Fault detection and fault tolerance method for navigation sensor

Abstract

The invention discloses a fault detection and fault tolerance method for a navigation sensor, and the method comprises the steps: S1, carrying out the segmentation processing of to-be-processed original data in a sliding window manner, and carrying out the normalization processing of the data in each sliding window; s2, carrying out feature extraction on the data normalized in the step S1 by adopting an FKPCA feature extraction method; s3, inputting the features extracted in the step S2 into an SVM classification model for fault detection; s4, building a fault signal active fault-tolerant network model based on BiLSTM, predicting detected fault data by using a BiLSTM neural network, and predicting the fault data through existing normal data so as to complete signal reconstruction; and S5, constructing an active fault tolerance method based on the FKPCA-SVM-BiLSTM. According to the method, the accuracy of sensor fault detection can be effectively improved, and dynamic reconstruction can be effectively carried out in time under various fault states.

Description

Technical Field

[0001] The present invention relates to the field of navigation and positioning technology, and in particular to a navigation sensor fault detection and fault tolerance method. Background Art

[0002] As modern battlefields evolve towards systematization, informatization, intelligence, and collaboration, navigation sensors are subject to interference from various factors during use, such as the internal electromagnetic environment and inclement weather. This can easily lead to abnormal sensor feedback data, seriously impacting the operational safety and stability of intelligent agents. Therefore, to prevent sensor failures from damaging system stability, employing appropriate fault-tolerant technologies to address them after detection is crucial for improving the stability of intelligent agents.

[0003] In recent years, fault detection and fault tolerance for navigation sensors have demonstrated significant practical value in multiple areas, including military strategy and commercial applications, attracting extensive research worldwide. Patent publication number CN119573686A discloses an oceanographic mapping system based on intelligent navigation using a deepwater exploration robot. This system incorporates a fault-tolerant control module that rapidly switches to a suboptimal navigation source to maintain navigation functionality when the primary navigation source fails. Patent publication number CN119573710A discloses a fault-tolerant method for a SINS and GNSS integrated navigation system based on an LSTM neural network. This method detects and tolerates both sudden and slow-changing faults in GNSS signals.

[0004] Currently, active fault tolerance methods for navigation sensor faults primarily focus on fault detection. For fault tolerance of fault information, the main approaches include isolation and substitution. Isolation directly eliminates faulty data, while substitution utilizes fault-tolerant technology to predict and replace faulty values. However, existing substitution methods primarily address fault tolerance for a single type of navigation sensor fault and fail to consider the impact of simultaneous faults in different sensor types on the navigation system. Therefore, there is an urgent need to develop a method for fault detection and active fault tolerance for multiple navigation sensor types to improve the operational stability of navigation systems. Summary of the Invention

[0005] The present invention aims to at least partially address one of the technical problems in the related art. To this end, one objective of the present invention is to propose a method for fault detection and fault tolerance for navigation sensors. First, a feature extraction module is designed with Frobenius Norm-based Kernel Principal Component Analysis (FKPCA) as the core to extract deep-level feature expressions of fault signal changes, thereby improving the reliability and detection accuracy of the system. Furthermore, a support vector machine (SVM) classification model is introduced to construct a fault detection model with FKPCA-SVM as the core, thereby improving the system's generalization ability when processing fault features and further enhancing prediction accuracy. Next, an active fault-tolerant network model for fault signals is designed with a bidirectional long short-term memory (BiLSTM) network as the core to obtain long-term dependencies between fault features at multiple moments, thereby improving the robustness of the control system in complex environments. Finally, an experimental scheme for fault detection and fault tolerance technology for navigation sensors is designed, and the detection performance and fault tolerance processing capabilities of the model under different fault conditions are analyzed.

[0006] According to a navigation sensor fault detection and fault tolerance method proposed by the present invention, the method steps are as follows:

[0007] S1: The original data to be processed is segmented using a sliding window method, and the data in each sliding window is normalized;

[0008] S2: Apply the normalized data in step S1 and perform feature extraction using the FKPCA feature extraction method;

[0009] S3: Apply the features extracted in step S2 and input them into the SVM classification model for fault detection;

[0010] S4: Build a BiLSTM-based active fault-tolerant network model for fault signals. Use the BiLSTM neural network to predict the detected fault data and use the existing normal data to predict the fault data, thereby completing signal reconstruction.

[0011] S5: Construct an active fault tolerance method based on FKPCA-SVM-BiLSTM.

[0012] Preferably, in step S1:

[0013] Navigation sensor data has temporal correlations, and this local analysis method, using a sliding window, can effectively identify abnormal signals. This sliding window method divides longer time series data into multiple shorter sub-sequences by shifting a fixed-length subsequence across the original sequence data at a specific step size. As time passes and data is updated, the window continuously incorporates new data and discards old data, thereby improving the model's update efficiency and adaptability.

[0014] Divide the long time series data of the navigation sensor into multiple short sub-time series:

[0015] The original data is: {x1,x2,x3,…,x n}, set the window size w=10 and the moving step size to 1;

[0016] The sliding window data at time t-2 is: w t-2 ={x t-11 ,x t-10 ,x t-9 ,…,x t-2};

[0017] The sliding window data at time t-1 is: w t-1 ={x t-10 ,x t-9 ,x t-8 ,…,x t-1};

[0018] By analogy, the sliding window data at time t is: w t ={x t-9 ,x t-8 ,x t-7 ,…,x t};

[0019] The maximum-minimum data normalization method is selected to process the original data. The formula is expressed as:

[0020]

[0021] Where x′ θ is the normalized data point, x θ is the original data point, w t is the data in a sliding window, min(w t ) is the minimum value in the sliding window data, max(w t ) is the maximum value within the sliding window data.

