Transition mode failure diagnosis method for tiltrotor aircraft

Abstract

The present application relates to the technical field of fault diagnosis of complex systems with disturbance, and discloses a fault diagnosis method for tilt rotor aircraft in transition mode, comprising: in order to improve the modeling accuracy, the linearization modeling error of the tilt rotor aircraft is expressed as an unknown disturbance term; the unknown input observer (UIO) is used to decouple the disturbance from the residual, an optimal BFDF algorithm is designed, the optimal value of the key gain matrix K1 is solved, the threshold logic is used for fault detection of the residual signal, and fault isolation is completed by comparing the quantization parameters of the relationship between the residual direction and the fault characteristic direction. The tilt rotor aircraft transition mode fault diagnosis method is more accurate in modeling the tilt rotor aircraft transition mode, the distribution matrix of the unknown input term is obtained through least squares identification, the optimal unknown input robust BFDF is designed, the threshold logic is used for fault detection of the residual signal, and the values with larger directional quantization parameters are isolated as fault.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fault diagnosis of flight control system in transition mode, in particular to a tilt-rotor aircraft transition mode fault diagnosis method. BACKGROUND

[0002] The statements in this section merely provide background technology related to the present disclosure and do not necessarily constitute prior art.

[0003] The tilt-rotor aircraft is in transition from helicopter mode (i n = 0°) to fixed-wing mode (i n = 90°), which is prone to failure. In order to diagnose the failure in a timely, accurate and efficient manner, a fault diagnosis module is usually used to diagnose the flight control system of the tilt-rotor aircraft during the transition process.

[0004] The commonly used nonlinear mathematical model of the tilt-rotor aircraft is in the form of a general nonlinear equation. The control quantity involved in the modeling of the aircraft body can be directly written in a linear relationship in the motion differential equation, while the control quantity involved in the modeling of the rotor is implicitly in the integral expression of the blade aerodynamic force and moment, which is not easy to directly express in a linear form in the final nonlinear motion equation. So far, there is no specific nonlinear equation form for the nonlinear mathematical model of the tilt-rotor aircraft.

[0005] The mathematical essence of the linear system model is to linearize the nonlinear system at the equilibrium point. There are generally two methods, one is the analytical method, that is, the analytical expressions of the aerodynamic force derivatives and the control derivatives are derived theoretically, and only the first-order small quantity is retained under the small perturbation assumption. This is the commonly used method, which has been successfully applied in practice. However, the linear system model obtained by this method has many simplifying assumptions, and many nonlinear, non-constant and high-order factors are lost. The other method is the numerical method, that is, the linearization equation at the equilibrium point is directly established from the nonlinear differential equation through numerical calculation. Since it is directly obtained from the nonlinear equation, it is possible to retain more nonlinear characteristics of the system, so this method is more flexible in application and is the development trend of linear system model. Therefore, the numerical method is used to linearize the nonlinear system of the tilt-rotor aircraft.

[0006] The nonlinear differential equation of the tilt-rotor aircraft is

[0007]

[0008] Where x(t)∈R n is the state vector; u(t)∈R r is the control input vector; y(t)∈R m is the output vector.

[0009] For equation (1) in equilibrium state (x) trim ,u trim Expanding by Taylor series, we get

[0010]

[0011] Where Δx=xx trim Δu=uu trim O f (x,u) represents higher-order terms with respect to x and u, O g (x) denotes a higher-order infinitesimal with respect to the system state. Let A be the infinitesimal of f in (x) trim ,u trim B is the Jacobian matrix of f with respect to x at the same point (i.e., with respect to x). Let C be an n×m matrix of elements (where n is the number of state vectors and m is the number of control inputs), and let C be the value of g at x = x. trim The Jacobian matrix at that location.

[0012]

[0013] Matrices A, B, and C are obtained using the numerical finite difference method. First, the parameters of the baseline equilibrium state are determined. Then, each element in A, B, and C under the equilibrium state is obtained through finite differences. Let the higher-order term O be... f (x,u) and O g (x) satisfies

[0014]

[0015] The original nonlinear system equations can be approximated by the following linearized equations.

