A multi-working-condition industrial process fault monitoring method and system based on stationarity decomposition and local adaptive residual learning
Patent Information
- Application Number
- CN202610996600.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-06
- Publication Date
- 2026-10-09
AI Technical Summary
[0006]本发明旨在解决多工况工业过程中因工况频繁变换、过渡漂移以及数据强耦合、非高斯分布等复杂特性所导致的监测模型易误报、漏报的问题，提供一种基于平稳性分解与局部自适应残差学习的多工况工业过程故障监测方法及系统
[0065]（1）通过联合优化非高斯性与分布平稳性，从强耦合、非高斯的多工况数据中提取跨工况一致的平稳独立源，缓解了传统方法易提取伪平稳特征的问题；
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Figure CN122885375A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of industrial process monitoring, and mainly to a multi-condition industrial process fault monitoring method and system based on stationary decomposition and local adaptive residual learning. Background Technology
[0002] With the continuous expansion of modern industrial systems and the increasing diversification of production demands, industrial processes typically operate under multiple conditions, including steady-state conditions, transient conditions, and complex scenarios involving condition switching. Methods based on multivariate statistical process monitoring, which map process data to a low-dimensional subspace and construct monitoring statistics, have been widely applied in the field of fault detection.
[0003] Existing methods, particularly traditional single-model approaches, attempt to construct a global monitoring model applicable to all operating conditions. However, when faced with multimodal, non-Gaussian, and strongly coupled process data, the global decision boundary struggles to distinguish between normal time-varying operating conditions and real fault disturbances, easily leading to high false alarms or missed alarms. While multi-model methods can establish independent monitoring models for each known operating condition, the prerequisite for accurately identifying the current process condition is difficult to meet in actual production, especially in complex scenarios covering frequent changes in operating conditions and transitional phases, where they have certain limitations in adaptability.
[0004] On the other hand, adaptive monitoring methods that have emerged in recent years track process time-varying changes by updating model parameters in real time. However, most methods only focus on the dynamic changes in the overall data distribution and fail to deeply explore the stationary common features existing across operating conditions. Some methods based on common feature extraction rely on distribution alignment or parameter sharing mechanisms. In scenarios with strong variable coupling and statistical non-Gaussian characteristics, they are prone to extracting pseudo-stationary or difficult-to-interpret features, leading to a decline in monitoring performance. Furthermore, existing methods lack an effective mechanism to distinguish between time-varying behavior under normal operating conditions and true fault signals, which restricts the reliability and practicality of monitoring systems.
[0005] Therefore, how to effectively extract consistent stationary features across multiple operating conditions in complex industrial processes that are multi-condition, strongly coupled, and non-Gaussian, and adaptively model normal time-varying behavior to improve the ability to distinguish between normal operating condition changes and real fault disturbances, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0006] This invention aims to solve the problem of false alarms and missed alarms in monitoring models caused by the frequent changes in operating conditions, transitional drift, strong data coupling, and non-Gaussian distribution in multi-condition industrial processes. It provides a multi-condition industrial process fault monitoring method and system based on stationary decomposition and local adaptive residual learning.
[0007] The technical solution adopted in this invention mainly consists of the following steps:
[0008] Step 100: Obtain historical data and online samples of multi-condition processes, and perform standardization and whitening preprocessing on the historical data to obtain whitened data;
[0009] Step 200: Construct a joint optimization objective for stationary independent component analysis, using non-Gaussianity to measure the independence of each component and the maximum mean difference of the kernel embedding mean in each time period to measure the distribution stationarity, and establish a joint optimization problem with orthogonal constraints;
[0010] Step 300: Solve for the orthogonal matrix on the Stiefel manifold using the Riemann gradient descent method, calculate the Riemann gradient, determine the step size through Armijo backtracking search, use QR decomposition to shrink back to ensure orthogonality, and obtain the orthogonal matrix through iterative convergence.
[0011] Step 400: Use an orthogonal matrix to decompose the whitened data into independent components. Based on the stationarity index of each independent component, classify the independent components with stationarity indices below a preset threshold into stationary layers, and classify the independent components with stationarity indices above a preset threshold into non-stationary layers.
[0012] Step 500: For online non-stationary layer samples, query the nearest neighbors by Euclidean distance, maintain a finite-capacity recursive memory set, calculate the local mean and covariance on the memory set, extract the low-variance residual direction through singular value decomposition, and calculate the residual components of online samples;
[0013] Step 600: Construct the first statistic based on stationary independent components, construct the second statistic based on residual components, determine the control limits by kernel density estimation, and use hierarchical decision rules combined with historical backtracking windows to judge the process status and distinguish between normal operating conditions and time-varying faults.