[0022] Preferably, in step S2, each normalized sliding window data is used as input data, and principal component analysis is performed in a higher-dimensional feature space using KPCA to extract the main features of the data:

[0023] S21: i-th sliding window data w i :w i =[x′ i-w+1 ,x′ i-w+2 ,…,x i ′] T ;

[0024] Use the nonlinear mapping function Φ to map the input sample data from the original space to the high-dimensional feature space:

[0025] Φ: d → D

[0026] Among them, d is the dimension of the original space, D is the dimension of the high-dimensional space, and the mapped data is:

[0027] Φ wi =[φ(x′ i-w+1 ),φ(x′ i-w+2 ),…,φ(x′ i )] T

[0028] Among them, φ(x i ′) is the i-th data mapped to the high-dimensional space;

[0029] S22: Perform linear principal component analysis in high-dimensional feature space. In high-dimensional space, the covariance matrix C is defined as:

[0030]

[0031] because:

[0032] CV c =λ c V c (3)

[0033] Substituting formula (2) into formula (3) yields:

[0034]

[0035] S23: Introducing the kernel technique, implicitly calculating the inner product in high-dimensional space through the kernel matrix K:

[0036] K mn =K(x′ m ,x n ′)=(φ(x′ m )·φ(x n ′) T ) (5)

[0037] Among them, K(x′ m ,xn ′) is the kernel function, which is the radial basis kernel function and is defined as:

[0038]

[0039] In high-dimensional space, data is centralized and the centralization matrix is ​​defined Replace K:

[0040]

[0041] Among them, 1 w is a w×w matrix with all elements being

[0042] Convert the eigenvalue decomposition problem into the eigenvalue decomposition problem of the kernel matrix:

[0043]

[0044] in, is the eigenvalue of the kernel matrix, The order is arranged from large to small, γ is the eigenvector corresponding to the eigenvalue of the kernel matrix, γ={γ1,γ2,…,γ p};

[0045] S24: In KPCA, the larger the eigenvalue, the more significant the change in that direction, and the more important the information reflected in the data. Generally, the first υ eigenvectors are selected to retain the principal components. While retaining the core features of the data to the maximum extent, it can also reduce the data dimension and reduce the complexity of the model. The selection of υ mainly depends on the cumulative contribution rate of the principal component. When the contribution rate reaches a certain proportion, it can represent the main information of the original data. First, the concept of contribution rate is introduced to calculate the contribution rate R of the eigenvalue. i :

[0046]

[0047] Among them, R i is the contribution rate of the i-th eigenvalue, is the i-th eigenvalue, is the sum of all eigenvalues, indicating the total variance of the data, and calculating the cumulative contribution rate G i :

[0048]

[0049] Contribution rate G i Start accumulating from the largest eigenvalue until the υth eigenvalue reaches the preset value, and retain the eigenvectors corresponding to the first υ eigenvalues;

[0050] S25: Project the retained υ eigenvectors into the principal component space to obtain the score matrix T′:

[0051]

[0052] Where V = [γ1,γ2,…,γ υ ];

[0053] Calculate the Frobenius norm of the score matrix T′:

[0054]

[0055] Among them, ||·|| F represents the Frobenius norm, ι ij Represents any element in the score matrix.

[0056] Preferably, in step S3:

[0057] S31: Dataset partitioning and preprocessing for SVM classification model;

[0058] Acquire navigation sensor data, including GNSS, IMU, and UWB sensors. Perform various fault simulations on the collected sensor data. Sensor faults include sudden faults, ramp faults, and sinusoidal faults. Each sensor corresponds to four types of data labels, including three types of fault labels and a normal label. The four types of data for each sensor are divided into training and test sets for the SVM classification model. The data in the training and test sets of the SVM classification model are preprocessed using a sliding window to segment the data. The segmented data is then normalized using maximum-minimum normalization.

[0059] S32: SVM classification model training;

[0060] S321: Construction of feature matrix of SVM classification model;

[0061] Input the preprocessed data of the four training sets corresponding to GNSS, IMU, and UWB in sequence, apply the FKPCA feature extraction method in step S2 to perform feature extraction, and generate a feature matrix containing four types of samples for each sensor. Each row of the matrix corresponds to the eigenvalue of a sliding window, that is, the calculation result of the Frobenius norm, and each column corresponds to a category.

[0062] S322: SVM classification model training;

[0063] Using the SVM nonlinear classification method, combined with the "one-to-one" multi-classification method, the SVM classification model was trained. For the four types of samples, six SVM binary classifiers were constructed. The feature matrix and the corresponding labels were input into the SVM classifier. The low-dimensional features were projected into a high-dimensional separable space through radial basis kernel function mapping. The model training was completed by optimizing the hyperplane decision boundary, and finally the SVM classification model was obtained.

[0064] S323: SVM classification model testing;

[0065] For the data preprocessed by the test set, the FKPCA feature extraction method in step S2 is applied to extract features, and the features are input into the trained SVM classification model for fault detection. The SVM classification model determines whether there is a fault through a multi-classifier voting mechanism. If the detection result is normal, it outputs no fault; if an abnormality is detected, it outputs the specific fault type, and finally completes the fault detection and classification. The output results of the SVM classification model are compared with the actual sample labels corresponding to the test set to evaluate the SVM classification model.

[0066] Preferably, in step S4:

[0067] S41: Data processing of BiLSTM-based fault signal active fault-tolerant network model;

[0068] The output of the navigation sensor has multi-dimensional and long time series characteristics. The GNSS output includes easting, northing, and celestial position coordinates, the IMU output includes three-axis acceleration and angular velocity data, and the UWB output includes ranging information. Using a dimension-based sliding window processing method, the raw data is sequentially processed into a 3*1 input matrix containing single-dimensional data of three consecutive time steps. The data is segmented to generate a sample set, and the sample set is divided into training samples, verification samples, and test samples according to a preset ratio.

[0069] S42: Training of BiLSTM-based fault signal active fault-tolerant network model;

[0070] The training sample set and the validation sample set are input into the BiLSTM neural network for training. The BiLSTM training method uses the values ​​of the first three time periods to predict the value of the next time period. This results in a BiLSTM-based fault signal active fault-tolerant network model for each navigation sensor.

[0071] S43: Evaluation of BiLSTM-based fault signal active fault-tolerant network model;

[0072] The test samples are input into the BiLSTM-based fault signal active fault-tolerant network model, and the performance indicators of the BiLSTM-based fault signal active fault-tolerant network model are evaluated according to the output results.

