Digital-analog combined aero-engine sensor fault estimation method

Abstract

The invention belongs to the technical field of aero-engine fault diagnosis, and discloses a digital-analog combined aero-engine sensor fault estimation method. According to the invention, a traditional Luenberger fault estimation observer is combined with an LSTM deep neural network, and a new sensor fault estimation method based on digital-analog combination is provided. According to the method, respective advantages of a model-based method and a data driving method are fused, so that the accuracy of fault estimation can be further improved, the convergence and robustness of the system can be ensured, and theoretical support is provided for fault estimation through deep learning. In addition, the Luenberger-LSTM digital-analog combined sensor fault estimation method designed by the patent also can predict the sensor fault of an aero-engine control system in real time, and provides valuable reference for deploying to an airborne system for online fault estimation in the future.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft engine fault diagnosis, and relates to a fault diagnosis method for an aircraft engine control system, and in particular to a joint sensor fault estimation method based on traditional models and data-driven artificial intelligence. Background Art

[0002] With the rapid development of the aviation industry, among all the performance of aircraft, safety has become the primary issue that people are most concerned about. As the "heart" of the aircraft, the aircraft engine is one of the important systems to ensure flight safety. In order to improve the safety of aircraft engines and further reduce maintenance costs, the research on fault diagnosis of aircraft engine control systems has aroused widespread interest and achieved a lot of results. In terms of content, fault diagnosis can be divided into fault detection, fault isolation and fault estimation. Among them, fault estimation can calculate the magnitude of the fault amplitude and lay the foundation for active fault-tolerant control. In terms of methods, fault diagnosis can be divided into model-based methods and data-driven methods. Model-based methods usually rely on the physical model of the system to construct observers to estimate sensor or actuator faults. However, since it is often difficult to obtain an accurate model of the system in engineering practice, model-based methods are subject to great restrictions. In contrast, data-driven methods can estimate the fault amplitude through historical data without relying on accurate physical models, so they have received widespread attention in practical applications. In the early stage of the development of data-driven fault diagnosis methods, some traditional machine learning methods, such as support vector machines and BP neural networks, were mainly used. Elgiz Baskaya et al. used support vector machines to study the fault diagnosis of UAV flight control systems in the article "Fault detection & diagnosis for small UAVs via machine learning". Qiu Hao et al. studied the problem of sensor fault detection during stable flight of spacecraft by improving BP neural network in the article "Simulation study of BP neural network for sensor fault diagnosis". With the development of GPU computing power, methods based on deep learning have gradually become a reality and have more powerful performance than traditional shallow neural networks, thus becoming a research hotspot in the field of fault diagnosis. Che Changchang et al. proposed a deep learning-based aeroengine fault fusion diagnosis model by combining deep belief networks and decision fusion algorithms in the article "Aeroengine bearing fault diagnosis based on multi-sensor fusion convolutional neural network". Yang Jie et al. used a one-dimensional convolutional neural network to extract and classify the vibration data of a certain aeroengine bearing fault obtained in the experiment in the article "Aeroengine bearing fault diagnosis based on multi-sensor fusion convolutional neural network". However, data-driven fault diagnosis methods represented by deep learning lack rigorous theoretical support and also have some defects in practical applications. For example, when faced with new situations that have not been trained with data, the fault estimation effect will be seriously reduced. Fault diagnosis methods based on the combination of digital and analog have attracted widespread interest in recent years.Zhu Chaojie et al. studied the actuator failure of UAV by using a proportional-integral observer based on a deep learning network in the paper "Actuator Fault Reconstruction for Quadrotors Using Deep Learning-Based Proportional Multiple-Integral Observer". However, there are still relatively few studies on sensor fault diagnosis methods based on the combination of digital and analog. Summary of the invention

[0003] In order to combine the advantages of model-based methods and data-driven methods, this paper proposes a new digital-analog sensor fault estimation method for aircraft engine control systems. This method achieves accurate reconstruction of sensor faults by designing a Luenberger-LSTM joint fault observer, while also ensuring that the performance of the Luenberger-LSTM joint fault observer is still within an acceptable range when the neural network is not trained.

