Industrial fault detection method based on local outlier factor and slowness constraint ica

Abstract

The application provides an industrial fault detection method based on local outlier factor and slow constraint ICA, and belongs to the technical field of industrial process fault detection. The technical scheme comprises the following steps: standardizing the training data, removing local abnormal samples by using a local outlier factor, and obtaining reliable training data; then, time lag difference expansion and whitening transformation are performed on the data to weaken variable correlation and enhance time sequence characteristics. Then, a slow constraint is introduced, a slow constraint independent component analysis method based on Newton iteration is used to solve a projection vector, and a process slow change feature is extracted by component-wise orthogonalization. Based on the constructed feature space, a statistical quantity is established, a control limit is determined by using kernel density estimation, and offline modeling is completed. In the detection stage, the test data is processed according to the same process and projected to the SCICA model, and fault detection is realized by comparing the statistical quantity with the control limit. The application enhances the detection ability of industrial process faults through outlier removal and slow change feature extraction.

Description

Technical Field

[0001] This invention relates to the field of industrial process fault detection technology, and in particular to an industrial fault detection method based on local outlier factor and slowness constraint ICA. Background Technology

[0002] With the evolution of the times and the leapfrog development of technology, modern industrial processes are rapidly moving towards greater complexity, intelligence, and efficiency, giving rise to a large number of large-scale manufacturing systems and highly complex industrial processes. However, the widespread application of high-tech equipment and the comprehensive implementation of intelligent production have also significantly increased the failure rate in industrial processes. Without reliable fault detection methods, sudden failures in production equipment and control systems can easily trigger chain reactions, even paralyzing the entire production process and causing huge economic losses. More serious failures may even lead to casualties and irreversible catastrophic accidents, causing a strong impact on society. Therefore, to ensure the safe, stable, and reliable operation of industrial production and to achieve accurate early warning before failures occur, researching an industrial fault detection method based on local outlier factors and slow-degree constraint ICA is of great significance for improving fault detection accuracy, avoiding major safety accidents, reducing economic losses, and minimizing casualties.

[0003] The Local Outlier Factor (LOF) algorithm is a density-based unsupervised outlier detection method. Its core mechanism is to identify anomalies by comparing the local density of a data point with that of its neighboring samples. Compared to traditional anomaly detection methods that rely on global distance or statistical distribution, the LOF algorithm can accurately locate sample points with local densities different from their neighbors, making it particularly suitable for complex scenarios with uneven data distribution and multiple density clusters. In industrial process data, due to factors such as operating condition switching and instantaneous sensor interference, outlier samples that deviate from the mainstream pattern are often mixed into the training data. These samples distort the normal statistical characteristics of industrial processes, leading to inaccurate control limit settings in subsequent monitoring models, and consequently causing false alarms or missed alarms in fault detection. Applying this algorithm to the training data cleaning stage of fault detection models can construct a cleaner and more representative "normal operating condition" dataset, laying a solid foundation for building robust monitoring statistics.

[0004] Independent Component Analysis (ICA), a classic blind source separation technique, aims to restore the statistical independence of source signals. This characteristic makes it well-suited for non-Gaussian distributed process data, effectively weakening the coupling correlation between industrial process variables and enabling the extraction of more representative statistical features from high-dimensional and multi-coupled process data after transformation. Existing research confirms that ICA can mine statistically independent potential structural features from non-Gaussian process data, thus finding widespread application in industrial process monitoring. In 2018, Zhou Le et al. invented a chemical process fault detection method with missing data (patent number CN201810734994.8), employing an iterative learning framework of ICA and autoregressive latent variables, which can compensate for modeling bias caused by missing data to some extent. However, this method heavily relies on the independence assumption of ICA and is highly sensitive to outliers, easily exhibiting projection instability under multivariate strongly coupled conditions; furthermore, the iterative solution has slow convergence and high computational cost, making it difficult to meet monitoring needs. Furthermore, the model's control limits rely on data distribution assumptions, which can easily lead to decreased detection performance under various fault scenarios, resulting in insufficient overall robustness and real-time performance. In 2022, Sun Bin et al. invented a data-driven industrial process fault detection method (patent number CN202210367561.X), which extracts features sequentially through Principal Component Analysis (PCA), ICA, and Canonical Correlation Analysis (CCA) and inputs them into the detection network to achieve a more general classification model. However, this method involves multiple feature extraction steps, all based on linear assumptions, making it sensitive to noise and outliers, and difficult to characterize the dynamic and nonlinear features of complex industrial processes. Simultaneously, the feature extraction and classification networks are independent, making end-to-end optimization impossible, leading to complex training, insufficient stability, and limiting its application in real-time monitoring scenarios.

