Fault detection method based on sparse representation

Abstract

The invention belongs to the field of fault diagnosis, and particularly relates to a fault detection method based on sparse representation, and the method comprises the steps: a preprocessing step: collecting normal working condition data samples under a preset working condition, and constructing a fault dictionary matrix; a control limit determination step of determining a sparse representation reconstruction error control limit and a distance control limit interval based on the fault dictionary matrix; in the field monitoring step, working field data are collected, and sparse representation reconstruction error statistics and distance statistics are calculated; and a fault detection step: judging whether the system has a fault by comparing the relationship between the statistical magnitude and the control limit. According to the method, accurate detection can be carried out under the condition that data does not obey normal distribution, the method has high detection sensitivity to tiny faults, meanwhile, the method is suitable for industrial process data of Gaussian and non-Gaussian distribution, and the accuracy and reliability of fault detection are effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis, specifically a fault detection method based on sparse representation. Background Technology

[0002] In modern industrial processes, the requirements for system safety and reliability are constantly increasing. Fault detection is a key technology for ensuring safe system operation and improving system reliability, and it is also a crucial step in improving product quality. As system complexity increases and the amount of component data continues to grow, fault detection methods based on multivariate statistics are receiving increasing attention.

[0003] For example, fault detection methods based on principal component analysis (PCA) have been widely used. However, in actual industrial settings, the data available for fault detection does not necessarily conform to a Gaussian distribution. PCA-based fault detection methods fail to yield satisfactory results when detecting non-Gaussian distributed data. This is because when applying PCA for fault detection, the SPE and T... 2 A statistical measure can accurately determine control limits only when the data follows a normal distribution. In actual fault detection processes, data may not follow a normal distribution. Therefore, fault detection methods based on principal component analysis (PCA) cannot accurately determine control limits in some cases. Furthermore, non-normally distributed data processed by PCA loses some fault information, resulting in a decrease in the fault detection rate.

[0004] For minor faults, methods such as PCA have also failed to provide a good detection solution. This is because minor faults have small amplitudes, and the signals themselves contain noise, making it difficult to separate minor faults from noisy signals, thus resulting in a low fault detection rate.

[0005] Real-world industrial data is highly perturbative, containing not only noise but also outliers. Existing fault detection methods do not adequately consider the impact of strong perturbations on fault detection, nor are there feature reduction methods developed to address the correlation between normal and fault data.

[0006] Therefore, the present invention provides a fault detection method based on sparse representation. Summary of the Invention

[0007] In order to overcome the shortcomings of the prior art, at least one technical problem raised in the background art is solved.

[0008] The technical solution adopted by this invention to solve its technical problem is: a fault detection method based on sparse representation, comprising the following steps: Preprocessing steps: Under preset operating conditions, first data samples of normal operating conditions are collected and normalized to construct a fault dictionary matrix X. Under the same preset operating conditions, second data samples of normal operating conditions are collected to construct a fault measurement matrix. ; Control limit determination steps: Based on the fault dictionary matrix X and the fault measurement matrix Determine the sparse representation reconstruction error control limit CLE and the distance control limit interval CLD_int; On-site monitoring steps: Collect on-site data z, and calculate the sparse representation reconstruction error statistic cl_ε and the sparse representation distance statistic cl_d based on the fault dictionary matrix X and the on-site data z; Fault detection steps: When the reconstruction error statistic cl_ε is less than the reconstruction error control limit CLE, and the sparse representation distance statistic cl_d is within the distance control limit interval CLD_int, the system is judged to be fault-free; otherwise, the system is judged to be faulty.

[0009] Furthermore, the preprocessing step of constructing the fault dictionary matrix X includes: The first data sample under normal operating conditions was collected under preset operating conditions. , where n is the number of times the first data sample is sampled, R^m represents an m-dimensional column vector, and m is the number of sensors; Constructing a measurement matrix under normal operating conditions ,in , ,…, express Column vectors; For matrix Each column is normalized so that The L2 norm of each column is 1; The normalized matrix is ​​set as the fault dictionary matrix X.

[0010] Furthermore, the steps for determining control limits include: The fault dictionary matrix X and the fault measurement matrix Solving the L0 norm optimization problem using column vectors in the problem, and determining the sparse representation to reconstruct the error sequence. and the sparse representation column vector sequence of the modeling stage at each time step ,in ; Reconstructing the error sequence from sparse representation Determine the control limit CLE for sparse representation reconstruction with confidence level λ; Based on the sparse representation of column vector sequences in the modeling stage Given an L1 norm sequence d_k, determine the lower control limit with confidence level η. and control limit This constitutes a closed distance control limit zone. .

