An industrial process fault monitoring method based on time information enhanced graph convolution autoencoder

Abstract

The application discloses an industrial process fault monitoring method based on a time information enhanced graph convolutional autoencoder, designs a variable-guided time regularization Gaussian kernel method to measure the correlation degree between variables, simultaneously introduces a sparse maximization function to adaptively reserve significant variable correlation, constructs a space perception graph structure across time, and comprehensively represents the spatial dependence between industrial process variables and the spatial dependence across time; a multilayer graph convolutional autoencoder network is constructed to extract local spatiotemporal correlation features, simultaneously a convolutional long short-term memory network is connected between the encoding layer and the decoding layer to capture long-term time dependence information of the sequence, the extraction capability of the spatiotemporal correlation features is enhanced, and data reconstruction is assisted. The method can fully extract the spatiotemporal correlation features of normal data of an industrial process, improves the reconstruction capability of the model on the normal data, realizes higher monitoring precision under an unsupervised task of an industrial process with a complex spatiotemporal correlation relationship, and is superior to the prior art.

Description

Technical Field

[0001] This invention relates to the field of fault monitoring technology in industrial processes, and specifically to a fault monitoring method for industrial processes based on a time-informed enhanced graph convolutional autoencoder. Background Technology

[0002] The process industry is a crucial component of the manufacturing sector and a vital pillar of China's national economy and social stability. With the rapid development of modern industrial intelligence and automation, the scale and complexity of industrial processes are increasing daily. In actual operation, factors such as equipment aging, changes in the operating environment, and staff negligence can lead to system failures that can cause anything from reduced production efficiency or production interruptions to severe equipment damage and personnel injuries. Therefore, developing advanced industrial process fault monitoring technologies to identify faults in industrial processes in a timely and accurate manner is of paramount importance for improving the safety and stability of industrial processes. However, the spatiotemporal dependence of actual industrial processes is extremely complex, mainly comprising three parts: cross-time interactions within the same variable (time dependence); interactions between different variables at the same point in time (spatial dependence); and interactions between different variables at different points in time (cross-time spatial dependence). Furthermore, some anomalies in industrial processes may experience time delays in propagation from one variable to another, posing significant challenges to industrial process fault monitoring.

[0003] Since industrial processes are mostly in normal operation, abnormal or fault data are rare and difficult to collect. Therefore, unsupervised industrial process fault monitoring methods that learn the characteristics of normal patterns to identify potential anomalies have been widely studied and developed, such as using Gaussian mixture models and isolated forests for industrial process fault monitoring. In recent years, with the development of sensor and computer technologies, a large amount of industrial process data has been collected and stored. Deep learning methods with powerful deep feature extraction capabilities have developed rapidly. Many scholars have adopted deep learning models, such as autoencoders (AEs), recurrent neural networks (RNNs) and their variants, and graph neural networks (GNNs), to mine the spatiotemporal dependency information in industrial process data for industrial process fault monitoring. For example, Xu et al. proposed an industrial process anomaly monitoring method based on a dual-sequence gated recurrent unit (Bi-SGRU), which utilizes autoencoders and GRUs to extract the nonlinear and dynamic features of process variables, achieving anomaly monitoring of industrial processes with pattern-specific sequence features. Song et al. proposed an industrial process fault monitoring method based on a spatiotemporal information-based dual-layer separation parallel autoencoder, which uses temporal feature extraction and a spatial graph module to capture temporal and spatial information in process data, achieving process fault monitoring. Zhao et al. proposed an industrial process fault monitoring method based on a spatiotemporal synchronization graph convolutional network, which uses a spatiotemporal synchronization modeling mechanism to construct a spatiotemporal synchronization graph convolutional module, effectively capturing complex local spatiotemporal correlations to achieve complex industrial process fault monitoring. However, the above research on fault monitoring based on the spatiotemporal dependence of process variables still has the following problems that need to be improved: 1) Different types of deep network models are used to extract spatial coupling and time-related information respectively. For example, Long Short-Term Memory Network (LSTM) and GRU focus on capturing time dependence, while Graph Neural Network (GNN) focuses on capturing spatial dependence. However, the problem of spatial dependence across time is ignored, which makes it impossible to accurately detect potential anomalies with time delays and affects the accuracy of fault monitoring; 2) Existing spatiotemporal graph convolutional network models only capture local spatiotemporal correlation information, resulting in insufficient extraction of long-term time-series related information and affecting the accuracy of fault monitoring.

