Aircraft system fault detection method based on unknown input observer

Abstract

The invention relates to the technical field of aircraft system fault detection, in particular to an aircraft system fault detection method based on an unknown input observer. According to the method, joint estimation of the state variable and the fault signal of the nonlinear aircraft system can be realized, and the influence of external disturbance on the estimation performance is effectively reduced. According to the method, the defects of an existing fault detection method based on residual signals can be overcome, the fault occurrence time can be provided, the estimated value of the fault amplitude can also be provided, the fault can be further processed in the later period, and the method has wider and profound theoretical significance and practical application value; estimated values of state variables and fault signals of the system can be provided at the same time, faults can be detected in time, and a certain foundation can be laid for monitoring dynamic behaviors of the system in real time and completing specific control tasks.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft system fault detection, and in particular to an aircraft system fault detection method based on an unknown input observer. Background Art

[0002] With the rapid development of science and technology, modern aviation technology is constantly innovating, and the integration and complexity of various aircraft systems are increasing. However, during the flight, the aircraft will face a variety of complex external environments. Many unfavorable factors will affect the performance and reliability of the aircraft to varying degrees and cause failures, and even have catastrophic consequences and lead to huge economic losses. It can be seen that the threat of failure to aircraft flight safety cannot be ignored. On the other hand, with the growing demand for the safety, reliability, maneuverability and maintainability of aircraft systems, effective solutions to fault diagnosis problems have received widespread attention.

[0003] The main purpose of fault diagnosis technology is to detect and accurately identify fault phenomena in an offline or online manner, which mainly includes fault detection, isolation, estimation and prediction, that is, to determine whether a fault has occurred, locate the location of the fault, identify the type of fault, and determine the magnitude of the fault and the time of occurrence. Among the many fault diagnosis methods, observer-based fault estimation can not only directly provide an estimate of the fault magnitude, but also has the advantages of easy fault location and determination of the time of fault occurrence. Because the unknown input observer has strong robustness to external disturbances and system uncertainties, it has attracted much attention.

[0004] At present, a lot of research has been done on the fault diagnosis of aircraft systems. However, the existing solutions are mainly based on residual signals to achieve fault detection, and detailed information such as the specific amplitude and change trend of the fault cannot be obtained. Related issues still need further in-depth research. In addition, in order to be closer to the actual application of engineering, it is necessary to fully consider the nonlinear characteristics of the aircraft system and the impact of external disturbances on the fault diagnosis results, and effectively suppress the negative impact brought by them to obtain satisfactory fault diagnosis performance. Summary of the invention

[0005] The technical problem to be solved by the present invention is: in view of the shortcomings of the above-mentioned existing fault diagnosis technical solutions, a method for aircraft system fault detection based on an adaptive unknown input observer is provided to achieve joint estimation of state variables and fault signals of nonlinear aircraft systems, thereby achieving the purpose of fault detection and effectively reducing the influence of external disturbances on fault diagnosis performance.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] The aircraft system fault detection method based on unknown input observer specifically includes the following steps:

[0008] S1: establishing a nonlinear state space model for an aircraft system, wherein the model is a nonlinear continuous time system with external disturbances, and mathematically representing a fault signal based on the state space model;

[0009] S2: Decompose the external disturbance signal into two parts: decoupling and non-decoupling;

[0010] S3: For the relevant system matrix, verify the conditions that the matrix rank needs to meet;

[0011] S4: To estimate the fault signal in the aircraft system, the relationship between the fault signal and the measured output signal of the system is constructed by referencing auxiliary variables;

[0012] S5: Based on the system measurement output signal, the expression of the adaptive unknown input observer is given to realize the joint estimation of the system state variables and fault signals;

[0013] S6: Define the estimation error variable, and combine the system state space model and the designed adaptive unknown input observer to obtain the dynamic equation of the estimation error system;

[0014] S7: Combining Lyapunov stability theory and matrix inequality techniques, the detailed design conditions of the gain matrix of the unknown input observer are given in the form of linear matrix inequalities;

[0015] S8: Algorithm 1 is given to elaborate the process of solving the gain matrix of the designed unknown input observer;

[0016] S9: Algorithm 2 is given for simultaneously obtaining real-time estimation values ​​of system state variables and fault signals;

[0017] S10: Verify the effectiveness of the proposed fault detection scheme for the aircraft system through the simulation platform, and adjust, improve and optimize the scheme based on the simulation results.