[0014] Furthermore, the specific operations for data preprocessing described in step 100 are as follows. Let... This represents historical data for a multi-condition process, where Indicates the number of samples. This represents the dimension of the variable. First, the historical data is standardized to obtain... Then, a whitening transformation is performed, and the covariance matrix is set. Feature decomposition into Therefore, the whitening transformation can be obtained as:
[0015]
[0016] in To whiten the data, satisfy Reverse whitening transformation to .
[0017] Furthermore, the stationary independent component analysis described in step 200 specifically includes: finding orthogonal matrices in the whitening space. ,satisfy This makes the transformed components To simultaneously satisfy the independence objective and the distribution stationarity constraint, we need to solve the following optimization problem:
[0018]
[0019] in, express Orthogonal group For the independence objective term, For the first The loss of stationarity of the distribution of each component For a set of stationary sources, and Let be the stationarity weighting coefficients. To measure the independence of the components, a contrast function is used. Let be... , No. Each component is The independence objective function is defined as follows:
[0020]
[0021] The negative value of the objective function corresponds to a measure of non-Gaussianity. Minimize This is equivalent to maximizing the non-Gaussianity of each component, thus achieving statistical independence. The Euclidean gradient of the independence term can be calculated as:
[0022]
[0023] To measure the stationarity of the component distribution, the training sequence is divided into fixed lengths. It is divided into multiple time periods. Let there be a total of... The time period, the first The time period label for each sample is .
[0024] For components The non-stationarity is measured by the maximum mean difference of the kernel embedding mean. Considering computational efficiency, a random Fourier feature approximation Gaussian kernel is used for the 1-dimensional component. Define a random Fourier feature map:
[0025]
[0026] in , , The feature dimension, The width of the Gaussian kernel is given. The mean embedding for each time period is calculated as follows:
[0027]
[0028] in For the first The number of samples in each time period. Then the population mean embedding is:
[0029]
[0030] The stationarity loss is defined as the weighted variance of the embeddings of the mean of each time period to the embedding of the population mean:
[0031]
[0032] when At that time, the weight was considered Completely stationary. The Euclidean gradient of the stationarity loss is calculated using the chain rule:
[0033]
[0034] Due to constraints The feasible region is a Stiefel manifold. .
[0035] Furthermore, the orthogonal matrix solution in step 300 employs the Riemann gradient descent method, the specific process of which is as follows. First, the Euclidean gradient of the objective function is calculated:
[0036]
[0037] Projecting the Euclidean gradient onto the tangent space of the Stiefel manifold yields the Riemann gradient:
[0038]
[0039] Use Armijo backtracking search to determine the step size. The updated formula is:
[0040]
[0041] Then, the candidate points are pulled back to the manifold using QR shrinking:
[0042]
[0043] in Denotes the orthogonality factor of QR decomposition, ensuring Repeat the above iterations until convergence.
[0044] Further, the process of decomposing the data into stationary and non-stationary layers in step 400 is as follows: The orthogonal matrix obtained through training with stationary independent component analysis... Whitening data can be decomposed into independent components. Based on the set S of stationary components, the independent components are divided into two layers:
[0045]
[0046]
[0047] Extracted latent variables Corresponding to consistent information across operating conditions, Time-varying information corresponding to normal operating conditions.
[0048] Furthermore, the recursive memory set construction and residual component analysis described in step 500 include the following: For online samples First, calculate its non-stationary components. Reconstruction of whitening Subsequently, on the offline non-stationary layer training set Query its Euclidean distance Neighbor To enhance temporal continuity and improve the numerical stability of local models, a recursive memory set is maintained:
[0049]
[0050] Set preset memory capacity for If the upper limit is set, the most recently added entries will be retained. Indexes.
[0051] In memory set Calculate local samples Mean and covariance:
[0052]
[0053] right Perform singular value decomposition and select the one with the smallest variance. Each direction is used as the residual direction. So, for centralized online non-stationary layers... Its residual components can be calculated:
[0054]
[0055] This component is used to measure the degree of deviation of online non-stationary layer samples from normal operating conditions. Because the local model is dynamically constructed based on similar samples in the non-stationary layer space, it can adaptively track the time-varying nature of normal operating conditions and is more sensitive to exogenous disturbances and anomalous noise.
