A Distributed Output Process Time Graph Convolution Modeling Method

Abstract

The present invention discloses a distributed output process time graph convolution modeling method, which comprises the following steps: 1) acquisition and integration of data; 2) construction of a topological graph: first, a topological graph is constructed according to prior knowledge in the actual chemical process, potential variable relationships are found in a data-driven manner, and the topological graph is supplemented according to these variable relationships, so that a complete topological graph is constructed; 3) modeling and training: a time graph convolution TGCN model is constructed to train the training data set, and other comparison models are established for model training; 4) model testing. By combining prior knowledge and data-driven methods to construct a topological graph, the present invention uses time graph convolution layers to simultaneously extract the variable correlation and time correlation of process variables, which not only improves the model prediction accuracy, but also helps to understand the relationship between variables and enhances the interpretability of the model.

Description

Technical Field

[0001] The present invention belongs to the technical field of process industry predictive modeling, and particularly relates to a distributed output process time graph convolutional modeling method. Background Art

[0002] In some chemical processes, process variables with distributed characteristics of the output have a great impact on product quality, such as the molecular weight distribution (MWD) in the polymerization process, the crystal size distribution (CSD) in the crystallization process, etc., which are collectively referred to as distributed processes. In order to achieve real-time monitoring of the process, it is necessary to perform real-time measurement on the distributed characteristics of the product. However, in order to ensure the smooth progress of the chemical reaction, the factory usually stores the product in a closed container. Therefore, only traditional solutions such as off-line analysis and delayed measurement can be used to replace real-time measurement. With the increase in process complexity, traditional solutions gradually become difficult to meet the production requirements. Therefore, soft sensing technology that can estimate difficult-to-measure variables from easily measurable variables has been widely applied to the characteristic measurement of products.

[0003] So far, soft sensing mainly falls into two categories: mechanism modeling methods and data-driven modeling methods. Mechanism modeling methods are based on physical and chemical reactions in industrial processes to establish approximate mathematical models, which have strong interpretability and anti-noise properties. However, with the complexity of industrial processes, the internal mechanism becomes complex, and it is difficult to summarize an approximate mathematical model. Therefore, mechanism modeling methods gradually become difficult. The data-driven method does not depend on the characteristics of the process mechanism, which makes it gradually become the mainstream soft sensing method. Classical data-driven methods such as B-spline neural networks and support vector regression (SVR) have been applied to the soft sensing tasks of distributed processes. In addition, in order to capture complex system behaviors such as non-linearity and non-Gaussianity, soft sensors based on deep neural networks (DNNs) have received extensive attention. Although DNNs have achieved great success in distributed output process modeling, their difficulty in integrating into the mechanism process makes it difficult to be used in applications involving safety. Therefore, the lack of interpretability is considered to be one of the greatest limitations of DNNs.

[0004] Graph Convolutional Neural Networks (GCNs) can mine the node relationships in non-Euclidean graph-structured data by constructing a variable relationship graph and propagate the information of nodes along the edges of the graph in a set way, which helps to understand the relationships between different nodes. Therefore, GCNs have strong spatial feature extraction capabilities. Introducing graph neural networks to model the distributed output process can help understand the connections between variables in the distributed output process and enhance the interpretability of the model, which solves the problem of the lack of interpretability in traditional deep learning. At the same time, in the distributed output process, there is a temporal correlation between variables. Extracting the temporal correlation between variables helps to improve the prediction accuracy of the model, while traditional GCNs cannot effectively extract the temporal correlation between variables. The Gated Recurrent Unit (GRU) has strong feature extraction capabilities, especially for the feature extraction of spatio-temporal sequences and time series, so it is often used in soft sensor modeling. However, the current soft sensor model based on GRU only considers extracting the temporal correlation of input variables and does not consider extracting variable correlations, which results in weak interpretability of the model. Adding a gated recurrent mechanism to the graph convolution mechanism can effectively extract the temporal correlation between variables, fully mine and extract useful features in time data while extracting variable correlations, which makes up for the disadvantage that graph convolution cannot effectively extract the temporal correlation between variables. The combination of graph convolution and the gated recurrent mechanism improves the model's ability to extract spatio-temporal correlations of variables and also enhances the interpretability of the model.