[0004] Therefore, new technologies need to be introduced to fully extract the spatiotemporal dependency features of normal industrial process data, improve the model's ability to reconstruct normal data, and enable accurate unsupervised fault monitoring of industrial processes with complex spatiotemporal relationships. Summary of the Invention

[0005] To address the problem of insufficient extraction of spatiotemporal dependency information in industrial process data, leading to low fault monitoring accuracy, a fault monitoring method for industrial processes based on a Temporal Information Enhanced Graph Convolutional Autoencoder (TIGCAE) is proposed. The method uses a variable-guided time-warped Gaussian kernel to measure the correlation between variables, while introducing a sparse maximization function to adaptively preserve significant variable correlations. A cross-temporal spatial awareness graph structure is constructed to comprehensively characterize the spatial dependencies between industrial process variables and their cross-temporal spatial dependencies. A multi-layer graph convolutional autoencoder network is built to extract local spatiotemporal correlation features. Simultaneously, a convolutional long short-term memory network is connected between the encoding and decoding layers to capture long-term temporal dependency information of the sequence, enhancing the extraction capability of spatiotemporal correlation features and assisting in data reconstruction.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] A method for industrial process fault monitoring based on time-informed augmented graph convolutional autoencoders, characterized by the following steps:

[0008] (1) Obtain historical operation data of industrial processes, divide the raw data into training data and test data, and perform data preprocessing on the training data and test data respectively;

[0009] (2) The Variable-guided Time Warping Gaussian Kernel (VTWGK) method is used to measure the correlation between variables. At the same time, a sparse maximization function is introduced to adaptively preserve the correlation between significant variables. A Cross-Time Spatial Aware Graph (CTSAG) structure is constructed to comprehensively represent the spatial dependence between variables and the spatial dependence across time.

[0010] (3) Construct a multi-layer graph convolutional autoencoder network to extract local spatiotemporal related features. At the same time, connect a convolutional long short-term memory network between the encoding and decoding layers to capture long-term temporal dependence information of the sequence, enhance the ability to extract spatiotemporal related features, and assist in data reconstruction.

[0011] (4) The mean squared error is used as the loss function for model training. For the feature vector and residual vector obtained from the training samples, the Hotling statistic and the squared prediction error statistic are calculated respectively. The control limit of the monitoring statistic is determined by kernel density estimation.

[0012] (5) Based on the trained monitoring model and the control limits of the determined monitoring statistics, the test samples are monitored for faults to complete the final fault monitoring task.

[0013] A method for monitoring industrial process faults based on a temporally enhanced graph convolutional autoencoder (TIGCAE) is characterized by the following specific process in step (1):

[0014] 1) Acquire historical operating data of the industrial process, including normal data and fault data. Divide the normal data into a 7:3 ratio, with 70% of the normal data used as training data. The remaining 30% of normal and fault data were used as test data. Where N represents the variable dimension of the training and test data, that is, the number of variables contained in each measurement, m represents the sequence length of the training data, and n represents the sequence length of the test data;

[0015] 2) Perform mean and variance normalization on both the training and test data. The specific calculation formula is as follows:

[0016]

[0017] in, and These are the i-th measurements of the k-th variable in the training and testing data, respectively. and These are the mean and standard deviation of the k-th variable, calculated using the training data, respectively. The specific calculation formulas are as follows:

[0018]

[0019] 3) Using a sliding window of length T, the standardized training and test data are sampled non-overlappingly along the sequence direction, dividing the original sequence into multiple window data. The p-th training sample can then be denoted as... The q-th test sample can be denoted as...

