Non-stationary industrial process fault detection method based on graph representation learning

Abstract

The application discloses a non-stationary industrial process fault detection method based on graph representation learning and belongs to the technical field of industrial process monitoring. The method comprises the following steps: acquiring operation data, dividing the operation data into multiple continuous time segments; analyzing statistical differences of operation data of each time segment, and constructing a statistical difference objective function; constructing a similarity matrix of sample points across time segments, constructing a transition probability matrix and an adjacency matrix; generating a graph Laplacian matrix, and constructing a graph representation learning objective function; introducing a weight coefficient to jointly optimize the statistical difference objective function and the graph representation learning objective function, and obtaining a stationary projection matrix; determining a control limit by using the stationary projection matrix; and collecting real-time operation data and performing fault detection on the real-time operation data. Through fusion of stationary subspace analysis and graph representation learning, the data stability is realized, the internal characteristics of the data are revealed, and the accuracy of fault detection is improved.

Description

Technical Field

[0001] This invention relates to the field of industrial process monitoring technology, and in particular to a method for detecting faults in non-stationary industrial processes based on graph representation learning. Background Technology

[0002] With the continuous expansion of industrial production scale and the increasing complexity of processes, ensuring product quality and process safety has become a core issue in the industrial manufacturing sector. Modern industrial processes are often characterized by high coupling and dynamic continuity; once a failure occurs, it can easily trigger a chain reaction, leading to significant economic losses or even environmental and safety accidents. Therefore, establishing a reliable process monitoring system to achieve timely fault diagnosis and effective elimination of abnormal factors is of great significance for ensuring the stable operation of industrial systems.

[0003] Among numerous data-driven methods, process monitoring techniques based on multivariate statistics (such as principal component analysis and partial least squares) have become common tools in industry due to their ease of implementation and lack of need for precise mechanistic models. However, in actual production, industrial processes often exhibit significant non-stationary characteristics due to various factors, and their statistical data characteristics change systematically over time. This non-stationarity can mask fault information, leading to increased false alarm and false negative rates in traditional methods, severely limiting their monitoring effectiveness in practical applications.

[0004] To address the challenges of monitoring nonstationary processes, cointegration analysis extracts stationary features by establishing long-term equilibrium relationships among nonstationary variables. However, this method typically requires all variables to have the same order of integration, an assumption that contradicts the diverse nonstationary characteristics of variables in real-world industrial processes. This often leads to model failure in practical applications and low fault detection rates. Summary of the Invention

[0005] This invention provides a fault detection method for non-stationary industrial processes based on graph representation learning, in order to solve the technical problem of low detection rate caused by insufficient monitoring capability of existing technologies for non-stationary processes.

[0006] In a first aspect, embodiments of the present invention provide a method for fault detection in non-stationary industrial processes based on graph representation learning, comprising:

[0007] Obtain operational data of a non-stationary industrial process operating normally, and divide the operational data into multiple continuous time segments;

[0008] Analyze the statistical differences in the data from each time segment, and construct a statistical difference objective function based on these differences.

[0009] Construct a similarity matrix for sample points across time segments, build a transition probability matrix based on the similarity matrix, and use an adaptive neighborhood strategy to build an adjacency matrix based on the transition probability matrix;

[0010] A graph Laplacian matrix is ​​generated based on the adjacency matrix, and a graph representation learning objective function is constructed based on the graph Laplacian matrix.

[0011] By introducing weighting coefficients, the statistical difference objective function and the graphical representation learning objective function are jointly optimized to obtain a stationary projection matrix;

[0012] Using the stationary projection matrix, the control limits of the Mahalanobis distance monitoring statistics are determined;

[0013] Collect real-time operating data of industrial processes, and use the control limits to detect faults in the real-time operating data.

