Aero-engine fault interval estimation method based on optimal set membership estimation

Abstract

The invention provides an aero-engine fault interval estimation method based on optimal set membership estimation, and belongs to the field of aviation. According to the method, the interval estimation problem of the sensor faults of the uncertain aero-engine system is considered, the fault interval of the engine is accurately predicted and estimated, appropriate measures can be taken, and it is ensured that the engine runs under the safe and reliable condition. The possible fault section can be predicted to help formulate a preventive maintenance plan, and potential safety risks are avoided. By estimating the fault interval, the time range or condition of the possible fault of the system can be predicted in advance. Therefore, the system can take preventive measures before a fault occurs, so that potential influences are reduced or avoided, and the fault-tolerant control capability is improved.

Description

Technical Field

[0001] The invention belongs to the field of aviation, and in particular relates to an aircraft engine fault interval estimation method based on optimal set membership estimation. Background Art

[0002] With the diversification of flight missions and the advancement of technology, the design of aircraft engine control systems has become increasingly complex, and they often need to work under high load for a long time in different environments. Due to mechanical vibration, aging of sensing components, changes in temperature and humidity, and electromagnetic interference, sensors in aircraft engine control systems are prone to failure. Research on fault interval estimation can help identify potential faults in engine control systems, detect and handle faults in a timely manner, and improve the safety of aircraft operations. By accurately and efficiently determining the fault interval of aircraft engine control systems, the cost of maintenance and repair can be reduced. Avoid unnecessary repairs and replacements, maximize the service life of components, and thus reduce aircraft operating costs. At the same time, fault interval estimation also provides more fault information for the design of fault-tolerant controllers, which helps to meet the challenges faced by highly intelligent and automated aircraft engine control systems in the future and ensure their safety and reliability.

[0003] State estimation is one of the important tasks in control theory and control engineering. Many state estimation methods, such as the famous Kalman filter, usually assume that the probability distribution of random uncertainty is known, which may not be applicable in practice. Unlike methods based on stochastic theory, set membership estimation methods only require that uncertainty is unknown but bounded, which is a more reasonable assumption. Therefore, set membership estimation has received widespread attention from researchers in recent years. Existing set membership estimation methods can be divided into two types. The first is the interval observer, which consists of two sub-observers and provides estimates of the lower and upper bounds of the state. The interval observer is designed based on the theory of monotone systems in order to make its error dynamic system stable and cooperative. However, the cooperative constraint may lead to greater conservatism and limit its scope of use. The other is to construct a set membership estimation method that contains all geometric sets of admissible state values ​​by analyzing the propagation of uncertainty. Different geometric sets are used to design set membership estimation methods, such as ellipsoids, parallelograms, and polyhedrons. Among these geometric sets, the central symmetric polyhedron is a good choice for set membership estimation because it can achieve a good balance between estimation accuracy and computational complexity. A key problem of the set membership estimation method is how to minimize the size of the error centrosymmetric polyhedron generator matrix to improve the estimation accuracy. To this end, the present invention proposes an optimal set membership estimation method to achieve interval estimation of aircraft engine faults. This method uses the F norm to describe the size of the generator matrix. Compared with the method of calculating the robust performance index of the error system and then using set membership estimation to obtain interval estimation, more accurate point estimation and interval estimation are obtained. This provides more accurate fault information for the design of aircraft engine fault-tolerant controllers, which is conducive to improving the fault-tolerant control effect and improving the safety and reliability of aircraft engine control systems. Summary of the invention

[0004] Aiming at the fault estimation problem of uncertain linear aircraft engine control system, the present invention provides an aircraft engine fault interval estimation method based on optimal set membership estimation.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for estimating an aircraft engine fault interval based on optimal set membership estimation comprises the following steps:

[0007] S1. Establishing uncertain linear aero-engine state space model:

[0008] Considering the influence of uncertainty, interference, noise and sensor failure on the system, the state space model of the system is written as follows:

[0009]

[0010] Among them, x k 、wk ,y k 、v k 、f k Represent the state of the system, process disturbance, measurement output, measurement noise and sensor failure respectively. A, E, C, D, F are the state matrix, disturbance matrix, output matrix, noise matrix and sensor failure matrix of the system represented by the known formula (1). ΔA and ΔC are uncertainty matrices, which are unknown but bounded and satisfy the following:

[0011]

[0012] in, is a matrix with all known elements non-negative, n x Indicates the number of rows in the state matrix, n y Represents the number of rows of the output matrix; matrices M1, N1, M2 and N2 are known, and Δ1 and Δ2 are unknown matrices satisfying and is the identity matrix with dimensions n1 and n2.