[0020] A method for monitoring industrial process faults based on a temporally enhanced graph convolutional autoencoder (TIGCAE), characterized in that the specific process of step (2) is as follows:

[0021] 1) Sample the data from each window obtained through sampling. As input, for any two variable time series in the sample and The absolute distance is used to calculate the distance d between measurements at any two time points in two sequences. i,j Constructing a matrix The specific calculation formula is as follows:

[0022]

[0023] in, This represents the i-th measurement in the Z-variable sequence. This represents the j-th measurement in the Y variable sequence;

[0024] Considering the time delay issue of variable sequences, the minimum cumulative distance is used to represent the distance between any two time points in the two sequences. The element in the i-th row and j-th column of matrix U is based on the current distance d. i,j and its three adjacent elements d i,j-1 ,d i-1,j ,d i-1,j-1 (Left, Top, Top Left) updated to minimum cumulative distance U i,j The specific calculation formula is as follows:

[0025] U i,j =d i,j +min(d i,j-1 ,d i-1,j ,d i-1,j-1 )#(6)

[0026] The dynamic time-warped distance is ultimately defined as the bottom-right element of matrix U, taking into account both spatial dependencies between variables and spatial dependencies across time. The distance matrix is ​​obtained by quantifying the distance similarity between any two variables.

[0027] 2) Using the designed variable-guided Gaussian kernel method, a similarity matrix is ​​constructed based on the distance matrix D obtained above.

[0028] For the element M in the i-th row and j-th column of matrix M i,j The specific calculation formula is as follows:

[0029]

[0030] Among them, D i,j σ represents the element in the i-th row and j-th column of the distance matrix D, i.e., the dynamic time-warped distance between variables i and j. i and σ j Let i and j represent the standard deviations of the corresponding rows of variables i and j in matrix D, respectively.

[0031] 3) Sparsify the constructed similarity matrix M using the sparse maximization function. For the i-th row of matrix M... The elements in the array, sorted in descending order, are M. i,1 ≥M i,2 ≥…≥M i,N ; Obtain the maximum k(M) i The value is calculated using the following formula:

[0032] k(M i )=max{k∈[1,N]|1+kM i,k >∑ j≤k M i,j}#(8)

[0033] Based on k(M) i Calculate the sparsity threshold The specific calculation formula is as follows:

[0034]

[0035] Based on sparse threshold The spatial perception map structure across time was calculated. The element A in the i-th row and j-th column i,j , is used to represent the correlation score between variable i and variable j, and the specific calculation formula is as follows:

[0036]

[0037] A method for monitoring industrial process faults based on a temporally enhanced graph convolutional autoencoder (TIGCAE) is characterized by the following specific process in step (3):

[0038] 1) Input the sampled sliding window data into a three-layer graph convolutional coding network. Set the variable dimension to the number of nodes in the graph structure and the temporal dimension to the initial features of each node. For the k-th graph convolutional layer, input the output of the previous graph convolutional layer. Multiplying with the spatially aware graph structure A across time, local feature weighting and fusion are performed on the graph data. Then, graph representation learning is achieved through convolutional layer operation with a kernel of 3, extracting local spatiotemporally relevant features. The specific calculation formula is as follows:

[0039]

[0040] in, W represents the output of the k-th graph convolutional coding layer, ⊙ represents the convolution operation, σ(·) represents the activation function, such as the ReLU activation function, and W... k Let b be the weight of the convolution kernel in the k-th convolutional layer. k This is the bias of the k-th convolutional layer;

[0041] 2) The hidden features output by each graph convolutional layer are used as input to the convolutional long short-term memory network. That is, the deep features of each sliding window of data are used as input to the convolutional long short-term memory network at each time step to extract long-term time dependency information of the time series data. The specific calculation formula for the convolutional long short-term memory network layer corresponding to the k-th graph convolutional layer is as follows:

[0042]

[0043] in, These represent the input gate, forget gate, and output gate of the k-th convolutional long short-term memory network layer at time t. and These represent the current output memory state and hidden state, respectively. Enter the current time. and These represent the memory state and hidden state from the previous moment, respectively. and They are respectively and In the weights of the input gate, This is the bias of the input gate. and They are respectively and In the weight of the forget gate, For the offset of the forget gate, and They are respectively and In the weight of memory units, For the bias of memory cells, and They are respectively and In the weights of the output gate, For the output gate bias, For convolution operation, tanh(·) is the tanh activation function, and σ(·) is the non-linear activation function Sigmoid.

