solve the above optimization problem. The specific expression is:

[0252]

[0253] where α k is the Lagrange multiplier. According to the KKT condition, ω, b, e in formula (15) are k ,α k Find the partial derivative and make it 0, eliminating the variables ω and e k , a nonlinear optimization problem can be transformed into a linear solution problem. The specific formula is as follows:

[0254]

[0255] where P = [1,…,1] T , A=[α1,…,αk T , Y = [y1, …, y k T , I is the identity matrix.

[0256] The least squares support vector machine LSSVM is an improvement on the principle of the support vector machine SVM, with characteristics such as fast solution speed and strong generalization ability. The specific model is:

[0257]

[0258]

[0259] where y out (x) is the predicted output of the model, K(x, x k ) is the Gaussian radial basis kernel function selected in the present invention, x is a certain fixed data in the training data, and x k is the k-th data in the training data.

[0260] Step six: According to the training samples in step four and the parameter conditions of the whale optimization algorithm in step five, train the LSSVM to obtain the optimal aero-engine sensor model. Use the classification accuracy as the fitness function and use the whale optimization algorithm WOA to optimize the penalty factor γ and the kernel function parameter σ 2 of the LSSVM model.

[0261] The whale optimization algorithm WOA is a new meta-heuristic optimization algorithm that simulates the bubble net hunting behavior of humpback whales in nature. The hunting behavior of whales is mainly divided into the following three parts:

[0262] I. Encircling the prey

[0263] Humpback whales identify different positions of the prey and encircle them. The WOA algorithm assumes that the current optimal candidate solution is the target prey position or the position closest to the optimal target prey position. Then, other individuals will continuously update their positions and try to approach the target position. The mathematical expression for position update is:

[0264] D = |CX * (t) - X(t)| (19)

[0265] X(t + 1) = X * (t) - AD (20)

[0266] A = 2ar1 - a (21)

[0267] C = 2r2 (22)

[0268]

[0269] ​​where t is the current iteration number, t max is the maximum number of iterations, X * (t) is the position vector of the current optimal solution, X(t) is the position vector of the current solution, A and C are the convergence coefficient vector and the oscillation coefficient vector respectively, the value of a linearly decreases from 2 to 0 as t increases, and r1 and r2 are random vectors within [0, 1].

[0270] II. Bubble attack

[0271] During the attack phase, the humpback whale has two attack methods to choose from, namely the shrinking encircling prey mechanism and the spiral position update mechanism. The probability of choosing each of the two attack methods is 50%. The position is updated through these two methods, and the mathematical expression for position update is as follows:

[0272]

[0273] where D ′ =|X * (t)-X(t)| is the distance between the i-th whale and the prey, d is a constant defining the spiral shape, l is a random number within [-1, 1], and p is a random number within [0, 1].

[0274] III. Search and predation

[0275] When the humpback whale preys on its prey, it will randomly search for the prey instead of using the currently found best target position to update the current target position. To avoid falling into the local optimum problem, the algorithm will perform a global search, and the mathematical expression for position update is as follows:

[0276] D = |CX rand (t)-X(t)| (25)

[0277] X(t + 1) = X rand (t)-AD (26)

[0278] where X rand (t) is the randomly selected position vector in the current population. When |A|≥1, the humpback whale will abandon approaching the current optimal position and perform a random search. When |A|<1, the humpback whale will use the position vector of the current optimal solution to update the position vector of the current solution, and according to the value of p, the algorithm can switch between the shrinking encircling mechanism and the spiral position update mechanism. Finally, when the maximum number of iterations is reached, the algorithm terminates.

[0279] WOA optimizes the penalty factor γ and the kernel function parameter σ of LSSVM 2 and the specific steps to generate the optimal model are as follows:

[0280] (1) Initialize the population size, maximum number of iterations, number of variables, and upper and lower limits of variables of the whale algorithm.

[0281] (2) Randomly initialize the positions of the whale population.

[0282] (3) Calculate the corresponding fitness values of each individual in the population and sort them. Select the optimal solution as the current global optimal solution, and update the positions according to formulas (19)-(26).

[0283] (4) Repeat step (3) until the current iteration number is equal to the maximum iteration number, and output the position with the best fitness and the two parameters γ and σ of LSSVM. 2 。

[0284] (5) Substitute the optimized penalty factor γ and kernel function parameter σ 2 obtained by optimization into LSSVM, and import the training data for training to obtain the optimal model.