[0011] Furthermore, the optimization problem under the L0 norm can be expressed as: Solve the optimization problem under the L0 norm: and satisfy the constraints. ; Where p is an empirical value. This is the sparse representation of the column vector sequence at time k in the modeling phase. Fault measurement matrix The column vector at time k.

[0012] Furthermore, the method also includes the detection of minute faults, wherein: The data samples collected in the preprocessing step are extended data samples with a time window length of t, and a minor fault dictionary matrix X is constructed. The control limit determination step determines the control limits applicable to the detection of minor faults based on the minor fault dictionary matrix X. The fault detection steps determine whether there are minor faults in the system.

[0013] Furthermore, the time window length t is determined based on the equipment operating cycle and sampling frequency, and It is used to capture the timing characteristics of faults.

[0014] Furthermore, the method introduces a time-constrained sparse representation, including: constructing a time-constrained matrix W to characterize the temporal correlation between data; Find the sparse matrix C such that it satisfies , where E is the outlier matrix in the residual and Z is the noise matrix in the residual.

[0015] Furthermore, the method also includes a feature dimensionality reduction step: Construct a robust adjacency graph based on sparse representation results; Calculate the intra-class scatter matrix and the inter-class scatter matrix; The dimension-reduced projection matrix G is obtained by solving the generalized eigenvalue problem; Fault detection is performed using the reduced-dimensional features.

[0016] The beneficial effects of this invention are as follows: 1. This invention presents a fault detection method based on sparse representation, proposing a novel fault detection framework based on sparse representation, and providing two control limits for online fault detection within this framework. For industrial process data that follows a non-Gaussian distribution, this method achieves a high level of fault detection.

[0017] 2. The fault detection method based on sparse representation described in this invention can detect minor faults with non-Gaussian distributions. When the fault level is comparable to the noise level of the signal, the fault detection level of minor faults is improved in this case by constructing a minor fault dictionary matrix and determining minor fault control limits.

[0018] 3. The fault detection method based on sparse representation described in this invention, for the detection of minor faults, adopts time window technology to construct a minor fault dictionary matrix, wherein the time window length t is determined according to the equipment operating cycle and sampling frequency, and is used to capture the temporal characteristics of the fault.

[0019] 4. The fault detection method based on sparse representation described in this invention also introduces a time-constrained sparse representation method (TCSR), and, considering the spatial and temporal characteristics of industrial process monitoring data, proposes a novel feature-reduced dimensionality reduction fault detection method (RCDR). This method fully utilizes the constructed robust adjacency graph and considers data characteristics; its scatter matrix is ​​specifically designed to take into account the data characteristics of fault detection. The intra-class scatter matrix simply uses the classical covariance matrix to represent the normal dataset, while the inter-class scatter matrix uses a predefined scatter matrix to represent the separability between normal and fault data. Attached Figure Description

[0020] The invention will now be further described with reference to the accompanying drawings.

[0021] Figure 1 This is a flowchart of the two fault detection methods of the present invention; Figure 2 This is a flowchart of a method for detecting minute faults based on sparse representation; Figure 3 This is a diagram showing the hardware and software modules of the fault detection system for this method and their data flow relationships. Detailed Implementation

[0022] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0023] like Figures 1 to 2 As shown in the embodiment of the present invention, a fault detection method based on sparse representation includes the following steps: Preprocessing steps: Under preset operating conditions, collect the first data sample of normal operating conditions and perform normalization processing to construct the fault dictionary matrix X. Under the same preset operating conditions, collect the second data sample of normal operating conditions to construct the fault measurement matrix Y0. Control limit determination steps: Determine the sparse representation reconstruction error control limit CLE and the distance control limit interval CLD_int based on the fault dictionary matrix X and the fault measurement matrix Y0; On-site monitoring steps: Collect on-site data z, and calculate the sparse representation reconstruction error statistic cl_ε and the sparse representation distance statistic cl_d based on the fault dictionary matrix X and the on-site data z; Fault detection steps: When the reconstruction error statistic cl_ε is less than the reconstruction error control limit CLE, and the sparse representation distance statistic cl_d is within the distance control limit interval CLD_int, the system is judged to be fault-free; otherwise, the system is judged to be faulty.

[0024] The preprocessing step of constructing the fault dictionary matrix X includes: The first data sample under normal operating conditions was collected under preset operating conditions. , where n is the number of times the first data sample is sampled, R^m represents an m-dimensional column vector, and m is the number of sensors; Constructing a measurement matrix under normal operating conditions ,in , ,…, express Column vectors; For matrix Each column is normalized so that The L2 norm of each column is 1; The normalized matrix is ​​set as the fault dictionary matrix X.

