A multi-sensor failure compensation method based on high-dimensional feature reconstruction

Abstract

The application belongs to the technical field of structural health management, and particularly relates to a multi-sensor failure compensation method based on high-dimensional feature reconstruction, comprising: initializing algorithm parameters, acquiring monitoring data by using multi-sensors, and converting the monitoring data into a matrix; standardizing observation values of the matrix to obtain a standardized data matrix, and obtaining a covariance matrix in a subspace after dimension reduction; based on an ADMM method, decomposing the covariance matrix in the subspace after dimension reduction to obtain a low-rank matrix and a sparse matrix; reconstructing missing sensor data based on the low-rank matrix and the sparse matrix to obtain a reconstructed sensor vector. The aviation aircraft sensor failure compensation algorithm based on high-dimensional feature reconstruction fully considers the coupling relationship between sensors and real-time requirements, significantly improves the prediction accuracy under the condition of missing fault sensors, and is suitable for wide application of various aircrafts such as civil aviation passenger planes and unmanned aerial vehicles.

Description

Technical Field

[0001] This application belongs to the field of structural health management technology, and specifically relates to a multi-sensor failure compensation method based on high-dimensional feature reconstruction. Background Technology

[0002] As modern aircraft structures become increasingly complex, numerous sensors (such as strain gauges, accelerometers, and pressure sensors) are deployed on the fuselage to monitor stress and vibration in critical components like wings and fuselages in real time. Load prediction algorithms based on this sensor data can quickly and accurately estimate structural loads during flight, helping aircraft avoid potential structural fatigue and safety risks. However, sensor failure is inevitable under harsh flight conditions or during long-term service. As sensor failure rates continue to rise, the usable dimensions of monitoring data decrease significantly, leading to the failure of load prediction algorithms and severely impacting flight safety and maintenance decisions.

[0003] Therefore, reconstructing fault sensor data is essential. Current methods for reconstructing fault sensor data mainly include:

[0004] 1. Linear interpolation and spline interpolation: These methods perform one-dimensional or multi-dimensional interpolation on missing sensor data, such as forward / backward padding, linear interpolation, and spline interpolation. However, they are only suitable for smooth, continuously changing scenarios and cannot capture local high-frequency changes. When multiple sensors fail simultaneously, the accuracy of time-series interpolation decreases significantly.

[0005] 2. Missing value imputation based on machine learning: such as KNN imputation, simple regression imputation, random forest / gradient boosting, and other predictive model imputation. The problems with this type of method are: when the sensor dimension p > 50, the overhead of nearest neighbor search or model training increases significantly; sufficient historical samples are needed to train the regressor, otherwise it cannot accurately map complex aerodynamic load characteristics; and the generalization ability across operating conditions is unstable, such as modeling bias under different aircraft attitudes and different airflow conditions.

[0006] 3. Finite element simulation or physical calculation: Using a high-precision finite element model, physical inversion and interpolation are performed on missing sensor values. This method requires pre-storing a large-scale mesh model, consuming significant computational resources; it is difficult to adapt to real-time monitoring, and a single simulation typically takes hundreds of milliseconds to several seconds, which does not meet the requirements of high-frequency data updates.

[0007] 4. Traditional statistical imputation: such as mean imputation, median imputation, mode imputation, etc. The disadvantage of this type of method is that it destroys the correlation structure of the original data, ignores the coupling relationship between different sensors, and causes severe distortion in high-dimensional coupled flight payload scenarios.

[0008] While traditional fault sensor data reconstruction methods offer some compensation in everyday scenarios with missing data, they struggle to accurately reconstruct high-dimensional coupled data when sensors experience widespread or multi-point failures. This is primarily due to the following reasons:

[0009] (1) High-dimensional coupling features are ignored: interpolation or simple statistical filling cannot take into account both the mechanical coupling between sensors and the overall trend, resulting in a large error in the load distribution reconstruction;

[0010] (2) Poor robustness to multi-sensor failure: Traditional machine learning methods are highly dependent on training samples. Once the failure mode is different from the existing data distribution, the reconstruction is severely distorted.