[0044] 3) Concatenate the hidden states of all time steps of the k-th convolutional long short-term memory network layer with the output of the previous graph convolutional decoding network layer along the channel dimension, and use this as the input to the current graph convolutional decoding network layer. This allows the long-term temporal dependency information extracted by the convolutional long short-term memory network to assist the graph convolutional decoding network in data reconstruction. The specific calculation formula is as follows:

[0045]

[0046] in, This is the input to the k-th graph convolutional decoding layer. This represents the output of the k-th graph convolutional decoding layer, where ⊙ represents the convolution operation, and σ(·) is the activation function, such as the ReLU activation function. The weights of the convolution kernel in the k-th deconvolution layer are... This is the bias of the k-th deconvolution layer;

[0047] A method for monitoring industrial process faults based on a temporally enhanced graph convolutional autoencoder (TIGCAE) is characterized by feeding the input data into the STGCRAE model for training. The specific process of step (4) is as follows:

[0048] 1) During the model training phase, preprocessed training samples are input into the model, and mean squared error (MSE) is used as the loss function for model training. The goal is to minimize the model loss. The specific formula for calculating the mean squared error loss is as follows:

[0049]

[0050] Among them, X i and These represent the i-th input sample and the reconstructed sample of the model, respectively.

[0051] 2) Based on the trained model, using the feature vectors and residual vectors obtained from normal training samples, calculate Hotelling's T(t) respectively. 2 The sum of the squared prediction error (SPE) statistic and the squared prediction error statistic are calculated using the following formulas:

[0052]

[0053] Where H is the feature vector. Let ∑ be the mean of the eigenvectors. H Let res be the covariance matrix of the eigenvectors, and res be the residual vector. Let ∑ be the mean of the residual vector. RES Let be the covariance matrix of the residual vector;

[0054] 3) Kernel density estimation is used to determine the monitoring statistic T. 2 The specific calculation formulas for kernel density estimation, along with the control limits of SPE, are as follows:

[0055]

[0056] Where n is the number of training samples, and h is the kernel density bandwidth parameter. The optimal bandwidth of 4 was obtained by visualizing the kernel density estimation curves under different bandwidths. T calculated for each sample 2 Statistic, SPE i The SPE statistic is calculated for each sample, where K(·) is the kernel function. When K(·) is a Gaussian kernel function, the above formula is expressed as:

[0057]

[0058] Among them, control limits for T2 and SPE statistics were determined by setting a 95% confidence level.

[0059] A method for monitoring industrial process faults based on a temporally enhanced graph convolutional autoencoder (TIGCAE) is characterized by feeding the input data into the STGCRAE model for training. The specific process of step (5) is as follows:

[0060] 1) In the model testing phase, the preprocessed test samples are input into the model. Based on the trained model, feature vectors and residual vectors are obtained using the test samples, and T is constructed accordingly. 2 The outlier score is calculated using the SPE statistic and the SPE statistic. If the outlier score exceeds the control limit of the statistic, a fault is considered to have occurred; otherwise, it is considered normal and no fault has occurred.

[0061] 2) The effectiveness of fault monitoring is evaluated using five metrics: False Alarm Rate (FAR), Fault Detection Rate (FDR), Recall, Accuracy, Precision, and F1 Score. The specific calculation formulas for these five metrics are as follows:

[0062]

[0063]

[0064] TP, TN, FP, and FN represent true positive, true negative, false positive, and false negative, respectively.

