Paper machine fault detection and diagnosis method based on multi-section sliding window kernel reconstruction analysis

Abstract

The invention belongs to the technical field of fault detection and diagnosis in a flow industrial process, and discloses a paper machine fault detection and diagnosis method based on multi-section sliding window kernel reconstruction analysis, which comprises the following steps of: constructing a sample through a sliding window mechanism, and performing nonlinear dimension reduction and reconstruction error extraction by adopting kernel principal component analysis; the modeling capability of the model for the complex nonlinear relationship is enhanced; a kernel density estimation method is introduced on the basis of reconstruction error statistics to adaptively set a control limit, and sensitive detection of tiny faults is achieved; by performing variable-level weighted analysis on the reconstruction error, main abnormal variables when the fault occurs are identified, and high-precision fault source positioning is realized. In order to verify the effectiveness of the method, the method is applied to typical fault scenes of multiple working sections in the papermaking process, the experimental result shows that the method can accurately detect and diagnose key abnormal variables in various faults, and the method has high fault interpretability and diagnosis reliability. The method is suitable for abnormal identification and process monitoring of key variables in a complex industrial process.

Description

Technical Field

[0001] This invention belongs to the field of fault detection and diagnosis technology in process industries, specifically relating to a paper machine fault detection and diagnosis method based on multi-segment sliding window kernel reconstruction analysis, which is applicable to intelligent monitoring scenarios with multivariable, strongly coupled, and time-varying characteristics in the paper industry. Background Technology

[0002] In modern papermaking, real-time monitoring and intelligent diagnosis of multivariate process data at key stages are necessary to ensure stable paper quality and reliable equipment operation. However, the papermaking process is characterized by numerous variables, strong temporal sequence, and complex coupling between different stages, posing challenges to the accuracy and real-time performance of traditional monitoring methods that rely on mechanistic modeling or static judgment. With the continuous improvement of industrial data acquisition capabilities and intelligent manufacturing levels, data-driven fault detection methods are gradually becoming the mainstream development direction.

[0003] While current mainstream methods possess a certain ability to identify anomalies, they still have significant limitations in addressing the nonlinear dynamic characteristics, historical dependencies, and cross-process integrated modeling of papermaking processes. On the one hand, some methods fail to effectively integrate the temporal structure information between samples, making it difficult to perceive the time-varying nature of the system's operating state. On the other hand, the use of static control limits also makes the model less robust to minor drifts or early faults, easily leading to false alarms or missed alarms. Furthermore, most existing methods remain at the level of global anomaly detection, lacking the ability to accurately locate fault source variables, thus limiting their practical engineering application value. Summary of the Invention

[0004] This invention addresses the aforementioned problems in the prior art by providing a paper machine fault detection and diagnosis method based on multi-segment sliding window core reconstruction analysis, comprising the following steps: A paper machine fault detection and diagnosis method based on multi-section sliding window core reconstruction analysis includes the following steps: S1. Data preprocessing: The Z-score standardization method is used to normalize the running data to eliminate the scale difference caused by different units. Normal data is divided into training dataset X, and sample data containing various faults is used as test set for model performance evaluation and fault detection verification. S2. Constructing a sliding window feature enhancement model: The sliding window mechanism is used to reconstruct the time series of the normalized data, construct a sample sequence containing time-dependent information, form an enhanced input sample with historical information, and expand the enhanced input sample into a high-dimensional time series vector to enhance the dynamic representation capability of the input features; S3. Constructing a Nonlinear Kernel Dimensionality Reduction Model: Based on the training dataset X, a kernel principal component analysis model is constructed. A radial basis function kernel is introduced to map the sliding window feature data to a high-dimensional feature space. In this high-dimensional feature space, the main structural information is extracted. While preserving the cumulative variance of the principal components, the optimal number of principal components is selected to achieve feature compression and reconstruction capabilities in the high-dimensional feature space. By calculating the reconstruction error and normalization bias of the samples, two monitoring statistics are constructed: the sum of squared reconstruction errors and a nonlinear dissimilarity measure, to capture potential anomalies. The formula for calculating the nonlinear dissimilarity measure is shown below:

[0005] in, Corresponding time index The sliding window vector at that location. The length of the sliding window; S4. Constructing a fault detection and diagnosis model: Input test set sample data containing various faults into the trained nonlinear kernel dimensionality reduction model, and calculate the corresponding sum of squared reconstruction errors and nonlinear dissimilarity measure in real time; use kernel density estimation method to model the normal data statistics distribution of training samples, adaptively and dynamically generate detection thresholds under a given confidence level, use reconstruction error contribution analysis method to calculate and rank the average reconstruction error contribution of each variable within the sliding window, extract the top 5 key variables, and realize the location of key fault sources.