[0056] Furthermore, the monitoring statistics and hierarchical decision rules described in step 600 are as follows.
[0057] The monitoring statistics are constructed based on stationary independent components and residual components as follows:
[0058]
[0059]
[0060] The confidence factor can be set, and the alarm control limit can be determined using the kernel density estimation method.
[0061] For online samples A hierarchical decision-making strategy is adopted to determine the process status. The extracted stationary independent components reflect the constraints of consistent operating conditions and should remain stationary during normal operating condition changes and transitions, while the non-stationary layer updates the model as the operating conditions change over time. To mitigate false alarms caused by noise, the decision rules are designed as follows:
[0062]
[0063] in This is the length of the history lookup window. If... If the limit is exceeded, it is judged as a fault. Exceeded limits, check past records. Within a time period If any limits are exceeded, it is considered a fault; otherwise, it is considered normal. This strategy uses the historical behavior of the stationary layer statistics to distinguish between abnormal occurrences and changes in normal operating conditions.
[0064] The beneficial effects of this invention are:
[0065] (1) By jointly optimizing non-Gaussianity and distribution stationarity, a consistent stationary independent source across working conditions is extracted from strongly coupled, non-Gaussian multi-working-condition data, which alleviates the problem of traditional methods easily extracting pseudo-stationary features.
[0066] (2) By dynamically maintaining the set of similar samples and extracting the direction of local residuals, the normal working conditions of non-stationary layers are adaptively tracked and time-varying, which improves the detection sensitivity of weak faults and slowly changing faults.
[0067] (3) Use the historical behavior of the stable layer to backtrack and verify the occasional over-limit of the residual layer, effectively distinguishing between normal operating condition changes and real faults, and improving the fault detection rate while maintaining a low false alarm rate.
[0068] (4) In complex operating condition switching scenarios, the method of the present invention shows high detection capability for multiple typical faults, especially in complex fault cases such as fault 14 and fault 17, it has a higher detection rate than existing methods. Attached Figure Description
[0069] To clearly illustrate the embodiments of the present invention or the prior art, the relevant drawings are briefly described below. It should be noted that the following drawings are only for some embodiments of the present invention. Those skilled in the art can obtain other drawings based on these drawings without any creative effort.
[0070] Appendix Figure 1 This invention presents a multi-condition industrial process fault monitoring method and system based on stationarity decomposition and local adaptive residual learning, and its overall flowchart is shown below.
[0071] Appendix Figure 2 This is a comparison chart of the monitoring results of four methods under normal operating condition switching scenarios according to the present invention;
[0072] Appendix Figure 3 This is a comparison chart of the monitoring results of the four methods in fault scenario 4 of the present invention;
[0073] Appendix Figure 4 This is a comparison chart of the monitoring results of the four methods under fault scenario 14. Detailed Implementation
[0074] The technical solution of the present invention has wide applicability and flexibility. The following embodiments are only examples. Those skilled in the art can flexibly adjust the implementation method according to actual needs and the technical solution of the present invention.
[0075] In this embodiment, combined with the appendix Figure 1 This is a multi-condition industrial process fault monitoring method and system based on stationarity decomposition and local adaptive residual learning, which mainly consists of the following steps:
[0076] Step 100: Obtain historical data and online samples of multi-condition processes, and perform standardization and whitening preprocessing on the historical data to obtain whitened data;
[0077] Step 200: Construct a joint optimization objective for stationary independent component analysis, using non-Gaussianity to measure the independence of each component and the maximum mean difference of the kernel embedding mean in each time period to measure the distribution stationarity, and establish a joint optimization problem with orthogonal constraints;
[0078] Step 300: Solve for the orthogonal matrix on the Stiefel manifold using the Riemann gradient descent method, calculate the Riemann gradient, determine the step size through Armijo backtracking search, use QR decomposition to shrink back to ensure orthogonality, and obtain the orthogonal matrix through iterative convergence.
[0079] Step 400: Use an orthogonal matrix to decompose the whitened data into independent components, and divide it into a stationary layer and a non-stationary layer according to the stationarity index. The stationary layer corresponds to consistent information across operating conditions, and the non-stationary layer corresponds to time-varying information under normal operating conditions.