[0011] (3) It is difficult to balance real-time performance and accuracy: Finite element simulation has high accuracy but huge computational cost. KNN filling also has a sharp drop in search efficiency when the sensor dimension is very high, making it impossible to achieve 100Hz level real-time monitoring.

[0012] Therefore, how to more effectively reconstruct sensor data is a problem that needs to be solved. Summary of the Invention

[0013] To address the aforementioned issues, this application provides a multi-sensor failure compensation method based on high-dimensional feature reconstruction, thereby resolving the problem of low accuracy in sensor data reconstruction in existing technologies.

[0014] The technical solution of this application is: a multi-sensor failure compensation method based on high-dimensional feature reconstruction, comprising:

[0015] Initialize algorithm parameters and acquire monitoring data using multiple sensors, then convert the monitoring data into a matrix. ;

[0016] For matrix The observed values ​​are standardized to obtain the standardized data matrix. After dimensionality reduction, the covariance matrix in the subspace is obtained. ;

[0017] Based on the ADMM method, the covariance matrix in the dimensionality-reduced subspace Decomposition yields a low-rank matrix. sparse matrix ;

[0018] Based on low-rank matrix sparse matrix The missing sensor data is reconstructed to obtain the reconstructed sensor vectors.

[0019] Preferably, the initialization algorithm parameters include the number of principal components n_components retained after PCA dimensionality reduction; and the nuclear norm regularization parameter of the low-rank matrix L. L1 norm regularization parameter of sparse matrix S The maximum number of iterations for the ADMM optimization algorithm Penalty parameters in ADMM Algorithm convergence threshold .

[0020] Preferably, the matrix for:

[0021] ;

[0022] in: For the sample size, For sensor dimensions; sensors that have failed are located in the matrix. Set an empty value in the corresponding position.

[0023] Preferably, for the matrix Missing position in use Perform initial imputation to obtain the standardized data matrix. , matrix Standardizing the observed values, we get:

[0024] ;

[0025] in Each is a matrix The Middle The mean and standard deviation of samples at non-missing locations are listed. A set consisting of the row and column indices of the observed values.

[0026] Preferably, the standardized data matrix Perform PCA dimensionality reduction.

[0027] Preferably, They are respectively:

[0028] ;

[0029] .

[0030] Preferably, the covariance matrix in the subspace is obtained. The process is as follows:

[0031] make This represents the standardized data matrix, which still has a size of 1. ;

[0032] Calculate the sample covariance matrix:

[0033] ;

[0034] For the sample covariance matrix Perform eigenvalue decomposition:

[0035] ;

[0036] in The eigenvector matrix, For eigenvalue diagonal matrices And assume ;

[0037] Take before The eigenvectors form the projection matrix:

[0038] ;

[0039] Dimensionally reduced data is obtained using the projection matrix and the standardized data matrix:

[0040] ;

[0041] And calculate the covariance matrix in the subspace:

[0042] .

[0043] Preferably, the covariance matrix in the dimensionality-reduced subspace The specific method for decomposition is as follows:

[0044] The optimization objective is defined as follows:

[0045]

[0046]

[0047] in: Represents a low-rank matrix nuclear norm number, Representing a sparse matrix The L1 norm, express It is a positive semi-definite matrix. For use in controlling low-rank matrices The regularization parameter for the nuclear norm penalty strength, β, is used to control the sparse matrix. The regularization parameter for the L1 norm penalty strength;

[0048] The optimization objective can be rewritten as an augmented Lagrange function as follows:

[0049]

[0050] in: Let the variables be Lagrange dual variables. For penalty parameters; Describing the Lagrange dual variable The inner product with the constraint residuals; This represents the squared Frobenius norm of the constraint residuals;

[0051] The low-rank matrix is ​​obtained by iterative solution. sparse matrix .