[0025] The steps for determining control limits include: The fault dictionary matrix X and the fault measurement matrix Solving the L0 norm optimization problem using column vectors in the problem, and determining the sparse representation to reconstruct the error sequence. and the sparse representation column vector sequence of the modeling stage at each time step ,in ; Reconstructing the error sequence from sparse representation Determine the control limit CLE for sparse representation reconstruction with confidence level λ; Based on the sparse representation of column vector sequences in the modeling stage Given an L1 norm sequence d_k, determine the lower control limit with confidence level η. and control limit This constitutes a closed distance control limit zone. .

[0026] Solving the optimization problem under the L0 norm is expressed as: Solve the optimization problem under the L0 norm: and satisfy the constraints. ; Where p is an empirical value. This is the sparse representation of the column vector sequence at time k in the modeling phase. Fault measurement matrix The column vector at time k; The method also includes the detection of minor faults, wherein: The data samples collected in the preprocessing step are extended data samples with a time window length of t, and a minor fault dictionary matrix X is constructed. The control limit determination step determines the control limits applicable to the detection of minor faults based on the minor fault dictionary matrix X. The fault detection steps determine whether there are minor faults in the system.

[0027] The time window length t is determined based on the equipment operating cycle and sampling frequency, and It is used to capture the timing characteristics of faults.

[0028] The method introduces a time-constrained sparse representation, including: constructing a time-constrained matrix W to characterize the temporal correlation between data; Find the sparse matrix C such that it satisfies , where E is the outlier matrix in the residual and Z is the noise matrix in the residual.

[0029] Furthermore, the method also includes a feature dimensionality reduction step: Construct a robust adjacency graph based on sparse representation results; Calculate the intra-class scatter matrix and the inter-class scatter matrix; The dimension-reduced projection matrix G is obtained by solving the generalized eigenvalue problem; Fault detection is performed using the reduced-dimensional features.

[0030] Example 1: General Fault Detection Method In the preprocessing step, normal operating condition data is collected under preset operating conditions. Assuming the object being detected contains m sensors, the collected normal operating condition data is... , representing the sensor's sampled value under normal operating conditions. This represents an m-dimensional column vector, where m is the number of sensors. Each sensor has n independent samples, where n is the sampling number for the first data sample. A normal operating condition measurement matrix can be constructed. ,in ,…, express The column vectors are used as the original samples needed to construct the dictionary.

[0031] For matrix Each column is normalized so that The L2 norm of each column is 1. The normalized matrix is ​​set as the fault dictionary matrix X.

[0032] In the control limit determination step, the fault dictionary matrix X and the fault measurement matrix are used. Solving the L0 norm optimization problem using column vectors in the problem, and determining the sparse representation to reconstruct the error sequence. and the sparse representation column vector sequence of the modeling stage at each time step ,in Then the error sequence is reconstructed from the sparse representation. Determine the control limit (CLE) for sparse representation reconstruction with confidence level λ. This is based on the sparse representation column vector sequence from the modeling phase. Given an L1 norm sequence d_k, determine the lower control limit with confidence level η. and control limit This constitutes a closed distance control limit zone. .

[0033] In the on-site monitoring step, work site data is collected under the same preset working conditions as the first data sample. Where N is the actual number of samples taken during the on-site monitoring process. Let z_j = z'j, and solve the optimization problem under the L0 norm at each current time step: and satisfy the constraints. Calculate the sparse representation reconstruction error statistic. Based on the sparse representation column vector in the detection phase. The L0 norm at the current sampling time determines the sparse representation distance statistic cl_d.

[0034] In the fault detection step, when the reconstruction error statistic cl_ε is less than the reconstruction error control limit CLE, and the sparse representation distance statistic cl_d is within the distance control limit interval... If the system is functioning correctly, it is determined that there is no fault; otherwise, it is determined that there is a fault.

[0035] Example 2: Detection method for minor faults.

[0036] Compared to Example 1, the main difference in this example lies in the method of constructing data samples in the preprocessing step. First data samples under normal operating conditions are collected under preset operating conditions. Where n is the number of times the first data sample is sampled, and t is the time window length. Construct a normal operating condition measurement matrix with a time window length of t. Measurement matrix under normal operating conditions Each column is normalized to make The L2 norm of each column is 1. The normalized matrix is ​​set as the micro-fault dictionary matrix X.

[0037] Similarly, a second data sample under normal operating conditions was collected under the same preset operating conditions as the first data sample. , where c is the number of times the second data sample is sampled. Construct a micro-fault measurement matrix. .

[0038] The control limit determination step, the on-site monitoring step, and the fault detection step are similar to those in Example 1, but the minor fault dictionary matrix and the minor fault measurement matrix are used for calculation and judgment.