[0005] How to solve the above problems is the research topic of this plan. Summary of the Invention

[0006] The purpose of this invention is to provide an industrial fault detection method based on local outlier factor and slowness constraint ICA, which solves the problems of insufficient detection rate and high false detection rate of traditional ICA detection methods in industrial processes. This method achieves efficient and robust fault detection in industrial processes by sequentially running three parts: data preprocessing and feature construction, SCICA model construction and fault detection.

[0007] The fault detection model consists of the following three parts:

[0008] Data preprocessing and feature engineering: The raw industrial process monitoring data is standardized to eliminate the influence of different dimensions; the Local Outlier Factor (LOF) algorithm is introduced to identify and remove outliers in the training data, improving the purity of the modeling data; then, time-delay differential extension is used to construct time series enhanced features, which enhance the capture of dynamic behavior and slowly changing structure of industrial processes by expanding the feature dimensions, thus realizing data-driven dynamic feature enhancement.

[0009] SCICA Model Construction: The expanded dataset is whitened to weaken the linear coupling between variables and to construct a data input with a consistent characteristic scale. Furthermore, a slowness matrix is ​​constructed based on the whitened data to characterize the time-varying characteristics of the variables, and the Newton-Raphson iteration method is used to solve for the slow components that can reflect the slowly changing dynamic structure.

[0010] Based on this, the feature components are sorted and filtered according to the slowness criterion to form the slow component space (SIS) and residual space (RS), and a multi-statistic fault monitoring model including I² statistic and SPE statistic is established to complete offline modeling.

[0011] Fault detection section: After standardizing, time-delay feature expansion, and whitening transformation of the test phase data according to the same process as the modeling phase, the data is projected onto the slowly varying feature subspace constructed by the SCICA model; the I² statistic and SPE statistic of the test samples are calculated and compared with the control limits obtained by kernel density estimation (KDE) in the modeling phase; fault detection is performed based on the statistic exceeding the limits; by comparing the output with the actual fault state, the detection accuracy and stability of the model are evaluated, and the effectiveness and superiority of the method of this invention in industrial fault scenarios are verified.

[0012] To achieve the aforementioned objectives, the present invention employs the following technical solution: an industrial fault detection method based on local outlier factor and slowness constraint ICA, comprising the following steps:

[0013] A. Modeling Phase

[0014] S1: Select normal operating condition data to construct the modeling training dataset: Then, standardization preprocessing is performed to obtain a standardized data matrix, denoted as . ;

[0015] S2: The LOF algorithm is used to remove outlier and noisy samples from the data. The local reachability density is calculated based on the Euclidean distance between samples, and the LOF score is obtained to obtain the normal data matrix. ;

[0016] S3: Yes Implement time-delay feature extension and construct first-order difference time-delay features, and form an extended feature matrix after feature extension. ;

[0017] S4: Yes Perform whitening transformation; calculate the covariance matrix of the matrix. Subsequently Perform eigenvalue decomposition to construct the whitening matrix The whitening transformation matrix is ​​obtained. ;

[0018] S5: Whitening Transformation Matrix Calculate the time difference and construct the time difference matrix. Constructing the slowness matrix ;

[0019] S6: Initialize the separation matrix for slow component analysis And perform orthogonalization;

[0020] S7: The slowness matrix calculated from step S5 Based on the slowness criterion, Newton's iterative method is used to solve for the slow component and update the weight vector. ;

[0021] S8: Sort and select independent components based on the slowness criterion to determine the projection matrix. ;

[0022] S9: Calculate the monitoring statistics after projecting the training data, and use kernel density estimation to determine the control limits;

[0023] B. Detection Phase

[0024] S10: Transfer the test dataset Perform the same preprocessing, time-delay feature expansion, and whitening transformation processes according to steps S1 to S4;

[0025] S11: Project the whitened test samples onto the SCICA model and calculate the statistics of the test dataset;

[0026] S12: Compare the statistics obtained in S11 with the control limits determined in step S9. If the statistics exceed the control limits, it is determined to be a fault and an alarm is triggered; otherwise, it is determined to be normal.