[0016]

[0017] For simplicity, Δ is removed from equation (5), and the above linearized equation is rewritten as:

[0018]

[0019] For equation (1), the above numerical method can be used to directly obtain the high-order linear model of the tiltrotor flight dynamics, where A, B, and C are n×n, n×r, and m×n matrices, respectively, and x and u are the small disturbances of the tiltrotor state vector and control vector relative to the reference state, respectively.

[0020] In 1971, Beard first studied the Beard Fault Detection Filter (BFDF) method using matrix algebra, and Jones described it in a state-space representation. Many researchers later developed the theory of BFDF. BFDF is a classic state estimation fault diagnosis method, characterized by its ability to make the fault residual output have a unidirectional characteristic related to the known fault direction. BFDF is well-designed, computationally inexpensive, and very suitable for fault detection in linear systems. However, its significant drawback is that it does not consider uncertainties related to the system during the design process, such as disturbances, noise, and modeling errors, leading to poor robustness. Since uncertainties are unavoidable in practical applications, these uncertain disturbances and system faults will affect the residuals. If these residuals are used for fault diagnosis, it becomes difficult to distinguish between the fault and the uncertain disturbances. Therefore, for reliable diagnosis, the disturbances must be decoupled from the residuals.

[0021] Unknown Input Observer (UIO) can decouple disturbances from state estimation errors. However, in designing robust BFDFs with unknown inputs, a key step in existing techniques is designing the gain matrix K1. However, K1 obtained using the eigenstructure configuration method is arbitrary, making it difficult to quickly identify and isolate disturbances.

[0022] Therefore, the main technical problem in the existing technology is: how to design the linearization of the nonlinear model of the tiltrotor and how to define the linearization error, obtain the optimal gain matrix in the robust BFDF observer with unknown input, minimize the observation error, and realize a fault diagnosis method for the transition mode of the tiltrotor to improve the fault diagnosis accuracy of the tiltrotor. Summary of the Invention

[0023] To overcome the shortcomings of the prior art, this invention provides an algorithm for optimally solving the gain matrix K1, which more accurately models the tiltrotor aircraft in transition mode. The linearization error of the model is represented as an unknown input term. The distribution matrix of the unknown input term is identified by least squares to obtain the optimal unknown input robust BFDF. Then, threshold logic is used to detect faults in the residual signal. Furthermore, the larger of the quantization parameters of the directional relationship between the residual and the fault characteristics is used as the fault diagnosis method for the transition mode of the tiltrotor aircraft isolated from the fault.

[0024] The technical solution adopted in this invention is: a fault diagnosis method for tiltrotor aircraft in transition mode, including nonlinear modeling of the tiltrotor aircraft in transition mode, and the fault diagnosis method further includes:

[0025] The linearization error in the modeling is represented as an unknown disturbance term, and the disturbance is decoupled from the residual using an Unknown Input Observer (UIO). An optimal BFDF algorithm is designed, introducing the crucial gain matrix K1 to give the residual a unidirectional characteristic. An optimal algorithm is designed to solve for the optimal value of K1, avoiding the arbitrariness of the value of the gain matrix K1. An optimal unknown input robust BFDF filter is designed, and specific calculation steps are given to obtain the relevant design matrix of the filter and estimate the state of the tiltrotor aircraft. Threshold logic is used to detect faults in the residual signal, and the values ​​of the quantization parameters with larger directional relationships between the residual and the fault characteristics are isolated as faults.

[0026] In this technical solution, considering the uncertainty of the transition mode linearization and failure of the tiltrotor aircraft, the system will be:

[0027]

[0028] In the formula: A, B, C, and E are known matrices with appropriate dimensions; x(t)∈R n It is a state vector; u(t)∈R r It is the control input vector; y(t)∈R m It is the output vector; d(t)∈R q It is an unknown input (or interference); f i μ i (t)(i = 1, 2, ..., k) describes the i-th actuator that has failed; f i ∈R n It is the fault event vector of the i-th actuator failure; μ i (t) is an unknown time-varying scalar function representing the development process of the fault; the set of fault event vectors F = [f1, f2, ..., f k ].

