Observer-Based Decentralized Fault Detection Method for Aircraft Systems

Abstract

The decentralized fault detection method for aircraft systems based on an observer belongs to the field of fault detection technology. Applying the CPS architecture in the field of aircraft system fault detection, fully considering the influence between subsystems, provides some valuable new ideas and examples for promoting the progress of aircraft system fault handling technology; due to the hierarchical, large-scale and complex nature of aircraft systems, the internal connections of the system are intricate, so it is difficult for a single-system model to fully describe its characteristics. In contrast, the interconnected large-scale system model adopted by the present invention is more suitable for describing aircraft systems. In addition, in order to describe more performance characteristics of aircraft systems and make the system model more general, the present invention adopts a generalized system model.

Description

Technical Field

[0001] The present invention relates to the technical field of fault detection, and particularly to a decentralized fault detection method for an aircraft system based on an observer under the architecture of a cyber-physical system. Background Art

[0002] With the progress of science and technology, aviation technology has developed vigorously, and the technological content, intelligence, and integration degree of aircraft airborne equipment are getting higher and higher. Compared with traditional aircraft, the new generation of aircraft systems adopt a large number of innovative technologies to improve the flight performance, intelligence level, safety performance, and combat effectiveness of the whole aircraft. However, as a typical complex system, an aircraft is composed of numerous precision components with a complex mechanical structure, resulting in the mutual coupling of various factors causing internal failures, which always affect the safe operation of the aircraft system. In addition, since an aircraft will face a complex and changeable external environment during flight, various adverse factors will affect the reliability and stability of the flight system to varying degrees. Once a failure occurs, it often causes huge losses and even catastrophic accidents such as plane crashes. For an aircraft system, high reliability is an important prerequisite for ensuring the safety and combat effectiveness of the aircraft. Therefore, to ensure that the aircraft can complete each mission safely and efficiently and meet the growing demand for high reliability, in addition to routine maintenance, it is also necessary to design and study effective fault detection and diagnosis algorithms.

[0003] Cyber-Physical Systems (CPS) deeply integrates computing, communication, and control capabilities on the basis of environmental perception, effectively improving the intelligence level of physical infrastructure. With the rapid development of computing and communication technologies, the application prospects of CPS are becoming increasingly wide. Microscopically, the perception, control, and signal transmission of each system inside an aircraft can constitute the CPS on board this aircraft. On the other hand, CPS proposes a series of new ideas and methods to solve problems for the needs of the informatization and networking of the new generation of physical devices. Applying the CPS architecture in the field of aircraft system fault detection is expected to promote the progress of aircraft system fault handling technology, as Figure 1 shown.

[0004] In recent years, scholars at home and abroad have paid increasing attention to the development of aircraft system health assessment and fault diagnosis methods, and related research is booming. However, the existing research results mainly model the aircraft system as a single system and then design a fault detection scheme based on the model, without fully suppressing the influence of external environmental disturbances on the fault detection performance. Due to the hierarchical, large-scale, and complex nature of the aircraft system, the internal connections of the system are intricate, and it is difficult for a single-system model to fully describe the characteristics of the aircraft system. In contrast, the interconnected large-scale system model is more suitable for describing the aircraft system and better meets the actual application requirements. In addition, there are extensive and complex cross-linking relationships among various aircraft systems and between components within the system. After a single component fails, it often leads to abnormal functions of downstream components / systems, causing fault propagation and triggering a chain reaction, thereby increasing the difficulty and complexity of fault detection. Moreover, during the flight of an aircraft, external environmental disturbances are widespread, and their impact on the fault detection performance cannot be underestimated. In summary, in order to conform to the trend of the development of new-generation aircraft, the fault diagnosis technology of aircraft systems also needs to be adjusted and updated accordingly. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a decentralized fault detection method for an aircraft system based on an observer in view of the deficiencies of the above-mentioned existing technologies. By comparing and analyzing the output results of a dynamic reduced-order observer with the actually measurable output data of the aircraft system, the corresponding residual signal is obtained, and an adaptive detection threshold with specified performance is designed to complete the fault detection of the aircraft system.

[0006] To solve the above technical problem, the technical solution adopted by the present invention is: a decentralized fault detection method for an aircraft system based on an observer.