[0073] Preferably, constructing an active fault-tolerance method based on FKPCA-SVM-BiLSTM in step S5 includes:

[0074] S51: data input;

[0075] Receive and record the data returned by the navigation sensor;

[0076] S52: data preprocessing;

[0077] Use the sliding window method to segment the data, and then use the maximum-minimum value normalization method to complete the data preprocessing;

[0078] S53: Feature extraction;

[0079] The FKPCA method is used to extract features from the preprocessed data;

[0080] S54: Fault detection;

[0081] The extracted features are input into the trained SVM classification model for fault detection. If the SVM classification model detects that the sensor data is fault-free, the original signal of the sensor is directly output; if the SVM classification model detects that the sensor data is faulty, step S55 is executed;

[0082] S55: dynamic prediction;

[0083] The valid data of the three moments before the fault point is located is input into the BiLSTM neural network for prediction. For example, at time t, an abnormal observation value x is detected. t When the fault signal active fault-tolerant network model based on BiLSTM of the corresponding sensor is automatically activated, the sliding window data (x t-3 ,x t-2 ,x t-1 ) as input, and the predicted value y at the fault moment is obtained through forward propagation calculation t ;

[0084] When a short-term continuous fault occurs, and the fault is detected at time t and time t+1, a recursive method is used to perform dynamic prediction, and the predicted value y at time t is t As the end data of the sliding window at time t+1, the data input to the BiLSTM-based fault signal active fault-tolerant network model is (x t-2 ,x t-1 ,y t ), the BiLSTM fault-tolerant model predicts the output as y t+1 .

[0085] Preferably, in step S24, the contribution rate Gi Starting from the largest eigenvalue, the accumulation is continued until the υth eigenvalue reaches 80% of the preset value, and the eigenvectors corresponding to the first υ eigenvalues ​​are retained.

[0086] Preferably, in step S41, a sliding window length of 3 seconds and a sliding step length of 1 second are selected to segment the data to generate a sample set, and training samples, verification samples, and test samples are prepared in a ratio of 7:2:1.

[0087] Preferably, in step S42, the BiLSTM neural network model architecture consists of 1 input layer, a hidden layer consisting of 3 BiLSTM layers, 1 fully connected layer and 1 regression layer, wherein each BiLSTM layer contains 100 hidden units. In the BiLSTM-based fault signal active fault-tolerant network model, the hidden layer contains 3 layers of bidirectional LSTM, the first two layers output the complete time series to retain the dynamic characteristics of the time series, the third layer extracts the hidden state of the last time step, the fully connected layer maps the high-dimensional hidden state output by the third BiLSTM layer to 1 dimension, and the regression layer calculates the mean square error loss function MSE and performs parameter optimization by back propagation.

[0088] Preferably, in the training process of the BiLSTM-based fault signal active fault-tolerant network model in step S42, the Adam optimizer is selected, the initial learning rate is set to 0.005, the batch size is 32, a total of 100 rounds of training are performed, and the validation set is combined to monitor whether overfitting occurs.

[0089] The beneficial effects of the present invention are as follows: the data is segmented and preprocessed using a sliding window method, which effectively captures the temporal characteristics of the navigation sensor; the kernel principal component analysis method is used to map the data to a high-dimensional feature space, and the feature matrix of each sliding window is extracted, and the feature matrix is ​​normalized using the Frobenius norm, which can effectively capture the changes in the total energy of each window; the SVM fault detection model is used to achieve accurate detection of navigation sensor faults; the BiLSTM neural network can simultaneously capture the temporal dependencies of navigation sensor data, thereby effectively learning the time series characteristics of the sensor; finally, an active fault-tolerant experimental scheme based on the FKPCA-SVM-BiLSTM neural network model is designed, which verifies that the model has certain detection performance and fault-tolerant processing capabilities under different fault conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In the attached figure:

[0091] Figure 1 Flowchart of the active fault-tolerance method of FKPCA-SVM-BiLSTM proposed in the present invention;

[0092] Figure 2 This is the sliding window data processing diagram proposed by the present invention;

[0093] Figure 3 This is the FKPCA feature extraction flow chart proposed by the present invention;

[0094] Figure 4 Flowchart of the fault detection method using the SVM classification model proposed in the present invention;

[0095] Figure 5 This is a framework diagram of the BiLSTM-based fault signal active fault-tolerant network model proposed in the present invention;

[0096] Figure 6 This is the predicted performance diagram of GNSS under sudden fault conditions proposed by the present invention;

[0097] Figure 7 This is the predicted performance diagram of the IMU under sinusoidal fault proposed by the present invention;

[0098] Figure 8 This is the predicted performance diagram of UWB under sudden fault conditions proposed by the present invention. DETAILED DESCRIPTION

[0099] A navigation sensor fault detection and fault tolerance method, the method steps are as follows:

[0100] S1: The original data to be processed is segmented using a sliding window method, and the data in each sliding window is normalized;

[0101] S2: Apply the normalized data in step S1 and perform feature extraction using the FKPCA feature extraction method;

[0102] S3: Apply the features extracted in step S2 and input them into the SVM classification model for fault detection;

[0103] S4: Build a BiLSTM-based active fault-tolerant network model for fault signals. Use the BiLSTM neural network to predict the detected fault data and use the existing normal data to predict the fault data, thereby completing signal reconstruction.

[0104] S5: Construct an active fault tolerance method based on FKPCA-SVM-BiLSTM.

[0105] Obviously, based on the above: the data is segmented and preprocessed using the sliding window method, which effectively captures the temporal characteristics of the navigation sensor; the kernel principal component analysis method is used to map the data to a high-dimensional feature space, and the feature matrix of each sliding window is extracted, and the feature matrix is ​​normalized using the Frobenius norm, which can effectively capture the changes in the total energy of each window; the SVM classification model can be used to accurately detect navigation sensor faults; the BiLSTM neural network can simultaneously capture the temporal dependencies of navigation sensor data, thereby effectively learning the time series characteristics of the sensor; finally, an active fault-tolerant method based on the FKPCA-SVM-BiLSTM neural network model is designed, and it is verified that the model has certain detection performance and fault-tolerant processing capabilities under different fault conditions.