[0027] The above content has fully presented the overall execution flow of the algorithm of this invention. In order to clearly explain the core implementation logic, the specific operation steps of each link are further explained in detail as follows.

[0028] Furthermore, in step S1, the modeling training dataset is... Preprocessing and normalization are performed to make the mean of all process variables 0 and the variance 1, resulting in a new data matrix set. The formula is as follows, where It is expressed as the mean of each variable. The standard deviation is denoted as .

[0029] (1)

[0030] (2)

[0031] (3)

[0032] Furthermore, in step S2, the Euclidean distance between any two samples is calculated. Determine the samples Nearest neighbor set Based on this, the reachability distance between samples is calculated. And further calculate the local reachability density of the sample. The formula is used for subsequent anomaly detection.

[0033] (4)

[0034] (5)

[0035] (6)

[0036] (7)

[0037] in, , For any sample, For the number of process variables, calculate the LOF score for each data point and remove those with LOF scores greater than a threshold. Abnormal samples, retained samples Finally, the normal data matrix after removing outliers is obtained. .

[0038] Furthermore, in step S3, the original cleaned normal data matrix To implement time-delay feature extension and incorporate dynamic information, a first-order difference is constructed for each variable. After feature construction is completed, the final extended feature matrix is ​​formed. The formula is as follows.

[0039] (8)

[0040] in, For the number of variables, For sample length, For the first Variables in The value at the previous time step. The first-order difference requires the value at the previous time step. But At any moment, there is no To maintain dimensionality consistency across all samples, missing historical data is padded with zeros at the boundaries. ,from Initially, the difference can be generated normally, yielding the difference characteristic matrix. The formula is as follows.

[0041] (9)

[0042] Normal data matrix The final extended feature matrix is ​​obtained by concatenating the left and right sides of the difference features. .

[0043] Furthermore, in step S4, the extended feature matrix needs to be... A whitening transformation is performed to eliminate the correlation between data features and unify the variance of each feature, and then the whitening transformation matrix is ​​solved. The formula is as follows.

[0044] (10)

[0045] (11)

[0046] (12)

[0047] (13)

[0048] in, Let covariance matrix be the variance matrix. The eigenvector matrix, It is an eigenvalue diagonal matrix. This represents the number of normal samples remaining after LOF outlier removal.

[0049] Furthermore, in step S5, the changes of each variable at adjacent time points are first obtained by calculating the time difference of the whitened data. This represents the instantaneous change of all variables. By stacking the difference samples in chronological order, the time difference matrix can be obtained. In order to extract the most representative slowly varying structure from the changes in variables, a slowly varying matrix is ​​constructed based on the time difference matrix. The formula is as follows.

[0050] (14)

[0051] (15)

[0052] (16)

[0053] in, Each row represents the changes of all variables at a time step, and each column represents the trajectory of a certain variable throughout the entire time series. (Slow-changing matrix) The rate of change of the characterizing variable is used for subsequent slow component analysis.

[0054] Furthermore, in step S6, the separation matrix for slow component analysis is initialized. To ensure that the separated independent components are statistically orthogonal, the initial separation matrix is ​​orthogonalized as follows.

[0055] (17)

[0056] (18)

[0057] Furthermore, in step S7, to obtain the independent components that satisfy the slow feature constraints, Newton's iteration method is used to optimize and solve for each projection vector to be determined. For each component... Iteratively update its corresponding weight vector The formula is as follows.

[0058] (19)

[0059] (20)

[0060] (twenty one)

[0061] (twenty two)

[0062] (twenty three)

[0063] (twenty four)

[0064] (25)

[0065] in, This is the slowness adjustment parameter. The gradient vector, It is a Hessian matrix.

