Method for detecting faults in an aircraft system based on an unknown input observer

Abstract

The present application 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. The present application can realize joint estimation of state variables and fault signals of a nonlinear aircraft system, and effectively reduce the influence of external disturbance on estimation performance. The present application can make up for the shortcomings of existing fault detection methods based on residual signals, not only can provide fault occurrence time, but also can provide an estimated value of fault amplitude, which is convenient for further processing of faults in the later stage, and has more extensive and far-reaching theoretical significance and practical application value. The present application can provide estimated values of state variables and fault signals of the system at the same time, not only can detect the existence of faults in time, but also can lay a certain foundation for real-time monitoring of dynamic behavior of the system and completion of specific control tasks.

Description

Technical Field

[0001] This invention relates to the field of aircraft system fault detection technology, and in particular to an aircraft system fault detection method based on an unknown input observer. Background Technology

[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 day by day. However, aircraft face a variety of complex external environments during flight, and many adverse factors can affect the performance and reliability of aircraft to varying degrees, causing malfunctions and even catastrophic consequences and huge economic losses. Therefore, the threat of malfunctions to aircraft flight safety cannot be ignored. On the other hand, with the ever-increasing demands 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 a timely manner, either offline or online. This includes fault detection, isolation, estimation, and prediction; that is, determining whether a fault has occurred, locating the fault's location, identifying the type of fault, and determining the fault's amplitude and timing. Among numerous fault diagnosis methods, observer-based fault estimation not only directly provides an estimate of the fault's amplitude but also has advantages such as easy fault location and determination of the fault's occurrence time. Because unknown input observers are highly robust to external disturbances and system uncertainties, they have attracted considerable attention.

[0004] Currently, extensive research has been conducted on fault diagnosis for aircraft systems. However, existing solutions primarily rely on residual signals for fault detection, failing to obtain detailed fault information such as amplitude and variation trends. Further in-depth research is needed to address these issues. Furthermore, to better reflect real-world engineering applications, it is necessary to fully consider the nonlinear characteristics of aircraft systems and the impact of external disturbances on fault diagnosis results, effectively suppressing their negative effects to achieve satisfactory fault diagnosis performance. Summary of the Invention

[0005] The technical problem this invention aims to solve is to provide an aircraft system fault detection method based on an adaptive unknown input observer, addressing the shortcomings of existing fault diagnosis technologies. This method achieves joint estimation of state variables and fault signals of the nonlinear aircraft system, thereby realizing fault detection and effectively reducing the impact of external disturbances on fault diagnosis performance.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

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

[0008] S1: Establish a nonlinear state-space model for the aircraft system. The model is a nonlinear continuous-time system with external disturbances, and perform mathematical characterization of the fault signal based on the state-space model.

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

[0010] S3: For the relevant system matrix, verify the conditions that the matrix rank must satisfy;

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

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

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

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

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

[0016] S9: Algorithm 2 is given, which is used to obtain real-time estimates of system state variables and fault signals simultaneously;

[0017] S10: Verify the effectiveness of the proposed fault detection scheme for the aircraft system through a 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. This model is a nonlinear continuous-time system with external disturbances, and the fault signal is mathematically represented based on this state-space model. The nonlinear state-space model is shown below:

[0019]

[0020] in, They represent dimensions n respectively x n u n x n f , and n y The nonlinear aircraft system includes its state variables, control input signals, nonlinear vector functions, fault signals, partially decoupled external bounded disturbances, and measured output signals. t represents time, and the symbol "∈" indicates a membership relation. and They represent dimensions n respectively x n u n f , and n y The Euclidean space. The first derivative of the fault signal g(t) with respect to time t is bounded, but its second derivative with respect to time t is not required. Nonlinear vector function. The Lipschitz condition must be satisfied, that is, The symbol "||" represents the norm of a matrix or vector. It is the Lipschitz constant. Matrices A, B, F, D, and C represent system matrices with appropriate dimensions.

[0021] Step 2: Remove external disturbances Decomposed into and Two parts, of which This indicates the decoupled part, that is, And matrix D1 satisfies full column rank.

[0022] Step 3: For the system matrix, verify that the following matrix conditions hold:

[0023] (1) The symbol “rank(CD1)” represents the rank of matrix CD1;

[0024] (2) Matrix Satisfies the requirement of full rank;

[0025] (3) This holds true for all complex numbers s with non-negative real parts, and s ≠ 0, with the sign... Representation matrix rank and Indicates a dimension of n x The identity matrix.