[0285] To test the fault detection performance of the method proposed in the present invention, GA-LSSVM, PSO-LSSVM, and WOA-LSSVM were run for 20 comparison experiments, and the test results are shown in Table 1.

[0286] Table 1 Comparison experiment results of running GA-LSSVM, PSO-LSSVM, and WOA-LSSVM for 20 times

[0287]

[0288] As can be seen from Table 1, when using the three algorithms GA, PSO, and WOA to optimize LSSVM, the effect of WOA on fault classification of residuals is better than the other two optimization algorithms. In addition, when the fitness curve is determined, it indicates that the overall algorithm tends to converge. From the fitness curves of full sensor faults Figure 3 and partial sensor faults Figure 4 it can be seen that the WOA optimization algorithm converges to reach the global optimal 100% classification accuracy at the 3rd generation and the 2nd generation respectively, while the other two algorithms fall into the local optimal state. At this time, the two parameters optimized by the WOA algorithm are γ = 352.4420, σ 2 = 13.7078 and γ = 4468.7, σ 2 = 14.8633.

[0289] Step Seven: Perform fault diagnosis according to the test samples in Step Four and the optimal aero-engine sensor model in Step Six.

[0290] It is known that by setting two labels, the normal state and the fault state, for each sensor in the aero-engine sensor control system. For example, the normal state label of the first sensor is 1, and the fault state label is 2. The normal state label of the second sensor is 3, and the fault state label is 4. That is, the entire control system has 2ny a label, and the label numbers increase sequentially from 1, 2, …, 2n y one by one.

[0291] If the residual label number corresponding to each sensor is odd, it indicates that the corresponding sensor is working properly; otherwise, the sensor has a fault. The specific sensor fault location strategy is

[0292]

[0293] where l is the number corresponding to the fault label, and S is the number of the corresponding faulty sensor.

[0294] According to the above fault location strategy, from Figure 5 it can be seen that all sensors detect faults. From Figure 6 it can be seen that some sensors detect faults, and the sensors numbered 2 and 4 have faults.

[0295] The present invention belongs to the field of control and provides a method for diagnosing sensor faults in an aeroengine control system, mainly a method for diagnosing aeroengine sensor faults based on a multi-objective fault detection observer and an improved LSSVM. Fault diagnosis is realized by classifying multi-objective faults for the residuals generated by the observer through the improved LSSVM model. The gain matrix L obtained by the multi-objective observer designed in the present invention makes the residuals robust to unknown disturbances and sensitive to faults; the improved LSSVM model can obtain a high-accuracy fault classification for minor faults, realize the fault diagnosis function, and diagnose early faults with small fault amplitudes, which is of great significance.

Claims

1. A fault diagnosis method for aero-engine sensors based on a multi-objective fault detection observer and improved LSSVM, characterized in that It includes the following steps: Establish a mathematical model of an aero-engine control system with model uncertainty; Determine a fault detection observer according to the mathematical model of the aero-engine control system; Determine an error system according to the fault detection observer, and the obtained error system includes a first subsystem and a second subsystem; Determine multi-objective constraint conditions according to the model uncertainty, robustness and fault sensitivity of the error system, and obtain an observer gain matrix according to the multi-objective constraint conditions; Obtain a residual robust to model uncertainty according to the fault detection observer; Initialize the basic parameters of an aero-engine sensor fault diagnosis model based on LSSVM according to the residual robust to model uncertainty; Optimize the kernel function parameters and penalty factors of the aero-engine sensor fault diagnosis model based on LSSVM by using the whale algorithm to obtain an optimal aero-engine sensor fault diagnosis model; Classify faults for the residuals obtained by the fault detection observer according to the optimal aero-engine sensor fault diagnosis model to obtain fault types; Among them, the model of the aero-engine control system with model uncertainty in the presence of sensor faults is represented by formula (1): where is the state vector, is the control input, is the measurement output, is the process disturbance, is the measurement noise, is the sensor fault; and respectively represent the n-dimensional and m×n-dimensional Euclidean spaces, and I n represents the n×n-dimensional identity matrix; A, B, C, D w , D v and F are known matrices of appropriate dimensions, and ΔA, ΔB, ΔC, and ΔF are parametric uncertainties. ΔA, ΔB, ΔC, and ΔF are unknown but bounded and satisfy Among them and are matrices with all non-negative elements that are known; ΔA = M1Δ1N1, ΔB = M2Δ2N2, ΔC = M3Δ3N3, ΔF = M4Δ4N4 (3) where M i and N i are known matrices of appropriate dimensions, i = 1, 2, 3, 4, and and are unknown matrices and satisfy 2. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and an improved LSSVM according to claim 1, wherein, The aero-engine control system model is obtained based on the following method: Establish a linearized state-space model of the aero-engine control system and discretize the state-space model; Consider interference noise and sensor faults, and establish an aero-engine control system model with model uncertainty in the presence of sensor faults.

3. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and an improved LSSVM according to claim 2, characterized in that, The state-space model of the aero-engine in the maximum ground state is: Where A, B, and C represent the system matrix, control matrix, and output matrix respectively; Δx = x - x0, Δu = u - u0, Δy = y - y0, n h , n l , m f , A8, respectively represent the high-pressure rotor speed, low-pressure rotor speed, main fuel supply, throat area of the tail nozzle, total pressure after the compressor, and total temperature after the turbine.

4. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to claim 1, wherein The fault detection observer is represented by formula (5): Among them is the state estimation, is the residual signal, is the observer gain matrix; Define the estimation error as Then the error system is represented by Equation (6): where A c = A - LC, F d = F + ΔF; The error system includes a first subsystem and a second subsystem. The first subsystem is represented by formula (7), and the second subsystem is represented by formula (8): Among them B f = -LF d , D x = [D w -LD v ΔA - LΔC ΔB], D y = [0 D v ΔC 0], d k = [w k v k x k u k T .​ 5. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and an improved LSSVM according to claim 4, characterized in that The fault detection observer satisfies the following multi-objective constraint conditions: where λ1 > 0, λ2 > 0, β > 0, 0 < α < 1, k represents the k-th moment, and e0 represents the initial error value; The design constraint conditions are transformed into solving the following linear matrix inequality: Where n d = n w + n v + n x + n u ,n w ,n v ,n x ,n u represents the dimension of the system matrix; Ψ x = Φ x + ∈1N x T N x ; Ψ y = Φ y + ∈2N y T N y ; Ω = Θ + ∈3V T V; N y = [0 0 0N0 0]; where * denotes the transpose of the symmetric term, 0 represents the zero matrix of appropriate dimension in a block matrix, <0 indicates that the matrix is negative definite, In the inequality, the scalars 0 < α < 1, γ1 > 0, β > 0 are constants given in advance, and are positive definite matrices, is an invertible matrix, the matrix The scalars ∈1 > 0, ∈2 > 0 and ∈3 > 0 are arbitrary scalars, and γ2 > 0 is a parameter to be optimized.

6. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to claim 5, characterized in that According to the YALMIP toolbox in MATLAB, the minimum feasible solution of γ2 that satisfies the linear matrix inequalities (11)-(13) is obtained, and at the same time, the matrices P, Q, G, and W are obtained. Furthermore, the optimal observer matrix gain L = G -1 W.

7. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and an improved LSSVM according to claim 1, wherein Obtaining the residual robust to model uncertainty according to the fault detection observer includes setting two tags, namely the normal state and the fault state, for each sensor of the aero-engine sensor control system. There are a total of 2n y tags for the entire aero-engine control system, and the tag numbers increase sequentially from 1, 2, …, 2n y one by one. The fault detection observer generates residuals with a known data volume for the corresponding state tags of each sensor.

8. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and improved LSSVM according to claim 1, wherein The initial LSSVM basic parameter aero-engine sensor fault diagnosis model establishes an identification model from the normal input-output space of the aero-engine control system model, and its function expression and constraint conditions are: where ω is the weight vector, γ is the penalty factor, is a non - linear mapping function that maps the data in the original feature space to a high - dimensional space, x k is the input vector, e k is the slack variable, b is the bias variable, and n is the total number of samples; Through Lagrange optimization of the Lagrange function, the expression is: where α k is the Lagrange multiplier. According to the KKT conditions, take the partial derivatives of ω, b, e k , α k in formula (15) and set them to 0, eliminating the variables ω and e k , transforming a non-linear optimization problem into a linear solution problem. The specific formula is as follows: where P = [1, …, 1] T , A = [α1, …, α k T , Y = [y1, …, y k T , and I is the identity matrix;​​ The least squares support vector machine LSSVM model is: where y out (x) is the model prediction output, and K(x, x k ) is the Gaussian radial basis kernel function selected by the present invention, x is a certain fixed data in the training data, and x k is the k-th data in the training data; The optimal aero-engine sensor fault diagnosis model optimizes the penalty factor γ and kernel function parameter σ of the least squares support vector machine (LSSVM) model based on the whale optimization algorithm (WOA), 2 using the classification accuracy as the fitness function. Among them, the whale optimization algorithm (WOA) optimizes the penalty factor γ and kernel function parameter σ of the least squares support vector machine (LSSVM). 2 The specific steps for generating the optimal model are as follows: (1) Initialize the population size, maximum number of iterations, number of variables, and upper and lower limits of variables of the whale algorithm; (2) Randomly initialize the positions of the whale population; (3) Calculate the corresponding fitness values of each individual in the population and sort them, select the optimal solution as the current global optimal solution, and update the position according to formulas (19)-(26); Assume that the current optimal candidate solution is the target position of the humpback whale prey. Whales that do not belong to the current optimal candidate solution position will continuously update their positions and try to approach the target position. The mathematical expression for position update is: D = |CX * (t) - X(t)| (19) X(t + 1) = X * (t) - AD(20) A = 2ar1 - a (21) C＝2r2 (22) where t is the current iteration number, and t max is the maximum iteration number, X * (t) is the position vector of the current optimal solution, X(t) is the position vector of the current solution, A and C are the convergence coefficient vector and the swing coefficient vector respectively, the value of a linearly decreases from 2 to 0 as t increases, and r1 and r2 are random vectors within [0, 1]; The attack methods of humpback whales include the mechanism of shrinking and surrounding prey and the mechanism of spiral position update. The probability of choosing each of the two attack methods is 50%. Humpback whales update their positions through these two attack methods. The mathematical expression for position update is: where D′ = |X * (t) - X(t)| is the distance between the i-th whale and the prey, d is a constant defining the spiral shape, l is a random number within [-1, 1], and p is a random number within [0, 1]; When hunting prey, humpback whales randomly search for prey instead of using the current best target position to update the current target position. The mathematical expression for position update is: D = |CX rand (t) - X(t)| (25) X(t + 1) = X rand (t) - AD(26) Where X rand (t) is a randomly selected position vector in the current population. When |A| ≥ 1, the humpback whale will abandon approaching the current optimal position and conduct a random search. When |A| < 1, the humpback whale will use the position vector of the current optimal solution to update the position vector of the current solution, and switch between the shrinking encircling mechanism and the spiral position update mechanism according to the value of p. Finally, when the maximum number of iterations is reached, the algorithm is terminated; (4) Repeat step (3) until the current iteration number is equal to the maximum iteration number, and output the position with the best fitness and the two parameters γ and σ of the least squares support vector machine LSSVM model 2 ; (5) Substitute the optimized penalty factor γ and kernel function parameter σ 2 into the least squares support vector machine (LSSVM) model, and import the training data for training to obtain the optimal aero-engine sensor fault diagnosis model.

9. The aero-engine sensor fault diagnosis method based on a multi-objective fault detection observer and an improved LSSVM according to claim 1, characterized in that According to the optimal aeroengine sensor fault diagnosis model, fault classification is performed on the residuals obtained by the fault detection observer to obtain the fault type, including inputting the residuals obtained by the fault detection observer into the optimized aeroengine sensor fault diagnosis model for fault diagnosis, and performing fault classification on the residuals under different sensor fault modes of the aeroengine. Specifically: By setting two labels, the normal state and the fault state, for each sensor of the aeroengine control system, the normal state label of the first sensor is 1, and the fault state label is 2; the normal state label of the second sensor is 3, and the fault state label is 4; the normal state label of the i-th sensor is 2i - 1, and the fault state label is 2i + 1. There are a total of 2n y labels for the entire aeroengine control system, and the label numbers increase sequentially from 1, 2,..., 2n y If the residual label number corresponding to each sensor is odd, then each sensor is working normally; otherwise, a sensor has a fault. Among them, the sensor fault location strategy is specifically Where l is the number corresponding to the fault label, and S is the number of the corresponding faulty sensor.

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