[0065] Beneficial effects

[0066] This invention designs an industrial process fault monitoring method based on a time-information-enhanced graph convolutional autoencoder. An improved variable-guided time-warped Gaussian kernel method is employed to measure the correlation between variables, enhancing the representation of spatial and temporal dependencies. A sparse maximization function is introduced to adaptively preserve significant variable correlations, constructing a temporal spatial perception graph structure that reduces noise interference and improves computational and storage efficiency. A multi-layer graph convolutional autoencoder network is constructed to extract local spatiotemporal correlation features, while a convolutional long short-term memory network is connected between the encoding and decoding layers to capture long-term temporal dependency information of the sequence, enhancing the extraction capability of spatiotemporal correlation features and improving the model's ability to reconstruct specific pattern data. This method solves the problems of complex spatiotemporal dependencies in industrial processes, making them difficult to fully extract, and the inability to accurately identify potential faults with propagation delays, leading to low fault monitoring accuracy in industrial processes. The proposed method can timely and accurately monitor faults in industrial processes with complex spatiotemporal relationships. Attached Figure Description

[0067] Figure 1 The diagram shown is a flowchart of the method of the present invention;

[0068] Figure 2 The following is a flowchart of the CTSAG structure;

[0069] Figure 3 The image shown is a schematic diagram of TIGCAE;

[0070] Figure 4 The image shown is a fault monitoring result for fault 1 on the TE process dataset.

[0071] Figure 5 The image shown is a fault monitoring result for fault 5 on the TE process dataset.

[0072] Figure 6 The image shown is a fault monitoring result for fault 10 on the TE process dataset.

[0073] Figure 7 The image shown is a fault monitoring result for fault 19 on the TE process dataset. Detailed Implementation

[0074] To address the shortcomings of existing technologies, this invention provides an industrial process fault monitoring method based on a temporally enhanced graph convolutional autoencoder (TIGCAE). This method fully exploits the spatiotemporal correlation features of normal industrial process data, enhances the model's ability to reconstruct normal data, and achieves higher monitoring accuracy in unsupervised tasks involving industrial processes with complex spatiotemporal relationships.

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] Reference Figure 1 This invention provides an industrial process fault monitoring method based on TIGCAE. First, a variable-guided time-warped Gaussian kernel method is used to measure the correlation between variables. Simultaneously, a sparse maximization function is introduced to adaptively preserve significant variable correlations, constructing a cross-time spatially aware graph (CTSAG) structure to comprehensively characterize the spatial dependencies and cross-time spatial dependencies between industrial process variables. The CTSAG structure flowchart is shown below. Figure 2 As shown in the diagram. Then, a multi-layer graph convolutional autoencoder network is constructed to extract local spatiotemporal related features. Simultaneously, a convolutional long short-term memory network is connected between the encoding and decoding layers to capture long-term temporal dependency information of the sequence, enhancing the ability to extract spatiotemporal related features and assisting in data reconstruction. A schematic diagram of TIGCAE is shown below. Figure 3 As shown in the figure, the mean squared error is used as the loss function for model training. For the feature vectors and residual vectors obtained from the training samples, the Hotelling statistic and the squared prediction error statistic are calculated respectively. The monitoring statistical limit is determined using kernel density estimation. Based on the trained monitoring model and the determined monitoring statistical limit, fault monitoring is performed on the test samples to achieve fault monitoring of industrial processes. The industrial process fault monitoring process based on TIGCAE is as follows: Figure 1 As shown.

[0077] The Tennessee-Eastman (TE) process, a benchmark simulation platform proposed by Eastman Semiconductor, is widely used to validate the performance of fault monitoring methods. This paper utilizes the TE process dataset to conduct industrial process fault monitoring experiments. The TE process includes 41 measured variables and 12 control variables, simulating normal conditions and 21 fault states for data acquisition. In this experiment, 33 variables were selected, including 22 measured variables and 11 control variables, for fault monitoring. The training data consisted of 400 normal samples, while the test data contained 900 samples for each fault class, with faults introduced after the 160th sample. The sliding window size was set to 10. Based on the TE dataset, this paper selected an optimal bandwidth of 4 by visualizing kernel density estimation curves under different bandwidths.