[0014] This invention provides a non-stationary industrial process fault detection method based on graph representation learning. The method acquires operational data of a non-stationary industrial process, divides the operational data into multiple continuous time segments, analyzes the statistical differences between the operational data of each time segment, and constructs a statistical difference objective function based on these differences. It then constructs a similarity matrix for sample points across time segments, builds a transition probability matrix based on the similarity matrix, and employs an adaptive neighborhood strategy to construct an adjacency matrix based on the transition probability matrix. A graph Laplacian matrix is ​​generated based on the adjacency matrix, and a graph representation learning objective function is constructed based on the graph Laplacian matrix. Weight coefficients are introduced to jointly optimize the statistical difference objective function and the graph representation learning objective function to obtain a stationary projection matrix. The stationary projection matrix is ​​used to determine the control limits for Mahalanobis distance monitoring statistics. Real-time operational data of the industrial process is collected, and fault detection is performed on the real-time operational data using the control limits. By integrating stationary subspace analysis and graph representation learning, and utilizing the cross-time segment similarity matrix and the adaptive neighborhood strategy, the method achieves alignment and mining of the manifold structure of cross-time segment data, thereby improving the accuracy and robustness of non-stationary industrial process fault detection. Attached Figure Description

[0015] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0016] Figure 1 This is a flowchart of the nonstationary industrial process fault detection method based on graph representation learning provided in Embodiment 1 of the present invention;

[0017] Figure 2This is a flowchart illustrating the construction of the statistical difference objective function for the nonstationary industrial process fault detection method based on graph representation learning provided in Embodiment 1 of the present invention;

[0018] Figure 3 This is a flowchart of the construction of the adjacency matrix in the non-stationary industrial process fault detection method based on graph representation learning provided in Embodiment 1 of the present invention. Detailed Implementation

[0019] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0020] Example 1

[0021] Figure 1 This is a flowchart of a non-stationary industrial process fault detection method based on graph representation learning provided in Embodiment 1 of the present invention. This embodiment can be applied to solve the problem of low fault detection sensitivity and high false alarm rate in non-stationary industrial processes due to traditional monitoring methods ignoring the inherent manifold structure and cross-time period correlation of data. Specifically, it includes the following steps:

[0022] Step 110: Obtain the operating data of a non-stationary industrial process in normal operation, and divide the operating data into multiple continuous time segments.

[0023] Non-stationary industrial processes refer to industrial systems whose statistical characteristics, such as mean, variance, and fluctuation patterns, change significantly over time. These processes are common in fields such as chemical engineering, metallurgy, wastewater treatment, and energy production. Their non-stationarity may stem from various factors, including production load adjustments, raw material fluctuations, changes in environmental conditions, equipment aging, or switching of operating modes. Because process characteristics are not fixed, traditional monitoring and fault diagnosis methods based on static models are often inapplicable. Therefore, data analysis methods that can adapt to time-varying characteristics are needed, such as dynamic modeling strategies based on time segmentation.

[0024] Acquiring operational data for a non-stationary industrial process refers to collecting multivariate time-series data reflecting the process state under normal operating conditions. This typically includes variables measured by multiple sensors, such as temperature, pressure, and flow rate, which form the basis for subsequent analysis. Dividing the operational data into multiple consecutive time segments means sequentially cutting the entire time-series data into several continuous and non-overlapping segments. The purpose is to capture the local dynamic characteristics and time-varying changes of the industrial process under non-stationary conditions. Data within each time segment can be considered as collected within a relatively stable short period, allowing the establishment of statistical or dynamic models within a local scope to better adapt to the time-varying behavior of the overall process. For example, in wastewater treatment, due to the influence of factors such as wastewater quality, influent flow rate, weather changes, and microbial treatment, it exhibits significant non-stationary characteristics. To address this process characteristic, a training dataset of the wastewater treatment process under normal operating conditions is first collected. , which includes One sample and The dataset is divided into several variables, standardized, and split into... A series of non-overlapping time segments The standardization process can employ the Z-score standardization method, which sets the mean of each column of variables in the dataset to 0 and the variance to 1, thereby effectively eliminating the bias caused by different units and absolute value ranges between different variables.

[0025] Step 120: Analyze the statistical differences in the running data of each time segment, and construct a statistical difference objective function based on the statistical differences.

[0026] Figure 2 This is a flowchart illustrating the construction of the statistical difference objective function for the nonstationary industrial process fault detection method based on graph representation learning, as described in Embodiment 1 of the present invention. Figure 2 The construction of the statistical difference objective function may include the following steps:

[0027] Step 210: Calculate the mean vector and covariance matrix for each time segment.

[0028] The mean vector is a characterization of the central tendency of the operating states of multiple variables within a time segment. For example, in wastewater treatment, a standardized time segment... , dimension This indicates that the segment contains [something], representing that the segment contains [something]. One sample and For each monitored variable, the mean vector is calculated for that time segment. Essentially, this involves calculating the average of all sample values ​​for each process variable within that segment, such as pH, COD, ammonia nitrogen concentration, dissolved oxygen (DO), and sludge concentration (MLSS). The result of this calculation is... The vector.