[0080] Step 500: For online non-stationary layer samples, query the nearest neighbors by Euclidean distance, maintain a finite-capacity recursive memory set, calculate the local mean and covariance on the memory set, extract the low-variance residual direction through singular value decomposition, and calculate the residual components of online samples;
[0081] Step 600: Construct the first statistic based on stationary independent components, construct the second statistic based on residual components, determine the control limits by kernel density estimation, and use hierarchical decision rules combined with historical backtracking windows to judge the process status and distinguish between normal operating conditions and time-varying faults.
[0082] The specific operations for data preprocessing described in step 100 are as follows. Let... This represents historical data for a multi-condition process, where Indicates the number of samples. This represents the dimension of the variable. First, the historical data is standardized to obtain... Then, a whitening transformation is performed, and the covariance matrix is set. Feature decomposition into Therefore, the whitening transformation can be obtained as:
[0083]
[0084] in To whiten data, satisfy Reverse whitening transformation to .
[0085] Further, in step 200 of this embodiment, the joint optimization process of the stationary independent component analysis is as follows: Finding orthogonal matrices in the whitening space. ,satisfy This makes the transformed components It simultaneously satisfies the independence objective and the distribution stationarity constraint. The joint optimization objective function and constraints are as follows:
[0086]
[0087] To measure the statistical independence of the components, non-Gaussianity is used as the comparison function. Let the th... Each component is The independence objective function is defined as follows:
[0088]
[0089] Minimizing this objective function is equivalent to maximizing the non-Gaussianity of each component, thereby achieving statistical independence of the signals from each potential source. The Euclidean gradient of this independence term with respect to the orthogonal matrix is calculated as follows:
[0090]
[0091] Furthermore, to measure the stationarity of the component distribution, the training sequence is divided into fixed lengths. It is divided into multiple time periods. Let there be C time periods in total, and the first time period is... The time period label for each sample is .
[0092] This embodiment uses the maximum mean difference of the kernel embedding mean to measure the nonstationarity of the components. To improve the computational efficiency of large-scale data, a stochastic Fourier feature is introduced to approximate the Gaussian kernel function. For a 1-dimensional component, its stochastic Fourier feature mapping function is:
[0093]
[0094] Furthermore, the mean embedding for each time period is as follows:
[0095]
[0096] The overall mean embedding is:
[0097]
[0098] The resulting distribution stationarity loss function is as follows:
[0099]
[0100] The Euclidean gradient of the loss function with respect to the orthogonal matrix is solved using the chain rule:
[0101]
[0102] Due to the existence of orthogonal constraints, the feasible region constitutes a Stiefel manifold.
[0103] Furthermore, as described in step 300, the Riemann gradient descent method is used to solve the above joint optimization problem:
[0104]
[0105] Calculate the Euclidean gradient of the global objective function and project it onto the tangent space of the Stiefel manifold to obtain the Riemann gradient. The projection operator and the expression for the Riemann gradient are as follows:
[0106]
[0107] The Armijo backtracking algorithm is used to adaptively determine the iteration step size, and the matrix update formula is:
[0108]
[0109] The updated candidate matrix is pulled back to the orthogonal Stiefel manifold through a QR decomposition shrinkage mechanism to ensure the orthogonal basis property of the matrix. The shrinkage formula is as follows:
[0110]
[0111] Repeat the above iterations until convergence.
[0112] Further, the process of decomposing the data into stationary and non-stationary layers in step 400 is as follows: The orthogonal matrix obtained through training with stationary independent component analysis... Whitening data can be decomposed into independent components. Based on the set S of stationary components, the independent components are divided into two layers:
[0113]
[0114]
[0115] Extracted latent variables Corresponding to consistent information across operating conditions, Time-varying information corresponding to normal operating conditions.
[0116] Furthermore, the recursive memory set construction and residual component analysis described in step 500 include the following: For the input online unknown sample, its projection in the original temporal space is first calculated based on the dewhitening reconstruction relation of the non-stationary layer. Subsequently, on the offline non-stationary layer training set Query its Euclidean distance Neighbor To enhance temporal continuity and improve the numerical stability of local models, a recursive memory set is maintained:
[0117]
[0118] When a new sample arrives, the most recently added sample is retained. An index. In the memory set. Calculate local samples Mean and covariance:
[0119]
[0120] Furthermore, on Perform singular value decomposition and select the one with the smallest variance. Each direction is used as the residual direction. So, for centralized online non-stationary layers... Its residual components can be calculated:
[0121]
[0122] The residual component dynamically reflects the degree of deviation of the online non-stationary sample from the time-varying trajectory of the current local normal operating condition.
