Kalman filter and neural network combined sensor fault reconstruction method

Abstract

The invention discloses a Kalman filter and neural network combined sensor fault reconstruction method, and belongs to the technical field of fault diagnosis. According to the method, an aero-engine state space model is firstly considered, a Bi-LSTM neural network fault observer corresponding to the aero-engine state space model is designed, a self-attention mechanism is fused to obtain a Bi-LSTM-Attention network to process an output value of the neural network, and the feature extraction effect of the neural network on a time sequence signal is improved. And then the designed KF and BLSTMA models are constructed into a combined fault observer, and high-precision reconstruction of sensor faults is completed. According to the scheme, the measurement precision of fault diagnosis is effectively improved, and meanwhile, the stable convergence characteristic and the quick response capability of the observation system are ensured. Meanwhile, the combined fault observer can achieve online prediction of the state of the sensor of the aero-engine control system, and the real-time processing capacity of the combined fault observer lays a technical foundation for hardware equipment deployment and on-line fault monitoring.

Description

Technical Field

[0001] The present invention belongs to the technical field of fault diagnosis, and relates to a fault diagnosis method for aviation engine system sensors, and a combination of a traditional state estimation method based on a Kalman filter and a data-driven fault estimation method based on a neural network. Background Art

[0002] With the continuous improvement of aircraft domestication, China's aviation industry is attracting increasing attention. Safety performance is always a top priority during the aircraft design and manufacturing process. The stable operation of the aircraft engine, the "heart" of the aircraft, plays a crucial role in ensuring flight safety. The measurement signals acquired by sensors installed at various locations on the engine serve as the fundamental information source for the control and fault diagnosis systems, and are crucial for the proper functioning of the engine system. The accuracy of sensor signals impacts the reliability of the engine control system. As engine control systems become increasingly complex, the requirements for the number and performance of sensor signals are increasing. Furthermore, sensors in aircraft engines are constantly exposed to harsh operating environments such as high temperature and high pressure, increasing the risk of failure. Therefore, research on sensor fault diagnosis technology and the accurate reconstruction of faulty sensor signals are crucial for improving aircraft engine reliability and operational efficiency.

[0003] Current aircraft engine fault diagnosis can be categorized into fault detection, fault isolation, and fault estimation techniques. High-precision fault estimation is fundamental to the development of fault detection and diagnosis, as well as monitoring and early warning technologies. Methodologically, fault estimation can be further categorized into model-based, data-driven, and combined digital-analog approaches. Model-based methods include Kalman filters and particle filters. These methods typically rely on physical or mathematical models of the system to estimate sensor faults. However, model-based methods are often only applicable to specific systems or components, resulting in less than ideal performance in practical engineering applications. Consequently, model-based methods face significant limitations in their application. Data-driven methods leverage the powerful feature extraction and nonlinear fitting capabilities of deep learning methods to estimate fault magnitudes directly from historical data without relying on precise physical models. Consequently, they have attracted widespread attention in practical applications. Data-driven fault diagnosis methods often utilize time series data, and networks such as GRU and LSTM within RNNs have been widely used. However, due to inherent limitations of their recursive mechanisms, RNNs and their variants still suffer from slow training speeds and memory loss.

[0004] Hybrid model-based approaches, by combining the theoretical foundations of physical models with the adaptability of data-driven models, can more accurately capture system anomalies and degradation trends, improving prediction accuracy while also offering better interpretability than data-driven models. In "Highly Accurate Manipulator Calibration via Extended Kalman Filter-Incorporated Residual Neural Network," Weiyi Yang et al. combined an extended Kalman filter with a neural network to recalibrate two types of errors in an industrial robot. In "Vehicle Dynamics Estimator Utilizing LSTM-Ensembled Adaptive Kalman Filter," Youpeng Zhang et al. achieved high-precision estimation of longitudinal velocity and sideslip angle in vehicle dynamics by integrating an LSTM network and an adaptive Kalman filter. High-precision digital-analog hybrid estimation methods based on the combination of Kalman filters and neural networks have achieved research results in many fields, but research on these hybrid methods in aircraft engine sensor fault diagnosis remains limited. Summary of the Invention

[0005] To combine model-based and data-driven approaches and leverage their respective strengths, this paper proposes a new sensor fault estimation method based on a combination of digital and analog inputs for aircraft engine control systems. This method achieves accurate reconstruction of sensor faults by designing a KF-BLSTMA (Kalman Filter-Bi-LSTM-Attention Network) joint fault observer. The constructed saturation function ensures that the performance of the KF-BLSTMA joint fault observer remains within acceptable limits even when the neural network is untrained.