[0006] Preferably, Gaussian filtering is used to smooth and reduce noise in the normal data statistics sequence.

[0007] Preferably, the operating data in step 1 comes from the paper machine production data of the paper mill, and the training dataset X contains the normal operation data of each key section in the paper production process. The key sections include, but are not limited to, the flow section, the wire section, the press section and the drying section.

[0008] Preferably, different typical faults and different types of abnormal modes are injected to construct a fault sample dataset Y for model performance evaluation and fault detection verification. Typical faults include, but are not limited to, high-concentration slurry blockage, vacuum system leakage and ventilation system failure, and abnormal modes include, but are not limited to, drift changes, periodic changes and amplitude changes.

[0009] By adopting the above solution, the present invention has the following beneficial effects compared with the prior art: This invention reconstructs and vectorizes the original process variables of multiple work sections using a sliding window mechanism, introducing historical dependencies to enhance the model's ability to perceive slow-drift and periodic disturbance faults. Based on this, a kernel principal component analysis model with a radial basis function kernel is used to nonlinearly map and compress the sliding window features, improving the model's ability to model high-dimensional coupled processes. A dual-statistic monitoring approach using the sum of squared reconstruction errors and a nonlinear dissimilarity metric is employed to balance reconstruction residual anomalies and changes in coupling structure, improving detection robustness. Furthermore, a kernel density estimation method is introduced to fit the distribution of statistics during the training phase, dynamically setting the detection threshold and enhancing the adaptive detection capability for abnormal states. Simultaneously, the statistical sequence is smoothed to improve the stability of the detection curve. Finally, the variables within the sliding window are ranked using a reconstruction error contribution analysis method, and the top 5 variables are extracted for key fault location. This integrates variable-level reconstruction error contribution analysis, enabling the location and diagnosis of key fault sources and enhancing the interpretability and practicality of the diagnostic process. This invention improves the sensitivity of detecting minor faults while effectively reducing the false alarm rate. It is suitable for complex monitoring scenarios in typical process industries such as papermaking and has strong robustness and promotional value. Attached Figure Description

[0010] Figure 1 This is a flowchart of the steps for a paper machine fault detection and diagnosis method based on multi-segment sliding window core reconstruction analysis; Figure 2 This is a visualization of the characteristics of typical fault 1; Figure 3 This is a visualization of the characteristics of typical fault 2; Figure 4 This is a visualization of the characteristics of typical fault 3; Figure 5 This is a characteristic visualization of typical fault 4; Figure 6 This is a visualization of the characteristics of typical fault 5; Figure 7 This is a visualization of the characteristics of typical fault 6; Figure 8 This is a visualization of the characteristics of typical fault 7; Figure 9 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 1; Figure 10 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 2; Figure 11 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 3; Figure 12 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 4; Figure 13 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 5; Figure 14 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 6; Figure 15 This is a graph showing the detection results of the SW-KPCA-KDE model for typical fault 7; Figure 16 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 1; Figure 17 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 2; Figure 18 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 3; Figure 19 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 4; Figure 20 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 5. Figure 21 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 6; Figure 22 This is a diagram showing the diagnostic results of the SW-KPCA-KDE model for typical fault 7. Detailed Implementation

[0011] The present invention will now be described more clearly and completely. Obviously, the examples described are only a part of the examples of the present invention, and not all of the embodiments.

[0012] Example 1:

[0013] like Figure 1 As shown, the method for detecting and diagnosing faults generated during the paper machine production process provided by this invention adopts the following technical solution: S1. Data Preprocessing: First, normal operation data of key sections in the papermaking industry (such as the flow section, pressing section, wire section, and drying section) were collected. Due to the inconsistency of dimensions among different variables, the Z-score standardization method was used to normalize all normal operation data to eliminate scale differences caused by different dimensions and ensure that all operation data variables are modeled and analyzed on the same scale. The normal data was divided into a training set, and the data containing 7 different faults was used as a test set for model performance evaluation (generalization evaluation and fault identification performance verification).