[0123] Furthermore, the monitoring statistics and hierarchical decision rules described in step 600 are as follows.
[0124] The monitoring statistics are constructed based on stationary independent components and residual components as follows:
[0125]
[0126]
[0127] The confidence factor can be set, and the alarm control limit can be determined using the kernel density estimation method.
[0128] Furthermore, for online samples A hierarchical decision-making strategy is adopted to determine the process status. The extracted stationary independent components reflect the constraints of consistent operating conditions and should remain stationary during normal operating condition changes and transitions, while the non-stationary layer updates the model as the operating conditions change over time. To mitigate false alarms caused by noise, the decision rules are designed as follows:
[0129]
[0130] Specifically, the data acquisition module acquires offline historical data and online sensor samples in real time during multi-condition production processes and inputs them into the data preprocessing module. The data preprocessing module first performs global standardization on the offline historical data to reduce differences in physical dimensions, then performs whitening transformation decoupling in the temporal domain, and finally outputs whitened feature data that satisfies statistical inconsistency and variance normalization in all dimensions, laying the foundation for subsequent feature extraction.
[0131] Furthermore, the stationary independent component extraction module receives the preprocessed whitened data and uses the Riemannian manifold optimization algorithm to find the optimal orthogonal matrix in the whitened space. This module performs adaptive iterative solution on the orthogonal Stiefel manifold, while maximizing the non-Gaussianity of the components to ensure statistical independence, and applying a distribution stationarity constraint based on the maximum mean difference, thereby extracting independent source signals with high stability across operating conditions from strongly coupled, non-Gaussian industrial data.
[0132] Based on this, the hierarchical decomposition module divides the overall system mapping space into two complementary monitoring subspaces using the optimal orthogonal matrix, according to the stationarity characteristics of the source signal. The stationary subspace is responsible for capturing consistent cross-condition information that remains constant during frequent changes in operating conditions, used to monitor the inherent mechanistic constraints of the process; while the non-stationary subspace is responsible for mapping the non-stationary components that carry time-varying information under normal operating conditions, thereby achieving hierarchical modeling and monitoring of complex multi-condition changing characteristics.
[0133] Furthermore, the instant residual learning module is specifically designed for real-time adaptive modeling of non-stationary layer data streams. For the input online samples, this module first retrieves multiple nearest neighbor samples from the offline non-stationary layer training set and dynamically constructs and maintains a fixed-capacity recursive memory set on the time axis. Subsequently, it calculates the local mean and covariance matrix within this set in real time, extracts the residual direction through singular value decomposition, and then solves for the instant residual components of the online samples. This adaptively tracks the drift of normal production operating points and reduces their impact on fault monitoring results.
[0134] Finally, the online monitoring and decision-making module constructs a two-layer monitoring statistic in parallel based on the independent components of the stationary layer and the instantaneous residual components. This module uses nonparametric kernel density estimation to dynamically and adaptively fit the alarm threshold and calls hierarchical control decision rules with historical backtracking windows. When the stationary layer statistic exceeds the limit, it is directly determined as a real fault; while when the stationary layer is normal and the residual layer exceeds the limit, the module distinguishes between normal operating condition switching fluctuations and real fault disturbances through backtracking verification, and finally outputs the process operation status and alarm signals to the safety monitoring system.
[0135] Dataset
[0136] In this embodiment, to verify the detection performance of the proposed multi-condition process hierarchical monitoring method based on stationary independent source extraction and instantaneous residual learning, a simulation case study is conducted using the internationally standard process industry testing platform—the Tennessee Eastman Process (TEP) dataset. This dataset originates from actual chemical production processes and contains rich time-varying characteristics of complex operating conditions such as strong coupling, non-Gaussian, and multimodal distributions. Based on the diverse requirements of product mass ratios and yields, this case study designs two different industrial operating modes to evaluate the model's adaptability to changes in the operating environment.
[0137] The offline training dataset is continuously sampled at fixed time intervals, covering complete normal operating condition transition scenarios. The process initially operates in the first operating mode and smoothly switches to the second operating mode at a preset time point. The entire training set fully records the steady-state operation within each mode, the frequent switching phases between modes, and long-term dynamic temporal transition scenarios, collecting thousands of normal samples rich in operating condition transition information. To achieve comprehensive process monitoring across the entire process, the dataset collects dozens of key process variables, including process measurement variables, component variables, and operating variables of each loop, to construct a high-dimensional historical training space.