[0006] The technical solution of the present invention:

[0007] The control variables, output variables, and fault amplitude data of the state-space equation of the system to be estimated serve as the training dataset for the neural network. The control variables and the measured output of the system serve as the network inputs, and the fault amplitude serves as the neural network output. The neural network model is trained offline using the collected input-output data samples to correct the Kalman filter's estimated values, thereby improving the estimation accuracy. Finally, the effectiveness of the designed method is verified using a model of an aircraft engine control system.

[0008] A sensor fault reconstruction method combining a Kalman filter and a neural network, the steps are as follows:

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

[0010] Consider the continuous-time controlled system as follows:

[0011]

[0012] Where x(t)∈R n represents the system state variables, Represents the first-order derivative of the system state variable; f(t)∈R f represents the additive fault of the sensor, 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 of Bi-LSTM neural network fault observer

[0014] The Bi-LSTM neural network processes contextual dependencies in sequence data by combining a recurrent neural network structure with forward and reverse LSTM layers. LSTM can solve the vanishing gradient problem of ordinary RNNs by introducing memory units and gating mechanisms (input gate, forget gate, output gate). The forget gate determines how much historical information is retained, the input gate controls the update of new information, and the output gate generates the hidden state at the current moment. The gating mechanism alleviates the vanishing gradient problem, and memory units are used to capture long-term dependencies. Bi-LSTM introduces bidirectional processing based on LSTM: the forward LSTM processes inputs in chronological order from the start to the end of the sequence, while the reverse LSTM processes in reverse order from the end to the start. By splicing the hidden states in two directions, Bi-LSTM can simultaneously utilize historical and future information. The calculation formulas for each step in LSTM are as follows:

[0015] Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i )

[0016] Forget gate: f t =σ(W f ·[h t-1 ,x t ]+b f )

[0017] Candidate memory cells:

[0018] Update memory unit

[0019] Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o )

[0020] Hidden state: h t =o t ⊙tanh(C t )

[0021] Where σ(g) is the activation function, e is the Hadamard product, W i ,W f ,W c ,W o and b i ,b f ,b c ,b o are the weight matrix and bias term of the gating mechanism, h t-1 ,C t-1 are the hidden state and the output of the memory unit at the previous moment, x t is the input at that moment.

[0022] S3. Bi-LSTM neural network fault observer with self-attention mechanism

[0023] The self-attention mechanism is embedded in the Bi-LSTM to form a Bi-LSTM-Attention network. The self-attention mechanism dynamically calculates the correlation weights between elements in the sequence and dynamically generates a contextual representation for each position, achieving efficient modeling of global dependencies. Its core idea is to allow each element in the sequence to interact with other elements and automatically learn which parts of information are more important. In specific implementations, the input sequence is linearly transformed to generate query, key, and value vectors. The attention weights are obtained by calculating the dot product of the query and all keys and normalizing them through the Softmax function. The weighted sum of the values ​​is then used to obtain the output. The self-attention calculation process is as follows:

[0024] Compute queries, keys, and values:

[0025] Attention calculation:

[0026] in is the learnable parameter matrix, d k is the dimension of attention; by scaling factor It can avoid the gradient instability caused by excessive dot product results. is the matrix composed of the input sequence, n is the sequence length, d model is the characteristic dimension.

[0027] The self-attention mechanism obtains attention weights by linearly transforming and dimensionalizing the input, thereby performing a weighted summation of the input. This mechanism can directly model the characteristics between any positions, surpassing the step-by-step transfer process of RNN networks. Furthermore, attention weights for all positions can be calculated simultaneously, significantly saving time.