[0029] In this technical solution, a BFDF observer is designed for system (7), and the state estimation error is... With residual r(t)

[0030]

[0031] In the formula: It is a state estimate; K∈R m×n It is the observer gain matrix; r(t)∈R m It is the residual vector.

[0032] As shown in equation (8), all faults and disturbances will affect the residual. If the residual is used to detect and isolate faults, it is not easy to distinguish between faults and disturbances. Therefore, the disturbance must be decoupled from the residual.

[0033] Definition 1 (Unknown Input Observer (UIO))

[0034] A system with interference can be described as

[0035]

[0036] Regardless of whether the system described by equation (9) has unknown inputs (disturbances), if the state estimation error vector e(t) of the observer asymptotically approaches zero, then the observer is defined as the unknown input observer of the system described by equation (9).

[0037] The structure of a full-order observer can be described as follows:

[0038]

[0039] In the formula: It is the estimated state vector; z∈R n It represents the state of the full-order observer; L, T, K, and H are the design matrices, which have been used to obtain unknown input decoupling and meet other design requirements.

[0040] When the observer (10) is used for the system (9), the state estimation error e(t) is controlled by the following equation:

[0041]

[0042] in

[0043] K = K1 + K2 (12)

[0044] If the following relation holds:

[0045] (HC-I)E=0 (13)

[0046] T = I - HC (14)

[0047] L=A-HCA-K1C (15)

[0048] K2=LH (16)

[0049] Then the state estimation error is:

[0050]

[0051] If L has all stable eigenvalues, e(t) will asymptotically approach zero, i.e. According to definition 1, this means that the observer (10) is an unknown input observer of the system (9). Designing such a UIO involves solving equations (12) to (16) to stabilize the eigenvalues ​​of matrix L.

[0052] Lemma 1 Equation (13) is solvable if and only if

[0053] rank(CE) = rank(E) (18)

[0054] The solution is

[0055] H = E[(CE)] T (CE)] -1 (CE) T (19)

[0056] The proof is omitted.

[0057] The necessary and sufficient condition for equation (10) of Theorem 1 to be the system (9) UIO is:

[0058] (1) rank(CE) = rank(E);

[0059] (2) (C,A1) can be detected.

[0060] in

[0061] A1 = AE[(CE)] T CE] -1 (CE) T CA (20)

[0062] The proof is omitted.

[0063] From equations (15), (19), and (20), we can obtain:

[0064] L=A1-K1C (21)

[0065] Note that K1 is the free parameter matrix when designing UIO. After K1 is determined, the other parameter matrices of UIO can be calculated from equations (12) to (16). The only constraint on K1 is that the system dynamic characteristic matrix L must be stable. The matrix K1 that can make matrix L stable is not unique because of the multivariate nature of the problem. That is to say, after the unknown input disturbance conditions are met, there is still a remaining design flexibility in the selection of K1.

[0066] Use the UIO described by equation (36) to generate residuals.

[0067]

[0068] When this UIO-based residual generator is applied to the system described by equation (8), its state estimation error is equal to the residual.

[0069]

[0070] As can be seen from equation (37), the effect of the disturbance has been decoupled from the residual. As noted in the note, once the robustness condition (in the sense of disturbance decoupling) is satisfied, the design of matrix K1 is arbitrary. This design freedom can be used to give the residual a unidirectional characteristic.

[0071] In this technical solution, a key step in designing a robust BFDF with unknown inputs is designing the gain matrix K1. K1 is typically solved using the eigenstructure collocation method. However, since the eigenvalues ​​of A1-K1C are arbitrarily allocated, the resulting K1 is arbitrary. Therefore, an algorithm for solving the optimal gain matrix K1 is proposed below.

[0072] Property 1: If x = (x1, x2, ..., x...) n ) T Let N(a,Σ) be an n-dimensional normal distribution, y = Cx be an m-dimensional random vector, and C ∈ R be a matrix. m×n Then y follows an m-dimensional normal distribution N(Ca,CΣC). T ).

[0073] Where a = (Ex1, Ex2, ..., Ex) n ) T ,

[0074]

[0075] Property 2: If A and B are square matrices, then tr(AB) = tr(BA).