[0138] The online test dataset independently includes a complete normal operating condition switching scenario and several typical fault scenarios, covering a variety of common industrial field faults such as random fluctuation anomalies and trend anomalies with continuously increasing amplitude. Each test case contains the same number of continuous online sensor samples, and all types of faults are introduced in the middle of operation. By comparing experiments with various adaptive monitoring methods and common feature extraction schemes, the continuous and stable monitoring performance of the hierarchical monitoring strategy described in this invention under complex operating condition changes is evaluated.
[0139] Parameter settings
[0140] In this embodiment, the model parameters are set as follows. During the stationary independent component extraction stage, the preset dimension of the stochastic Fourier feature map is set to 500 to balance computational efficiency and approximation accuracy. When using the Riemannian manifold optimization algorithm to solve for the optimal orthogonal matrix, the initial iteration step size is set to 0.01, and backtracking search is used for adaptive fine-tuning. The convergence threshold of the objective function is set to 10. -5 The maximum number of iterations is limited to 500 to ensure efficient convergence of manifold optimization. During the instantaneous adaptive residual component extraction process in the non-stationary layer, the nearest neighbor parameter used for calculating the neighborhood is set to 10, while the upper limit of the recursive memory set is set to 50. The cumulative variance contribution rate threshold for the residual direction extracted after local singular value decomposition is set to 95% to adaptively determine the dimension of the residual subspace. Furthermore, the confidence factor in the online monitoring module is set to 0.95 to construct the control limits of the statistics, and the historical backtracking window length in the hierarchical decision rule is set to 5 sampling intervals, thereby effectively suppressing process noise and reducing system false alarms.
[0141] Evaluation indicators
[0142] This embodiment uses Fault Detection Rate (FDR) and False Alarm Rate (FAR) as evaluation metrics for multi-condition process monitoring performance. FDR characterizes the proportion of samples where faults occur that are correctly detected, reflecting the model's ability and sensitivity to detect abnormal states. FAR characterizes the proportion of samples where faults occur incorrectly, reflecting the model's ability to distinguish between normal operating conditions and noise interference. By comprehensively comparing FDR and FAR under different scenarios, the overall detection accuracy, time-varying adaptive capability, and robustness of the monitoring model in complex multi-condition changing tasks can be objectively measured.
[0143] Comparative experiments of different models
[0144] To verify the fault detection performance of the proposed hierarchical monitoring method under complex operating condition changes, it was compared with the current mainstream process monitoring algorithms JIT-PCA, CUSD, and SLSSA under the same test environment. The specific experimental results are shown in Table 1. Table 1 shows the typical fault monitoring results under mode 1 conditions, indicating that the proposed method exhibits better performance across multiple core evaluation indicators. Especially when facing faults of the random fluctuation type 10, the fault detection rates of traditional comparative methods are all at a low level, while the proposed method improves this to 82.2%. This demonstrates that the stationary independent component analysis method based on joint optimization of non-Gaussianity and distributional stationarity can extract common features with high stability, thereby enabling the constructed monitoring statistics to better distinguish between normal operating condition fluctuations and abnormal fault disturbances, improving the detection stability and fault sensitivity for multi-condition time-varying processes.
[0145] Table 1 Fault Detection Rate of TEP Cases under Mode 1
[0146] 1 0.988 0.992 0.994 0.996 2 0.984 0.946 0.960 0.964 5 0.026 0.012 0.000 0.012 7 1.000 1.000 1.000 1.000 8 0.958 0.942 0.952 0.958 10 0.028 0.058 0.764 0.822 11 0.432 0.410 0.910 0.956 12 0.178 0.124 0.088 0.174 13 0.922 0.904 0.960 0.968 16 0.016 0.002 0.002 0.012 17 0.478 0.400 0.678 0.940 18 0.402 0.626 0.660 0.714 19 0.250 0.612 0.914 0.956 20 0.942 0.946 0.942 0.950 AveFDR 0.543 0.570 0.702 0.744 AveFAR 0.013 0.004 0.004 0.013
[0147] Meanwhile, to further verify the generalization ability of the method of the present invention under different operating modes, Table 2 supplements the experimental data of the comparative tests of various mainstream monitoring models under operating mode 2. The experimental results show that its performance trend is highly consistent with that of mode 1. In complex industrial environments with multimodal, strong coupling and non-Gaussian characteristics, comparative methods such as CUSD show a significant decline in detection rate for some complex faults due to the lack of adaptability of the extracted common features to specific operating conditions. However, the method of the present invention still achieves an average fault detection rate of 76.9% under mode 2 conditions, and the average false alarm rate remains within the range of 1.2%. Based on multiple sets of comparative cases, it can be concluded that the method of the present invention, by introducing the synergistic advantages of consistent stationary independent subspaces across operating conditions and local residual modeling, exhibits a lower false alarm rate and a higher fault detection rate, demonstrating good cross-modal adaptive ability and generalization performance while ensuring overall monitoring reliability.