[0078] For hyperparameter design, the TIGCAE model uses the Adam optimizer with an initial learning rate of 0.001, a batch size of 10 for each input, and 300 training iterations. For model structure design, an encoder-decoder architecture is used to build the TIGCAE network model. The encoder network uses three graph convolutional layers, with the output of each layer serving as the input to a convolutional long short-term memory layer (LSS). The LSS is set to 3 layers. The decoder network also has three graph deconvolutional layers. The network structure and parameters of TIGCAE are shown in Table 1.

[0079] Based on the above description, and in accordance with the invention, the specific process is implemented as follows:

[0080] 1) Obtain historical operation data of industrial processes, divide the raw data into training data and test data, and perform data preprocessing on the training data and test data respectively according to formulas (1)-(4);

[0081] 2) Construct a spatial perception map across time, and comprehensively characterize the spatial dependence and spatial dependence relationship between variables across time according to formulas (5)-(10);

[0082] 3) Construct a multi-layer graph convolutional coding network and extract local spatiotemporal correlation features according to formula (11);

[0083] 4) Construct a convolutional long short-term memory network layer and extract long-term time dependency information of time series data according to formulas (12)-(16);

[0084] 5) Construct a multi-layer graph convolutional decoding network and reconstruct the data according to formulas (17)-(18);

[0085] 6) Build the overall network model and train the model according to formula (19);

[0086] 7) Based on the trained model, calculate the monitoring statistics according to formulas (20)-(22), and determine the control limits of the monitoring statistics according to formulas (25)-(26);

[0087] 8) Use test data for fault monitoring, and evaluate the monitoring results according to the five monitoring indicators in formulas (27)-(31).

[0088] Test data is used to evaluate the model's fault detection performance, and the occurrence of a fault is determined based on the monitoring statistical limits. Figure 4 The fault detection performance of the TIGCAE model on fault 1 of the TE process dataset is demonstrated. Figure 5 The TIGCAE model was demonstrated to detect fault 5 on the TE process dataset. Figure 6 The fault detection performance of the TIGCAE model on fault 10 of the TE process dataset is demonstrated. Figure 7 Table 1 demonstrates the fault monitoring performance of the TIGCAE model on fault 19 in the TE process dataset. Table 2 details the fault monitoring evaluation results of the TIGCAE model on the TE process dataset based on five monitoring indicators. Table 3 details the comparison of the fault monitoring performance of the TIGCAE model and its nine comparative models under the fault detection rate (FDR) indicator. As shown in Table 3, the proposed TIGCAE model achieves the best fault detection rate for 14 out of 21 fault types, with an average fault detection rate of 88.1% for all 21 types, outperforming other comparative models. Taking fault 19 as an example, the proposed TIGCAE model achieves an FDR of 96.1% for fault 19, which is 81.6% and 64.8% higher than the typical machine learning models PCA and AE, respectively, and an average 21.2% higher than other graph network models. In conclusion, this invention fully exploits the spatiotemporal correlation characteristics of normal industrial process data, enhances the model's ability to reconstruct normal data, and achieves higher monitoring accuracy in unsupervised tasks involving complex spatiotemporal relationships in industrial processes.

[0089] Table 1. TIGCAE Network Structure and Parameters

[0090]

[0091]

[0092] Table 2 shows the fault monitoring results on the TE dataset.