[0028] All neural networks involved were deployed through offline training. The training dataset was generated from the state-space equations of the aircraft engine. The sensor involved in the fault was the high-pressure rotor speed sensor. The sensor sampling time was 0.025 seconds. 10,000 samples were collected for each sensor fault. The training set and test set were split in a ratio of 7:3, and the training batch size was set to 64. The specific structure of the Bi-LSTM-Attention network is shown in the figure below. Figure 2 As shown, the input sequence first passes through a Bi-LSTM layer, then uses the ReLU activation function and a Dropout layer to prevent excessive gradients and overfitting. Then, an LSTM layer and a self-attention layer are constructed to enhance feature extraction of the input data, and finally, a linear layer generates predictions. The Bi-LSTM layer consists of two LSTM layers with 256 hidden units. During training, the dropout rate of the Dropout layer is set to 0.2. Furthermore, the number of training iterations is set to 300, with an initial learning rate of 1e-3. The Adam optimizer and learning rate decay mechanism are used to prevent overfitting. The neural network is trained using the Deep Learning Toolbox in Matlab 2024a and an NVIDIA RTX 4070 GPU.

[0029] S4. Design Kalman filter

[0030] The Kalman filter (KF) model can achieve optimal estimation in the sense of minimum mean square error under the conditions of linear systems and Gaussian noise. It automatically adjusts the weights of the prior estimate and the uncertainty of the measurement process. Its efficient real-time processing capability and good interpretability have been successfully applied in many research fields. This patent considers estimating fault values ​​based on the KF observer. In discrete time, the KF performs a prediction and update step for each time step k.

[0031] The prediction step formula is:

[0032] Prior estimate: x k|k-1 =Ax k-1|k-1 +Bu k +Dw k

[0033] Prior error covariance: Pk|k-1 =AP k-1|k-1 A T +Q k

[0034] The update step formula is:

[0035] Kalman gain: K = P k|k C T (CP k|k-1 C T +R k ) -1

[0036] Posterior estimate: x k|k =x k|k-1 +K(y k -Cx k|k-1 -Ef k )

[0037] Posterior error covariance: P k|k =(I-KC) -1 P k|k-1

[0038] where x k-1|k-1 , x k|k-1 , x k|k are the posterior estimate of the state quantity at the previous moment, the prior estimate of the state quantity at the current moment, and the posterior estimate of the state quantity at the current moment; u k is the system input at the current moment; P k-1|k-1 , P k|k-1 , P k|k are the posterior estimation covariance matrix of the previous moment, the prior estimation covariance matrix of the current moment, and the posterior estimation covariance matrix of the current moment respectively; Q k and R k are the process noise covariance matrix and the measurement noise covariance matrix respectively; A, B, C, D, E are the same as the matrices in the continuous-time controlled system in S1.

[0039] S5. Design of a KF-BLSTMA digital-analog combined fault observer strategy

[0040] In order to ensure the stable convergence of the Kalman filter estimation results, the controlled system must first be measurable and observable. Then, the necessary condition to ensure the performance of the observer is that the number of measurable parameters n is not less than the number of gas path characteristic parameters to be estimated, and n ≥ dim (x), where x is the system state.

[0041] The digital-analog combined sensor joint fault observer is constructed as follows:

[0042]

[0043] Among them, A, B, C, D, E represent the system constant matrix; Represent the prior and a posteriori estimates of the system state by the Kalman filter, and use the a posteriori estimate and the system output measurement value y k-1 Get the Kalman filter's observation value of the fault represents the output of the BLSTMA neural network fault estimation observer; represents the estimated value of the joint observer for the sensor fault; BLSTMA(g) represents the output of the BLSTMA network. The saturation function g(g) is expressed as follows:

[0044]

[0045] Here, α is a preselected parameter representing the bounds of the error correction term, and x and y are the time series prediction outputs of the neural network and Kalman filter for sensor failures, respectively. The saturation function causes the neural network to have large errors in its predictions when it is not trained, but has a limited impact on the KF observer.

[0046] When designing a combined digital-analog sensor fault estimation method, we first considered an aircraft engine state-space model and designed a corresponding Bi-LSTM neural network fault observer. We then incorporated a self-attention mechanism to create a Bi-LSTM-Attention network to process the neural network's output, improving the neural network's ability to extract features from time series signals. We then constructed a joint fault observer using the designed KF and BLSTMA models to achieve high-precision reconstruction of sensor faults.