[0076] Equation (18) is K1 obtained by the characteristic structure configuration method:

[0077]

[0078] Among them (CF) + =((CF) T (CF)) -1 (CF) T E is any n×m dimensional matrix; I is an m-dimensional identity matrix.

[0079] According to equation (23), the gain matrix K1 can be re-expressed as follows:

[0080] K1 = K 1a +K 1b W T (twenty four)

[0081] K 1a =[A1f1-λ1f1,A1f2-λ2f2,…,A1f k -λ k f k (CF) + K 1b ∈Rn×m Let W be any matrix, and W = (I - (CF)(CF)) + ) T .

[0082] Define the covariance matrix P as

[0083]

[0084] In the formula, Let P be the state error vector, and let P be a symmetric positive definite matrix.

[0085] Let the performance index function J be the energy of the output error vector r(t) of the system (22) when no fault occurs, as follows:

[0086]

[0087] Where r(t) = (r1(t), r2(t), ..., r m (t)) T .

[0088] when Then, the performance index of equation (26) can be written as

[0089] J = tr(PC) T C) (27)

[0090] In the formula, tr(X) represents the sum of the diagonal elements of matrix X.

[0091] Proof: Expanding equation (26), we get

[0092]

[0093] Depend on have to

[0094]

[0095] but

[0096] therefore

[0097] From property 1, we get

[0098] J = tr(CPC) T )

[0099] By property 2, if the dimension m = n, then

[0100] J = tr(PC) T C)

[0101] Q.E.D.

[0102] In this technical solution, when μ i When (t) = 0, the system error equation (22) is expressed as follows:

[0103]

[0104] According to Lyapunov stability theory, if there exist positive definite matrices P and gain matrix K1 such that the following equation holds, then the observer A1-K1C is asymptotically stable.

[0105] (A1-K1C) T P+P(A1-K1C)<0 (29)

[0106] Substituting equation (24) into equation (29) and simplifying, we get

[0107]

[0108] If the eigenvalue λ of A1-K1C is a variable, when k < n,

[0109] K 1a =K 1a (λ) (31)

[0110] Substituting equation (31) into equation (30), we get

[0111]

[0112] Therefore, the problem of finding the optimal gain matrix K1 is transformed into:

[0113]

[0114] Equation (32) is the constraint equation.

[0115] In this technical solution, the design steps of the optimal unknown input robust BFDF are given below:

[0116] Step 1: Check the rank condition of matrices E and CE: If rank(CE) ≠ rank(E), then there is no observer gain matrix K. Proceed to Step 6.

[0117] Step 2: Calculate matrices H and T according to equations (19) and (14) to satisfy the interference decoupling conditions.

[0118] Step 3: Calculate A1 according to formula (20).

[0119] Step 4: Calculate based on the proposed optimal algorithm

[0120] Step 4.1: Select initial eigenvalues ​​λ 0 <0, J0 =tr(IC T C) Given a termination error ε > 0, let i = 0;

[0121] Step 4.2: Let λ i+1 =λ i -1, then K 1a (λ)=K 1a (λ i+1 );

[0122] Step 4.3: Given any matrix K 1b ;

[0123] Step 4.4: Solve equation (32), if P = P T And the smallest eigenvalue of P is greater than 0, thus obtaining the optimal variable P. * and the corresponding matrix at this time Proceed to Step 4.5; otherwise proceed to Step 4.3.

[0124] Step 4.5: J i+1 =tr(P * C T C), if To obtain the optimal J * and K 1a (λ * If the condition is not met, proceed to Step 4.6; otherwise, let i = i + 1 and proceed to Step 4.2.

[0125] Step 4.6: Obtain

[0126] Step 5: Calculate matrix K according to equations (12) and (16).

[0127] Step 6: End.

[0128] In this technical solution, when using threshold logic to perform fault detection on the residual signal, a threshold T is first given. r If the norm of the residual signal is less than the threshold T r If the result is positive, it indicates that a fault has occurred; otherwise, no fault has occurred.

[0129]

[0130] In this technical solution, when performing fault isolation based on directional residuals, 2CTf is defined. i The direction is called the characteristic direction of the i-th actuator fault.

[0131] Vector CTf i The directional relationship with r(t) can be quantified by relevant parameters, which are described as follows:

[0132]

[0133] If corr j >corr k Therefore, the j-th executor is more likely to fail than the k-th executor.