[0106] The design concept of this invention is as follows: an active fault-tolerance method based on FKPCA-SVM-BiLSTM is set up. A feature extraction module with FKPCA as the core is set up to extract deep-level feature expressions of fault signal changes, improving the reliability and detection accuracy of the system. Then, an SVM classification model is introduced to construct a fault detection model with FKPCA-SVM as the core to enhance the system's generalization ability when processing fault features and further improve prediction accuracy. Next, an active fault-tolerant network model of the fault signal is designed with BiLSTM as the core to obtain long-term dependencies between fault features at multiple moments, thereby improving the robustness of the control system in complex environments. Finally, an experimental scheme for fault detection and fault tolerance technology of navigation sensors is designed to analyze the detection performance and fault-tolerant processing capabilities of the model under different fault conditions.

[0107] Next, combine Figure 1 The FKPCA-SVM-BiLSTM fault-tolerant solution diagram shown in the figure introduces the method. The specific implementation steps are:

[0108] (1) Obtain navigation sensor data and preprocess it using sliding window normalization:

[0109] like Figure 2 As shown in the sliding window data processing diagram, assuming that the original data {x1,x2,x3,…,x n}, set the window size w = 10, the moving step size is 1, then the sliding window data at time t-2 is w t-2 ={x t-11 ,x t-10 ,x t-9 ,…,x t-2}, the sliding window data at time t-1 is w t-1 ={x t-10 ,x t-9 ,x t-8 ,…,x t-1}, and so on, the sliding window data at time t is w t ={x t-9 ,x t-8 ,x t-7 ,…,x t In fault information identification based on sliding windows, each time the window is slid, the data within the window needs to be normalized to eliminate the influence of different data ranges. This embodiment selects the maximum-minimum data normalization method, which is expressed as:

[0110]

[0111] Where x′ θ is the normalized data point, x θ is the original data point, w t is the data in a sliding window, min(w t ) is the minimum value in the sliding window data, max(w t ) is the maximum value within the sliding window data.

[0112] (2) Use FKPCA for feature extraction, the process is as follows Figure 3 As shown, the specific KPCA steps are as follows: take the normalized sliding window data as input data and take the i-th sliding window data as an example, w i =[x′ i-w+1 ,x′ i-w+2 ,…,x i ′] T , use the nonlinear mapping function Φ to map the input sample data from the original space to the high-dimensional feature space: Φ: d → D , where d is the dimension of the original space, D is the dimension of the high-dimensional space, and the mapped data is: Φ wi =[φ(x′ i-w+1 ),φ(x′ i-w+2 ),…,φ(x′ i )] T .

[0113] Then, linear principal component analysis is performed in this high-dimensional feature space. In the high-dimensional space, the covariance matrix C is defined as:

[0114]

[0115] The goal of principal component analysis is to find the eigenvalue λ of the covariance matrix C c and the eigenvector V c :

[0116] CV c =λ c Vc (3)

[0117] Substituting formula (2) into formula (3) yields:

[0118]

[0119] Since the mapping function φ(·) is not explicitly defined, Φ cannot be calculated. wi Φ wi T , so the kernel trick is introduced to implicitly calculate the inner product in high-dimensional space through the kernel matrix K:

[0120] K mn =K(x′ m ,x n ′)=(φ(x′ m )·φ(x n ′) T ) (5)

[0121] Among them, K(x′ m ,x n ′) is a kernel function, and the kernel function selected in the present invention is a radial basis kernel function, which is defined as:

[0122]

[0123] In high-dimensional space, data needs to be centralized, so the centralized matrix is ​​defined Replace K to achieve:

[0124]

[0125] Among them, 1 w is a w×w matrix with all elements being

[0126] Through the above kernel technique, the eigenvalue decomposition problem is transformed into the eigenvalue decomposition problem of the kernel matrix:

[0127]

[0128] in, is the eigenvalue of the kernel matrix, The order is arranged from large to small, γ is the eigenvector corresponding to the eigenvalue of the kernel matrix, γ={γ1,γ2,…,γ p};

[0129] In KPCA, the larger the eigenvalue, the more significant the change in that direction, and the more important the information reflected in the data. Generally, the first υ eigenvectors are selected to retain the principal components. While retaining the core features of the data to the maximum extent, it can also reduce the data dimension and reduce the complexity of the model. The selection of υ mainly depends on the cumulative contribution rate of the principal component. When the contribution rate reaches a certain proportion, it can represent the main information of the original data. First, the concept of contribution rate is introduced to calculate the contribution rate R of the eigenvalue. i :

[0130]

[0131] Among them, R i is the contribution rate of the i-th eigenvalue, is the i-th eigenvalue, is the sum of all eigenvalues, indicating the total variance of the data, and calculating the cumulative contribution rate G i :

[0132]

[0133] Contribution rate G i Starting from the largest eigenvalue, the accumulation is continued until the υth eigenvalue reaches the preset value, and the eigenvectors corresponding to the first υ eigenvalues ​​are retained. In this embodiment, the cumulative contribution rate G is set to i The benchmark is 80%, until the accumulated υth eigenvalue reaches 80% of the preset value, and the eigenvectors corresponding to the first υ eigenvalues ​​are retained;

[0134] Project the retained υ eigenvectors into the principal component space to obtain the score matrix T′:

[0135]

[0136] Where V = [γ1,γ2,…,γ υ ];

[0137] Calculate the Frobenius norm of the score matrix T′. The Frobenius norm reflects the overall energy of the projection of the data on the principal component by calculating the square root of the sum of the squares of all elements of the matrix. Therefore, it can effectively retain the main information in the original data. It is calculated as follows:

[0138]

[0139] Among them, ||·|| F represents the Frobenius norm, ι ij Represents any element in the score matrix.