[0047] Compared with a single model-based fault diagnosis module, the KF-BLSTMA digital-analog combined sensor fault estimation method takes into account the deviation between the real engine measurement data and the theoretical data of the system state model. When the estimation deviation of the Kalman filter is too large, the output residual can be made to Closer to the true value f, that is, the model can continuously and accurately estimate the changes in sensor data. The deployment of the KF-BLSTMA joint fault observer is completed through the Kalman Filter and Stateful Predict modules in the Simulink environment in Matlab 2024a.

[0048] Beneficial effects of the present invention: By combining the model-driven Kalman filter fault observer with the data-driven BLSTMA deep neural network architecture, an innovative digital-analog combined sensor fault estimation method is proposed. This solution combines the characteristics and advantages of traditional model analysis methods and emerging data-driven technologies. It not only effectively improves the measurement accuracy of fault diagnosis, but also ensures the stable convergence characteristics and rapid response capabilities of the observation system. More importantly, it provides a technical path for the application of deep learning technology in the field of fault estimation. At the same time, the KF-BLSTMA joint observer designed in this study can realize the online prediction of the sensor status of the aircraft engine control system. Its real-time processing capability lays a technical foundation for the deployment of hardware equipment and the implementation of online fault monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flowchart of the digital-analog combined KF-BLSTMA joint fault solution.

[0050] Figure 2 is the structural diagram of the BLSTMA neural network. At time k, the input of the neural network is

[0051]

[0052] Figure 3 The fault estimation effect of the KF-BLSTMA combined observer in the present invention is compared with the Kalman filter when a sinusoidal periodic interference occurs in a soft fault of the high-pressure rotor speed sensor.

[0053] Figure 4 for Figure 3 A partial enlarged view of .

[0054] Figure 5 When a bias fault occurs in a hard fault of the high-voltage rotor speed sensor, the fault estimation effect of the KF-BLSTMA joint observer in the present invention is compared with the Kalman filter.

[0055] Figure 6 for Figure 5 A partial enlarged view of . DETAILED DESCRIPTION

[0056] The present invention is further described below based on the technical solutions and accompanying drawings.

[0057] The flow chart of the sensor fault estimation method based on KF-BLSTMA digital-analog combination is as follows: Figure 1 shown.

[0058] The simulation verification is as follows:

[0059] This paper 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 KF-BLSTMA sensor fault estimation method. The output variables are: [N2,π T ], where N2 is the high-pressure rotor speed, π T is the turbine outlet pressure drop ratio. The control input variable is selected as: [Wf, A8], where Wf is the main fuel flow rate and A8 is the tail nozzle area.

[0060] When a drift fault occurs in the high-pressure rotor speed sensor of an aircraft engine, its system matrix is ​​as follows:

[0061]

[0062] In the simulation setting, the parameter α is set to 1, Gaussian noise with a variance of 1e-2 is injected as process noise, and the process noise covariance matrix Q is set to 1e-2, and the measurement noise covariance matrix R is set to 1e-4.

[0063] Since the magnitudes of the variables in the aircraft engine control system vary greatly, all variables involved in this patent need to be normalized. The specific method is as follows:

[0064]

[0065] Among them, x max ,x min are the maximum and minimum values ​​of the data x to be normalized.

[0066] Sensor faults are generally categorized by severity into soft and hard faults. Soft faults occur when the sensor signal experiences small changes in amplitude or rate, such as due to component aging. These include periodic interference, drift, and impact faults. Furthermore, hard faults (such as structural damage) often result in larger variations in the sensor's measured value, such as bias faults, open circuit faults, and short circuit faults. Common sensor fault categories, causes, and simulation methods are shown in Table 1.