[0093]

[0094] Table 3 Comparison of FDR fault monitoring performance on the TE dataset

[0095]

Claims

1. A method for industrial process fault monitoring based on a time-informed augmented graph convolutional autoencoder, characterized in that, Includes the following steps: (1) Obtain historical operation data of industrial processes, divide the raw data into training data and test data, and perform data preprocessing on the training data and test data respectively; (2) The correlation between variables is measured by the variable-guided time warping Gaussian kernel method. At the same time, a sparse maximization function is introduced to adaptively retain the correlation between significant variables. A cross-time spatial perception graph structure is constructed to comprehensively characterize the spatial dependence and cross-time spatial dependence between industrial process variables. (3) Construct a multi-layer graph convolutional autoencoder network to extract local spatiotemporal related features. At the same time, connect a convolutional long short-term memory network between the encoding and decoding layers to capture long-term temporal dependence information of the sequence, enhance the ability to extract spatiotemporal related features, and assist in data reconstruction. (4) The mean squared error is used as the loss function for model training. For the feature vector and residual vector obtained from the training samples, the Hotling statistic and the squared prediction error statistic are calculated respectively. The control limit of the monitoring statistic is determined by kernel density estimation. (5) The monitoring model trained in step (3) and the control limits of the monitoring statistics determined in step (4) are used to monitor the test samples for faults, thus completing the final fault monitoring task. The specific steps of step (1) are as follows: 1) Acquire historical operating data of the industrial process, including normal data and fault data. Divide the normal data into a 7:3 ratio, with 70% of the normal data used as training data. The remaining 30% of normal and fault data were used as test data. Where N represents the variable dimension of the training and test data, that is, the number of variables contained in each measurement, m represents the sequence length of the training data, and n represents the sequence length of the test data; 2) Perform mean and variance normalization on both the training and test data. The specific calculation formula is as follows: in, and These are the i-th measurements of the k-th variable in the training and testing data, respectively. and These are the mean and standard deviation of the k-th variable, calculated using the training data, respectively. The specific calculation formulas are as follows: 3) Using a sliding window of length T, the standardized training and test data are sampled non-overlappingly along the sequence direction, dividing the original sequence into multiple window data. The p-th training sample is denoted as... The q-th test sample can be denoted as... The specific steps of step (2) are as follows: 1) Sample the data from each window obtained through sampling. As input, for any two variable time series in the sample and The absolute distance is used to calculate the distance d between measurements at any two time points in two sequences. i,j Constructing a matrix The specific calculation formula is as follows: in, This represents the i-th measurement in the Z-variable sequence. This represents the j-th measurement in the Y variable sequence; Considering the time delay issue of variable sequences, the minimum cumulative distance is used to represent the distance between any two time points in the two sequences. The element in the i-th row and j-th column of matrix U is based on the current distance d. i,j and its three adjacent elements d i,j-1 ,d i-1,j ,d i-1,j-1 Updated to minimum cumulative distance U i,j The specific calculation formula is as follows: U i,j =d i,j +min(d i,j-1 ,d i-1,j ,d i-1,j-1 )#(6) The dynamic time-warped distance is ultimately defined as the bottom-right element of matrix U, taking into account both spatial dependencies between variables and spatial dependencies across time. The distance matrix is ​​obtained by quantifying the distance similarity between any two variables. 2) Using the designed variable-guided Gaussian kernel method, a similarity matrix is ​​constructed based on the distance matrix D obtained above. For the element M in the i-th row and j-th column of matrix M i,j The specific calculation formula is as follows: Among them, D i,j σ represents the element in the i-th row and j-th column of the distance matrix D, i.e., the dynamic time-warped distance between variables i and j. i and σ j Let i and j represent the standard deviations of the corresponding rows of variables i and j in matrix D, respectively. 3) Sparsify the constructed similarity matrix D using the sparse maximization function. For the i-th row of matrix M... The elements in the array, sorted in descending order, are M. i,1 ≥M i,2 ≥…≥M i,N ; Obtain the maximum k(M) i The value is calculated using the following formula: Based on k(M) i Calculate the sparsity threshold The specific calculation formula is as follows: Based on sparse threshold The spatial perception map structure across time was calculated. The element A in the i-th row and j-th column i,j , is used to represent the correlation score between variable i and variable j, and the specific calculation formula is as follows: .