[0007] The decentralized fault detection method for an aircraft system based on an observer includes:

[0008] S1: Based on the interconnected large-scale system modeling method, establish a dynamic model for the aircraft system, where the dynamic model is an interconnected large-scale system composed of N interconnected generalized subsystems under the influence of external disturbances and measurement noises;

[0009] S2: By adopting graph theory, decompose the interconnected large-scale system into N interconnected subsystems;

[0010] S3: Mathematically characterize sensor faults based on the dynamic model;

[0011] S4: Decouple the coupling terms in the interconnected subsystems by multiplying by a nullifying matrix;

[0012] S5: Verify the observability of the relevant matrices of each subsystem to provide a basic guarantee for the subsequent design of the observer;

[0013] S6: Integrate the CPS architecture to achieve the fault detection objectives of each subsystem, reduce the complexity of the design scheme, and ensure good fault detection performance. Design a dynamic reduced-order observer based on the measurable output of the system;

[0014] S7: Describe the numerical relationships between the gain matrices of the designed dynamic reduced-order observer;

[0015] S8: To achieve the purpose of fault detection, define a residual signal based on the output result of the dynamic reduced-order observer and the actual measurable output data of the system;

[0016] S9: Based on linear matrix inequality technology, give the detailed design conditions for the gain matrix of the dynamic reduced-order observer;

[0017] S10: Give the specific expression for solving the gain matrix of the dynamic reduced-order observer and design an adaptive detection threshold with specified performance;

[0018] S11: Based on the above steps, give the fault detection algorithm. Specifically, compare the residual signal with the designed adaptive detection threshold: if the residual signal is greater than or equal to the adaptive detection threshold, the sensor of the corresponding subsystem fails; if the residual signal is less than the adaptive detection threshold, the sensor of the corresponding subsystem is fault-free;

[0019] S12: Verify the effectiveness of the designed fault detection scheme through the Matlab simulation platform and optimize and improve the scheme based on the simulation results.

[0020] An observer-based decentralized fault detection method for aircraft systems, the specific steps are as follows:

[0021] Step 1: Since the aircraft system is inherently hierarchical, large-scale, and complex, and the internal cross-linking relationships of the system are intricate, it is difficult for a single-system model to fully describe the characteristics of the aircraft system. In contrast, the interconnected large-scale system model is more suitable for describing the aircraft system. In addition, in order to describe more performance characteristics of the aircraft system and be more general, a generalized system model is adopted in the present invention.

[0022] Based on the interconnected large-scale system modeling technology, establish a dynamic model for the aircraft system, and the dynamic model is an interconnected large-scale system composed of N interconnected generalized subsystems under the influence of external disturbances and measurement noises. The interconnected large-scale system model is as follows;

[0023]

[0024] where

[0025] x(t) = col(x1(t),...,x N (t)), D = blkdiag{D1,...,DN}

[0026] u(t) = col(u1(t),..., u N (t)), E = blkdiag{E1,..., E N}

[0027] d(t) = col(d1(t),..., d N (t)), B = blkdiag{B1,..., B N}

[0028] y(t) = col(y1(t),..., y N (t)), W = blkdiag{W1,..., W N}

[0029] v(t) = col(v1(t),..., v N (t)), C = blkdiag{C1,..., C N}

[0030]

[0031] where i ∈ {1,..., N}, respectively represent the state variables, control inputs, and measurement outputs of the i-th subsystem; the symbol "∈" represents the membership relation, and respectively represent the n-dimensional Euclidean space and the set of m×n-dimensional real matrices; respectively represent the bounded external disturbances and measurement noises in the i-th subsystem, and respectively have known upper bounds and The constant matrices A ij , B i , C i , D i , W i , E i represent the known system matrices of the i-th subsystem and have appropriate dimensions. col(σ1(t),..., σ n (t)) represents the column vector The superscript "T" represents the transpose of a matrix or vector, blkdiag{...} represents a block diagonal matrix, represents the first derivative of x(t) with respect to time.

[0032] Step 2: For an interconnected large-scale system, a centralized fault detection scheme often leads to an overloaded system due to frequent information interaction, thus correspondingly increasing the cost of system fault detection. Based on the above situation, in order to improve the economy and reliability of the fault detection system, the present invention adopts a decentralized fault detection method.