[0004] The technical solution of the present invention:

[0005] A digital-analog combined aircraft engine sensor fault estimation method, the steps are as follows:

[0006] First, the measurable output, state quantity and control input of the controlled system are used as the input of the long short-term memory neural network (LSTM), and the fault amplitude is used as the output of the LSTM network; then the offline trained LSTM network is imported, and the estimated value of the Luenberger fault observer is corrected by the time series prediction value of the LSTM network, so as to further improve the estimation accuracy of the fault amplitude; finally, an aircraft engine control system model is used to verify the effectiveness of the proposed Luenberger-LSTM sensor joint fault observation method;

[0007] Mathematical symbols are defined as follows:

[0008] X T represents the transpose of matrix X, X -1 represents the inverse of matrix X, [X] s =X+X T , “*” is the abbreviation for the symmetric position in a symmetric matrix; diag{...} represents a block diagonal matrix, and col{...} represents a column vector consisting of elements.

[0009] S1. Establish the state space model of the aircraft engine controlled system;

[0010] Considering the state space model of the aircraft engine controlled system near a certain steady-state operating point, it is shown as follows:

[0011]

[0012] Where x(t)∈R n Indicates the system status. Represents the first-order derivative of the system state; f(t)∈R f represents the sensor additive fault, w(t)∈R w represents the external disturbance of the system, u(t)∈R m represents the system input, y(t)∈R p represents the system measurement output, A, B, C, D, E represent the system constant matrix; assume that the system is observable and controllable;

[0013] S2. Design LSTM neural network

[0014] LSTM neural network is a recurrent neural network (RNN) that can learn long-term dependencies between time steps of sequence data. Compared with traditional RNN, LSTM better solves the gradient vanishing and gradient exploding problems of neural networks during data training. This patent creates an LSTM neural network for time series prediction based on "sequence to single" regression, which contains a sequence input layer, two LSTM layers, a fully connected layer and a regression output layer. The structure of the LSTM neural network is as follows Figure 2 As shown in Figure 1, the input of the LSTM neural network is the sensor measurement output and input of the aircraft engine controlled system, and the corresponding network output is the sensor fault amplitude. The learnable weights of LSTM include input weight W, loop weight R and bias b, and their matrix representation is as follows:

[0015]

[0016] Among them, i, f, g, and o represent the input gate, forget gate, candidate unit, and output gate respectively;

[0017] The cell state at time t-1 is c t-1 ,

[0018] The cell state at time step t is c t =f t ⊙c t-1 +i t ⊙g t ,

[0019] The hidden state at time step t is h t =o t ⊙tanh(c t ),

[0020] The component at the input gate t is i t =σ g (W i z t +R i h t-1 +b i ),

[0021] The component at the forget gate t is f t =σ g (W f z t +R f h t-1 +b f ),

[0022] The component at candidate unit t is g t =tanh(W g z t +R g h t-1 +b g ),

[0023] The component at the output gate t is o t =σ g (W o z t +R o h t-1 +b o );

[0024] σ g is the state activation function, usually selected as the sigmoid function, and its expression is

[0025]

[0026] The state output h of the hidden layer t The sensor fault f(t) selected as the controlled system;

[0027] The training of LSTM neural network is carried out by supervised learning. In this patent, the data set is generated by the continuous-time system model of the aircraft engine, and the sensor failure is mainly the failure of the high-pressure rotor speed sensor. The sampling time of the sensor is 0.025s, and a total of 10,000 data pairs are collected. The division ratio of the training set and the test set is 7:3, and the number of training batches selected each time is 8. The estimation accuracy can be improved by increasing the number of neurons, but too many neurons will also lead to overfitting. Therefore, we use a two-layer LSTM neural network here, each layer of the neural network has 128 LSTM module units, and the discard rate of each step of the LSTM neural network training is set to 20%; in addition, we use the Adam optimizer for the gradient descent algorithm for training the neural network. In order to further enhance the feature extraction capability of the input data, we use a two-layer LSTM network structure here. The training process of LSTM is completed by the deep learning toolbox in Matlab 2023a and the NVIDIA RTX3050Ti GPU.