[0014] S2. Constructing a Sliding Window (SW) Enhanced Model: To capture the temporal evolution trends and potential coupling relationships of variables, a sliding window mechanism is used to reconstruct the time series of normalized data, constructing a sample sequence containing time-dependent information, forming an enhanced input sample with historical information. By setting an appropriate sliding window length, the original data sequence is sliced ​​along the time axis, and samples are constructed by sliding with a fixed window length in the time dimension, obtaining multi-dimensional time segments at each moment, generating high-dimensional samples with time dependencies, and expanding them into a high-dimensional time series vector, enhancing the dynamic representation capability of the input features. By converting the original sequence into a sample sequence containing local dynamic information, this method can capture the historical evolution patterns of variables, providing a more sufficient information basis for subsequent nonlinear dimensionality reduction and anomaly modeling, thereby improving the sensitivity to dynamic fault modes such as slow drift and periodic perturbations. This method can embed the variable states at the current moment and several past moments into the model input in a unified manner, effectively preserving the temporal dynamic structure between samples. The expanded high-dimensional time series vector not only contains the static relationships between variables, but also integrates their trend characteristics over time.

[0015] S3. Constructing a Nonlinear Kernel Dimensionality Reduction Model: To enhance the modeling capability for nonlinear features, a kernel principal component analysis (KPCA) model is constructed based on the training set. By introducing a radial basis function (RBF), the sliding window features are mapped to a high-dimensional feature space. In this high-dimensional feature space, the main structural information is extracted. While retaining the cumulative variance of the principal components, the optimal number of principal components is selected to achieve feature compression and reconstruction capabilities in the high-dimensional feature space. By calculating the reconstruction error and normalization deviation of the samples, two types of monitoring statistics are constructed: the sum of squared reconstruction errors (SPE) and the nonlinear dissimilarity measure (DIS). SPE and DIS are used as statistics to measure the degree of data anomalies, measuring whether the samples deviate from the normal operating mode, thereby capturing potential abnormal behavior or system instability. Among them, SPE mainly reflects the magnitude of the residual of the sample in the sense of kernel reconstruction, and is more sensitive to anomalies caused by noise interference, local mutations, or the accumulation of reconstruction errors. DIS is used to characterize the degree of nonlinear difference of the samples in the kernel feature space, and has a supplementary discriminative ability for anomalies such as related structural changes and slow drifts in strongly coupled processes that are not easily amplified immediately in the residuals. The two can complement each other under different failure modes, improving the stability and robustness of detection.

[0016] S4. Constructing a Fault Detection and Diagnosis Model: Input test set samples containing various faults into the trained KPCA model and calculate their corresponding SPE and DIS values ​​in real time. To improve the model's adaptability under different operating conditions, the kernel density estimation (KDE) method is used to model the normal data statistics distribution of the training samples, thereby adaptively and dynamically generating detection thresholds at a given confidence level, replacing the traditional static limit setting method, and avoiding control limit bias and false alarm risks caused by the Gaussian distribution assumption. At the same time, to improve the stability of the online monitoring curve, Gaussian filtering is used to smooth and denoise the statistical sequence, reducing misjudgments caused by sudden noise. To locate the root cause of the anomaly, reconstruction error contribution analysis is further used to calculate and rank the average reconstruction error contribution of each variable within the sliding window, extract the top 5 key variables, realize the location of key fault sources, and thus achieve accurate diagnosis and interpretable output of the fault source.

[0017] S5. Generalization Ability and Comparative Evaluation of Fault Detection and Diagnosis Models: To verify the generalization ability and stability of this method in practical industrial applications, a multi-model comparison experiment was designed. Based on the constructed fault detection and diagnosis model, under the same fault scenarios and data conditions, Principal Component Analysis (PCA), KPCA, KPCA-KDE, SW-PCA-KDE, and SW-KPCA-3 were respectively introduced. These five typical comparative methods were used as comparative models for performance evaluation. Comparative experiments were conducted in seven typical fault scenarios to evaluate the model's detection performance under different fault types. Using fault identification accuracy and variable location accuracy as indicators, the performance advantages and engineering practical value of the proposed method in nonlinear, time-delay, and multi-segment dynamic processes were comprehensively verified. Evaluation indicators included fault detection accuracy, false alarm rate, and F1 score. The results show that the proposed method exhibits superior detection accuracy and robustness in handling nonlinear systems, time-delay processes, and multi-segment data fusion tasks, demonstrating good potential for engineering applications.