[0029] The covariance matrix reveals the correlation patterns and fluctuation structure of variables within a time segment. For example, in wastewater treatment, for a given time segment... ,calculate The covariance matrix reveals the more complex statistical structure within a given event segment. The diagonal elements of the covariance matrix represent the variance of each variable itself, describing the magnitude of its fluctuation within that time period; while the off-diagonal elements represent the covariance between any two different variables, precisely quantifying the degree and direction of their linear correlation. In multivariate coupled processes like wastewater treatment, the correlations between variables reveal the core process mechanisms. For example, dissolved oxygen (DO) levels are typically strongly correlated with aeration rate and influent organic load; sludge concentration (MLSS) interacts with sludge return ratio and settling performance. Therefore, the covariance matrix of a given time segment can be viewed as a snapshot of the inherent correlation patterns and overall volatility of the process operation within that period. When a process transitions from one stable operating condition to another, such as switching from low-load to high-load operation, not only does the mean center shift, but the covariance structure between variables often changes significantly. By comparing the covariance matrices of different time segments, the intrinsic dynamic evolution caused by non-stationarity can be identified.

[0030] Step 220: Calculate the average of the mean vector and the average of the covariance matrix for all time segments.

[0031] For example, the N mean vectors obtained in step 210 can be averaged again to obtain a global mean vector. This vector transcends any single time segment and represents the long-term average operating level of all process variables under the diverse operating conditions covered by the entire training data. The N covariance matrices obtained in step 210 (each characterizing the variable correlation and fluctuation structure of a local time period) can be mathematically averaged to obtain a global covariance matrix. This matrix integrates the variable relationship patterns under different time periods and operating conditions, representing the overall, average correlation strength and cooperative fluctuation range among all variables during normal production.

[0032] Step 230: Using KL divergence, based on the mean vector, covariance matrix, average of the mean vector, and average of the covariance matrix of each time segment, analyze the statistical differences in the running data of each time segment to construct a difference objective function.

[0033] Stationary subspace analysis models quantify the statistical differences between different time segments using Kullback-Leibler (KL) divergence. KL divergence is an asymmetric measure of the difference between two probability distributions, widely used in information theory and statistics. When two distributions are identical, their KL divergence is zero; the greater the difference, the higher the divergence value. In stationary subspace analysis, the degree to which a time segment deviates from the average steady state is objectively reflected by calculating the KL divergence between the projected probability distribution of each time segment and the overall average projected distribution.

[0034] For example, based on the mean vector, covariance matrix, average of the mean vector, and average of the covariance matrix obtained in steps 210 and 220, it can be assumed that each time segment passes through a common stationary projection matrix. After the transformation, the data follows a Gaussian distribution. The overall average distribution of all time segments is The objective function is to minimize the average KL divergence between each fragment distribution and the mean distribution. The objective function is expressed as: =min ,in For a stationary projection matrix, yes The transpose of N, where N is the total number of time segments. Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. Let KL divergence be the term. Under the assumption of a Gaussian distribution, KL divergence can be decomposed into two terms: the first term... The second term measures the degree of deviation of the projected mean vector. The difference is related to the structure of the projected covariance matrix and reflects the differences in fluctuation patterns. By jointly optimizing these two terms, the statistical characteristics of different time segments in the projected subspace are made as consistent as possible. Considering the high computational complexity of the above objective function, to improve optimization efficiency, the logarithmic term in the original formula can be replaced with its upper bound estimate based on the second-order Taylor approximation. Then, the difference objective function can be expressed as: ,in, For a stationary projection matrix, Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. The total number of time segments. For statistical difference matrix, , Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. Let be the total number of time segments. The original objective function aims to minimize the KL divergence between the distribution of each time segment and the global average distribution. It includes logarithmic determinant terms. The computational complexity is high, especially in high-dimensional and large-scale data scenarios. To improve computational efficiency, a method focusing on the global average covariance matrix is ​​employed. right A second-order Taylor expansion is performed to obtain a local upper bound estimate. Essentially, a quadratic function is used to approximate the logarithmic function of the unknown, transforming the complex nonlinear optimization problem into a quadratic optimization problem, thereby significantly reducing the computational burden.