[0005] However, GCN can only be applied when the graph structure expressing variable dependencies is available. Due to the complex system behavior of the distributed output process, it is very difficult to construct a topological network graph between variables, while data-driven has the advantage of being able to obtain important feature variables from data. Extract key feature variables from known data through data-driven and use it as prior knowledge to supplement the topological network graph, which takes into account the interpretability of the model while solving the graph construction problem. Summary of the Invention

[0006] Aiming at the problem that the existing soft sensor methods lack interpretability in predicting the distributed output process, the purpose of the present invention is to provide a time graph convolution modeling method based on the distributed output process, construct a topological graph between variables using prior knowledge, and use a data-driven method to extract key feature variables to supplement the prior knowledge graph construction. The addition of prior knowledge helps to understand the relationships between variables and enhances the interpretability of the model. Use graph convolution and gated recurrent mechanism to extract variable correlations and temporal correlations between variables. Taking the styrene radical polymerization process as an example, compared with traditional methods, it reflects the effectiveness of the proposed method.

[0007] The specific technical solutions are as follows:

[0008] A distributed output process time graph convolution modeling method, comprising the following steps:

[0009] 1) Acquisition and integration of data

[0010] First, according to the actual operating conditions in the chemical production process, collect data with different characteristics, divide the data set into a training data set and a test training set, and perform normalization processing.

[0011] Step 1.1: Divide the collected data set into a training data set and a test data set according to a ratio of 1:1;

[0012] Step 1.2: Perform normalization processing on the training data set and the test data set. The data standardization formula is

[0013]

[0014] where X' is the data after normalization processing, X is the original data without normalization processing, X min is the minimum value of the data, and X max is the maximum value of the data.

[0015] 2) Topological graph construction

[0016] First, construct a topological graph according to the prior knowledge in the actual chemical process, use a data-driven method to find potential variable relationships, and supplement the topological graph according to these variable relationships, so that a complete topological graph is constructed.

[0017] Step 2.1: First, find the relationships between variables according to the prior knowledge in the chemical process, and construct a variable topological graph according to the relationships between variables;

[0018] Step 2.2: Use a data-driven method to find potential key variable relationships. Taking a data set of n training data samples and m feature variables as an example, use mutual information MI to measure the strength of the relationship between each feature variable in the data set and the training data label y, arrange the variables in descending order of MI, and select the top 20% of the variables to complete feature selection. The calculation formula of MI is as follows:

[0019]

[0020] where P(x,y) is the joint probability distribution between random variables x and y;

[0021] Step 2.3: Calculate the mutual information MI between the variables after screening, select the top 50% of the variable relationships as the basis for supplementary graph construction, and complete the construction of the variable topological graph.

[0022] 3) Modeling training

[0023] Build a temporal graph convolutional TGCN model to train the training dataset, and at the same time establish other comparison models for model training.

[0024] Step 3.1: Establish a TGCN model. Input the constructed complete variable topology graph in the form of an adjacency matrix into the TGCN. Input the divided training dataset into the model, and use the TGCN to extract the variable correlation and temporal correlation of the variables. The temporal graph convolutional layer TGCL is composed of a graph convolutional network and a gated recurrent unit.

[0025]

[0026] where A represents the input adjacency matrix, D = ∑ j A j represents the degree matrix of the adjacency matrix, H is the feature vector of the current layer, l represents the number of layers, σ represents the ReLU(·) activation function, and W represents the trainable parameters;

[0027] The gated recurrent unit is an algorithm that determines the future state of a certain unit in the network through the current input and the past state, expressed as:

[0028] u t = σ(W u [h t-1 , x t )

[0029] r t = σ(W r [h t-1 , x t )

[0030] c t = tanh(W c [r t *h t-1 , x t )

[0031] h t = u t *h t-1 + (1 - u t ) * c t

[0032] where u t represents the result of the update gate, r t represents the result of the reset gate, c t represents the result of the current memory cell, h t and h t-1 represent the module output results at time t and time t - 1 respectively, W u , W r and Wc respectively represent the trainable weights corresponding to the update gate, reset gate, and memory unit,