[0033] To this end, first, by combining graph theory, the above-mentioned interconnected large-scale system (1) is decomposed into N interconnected subsystems, and the dynamics of the i-th subsystem are as follows:

[0034]

[0035] where Π i = [A ij ], (A ij ≠ 0, i ∈ {1,..., N}, j ∈ {1,..., N}), and the influence of the state variable x j (t) of the adjacent subsystem on x i (t) is regarded as an unknown input term in the i-th subsystem Assume that the matrix Π i is a column full-rank matrix.

[0036] Step 3: Based on the above system model, mathematically characterize the sensor fault:

[0037] For the i-th subsystem (2), considering the influence of the sensor fault, the corresponding system dynamics are as follows:

[0038]

[0039] where represents the sensor fault signal in the i-th subsystem.

[0040] Step 4: Since the internal modules of the interconnected system are interconnected with each other, the influence of faults is likely to spread after a fault occurs in each module of the system. That is, there are extensive and complex cross-linking relationships among the various systems of the aircraft and among the components within the system. After a single component fails, it often leads to abnormal functions of downstream components / systems, causing fault propagation and triggering a chain reaction, increasing the difficulty and complexity of fault detection. In the present invention, the coupling terms in the interconnected subsystems are decoupled by multiplying the annihilating matrix.

[0041] Let represent the left annihilating matrix of the matrix Π i , that is Multiply both ends of the first equation in equation (3) by the matrix to obtain the following expression:

[0042]

[0043] where \(i\in\{1,\ldots,N\}\) and

[0044]

[0045]

[0046] Step 5: Verify that the matrix pair is regular, impulse-free, the initial conditions are consistent, and the matrix pair is observable.

[0047] Step 6: Combine the CPS architecture to achieve the fault detection objectives of each subsystem. To estimate the state variables of the \(i\)-th subsystem while reducing the computational complexity, design a dynamic reduced-order observer as follows:

[0048]

[0049] where \(i\in\{1,\ldots,N\}\), and represent the state variables of the designed dynamic reduced-order observer, represent the first-order derivatives of \(z\) i (t) and \(\varphi\) i (t) with respect to time, respectively; is the estimated value of the system state variable , is the output of the designed observer. The following matrices are the observer gain matrices to be designed:

[0050]

[0051]

[0052]

[0053] Step 7: Select an arbitrary matrix such that the following conditions hold:

[0054]

[0055] where represents the identity matrix of dimension \(n\) i , and the symbol represents the zero matrix of dimension \(m\times n\).

[0056] Let the matrix be row full rank and satisfy the following conditions:

[0057]

[0058] That is and are equivalent matrices, where rank[] represents the rank of the matrix.

[0059] Step 8: For the purpose of completing fault detection, for the i-th subsystem, based on the output result of the dynamic reduced-order observer and the actually measurable output data of the system, define the residual signal τ i (t) as follows:

[0060]

[0061] Step 9: Based on the linear matrix inequality technique, for the designed dynamic reduced-order observer (5), give the following detailed design conditions for the gain matrix:

[0062] For a given positive number b i , a 1i , a 2i (i ∈ {1,..., N}), if there exist positive definite matrices and such that the following linear matrix inequality holds:

[0063]

[0064] where * represents the symmetric terms in the symmetric matrix, and

[0065]

[0066] where the symbol represents the pseudo-inverse of the matrix, χ 3i represents an arbitrary matrix; χ 1i represents an unknown matrix, and the detailed solution method will be given later; then the designed dynamic reduced-order observer (5) can ensure that the following two conditions hold:

[0067] (a) When there is no sensor fault in the i-th subsystem, all signals in the estimation error system are uniformly ultimately bounded;

[0068] (b) When there is no sensor fault in the i-th subsystem, the corresponding residual signal satisfies the following expression:

[0069]

[0070] where ||θ i (t)|| ∞ represents the infinity norm of θ i (t), and

[0071]

[0072]

[0073]

[0074]

[0075] Step 10: The gain matrix of the designed dynamic dimensionality reduction observer (5) can be obtained through Formula (7) and the following expressions:

[0076]

[0077] Among them, similar to the processing method of the existing results, we set the matrix χ 2i to the zero matrix; for the i-th subsystem, combined with L ∞ performance index, design the following adaptive detection threshold with specified performance:

[0078]

[0079] Among them, represents the maximum eigenvalue of the matrix ;

[0080] Step 11: Based on the above Steps 1-10, to achieve the purpose of fault detection, the following fault detection algorithm is given:

[0081] Fault Detection Algorithm 1

[0082] Input: Matrices C i and D i , i = 1,..., N;

[0083] Necessary condition: The linear matrix inequality presented in Formula (9) holds;

[0084] Output: A fault occurs in the i-th subsystem;

[0085] Step 1: Select the appropriate matrix according to Formula (7)

[0086] Step 2: Calculate the matrices G i and

[0087] Step 3: Calculate the matrices β 1i , β 2i , β 3i , β 4i , α 1i , α 2i and α 3i ;

[0088] Step 4: Calculate matrix Γ according to the linear matrix inequality (9) i ;

[0089] Step 5: Calculate all the gain matrices of the designed dynamic reduced-order observer (5) according to formula (11): N i , M i , F i , H i , Q i , K i , Φ i , S i and T i ;

[0090] Step 6: Start the loop

[0091] Step 7: Run the dynamic reduced-order observer (5), and calculate the residual value τ i (t) and the adaptive threshold

[0092] Step 8: If then

[0093] The sensor in the i-th subsystem has failed;

[0094] Return the value of i;

[0095] Step 9: End the loop

[0096] Specifically, in the above fault detection algorithm 1, mainly the residual signal of the i-th subsystem is compared with the designed adaptive detection threshold:

[0097] If the obtained residual signal is greater than or equal to the adaptive detection threshold, the sensor of the corresponding subsystem has failed;

[0098] If the obtained residual signal is less than the adaptive detection threshold, the sensor of the corresponding subsystem has no fault.

[0099] Step 12: Verify the effectiveness of the designed fault detection scheme through the Matlab software simulation platform, and optimize and adjust the design parameters in the scheme to ensure that the fault detection scheme has good performance.

[0100] A decentralized fault detection process for an aircraft system based on an observer is shown in detail in fault detection algorithm 1 and Figure 2 as shown.

[0101] The beneficial effects of adopting the above technical solutions are as follows: The present invention provides a decentralized fault detection method and process for an aircraft system based on an observer, which is used to improve the fault diagnosis ability of the aircraft system.

[0102] (1) By combining the advantages of a dynamic reduced-dimension dynamic observer, the present invention provides a fault diagnosis method with a lower design complexity for an aircraft system. Compared with the existing scheme based on a full-dimension state observer, the scheme designed by the present invention takes more fully into account the actual application requirements;

[0103] (2) Applying the CPS architecture in the field of aircraft system fault detection, fully considering the influence between subsystems, provides some valuable new ideas and examples for promoting the progress of aircraft system fault handling technology;

[0104] (3) Since the aircraft system inherently has hierarchy, scale, and complexity, and the internal connections of the system are intricate, it is difficult for a single-system model to fully describe its characteristics. In contrast, the interconnected large-scale system model adopted by the present invention is more suitable for describing the aircraft system. In addition, in order to describe more performance characteristics of the aircraft system and make the system model more general, the present invention adopts a generalized system model;

[0105] (4) For an interconnected large-scale system, a centralized fault detection method often causes the system to be overloaded due to frequent information interaction, thereby increasing the cost of system fault detection. In order to improve the economy and reliability of the fault detection system, the present invention adopts a decentralized fault detection method;

[0106] (5) There are extensive and complex cross-linking relationships between aircraft systems and between components within the system. After a single component fails, it often causes abnormal functions of downstream components / systems, resulting in fault propagation and triggering a chain reaction, increasing the difficulty and complexity of fault detection. In the present invention, by combining the method of null matrix, decoupling processing is performed on the coupling terms in the interconnected system, effectively isolating the influence of faults in the interconnected subsystems, and thereby improving the performance of the designed fault detection scheme;

[0107] (6) By combining the L ∞ performance index, the present invention designs an adaptive fault detection threshold with specified performance. Compared with a fixed-value threshold, this threshold has better robustness and less conservativeness to external disturbances, and thus can better suppress the influence of external disturbances and effectively improve the fault detection performance. Brief Description of the Drawings