[0018] Step 1: Establish a nonlinear state space model for the aircraft system, which is a nonlinear continuous time system with external disturbances, and mathematically characterize the fault signal based on the state space model. The nonlinear state space model is as follows:

[0019]

[0020] in, Respectively represent the dimension n x , n u , n x , n f , and n y The state variables, control input signals, nonlinear vector functions, fault signals, partially decoupled external bounded disturbances and measured output signals of the nonlinear aircraft system. t represents time, and the symbol “∈” represents the relationship. and Respectively represent the dimension n x , n u , n f , and n y The first-order derivative of the fault signal g(t) with respect to time t is bounded, but there is no requirement for its second-order derivative with respect to time t. Nonlinear vector function Satisfies the Lipschitz condition, that is, The symbol “|| ||” represents the norm of a matrix or vector. is the Lipschitz constant. The matrices A, B, F, D, and C represent system matrices with appropriate dimensions.

[0021] Step 2: Disturb the external environment Decompose into and Two parts, including represents the decoupled part, that is, And the matrix D 1 Satisfies column full rank.

[0022] Step 3: Verify that the following matrix conditions hold for the system matrix:

[0023] (1) Symbol "rank(CD 1 )” represents the matrix CD 1 rank;

[0024] (2) Matrix Satisfy column full rank;

[0025] (3) For all complex numbers s with nonnegative real part, and s ≠ 0, the sign Representation Matrix The rank and Indicates the dimension is n x The identity matrix of .

[0026] Step 4: In order to estimate the fault signal in the aircraft system and make full use of the measured output signal of the system, the following auxiliary variables are referenced based on the fault signal g(t) and the measured output signal y(t) of the system:

[0027] f(t)=g(t)+Ey(t) (2)

[0028] The matrix E is the learning matrix that needs to be designed, and its detailed design conditions will be given later.

[0029] From formula (2), we can get

[0030]

[0031] Step 5: Based on the auxiliary variables in equation (2) and the measured output signal of the system, an adaptive unknown input observer is designed as shown below to achieve joint estimation of the system state variable x(t) and the fault signal g(t):

[0032] in, Indicates the dimension is n x The state variables of the observer. Represents the estimated value of f(t), and its dimension is n f . Matrix N, P, G, L, L f is the gain matrix of the observer to be designed, and the detailed design conditions will be given later.

[0033] From the adaptive unknown input observer given in equation (4), we can obtain the estimated values ​​of the system state variable x(t) and fault signal g(t):

[0034]

[0035] in and They represent the estimated values ​​of the system state variable x(t) and fault signal g(t) respectively.

[0036] Step 6: Define the estimated error variables for the state variables and auxiliary variables of the system as shown below:

[0037]

[0038] in and They represent the estimated error variables for the system state variables and the auxiliary variables respectively.

[0039] Based on the system state space model in equation (1) and the adaptive unknown input observer in equation (4), the following dynamic equation of the estimation error system is obtained:

[0040]

[0041] in

[0042] The gain matrix of the observer is designed so that the following matrix conditions hold:

[0043]

[0044] Then, we get the estimated error system as follows:

[0045]

[0046] Step 7: Combining Lyapunov stability theory and matrix inequality technology, the detailed design conditions of the gain matrix of the following observer are given in the form of linear matrix inequality.

[0047] For a given positive number β 1 , β 2 , β 3 and β 4 , if there exist symmetric positive definite matrices Q and R, the matrix M z , W, and M f , so that the following linear matrix inequality holds:

[0048]

[0049] in The symbol "*" represents the symmetric term in a symmetric matrix, He(WCF) = WCF + (WCF) T , the superscript "T" represents the transpose of the matrix, and the symbol "I" represents the identity matrix with the appropriate dimension. Then it can be inferred that the adaptive unknown input observer designed in equation (4) can ensure that all variables in the estimation error system shown in equation (8) are bounded.