[0028] S3. Design the Luenberger-LSTM joint fault observer and construct the augmented error dynamic system;

[0029] The digital-analog combined sensor joint fault observer is constructed as follows:

[0030]

[0031] in, represents the state variables of the fault estimation observer, represents the output of the fault estimation observer, L, F are the gain matrices of the fault estimation observer that need to be designed, represents the first-order derivative of the observer state variable, It represents the estimated value of the sensor fault by the joint observer. The expression of the saturation function Δf is as follows:

[0032]

[0033] Among them, α is a pre-selected parameter, which represents the upper bound of the error correction term, It is the time series prediction output of the long short-term memory neural network for sensor failure.

[0034] Design the state feedback controller as

[0035]

[0036] Defining variables ξ(t)=col{e x (t),e f (txt)}, Then the augmented error dynamic system is expressed as:

[0037]

[0038] in

[0039] A 1 =A e -L 1 C 1 ,A 2 =[-BK 0],A 3 =A+BK,

[0040] B 2 =[D 00], C 1 =[CE]

[0041] Where I represents the unit matrix;

[0042] The lemmas required to prove the method of this patent are given below.

[0043] Lemma 1. For a column-full rank matrix H∈R n×m , there are always two positive definite matrices X∈R n×n and Y∈R m×m satisfy:

[0044]

[0045] Among them, X 1 ∈R m×n ,X 2 ∈R (n-m)×n ,Σ=diag{σ 1 ,σ 2 ,...,σ m},σ i (i=1,2,...,m) are the non-zero singular values ​​of the matrix H. If the matrix W∈R n×n It can be written as follows:

[0046]

[0047] Among them, W 11 >0,W 22 > 0, then there exists a non-singular matrix Z∈R m×m Satisfies HZ=WH.

[0048] S4. Theorem 1 is given below to make the augmented system (4) robust to external disturbances.

[0049] Theorem 1 Given a positive parameter γ, if there exists a positive definite matrix P such that

[0050]

[0051] M 1 =[0 0I],

[0052] Then the error dynamic system (4) is asymptotically stable and satisfies H ∞ Performance indicator γ.

[0053] Proof: The Lyapunov function is constructed as follows:

[0054] V(t)=ξ T (t)Pξ(t), (6)

[0055] Taking the derivative of the Lyapunov function with respect to time, we get:

[0056]

[0057] Construct a helper function like this:

[0058]

[0059] Define the variable: ξ 1 (t) = col{ξ(t), d(t)}, combining (7)-(8), we can get the following inequality:

[0060]

[0061] in,

[0062]

[0063] Under the condition of Ξ'<0, it can be obtained that when w(t)=0, Thus, the asymptotic stability of the augmented system (4) without external interference is proved. Integrating both ends of inequality (9) from t = 0 to ∞, under zero initial conditions, we can obtain ||x(t)|| 2 ≤γ 2 ||d(t)|| 2 , thus proving that the error dynamic system (4) satisfies H ∞ Performance indicator γ.

[0064] S6. Since the observer gain and controller gain in Theorem 1 are coupled with the unknown matrix and are difficult to solve directly through linear matrix inequalities, it is necessary to decouple the observer gain and controller gain through mathematical transformation.

[0065] Theorem 2 Given that the parameter γ is positive, if there exists a positive definite matrix P1 ,P 2 ,W 01 ,W 02 , there exists a matrix L', K' such that

[0066]

[0067] in,

[0068] Then the error dynamic system (4) is asymptotically stable and satisfies H ∞ Performance index γ. At the same time, if the inequality in equation (11) has a feasible solution, the fault detection observer gain matrices L and E are given by The calculation expression of controller gain K is obtained as follows: (The parameter matrix in the calculation expression of the controller gain K is explained in the proof below).