[0066] Furthermore, in step S8, the slowness value of each independent component is... Quantitative calculations were performed, and all slowness values ​​were then sorted in ascending order of rate of change to identify target components exhibiting slow evolution characteristics over time. Subsequently, the weight vector was rearranged based on the sorting results, and several slow components that best reflected the steady-state trend of the process were selected, along with their cumulative contribution rates. Reaching the threshold The former The slow principal components constitute the projection matrix. The formula is as follows.

[0067] (26)

[0068] (27)

[0069] (28)

[0070] Furthermore, in step S9, the training data is projected onto the slow component space to obtain the slow features. ,Sure Statistics and The statistic is calculated using the following formula.

[0071] (29)

[0072] (30)

[0073] (31)

[0074] in, To reconstruct the data, use normal operating conditions. and For each sample, control limits for the statistics were calculated using the KDE method. , The formula is as follows.

[0075] (32)

[0076] (33)

[0077] (34)

[0078] (35)

[0079] Furthermore, in step S10, the mean obtained during the training phase is used. and standard deviation For the test dataset Standardize the data. Constructing first-order difference time delay characteristics The first row is padded with zeros at the boundary. The formula is as follows.

[0080] (36)

[0081] (37)

[0082] The final constructed test data expansion matrix is ​​as follows Its dimensions are .

[0083] Using the whitening matrix obtained during the training phase The test data are linearly transformed using the following formula.

[0084] (38)

[0085] in, The covariance matrix of the training data in step S4 Obtained by decomposition.

[0086] Furthermore, in step S11, the main slow features projected onto the SCICA model from the test dataset are calculated. The test dataset Statistics and Statistic, To reconstruct the data, the formula is as follows.

[0087] (39)

[0088] (40)

[0089] (41)

[0090] Furthermore, in step S12, fault detection is performed based on control limits; if... or If the industrial process malfunctions, an alarm mechanism is triggered; if all statistics are within the control limits, the process is considered to be operating normally.

[0091] In the above method, steps S1 to S9 constitute the offline modeling stage of the SCICA model, and steps S10 to S12 are the stages of fault detection on the test data and fault judgment based on statistics and control limits.

[0092] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0093] (1) This invention introduces the LOF algorithm based on local density bias to achieve accurate identification and removal of outliers in the training data. This mechanism effectively reduces the interference of abnormal samples on the statistical structure of the model, ensures the purity and consistency of the modeling data, and makes subsequent feature extraction and control limit estimation more stable and reliable, thereby significantly enhancing the robustness of the fault detection model under complex working conditions.

[0094] (2) This invention utilizes time-delay feature extension technology to construct enhanced time series features, fully capturing the dynamic coupling relationship and slowly changing structure between industrial process variables. By introducing multi-order lag terms and difference terms, this invention can enhance the data's ability to characterize the dynamic laws of the process, enabling the model to have higher sensitivity and recognition capabilities when facing trend-based, coupled, and dynamically changing faults, providing more comprehensive and effective feature support for fault detection.

[0095] (3) This invention introduces a SCICA feature extraction mechanism based on the slow-varying characteristics, prioritizing the extraction of key features that reflect the slowly varying dynamic structure of the process. This method obtains representative slowly varying projection components based on slowness constraints and optimization solutions, making the extracted features more consistent with the operating rules of continuous industrial processes; in Statistics and Under the joint monitoring framework of statistics, the accuracy, stability and feature separability of fault detection are significantly improved. Attached Figure Description

[0096] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0097] Figure 1 This is a flowchart of the fault detection method of the present invention;

[0098] Figure 2 This is a flowchart of the offline modeling and detection process of the method of the present invention;

[0099] Figure 3 This is a process flow diagram of the TE chemical process used in the implementation of this invention;

[0100] Figure 4 The above is a diagram showing the detection results of TE process fault 1 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) Test results; (b) LOF-SCICA-SPE test results;

[0101] Figure 5 The above is a diagram showing the detection results of TE process fault 4 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2(a) Test results; (b) LOF-SCICA-SPE test results;

[0102] Figure 6 The above is a diagram showing the detection results of fault 8 in the TE process using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) Test results; (b) LOF-SCICA-SPE test results;