[0026] Step 4: To estimate the fault signal in the aircraft system and fully utilize the system's measured output signal, the following auxiliary variables are used based on the fault signal g(t) and the system's measured output signal y(t):

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

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

[0029] From equation (2), we can obtain

[0030]

[0031] Step 5: Based on the auxiliary variables in equation (2) and the measured output signal of the system, design the following adaptive unknown input observer to achieve joint estimation of the system's state variable x(t) and fault signal g(t):

[0032] in, Indicates a dimension of n x The state variables of the observer. Let f(t) be an estimate of f(t) with dimension n. f Matrix N, P, G,L, L f The gain matrix of the observer to be designed is given below, and detailed design conditions will be provided later.

[0033] From the adaptive unknown input observer given in equation (4), the estimated values ​​of the system's state variable x(t) and fault signal g(t) can be obtained as follows:

[0034]

[0035] in and Let x(t) and g(t) represent the estimated values ​​of the system's state variable and fault signal, respectively.

[0036] Step 6: Define the estimation error variables for the system's state variables and auxiliary variables as shown below:

[0037]

[0038] in and These represent the estimation error variables for the system's 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 dynamic equation of the estimation error system is obtained as follows:

[0040]

[0041] in

[0042] Design the gain matrix of the observer such that the following matrix condition holds:

[0043]

[0044] Therefore, the estimation error system is obtained as shown below:

[0045]

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

[0047] For given positive numbers β1, β2, β3, and β4, if there exist symmetric positive definite matrices Q and R, and matrix M... z W and M f This makes the following linear matrix inequality hold:

[0048]

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

[0050] Step 8: The gain matrix of the adaptive unknown input observer designed in equation (4) can be obtained by using the following algorithm 1.

[0051] Algorithm 1:

[0052] ① Matrix G = D1((CD1) T (CD1) -1 (CD1) T +G0(I-CD1((CD1) T (CD1) -1 (CD1) T ), where matrix G0 is chosen by the designer, and the matrix is ​​calculated.

[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 was obtained after calculation:

[0055]

[0056] Step 9: For the system in equation (1), the estimated values ​​of the system's state variable x(t) and fault signal g(t) are obtained by the following algorithm 2.

[0057] Algorithm 2:

[0058] ① Combining the system matrix in equation (2) and setting the value of G0, through...

[0059] G = D1((CD1) T (CD1) -1 (CD1) T +G0(I-CD1((CD1) T (CD1) -1 (CD1) T )

[0060] Obtain the values ​​of matrix G;

[0061] ②by Calculate the matrix The value of ;

[0062] ③ Combining the system matrix and matrix in equation (2) By setting the values ​​of positive numbers β1, β2, β3, and β4, and solving the linear matrix inequality shown in equation (9), we obtain the positive definite matrices Q, R, and M. z W and M f The value of ;

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

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

[0065] ⑥ From the following formula

[0066]

[0067] Obtain estimates of the system's state variable 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 a 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 as follows:

[0070] This invention provides a fault detection method for aircraft systems based on an adaptive unknown input observer, which can achieve joint estimation of state variables and fault signals of nonlinear aircraft systems and effectively reduce the impact of external disturbances on estimation performance. (1) It can make up for the shortcomings of existing fault detection methods based on residual signals. It can provide not only the fault occurrence time, but also the estimated value of the fault amplitude, which is convenient for further processing of the fault in the later stage. It has a wider and more profound theoretical significance and practical application value. (2) It can provide the estimated values ​​of the system's state variables and fault signals at the same time. It 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 completion of specific control tasks. (3) Unlike the existing joint estimation schemes for state variables and fault signals, the adaptive unknown input observer scheme proposed in this invention does not require the second derivative of the fault signal with respect to time to be zero or sufficiently small, which relaxes the restrictions of the existing schemes to a certain extent. (4) This invention adopts an unknown input observer scheme, which increases the number of gain matrices of the observer compared with the traditional observer scheme, thereby increasing the design freedom. (5) Based on the system's output measurement value, auxiliary variables are introduced 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, an output error correction term is introduced. The performance of fault signal estimation can be improved by making full use of the system's output measurements and increasing design freedom. Attached Figure Description

[0071] Figure 1 This is a flowchart of the present invention;

[0072] Figure 2 This is a schematic diagram of the adaptive unknown input observer designed in this invention;

[0073] Figure 3 This is a flowchart of Algorithm 2 proposed in this invention;

[0074] Figure 4 The estimated value and its true value of the system state variable x1(t) provided in the embodiments of the present invention;

[0075] Figure 5 The estimated value and its true value of the system's state variable x2(t) are provided for embodiments of the present invention.