[0140] (3) SVM fault detection is mainly divided into data set division and preprocessing, model training and model testing. The specific steps are as follows: Figure 4 As shown;

[0141] 1) Dataset division and preprocessing:

[0142] First, the method collects navigation sensor data from the drone, including three sensors: GNSS, IMU, and UWB. The collected sensor data is subjected to various fault simulations (sudden failure, ramp failure, and sinusoidal failure), resulting in four data labels for each sensor (normal + three types of failure). The four types of data for each sensor are divided into training and test sets. The training set is used to train the SVM model, and the test set is used to verify the detection performance of the trained model. The training and test sets are preprocessed by segmenting the data using a sliding window. The segmented data is then normalized using a maximum-minimum method to eliminate the influence of different data ranges.

[0143] 2) Model training:

[0144] ① Feature matrix construction: Input the preprocessed data of the four training sets of GNSS, IMU, and UWB in sequence, apply the FKPCA feature extraction method in step S2 to extract features from the data in sequence, and generate a feature matrix containing four types of samples for each sensor. Each row of the matrix corresponds to the eigenvalue of a sliding window (i.e., the calculation result of the Frobenius norm), and each column corresponds to a category.

[0145] ② Multi-classifier model training: Utilizing the SVM nonlinear classification method, combined with a one-on-one multi-classification approach, we train an SVM multi-classification model. Six SVM binary classifiers are constructed for each of the four sample types. The feature matrix and corresponding labels are input into the SVM classifier. This method uses radial basis kernel mapping to project low-dimensional features into a high-dimensional separable space. Model training is completed by optimizing the hyperplane decision boundary, ultimately yielding an SVM fault detection model.

[0146] 3) Model testing:

[0147] After preprocessing the test set data, feature extraction is performed using FKPCA, and these features are then input into the trained SVM model for fault detection. The SVM uses a multi-classifier voting mechanism to determine whether a fault exists: if the detection result is normal, a "no fault" is output; if an anomaly is detected, the specific fault type is output, ultimately completing fault detection and classification. Model evaluation of the SVM classifier for fault detection primarily includes metrics such as accuracy (ACC), false alarm rate (FAR), missed detection rate (MDR), and recall (REC). These metrics can be calculated using a confusion matrix. True positives (TP) represent the number of positive samples correctly predicted by the model, false positives (FP) represent the number of negative samples incorrectly predicted as positive by the model, true negatives (TN) represent the number of negative samples correctly predicted by the model, and false negatives (FN) represent the number of positive samples incorrectly predicted as negative by the model.

[0148] The confusion matrix can be used to determine various performance indicators. In model evaluation, ACC refers to the proportion of correct classifications in the model as a whole. The larger the value, the stronger the comprehensive discrimination ability of the model. The calculation formula is:

[0149]

[0150] FAR refers to the proportion of samples that are actually negative and are judged to be positive. The smaller the value, the better. The calculation formula is:

[0151]

[0152] MDR reflects the degree of failure to accurately identify samples that are actually positive, that is, the proportion of actual positive samples that are mistakenly judged as negative. The smaller the value, the better. The calculation formula is:

[0153]

[0154] REC refers to the proportion of correctly identified positive samples among all positive samples. The larger the value, the better the model capability. The calculation formula is:

[0155]

[0156] (4) For the faults detected by SVM, the BiLSTM neural network fault tolerance model is used to dynamically predict the faults. The valid data three moments before the fault point is located and input into the BiLSTM neural network for prediction. For example, at time t, an abnormal observation value x is detected. t When the fault occurs, the BiLSTM fault-tolerant prediction model of the corresponding sensor is automatically activated to extract the sliding window data (x t-3,x t-2 ,x t-1 ) as input, and the predicted value y at the fault moment is obtained through forward propagation calculation t If a short-term continuous fault occurs, if the fault is also detected at time t+1, a recursive method is used to perform dynamic prediction, and the predicted value y at time t is t As the end data of the sliding window at time t+1, the data input to the BiLSTM fault-tolerant prediction model is (x t-2 ,x t-1 ,y t ), the BiLSTM fault-tolerant model predicts the output as y t+1 The BiLSTM fault-tolerant model framework is shown in the figure below: Figure 5 As shown in Figure 2, the process is divided into three steps: data preprocessing, model training, and model evaluation. The specific steps are as follows:

[0157] 1) Data preprocessing

[0158] The output of navigation sensors has multi-dimensional and long time series characteristics. For example, the output of GNSS contains easting, northing, and celestial position coordinates, the output of IMU contains three-axis acceleration and angular velocity data, and the output of UWB contains ranging information. Therefore, this section adopts a dimension-based sliding window processing method to sequentially process the raw data into a 3*1 input matrix (single-dimensional data containing three consecutive time steps, such as GNSS easting data for a continuous 3-second period). In this embodiment, a sliding window length of 3 seconds and a sliding step size of 1 second are selected to segment the data to generate a sample set. Training samples, validation samples, and test samples are generated in a ratio of 7:2:1. The structure of the sample set is shown in Table 1:

[0159] Table 1 Sample set structure

[0160]

[0161] Among them, sample 1 uses the data (x1, x2, x3) from the 1st to the 3rd second of a certain dimension of the sensor as input data, and the data x4 at the 4th second as output data; sample 2 slides the time step of 1 second, uses the data (x2, x3, x4) from the 2nd to the 4th second as input data, and the data x5 at the 5th second as output data, and so on, to complete the production of all sample sets.

[0162] 2) Model training

[0163] The bidirectional stacking structure of the BiLSTM neural network fully captures the temporal dependencies of navigation sensors. The prepared sample sets (including training and validation samples) are fed into the BiLSTM neural network for training. The BiLSTM training method uses the values ​​of the previous three time periods to predict the value of the next time period, thereby obtaining a BiLSTM fault-tolerant prediction model for each navigation sensor.