[0067] Table 1 Common sensor failure categories, causes and simulation methods

[0068]

[0069] To verify the BLSTMA network designed in this patent, a soft fault of an aircraft engine high-pressure rotor sensor was set for network training and a hard fault was set for testing. Specifically, the settings were sinusoidal periodic interference in the soft fault and offset fault in the hard fault. The expression is:

[0070] Sinusoidal periodic interference:

[0071] Bias Fault:

[0072] At the same time, in order to verify the effectiveness and advanced performance of the KF-BLSTMA network in improving the KF fault estimation effect, the KF, KF-Bi-LSTM and KF-GRU-Attention joint fault estimators are used as comparative experiments. The network structure and parameter settings of KF-Bi-LSTM and KF-GRU-Attention are consistent with those of KF-BLSTMA. The evaluation indicators are selected as MAE and RMSE, and the calculation formula is as follows:

[0073]

[0074] Where n is the number of samples in the test set, y k and are the estimated true value and estimated value respectively.

[0075] The fault estimation effect of the KF-BLSTMA joint observer in this invention is as follows: Figure 3 As shown; Figure 4 The corresponding diagram is a partial magnified effect diagram of the observation results when a periodic interference fault occurs. Figure 5 is the observation result when bias fault occurs, Figure 6 The corresponding diagram is a partial magnified effect diagram of the observation results when a bias fault occurs. Figure 4 and Figure 6 It can be seen from the results that the fault estimation effect of the KF-BLSTMA joint observer proposed in this invention is better than that of the traditional Kalman filter fault observer after training, which proves the effectiveness of the digital-analog combination method.

[0076] The results of the comparative experiment between the KF-BLSTMA joint observer in this invention and the joint observers of two other neural networks are shown in Table 2. It can be seen that KF-Bi-LSTM-Attention outperforms KF-Bi-LSTM in all indicators, which shows that the attention mechanism can improve the accuracy of fault estimation, and KF-Bi-LSTM-Attention is the best in both fault indicators.

[0077] Table 2 Comparison of performance indicators of different neural network test data sets

[0078]

Claims

1. A sensor fault reconstruction method combining Kalman filter and neural network, characterized in that: Here are the steps: S1. Establish a state-space model of the aircraft engine controlled object; S2. Design a Bi-LSTM neural network fault observer; S3. Bi-LSTM neural network fault observer with self-attention mechanism; S4. Design Kalman filter KF; S5. Design a combined strategy for the KF-BLSTMA digital-analog combined fault observer.

2. The sensor fault reconstruction method combining a Kalman filter and a neural network according to claim 1, characterized in that: The step S1 is specifically as follows: Consider the continuous-time controlled system as follows: Where x(t)∈R n represents the system state variables, Represents the first-order derivative of the system state variable; f(t)∈R f represents the additive fault of the sensor, 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.

3. The sensor fault reconstruction method combining a Kalman filter and a neural network according to claim 1, characterized in that: The step S2 is specifically as follows: The Bi-LSTM neural network processes contextual dependencies in sequence data by combining a recurrent neural network structure with forward and backward LSTM layers. LSTM can solve the vanishing gradient problem of ordinary RNNs by introducing memory cells and gating mechanisms. The forget gate determines how much historical information is retained, the input gate controls the update of new information, and the output gate generates the hidden state at the current moment. The gating mechanism alleviates the vanishing gradient problem and uses memory cells to capture long-term dependencies. Bi-LSTM introduces bidirectional processing based on LSTM: the forward LSTM processes the input in chronological order from the start to the end of the sequence, while the backward LSTM processes it in reverse order from the end to the start. By splicing the hidden states in both directions, Bi-LSTM can simultaneously utilize historical and future information. The calculation formulas for each step in LSTM are as follows: Input gate: i t =σ(W i ·[h t-1 ,x t ]+b i ) Forget gate: f t =σ(W f ·[h t-1 ,x t ]+b f ) Candidate memory cells: Update memory unit Output gate: o t =σ(W o ·[h t-1 ,x t ]+b o ) Hidden state: h t =o t ⊙tanh(C t ) Where σ(g) is the activation function, e is the Hadamard product, W i ,W f ,W c ,W o and b i ,b f ,b c ,b o are the weight matrix and bias term of the gating mechanism, h t-1 ,C t-1 They are the hidden state and the output of the memory unit at the previous moment, x t is the input at that moment.