[0108] In order to more clearly illustrate the technical solutions of the present invention, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0109] Figure 1It is a block diagram of aircraft system fault diagnosis based on the cyber-physical system framework;

[0110] Figure 2 It is the overall process of the aircraft system fault diagnosis solution proposed by the present invention;

[0111] Figure 3 It is the flow chart of the fault diagnosis algorithm proposed by the present invention;

[0112] Figure 4 It is the situation of fault detection of three subsystems in the first fault case provided by the embodiment of the present invention;

[0113] Figure 5 It is the situation of fault detection of three subsystems in the second fault case provided by the embodiment of the present invention. Detailed implementation manners

[0114] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0115] In this embodiment, a simplified system model of an IEEE-30 node system composed of six motors is considered, and a decentralized fault detection method and process for aircraft systems based on an observer in the present invention are used.

[0116] A decentralized fault detection method and process for aircraft systems based on an observer includes the following steps:

[0117] Step 1: For the system considered in this embodiment, construct an interconnected large system as shown in formula (1). This system has 12 state variables, and the corresponding system matrices are as follows:

[0118]

[0119]

[0120]

[0121]

[0122] D x = diag{0.045 0.064 0.080 0.093 0.103 0.111}

[0123] X d = diag{15 18 20 25 25 30}

[0124] X d -1 = diag{0.067 0.056 0.05 0.04 0.04 0.03}

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] In addition, since the designed fault detection scheme is not affected by the system control input, here we adopt a processing method similar to the existing results to set the input to zero, that is, B = 0, u(t) = 0. In addition, C = I 12 .

[0132] Step 2: Using graph theory, decompose the above large interconnected system into 3 interconnected subsystems as described in formula (2), where the matrices of the corresponding subsystems are shown as follows:

[0133]

[0134]

[0135]

[0136]

[0137] Assume that each subsystem has a local information processor for measuring the angle of the motor, and the considered system is affected by the following external disturbances and measurement noises:

[0138]

[0139]

[0140] d1(t) = 0.25cos(t), d2(t) = 0.22sin(t), d3(t) = 0.27sin(t)

[0141] Moreover, the measurement noise of the first subsystem is bounded white noise with an energy of 0.002 and a sampling time of 0.1, the measurement noise of the second subsystem is bounded white noise with an energy of 0.002 and a sampling time of 0.1, and the measurement noise of the third subsystem is bounded white noise with an energy of 0.0025 and a sampling time of 0.1. In this embodiment, the initial condition of the system is selected as x(0) = [0.1 0.1 0.05 0.05 0.1 0.1 0 0 0 0 0 0].

[0142] Step 3: The simulation time is 50 seconds. To verify the fault detection scheme, consider the following two sensor fault situations:

[0143] (1) Fault situation 1: A sensor fault occurs in subsystem 1 at 15 seconds, and the fault signal is η1(t) = 0.1t. A sensor fault occurs in subsystem 3 at 20 seconds, and the fault signal is η3(t) = 5.5cos(t);

[0144] (2) Fault situation 2: A sensor fault occurs in subsystem 2 at 15 seconds, and the fault signal is η2(t) = 0.15t. A sensor fault occurs in subsystem 3 at 20 seconds, and the fault signal is η3(t) = 3.5sin(t).

[0145] Step 4: Use the method of multiplying by the annihilating matrix to decouple the coupling terms in the interconnected system. In this embodiment, for the i-th subsystem (i = 1, 2, 3), multiply by the following left annihilating matrix:

[0146]

[0147] Furthermore, the system shown in formula (4) is obtained, where the corresponding system matrices are as follows:

[0148]

[0149] Step 5: Through numerical calculation verification, it can be obtained that the matrix pair is regular, impulse-free, and the initial condition x i (0) is consistent. The matrix pair is observable, where i ∈ {1, 2, 3}.

[0150] Step 6: To estimate the state variables of the i-th subsystem (i ∈ {1, 2, 3}) and at the same time reduce the computational complexity, design a dynamic reduced-order observer as shown in formula (5), where the gain matrices to be solved are respectively:

[0151]

[0152]

[0153]

[0154] Step 7: To make the equality condition in formula (6) hold, select the following matrix in this embodiment

[0155]

[0156] Step 8: To achieve the purpose of fault detection, for the i-th subsystem, based on the output result of the dynamic reduced-order observer and the actual output data of the system, define the following residual signal τ i (t):

[0157]

[0158] Step 9: Based on the observer gain matrix design conditions given in formula (9), use the LMI toolbox in Matlab to solve the gain matrix of the designed dynamic reduced-order observer (5), where the values of the relevant design parameters are: b i = 2.5, a 1i = 0.8, a 2i = 0.8, i ∈ {1, 2, 3}.