[0018] The advantage of this method lies in its integration of key modules, such as the SW feature enhancement mechanism, kernel space reconstruction statistics (SPE&DIS) evaluation, KDE control limit calculation, statistical smoothing, and variable-level reconstruction contribution analysis, based on the KPCA method. This establishes an intelligent fault detection and diagnosis method for multiple production stages. This method effectively characterizes the nonlinear behavior and dynamic time-varying characteristics of the papermaking process, improving fault detection sensitivity while enhancing the ability to locate key variables, and exhibits good stability and interpretability.

[0019] In step S1, normal operation data and fault injection data from each key stage of the papermaking process are collected to form an input sample set. The input sample matrix is ​​as follows: (1) In the formula, For the length of time, For variable dimensions, Indicates the first The variable vector at each time step.

[0020] S11: Perform Z-score standardization on the input sample matrix. The standardization formula is as follows: (2) In the formula, and The first The sample mean and standard deviation of each variable. The standardized data are denoted as: (3) In the formula, For the length of time, For variable dimensions.

[0021] The standardized data is used to divide the training set and the test set. The training set consists of all normal data, and the test set consists of fault data from multiple work sections.

[0022] In step S2, the sliding window (SW) enhancement model is constructed as follows: S21: Introduce a length of [length] in the time dimension. A sliding window is used to construct high-dimensional features that include temporal dependencies. For each time step... Constructing local time segments: (4) S22: Expand the segment into a vector row by row: (5) In the formula, Indicates row-major order Matrix expanded to length A one-dimensional vector.

[0023] S23: Finally, construct the high-dimensional sliding window feature matrix: (6) This structure effectively integrates dynamic information between variables and time series, providing temporal support for nonlinear modeling.

[0024] In step S3, based on the enhanced high-dimensional time-series features through the sliding window, a kernel principal component analysis model with a radial basis function is constructed. The latent principal feature structure is extracted through nonlinear mapping, and the optimal number of principal components is automatically selected based on the cumulative feature variance, achieving effective compression and reconstruction of feature information. S31: The nonlinear mapping constructs the feature space as follows: Let the input sample matrix after the sliding window construction be: (7) in, For the sample size, Dimensions for each sample ( Corresponding time index The sliding window vector at that point, i.e. , .

[0025] Each input sample Through nonlinear mapping function Mapping to a high-dimensional feature space enhances the linear separability and feature representation ability of the data. (8) The construction is not displayed in actual calculations. Instead, it is through kernel functions. We directly calculate the inner product of samples in the feature space, thus avoiding explicit calculations in the high-dimensional feature space. (9) S32: Define the kernel function and construct the kernel matrix: The inner product of samples in a high-dimensional feature space is calculated using a radial basis function (RBF) kernel, which is used to measure and define the nonlinear similarity between samples: (10) In the formula, This is the kernel width parameter.

[0026] Construct the kernel matrix: (11) By centering K, we obtain the centered kernel matrix. : (12) In the formula, .

[0027] S33: Principal Component Extraction and Dimensionality Reduction Transformation For the centralized kernel matrix Perform eigenvalue decomposition: (13) In the formula, For eigenvalues, This is the corresponding feature vector.

[0028] Selecting based on the proportion of cumulative eigenvalues One principal component, such that: (14) Construct the dimension reduction transformation matrix: (15) In the formula, For the kernel matrix The former A matrix composed of eigenvectors To and corresponding A diagonal matrix composed of eigenvalues.

[0029] S34: Reconstruction and Statistical Modeling dimensionality-reduced samples Projecting back into the original space yields a reconstructed sample. : (16) Calculate the sum of squared reconstruction errors (SPE): (17) Calculate the nonlinear dissimilarity metric DIS: (18) In step S4, a fault detection and diagnosis model is constructed: S41: Constructing a kernel density estimation model for control limits: Using KPCA of normal data to reconstruct the error series, construct two types of monitoring statistics, SPE and DIS, and obtain adaptive control limits based on the KDE method.