[0069] Proof: Let the positive definite matrix

[0070]

[0071] We can get:

[0072]

[0073] Then (5) becomes

[0074]

[0075] in, For a column-full rank matrix B, there exists an orthogonal matrix G 0 ∈R n×n ,Z∈R m×m satisfy:

[0076]

[0077] Among them, G 01 ∈R m×n ,G 02 ∈R (n-m)×n ,Ψ=diag{σ 1 ,σ 2 ,...,σ m},σ i (i=1,2,...,m) represents the non-zero singular values ​​of matrix B. According to Lemma 1, if the matrix P 2 It can be expressed as:

[0078]

[0079] Among them, W 01 >0,W 02> 0, then there exists a non-singular matrix M such that P 2 B=BM, and define matrices K'=MK and L'=P 1 L 1 Obviously, inequality (5) can be obtained from inequality (12). Using the proof process of Theorem 1, system (4) is asymptotically stable and satisfies ||x(t)|| 2 ≤γ||d(t)|| 2 .

[0080] Beneficial effects of the present invention: The present invention proposes a new digital-analog combined sensor fault estimation method by combining the traditional Luenberger fault estimation observer with the LSTM deep neural network. The present invention combines the respective advantages of the model-based method and the data-driven method, which can not only further improve the accuracy of fault estimation, but also ensure the convergence and robustness of the system, and provide theoretical support for fault estimation through deep learning. In addition, the Luenberger-LSTM digital-analog combined sensor fault estimation method designed in this patent can also perform real-time prediction of sensor faults in aircraft engine control systems, providing a valuable reference for future deployment in airborne systems for online fault estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 Flowchart of the Luenberger-LSTM joint fault solution combining digital and analog.

[0082] Figure 2 is the structural diagram of the LSTM neural network. At time t, the input of the neural network is

[0083]

[0084] The output of the neural network during training is the injected value f of the sensor fault t , is the predicted value of sensor failure during online deployment t .

[0085] Figure 3 When a high-pressure rotor speed sensor has a sinusoidal fluctuation fault, the fault estimation effect of the Luenberger-LSTM joint observer in the present invention is adopted.

[0086] Figure 4 for Figure 3 A partial enlarged view of .

[0087] Figure 5 When a ramp fault occurs in the high-pressure rotor speed sensor, the fault estimation effect of the Luenberger-LSTM joint observer in the present invention is adopted.

[0088] Figure 6 for Figure 5 A partial enlarged view of .

[0089] Figure 7 It is the trajectory state of the state variables of the controlled system under the designed controller when the high-pressure rotor speed sensor has a sinusoidal fluctuation fault. DETAILED DESCRIPTION

[0090] The specific implementation of the present invention is further described below in conjunction with the technical scheme and the accompanying drawings.

[0091] The flow chart of the sensor fault estimation method based on Luenberger-LSTM digital-analog combination is as follows: Figure 1 The simulation verification is as follows:

[0092] The present invention will use a linear model of an aircraft engine control system working near a certain steady-state point to verify the effectiveness of the proposed Luenberger-LSTM sensor fault estimation method. The output variable is: y = [ΔN 2 ,Δπ T ] T , where N 2 is the high pressure rotor speed, π T is the turbine outlet pressure drop ratio. The control input variable is selected as: u=[ΔWFM,ΔA8] T , where WFM is the main fuel flow rate and A8 is the tail nozzle area.

[0093] When a drift failure occurs in the high pressure rotor speed sensor of an aircraft engine, its system matrix is ​​as follows:

[0094]

[0095]

[0096] Assume that the sampling period is 0.025s. According to Theorem 2, the gain of the Luenberger-LSTM joint fault observer is obtained by solving the following optimization problem:

[0097] minγ

[0098] st constraint (11).

[0099] Given γ = 1.5, by solving the above convex optimization problem, we can obtain the fault estimation observer gain and state feedback controller gain matrix as shown below:

[0100] F=[1.0269 0.0604],

[0101] In order to verify why this patent uses LSTM neural network for time series prediction of sensor faults instead of other neural network models, Table 1 compares the estimation effects of different deep learning models on sensor faults. Here, the time domain convolutional neural network (TCN), TCN-LSTM network and TCN-LSTM network based on multi-head attention mechanism (TCN-LSTM-Multihead-Attention) are selected to compare the fault estimation effect with LSTM. Among them, the two performance indicators selected in Table 1 are as follows:

[0102] 1. Mean absolute error (MAE): The average of the absolute values ​​of the errors. The formula is:

[0103]

[0104] Among them, n is the number of samples, y k is the true value, is the predicted value. MAE is not sensitive to outliers and cannot reflect the distribution of prediction errors.