[0013] In addition, without loss of generality, the initial state, process disturbance, and measurement noise are assumed to be unknown, but the following conditions are satisfied:

[0014]

[0015] Among them, x0 represents the initial value of the state, represents the initial value of the state estimate, and is a known vector.

[0016] S1.1 In order to achieve the sensor failure f k and the state of the system x k For interval estimation, consider the following augmented system state space model:

[0017]

[0018] in, is the augmented state, h k =f k+1 -f k Sensor failure rate of change, ΔC=[ΔC 0], Represents the identity matrix.

[0019] Without loss of generality, and h k is unknown and bounded, satisfying the following:

[0020]

[0021] in, and is a known vector, nf The number of the row representing the failure.

[0022] Then, the vectors in equations (3) and (5) can be described as the following central symmetric polyhedron:

[0023]

[0024] in, Represents the initial value of the augmented state, which is equivalent to definition W=<0,H w >,V=<0,H v >,H=<0,H h >.

[0025] S2. Design the optimal set membership observer for the augmented system state space model (4) obtained in S1.1. This process includes two parts, namely state prediction and measurement update:

[0026] 1) Status prediction

[0027] Considering the augmented system state space model (4), define the interval matrix represent the upper bounds of the interval matrices [A] and [C] respectively; therefore, we can get Given So Symmetric polyhedron at the center of the prediction The inner part is bounded, as shown below:

[0028]

[0029] in, is an augmented state, equivalent to

[0030] The specific parameters of the augmented state prediction set are as follows:

[0031]

[0032] in, Denotes the generator matrix H k The downgrade of 1 m Represents an m-row matrix with all elements set to 1.

[0033] It is worth noting that the prediction step of the augmented state uses the central symmetric polyhedron set of the augmented state at the previous moment, as well as the central symmetric polyhedron set of control inputs, process disturbances, fault change rates, and parameter uncertainties to generate the prediction set.

[0034] 2) Measurement update

[0035] The measurement update step of the augmented state uses the augmented state prediction set and the measurement output to obtain the central symmetric polyhedron set of the augmented state at the current moment. The specific process is as follows:

[0036]

[0037] in, D v =DH v , is the gain of the optimal set membership estimate observer.

[0038] S3. From the analysis of S2, we can see that express However, directly finding the gain matrix G makes Minimization is difficult to solve, the amount of calculation is large, and it is not suitable for practical applications. Using the optimality principle, an optimal solution G can be obtained * make The Fourier norm of Minimize is minimize Gain matrix G * Obtained through the following theorem:

[0039] Theorem 1: Given Then make The Fourier norm of The optimal gain to minimize is as follows:

[0040]

[0041] Proof: In order to generate the matrix The Fourier norm of Minimize It is expressed as follows:

[0042]

[0043] in, So, The Fourier norm of can be re-expressed as:

[0044]

[0045] Furthermore, combined with the definition of matrix operations, taking the partial derivative of (12) with respect to G yields:

[0046]

[0047] Finally, by command The optimal gain G can be obtained * , expressed as:

[0048]

[0049] The beneficial effects of the present invention are as follows: the interval estimation problem of sensor failure in an uncertain aero-engine system is considered. By accurately predicting and estimating the engine failure interval, appropriate measures can be taken to ensure that the engine operates under safe and reliable conditions. Predicting possible failure intervals can help formulate preventive maintenance plans and avoid potential safety risks. By estimating the failure interval, the time range or conditions under which the system may fail can be predicted in advance. This enables the system to take preventive measures before a failure occurs to mitigate or avoid potential impacts and improve fault-tolerant control capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of the algorithm for estimating the fault interval of an aircraft engine based on optimal set membership estimation;

[0051] Figure 2 This is the result diagram of aircraft engine fault point estimation based on optimal set membership estimation;

[0052] Figure 3 This is the result diagram of aircraft engine fault interval estimation based on optimal set membership estimation;

[0053] Figure 4 This is the result diagram of aircraft engine state interval estimation based on optimal set membership estimation; DETAILED DESCRIPTION

[0054] The continuous system model of an aircraft engine of a certain research institute is discretized using the Euler one-step method. The sampling time interval T s = 0.025s. Then, considering parameter uncertainty, faults, and noise interference in system (1), the corresponding parameter matrix is ​​as follows:

[0055]

[0056] in, is a random signal with a value between 0 and 1.