[0030] Let the sliding window input for normal data samples be... After KPCA transformation and reconstruction, the SPE and DIS index sequences can be obtained: (19) (20) The distribution functions of SPE and DIS are modeled using the KDE method: (twenty one) (twenty two) In the formula, This is the bandwidth parameter.

[0031] At confidence level Next, solve for the control limits of SPE. With DIS control limit The cumulative distribution satisfies: (twenty three) S42: Transfer fault sample data Inputting the data into the trained KPCA model yields the reconstruction error sequence, and its SPE and DIS are calculated: (twenty four) (25) The judgment rules are as follows: (26) S43: Analyze the contribution of reconstruction error to variables, and perform variable-level averaging statistics on the reconstruction error at all times in the fault detection samples: Let the reconstruction error be: (27) In the formula, The length of the sliding window. For variable dimensions.

[0032] Average variable error for each sample over the sliding window: (28) Finally, the average error contribution of all sample variables is obtained: (29) Extract the top 5 variables by contribution: (30) These variables are identified as potential sources of failure or influencing variables, enabling interpretable fault localization at the variable level.

[0033] In step S5, five comparison models are introduced to evaluate the generalization ability and detection performance of the fault detection and diagnosis model. Test set data is fed into the model for detection. Based on the model's anomaly detection results and the actual fault labels, three performance metrics are calculated: Fault Detection Rate (FDR), False Alarm Rate (FAR), and F1 score. FDR represents the proportion of real fault samples successfully identified by the model out of all actual fault samples; a value closer to 100% indicates stronger fault detection capability. FAR represents the proportion of normal samples that the model misclassifies as faults out of all normal samples; a lower value indicates a more stable model and a lower risk of false alarms. The F1 score is a comprehensive evaluation metric that balances detection accuracy and completeness; a value closer to 1 indicates superior detection performance. These three metrics are used together to evaluate the model's detection sensitivity and robustness under various fault conditions.

[0034] S51: To eliminate the interference of instantaneous fluctuations in the monitoring statistics on the detection results, a one-dimensional Gaussian filter is used for smoothing. (31) (32) In the formula, the smoothing parameter This can improve the stability of abnormal curves and increase fault tolerance.

[0035] S52: Set the real label based on the fault origin and in conjunction with the test results calculate: FDR: (33) In the formula, TP represents the number of correctly detected fault points, and FN represents the number of missed faults.

[0036] FAR: (34) In the formula, FP represents the false alarm point, and TN represents the correctly identified normal point.

[0037] F1 score: (35) In the formula, TP represents the number of correctly detected fault points, FP represents false alarm points, FN represents missed alarms, and TN represents correctly identified normal points.

[0038] Example 2: Taking the paper machine production process of a paper mill as an example, the paper machine production data used for modeling includes the flow section (21 variables), wire section (10 variables), press section (27 variables), and dryer section (13 variables). The data used for fault detection and diagnosis includes drift-type faults (high-concentration pulp blockage in the flow section, insufficient vacuum water absorption in the press section, steam pressure fluctuations in the dryer section, and leakage in the wire section vacuum system), periodic disturbance-type faults (overpressure of the press section's first pressure shoe sleeve), proportional expansion-type faults (failure of the flow section's dilution water screen), and proportional reduction-type faults (failure of the dryer section's exhaust system). All of these faults are introduced starting from the 201st sample. Each production department in both sets of data contains 442 sample points. Figure 1 The present invention will be further described as follows: Step 1: Normal production data collected from each department (conveyor, wire mesh, pressing, and drying) under stable operating conditions is used as the training set to build and train the fault detection model. Simultaneously, multi-section data simulated with seven typical fault types is used as the test set to evaluate the detection performance and diagnostic capabilities of the fault detection model under different abnormal conditions. The characteristics of the seven different fault types are as follows: Figure 2-8 As shown.

[0039] Step 2: Construct the standardized multivariate time series data according to the set sliding window length, and introduce the past into each sample in the time dimension. Historical information at each time point. By vectorizing and expanding each time segment to form a high-dimensional time-series sample matrix, the model's ability to model the dynamic evolution of variables is enhanced. This processing method can significantly improve the perception of faults such as slow process drift and periodic disturbances, and is an important foundation for subsequent nonlinear feature extraction and modeling.