[0035] By following the steps above, we can construct a statistical difference objective function by analyzing the statistical differences in the data from each time segment.

[0036] Step 130: Construct a similarity matrix for sample points across time segments, build a transition probability matrix based on the similarity matrix, and construct an adjacency matrix based on the transition probability matrix using an adaptive neighborhood strategy.

[0037] Figure 3 This is a flowchart illustrating the construction of the adjacency matrix in the nonstationary industrial process fault detection method based on graph representation learning as described in Embodiment 1 of the present invention. Figure 3 The construction of the adjacency matrix may include the following steps:

[0038] Step 310: Construct a similarity matrix for sample points across time segments.

[0039] A similarity matrix is ​​a core mathematical structure used to describe the strength of pairwise relationships between sample points in a dataset. For example, suppose the training dataset... Then the data matrix of the i-th time segment can be represented as Two sample points and Belonging to different time segments and Then, the similarity matrix of the sample points across the time segment can be constructed using the Gromov-Wasserstein distance, as follows: ,in, This indicates the parameters set based on experience. Represents sample points and The GW distance between the two sample points and Belonging to different time segments and By comparing the relative positions of sample points within their respective time segments, rather than directly comparing their numerical differences, this effectively overcomes the measurement distortion caused by mean drift and scale changes in non-stationary processes. This is particularly relevant for samples belonging to different time segments. and Two sample points and First, calculate the GW distance between them. This distance essentially measures the difference between the distance distributions of two points and other sample points within their respective segments, reflecting whether their roles in the local structure are similar. Based on this, a negative exponential function is used... This distance is mapped to a similarity metric between 0 and 1. If two points have completely identical structural roles in their respective segments, the GW distance approaches 0, and the similarity approaches 1; conversely, the greater the structural difference, the closer the similarity approaches 0. Parameters This is used to adjust the sensitivity of similarity to changes in distance. Ultimately, a similarity matrix is ​​constructed.

[0040] Step 320: Construct a transition probability matrix based on the similarity matrix.

[0041] The transition probability matrix is ​​a core concept in graph theory and random walk models. It describes the probability distribution of randomly moving from a sample point to any of its neighboring nodes on a graph composed of data points. For example, the element in the p-th row and q-th column of the matrix defines the transition probability from node p to any of its neighboring nodes. One-step transfer to node The probability is calculated by the sum of the elements in each row of the matrix, which is 1, forming a complete probability distribution. Therefore, it essentially transforms the similarity matrix, which describes the static connection strength between nodes, into a mathematical model that characterizes the dynamic random access relationship between nodes.

[0042] For example, a transition probability matrix can be constructed based on the similarity matrix obtained in step 310, and the transition probability matrix is ​​expressed as follows: ,in, Indicates from sample point to sample point The one-step transition probability, Let be the number of samples in the i-th time segment. Represents sample points The sum of similarity weights for all sample points within the same time segment is used to normalize the transition probability. The numerator in the formula... Representative sample points and The original structural similarity between points is obtained by transforming the GW distance with a negative exponential factor. However, the connectivity activity varies among different sample points. Some points may be highly similar to most points within a segment, resulting in generally high similarity weights; while others have weaker overall associations. Directly using the original weights would interfere with a fair assessment of the relative association strength between point pairs. Therefore, the denominator... Its function is to sample points Normalize all out-degree connections; it calculates the sample points. The same time segment as described All The sum of similarity scores for each sample point. This is obtained by dividing each original weight by this sum. It satisfies the fundamental property of probability: for any fixed point The sum of the probabilities of a sample point moving to any possible target point within its segment is exactly 1. This makes each sample point correspond to a complete discrete probability distribution.

[0043] Step 330: Calculate the t-step transition probability matrix based on the aforementioned transition probability matrix.

[0044] The t-step transition probability matrix, in a graph or network-based random walk model, describes the probability distribution of reaching any node in the graph after exactly t steps of random walks, starting from any node. For example, the transition probability matrix obtained in step 320 can be... The matrix obtained by raising the power of t, i.e. The elements in this matrix Indicates from sample point Starting from the point, the sample point is reached after exactly t random walks. The probability of this. Through this multi-step diffusion mechanism, the model can mine broader global information in the data manifold, thereby aligning the intrinsic geometry of different time segments.

[0045] Step 340: An adaptive neighborhood strategy is used to assign neighbors to sample points.