[0105] 2. Root mean square error (RMSE): It is the square root of the average of the sum of squared errors. Its formula is:

[0106]

[0107] Here, n is also the number of samples, y k is the true value, is the predicted value. RMSE is sensitive to outliers and can reflect the distribution of prediction errors.

[0108] Table 1 Comparison of performance indicators of test datasets of different deep learning networks

[0109]

[0110] It should be pointed out that the selection of neural network should be based on the characteristics of the training data, not the more complex the better. The performance comparison in Table 1 shows that based on the same data set, the LSTM network has better prediction effect on bias sensor failure than the TCN network, TCN-LSTM network and TCN-LSTM network based on multi-head attention mechanism.

[0111] Consider that the aircraft engine high pressure rotor speed sensor has a fluctuation fault f(t) as shown below at 50 seconds:

[0112]

[0113] When the aero-engine high-pressure rotor speed sensor has the above-mentioned sinusoidal drift fault, the fault estimation effect of the Luenberger-LSTM joint observer in the present invention is as follows: Figure 3 As shown, the corresponding local magnification effect is as follows Figure 4 shown.

[0114] When the aircraft engine high pressure rotor sensor has a ramp fault as shown below:

[0115]

[0116] The fault estimation effect of the Luenberger-LSTM joint observer in the present invention is as follows: Figure 5 The corresponding local magnification effect is shown in Figure 6 As shown. Figure 4 and Figure 6 It can be seen from the figure that the fault estimation effect of the Luenberger-LSTM joint observer proposed in the present invention is better than that of the traditional Luenberger fault observer. Figure 7 This is the trajectory change of the state variables of the aircraft engine under the jointly designed controller. It can be seen that the designed state feedback controller still has a good control effect even when the sensor fails, and the state variables of the controlled object can converge in a very short time.