[0052] Preferably, the specific method for iterative solution is as follows:

[0053] 1) Update Projected onto a positive semidefinite space

[0054] ;

[0055] in For the first The sparse matrix obtained in the second iteration estimate, This represents the operator that projects a matrix onto a positive semi-definite cone;

[0056] 2) To Apply nuclear norm thresholding to obtain

[0057] ;

[0058] in The soft threshold operator represents singular values;

[0059] 3) Apply an L1 soft threshold to the residuals to obtain... :

[0060] ;

[0061] in It is an element-level soft threshold operator;

[0062] 4) Update the Lagrange dual variable

[0063] ;

[0064] 5) Check convergence: Stop iteration if the following norms satisfy a certain threshold:

[0065] .

[0066] Preferably, during iterative solution, , , The initial values ​​of the matrices are all zeros.

[0067] Preferably, based on a low-rank matrix sparse matrix Reconstructing the missing sensor data, specifically:

[0068] Suppose a certain part of the observation vector is missing. The set of missing indices is The set of observation indexes is :

[0069] Step 4.1: Impute missing values ​​with the mean to obtain the initial estimated vector. ;

[0070] Step 4.2: For the initial estimated vector Normalization is performed to obtain the normalized estimated vector. Then project it onto the PCA subspace to obtain ;

[0071] Step 4.3: Based on the set of missing indices and observation index set , for The blocks are as follows:

[0072] ;

[0073] in, Represents the covariance submatrix between observation sensors; This represents the covariance submatrix of the observed sensor and the missing sensor; This represents the covariance submatrix between the missing sensor and the observed sensor. Represents the covariance submatrix among the missing sensors;

[0074] The subspace coordinates can also be divided into blocks accordingly:

[0075] ;

[0076] Establish conditional expectations: This yields the complete subspace representation:

[0077] ;

[0078] Step 4.4: Inverse project the subspace to the original dimension

[0079] ;

[0080] ;

[0081] in This represents element-wise multiplication. A vector of mean and standard deviation;

[0082] Step 4.5: Replace the missing index with the estimated value obtained in Step 4.4:

[0083] .

[0084] Preferably, the reconstructed sensor vector is:

[0085] .

[0086] The multi-sensor failure compensation method based on high-dimensional feature reconstruction proposed in this application has the following advantages:

[0087] The aircraft sensor failure compensation algorithm based on high-dimensional feature reconstruction fully considers the coupling relationship between sensors and the real-time requirements, significantly improving the prediction accuracy in the case of missing faulty sensors. It is suitable for a wide range of applications in various aircraft such as civil airliners and drones. At the same time, this algorithm can also be used in other high-dimensional data missing scenarios.

[0088] Balancing overall and local features: By capturing the overall stress distribution and modes of the structure through low-rank kernel norms and identifying abrupt changes in fault points through sparse terms, it still has excellent reconstruction accuracy in scenarios with multiple missing points.

[0089] Tolerance for multiple failures: Even when the number of failed nodes is as high as 20% or even 40%, the method of this invention can still obtain stable reconstruction results;

[0090] High real-time performance: The subspace dimension obtained by dimensionality reduction is much smaller than the original dimension, which can control the reconstruction iteration overhead in milliseconds, making it suitable for real-time health monitoring. Attached Figure Description

[0091] Figure 1 This is a schematic diagram of the overall process of this application;

[0092] Figure 2 This is a graph showing the trend of the predicted indicators in this application as sensor failures increase;

[0093] Figure 3 This is a schematic diagram comparing the performance of different reconstruction algorithms and HDCR in this application;

[0094] Figure 4 This is a diagram illustrating the comparison of the algorithm's running efficiency in this application. Detailed Implementation

[0095] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0096] The first aspect of this application provides a multi-sensor failure compensation method based on high-dimensional feature reconstruction, such as... Figure 1 As shown, it includes the following steps:

[0097] Step 1: Initialize algorithm parameters and acquire monitoring data using multiple sensors, then convert the monitoring data into a matrix. .