[0046] Adaptive neighborhood strategy is a dynamic graph construction method. Its core idea is to automatically determine the optimal number of neighbors for each sample point based on its local data distribution and connectivity strength, rather than pre-setting a fixed number of neighbors for all points. In monitoring non-stationary processes, due to differences in data density and manifold structure across different time segments, a fixed number of neighbors may introduce noisy connections in some areas or lose important associations in others. The adaptive strategy, by examining the closeness between each point and its potential neighbors, adaptively defines its local neighborhood range, thereby constructing a more robust graph model that better reflects the inherent geometric structure of the data.

[0047] For example, the core of the adaptive neighborhood strategy lies in dynamically determining the neighborhood range of each sample point based on its multi-step connectivity strength within the graph structure. Specifically, for a given sample point... First, determine the t-step transition probability to reach all other points. Arranged in descending order, higher probability values ​​indicate a stronger and more stable indirect association established between two points through multi-step random walks. Based on this, a probability accumulation threshold is set. Starting from the point with the highest probability, the transition probabilities are sequentially accumulated until the cumulative probability reaches or exceeds the threshold for the first time. ,Right now At this point, the number of points involved is adaptively determined as the number of neighbors of that point. Ultimately, the top-ranked The point was selected as The neighborhood set is used to flexibly adjust the neighborhood size based on the differences in manifold density and connectivity of the local region where each point is located: in densely structured regions, fewer neighbors are needed to capture the main associations; in sparsely structured or transitional regions, more neighbors are automatically included to fully describe their contextual relationships.

[0048] Step 350: Construct an adjacency matrix based on the set of neighbor relationships.

[0049] For example, reliable neighbor relationships selected using an adaptive strategy are used to sparsify the original fully connected similarity matrix induced by GW distance, thereby constructing a graph model that preserves the essential manifold structure while being computationally efficient and stable. For example, the adjacency matrix is ​​represented as: Among them, two sample points and Belonging to different time segments and and Representing sample points respectively and The set of neighbor relationships. Only if the sample point belong Neighbor set ,or belong Neighbor set At that time, matrix elements Only then are they assigned the original similarity weights. Otherwise, the element is set to 0. This logic ensures that a connection is established as long as either party considers the other a neighbor, enhancing the robustness of capturing important associations.

[0050] Step 140: Generate a graph Laplacian matrix based on the adjacency matrix, and construct a graph representation learning objective function based on the graph Laplacian matrix.

[0051] The graph Laplacian matrix is ​​a core operator in spectral graph theory, encoding the structural information of a graph into an algebraic form that can be used for mathematical analysis and optimization. For example, firstly, the adjacency matrix generated in step 130 can be used... Calculate the corresponding degree matrix The degree matrix is ​​a diagonal matrix, and each element on its diagonal is obtained by summing all elements in the i-th row of the adjacency matrix, i.e. This value quantifies the total connectivity strength of each node in the graph. Subsequently, the graph Laplacian matrix... Through the degree matrix Adjacency Matrix The simple difference operation is generated, and its expression is: The calculated Laplacian matrix contains off-diagonal elements that carry topological connectivity information of the graph, while diagonal elements reflect the local structural importance of nodes, transforming the sparse manifold structure in the adjacency matrix into a standard algebraic operator. Then, multiple graph Laplacian matrices characterizing the manifold connectivity between every two different time segments are used... Integrate into a unified global graph operator. Each It only reflects the local geometric constraints between fragment i and fragment j, while by considering all possible time segments... Summing the corresponding Laplace matrices, i.e. ,in, The joint Laplacian matrix is ​​essentially a linear superposition of all these pairwise structural constraints, forming a global structural regularization term that covers the entire time-segmented dataset.

[0052] For example, according to the joint Laplace matrix Construct a graph representation learning objective function, wherein the graph representation learning objective function is defined as: ,in, It is a stationary projection matrix. yes transpose, Let be the number of samples in the i-th time segment. For indexing different time segments, This is the index of the sample point within the time segment. The global data matrix consists of sample points from all time segments. yes transpose, yes transpose, yes transpose, The Euclidean norm of a vector. The trace operation of a matrix is ​​represented. By introducing a joint Laplacian matrix as a regularization constraint, the manifold alignment problem across time segments is transformed into an optimizable stationary projection matrix learning problem. Objective function. pass This ensures that after all sample points are projected into the low-dimensional space, the distance between each pair of points is equal to the graph connection weights they correspond to in the original high-dimensional space. As consistent as possible: for weights For larger points, the optimization process will force their projected distance. The smaller the weight, the weaker the constraint; conversely, for point pairs with smaller weights, the constraint is weaker. This idea is expressed mathematically. This is directly reflected. Secondly, it utilizes the joint Laplace matrix. Due to the algebraic properties of the expression, the summation is equivalently transformed into the form of the matrix trace. .