[0164] The neural network model architecture set in this embodiment consists of 1 input layer, 3 BiLSTM layers, 1 fully connected layer and 1 regression layer, where each BiLSTM layer contains 100 hidden units. The training parameter configuration is shown in Table 2:

[0165] Table 2 Model parameter configuration

[0166]

[0167] In the BiLSTM fault-tolerant model, the hidden layer contains three layers of bidirectional LSTM. The first two layers output the complete time series to retain the dynamic characteristics of the time series. The third layer extracts the hidden state of the last time step. The fully connected layer maps the high-dimensional hidden state output by the third layer of BiLSTM to one dimension. The regression layer calculates the mean square error loss function (MSE) and optimizes the parameters by backpropagation. In this embodiment, the Adam optimizer is used for the entire training process, with an initial learning rate of 0.005 and a batch size of 32. A total of 100 rounds of training are performed, and the validation set is used to monitor whether overfitting occurs.

[0168] 3) Model evaluation

[0169] The model performance was evaluated using indicators such as root mean square error (RMSE), mean absolute error (MAE) and Pearson correlation coefficient (PCC).

[0170] RMSE reflects the difference between the predicted value and the actual measured value of the sensor. The smaller the RMSE, the better the prediction performance of the model. The RMSE calculation method is shown in formula (17):

[0171]

[0172] MAE represents the average of the absolute differences between the predicted value and the true observed value. The smaller the MAE, the smaller the model prediction error and the better the model performance. The calculation method is shown in formula (18):

[0173]

[0174] PCC reflects the correlation between the predicted value and the true observed value. The PCC value range is [-1, 1]. The closer the PCC is to 1, the better the model performance. The calculation method is shown in formula (19):

[0175]

[0176] In formulas (17) to (19), N represents the number of samples, y pred Represents the model prediction value, y actual Indicates the actual measurement value of the sensor. represents the average of the predicted values, Indicates the average value of the measured values.

[0177] (5) Establishment of fault data set

[0178] The navigation sensor dataset is derived from data generated by a mobile agent. The dataset used for model training consists of data collected during normal, continuous movement, recorded by sensors including GNSS and IMUs. The dataset used for model testing is generated by assuming different types of faults within specific time periods within the training dataset. Furthermore, UWB data simulates the dynamic ranging of a UAV by outputting real-time ranging information between a virtual UWB module and a mobile vehicle.

[0179] Navigation sensor faults can be divided into two categories based on the rate of change of the fault signal: sudden change faults and slow change faults. Based on the typical fault conditions of the actual system, three major fault categories are set as follows: (1) sinusoidal faults; (2) ramp faults; and (3) sudden change faults. The fault parameter settings and sample distribution are shown in Table 3:

[0180] Table 3 Fault signal parameters and sample distribution

[0181]

[0182] In Table 3, the fault time is set to 2000-3000 seconds, the fault amplitude is changed every 100 seconds, the sudden fault changes the size of ζ, the ramp fault changes the size of the slope k, and the sinusoidal fault changes the amplitude A, frequency f, and phase This is used to form a rich fault data set.

[0183] (6) Fault detection experiment

[0184] In order to intuitively show the classification and detection capabilities of the FKPCA-SVM detection model for different types of fault data, the evaluation indicators in the model are calculated, and the quantitative results are shown in Table 4:

[0185] Table 4 Performance indicators under different fault types

[0186]

[0187] Table 4 shows that the FKPCA-SVM module significantly outperforms other label types in detecting faults of categories 4, 8, 9, and 10. For samples with the remaining label types, the model's average recall rate reaches 98.22%. This result demonstrates that the fault detection module designed in this paper can more accurately capture changes in navigation sensor fault data, thereby significantly improving the accuracy and timeliness of fault detection.

[0188] (7) Active fault-tolerance experiment

[0189] Assume that the GNSS sensor east direction (x-axis) and north direction (y-axis) have a sudden fault generation interval set between 20 seconds and 40 seconds. Figure 6 The following is a comparison chart of the predicted output effects of GNSS sensors under sudden fault conditions. Figure 6 Analysis shows that when the detection system determines that the GNSS sensor's x-axis and y-axis are faulty, the difference between the BiLSTM-predicted output and the actual value at the fault location is not significant. Therefore, the BiLSTM-predicted value can be used to replace the fault data. Furthermore, compared with the LSTM model, the BiLSTM fault-tolerance model's prediction results are closer to the original normal sensor data corresponding to the fault period (blue dashed line). This further demonstrates that the FKPCA-SVM-BiLSTM active fault-tolerance method can better ensure that the fault-tolerance method is effective and timely.

[0190] The selected IMU sensor introduces a sinusoidal fault between the 92nd and 110th seconds. Figure 7 The figure shows the predicted output effect of the IMU sensor under the sinusoidal fault state. Figure 7 From the simulation results, although the prediction results of the BiLSTM fault-tolerant model and the LSTM model both show certain prediction capabilities, the output value predicted by the BiLSTM model is closer to the normal output of the sensor.

[0191] To verify the fault-tolerance model's adaptability to distance fault information output by the UWB sensor, three time periods with different distance change rates were selected. The intervals from 65 to 80 seconds and from 175 to 185 seconds exhibited gentle distance changes, allowing for the simulation of sudden faults by dropping UWB packets. The interval from 110 to 130 seconds exhibited rapid distance changes, allowing for the simulation of sudden faults by setting step values. Figure 8 The following figure shows the predicted output of the UWB under a sudden fault condition. Analysis of the figure shows that during the three fault time periods, the prediction results of the BiLSTM active fault-tolerance model are closer to the normal sensor output than those of the LSTM. While the overall trend of the LSTM prediction results is consistent with the normal sensor output, there is still a certain gap.

[0192] Furthermore, to quantitatively analyze the effectiveness of the BiLSTM active fault-tolerance model, we compared the quantitative indicators of the LSTM model. Different fault-tolerance models were implemented on the navigation sensor, and the corresponding indicator parameter values ​​were calculated. The fault-tolerance performance indicators such as RMSE, MAE, and PCC were obtained, as shown in Table 5.

[0193] Table 5 Performance comparison of different fault-tolerant models

[0194]

[0195]

[0196] Comparative analysis shows that the prediction indicators of the BiLSTM model on various data are significantly better than those of the LSTM model, indicating that it has stronger fault tolerance.