[0050] Step 8: Through the following Algorithm 1, the gain matrix of the adaptive unknown input observer designed in equation (4) can be solved.

[0051] Algorithm 1:

[0052] ① Matrix G = D 1 ((CD 1 ) T (CD 1 )) -1 (CD 1 ) T +G 0 (I-CD 1 ((CD 1 ) T (CD 1 )) -1 (CD 1 ) T ), where the matrix G 0 The designer chooses and calculates the matrix

[0053] ② By solving the linear matrix inequality in equation (9), we can obtain the symmetric positive definite matrices Q, R, and M z , W, and M f The value of

[0054] ③ The following gain matrix is ​​obtained after calculation:

[0055]

[0056] Step 9: For the system in equation (1), obtain the estimated values ​​of the system state variable x(t) and fault signal g(t) through the following Algorithm 2.

[0057] Algorithm 2:

[0058] ① Combine the system matrix in (2) and set G 0 The value of

[0059] G=D 1 ((CD 1 ) T (CD 1 )) -1 (CD 1 ) T +G 0 (I-CD 1 ((CD 1 ) T (CD 1 )) -1 (CD 1 ) T )

[0060] Get the value of matrix G;

[0061] ② By Calculate the matrix The value of

[0062] ③ Combine the system matrix and matrix in formula (2) Set a positive β 1 , β 2 , β 3 and β 4 By solving the linear matrix inequality shown in equation (9), we can obtain the positive definite matrices Q, R, and M z , W, and M f The value of

[0063] ④ The observer gain matrix N, P, L is calculated by formula (10). L f , the value of E;

[0064] ⑤ Run the adaptive unknown input observer in equation (4) to obtain the variables z(t) and Real-time value of

[0065] ⑥From the following formula

[0066]

[0067] Obtain estimates of the system state variables x(t) and fault signal g(t) and

[0068] Step 10: Verify the effectiveness of the proposed fault detection scheme for the aircraft system through the simulation platform, and adjust, improve and optimize the scheme based on the simulation results.

[0069] The beneficial effects of adopting the above technical solution are:

[0070] The present invention provides an aircraft system fault detection method based on an adaptive unknown input observer, which can realize the joint estimation of state variables and fault signals of a nonlinear aircraft system and effectively reduce the influence of external disturbances on the estimation performance. (1) It can make up for the shortcomings of the existing fault detection method based on residual signals. It can not only provide the time of fault occurrence, but also provide an estimate of the fault amplitude, which is convenient for further processing of the fault in the later stage. It has more extensive and far-reaching theoretical significance and practical application value; (2) It can simultaneously provide estimates of the system state variables and fault signals, which can not only detect the existence of faults in time, but also lay a certain foundation for real-time monitoring of the dynamic behavior of the system and completing specific control tasks; (3) Different from the existing joint estimation scheme of state variables and fault signals, the adaptive unknown input observer scheme proposed in the present invention does not require the second-order derivative of the fault signal with respect to time to be zero or sufficiently small, that is, it relaxes the restrictions of the existing scheme to a certain extent; (4) The present invention adopts an unknown input observer scheme, which increases the number of observer gain matrices compared with the traditional observer scheme, thereby increasing the degree of freedom of design; (5) Auxiliary variables are introduced based on the output measurement value of the system to realize the estimation of the fault signal and make full use of the available output measurement value; (6) In the estimation of the fault signal, the output error correction term is introduced The estimation performance of fault signals is improved by making full use of the output measurements of the system and increasing the design freedom. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 is a flow chart of the present invention;

[0072] Figure 2 The schematic diagram of the adaptive unknown input observer designed for the present invention;

[0073] Figure 3 It is a flowchart of Algorithm 2 proposed by the present invention;