[0159] Step 10: In this embodiment, the gain matrix of the dynamic reduced-order observer (5) can be obtained through formulas (7) and (10) as follows:

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170] Based on formula (11), for the i-th subsystem, design the following adaptive detection threshold with specified performance:

[0171]

[0172] Step 11: Based on the above steps, select the initial conditions of the observer to be zero and run the fault detection algorithm 1. The corresponding simulation results are obtained on the Matlab simulation platform, as shown in Figure 4 and 5 shown.

[0173] For fault case 1: A sensor fault occurs in subsystem 1 at 15 seconds, and the fault signal is η1(t) = 0.1t. A sensor fault occurs in subsystem 3 at 20 seconds, and the fault signal is η3(t) = 5.5cos(t). Figure 4 The corresponding simulation results are given (the dashed line in the figure represents the adaptive detection threshold with specified performance, and the solid line represents the corresponding residual signal). It can be seen from the figure that when faults occur in subsystems 1 and 3, the corresponding residual signals quickly exceed the threshold, and thus it can be determined that there are sensor faults in the corresponding subsystems. In addition, since the residual signal corresponding to subsystem 2 never exceeds the threshold, it can be determined that subsystem 2 has no fault, that is, the fault effects in subsystems 1 and 3 do not cause a false alarm in subsystem 2. Thus, it can be obtained that the simulation results are consistent with the theoretical derivation, proving the effectiveness of the proposed fault detection scheme.

[0174] For fault case 2: A sensor fault occurs in subsystem 2 at 15 seconds, and the fault signal is η2(t) = 0.15t. A sensor fault occurs in subsystem 3 at 20 seconds, and the fault signal is η3(t) = 3.5sin(t). Figure 5 The corresponding simulation results are given (the dashed line in the figure represents the adaptive detection threshold with specified performance, and the solid line represents the corresponding residual signal). It can be seen from the figure that when faults occur in subsystems 2 and 3, the corresponding residual signals quickly exceed the threshold, and thus it can be determined that there are sensor faults in the corresponding subsystems. In addition, since the residual signal corresponding to subsystem 1 never exceeds the threshold, it can be determined that subsystem 1 has no fault, that is, the fault effects in subsystems 2 and 3 do not cause a false alarm in subsystem 1. Thus, it can be obtained that the simulation results are consistent with the theoretical derivation, further proving the effectiveness of the proposed fault detection scheme.

[0175] Step 11: Verify the effectiveness of the designed fault detection scheme through the Matlab software simulation platform and optimize and adjust the parameters in the scheme to ensure that the fault detection scheme has better performance. In this embodiment, the parameters such as b i , a 1i , a 2i , i ∈ {1, 2, 3} can be adjusted to obtain better detection performance.

[0176] In this embodiment, it can be seen that when the design conditions of the dimensionality reduction dynamic observer are satisfied, the faults in the interconnected subsystems can be quickly detected and satisfactory detection performance can be obtained by finally comparing the corresponding residual signals with the designed adaptive detection threshold. In addition, in order to improve the economy and reliability of the fault detection system, the present invention adopts a decentralized fault detection method, which is different from the existing centralized fault detection method. The centralized fault detection method often increases the system load due to frequent information interaction.