[0053] Step 150: Introduce weighting coefficients to jointly optimize the statistical difference objective function and the graph representation learning objective function to obtain a stationary projection matrix.

[0054] For example, based on the statistical difference objective function and the graphical representation learning objective function obtained in steps 120 and 140, weight coefficients can be introduced to construct a joint optimization objective function, which can be expressed as: ,in, The statistical difference matrix constructed for the statistical difference objective function. These are the weighting coefficients. = = + , Represents the joint optimization matrix. For a stationary projection matrix, Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. This represents the total number of time segments. The core idea is to linearly weight two different but complementary objectives: the first term... Derived from the statistical difference objective function, its purpose is to minimize the statistical fluctuations of the projected features across different time segments, ensuring the stationarity of the extracted features; the second term The learning objective function, derived from graph representation, aims to minimize the total variation of the projected data on the joint manifold, ensuring that the distances between point pairs across time segments are as close as possible in the low-dimensional subspace. This is achieved by introducing weight coefficients. This allows for flexible adjustment of the trade-off between statistical stationarity and manifold structure. Ultimately, the joint objective was rewritten as... The trace minimization form, where = It is a joint optimization matrix that integrates statistical differences and graph structure information. Secondly, it transforms the solution of the joint optimization objective function into a complete process of solving a computable generalized eigenvalue problem. First, it introduces the Lagrange multiplier matrix... The original optimization problem with orthogonal constraints is transformed into an unconstrained Lagrangian function problem. ,Right now ,in, For Lagrange multipliers, For the identity matrix, the equality constraint terms This is used to ensure that the projected features have a stable unit covariance structure. This is achieved by using the Lagrangian function with respect to the stationary projection matrix. By taking the derivative and setting it to zero, the core generalized eigenvalue equation can be derived. In this equation, It is a joint matrix that integrates statistical stationarity and graph structure manifold information. It is the global average covariance matrix, and its eigenvalues ​​are... The magnitude reflects the corresponding feature vector The overall cost of the represented direction. To minimize the objective function, the direction with the minimum cost needs to be selected. Therefore, the solved eigenvalues ​​are arranged in ascending order, and the eigenvectors corresponding to the first d smallest eigenvalues ​​are used to form a row vector group, thus obtaining the stationary projection matrix. This process, from an optimization theory perspective, guarantees that the desired stationary projection matrix can simultaneously achieve the dual objectives of statistical stationarity and manifold structure alignment while satisfying orthogonality constraints.

[0055] Step 160: Using the stationary projection matrix, determine the control limits of the Mahalanobis distance monitoring statistics.

[0056] In multivariate statistical process monitoring, Mahalanobis distance, monitoring statistics, and control limits are three closely related core concepts. Mahalanobis distance is a distance metric that considers the correlation between variables. It measures the statistical distance between a sample point and a multivariate distribution center. Its calculation is standardized by the inverse of the covariance matrix, making the result unaffected by the dimensions of the variables and collinearity. Monitoring statistics can refer to numerical indicators built based on Mahalanobis distance, used to quantify the degree to which new samples deviate from the normal state. Control limits are statistical thresholds that define the maximum acceptable value of the monitoring statistic within the normal fluctuation range. If the statistic exceeds this control limit, it indicates that the process is likely to have an anomaly or malfunction. For example, firstly, the original training data is projected using a stationary projection matrix. Projecting onto a stationary subspace yields stationary features. ,in The projection matrix is ​​stationary. Secondly, in the stationary feature space, monitoring statistics are constructed based on Mahalanobis distance. Finally, kernel density estimation is used to estimate the Mahalanobis distance values ​​projected from the training data. Control limits in the distribution estimate.

[0057] Step 170: Collect real-time operating data of the industrial process, and use the control limits to detect faults in the real-time operating data.