[0039] Example 3: Fault detection method combining time constraints and feature dimensionality reduction: Based on the above embodiments, this embodiment introduces time-constrained sparse representation and feature dimensionality reduction methods to handle fault detection problems under strong perturbations.

[0040] Assuming the object being detected contains d sensors, the data collected under normal operating conditions at a single moment... First, solve for the sparse matrix C such that it satisfies the following relationship: In this matrix, the diagonal elements of C are 0, and W is the time constraint matrix, whose parameters are determined based on the actual situation on site.

[0041] Then, the within-class scatter matrix and between-class scatter matrix are calculated, and the dimension-reduced projection matrix G is obtained by solving the generalized eigenvalue problem. Finally, the dimension-reduced features are used for fault detection; given an online obtained x, the statistic is calculated. ,when The timeout exceeded the control limit, indicating a malfunction.

[0042] To visually demonstrate the performance difference between the method described in this invention and the traditional Principal Component Analysis (PCA) method, the following table compares their key statistical results in simulation experiments:

[0043] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A fault detection method based on sparse representation, characterized in that: Includes the following steps: Preprocessing steps: Under preset operating conditions, first data samples of normal operating conditions are collected and normalized to construct a fault dictionary matrix X. Under the same preset operating conditions, second data samples of normal operating conditions are collected to construct a fault measurement matrix. ; Control limit determination steps: Based on the fault dictionary matrix X and the fault measurement matrix Determine the sparse representation reconstruction error control limit (CLE) and the distance control limit interval. ; On-site monitoring steps: Collect on-site data z, and calculate the sparse representation reconstruction error statistic based on the fault dictionary matrix X and the on-site data z. and sparse representation distance statistics ; Fault detection steps: When reconstructing error statistics The distance statistic is less than the reconstruction error control limit (CLE) and sparsely represents the distance statistic. Within the distance control limit range If the system is functioning correctly, it is determined that there is no fault; otherwise, it is determined that there is a fault.

2. The fault detection method based on sparse representation according to claim 1, characterized in that: The preprocessing step of constructing the fault dictionary matrix X includes: The first data sample under normal operating conditions was collected under preset operating conditions. , where n is the number of times the first data sample is sampled, R^m represents an m-dimensional column vector, and m is the number of sensors; Constructing a measurement matrix under normal operating conditions ,in , ,…, express Column vectors; For matrix Each column is normalized so that The L2 norm of each column is 1; The normalized matrix is ​​set as the fault dictionary matrix X.

3. The fault detection method based on sparse representation according to claim 2, characterized in that: The control limit determination step includes: The fault dictionary matrix X and the fault measurement matrix Solving the L0 norm optimization problem using column vectors in the problem, and determining the sparse representation to reconstruct the error sequence. and the sparse representation column vector sequence of the modeling stage at each time step ,in ; Reconstructing the error sequence from sparse representation Determine the control limit CLE for sparse representation reconstruction with confidence level λ; Based on the sparse representation of column vector sequences in the modeling stage Given an L1 norm sequence d_k, determine the lower control limit with confidence level η. and control limit This constitutes a closed distance control limit zone. .

4. The fault detection method based on sparse representation according to claim 3, characterized in that: The optimization problem under the L0 norm is expressed as follows: Solve the optimization problem under the L0 norm: Where p is an empirical value This is the sparse representation of the column vector sequence at time k in the modeling phase. Fault measurement matrix The column vector at time k.

5. The fault detection method based on sparse representation according to claim 1, characterized in that: The method also includes the detection of minor faults, wherein: The data samples collected in the preprocessing step are extended data samples with a time window length of t, and a minor fault dictionary matrix X is constructed. The control limit determination step determines the control limits applicable to the detection of minor faults based on the minor fault dictionary matrix X. The fault detection steps determine whether there are minor faults in the system.

6. The fault detection method based on sparse representation according to claim 5, characterized in that: The time window length t is determined based on the device operating cycle and sampling frequency, and It is used to capture the timing characteristics of faults.

7. The fault detection method based on sparse representation according to claim 1, characterized in that: The method introduces a time-constrained sparse representation, including: constructing a time-constrained matrix W to characterize the temporal correlation between data; Find the sparse matrix C such that it satisfies , where E is the outlier matrix in the residual and Z is the noise matrix in the residual.

8. The fault detection method based on sparse representation according to claim 1, characterized in that: The method also includes a feature dimensionality reduction step: Construct a robust adjacency graph based on sparse representation results; Calculate the intra-class scatter matrix and the inter-class scatter matrix; The dimension-reduced projection matrix G is obtained by solving the generalized eigenvalue problem; Fault detection is performed using the reduced-dimensional features.

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