[0098] The initialization algorithm parameters include:

[0099]

[0100] Where: n_components represents the number of principal components retained after PCA dimensionality reduction; The nuclear norm (sum of singular values) regularization parameter represents the low-rank matrix L; The L1 norm regularization parameter represents the sparse matrix S; This indicates the maximum number of iterations for the ADMM optimization algorithm; This represents the penalty parameter (augmented Lagrange factor) in ADMM. This represents the threshold for determining algorithm convergence.

[0101] Preferably, monitoring data such as stress, pressure, and vibration are acquired from various sensors on the aircraft and recorded as a matrix. ,for:

[0102] ;

[0103] in: For the sample size, For sensor dimensions;

[0104] If some sensors fail at certain times, it will affect the matrix. The corresponding position contains a null value (NaN). For example, suppose sensors #5 and #8 fail at some point.

[0105] Define the set of exact locations as:

[0106] Create a set from the row and column indices of the missing values:

[0107] ;

[0108] The set of locations of the observations is

[0109]

[0110] Step 2, for the matrix The observed values ​​are standardized to obtain the standardized data matrix. After dimensionality reduction, the covariance matrix in the subspace is obtained. .

[0111] For matrix The observed values ​​are standardized as follows:

[0112] For each sensor (for the matrix) Calculate the sample mean and standard deviation for non-missing locations (from one column in the observation set). Inside:

[0113] ;

[0114] ;

[0115] in, This is the arithmetic mean of the valid data (non-missing values) from the j-th sensor; Let be the standard deviation of the j-th sensor, which is the degree of dispersion of the data around its mean. The subtraction of 1 from the denominator in the square root is to obtain an unbiased estimate.

[0116] For missing positions Then use Alternatively, use other interpolation methods for initial filling to facilitate subsequent PCA processing.

[0117] Preferably, PCA dimensionality reduction is applied to remove sensor errors caused by multicollinearity and reduce subsequent computational load.

[0118] make This represents the standardized data matrix, which still has a size of 1. ;

[0119] Calculate the sample covariance matrix:

[0120] ;

[0121] For the sample covariance matrix Perform eigenvalue decomposition:

[0122] ;

[0123] in The eigenvector matrix, For eigenvalue diagonal matrices And assume ;

[0124] Take before The eigenvectors form the projection matrix:

[0125] ;

[0126] Dimensionally reduced data is obtained using the projection matrix and the standardized data matrix:

[0127] ;

[0128] And calculate the covariance matrix in the subspace:

[0129] .

[0130] Step 3: Considering the characteristics of sensor data in the aviation field (high dimension, high correlation, sparse faults), the low-rank terms are regarded as the inherent structure of the data, and the sparse terms are regarded as abnormal / fault components. Thus, the sensor fault reconstruction problem is transformed into a low-rank + sparse decomposition problem of the covariance matrix.

[0131] Based on the ADMM method, the covariance matrix in the dimensionality-reduced subspace Decomposition yields a low-rank matrix. sparse matrix ;

[0132] Preferably, the covariance matrix in the dimensionality-reduced subspace The specific method for decomposition is as follows:

[0133] The optimization objective is defined as follows:

[0134]

[0135]

[0136] in: Represents the nuclear norm (matrix) (the sum of singular values) L1 norm (matrix) (the sum of the absolute values ​​of the elements) express It is a positive semi-definite matrix. Used to control low-rank matrices The regularization parameter for the nuclear norm (sum of singular values) penalty strength, increasing α will make the model tend to include more information in the sparse anomaly matrix. β is used to control the sparse matrix. The regularization parameter for the L1 norm (sum of absolute values ​​of elements) penalty strength, increasing β means that the model tends to classify more information into the low-rank structure L;

[0137] The optimization objective can be rewritten as an augmented Lagrange function as follows:

[0138]

[0139] in: Let the variables be Lagrange dual variables. For penalty parameters; Describing the Lagrange dual variable The inner product with the constraint residuals; This represents the squared Frobenius norm of the constraint residuals;

[0140] The Frobenius norm is:

[0141]

[0142] A matrix can be viewed as a point in a high-dimensional space, and the Frobenius norm is the Euclidean distance from that point to the origin, used to measure the overall size of the matrix elements.