[0177] 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 of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and 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. Observer-based decentralized fault detection method for aircraft systems, characterized in that The steps are as follows: S1: Based on the interconnected large - system modeling method, establish a dynamic model for the aircraft system. The dynamic model is an interconnected large - system composed of N interconnected generalized subsystems under the influence of external disturbances and measurement noises; S2: By adopting graph theory, decompose the interconnected large - system into N interconnected subsystems; S3: Mathematically characterize sensor faults based on the dynamic model; S4: Through the method of multiplying by the annihilation matrix, decouple the coupling terms in the interconnected subsystems; S5: Verify the observability of the relevant matrices of each subsystem to provide a basic guarantee for the subsequent design of the observer; S6: Combine the CPS architecture to achieve the fault - detection objectives of each subsystem, reduce the complexity of the design scheme, and at the same time ensure good fault - detection performance. Design a dynamic reduced - order observer based on the measurable output of the system; S7: Describe the numerical relationship between the gain matrices of the designed dynamic reduced - order observer; S8: To achieve the purpose of fault detection, define a residual signal based on the output result of the dynamic reduced - order observer and the actual measurable output data of the system; S9: Based on linear matrix inequality technology, give the detailed design conditions for the gain matrix of the dynamic reduced - order observer; S10: Give the specific expression for solving the gain matrix of the dynamic reduced - order observer and design an adaptive detection threshold with specified performance; S11: Based on the above steps, give a fault - detection algorithm. Specifically, compare the residual signal with the designed adaptive detection threshold: if the residual signal is greater than or equal to the adaptive detection threshold, the sensor of the corresponding subsystem fails; if the residual signal is less than the adaptive detection threshold, the sensor of the corresponding subsystem is fault - free; S12: Verify the effectiveness of the designed fault - detection scheme through the Matlab simulation platform and optimize and improve the scheme based on the simulation results.

2. The decentralized fault detection method for an aircraft system based on an observer according to claim 1, wherein In the above step S1: The model of the interconnected large - system is as follows: Where x(t) = col(x1(t),...,x N (t)), D = blkdiag{D1,...,D N} u(t) = col(u1(t),...,u N (t)), E = blkdiag{E1,...,E N} d(t) = col(d1(t),...,d N (t)), B = blkdiag{B1,...,B N} y(t) = col(y1(t),...,y N (t)), W = blkdiag{W1,...,W N} v(t) = col(v1(t),..., v N (t)), C = blkdiag{C1,..., C N} where \(i\in\{1,\ldots,N\}\), represent the state variable, control input, and measurement output of the \(i\)-th subsystem respectively; the symbol "\(\in\)" represents the membership relation, and represent the \(n -\)dimensional Euclidean space and the set of \(m\times n\) real matrices respectively; represent the bounded external disturbance and measurement noise in the \(i\)-th subsystem respectively, and they have known upper bounds and The constant matrices \(A\) ij , \(B\) i , \(C\) i , \(D\) i , \(W\) i , \(E\) i represent the known system matrices of the \(i\)-th subsystem and have appropriate dimensions; \(\text{col}(\sigma_1(t),\ldots,\sigma\) n (t)) represents a column vector The superscript "\(T\)" represents the transpose of a matrix or vector, and \(\text{blkdiag}\{\ldots\}\) represents a block - diagonal matrix, represents the first - order derivative of \(x(t)\) with respect to time.

3. The decentralized fault detection method for an aircraft system based on an observer according to claim 2, characterized in that, In the above step S2: Adopt a decentralized fault - detection method: First, by combining graph theory, decompose the above - mentioned interconnected large - system model (1) into N interconnected subsystems. The dynamics of the i - th subsystem are as follows: where Π i =[A ij , A ij ≠0, i ∈ {1, ..., N}, j ∈ {1, ..., N}, considering the influence of the state variable x j (t) on x i (t) as an unknown input term in the i-th subsystem Suppose the matrix Π i is a column full-rank matrix.

4. The decentralized fault detection method for an aircraft system based on an observer according to claim 3, characterized in that, In the above step S3: Based on the dynamic model, mathematically characterize sensor faults: For the i - th subsystem (2), considering the influence of sensor faults, the corresponding system dynamics are as follows: wherein represents the sensor fault signal in the i-th subsystem.

5. The decentralized fault detection method for an aircraft system based on an observer according to claim 4, characterized in that In the above step S4: Through the method of multiplying by the annihilation matrix, decouple the coupling terms in the interconnected subsystems; Let denote the left annihilator matrix of matrix Π i , that is Multiply both sides of the first equation in equation (3) by matrix to obtain the following expression: Where i ∈ {1,..., N} and In the step S5 described above: verify that the matrix pair is regular and impulse-free, and the initial condition is consistent, and the matrix pair is observable.