[0058] For example, real-time operational data of industrial processes can be collected using standard data interfaces (such as OPC) of sensor networks or industrial automation systems (such as DCS / PLC / SCADA). The collected real-time operational data is analyzed using a stationary projection matrix. Projecting onto a stationary subspace yields stationary features. ,in The projection matrix is ​​stationary. Secondly, in the stationary feature space, monitoring statistics are constructed based on Mahalanobis distance. Finally, the new sample data is evaluated. Does the monitoring statistics exceed the control limits? If the value exceeds the limit, it is considered fault data.

[0059] This embodiment acquires operational data of a non-stationary industrial process and divides the data into multiple continuous time segments. It analyzes the statistical differences between the data in each time segment and constructs a statistical difference objective function based on these differences. A similarity matrix is ​​constructed for sample points across time segments, and a transition probability matrix is ​​built based on this similarity matrix. An adaptive neighborhood strategy is then employed to construct an adjacency matrix based on the transition probability matrix. A graph Laplacian matrix is ​​generated from the adjacency matrix, and a graph representation learning objective function is constructed based on this graph Laplacian matrix. Weight coefficients are introduced to jointly optimize the statistical difference objective function and the graph representation learning objective function, resulting in a stationary projection matrix. The stationary projection matrix is ​​used to determine the control limits for Mahalanobis distance monitoring statistics. Real-time operational data of the industrial process is collected, and fault detection is performed on this real-time operational data using the control limits. By integrating stationary subspace analysis and graph representation learning, and utilizing the cross-time segment similarity matrix and the adaptive neighborhood strategy, the alignment and mining of the manifold structure of cross-time segment data are achieved, thereby improving the accuracy and robustness of fault detection in non-stationary industrial processes.

[0060] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A non-stationary industrial process fault detection method based on graph representation learning, characterized in that, include: Obtain operational data of a non-stationary industrial process operating normally, and divide the operational data into multiple continuous time segments; Analyze the statistical differences in the data from each time segment, and construct a statistical difference objective function based on these differences. A similarity matrix for sample points across time segments is constructed using the Gromov-Wasserstein distance. A transition probability matrix is ​​then constructed based on this similarity matrix. Finally, the transition probability matrix is ​​used to calculate... The transition probability matrix is ​​used to assign neighbors to sample points using an adaptive neighborhood strategy. The step transition probability matrix is ​​arranged in descending order to determine the number of neighbors. , will the former Each corresponding sample point is determined as the set of neighbor relationships of the sample point, and an adjacency matrix is ​​constructed based on the set of neighbor relationships. A graph Laplacian matrix is ​​generated based on the adjacency matrix, and a graph representation learning objective function is constructed based on the graph Laplacian matrix. By introducing weighting coefficients, the statistical difference objective function and the graphical representation learning objective function are jointly optimized to obtain a stationary projection matrix; Using the stationary projection matrix, the control limits of the Mahalanobis distance monitoring statistics are determined; Collect real-time operating data of industrial processes, and use the control limits to detect faults in the real-time operating data.

2. The method of claim 1, wherein, The method of constructing a similarity matrix for sample points across time segments using Gromov-Wasserstein distance includes: A similarity matrix for sample points across time segments is constructed using the Gromov-Wasserstein distance. The similarity matrix is ​​defined as follows: in, This indicates the parameters set based on experience. Represents sample points and The GW distance between the two sample points and Belonging to different time segments and .

3. The method of claim 2, wherein, The transition probability matrix is ​​constructed based on the similarity matrix, and the transition probability matrix is ​​calculated based on the transition probability matrix. The transition probability matrix is ​​used to assign neighbors to sample points using an adaptive neighborhood strategy. The step transition probability matrix is ​​arranged in descending order to determine the number of neighbors. , will the former Each corresponding sample point is determined as the set of neighbor relationships for that sample point. Based on the set of neighbor relationships, an adjacency matrix is ​​constructed, including: A transition probability matrix is ​​constructed based on the similarity matrix, and the transition probability matrix is ​​defined as follows: wherein, denotes the one-step transition probability from sample point to sample point , is the number of samples within the i-th time slice, denotes the sum of the similarity weights of sample point with all sample points within the same time slice, which serves to normalize the transition probability; Based on the transition probability matrix, calculate At step 2, the transition probability matrix is calculated At step 2, the transition probability matrix is calculated ; An adaptive neighborhood strategy is used to assign neighbors to sample points. Step transition probability matrix Sort in descending order and determine the number of neighbors. , will the former Each corresponding sample point is determined as the set of neighbor relationships for the sample point, and the number of neighbors... The following relationship must be satisfied: wherein, is a determined number of neighbors, is a preset threshold value, is step transition probability matrix; Based on the set of neighbor relationships, an adjacency matrix is ​​constructed, and the adjacency matrix is ​​represented as follows: where two sample points and belong to different time segments and and represent the neighbor relationship set of sample points and respectively.