[0134] Compared with the prior art, the beneficial effects of the present invention are:

[0135] Fault diagnosis is performed using optimal unknown input robust BFDF (the method of this invention) and unknown input robust BFDF (method 1). Simulation results show that:

[0136] 1) When using directional residuals for fault isolation, the accuracy of the fault diagnosis method is high because the gain matrix is ​​obtained through an optimal algorithm.

[0137] 2) When linearizing the nonlinear model of the tiltrotor aircraft, linearization error will inevitably be introduced. In order to model the system more accurately, the linearization error is represented as an unknown input disturbance term. The distribution matrix of the unknown input term is then obtained by least squares identification, which can also increase the accuracy of fault isolation.

[0138] In summary, the tiltrotor aircraft transition mode fault diagnosis method of the present invention can more accurately model the transition mode of the tiltrotor aircraft. The distribution matrix of the unknown input terms is identified by least squares to obtain the optimal unknown input robust BFDF. Then, threshold logic is used to detect faults in the residual signal. Furthermore, the values ​​of the directional relationship parameters between the residual and the fault characteristics with larger values ​​are used as faults to be accurately, efficiently and quickly isolated. Attached Figure Description

[0139] Figure 1 A flowchart for a fault diagnosis method for the transition mode of a tiltrotor aircraft;

[0140] Figure 2 This is a graph showing the relationship between the cost function and the eigenvalues.

[0141] Figure 3 The residual curve is shown under fault-free conditions.

[0142] Figure 4 The pitch angle and its angular rate residual curve at the time of fault 1.

[0143] Figure 5 The pitch angle and its angular rate residual curve at the time of fault 2.

[0144] Figure 6 The pitch angle and its angular rate residual curves at the time of fault 3 are shown. Detailed Implementation

[0145] This paper describes a fault diagnosis method for transient mode using a fault diagnosis system for a tiltrotor aircraft during flight. Specifically, an actuator failure occurs during the transient process of the tiltrotor aircraft, and the flight control system uses a fault diagnosis module for fault diagnosis. Simulation experiments were conducted on an IBM computer (Pentium 4, CPU 3.00GHz, 2GB RAM) using Matlab R2009a. The simulation model was implemented using S-functions in MATLAB Simulink. The simulation process involves the tiltrotor aircraft transitioning from helicopter mode (i... n =0°) to fixed-wing mode (i n The transition is performed at a 90° angle, with an initial flight altitude of 1500m and an initial flight speed of 40m / s. The normal transition takes 16.5s.

[0146] Linearizing the nonlinear tiltrotor model, we obtain matrices A, B, and C in equation (7) as follows:

[0147]

[0148]

[0149] During the normal transition of a tiltrotor aircraft, a fault is assumed to be injected at 3 seconds, and the fault occurrence time is between 3 seconds and 16.5 seconds. Three fault types are considered, as shown in Table 1.

[0150] Table 1 Actuator Fault Types

[0151] Fault type Symbol Abbreviation Total loss failure f1 Fault 1 Longitudinal cyclic variation failure f2 Fault 2 Elevator failure f3 Fault 3

[0152] In Table 1, the collective pitch failure rate of fault 1 is 60%; the longitudinal cyclic pitch failure rate of fault 2 is 40%; and the elevator failure rate of fault 3 is 30%. Therefore, we obtain...

[0153] F = [f1 f2 f3]

[0154] = [-0.6b1 -0.4b2 -0.3b3]

[0155] 1.1 Determination of the Unknown Distribution Matrix

[0156] Linearization inevitably introduces linearization error. To model the system more accurately, this linearization error can be represented as an unknown input disturbance term Ed(x(t)), and the second-order term of the Taylor expansion can be included in the system dynamic equations, as follows:

[0157]

[0158] Matrices A and B are the same as those in the linear model. The Ed(x(t)) term describes the modeling error, and the vector d(t) contains second-order terms of x(t), such as:

[0159] d(t)=[u 2 ,w 2 ,θ 2 ,q 2 ,z 2 ] T

[0160] The unknown distribution matrix E can be obtained by least squares identification.