[0040] Step 3: Construct a KPCA model using RBF to perform nonlinear mapping and feature compression on the time-series samples enhanced by the sliding window. Select the optimal kernel width parameter through grid search. The number of principal components is automatically selected based on the cumulative feature variance threshold (95%). During this process, the model is trained only on normal data to ensure the accuracy and generalization of the reconstructed structure. The determination of the number of principal components is based on minimizing the mean reconstruction error, thereby optimizing the robustness and anomaly sensitivity of the SPE and DIS indices. Given the differences in temporal characteristics and variable perturbation patterns among different types of faults, this paper designs optimal parameter combinations for each type of fault scenario. This includes the sliding window length (… ), KPCA kernel width ( ), optimal number of principal components ( ) and smoothing factor ( The optimal model configurations for various fault types are shown in Table 1.

[0041] Table 1 Optimal parameters for various fault models

[0042] Step 4: Input simulated fault data into the trained KPCA model. Calculate the corresponding SPE and DIS as monitoring statistics. Use KDE to fit the distribution of statistics during the training phase, and dynamically set the detection threshold at a 99% confidence level to improve the detection's adaptability to different anomaly distributions. To enhance curve readability, Gaussian filtering is used for smoothing. Subsequently, FDR, FAR, and F1 scores are calculated to evaluate the detection results. The detection results for the seven types of faults are shown in [see...]. Figure 9-15 Furthermore, to facilitate fault tracing, the average reconstruction error of each variable was calculated within each time window. Variables were then ranked according to their contribution, and the top 5 variables were extracted for key fault location. For detailed diagnostic information, please refer to [link to diagnostic details]. Figure 16-22See Table 2-8. Subsequently, the extracted key variables were compared and analyzed with the actual fault source variables that changed during the fault injection process. The diagnostic results show that, except for the "first-stage shoe sleeve overpressure" fault where the "first-stage shoe sleeve pressure zone oil pressure" variable was not identified, and the "first-stage screen inlet pressure" variable was not identified in the "dilution water screen failure" fault, all other key variables for the remaining faults successfully appeared among the top 5 contributing variables. The diagnostic accuracy reached a high level, indicating that the proposed fault diagnosis method has good interpretability and effectiveness in capturing fault-related variables.

[0043] Table 2 Diagnostic results of fault 1

[0044] Table 3 Diagnostic results of fault 2

[0045] Table 4 Diagnostic results of fault 3

[0046] Table 5 Diagnostic results for fault 4

[0047] Table 6 Diagnostic results of fault 5

[0048] Table 7 Diagnostic results of fault 6

[0049] Table 8 Diagnostic results of fault 7

[0050] Step 5: On the same dataset, comparisons were made between standard PCA, KPCA, KPCA-KDE, SW-PCA-KDE, and 3... Control Limits Method (SW-KPCA-3) Five typical methods, including sliding window and kernel density estimation, were proposed and systematically evaluated under seven representative fault conditions. Using FDR, FAR, and F1 score as core evaluation indicators, the stability and diagnostic accuracy of the proposed method were comprehensively verified in nonlinear, time-varying, and multi-segment process scenarios. Tables 9-14 show the performance comparison of the six models on the test set. The results show that the fault detection model based on sliding window kernel principal component analysis combined with kernel density estimation achieved the best results in all three evaluation indicators (FDR, FAR, and F1 score) on the test set. Compared with the traditional PCA method, the SW-KPCA-KDE model optimized based on sliding window and kernel density estimation shows significant advantages in fault detection tasks. In terms of FDR (Fault Detection), the model achieves an average improvement of over 50%, with particularly outstanding performance in multiple fault types (such as faults 2, 4, 6, and 7), reaching a maximum improvement of 83.82%, effectively enhancing the detection capability for early, complex, and minor faults. Regarding FAR (Fault Accuracy Detection), the model maintains an extremely low false alarm rate in both SPE (Severe Detection) and DIS (Disruptive Instability) detection, with an average FAR of only 0.45%, lower than KPCA and SW-KPCA-3. Using methods such as [unspecified], the SW-KPCA-KDE achieved a significant improvement in the F1 score of the comprehensive performance index under both SPE and DIS dual channels, verifying its superior performance in fault detection accuracy and stability.