[0148] Table 2 Fault Detection Rate of TEP Cases under Mode 2
[0149] 1 0.990 0.990 0.994 0.994 2 0.984 0.980 0.972 0.972 4 0.016 0.000 0.998 0.998 5 0.024 0.000 0.004 0.018 7 0.998 0.998 0.998 0.998 8 0.956 0.936 0.960 0.962 10 0.036 0.078 0.716 0.788 11 0.444 0.154 0.716 0.882 12 0.126 0.022 0.086 0.204 13 0.986 0.984 0.984 0.986 14 0.046 0.054 0.862 0.998 16 0.014 0.000 0.002 0.010 17 0.326 0.080 0.488 0.876 18 0.446 0.668 0.700 0.752 19 0.242 0.608 0.922 0.950 20 0.900 0.892 0.900 0.912 AveFDR 0.471 0.465 0.706 0.769 AveFAR 0.022 0.000 0.003 0.012
[0150] Appendix Figure 2 To be continued Figure 4 The statistical monitoring curves of the four methods are further presented in three typical test scenarios. In the normal operating condition switching scenario (see attached...) Figure 2 In the fault scenario (see attached diagram), the statistics of JIT-PCA, CUSD, and SLSSA methods fluctuated significantly and frequently exceeded control limits during the condition switching phase, while the statistics of the stable layer of the method of this invention remained stable overall, and false alarms were significantly reduced after verification by the hierarchical decision rule. In fault scenario 4 (see attached diagram), Figure 3 In the case of fault 14, the statistical value of the comparative method showed no significant upward trend after the fault was introduced, making it difficult to distinguish from normal fluctuations. However, the statistical value of the method of this invention rapidly and continuously increased after the fault was introduced and stably exceeded the control limit, indicating timely detection and response. Figure 4 In the case of a fault that is slow and gradual, the statistical changes of the comparison method are not obvious or there is a drop and missed detection. However, the statistical changes of the method of the present invention show a continuous and stable upward trend, which is in stark contrast to the normal stage before the fault, and shows a better ability to detect gradual faults.
[0151] In summary, this invention discloses a multi-condition industrial process fault monitoring method and system based on stationary decomposition and local adaptive residual learning. This method analyzes the statistical characteristics of strongly coupled, non-Gaussian data in industrial processes, introduces a Riemannian manifold optimization algorithm in the preprocessing space to extract consistent stationary independent signal flows across operating conditions, and accordingly divides the high-dimensional process space into stationary and non-stationary subspaces. For non-stationary components whose statistical characteristics drift with continuous changes in operating conditions, an instant learning mechanism is introduced to dynamically maintain the recursive memory set and perform adaptive residual extraction. Finally, a hierarchical decision rule with a historical backtracking window is used to achieve continuous online fault monitoring. Experimental results show that the method of this invention, while ensuring operational efficiency, has a low false alarm rate in complex operating condition switching scenarios and exhibits high detection performance in most typical fault detection tasks, with an overall average fault detection rate superior to existing comparative methods. The method possesses good robustness, detection sensitivity, and industrial generalization value, providing a practical autonomous safety assurance solution for intelligent operation and maintenance in modern process industries.