[0076] Figure 6 The estimated value and its true value of the system state variable x3(t) provided for embodiments of the present invention;

[0077] Figure 7 The estimated value of the fault signal g(t) and its true value are provided for embodiments of the present invention;

[0078] Figure 8 The estimation error of the system's state variables provided in the embodiments of the present invention And the estimation error of fault signals Detailed Implementation

[0079] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

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

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

[0082] Step 1: In this embodiment, we consider the longitudinal dynamics model of a certain type of aircraft system, whose state-space model is shown below:

[0083]

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

[0085]

[0086] Step 2: Remove external disturbances Decomposed into and in This represents a decoupled disturbance signal, i.e. Furthermore, the fault distribution matrix D1 satisfies full column rank. Specifically, as shown below:

[0087]

[0088] in This represents a decoupled disturbance signal, i.e. And matrix D1 satisfies full column rank.

[0089] Step 3: Combining the system matrix from Step 1, verify that the following matrix conditions hold:

[0090] (1)

[0091] (2) Matrix Satisfies the requirement of full rank;

[0092] (3) This holds for all complex numbers s with non-negative real parts, and s≠0.

[0093] Step 4: Refer to the auxiliary variable 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 system's state variables and fault signals.

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

[0096] Step 7: Set positive numbers β = 0.1, β2 = 0.1, β3 = 1 and β4 = 0.2. By solving the linear matrix inequality shown in equation (9), obtain matrices Q, R, and M. z W, M f The value of .

[0097] Step 8: Select G0 = 0, and obtain the gain matrix K of the designed adaptive unknown input observer using Algorithm 1. z E, L f L z The values ​​of N and P.

[0098] Step 9: Obtain estimates of the system's state variables using Algorithm 2. and the estimated value of the fault signal

[0099] Step 10: Verify the effectiveness of the proposed fault detection scheme using the MATLAB simulation platform. In the simulation, the initial value of this embodiment is set to x(0) = [x1(0) x2(0) x3(0)]. T =[1 2 0] T , The total simulation time was 80 seconds, and the results were as follows: Figure 4-8 The simulation result curve is shown.