[0161] Given a sequence of input u, the values ​​of u (1) ,u (2) ,…,u (N) The corresponding state response value x is obtained. (1) ,x (2) ,…,x (N) and d (1) ,d (2) ,…,d (N) They satisfy the following system of steady-state equations

[0162]

[0163] If N is greater than the dimension of d(x), then the least squares estimate of the unknown matrix E is:

[0164] E * =[Γ + Ψ] T

[0165] In the formula: Γ + It is a pseudo-inverse of Γ, and

[0166]

[0167] Taking N=8, the estimated E can be obtained based on simulation. * ,as follows:

[0168] E * Not a full-rank matrix (rank(E) * =4), therefore it should be decomposed into E * =E1E2, where E1 is a column full-rank matrix and is used for filter design in Section 4.

[0169]

[0170] 1.2 Residual Generation

[0171] Since rank(CE1) = rank(E1) = 4, there exists an observer gain matrix K. Following the design steps of an optimal unknown-input robust BFDF, the filter parameter matrices can be obtained as follows:

[0172]

[0173]

[0174]

[0175] Based on Step 4, the relationship between the eigenvalue λ and the cost function J is obtained as follows: Figure 2 As shown. When λ = -3.8, J reaches its minimum value, and the corresponding optimal matrix K is obtained. 1a (λ * )and Optimal gain matrix as follows

[0176]

[0177] Calculate matrix K according to equations (12) and (16) as follows:

[0178]

[0179] Figure 3 , Figure 4 , Figure 5 and Figure 6 The output signals for generating residuals are given for no fault and for faults 1, 2 and 3, respectively.

[0180] Depend on Figure 3 It is known that, when there is no fault, the filter designed in this invention can basically reproduce the original system state.

[0181] Figures 4 to 6 Only two typical and representative residual signals are given: pitch angle and pitch rate. As shown in the figure, when a fault occurs, the output error will jump, but the specific circumstances of the jump differ for each state. The change in the filter output error indicates a fault. Equation (33) shows that the fault occurrence times are 3.1s, 3.07s, and 3.09s, respectively. At this time, T... r The values ​​are 0.005, 0.02, and 0.005, respectively.

[0182] 1.3 Analysis of Robust Fault Diagnosis Results

[0183] The optimal unknown input robust BFDF (the method of this invention) and unknown input robust BFDF (method 1) were used to diagnose actuator faults in the transition mode of the tiltrotor aircraft. The diagnosis results are shown in Tables 2 and 3.

[0184] Table 2. Actuator Fault Diagnosis Results (Method 1)

[0185]

[0186] Table 3. Actuator Fault Diagnosis Results (Method of this Invention)

[0187]

[0188] Analysis of Tables 2 and 3: From the diagnostic results obtained by Method 1 (Table 2), it can be seen that the residual r(t) generated when system fault 1 occurs is related to the directional residual parameters of CTf1, CTf2, and CTf3. The values ​​are 0.0594, 0.0212, and 0.0318, respectively.

[0189] Since corr1 > corr3 > corr2, fault 1 can be correctly isolated. Similarly, fault 3 can also be correctly isolated. However, when fault 2 occurs, it will be mistakenly identified as fault 3 because corr3 is the largest of all three directional residual parameters at this time. The diagnostic results obtained from the method of this invention (Table 3) show that faults 1 to 3 correspond to... All values ​​are at their maximum, thus ensuring proper isolation and demonstrating the effectiveness of the method of this invention.

[0190] This invention proposes a method for optimally solving the robust BFDF gain matrix for unknown inputs in the fault diagnosis of the flight control system under the transition mode of a tiltrotor aircraft.

[0191] During simulation, optimal unknown input robust BFDF (the method of this invention) and unknown input robust BFDF (method 1) were used for fault diagnosis. Based on the simulation results, the following conclusions were drawn:

[0192] 1) When using directional residuals for fault isolation, the method of this invention has a higher accuracy than method 1 because the gain matrix is ​​obtained through the optimal algorithm.

[0193] 2) When linearizing the nonlinear model of the tiltrotor aircraft, linearization error will inevitably be introduced. In order to model the system more accurately, the linearization error is represented as an unknown input disturbance term. The distribution matrix of the unknown input term is then obtained by least squares identification, which can also increase the accuracy of fault isolation.