[0074] Figure 4 The state variable x of the system provided in the embodiment of the present invention 1 The estimated value of (t) and its true value;

[0075] Figure 5 The state variable x of the system provided in the embodiment of the present invention 2 The estimated value of (t) and its true value;

[0076] Figure 6 The state variable x of the system provided in the embodiment of the present invention 3 The estimated value of (t) and its true value;

[0077] Figure 7 The estimated value and true value of the fault signal g(t) provided by the embodiment of the present invention;

[0078] Figure 8 The estimation error of the state variable of the system provided by the embodiment of the present invention and the estimation error of the fault signal DETAILED DESCRIPTION

[0079] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0080] This embodiment takes the longitudinal dynamics model of a certain type of aircraft system as an example and uses the aircraft system fault detection method based on unknown input observer provided by the present invention.

[0081] The aircraft system fault detection method based on unknown input observer includes the following steps:

[0082] Step 1: In this embodiment, a longitudinal dynamics model of a certain type of aircraft system is considered, and its state space model is as follows:

[0083]

[0084] The above equation can be expressed as the state space equation described in equation (1), where

[0085]

[0086] Step 2: Disturb the external environment Decompose into and in represents the decoupled disturbance signal, that is, And the fault distribution matrix D 1 Satisfy column full rank. The details are as follows:

[0087]

[0088] in represents the decoupled disturbance signal, that is, And the matrix D 1 Satisfies column full rank.

[0089] Step 3: Combine the system matrix in step 1 and verify that the following matrix conditions hold:

[0090] (1)

[0091] (2) Matrix Satisfy column full rank;

[0092] (3) This holds for all complex numbers s with nonnegative real part, and s ≠ 0.

[0093] Step 4: Reference the auxiliary variables shown in equation (4): f(t) = g(t) + Ey(t).

[0094] Step 5: Based on the measured output signal of the system, design the adaptive unknown input observer shown in equation (4) to achieve joint estimation of the state variables and fault signals of the system.

[0095] Step 6: Obtain the estimation errors of the system's state variables and auxiliary variables from equation (6).

[0096] Step 7: Set the positive number β = 0.1, β 2 =0.1,β 3 =1 and β 4 = 0.2, by solving the linear matrix inequality shown in equation (9), we get the matrices Q, R, M z , W, M f The value of .

[0097] Step 8: Select G 0 = 0, and the gain matrix K of the designed adaptive unknown input observer is obtained through Algorithm 1. z , E, L f , L z , N, P values.

[0098] Step 9: Obtain the estimated value of the system state variable through Algorithm 2 and the estimated value of the fault signal

[0099] Step 10: Verify the effectiveness of the proposed fault detection scheme through the MATLAB simulation platform. In the simulation, the initial value of this embodiment is set to x(0) = [x 1 (0) x 2 (0) x 3 (0)] T =[1 2 0] T , The total simulation time is 80 seconds, and the following is obtained: Figure 4-8 The simulation result curve is shown.

[0100] The designed adaptive observer is applied to this embodiment. It can be seen from the simulation result diagram that even in the presence of external disturbances, the designed adaptive unknown input observer can still realize the joint estimation of the state variables and fault signals of the nonlinear aircraft system and obtain satisfactory estimation performance, thereby achieving the purpose of fault detection.