[0103] Figure 7 The above is a diagram showing the detection results of TE process fault 10 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) Test results; (b) LOF-SCICA-SPE test results;

[0104] Figure 8 The above is a diagram showing the detection results of TE process fault 11 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) Test results; (b) LOF-SCICA-SPE test results;

[0105] Figure 9 The above is a diagram showing the detection results of TE process fault 12 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) Test results; (b) LOF-SCICA-SPE test results;

[0106] Figure 10 The above is a diagram showing the detection results of TE process fault 16 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) Test results; (b) LOF-SCICA-SPE test results;

[0107] Figure 11 The diagram shows the detection results of TE process fault 19 using the present invention in an embodiment of the present invention; wherein, (a) is LOF-SCICA-I 2 (a) is the test result; (b) is the LOF-SCICA-SPE test result. Detailed Implementation

[0108] The present invention will be specifically described below through exemplary embodiments. To more clearly demonstrate the beneficial effects of the fault detection method proposed in this invention, the technical details and application effects of the method will be further explained below in conjunction with specific embodiments.

[0109] Example 1:

[0110] The Tennessee-Eastman (TE) process, designed and developed by Downs et al. in 1993, is a standardized simulation platform capable of simulating the operating conditions of actual industrial processes. This process model was first proposed in the process control academic community and publicly released in FORTRAN source code form. Its core function is to describe the complex nonlinear relationships between devices, materials, and energy in industrial systems. With its characteristics of encompassing multiple operating units, rich failure modes, and repeatable data, the TE process has been widely applied in many research areas such as process optimization, predictive control, fault diagnosis, and control, resulting in numerous advanced research achievements. In the field of process fault diagnosis, the TE process has become a mainstream benchmark platform for experts and scholars to verify the effectiveness of various new methods, which is the key reason why this paper selects this simulation platform to verify the feasibility of the proposed algorithm.

[0111] The TE process comprises five core operating units: reactor, condenser, gas / liquid separator, compressor, and stripper. It involves the chemical reactions of eight components: A, B, C, D, E, F, G, and H. A, C, D, and E are gaseous reactants; B is an inert catalyst; G and H are liquid target products; and F is a byproduct. The process flow is as follows: reactants and catalyst enter the reactor to complete the reaction. The product is cooled by the condenser into a gas-liquid mixture and then enters the separator. The separated gaseous component is vented and recycled back to the reactor via the compressor. The liquid component is sent to the stripper for further separation. Unreacted components are recycled back to the reactor. Finally, products G and H are extracted from the bottom of the stripper. The TE chemical process flow is as follows: Figure 3 As shown.

[0112] The TE process is characterized by its complexity and large number of variables, including 41 measurement variables and 12 operational variables. Regarding data setup, the training dataset covers 500 normal operating condition samples; the test dataset consists of 21 groups, each containing 960 fault samples. All test samples are introduced with faults starting from the 161st acquisition time. Based on the differences in fault type, they can be divided into 21 specific faults, and detailed information for each fault is shown in Table 1.

[0113] Table 1 Fault Types in the TE Process

[0114] To evaluate the fault detection performance of different methods, this study uses three key performance indicators for comparison: Fault Detection Rate (FDR) and Fault False Alarm Rate (FAR). FDR refers to the probability that a monitoring statistic correctly exceeds the control limit during a fault occurrence; FAR refers to the probability that a monitoring statistic falsely exceeds the control limit under normal operating conditions. Generally, when a detection method exhibits a low FAR and a high FDR, its fault detection performance is considered more stable and reliable. Conversely, its fault detection performance is considered worse. The specific formulas for FDR and FAR are as follows.

[0115] (42)

[0116] (43)

[0117] in, and These represent the number of fault samples incorrectly detected before the fault occurred and the number of fault samples correctly detected after the fault occurred. and These represent the number of normal samples and the number of faulty samples, respectively.

[0118] See Figures 1 to 2 The specific steps in this embodiment are as follows:

[0119] A. Modeling Phase

[0120] Step S1: Select operational data under normal industrial production conditions to construct a modeling training dataset. Preprocessing and normalization operations are performed, and the new data matrix obtained after processing is denoted as... .