[0057] By seeking The Fourier norm of Minimize, and get the observer gain matrix based on the optimal set membership estimation as:

[0058]

[0059] The flow chart of the aircraft engine fault interval estimation algorithm based on optimal set membership estimation is as follows: Figure 1 Next, in order to verify the significant performance of the optimal set membership estimation observer in terms of fault interval, we simulate it. The simulation results are shown in Figure 2-Figure 4 As shown, Figure 2 The figure shows the result of aircraft engine fault point estimation based on optimal set membership estimation. It can be seen that the fault point estimation accuracy obtained by the proposed method is better than that of the Romberg observer. This is due to the fact that the optimal set membership estimation observer utilizes the structure of the Kalman filter and minimizes the Fourier norm of the set membership estimation matrix to obtain the optimal observer gain. Figure 3 As shown in Figure 2, the fault interval estimation based on the optimal set membership estimation method is more accurate, which provides more accurate fault information for the subsequent design of the fault-tolerant controller and ensures the safety and reliability of the system. Figure 4 The state interval estimation result is given. More accurate state interval estimation can provide accurate state information when the aircraft engine state is unpredictable, providing guarantee for the design of subsequent controllers.

[0060] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for estimating the fault interval of an aircraft engine based on optimal set membership estimation, characterized in that: The following steps are involved: S1. Establishing uncertain linear aero-engine state space model: Considering the influence of uncertainty, interference, noise and sensor failure on the system, the state space model of the system is written as follows: Among them, x k 、w k ,y k 、v k 、f k Represent the state of the system, process disturbance, measurement output, measurement noise and sensor failure respectively; A, E, C, D, F are the state matrix, disturbance matrix, output matrix, noise matrix and sensor failure matrix of the system represented by the known formula (1); ΔA and ΔC are uncertainty matrices, which are unknown but bounded and satisfy the following: in, is a matrix with all known elements non-negative, n x Indicates the number of rows in the state matrix, n y Represents the number of rows of the output matrix; matrices M1, N1, M2 and N2 are known, and Δ1 and Δ2 are unknown matrices satisfying and is the identity matrix with dimensions n1 and n2; In addition, without loss of generality, the initial state, process disturbance, and measurement noise are assumed to be unknown, but the following conditions are satisfied: Among them, x0 represents the initial value of the state, represents the initial value of the state estimate, and is a known vector; S1.1 In order to achieve the sensor failure f k and the state of the system x k For interval estimation, consider the following augmented system state space model: in, is the augmented state, h k =f k+1 -f k Sensor failure rate of change, ΔC=[ΔC0], represents the identity matrix; Without loss of generality, and h k is unknown and bounded, satisfying the following: in, and is a known vector, nf The number of rows indicating the failure; Then, the vectors in equations (3) and (5) can be described as the following central symmetric polyhedron: in, Represents the initial value of the augmented state, which is equivalent to definition W=<0,H w >,V=<0,H v >,H=<0,H h > S2. Design the optimal set membership observer for the augmented system state space model (4) obtained in S1.

1. This process includes two parts, namely state prediction and measurement update: 1) Status prediction Considering the augmented system state space model (4), define the interval matrix represent the upper bounds of the interval matrices [A] and [C] respectively; therefore, we can get Given So Symmetric polyhedron at the center of the prediction The inner part is bounded, as shown below: in, is an augmented state, equivalent to The specific parameters of the augmented state prediction set are as follows: in, Denotes the generator matrix H k The downgrade of 1 m represents an m-row matrix with all elements being 1; The augmented state prediction step generates a prediction set using the central symmetric polyhedron set of the augmented state at the previous moment, as well as the central symmetric polyhedron set of the control input, process disturbance, fault change rate and parameter uncertainty; 2) Measurement update The measurement update step of the augmented state uses the augmented state prediction set and the measurement output to obtain the central symmetric polyhedron set of the augmented state at the current moment; the specific process is as follows: in, D v =DH v , is the gain of the optimal set membership estimate observer; S3. From the analysis of S2, we can see that express However, directly finding the gain matrix G makes Minimization is difficult to solve, the amount of calculation is large, and it is not suitable for practical applications; using the optimality principle, an optimal solution G can be obtained * make The Fourier norm of Minimize is minimize Gain matrix G * Obtained through the following theorem: Theorem 1: Given Then make The Fourier norm of The optimal gain to minimize is as follows: Proof: In order to generate the matrix The Fourier norm of Minimize It is expressed as follows: in, So, The Fourier norm of can be re-expressed as: Furthermore, combined with the definition of matrix operations, taking the partial derivative of (12) with respect to G yields: Finally, by command The optimal gain G can be obtained * , expressed as:

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