[0197] First, the performance indicators of the GNSS sensor show that the BiLSTM model's RMSE (2.14m) and MAE (1.83m) are significantly lower than those of the LSTM model (RMSE = 9.632m, MAE = 8.650m), with error reductions of 77.8% and 78.8%, respectively. This demonstrates that BiLSTM improves prediction accuracy by modeling bidirectional time series features, effectively avoiding the accuracy degradation of LSTM due to unidirectional time series processing. Furthermore, the PCC index for both BiLSTM and LSTM reaches 1.000, indicating that both models have a strong linear correlation between GNSS prediction results and true values. This also demonstrates that time series neural network models have strong learning and modeling capabilities for time series sensor data.

[0198] Secondly, for IMU sensors, BiLSTM achieves lower RMSE (0.018g) and MAE (0.013g) in acceleration prediction than LSTM (RMSE = 0.021g, MAE = 0.015g), with error reductions of 14.3% and 13.3%, respectively. It also boasts a higher PCC (0.953), demonstrating that BiLSTM can more accurately capture the temporal correlation of acceleration signals. In angular velocity prediction, BiLSTM achieves lower RMSE (0.263° / s) and MAE (0.184° / s) than LSTM (RMSE = 0.367° / s, MAE = 0.249° / s), and its PCC (0.9164) is closer to 1, demonstrating superior overall performance.

[0199] Finally, the UWB sensor's metrics further validated the BiLSTM's superior fault-tolerance performance: its distance prediction RMSE (2.242m) and MAE (2.018m) were both approximately 75% lower than those of the LSTM (9.078m and 8.185m). The PCCs for the BiLSTM and LSTM were 0.99 and 1.00, respectively, indicating a strong linear correlation between the predictions of both models and the true values.

[0200] Overall, time series neural networks can effectively extract time series features when processing navigation sensor data and have a certain degree of fault tolerance. Specifically, the BiLSTM neural network model, with its bidirectional time series modeling capabilities, demonstrated higher accuracy in predicting navigation sensor failures.

Claims

1. A navigation sensor fault detection and fault tolerance method, characterized in that: The method steps are as follows: S1: The original data to be processed is segmented using a sliding window method, and the data in each sliding window is normalized; S2: Apply the normalized data in step S1 and perform feature extraction using the FKPCA feature extraction method; S3: Apply the features extracted in step S2 and input them into the SVM classification model for fault detection; S4: Build a BiLSTM-based active fault-tolerant network model for fault signals. Use the BiLSTM neural network to predict the detected fault data and use the existing normal data to predict the fault data, thereby completing signal reconstruction. S5: Construct an active fault tolerance method based on FKPCA-SVM-BiLSTM.

2. A navigation sensor fault detection and fault tolerance method according to claim 1, characterized in that: In step S1: Divide the long time series data of the navigation sensor into multiple short sub-time series: The original data is: {x1,x2,x3,…,x n }, set the window size w=10 and the moving step size to 1; The sliding window data at time t-2 is: w t-2 ={x t-11 ,x t-10 ,x t-9 ,…,x t-2 }; The sliding window data at time t-1 is: w t-1 ={x t-10 ,x t-9 ,x t-8 ,…,x t-1 }; By analogy, the sliding window data at time t is: w t ={x t-9 ,x t-8 ,x t-7 ,…,x t }; The maximum-minimum data normalization method is selected to process the original data. The formula is expressed as: Where x′ θ is the normalized data point, x θ is the original data point, w t is the data in a sliding window, min(w t ) is the minimum value in the sliding window data, max(w t ) is the maximum value within the sliding window data.

3. A navigation sensor fault detection and fault tolerance method according to claim 2, characterized in that: In step S2, the FKPCA feature extraction method is used for feature extraction: S21: i-th sliding window data w i :w i =[x′ i-w+1 ,x′ i-w+2 ,…,x′ i ] T ; Use the nonlinear mapping function Φ to map the input sample data from the original space to the high-dimensional feature space: F: d → D Among them, d is the dimension of the original space, D is the dimension of the high-dimensional space, and the mapped data is: F wi =[φ(x′ i-w+1 ),φ(x′ i-w+2 ),…,φ(x′ i )] T Among them, φ(x′ i ) is the i-th data mapped to the high-dimensional space; S22: Perform linear principal component analysis in high-dimensional feature space. In high-dimensional space, the covariance matrix C is defined as: because: CV c =λ c V c (3) Substituting formula (2) into formula (3) yields: S23: Introducing the kernel technique, implicitly calculating the inner product in high-dimensional space through the kernel matrix K: K mn =K(x′ m ,x′ n )=(φ(x′ m )·φ(x′ n ) T ) (5) Among them, K(x′ m ,x′ n ) is the kernel function, which is the radial basis kernel function and is defined as: In high-dimensional space, data is centralized and the centralization matrix is ​​defined Replace K: Among them, 1 w is a w×w matrix with all elements being Convert the eigenvalue decomposition problem into the eigenvalue decomposition problem of the kernel matrix: in, is the eigenvalue of the kernel matrix, The order is arranged from large to small, γ is the eigenvector corresponding to the eigenvalue of the kernel matrix, γ={γ1,γ2,…,γ p }; S24: Calculate the contribution rate R of the eigenvalue i : Among them, R i is the contribution rate of the i-th eigenvalue, is the i-th eigenvalue, is the sum of all eigenvalues, indicating the total variance of the data, and calculating the cumulative contribution rate G i : Contribution rate G i Start accumulating from the largest eigenvalue until the υth eigenvalue reaches the preset value, and retain the eigenvectors corresponding to the first υ eigenvalues; S25: Project the retained υ eigenvectors into the principal component space to obtain the score matrix T′: Where, V=[γ1,γ2,…,γ υ ]; Calculate the Frobenius norm of the score matrix T′: Among them, ||·|| F represents the Frobenius norm, ι ij Represents any element in the score matrix.