[0121] , , ;

[0122] Step S2: Calculate the Euclidean distance between any two samples. Determine the samples Nearest neighbor set Based on this, the reachability distance between samples is calculated. And further calculate the local reachability density of the sample. Calculate the LOF score for each data point and remove those with an LOF score greater than a threshold. Abnormal samples, retained samples Finally, the matrix after removing outliers is obtained. (This embodiment) Take the 95th percentile of the LOF distribution.

[0123] , , , ;

[0124] Step S3: Convert the normal data matrix Implement time-delay feature extension and construct first-order differences for each variable. After feature construction is completed, the final extended feature matrix is ​​formed. ,exist At any given moment, zeros are padded to the boundaries of non-existent historical data. The difference feature matrix is ​​obtained. The original cleaned matrix is ​​concatenated with the difference features to obtain the final extended matrix. .

[0125] , ;

[0126] Step S4: For the extended feature matrix Perform whitening transformation and then solve for the whitening transformation matrix. (After removing outliers in this embodiment) (475).

[0127] , , , ;

[0128] Step S5: Calculate the time difference of the whitened data to obtain the changes of each variable at adjacent time points. , will all The difference samples are stacked in chronological order to obtain the time difference matrix. Constructing a slowly varying matrix .

[0129] , , ;

[0130] Step S6: Initialize the separation matrix for slow component analysis Furthermore, the initial separation matrix is ​​orthogonalized.

[0131] , ;

[0132] Step S7: Optimize and solve for each projection vector using Newton's iteration method. For each component... Iteratively update its corresponding weight vector (This embodiment) Take 6).

[0133] , , , , , , ;

[0134] Step S8: By calculating the slowness value of each independent component Quantitative calculations were performed, and all slowness values ​​were sorted in ascending order of their rate of change, selecting the cumulative contribution rate. Reaching the threshold The former The slow principal components constitute the projection matrix. (This embodiment) Take 90%, By meeting the threshold Calculations show that in example fault 1 ).

[0135] , , ;

[0136] Step S9: Project the training data onto the slow component space and solve for the slow features. ,Sure Statistics and Statistics.

[0137] , , ;

[0138] Based on the KDE method, according to a given confidence level Calculate the control limits of the statistics separately , (This embodiment) Take 99%.

[0139] , , , ;

[0140] B. Detection Phase

[0141] Step S10: Use the mean obtained during the training phase and standard deviation For the test dataset Standardization is performed to construct first-order difference time delay characteristics. Similarly, the first row is padded with zeros at the boundaries. The final constructed test data extended matrix is ​​as follows: .

[0142] , ;

[0143] Step S11: Calculate the principal slow features projected onto the SCICA space from the test dataset. The test dataset Statistics and Statistics.

[0144] , , ;

[0145] Step S12: Perform fault detection based on control limits, if or If the industrial process is deemed to have malfunctioned, an alarm mechanism is triggered; if all statistics are within the control limits, the process is deemed to be operating normally. This embodiment uses two key performance indicators, Fault Detection Rate (FDR) and Fault False Alarm Rate (FAR), to evaluate the effectiveness of the detection model.

[0146] , .

[0147] In this embodiment, eight representative faults were selected from the 21 faults preset in the TE chemical process. The simulation was carried out according to the above steps. In order to more intuitively demonstrate the LOF-SCICA fault detection effect of the method in this embodiment, the traditional ICA fault detection method and the LOF-SCICA fault detection method were compared using the two indicators FDR and FAR respectively. The detailed comparison results are shown in Tables 2 and 3.

[0148] Table 2. Comparison of FDR (%) of traditional algorithm and the method of this invention for 8 faults in the TE process.

[0149]

[0150] Table 3. Comparison of FAR (%) for eight faults in the TE process between the traditional algorithm and the method of this invention.