[0143] When optimizing the iterative solution, , , The initial values ​​of all matrices are set to all zeros, allowing the algorithm to discover the data structure itself and preventing the introduction of human bias.

[0144] The low-rank matrix is ​​obtained by iterative solution. sparse matrix .

[0145] Preferably, the specific method for iterative solution is as follows:

[0146] 1) Update Projected onto a positive semidefinite space

[0147] ;

[0148] in For the first The sparse matrix obtained in the second iteration It is estimated that, together with the positive semidefinite projection of the scaled Lagrange multipliers, it can be regarded as the "candidate update value" of the L matrix. This represents the operator that projects a matrix onto a positive semi-definite cone, i.e.:

[0149]

[0150] like If it is in the form of characteristic decomposition, then This means that all eigenvalues ​​less than 0 are truncated to 0.

[0151] 2) To Apply nuclear norm thresholding to obtain

[0152] ;

[0153] in The soft thresholding operator represents singular values; if If it is a singular value decomposition, then

[0154] .

[0155] 3) Apply an L1 soft threshold to the residuals to obtain... :

[0156] ;

[0157] in It is an element-level soft threshold operator:

[0158] .

[0159] 4) Update the Lagrange dual variable :

[0160] ;

[0161] 5) Check convergence: Stop iteration if the following norms satisfy a certain threshold:

[0162] .

[0163] Step 4, based on the low-rank matrix sparse matrix Reconstruct missing sensor data.

[0164] Specifically:

[0165] Suppose a certain part of the observation vector is missing. The set of missing indices is The set of observation indexes is :

[0166] Step 4.1: Fill in missing values ​​with the mean:

[0167] ;

[0168] Obtain the initial estimation vector ;

[0169] Step 4.2: For the initial estimated vector Normalization is performed:

[0170] ;

[0171] Obtain the normalized estimated vector Then project it onto the PCA subspace to obtain

[0172] .

[0173] Step 4.3: Refining and reconstructing within the subspace:

[0174] make This represents the low-rank covariance estimate obtained in step 3, with dimension . .

[0175] Missing index (Indices representing the set of missing sensors) and observation index (This represents the set of indices for the observation sensors, that is...) In the subspace coordinates of the complement of the set, further refinement is performed using conditional covariance.

[0176] Will The blocks are as follows:

[0177] ;

[0178] in, This represents the covariance submatrix between observation sensors (where rows and columns correspond to the sensors). ); Represents the covariance submatrix of the observed sensors and the missing sensors (rows correspond to observed sensors). The column corresponds to the missing sensor. ); This represents the covariance submatrix between the missing sensor and the observed sensor (rows correspond to missing sensor). The column corresponds to the observation sensor. ); This represents the covariance submatrix among the missing sensors (where each row and column corresponds to a missing sensor). ).

[0179] The subspace coordinates can also be divided into blocks accordingly:

[0180] ;

[0181] To estimate the missing part based on the known part, we can consider conditional expectation: ;

[0182] We obtain the complete subspace representation:

[0183] ;

[0184] Step 4.4: Inverse project the subspace to the original dimension

[0185] ;

[0186] ;

[0187] in This represents element-wise multiplication. A vector of mean and standard deviation;

[0188] Step 4.5: Replace the missing index with the estimated value obtained in Step 4.4:

[0189] .

[0190] Step 5: Obtain the reconstructed sensor vector.

[0191] The reconstructed sensor vector is:

[0192] .

[0193] The sensor vector no longer contains missing values ​​and can be directly used for aircraft load analysis and health assessment scenarios.

[0194] If a new faulty sensor is detected during subsequent monitoring, the above process can be repeated for the data at the corresponding time point, thereby reconstructing the data online or in batches to continuously obtain complete high-dimensional data.