[0101] In this embodiment, it can be seen that when the design conditions of the adaptive unknown input observer are met, even in the presence of external disturbances, the joint estimation of the state variables and fault signals of the system can still be achieved, and satisfactory estimation performance can be obtained.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An aircraft system fault detection method based on an unknown input observer, characterized in that: The following steps are involved: S1: establishing a nonlinear state space model for an aircraft system, wherein the model is a nonlinear continuous time system with external disturbances, and mathematically representing a fault signal based on the state space model; S2: Decompose the external disturbance signal into two parts: decoupling and non-decoupling; S3: For the relevant system matrix, verify the conditions that the matrix rank needs to meet; S4: To estimate the fault signal in the aircraft system, the relationship between the fault signal and the measured output signal of the system is constructed by referencing auxiliary variables; Based on the fault signal g(t) and the measured output signal y(t) of the system, the following auxiliary variables are referenced: f(t)=g(t)+Ey(t) (2) The matrix E is the learning matrix to be designed, and its detailed design conditions will be given later; From formula (2), we can get S5: Based on the system measurement output signal, the expression of the adaptive unknown input observer is given to realize the joint estimation of the system state variables and fault signals; Based on the auxiliary variables in equation (2) and the measured output signal of the system, an adaptive unknown input observer as shown in equation (4) is designed to achieve joint estimation of the system state variable x(t) and fault signal g(t): in, Indicates the dimension is n x The state variables of the observer; Represents the estimated value of f(t), and its dimension is n f ; Matrix N, P, G, L, L f is the gain matrix of the observer to be designed, and the detailed design conditions will be given later; From the adaptive unknown input observer given in equation (4), we can obtain the estimated values ​​of the system state variable x(t) and fault signal g(t): in and They represent the estimated values ​​of the system state variable x(t) and fault signal g(t), respectively; S6: Define the estimated error variable, and combine the system state space model and the designed adaptive unknown input observer to obtain the dynamic equation of the estimated error system; S7: Combining Lyapunov stability theory and matrix inequality techniques, the detailed design conditions of the gain matrix of the unknown input observer are given in the form of linear matrix inequalities; S8: Algorithm 1 is given to elaborate the process of solving the gain matrix of the designed unknown input observer; Algorithm 1: ①Matrix G = D1((CD1) T (CD1) -1 (CD1) T +G0(I-CD1((CD1) T (CD1) -1 (CD1) T ), where matrix G0 is selected by the designer, and the matrix is ​​calculated ② By solving the linear matrix inequality in equation (9), we can obtain the symmetric positive definite matrices Q, R, and M z , W, and M f The value of ③ The following gain matrix is ​​obtained after calculation: S9: Algorithm 2 is given for simultaneously obtaining real-time estimation values ​​of system state variables and fault signals; S10: Verify the effectiveness of the proposed fault detection scheme for the aircraft system through the simulation platform, and adjust, improve and optimize the scheme based on the simulation results.

2. The aircraft system fault detection method based on unknown input observer according to claim 1, characterized in that: The algorithm 2 is specifically as follows: Algorithm 2: ① Combine the system matrix in (2) and set the value of G0, through G=D1((CD1) T (CD1)) -1 (CD1) T +G0(I-CD1((CD1) T (CD1)) -1 (CD1) T ) Get the value of matrix G; ② By Calculate the matrix The value of ③ Combine the system matrix and matrix in formula (2) Set the values ​​of positive numbers β1, β2, β3 and β4, and solve the linear matrix inequality shown in equation (9) to obtain the positive definite matrices Q, R, and M z , W, and M f The value of ④ The observer gain matrix N, P, L is calculated by formula (10). L f , the value of E; ⑤ Run the adaptive unknown input observer in equation (4) to obtain the variables z(t) and Real-time value of ⑥From the following formula Obtain estimates of the system state variables x(t) and fault signal g(t) and 3. The aircraft system fault detection method based on unknown input observer according to claim 1 or 2, characterized in that: The specific operations of step 1 are as follows: A nonlinear state space model for the aircraft system is established, wherein the model is a nonlinear continuous time system with external disturbances, and a fault signal is mathematically characterized based on the state space model; the nonlinear state space model is as follows: in, Respectively represent the dimension n x , n u , n x , n f , and n y The state variables, control input signals, nonlinear vector functions, fault signals, partially decoupled external bounded disturbances and measured output signals of the nonlinear aircraft system; t represents time, and the symbol "∈" represents the relationship. and Respectively represent the dimension n x , n u , n f , and n y The first-order derivative of the fault signal g(t) with respect to time t is bounded, but there is no requirement for its second-order derivative with respect to time t; nonlinear vector function Satisfies the Lipschitz condition, that is, The symbol "||||" represents the norm of a matrix or vector. is the Lipschitz constant; matrices A, B, F, D, and C represent system matrices with appropriate dimensions.