[0151]

[0152] As can be clearly seen from Table 2-3, and as referenced... Figures 4 to 11 This method significantly outperforms the traditional ICA method in faults 1, 4, 8, 10, 11, 12, 16, and 19. Specifically, LOF-SCICA... The statistical average FDR is 96.48%, according to ICA. The average FDR of the statistical measure is 88.4%; LOF-SCICA The average FDR of the statistical measure is 93%, and that of the ICA is... The average FDR was 80.11%, indicating that the FDR of LOF-SCICA all showed varying degrees of improvement. Meanwhile, the FDR of LOF-SCICA... The statistical mean FAR is 3.4%, and the ICA's... The statistical mean FAR is 7.34%; LOF-SCICA The statistical mean FAR is 1.44%, and the ICA's... The average FAR was 3.06%, indicating that the FAR of LOF-SCICA was reduced to varying degrees. In summary, this method uses the LOF algorithm to remove obviously isolated outliers before modeling, and then uses the SCICA algorithm to extract non-Gaussian independent components from the mixture variables to construct an augmented matrix, reducing autocorrelation between samples and effectively improving the algorithm's fault detection performance and reducing the false alarm rate. Therefore, this method demonstrates high adaptability and value in complex industrial monitoring and is more suitable for monitoring industrial processes with mixed Gaussian and non-Gaussian distributions.

[0153] It should be noted that the above embodiments are only used to illustrate the implementation methods and potential advantages of the present invention, and their specific content should not be construed as limiting the scope of protection of the present invention. Within the scope covered by the core technical solution of the present invention, any equivalent substitution or simple improvement made based on the principles of the present invention should be considered to fall within the protection scope of the appended patent application claims.

Claims

1. An industrial fault detection method based on local outlier factor and slowness constraint ICA, characterized in that, Includes the following steps: A. Modeling Phase S1: Select normal operating condition data to construct the modeling training dataset: Then, standardization preprocessing is performed to obtain a standardized data matrix, denoted as . ; S2: The LOF algorithm is used to remove outlier and noisy samples from the data. The local reachability density is calculated based on the Euclidean distance between samples, and the LOF score is obtained to obtain the normal data matrix. ; S3: For normal data matrix Implement time-delay feature extension and construct first-order difference time-delay features, and form an extended feature matrix after feature extension. ; S4: For the extended characteristic matrix Perform whitening transformation processing; Calculate the covariance matrix of this matrix. Then the covariance matrix Perform eigenvalue decomposition to construct the whitening matrix The whitening transformation matrix is ​​obtained. ; S5: Whitening Transformation Matrix Calculate the time difference and construct the time difference matrix. Constructing the slowness matrix ; S6: Initialize the separation matrix for slow component analysis And perform orthogonalization; S7: The slowness matrix calculated from step S5 Based on the slowness criterion, Newton's iterative method is used to solve for the slow component and update the weight vector. ; S8: Sort and select independent components based on the slowness criterion to determine the projection matrix. ; S9: Calculate the monitoring statistics after projecting the training data, and use kernel density estimation to determine the control limits; B. Detection Phase S10: Transfer the test dataset Perform the same preprocessing, time-delay feature expansion, and whitening transformation processes according to steps S1 to S4; S11: Project the whitened test samples onto the SCICA model and calculate the statistics of the test dataset; S12: Compare the statistics obtained in step S11 with the control limits determined in step S9. If the statistics exceed the control limits, it is determined to be a fault and an alarm is triggered; otherwise, it is determined to be normal.

2. The industrial fault detection method based on local outlier factor and slowness constraint ICA as described in claim 1, characterized in that, In S1, the modeling training dataset Preprocessing and normalization are performed to make the mean of all process variables 0 and the variance 1, resulting in a new data matrix set. The formula is as follows: (1)； (2)； (3)； in, It is expressed as the mean of each variable. Standard deviation; In S2, the Euclidean distance between any two samples is calculated. Determine the samples Nearest neighbor set Based on this, the reachability distance between samples is calculated. And further calculate the local reachability density of the sample. The formula is used for subsequent anomaly detection and is as follows: (4)； (5)； (6)； (7)； in, , For any sample, For the number of process variables, calculate the LOF score for each data point and remove those with LOF scores greater than a threshold. Abnormal samples, retained samples Finally, the normal data matrix after removing outliers is obtained. .