[0051] Table 9 Comparison of FDR (SPE) for different models

[0052] Table 10 Comparison of FDR (DIS) for different models

[0053] Table 11 Comparison of FAR (SPE) for different models

[0054] Table 12 Comparison of FAR (DIS) for different models

[0055] Table 13 Comparison of F1 scores (SPE) for different models

[0056] Table 14 Comparison of F1 scores (DIS) for different models

[0057] This invention addresses the challenges of highly nonlinear, complex dynamic characteristics, severe variable coupling, and non-stationary data distribution in industrial processes such as papermaking. It proposes an intelligent fault detection and diagnosis method based on sliding window-kernel principal component analysis-kernel density estimation (SW-KPCA-KDE). This method enhances the model's ability to capture time-series features through a sliding window mechanism, effectively reduces the dimensionality of high-dimensional nonlinear features using KPCA, and adaptively constructs statistical control limits using kernel density estimation technology to achieve sensitive identification of abnormal operating conditions. Furthermore, by analyzing the contribution of principal component reconstruction errors, it further enables variable-level fault location and diagnosis.

[0058] The basic principles, main features, and advantages of this invention have been described above. The above description is merely a preferred embodiment of the invention, and the scope of protection of this invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope demonstrated by this invention should be included within the scope of protection of this invention. Therefore, the scope of protection of this invention should be defined by the appended claims and their equivalents.

Claims

1. A paper machine fault detection and diagnosis method based on multi-section sliding window core reconstruction analysis, characterized in that, Includes the following steps: S1. Data preprocessing: The Z-score standardization method is used to normalize the running data to eliminate the scale difference caused by different units. Normal data is divided into training dataset X, and sample data containing various faults is used as test set for model performance evaluation and fault detection verification. S2. Constructing a sliding window feature enhancement model: The sliding window mechanism is used to reconstruct the time series of the normalized data, construct a sample sequence containing time-dependent information, form an enhanced input sample with historical information, and expand the enhanced input sample into a high-dimensional time series vector to enhance the dynamic representation capability of the input features; S3. Constructing a nonlinear kernel dimensionality reduction model: Based on the training dataset X, a kernel principal component analysis model is constructed. A radial basis function is introduced to map the sliding window feature data to a high-dimensional feature space. In this high-dimensional feature space, the main structural information is extracted. While retaining the cumulative feature variance of the principal components, the optimal number of principal components is selected to achieve feature compression and reconstruction capabilities in the high-dimensional feature space. By calculating the reconstruction error and normalization deviation of the samples, two types of monitoring statistics, namely the sum of squared reconstruction errors and the nonlinear dissimilarity measure, are constructed to capture potential abnormal features. The formula for calculating the nonlinear dissimilarity metric is shown below: ； in, Corresponding time index The sliding window vector at that location. The length of the sliding window; S4. Constructing a fault detection and diagnosis model: Input test set sample data containing various faults into the trained nonlinear kernel dimensionality reduction model, and calculate the corresponding sum of squared reconstruction errors and nonlinear dissimilarity measure in real time; use kernel density estimation method to model the normal data statistics distribution of training samples, adaptively and dynamically generate detection thresholds under a given confidence level, use reconstruction error contribution analysis method to calculate and rank the average reconstruction error contribution of each variable within the sliding window, extract the top 5 key variables, and realize the location of key fault sources.

2. The paper machine fault detection and diagnosis method based on multi-section sliding window core reconstruction analysis according to claim 1, characterized in that, Gaussian filtering is used to smooth and reduce noise in normal data statistics sequences.

3. The paper machine fault detection and diagnosis method based on multi-section sliding window core reconstruction analysis according to claim 1, characterized in that, The operational data in step 1 comes from the paper machine production data of the paper mill. The training dataset X contains the normal operation data of each key section in the paper production process. The key sections include, but are not limited to, the flow section, the wire section, the press section, and the drying section.

4. The paper machine fault detection and diagnosis method based on multi-segment sliding window core reconstruction analysis according to claim 1, characterized in that, A fault sample dataset Y is constructed by injecting different typical faults and different types of abnormal modes for model performance evaluation and fault detection verification. Typical faults include, but are not limited to, high-concentration slurry blockage, vacuum system leakage and ventilation system failure. Abnormal modes include, but are not limited to, drift changes, periodic changes and amplitude changes.

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