[0100] Applying the designed adaptive observer to this embodiment, the simulation results show that even with external disturbances, the designed adaptive unknown input observer can still achieve 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 system's state variables and fault signals 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, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions 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. A method for aircraft system fault detection based on an unknown input observer, characterized in that, Includes the following steps: S1: Establish a nonlinear state-space model for the aircraft system. The model is a nonlinear continuous-time system with external disturbances, and perform mathematical characterization of the fault signal based on the state-space model. The nonlinear state-space model is shown below: in, They represent dimensions n respectively x n u n x n f , and n y The nonlinear aircraft system includes state variables, control input signals, nonlinear vector functions, fault signals, partially decoupled external bounded disturbances, and the system's measured output signals; t represents time, and the symbol "∈" indicates a membership relation. and They represent dimensions n respectively x n u n f , and n y The Euclidean space; the first derivative of the fault signal g(t) with respect to time t is bounded, but its second derivative with respect to time t is not required; nonlinear vector function The Lipschitz condition must be satisfied, 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; S2: Decompose the external disturbance signal into two parts: decouplingable and non-decoupling; S3: For the relevant system matrix, verify the conditions that the matrix rank must satisfy; S4: To estimate fault signals in aircraft systems, the relationship between fault signals and the measured output signals of the system is constructed by referencing auxiliary variables; Based on the fault signal g(t) and the system's measured output signal y(t), the following auxiliary variables are referenced: f(t)=g(t)+Ey(t) (2) Matrix E is the learning matrix to be designed, and its detailed design conditions will be given later. From equation (2), we can obtain S5: Based on the system measurement output signal, give the expression of the adaptive unknown input observer to realize the joint estimation of system state variables and fault signals; Based on the auxiliary variable 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's state variable x(t) and fault signal g(t): in, Indicates a dimension of n x The state variables of the observer; Let f(t) be an estimate of f(t) with dimension n. f ; Matrix N, P, G,L, L f The gain matrix of the observer to be designed will be given in detail later. From the adaptive unknown input observer given in equation (4), the estimated values ​​of the system's state variable x(t) and fault signal g(t) can be obtained as follows: in and Let x(t) and g(t) represent the estimated values ​​of the system's state variable and the fault signal, respectively. S6: Define the estimation error variable, and obtain the dynamic equation of the estimation error system by combining the system state-space model and the designed adaptive unknown input observer; the specific operation is as follows: Define the estimation error variables for the system's state variables and auxiliary variables as follows: in and These represent the estimation error variables for the system's state variables and the auxiliary variables, respectively. 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 Design the gain matrix of the observer such that the following matrix condition holds: Therefore, the estimation error system is obtained as shown below: S7: Combining Lyapunov stability theory and matrix inequality techniques, the detailed design conditions for the gain matrix of the unknown input observer are given in the form of linear matrix inequalities; the specific operation is as follows: Combining Lyapunov stability theory and matrix inequality techniques, the detailed design conditions for the gain matrix of the following observer are given in the form of linear matrix inequalities. For given positive numbers β1, β2, β3, and β4, if there exist symmetric positive definite matrices Q and R, and matrix M... z W and M f This makes the following linear matrix inequality hold: in The symbol "*" represents a symmetric term in a symmetric matrix, and He(WCF) = WCF + (WCF). T The superscript "T" indicates the transpose of the matrix, and the symbol "I" indicates the identity matrix with appropriate dimensions; then it can be deduced that the adaptive unknown input observer designed in equation (4) can guarantee that all variables in the estimation error system shown in equation (8) are bounded; S8: Algorithm 1 is given, which details the process of solving the gain matrix of the designed unknown input observer; Algorithm 1: ① Matrix G = D1((CD1) T (CD1) -1 (CD1) T +G0(I-CD1((CD1) T (CD1) -1 (CD1) T ), where matrix G0 is chosen 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 possible values ​​of ; ③ The following gain matrix was obtained after calculation: S9: Algorithm 2 is given, which is used to obtain real-time estimates of system state variables and fault signals simultaneously; S10: Verify the effectiveness of the proposed fault detection scheme for the aircraft system through a simulation platform, and adjust, improve and optimize the scheme based on the simulation results.

2. The aircraft system fault detection method based on an unknown input observer as described in claim 1, characterized in that, The specific details of Algorithm 2 are as follows: Algorithm 2: ① Combining the system matrix in equation (2) and setting the value of G0, through... G=D1((CD1) T (CD1)) -1 (CD1) T +G0(I-CD1((CD1) T (CD1)) -1 (CD1) T ) Obtain the values ​​of matrix G; ②by Calculate the matrix The possible values ​​of ; ③ Combining the system matrix and matrix in equation (2) By setting the values ​​of positive numbers β1, β2, β3, and β4, and solving the linear matrix inequality shown in equation (9), we obtain the positive definite matrices Q, R, and M. z W and M f The possible values ​​of ; ④ The gain matrix N, P, L of the observer is calculated from equation (10). L f The value of E; ⑤ Run the adaptive unknown input observer in equation (4) to obtain the variable z(t) and Real-time value; ⑥ From the following formula Obtain estimates of the system's state variable x(t) and fault signal g(t). and 3. The aircraft system fault detection method based on an unknown input observer as described in claim 1 or 2, characterized in that, The specific operation of step 2 is as follows: External disturbances Decomposed into and Two parts, of which This indicates the decoupled part, that is, And matrix D1 satisfies full column rank.

4. The aircraft system fault detection method based on an unknown input observer as described in claim 1 or 2, characterized in that, The specific operation of step 3 is as follows: For the system matrix, verify that the following matrix conditions hold: (1) The symbol "rank(CD1)" represents the rank of matrix CD1; (2) Matrix Satisfies the requirement of full rank; (3) This holds true for all complex numbers s with non-negative real parts, and s ≠ 0, with the sign... Representation matrix rank and Indicates a dimension of n x The identity matrix.

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