2. The industrial process fault monitoring method based on a time-information-enhanced graph convolutional autoencoder according to claim 1, characterized in that, The specific steps of step (3) are as follows: 1) Input the sampled sliding window data into a three-layer graph convolutional coding network. Set the variable dimension to the number of nodes in the graph structure and the temporal dimension to the initial features of each node. For the k-th graph convolutional layer, input the output of the previous graph convolutional layer. Multiplying with the spatially aware graph structure A across time, local feature weighting and fusion are performed on the graph data. Then, graph representation learning is achieved through convolutional layer operation with a kernel of 3, extracting local spatiotemporally relevant features. The specific calculation formula is as follows: in, Let W be the output of the k-th graph convolutional coding layer, ⊙ be the convolution operation, σ(·) be the activation function, and W be the output of the graph convolutional coding layer. k Let b be the weight of the convolution kernel in the k-th convolutional layer. k This is the bias of the k-th convolutional layer; 2) The hidden features output by each graph convolutional layer are used as input to the convolutional long short-term memory network. That is, the deep features of each sliding window of data are used as input to the convolutional long short-term memory network at each time step to extract long-term time dependency information of the time series data. The specific calculation formula for the convolutional long short-term memory network layer corresponding to the k-th graph convolutional layer is as follows: in, These represent the input gate, forget gate, and output gate of the k-th convolutional long short-term memory network layer at time t. and These represent the current output memory state and hidden state, respectively. Enter the current time. and These represent the memory state and hidden state from the previous moment, respectively. and They are respectively and In the weights of the input gate, This is the bias of the input gate. and They are respectively and In the weight of the forget gate, For the offset of the forget gate, and They are respectively and In the weight of memory units, For the bias of memory cells, and They are respectively and In the weights of the output gate, This is the bias for the output gate. For convolution operation, tanh(·) is the tanh activation function, and σ(·) is the non-linear activation function Sigmoid. 3) Concatenate the hidden states of all time steps of the k-th convolutional long short-term memory network layer with the output of the previous graph convolutional decoding network layer along the channel dimension, and use this as the input to the current graph convolutional decoding network layer. This allows the long-term temporal dependency information extracted by the convolutional long short-term memory network to assist the graph convolutional decoding network in data reconstruction. The specific calculation formula is as follows: in, This is the input to the k-th graph convolutional decoding layer. Let ⊙ be the output of the k-th graph convolutional decoding layer, ⊙ be the convolution operation, and σ(·) be the activation function. The weights of the convolution kernel in the k-th deconvolution layer are... This is the bias of the k-th deconvolution layer.

3. The industrial process fault monitoring method based on a time-information-enhanced graph convolutional autoencoder according to claim 1, characterized in that, The specific steps in step (4) are as follows: 1) The mean squared error (MSE) is used as the loss function for model training. The specific formula for calculating the mean squared error loss is as follows: Among them, X i and These represent the input sample and the reconstructed sample of the model, respectively. 2) Using the feature vectors and residual vectors obtained from normal training samples, calculate Hotelling's T(t) respectively. 2 The sum of the squared prediction error (SPE) statistic and the squared prediction error statistic are calculated using the following formulas: Where H is the feature vector. Let ∑ be the mean of the eigenvectors. H Let res be the covariance matrix of the eigenvectors, and res be the residual vector. Let ∑ be the mean of the residual vector. RES Let be the covariance matrix of the residual vector; 3) Kernel density estimation is used to determine the monitoring statistic T. 2 The specific calculation formulas for kernel density estimation, along with the control limits of SPE, are as follows: Where n is the number of training samples, and h is the kernel density bandwidth parameter. The optimal bandwidth of 4 was obtained by visualizing the kernel density estimation curves under different bandwidths. T calculated for each sample 2 Statistic, SPE i The SPE statistic is calculated for each sample, where K(·) is the kernel function. When K(·) is a Gaussian kernel function, the above formula is expressed as: Among them, control limits for T2 and SPE statistics were determined by setting a 95% confidence level.

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