[0194] The embodiments disclosed herein are preferred embodiments, but are not limited thereto. Those skilled in the art can readily grasp the spirit of the present invention based on the above embodiments and make different extensions and variations, but as long as they do not depart from the spirit of the present invention, they are all within the protection scope of the present invention.

Claims

1. A fault diagnosis method for tiltrotor aircraft in transition mode, comprising nonlinear modeling of the tiltrotor aircraft in transition mode, characterized in that, The fault diagnosis method further includes: The linearization error in the modeling is represented as an unknown disturbance term, and the disturbance is decoupled from the residual using an unknown input observer (UIO). The optimal BFDF algorithm is designed, and the most critical gain matrix K1 is introduced to make the residual have a unidirectional characteristic. The optimal algorithm is designed to solve for the optimal value of K1, thus avoiding the arbitrariness of the value of the gain matrix K1. Design an optimal robust BFDF filter for unknown inputs, provide specific calculation steps, derive the relevant design matrix of the filter, and estimate the state of the tiltrotor aircraft; Threshold logic is used to detect faults in the residual signal, and the larger values ​​of the quantization parameters that show the directional relationship between the residual and the fault characteristics are isolated as faults. The algorithm for the optimal gain matrix K1 is as follows: According to property 1, if x = (x1, x2, ..., x...) n ) T Let N(a,Σ) be an n-dimensional normal distribution, y = Cx be an m-dimensional random vector, and C ∈ R be a matrix. m×n Then y follows an m-dimensional normal distribution N(Ca,CΣC). T ); Where a = (Ex1, Ex2, ..., Ex) n ) T , According to property 2, if A and B are square matrices, then tr(AB) = tr(BA); Equation (23) is K1 obtained by the characteristic structure configuration method: Among them (CF) + =((CF) T (CF)) -1 (CF) T E is any n×m dimensional matrix; I is an m-dimensional identity matrix; According to equation (23), the gain matrix K1 can be re-expressed as follows: K1=K 1a +K 1b IN T (24) K 1a =[A1f1-λ1f1,A1f2-λ2f2,…,A1f k -λ k f k (CF) + K 1b ∈R n×m For any matrix, W=(I-(CF)(CF) + ) T ; Define the covariance matrix P as In the formula, Let P be the state error vector, and let P be a symmetric positive definite matrix. Take the performance index function J as the energy of the output error vector r(t) of the uncertain system (7) described by equation (8) when no fault occurs, as follows: Where r(t) = (r1(t), r2(t), ..., r m (t)) T Equation (8) represents the state estimation error of the BFDF observer designed for the uncertain system (7). With the residual r(t), i.e. In the formula: It is a state estimate; K∈R m×n It is the observer gain matrix; r(t)∈R m It is the residual vector; when Then, the performance index of equation (26) can be written as J=tr(PC T C) (27) In the formula, tr(X) represents the sum of the diagonal elements of matrix X; When μ i When (t) = 0, the system error equation (22) is expressed as follows: According to Lyapunov stability theory, if there exist positive definite matrices P and gain matrix K1 such that the following equation holds, then the observer A1-K1C is asymptotically stable. (A1-K1C) T P+P(A1-K1C)<0 (29) Substituting equation (24) into equation (29) and simplifying, we get If the eigenvalue λ of A1-K1C is a variable, when k < n, K 1a =K 1a (l) (31) Substituting equation (31) into equation (30), we get Therefore, the problem of finding the optimal gain matrix K1 is transformed into: Equation (32) is the constraint equation.

2. The method for diagnosing transition mode faults in tiltrotor aircraft according to claim 1, characterized in that, The tiltrotor aircraft in transition mode is modeled nonlinearly as follows: where x(t)∈R n It is a state vector; u(t)∈R r It is the control input vector; y(t)∈R m It is the output vector; For tiltrotor aircraft, consider an uncertain system with disturbances and potential failures: In the formula: A, B, C, and E are known matrices with appropriate dimensions; x(t)∈R n It is a state vector; u(t)∈R r It is the control input vector; y(t)∈R m It is the output vector; d(t)∈R q It is a modeling error interference term; f i μ i (t)(i = 1, 2, ..., k) describes the i-th actuator that has failed; f i ∈R n It is the story event vector of the i-th actuator failure; μ i (t) is an unknown time-varying scalar function representing the development process of the fault; the set of fault event vectors F = [f1, f2, ..., f k ].