4. The sensor fault reconstruction method combining a Kalman filter and a neural network according to claim 1, characterized in that: The step S3 is specifically as follows: The self-attention mechanism is embedded in the Bi-LSTM to obtain the Bi-LSTM-Attention network. The self-attention mechanism dynamically calculates the correlation weights between elements in the sequence and dynamically generates the contextual representation of each position, achieving efficient modeling of global dependencies. The core idea is to allow each element in the sequence to interact with other elements and automatically learn which parts of information are more important. In specific implementation, the input sequence is linearly transformed to generate query, key, and value vectors. The attention weight is obtained by calculating the dot product of the query and all keys and normalizing it through the Softmax function. The weighted sum is then used to obtain the output value. The calculation process of self-attention is as follows: Compute queries, keys, and values: Attention calculation: in is the learnable parameter matrix, d k is the dimension of attention; by scaling factor It can avoid the gradient instability caused by excessive dot product results. is the matrix composed of the input sequence, n is the sequence length, d model is the characteristic dimension; The self-attention mechanism obtains attention weights by linearly transforming and dimensionalizing the input, thereby performing weighted summation on the input; The input sequence first passes through a Bi-LSTM layer, and then uses the ReLU activation function and Dropout layer to avoid problems such as excessive gradients and overfitting. Then, an LSTM layer and a self-attention layer are constructed to enhance the feature extraction capability of the input data, and finally a linear layer is used to generate a prediction result.

5. The sensor fault reconstruction method combining a Kalman filter and a neural network according to claim 1, characterized in that: The step S4 is specifically as follows: The Kalman filter can achieve the optimal estimation in the sense of minimum mean square error under the conditions of linear system and Gaussian noise. It automatically adjusts the weight of the prior estimation and the uncertainty of the measurement process, and estimates the fault value based on the KF observer. In discrete time, the KF performs a prediction and update step for each time step k. The prediction step formula is: Prior estimate: x k|k-1 =Ax k-1|k-1 +Bu k +Dw k Prior error covariance: P k|k-1 =AP k-1|k-1 A T +Q k The update step formula is: Kalman gain: K = P k|k C T (CP k|k-1 C T +R k ) -1 Posterior estimate: x k|k =x k|k-1 +K(y k -Cx k|k-1 -Ef k ) Posterior error covariance: P k|k =(I-KC) -1 P k|k-1 where x k-1|k-1 , x k|k-1 , x k|k are the posterior estimate of the state quantity at the previous moment, the prior estimate of the state quantity at the current moment, and the posterior estimate of the state quantity at the current moment; u k is the system input at the current moment; P k-1|k-1 , P k|k-1 , P k|k are the posterior estimation covariance matrix of the previous moment, the prior estimation covariance matrix of the current moment, and the posterior estimation covariance matrix of the current moment respectively; Q k and R k are the process noise covariance matrix and the measurement noise covariance matrix respectively; A, B, C, D, E are the same as the matrices in the continuous-time controlled system in S1.

6. The sensor fault reconstruction method combining a Kalman filter and a neural network according to claim 1, characterized in that: The step S5 is specifically as follows: In order to ensure the stable convergence of the Kalman filter estimation results, the controlled system must first be measurable and observable. Then, the necessary condition to ensure the performance of the observer is that the number of measurable parameters n is not less than the number of gas path characteristic parameters to be estimated, and n ≥ dim (x), where x is the system state. The digital-analog combined sensor joint fault observer is constructed as follows: Among them, A, B, C, D represent the system constant matrix; Represent the prior and a posteriori estimates of the system state by the Kalman filter, and use the a posteriori estimate and the system output measurement value y k-1 Get the Kalman filter's observation value of the fault represents the output of the BLSTMA neural network fault estimation observer; represents the estimated value of the joint observer for the sensor fault; BLSTMA(g) represents the output of the BLSTMA network; the expression of the saturation function g(g) is as follows: Among them, α is a pre-selected parameter that represents the boundary of the error correction term, x and y are the time series prediction outputs of the neural network and Kalman filter for sensor failure, respectively; the saturation function causes the neural network to have large errors in the predicted value when untrained conditions occur, but the impact on the KF observer is limited.

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