Claims

1. A digital-analog combined aircraft engine sensor fault estimation method, characterized in that: Here are the steps: S1. Establish the state space model of the aircraft engine controlled system; Considering the state space model of the aircraft engine controlled system near a certain steady-state point, it is shown as follows: Where x(t)∈R n Indicates the system status. Represents the first-order derivative of the system state; f(t)∈R f represents the sensor additive fault, w(t)∈R w represents the external disturbance of the system, u(t)∈R m represents the system input, y(t)∈R p represents the system measurement output, A, B, C, D, E represent the system constant matrix; assume that the system is observable and controllable; S2. Design LSTM deep neural network For "sequence to single" regression, an LSTM deep neural network is created for time series prediction, which includes a sequence input layer, two LSTM layers, a fully connected layer, and a regression output layer. The input of the LSTM deep neural network is the sensor measurement output and input of the aircraft engine controlled system, and the corresponding network output is the sensor fault amplitude. The learnable weights of the LSTM deep neural network include input weight W, loop weight R, and bias b, and their matrix representation is as follows: Among them, i, f, g, and o represent the input gate, forget gate, candidate unit, and output gate respectively; The cell state at time t-1 is c t-1 , The cell state at time step t is c t =f t ⊙c t-1 +i t ⊙g t , The hidden state at time step t is h t =o t ⊙tanh(c t ), The component at the input gate t is i t =σ g (W i z t +R i h t-1 +b i ), The component at the forget gate t is f t =σ g (W f z t +R f h t-1 +b f ), The component at candidate unit t is g t =tanh(W g z t +R g h t-1 +b g ), The component at the output gate t is o t =σ g (W o z t +R o h t-1 +b o ); σ g As the state activation function, select the sigmoid function, whose expression is: The state output h of the hidden layer t The sensor fault f(t) selected as the controlled system; The training of LSTM neural network is carried out by supervised learning; the data set is generated by the continuous-time system model of the aircraft engine, and the sensor failure is mainly the high-pressure rotor speed sensor failure; therefore, a two-layer LSTM neural network is selected, each layer of LSTM neural network contains 128 LSTM module units, and the discard rate of each step of LSTM neural network training is set to 20%; in addition, the Adam optimizer is selected for the gradient descent algorithm of training LSTM neural network; the training process of LSTM neural network is completed by the deep learning toolbox in Matlab2023a and NVIDIA RTX3050Ti GPU; S3. Design the Luenberger-LSTM joint fault observer and construct the augmented error dynamic system; The digital-analog combined sensor joint fault observer is constructed as follows: in, represents the state variables of the fault estimation observer, represents the output of the fault estimation observer, L, F are the gains of the fault estimation observer that need to be designed, represents the first-order derivative of the observer state variable, represents the estimated value of the joint observer for the sensor fault; the expression of the saturation function Δf is as follows: Among them, α is a pre-selected parameter, which represents the upper bound of the error correction term; It is the time series prediction output of the long short-term memory neural network for sensor failure; Design the state feedback controller as: Where K is the controller gain; Defining variables ξ(t)=col{e x (t),e f (txt)}, Then the augmented error dynamic system is expressed as: in, <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr"> A1=A<h2 style=";text-align:left;direction:ltr"> e <h2 style=";text-align:left;direction:ltr"> -L1C1,A2=[-BK 0],A3=A+BK,<h2 style=";text-align:left;direction:ltr"> B2=[D 0 0], C1=[C E] Where I represents the identity matrix; Lemma 1 For a column-full rank matrix H∈R n×m , there are always two positive definite matrices X∈R n×n and Y∈R m×m satisfy: Where X1∈R m×n ,X2∈R (n-m)×n ,Σ=diag{σ1,σ2,...,σ m },σ i (i=1,2,...,m) are the non-zero singular values ​​of the matrix H; if the matrix W∈R n×n Written in the following form: Among them, W 11 >0,W 22 > 0, then there exists a non-singular matrix Z∈R m×m Satisfy HZ=WH; S4. By giving Theorem 1, the augmented error dynamic system is made robust to external disturbances; Theorem 1 Given a positive parameter γ, if there exists a positive definite matrix P such that M1=[0 0 I], Where * is the abbreviation of the symmetric position in the symmetric matrix; Then the augmented error dynamic system is asymptotically stable and satisfies H ∞ Performance index γ; Proof: The Lyapunov function is constructed as follows: V(t)=ξ T (t)Pξ(t), (6) Taking the derivative of the Lyapunov function with respect to time, we get: Construct a helper function like this: Define variables: ξ1(t) = col{ξ(t), d(t)}, combine (7)-(8), and we get the following inequality: in, Under the condition of Ξ'<0, when w(t)=0, Thus, the asymptotic stability of the augmented error dynamic system in the absence of external interference is proved; integrating both ends of inequality (9) from t = 0 to ∞, under zero initial conditions, we obtain ||x(t)|| 2 ≤γ 2 ||d(t)|| 2 , thus proving that the augmented error dynamic system satisfies H ∞ Performance index γ; S5. Since the observer gain and controller gain in Theorem 1 are coupled with the unknown matrix, it is difficult to solve them directly through linear matrix inequality. Therefore, it is necessary to decouple the observer gain and controller gain through mathematical transformation. Theorem 2 Given that the parameter γ is positive; if there exist positive definite matrices P1, P2, W 01 ,W 02 , there exists a matrix L', K' such that in, Then the augmented error dynamic system is asymptotically stable and satisfies H ∞ performance index γ; at the same time, if the inequality in equation (11) has a feasible solution, the fault estimation observer gains L and E are L1 = P1 -1 L' is obtained, and the calculation expression of the controller gain K is Proof: Let the positive definite matrix get: Then formula (5) becomes: in, For a column-full rank matrix B, there exists an orthogonal matrix G0∈R n×n ,Z∈R m×m satisfy: Among them, G 01 ∈R m×n ,G 02 ∈R (n-m)×n ,Ψ=diag{σ1,σ2,...,σ m },σ i (i=1,2,...,m) represents the non-zero singular values ​​of matrix B; According to Lemma 1, if the matrix P2 is represented as: Among them, W 01 >0,W 02 >0, then there exists a non-singular matrix M such that P2B=BM, and define matrices K'=MK and L'=P1L1; Obviously, inequality (5) is obtained from inequality (12); using the proof process of Theorem 1, system (4) is asymptotically stable and satisfies ||x(t)||2≤γ||d(t)||2.

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