Claims
1. A multi-condition industrial process fault monitoring method based on stationary decomposition and local adaptive residual learning, characterized in that... Includes the following steps: Step 100: Obtain historical data and online samples of multi-condition processes, and perform standardization and whitening preprocessing on the historical data to obtain whitened data; Step 200: Construct a joint optimization objective for stationary independent component analysis, using non-Gaussianity to measure the independence of each component and the maximum mean difference of the kernel embedding mean in each time period to measure the distribution stationarity, and establish a joint optimization problem with orthogonal constraints; Step 300: Solve for the orthogonal matrix on the Stiefel manifold using the Riemann gradient descent method, calculate the Riemann gradient, determine the step size through Armijo backtracking search, use QR decomposition to shrink back to ensure orthogonality, and obtain the orthogonal matrix through iterative convergence. Step 400: Use an orthogonal matrix to decompose the whitened data into independent components. Based on the stationarity index of each independent component, classify the independent components with stationarity indices below a preset threshold into stationary layers, and classify the independent components with stationarity indices above a preset threshold into non-stationary layers. Step 500: For online non-stationary layer samples, query the nearest neighbors by Euclidean distance, maintain a finite-capacity recursive memory set, calculate the local mean and covariance on the memory set, extract the low-variance residual direction through singular value decomposition, and calculate the residual components of online samples; Step 600: Construct the first statistic based on stationary independent components, construct the second statistic based on residual components, determine the control limits by kernel density estimation, and use hierarchical decision rules combined with historical backtracking windows to judge the process status and distinguish between normal operating conditions and time-varying faults.
2. The adaptive fault monitoring method according to claim 1, characterized in that, The stationary independent component analysis described in step 200 includes: setting the independence objective function as a measure of the non-Gaussianity of each component, setting the distribution stationarity loss as the weighted variance of the kernel embedding mean to the overall mean embedding in each time period, and identifying stationary independent source signals from non-Gaussian, strongly coupled data by jointly optimizing the above objective and applying orthogonal constraints.
3. The adaptive fault monitoring method according to claim 1, characterized in that, The joint optimization described in step 300 employs the Riemann gradient descent method: the Euclidean gradient of the objective function is calculated, projected onto the tangent space of the Stiefel manifold to obtain the Riemann gradient, the step size is determined using the Armijo backtracking search, and the updated matrix is pulled back to the orthogonal AC form through QR shrinkage, iterating until convergence.
4. The adaptive fault monitoring method according to claim 1, characterized in that, The stationarity hierarchical decomposition in step 400 includes: mapping the whitened data into independent components using the obtained orthogonal matrix, and dividing them into stationary and non-stationary layers according to the stationarity metric of each component; wherein the stationary layer contains common feature components that are consistent across operating conditions, and the non-stationary layer contains dynamic components that vary with operating conditions over time.
5. The adaptive fault monitoring method according to claim 1, characterized in that, The construction of the recursive memory set in step 500 includes: determining the local neighborhood based on the similarity relationship between online samples and offline non-stationary layer samples, and maintaining a dynamically updated finite-capacity memory set to enhance temporal continuity and the numerical stability of the local model.
6. The adaptive fault monitoring method according to claim 1, characterized in that, The residual component analysis described in step 500 includes: calculating the mean and covariance of local samples on the memory set, performing singular value decomposition on the covariance, selecting the direction that characterizes the low variance variation of local samples to construct the residual subspace, and calculating the residual components of the centered online non-stationary layer samples to measure the degree of deviation of the samples from normal operating conditions.
7. The adaptive fault monitoring method according to claim 1, characterized in that, The monitoring statistics mentioned in step 600 include: a first statistic constructed based on stationary independent components and a second statistic constructed based on residual components, the control limits of which are determined by kernel density estimation method.
8. The adaptive fault monitoring method according to claim 7, characterized in that, The hierarchical decision rule is as follows: if the first statistic exceeds the limit, it is determined to be a fault; if the first statistic does not exceed the limit but the second statistic exceeds the limit, then check whether the first statistic of the M consecutive sampling times before the current time exceeds the limit. If it does, it is determined to be a fault; otherwise, it is determined to be normal.
9. A multi-condition industrial process fault monitoring system based on stationary decomposition and local adaptive residual learning, characterized in that, The system includes a data acquisition module, a data preprocessing module, a stationary independent component extraction module, a hierarchical decomposition module, an instantaneous residual learning module, and an online monitoring and decision-making module. Specifically: the data acquisition module acquires historical data and online samples from multiple operating conditions; the data preprocessing module standardizes and whitens the historical data; the stationary independent component extraction module constructs a joint optimization objective and solves for the orthogonal matrix on the Stiefel manifold using Riemann gradient descent, extracting stationary independent source signals from the whitened data; the hierarchical decomposition module decomposes the data into stationary and non-stationary layers; the instantaneous residual learning module adaptively models the non-stationary layer and calculates residual components; and the online monitoring and decision-making module constructs monitoring statistics and executes hierarchical decision rules.