6. The decentralized fault detection method for an aircraft system based on an observer according to claim 5, characterized in that In the above step S6: Design a dynamic reduced - order observer as follows: where \(i\in\{1,\ldots,N\}\), and represent the state variables of the designed dynamic dimensionality reduction observer, respectively represent the first-order derivatives of \(z\) i (t), \(\varphi\) i (t) with respect to time; is the estimated value of the system state variable , is the output of the designed observer; The following matrices are the observer gain matrices to be designed:

7. The decentralized fault detection method for an aircraft system based on an observer according to claim 6, characterized in that, In the said step S7: Select an arbitrary matrix such that the following conditions are satisfied: Among them represents the identity matrix of dimension n i , the symbol represents the zero matrix of dimension m×n; Let the matrix be row full rank and satisfy the following conditions: That is and are equivalent matrices, where rank[] represents the rank of the matrix; In the said step S8: For the purpose of completing fault detection, for the i-th subsystem, based on the output result of the dynamic dimensionality reduction observer and the actually measurable output data of the system, a residual signal τ i (t) is defined as follows:

8. The decentralized fault detection method for an aircraft system based on an observer according to claim 7, characterized in that In the above step S9: Based on linear matrix inequality technology, for the designed dynamic reduced - order observer (5), give the detailed design conditions for the gain matrix as follows: For a given positive number b i , a 1i , a 2i , i ∈ {1,..., N}, if there exist positive definite matrices and such that the following linear matrix inequality holds: Where * represents the symmetric terms in the symmetric matrix, and where the symbol represents the pseudo-inverse of a matrix, χ 3i represents an arbitrary matrix; χ 1i represents an unknown matrix, and a detailed solution method will be given later; then the designed dynamic dimensionality reduction observer (5) can ensure that the following two conditions are satisfied: (a) When there is no sensor fault in the i - th subsystem, all signals in the estimation - error system are uniformly ultimately bounded; (b) When there is no sensor fault in the i - th subsystem, the corresponding residual signal satisfies the following expression: where ||θ i (t)|| ∞ denotes the infinity norm of θ i (t), and 9. The decentralized fault detection method for an aircraft system based on an observer according to claim 8, characterized in that In the above-mentioned step S10: The gain matrix of the designed dynamic dimensionality reduction observer (5) can be obtained through formula (7) and the following expressions: Among them, similar to the processing method of the existing results, the matrix χ 2i is set to the zero matrix; For the i-th subsystem, combined with L ∞ performance metrics, design an adaptive detection threshold with specified performance as shown below: Among them, represents the largest eigenvalue of the matrix .

10. The decentralized fault detection method for an aircraft system based on an observer according to claim 9, characterized in that, The specific content of the above-mentioned step S11 is: Based on the above steps S1 - 10, for the purpose of completing fault detection, the following fault detection algorithm is given: Fault Detection Algorithm 1 Input: Matrix C i and D i , i = 1,..., N; Necessary condition: The linear matrix inequality presented in formula (9) holds; Output: The i-th subsystem has a fault; Step1: Select a suitable matrix according to formula (7) Step 2: Calculate matrix G according to formula (11) i and Step 3: Calculate matrix β according to formulas (10) and (11) 1i , β 2i , β 3i , β 4i , α 1i , α 2i and α 3i ; Step4: Calculate the matrix Γ according to the linear matrix inequality (9) i ; Step 5: Calculate all the gain matrices of the designed dynamic dimensionality reduction observer (5) according to formula (11): N i , M i , F i , H i , Q i , K i , Φ i , S i and T i ; Step6: Start the loop Step 7: Run the dynamic dimensionality reduction observer (5), and calculate the residual value τ i (t) and the adaptive threshold Step8: If then the sensor in the i-th subsystem fails; return the value of i; Step9: End the loop Specifically, in the above Fault Detection Algorithm 1, the residual signal of the i-th subsystem is mainly compared with the designed adaptive detection threshold: (a) If the obtained residual signal is greater than or equal to the adaptive detection threshold, the sensor of the corresponding subsystem has a fault; (b) If the obtained residual signal is less than the adaptive detection threshold, the sensor of the corresponding subsystem has no fault; The specific content of the above-mentioned step S12 is: Verify the effectiveness of the designed fault detection scheme through the Matlab software simulation platform, and optimize and adjust the design parameters in the scheme to ensure that the fault detection scheme has good performance.

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