4. A navigation sensor fault detection and fault tolerance method according to claim 3, characterized in that: In step S3: S31: Dataset partitioning and preprocessing for SVM classification model; Acquire navigation sensor data, including GNSS, IMU, and UWB sensors. Perform various fault simulations on the collected sensor data. Sensor faults include sudden faults, ramp faults, and sinusoidal faults. Each sensor corresponds to four types of data labels, including three types of fault labels and a normal label. The four types of data for each sensor are divided into training and test sets for the SVM classification model. The data in the training and test sets of the SVM classification model are preprocessed using a sliding window to segment the data. The segmented data is then normalized using maximum-minimum normalization. S32: SVM classification model training; S321: Construction of feature matrix of SVM classification model; Input the preprocessed data of the four training sets corresponding to GNSS, IMU, and UWB in sequence, apply the FKPCA feature extraction method in step S2 to perform feature extraction, and generate a feature matrix containing four types of samples for each sensor. Each row of the matrix corresponds to the eigenvalue of a sliding window, that is, the calculation result of the Frobenius norm, and each column corresponds to a category. S322: SVM classification model training; Using the SVM nonlinear classification method, combined with the "one-to-one" multi-classification method, the SVM classification model was trained. For the four types of samples, six SVM binary classifiers were constructed. The feature matrix and the corresponding labels were input into the SVM classifier. The low-dimensional features were projected into a high-dimensional separable space through radial basis kernel mapping. The model training was completed by optimizing the hyperplane decision boundary, and the SVM classification model was finally obtained. S323: SVM classification model testing; For the preprocessed data of the test set, the FKPCA feature extraction method in step S2 is applied to extract features, and the features are input into the trained SVM classification model for fault detection. The SVM classification model uses a multi-classifier voting mechanism to determine whether there is a fault. If the detection result is normal, the output is no fault; If an anomaly is detected, the specific fault type is output, and finally the fault detection and classification are completed. The output results of the SVM classification model are compared with the actual sample labels corresponding to the test set to evaluate the SVM classification model.

5. The navigation sensor fault detection and fault tolerance method according to claim 4, characterized in that: In step S4: S41: Data processing of BiLSTM-based fault signal active fault-tolerant network model; The output of the navigation sensor has multi-dimensional and long time series characteristics. The GNSS output includes easting, northing, and celestial position coordinates, the IMU output includes three-axis acceleration and angular velocity data, and the UWB output includes ranging information. Using a dimension-based sliding window processing method, the raw data is sequentially processed into a 3*1 input matrix containing single-dimensional data of three consecutive time steps. The data is segmented to generate a sample set, and the sample set is divided into training samples, verification samples, and test samples according to a preset ratio. S42: Training of BiLSTM-based fault signal active fault-tolerant network model; The training sample set and the validation sample set are input into the BiLSTM neural network for training. The BiLSTM training method uses the values ​​of the first three time periods to predict the value of the next time period. This results in a BiLSTM-based fault signal active fault-tolerant network model for each navigation sensor. S43: Evaluation of BiLSTM-based fault signal active fault-tolerant network model; The test samples are input into the BiLSTM-based fault signal active fault-tolerant network model, and the performance indicators of the BiLSTM-based fault signal active fault-tolerant network model are evaluated according to the output results.

6. The navigation sensor fault detection and fault tolerance method according to claim 5, characterized in that: In step S5, the active fault tolerance method based on FKPCA-SVM-BiLSTM is constructed, including: S51: data input; Receive and record the data returned by the navigation sensor; S52: data preprocessing; Use the sliding window method to segment the data, and then use the maximum-minimum value normalization method to complete the data preprocessing; S53: Feature extraction; The FKPCA method is used to extract features from the preprocessed data; S54: Fault detection; The extracted features are input into the trained SVM classification model for fault detection. If the SVM classification model detects that the sensor data is fault-free, the original signal of the sensor is directly output; if the SVM classification model detects that the sensor data is faulty, step S55 is executed; S55: dynamic prediction; The valid data of the three moments before the fault point is located is input into the BiLSTM neural network for prediction. For example, at time t, an abnormal observation value x is detected. t When the fault signal active fault-tolerant network model based on BiLSTM of the corresponding sensor is automatically activated, the sliding window data (x t-3 ,x t-2 ,x t-1 ) as input, and the predicted value y at the fault moment is obtained through forward propagation calculation t ; When a short-term continuous fault occurs, and the fault is detected at time t and time t+1, a recursive method is used to perform dynamic prediction, and the predicted value y at time t is t As the end data of the sliding window at time t+1, the data input to the BiLSTM-based fault signal active fault-tolerant network model is (x t-2 ,x t-1 ,y t ), the BiLSTM fault-tolerant model predicts the output as y t+1 .

7. The navigation sensor fault detection and fault tolerance method according to claim 3, characterized in that: In step S24, the contribution rate G i Starting from the largest eigenvalue, the accumulation is continued until the υth eigenvalue reaches 80% of the preset value, and the eigenvectors corresponding to the first υ eigenvalues ​​are retained.

8. The navigation sensor fault detection and fault tolerance method according to claim 5, characterized in that: In step S41, a sliding window length of 3 seconds and a sliding step size of 1 second are selected to segment the data to generate a sample set, and training samples, verification samples, and test samples are prepared in a ratio of 7:2:

1.

9. The navigation sensor fault detection and fault tolerance method according to claim 5, characterized in that: In step S42, the BiLSTM neural network model architecture consists of 1 input layer, a hidden layer consisting of 3 BiLSTM layers, 1 fully connected layer and 1 regression layer, where each BiLSTM layer contains 100 hidden units. In the BiLSTM-based fault signal active fault-tolerant network model, the hidden layer contains 3 layers of bidirectional LSTM. The first two layers output the complete time series to retain the dynamic characteristics of the time series. The third layer extracts the hidden state of the last time step. The fully connected layer maps the high-dimensional hidden state output by the third BiLSTM layer to 1 dimension. The regression layer calculates the mean square error loss function MSE and optimizes the parameters by back propagation.

10. The navigation sensor fault detection and fault tolerance method according to claim 9, characterized in that: In step S42, during the training of the BiLSTM-based fault signal active fault-tolerant network model, the Adam optimizer is selected, the initial learning rate is set to 0.005, the batch size is 32, a total of 100 rounds of training are performed, and the validation set is used to monitor whether overfitting occurs.

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