[0195] The above is a description of the HDCR algorithm process. By performing "low-rank + sparse" decomposition in the dimensionality reduction space, combined with matrix decomposition and data reconstruction achieved by augmented Lagrange multiplication method (ADMM), it can still accurately estimate high-dimensional sensor data even in the presence of faults and sparse anomalies, providing stable and high-quality data input for subsequent data processing and prediction.

[0196] A comparative test will be conducted using a specific example to illustrate this:

[0197] To better illustrate the technical advantages of this application, the following compares the performance of traditional interpolation, KNN filling, and the HDCR of this invention in multi-sensor fault scenarios:

[0198] Scenario design: Taking a certain type of aircraft wing box assembly as an example, there are 120 strain sensors on the surface, and p ∈ [1, 3, 10, 20, 30, 40, 50, 60] random faults are selected;

[0199] Comparison methods: (1) Linear interpolation: interpolation is performed on the time-series missing points. (2) KNNImputer: k=5, the nearest neighbor is searched by Euclidean distance to fill in the missing points. (3) HDCR (this invention): n_components=15, alpha=0.1, beta=0.1.

[0200] Test results:

[0201] 1. Algorithm performance test

[0202] like Figure 2 The figure shows the change in the accuracy of the load prediction algorithm as the number of sensor failures increases, with the reconstructed data as input. It can be seen that after 30 sensors (25%) fail, the load algorithm can still maintain an excellent level (average error below 5%), after 40 sensors (33%) fail, the load algorithm can achieve a good level (average error below 15%), and after 50 sensors (42%) fail, the load algorithm can still achieve a passable level (average error below 25%).

[0203] 2. Algorithm Comparison Experiment

[0204] like Figure 3 The figure shows a performance comparison of different algorithms. It can be seen that, under different numbers of sensor failures (1, 3, 10, 20, 30, 40, 50, 60), the HDCR algorithm (red curve in the figure) has the best compensation effect, and all performance curves (MAE, RMSE, R2, maximum error, minimum error, average error) are optimal.

[0205] 3. Algorithm Real-Time Performance Test

[0206] As shown in Table 1 and Figure 4 The table shows the reconstruction time of the algorithms. It can be seen that among the three compensation algorithms, linear interpolation takes the shortest time, almost negligible, while KNN takes the longest. Figure 2 As can be seen, the linear interpolation algorithm has the largest error. Therefore, the algorithm of this invention can achieve a faster speed and the highest accuracy among all algorithms, meeting the needs of real-time monitoring and health prediction of aircraft.

[0207] Table 1 Comparison of Algorithm Real-Time Performance

[0208]

[0209] It is evident that in the event of multiple sensor failures, linear interpolation and KNNImputer face severe dimensionality issues or data distortion due to missing data, while the HDCR algorithm of this invention maintains good real-time performance while ensuring accuracy.

[0210] As can be seen from the detailed description of the above technical solution, the aircraft sensor failure compensation algorithm based on high-dimensional feature reconstruction in this application fully considers the coupling relationship between sensors and the real-time requirements, significantly improving the prediction accuracy in the case of missing faulty sensors. It is suitable for a wide range of applications in various aircraft such as civil airliners and drones. Furthermore, this algorithm can also be used in other high-dimensional data missing scenarios, such as wind turbine blade monitoring and chip structure health prediction, demonstrating good versatility and scalability.

[0211] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-sensor failure compensation method based on high-dimensional feature reconstruction, characterized in that, include: Initialize algorithm parameters and acquire monitoring data using multiple sensors, then convert the monitoring data into a matrix. ; For matrix The observed values ​​are standardized to obtain the standardized data matrix. After dimensionality reduction, the covariance matrix in the subspace is obtained. ; Based on the ADMM method, the covariance matrix in the dimensionality-reduced subspace Decomposition yields a low-rank matrix. sparse matrix ; Based on low-rank matrix sparse matrix The missing sensor data is reconstructed to obtain the reconstructed sensor vectors.

2. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 1, characterized in that, The initialization algorithm parameters include the number of principal components n_components retained after PCA dimensionality reduction; and the kernel norm regularization parameter of the low-rank matrix L. ; L1 norm regularization parameter of sparse matrix S The maximum number of iterations for the ADMM optimization algorithm Penalty parameters in ADMM Algorithm convergence threshold .

3. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 2, characterized in that, The matrix for: ； in: For the sample size, For sensor dimensions; sensors that have failed are located in the matrix. Set an empty value in the corresponding position.

4. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 2, characterized in that, For matrix Missing position in use Perform initial imputation to obtain the standardized data matrix. , matrix Standardizing the observed values, we get: ； in Each is a matrix The Middle The mean and standard deviation of samples at non-missing locations are listed. A set consisting of the row and column indices of the observed values.

5. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 4, characterized in that, For the standardized data matrix Perform PCA dimensionality reduction.

6. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 4, characterized in that, The They are respectively: ； 。 7. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 1, characterized in that, Obtain the covariance matrix in the subspace The process is as follows: make This represents the standardized data matrix, which still has a size of 1. ; Calculate the sample covariance matrix: ； For the sample covariance matrix Perform eigenvalue decomposition: ； in The eigenvector matrix, For eigenvalue diagonal matrices And assume ; Take before The eigenvectors form the projection matrix: ； Dimensionally reduced data is obtained using the projection matrix and the standardized data matrix: ； And calculate the covariance matrix in the subspace: 。 8. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 1, characterized in that, The covariance matrix in the dimensionality-reduced subspace The specific method for decomposition is as follows: The optimization objective is defined as follows: in: Represents a low-rank matrix nuclear norm number, Representing a sparse matrix The L1 norm, express It is a positive semi-definite matrix. For use in controlling low-rank matrices The regularization parameter for the nuclear norm penalty strength, β, is used to control the sparse matrix. The regularization parameter for the L1 norm penalty strength; The optimization objective can be rewritten as an augmented Lagrange function as follows: in: Let the variables be Lagrange dual variables. For penalty parameters; Describing the Lagrange dual variable The inner product with the constraint residuals; This represents the squared Frobenius norm of the constraint residuals; The low-rank matrix is ​​obtained by iterative solution. sparse matrix .

9. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 8, characterized in that, The specific method for iterative solution is as follows: 1) Update Projected onto a positive semidefinite space ； in For the first The sparse matrix obtained in the second iteration estimate, This represents the operator that projects a matrix onto a positive semi-definite cone; 2) To Apply nuclear norm thresholding to obtain ； in The soft threshold operator represents singular values; 3) Apply an L1 soft threshold to the residuals to obtain... : ； in It is an element-level soft threshold operator; 4) Update the Lagrange dual variable : ； 5) Check convergence: Stop iteration if the following norms satisfy a certain threshold: 。 10. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 9, characterized in that, When performing iterative solutions, , , The initial values ​​of the matrices are all zeros.

11. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 1, characterized in that, Based on low-rank matrix sparse matrix Reconstructing the missing sensor data, specifically: Suppose a certain part of the observation vector is missing. The set of missing indices is The set of observation indexes is : Step 4.1: Impute missing values ​​with the mean to obtain the initial estimated vector. ; Step 4.2: For the initial estimated vector Normalization is performed to obtain the normalized estimated vector. Then project it onto the PCA subspace to obtain ; Step 4.3: Based on the set of missing indices and observation index set , for The blocks are as follows: ； in, Represents the covariance submatrix between observation sensors; This represents the covariance submatrix of the observed sensor and the missing sensor; This represents the covariance submatrix between the missing sensor and the observed sensor. Represents the covariance submatrix among the missing sensors; The subspace coordinates can also be divided into blocks accordingly: ； Establish conditional expectations: This yields the complete subspace representation: ； Step 4.4: Inverse project the subspace back to the original dimension: ； ； in This represents element-wise multiplication. A vector of mean and standard deviation; Step 4.5: Replace the missing index with the estimated value obtained in Step 4.4: 。 12. The multi-sensor failure compensation method based on high-dimensional feature reconstruction as described in claim 11, characterized in that, The reconstructed sensor vector is: 。

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