4. The method of claim 3, wherein, The step of generating a graph Laplacian matrix based on the adjacency matrix and constructing a graph representation learning objective function based on the graph Laplacian matrix includes: According to the adjacency matrix Generate degree matrix ; generating the graph Laplacian matrix based on the adjacency matrix and the degree matrix generating a joint Laplacian matrix from the graph Laplacian matrix ; based on the joint laplacian matrix a graph representation learning objective function defined as: in, It is a stationary projection matrix. yes transpose, Let be the number of samples in the i-th time segment. For indexing different time segments, This is the index of the sample point within the time segment. The global data matrix consists of sample points from all time segments. yes transpose, The Euclidean norm of a vector. yes transpose, yes transpose, Represents the trace operation of a matrix.

5. The method of claim 4, wherein, The introduction of weighting coefficients to jointly optimize the statistical difference objective function and the graphical representation learning objective function yields a stationary projection matrix, including: Based on the statistical difference objective function and the graph representation learning objective function, weight coefficients are introduced to construct a joint optimization objective function, which is expressed as follows: in, The statistical difference matrix constructed for the statistical difference objective function. These are the weighting coefficients. = = + , Denotes the joint optimization matrix. For a stationary projection matrix, yes transpose, yes transpose, Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. This represents the total number of time segments. Solving the joint optimization objective function using the Lagrange multiplier method transforms it into: ； wherein is a Lagrange multiplier, is an identity matrix; Solving the joint optimization objective function is transformed into solving the generalized eigenvalue decomposition problem, which is expressed as: ,in, For generalized eigenvectors, These are generalized eigenvalues; The generalized eigenvalues ​​obtained from solving the generalized eigenvalue decomposition problem are arranged in ascending order, and the matrix composed of the eigenvectors corresponding to the first d smallest eigenvalues ​​is the stationary projection matrix.

6. The method of claim 1, wherein, The analysis of statistical differences in the operational data across different time segments, and the construction of a statistical difference objective function based on these differences, includes: Calculate the mean vector and covariance matrix for each time segment; Calculate the average of the mean vectors and the average of the covariance matrices for all time segments; Using KL divergence, based on the mean vector, covariance matrix, average of the mean vector, and average of the covariance matrix of each time segment, a difference objective function is constructed by analyzing the statistical differences in the operational data of each time segment. The difference objective function is expressed as follows: in, For a stationary projection matrix, Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. The total number of time segments. For statistical difference matrix, , Let be the mean vector of the sample points in the i-th time segment. Let be the covariance matrix of the sample points in the i-th time segment. The average of the mean vectors of all time segments. The average of the covariance matrices for all time segments. This represents the total number of time segments.

7. The method of claim 1, wherein, The process of determining the control limits of the Mahalanobis distance monitoring statistics using the stationary projection matrix includes: The stationary projection matrix is ​​used to project the normally functioning operating data to obtain the stationary characteristics of the normally functioning operating data. ,in It is a stationary projection matrix; The stationary characteristics of the normal operation data are used to construct monitoring statistics for the normal operation data using Mahalanobis distance; Control limits for monitoring statistics of the normal operating data are calculated using kernel density estimation.

8. The method of claim 1, wherein, The process of acquiring operational data for a non-stationary industrial process involves dividing the operational data into multiple continuous time segments, including: To obtain operational data for the normal operation of non-stationary industrial processes; The normal operating data is standardized to obtain standardized operating data; The standardized operational data is divided into multiple consecutive time segments.

9. The method of claim 1, wherein, The process of collecting real-time operational data from industrial processes and using the control limits to detect faults in the real-time operational data includes: Collect real-time operational data of industrial processes; The stationary projection matrix is used for projecting the real-time operation data to obtain stationary characteristics of the real-time operation data wherein is the stationary projection matrix The stationary characteristics of the real-time running data are used to construct monitoring statistics for the real-time running data using Mahalanobis distance; The control limits are used to monitor and detect faults in the real-time operating data.

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