4. The aircraft system fault detection method based on unknown input observer according to claim 1 or 2, characterized in that: The specific operations of step 2 are as follows: Disturb the outside world Decompose into and Two parts, including represents the decoupled part, that is, And the matrix D1 satisfies full column rank.

5. The aircraft system fault detection method based on unknown input observer according to claim 3, characterized in that: The specific operations of step 2 are as follows: Disturb the outside world Decompose into and Two parts, including represents the decoupled part, that is, And the matrix D1 satisfies full column rank.

6. The aircraft system fault detection method based on unknown input observer according to claim 1, 2 or 5, characterized in that: The specific operations of step 3 are as follows: For the system matrix, verify that the following matrix conditions hold: (1) The symbol "rank(CD1)" represents the rank of the matrix CD1; (2) Matrix Satisfy column full rank; (3) For all complex numbers s with nonnegative real part, and s ≠ 0, the sign Representation Matrix The rank and Indicates the dimension is n x The identity matrix of .

7. The aircraft system fault detection method based on unknown input observer according to claim 1, 2 or 5, characterized in that: The specific operations of step 6 are as follows: Define the estimated error variables for the state variables and auxiliary variables of the system as follows: in and Respectively represent the estimated error variables for the system state variables and the auxiliary variables; Based on the system state space model in equation (1) and the adaptive unknown input observer in equation (4), the dynamic equation of the estimation error system is obtained as follows: in The gain matrix of the observer is designed so that the following matrix conditions hold: Then, we get the estimated error system as follows:

8. The aircraft system fault detection method based on unknown input observer according to claim 1, 2 or 5, characterized in that: The specific operations of step 7 are as follows: Combining Lyapunov stability theory and matrix inequality technology, the detailed design conditions of the gain matrix of the following observer are given in the form of linear matrix inequality; For given positive numbers β1, β2, β3, and β4, if there exist symmetric positive definite matrices Q and R, the matrix M z , W, and M f , so that the following linear matrix inequality holds: in The symbol "*" represents the symmetric term in a symmetric matrix, He(WCF)=WCF+(WCF) T , the superscript "T" represents the transpose of the matrix, and the symbol "I" represents the identity matrix with appropriate dimensions; then it can be inferred that the adaptive unknown input observer designed in equation (4) can ensure that all variables in the estimation error system shown in equation (8) are bounded.

9. The aircraft system fault detection method based on unknown input observer according to claim 3, characterized in that: The specific operations of step 7 are as follows: Combining Lyapunov stability theory and matrix inequality technology, the detailed design conditions of the gain matrix of the following observer are given in the form of linear matrix inequality; For given positive numbers β1, β2, β3, and β4, if there exist symmetric positive definite matrices Q and R, the matrix M z , W, and M f , so that the following linear matrix inequality holds: in The symbol "*" represents the symmetric term in a symmetric matrix, He(WCF)=WCF+(WCF) T , the superscript "T" represents the transpose of the matrix, and the symbol "I" represents the identity matrix with appropriate dimensions; then it can be inferred that the adaptive unknown input observer designed in equation (4) can ensure that all variables in the estimation error system shown in equation (8) are bounded.

10. The aircraft system fault detection method based on unknown input observer according to claim 4, characterized in that: The specific operations of step 7 are as follows: Combining Lyapunov stability theory and matrix inequality technology, the detailed design conditions of the gain matrix of the following observer are given in the form of linear matrix inequality; For given positive numbers β1, β2, β3, and β4, if there exist symmetric positive definite matrices Q and R, the matrix M z , W, and M f , so that the following linear matrix inequality holds: in The symbol "*" represents the symmetric term in a symmetric matrix, He(WCF)=WCF+(WCF) T , the superscript "T" represents the transpose of the matrix, and the symbol "I" represents the identity matrix with appropriate dimensions; then it can be inferred that the adaptive unknown input observer designed in equation (4) can ensure that all variables in the estimation error system shown in equation (8) are bounded.

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