3. The method for diagnosing transition mode faults in tiltrotor aircraft according to claim 2, characterized in that, For an uncertain system (7), a BFDF observer is designed, and the state estimation error is... The residual r(t) is: In the formula: It is a state estimate; K∈R m×n It is the observer gain matrix; r(t)∈R m It is the residual vector; The tiltrotor system with disturbance transition mode is described by Equation (9): Regardless of whether the system described by Equation (9) has unknown inputs and / or disturbances, if the state estimation error vector e(t) of the designed BFDF observer asymptotically approaches zero, then the BFDF observer is defined as the unknown input observer of the system described by Equation (9). The system described by equation (9) is then observed using a full-order unknown input observer, the structure of which is described by equation (10): In formula (10): It is the estimated state vector; z∈R n This represents the state of the full-order observer; L, T, K, and H are design matrices, obtained to decouple unknown inputs and meet other design requirements; When the full-order unknown input observer of equation (10) is used to observe the system described by equation (9), the state estimation error e(t) is controlled by the following equation: in: K = K1 + K2 (12) If the following relation holds: (HC-I)E=0 (13) T = I - HC (14) L=A-HCA-K1C (15) K2=LH (16) Then the state estimation error is: When L has all stable eigenvalues, e(t) will asymptotically approach zero, that is... A BFDF observer is defined as an unknown input observer of the system described by equation (10); Equation (13) is solvable if and only if rank(CE) = rank(E) (18) The solution is H=E[(CE) T (WHAT)] -1 (WHAT) T (19); Use the UIO described by equation (36) to generate residuals: When this UIO-based residual generator is applied to the system described by equation (8), its state estimation error and residual are: As can be seen from equation (37), the effect of the disturbance has been decoupled from the residual.

4. The method for diagnosing transition mode faults in tiltrotor aircraft according to claim 3, characterized in that, The calculation steps for the optimal unknown input robust BFDF are as follows: Step 1: Check the rank condition of matrices E and CE: If rank(CE) ≠ rank(E), then there is no observer gain matrix K. Proceed to Step 6. Step 2: Calculate matrices H and T according to equations (19) and (14) to satisfy the interference decoupling conditions; Step 3: Calculate A1 according to formula (20); Step 4: Calculate based on the proposed optimal algorithm Step 4.1: Select initial eigenvalues ​​λ 0 <0, J 0 =tr(IC T C) Given a termination error ε > 0, let i = 0; Step4.2:Set i+1 =λ i -1, K 1a (λ)=K 1a (l i+1 ); Step 4.3: Given any matrix K 1b ; Step 4.4: Solve equation (32), if P = P T And the smallest eigenvalue of P is greater than 0, thus obtaining the optimal variable P. * and the corresponding matrix at this time Proceed to Step 4.5, otherwise proceed to Step 4.3; Step 4.5: J i+1 =tr(P * C T C), if To obtain the optimal J * and K 1a (λ * If the first step is 1, proceed to Step 4.6; otherwise, let i = i + 1 and proceed to Step 4.

2. Step 4.6: Obtain Step 5: Calculate matrix K according to equations (12) and (16); Step 6: End.

5. The method for diagnosing transition mode faults in tiltrotor aircraft according to claim 1, characterized in that, When using threshold logic to perform fault detection on residual signals, a threshold T is first given. r If the norm of the residual signal is less than the threshold T r If it is positive, it indicates that a fault has occurred; otherwise, no fault has occurred.

6. The method for diagnosing transition mode faults in tiltrotor aircraft according to claim 5, characterized in that, CTf i The direction is called the characteristic direction of the i-th actuator fault. Vector CTf i The directional relationship with r(t) can be quantified by relevant parameters, which are described as follows: If corr j >corr k Therefore, the j-th executor has a higher probability of failure than the k-th executor.

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