3. The industrial fault detection method based on local outlier factor and slowness constraint ICA according to claim 2, characterized in that, In S3, the original cleaned normal data matrix Implement time-delay feature extension and construct first-order differences for each variable. After feature construction is completed, the final extended feature matrix is ​​formed. The formula is as follows: (8)； in, For the number of variables, For sample length, For the first Variables in The value at time; ,from Initially, the difference is generated normally, yielding the difference feature matrix. The formula is as follows: (9)； Normal data matrix The final extended feature matrix is ​​obtained by concatenating the left and right sides of the difference features. .

4. The industrial fault detection method based on local outlier factor and slowness constraint ICA according to claim 3, characterized in that, In S4, the extended feature matrix Whitening transformation is performed to eliminate correlations between data features and unify the variances of each feature, and then the whitening transformation matrix is ​​solved. The formula is as follows: (10)； (11)； (12)； (13)； in, Let covariance matrix be the variance matrix. The eigenvector matrix, It is an eigenvalue diagonal matrix. This represents the number of normal samples remaining after LOF outlier removal.

5. The industrial fault detection method based on local outlier factor and slowness constraint ICA according to claim 4, characterized in that, In step S5, the changes of each variable at adjacent time points are first obtained by calculating the time difference of the whitened data. This represents the instantaneous change of all variables; (The rest of the text appears to be a list of variables and their meanings, possibly related to a specific variable or variable.) The difference samples are stacked in chronological order to obtain the time difference matrix. Constructing a slowly varying matrix based on the time difference matrix The formula is as follows: (14)； (15)； (16)； in, Each row represents the changes of all variables at a time step, and each column represents the trajectory of a certain variable throughout the entire time series. (Slow-changing matrix) The rate of change of the characterizing variable is used for subsequent slow component analysis.

6. The industrial fault detection method based on local outlier factor and slowness constraint ICA according to claim 5, characterized in that, In step S6, the separation matrix for slow component analysis is initialized. The initial separation matrix is ​​orthogonalized using the following formula: (17)； (18)。 7. The industrial fault detection method based on local outlier factor and slowness constraint ICA as described in claim 6, characterized in that, In step S7, Newton's iteration method is used to optimize and solve for each projection vector to be determined; for each component Iteratively update its corresponding weight vector The formula is as follows: (19)； (20)； (21)； (22)； (23)； (24)； (25)； in, This is the slowness adjustment parameter. The gradient vector, It is a Hessian matrix.

8. The industrial fault detection method based on local outlier factor and slowness constraint ICA according to claim 7, characterized in that, In step S8, the slowness value of each independent component is... Quantitative calculations are performed, and then all slowness values ​​are sorted in ascending order from low to high according to the rate of change in order to identify the target components that exhibit slow evolution characteristics on the time scale. The weight vectors were then rearranged based on the sorting results, and several slow components that best reflected the steady trend of the process were selected, along with their cumulative contribution rates. Reaching the threshold The former The slow principal components constitute the projection matrix. The formula is as follows: (26)； (27)； (28)。 9. The industrial fault detection method based on local outlier factor and slowness constraint ICA as described in claim 8, characterized in that, In step S9, the training data is projected onto the slow component space to obtain the slow features. ,Sure Statistics and The statistic is calculated using the following formula: (29)； (30)； (31)； in, To reconstruct the data, use normal operating conditions. and For each sample, control limits for the statistics were calculated using the KDE method. , The formula is as follows: (32)； (33)； (34)； (35)。 10. The industrial fault detection method based on local outlier factor and slowness constraint ICA according to claim 9, characterized in that, In step S10, the mean obtained during the training phase is used. and standard deviation For the test dataset Standardize the data. Constructing first-order difference time delay characteristics The first row is padded with zeros at the boundary. The formula is as follows: (36)； (37)； The final constructed test data expansion matrix is ​​as follows Its dimensions are ; Using the whitening matrix obtained during the training phase The test data are linearly transformed using the following formula: (38)； in, The covariance matrix of the training data in step S4 Obtained by decomposition; In step S11, the main slow features projected onto the SCICA model from the test dataset are calculated. The test dataset Statistics and Statistic, To reconstruct the data, the formula is as follows: (39)； (40)； (41)； In step S12, fault detection is performed based on control limits. If or If the industrial process malfunctions, an alarm mechanism is triggered; if all statistics are within the control limits, the process is considered to be operating normally.

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