[0033] Input the input data X t and the adjacency matrix A into the graph convolutional network to obtain the feature X' extracted after graph convolution t , take X' t and the output h at the previous moment t-1 as the input of the GRU, and obtain the hidden state h at the current moment after the gated recurrent mechanism t and the prediction result Y t , and stack TGCL to achieve the prediction of the target variable,

[0034] The calculation process of TGCL is expressed by the following formula, where GC(·) represents the graph convolution mechanism, GC u , GC r and GC c respectively represent the graph convolution mechanisms with different learnable weight matrices W u , W r and W c , b u , b r and b c are biases, and tanh(·) is the activation function,

[0035] u t = σ(W u [GC u (A, X), h t-1 +b u )

[0036] r t = σ(W r [GC r (A, X), h t-1 +b r )

[0037] c t = tanh(W c [GC c (A, X), (r t *h t-1 )]+b c )

[0038] h t = u t *h t-1 +(1 - u t )*c t

[0039] Step 3.2: Use the fully connected layer FCL to output the prediction result, which is expressed by the following formula:

[0040] Y' = FCL(h1)

[0041] Where Y' represents the prediction result of the model at time t;

[0042] Step 3.3: Train the model by optimizing the loss function composed of the prediction result and the labels of the training dataset. The formula of the loss function is expressed as follows:

[0043]

[0044]

[0045] Where Y represents the label data, γ represents the hyperparameter term of regularization, and L reg is the regression term used to avoid overfitting, and W train represents all the trainable weight parameters in the training process of the TGCN model;

[0046] Step 3.4: Input the training dataset into the contrast model for training.

[0047] 4) Model testing

[0048] Make predictions on the test dataset,

[0049] Step 4.1: Input the test dataset into the trained TGCN model for testing, and at the same time use the trained contrast model to test the test dataset;

[0050] Step 4.2: Compare the test results of the TGCN model and other contrast models.

[0051] The beneficial effects of the present invention are mainly manifested in that the present invention proposes a modeling method based on temporal graph convolution, constructs a topological graph by combining prior knowledge and data-driven methods, and uses the temporal graph convolutional layer to simultaneously extract the variable correlation and temporal correlation of process variables. While improving the model prediction accuracy, it helps to understand the relationship between variables and enhance the interpretability of the model. Description of the drawings

[0052] Figure 1 It is the structural diagram of the temporal graph convolutional layer of the present invention;

[0053] Figure 2 It is the schematic diagram of the gated recurrent unit of the present invention;

[0054] Figure 3 It is the structural diagram of the soft sensor model based on temporal graph convolution of the present invention;

[0055] Figure 4 It is the prior topological subgraph constructed based on the kinetic equation of the styrene radical polymerization process of the present invention;

[0056] Figure 5 This is the process of the present invention to construct a causal topology graph by supplementing variable relationships on the basis of the prior sub-graph based on mutual information.

[0057] Figure 6 This is the prediction result of the five soft sensing models of the present invention for the MWD of styrene radical polymerization. Detailed implementation manners

[0058] The present invention will be further described below in conjunction with the accompanying drawings of the specification and embodiments, but the protection scope of the present invention is not limited thereto.

[0059] A distributed output process time graph convolution modeling method includes the following steps:

[0060] 1) Acquisition and integration of data

[0061] First, according to the actual operating conditions in the chemical production process, data with different characteristics are collected, and the data set is divided into a training data set and a test training set and normalized.

[0062] Step 1.1: Divide the collected data set into a training data set and a test data set according to a ratio of 1:1; Step 1.2: Normalize the training data set and the test data set. The data standardization formula is

[0063]

[0064] where X' is the data after standardization processing, X is the original data without standardization processing, X min is the minimum value of the data, and X max is the maximum value of the data.

[0065] 2) Topology graph construction

[0066] First, a topology graph is constructed according to the prior knowledge in the actual chemical process, and a data-driven method is used to find potential variable relationships, and the topology graph is supplemented according to these variable relationships, so that a complete topology graph is constructed.

[0067] Step 2.1: First, find the relationships between variables according to the prior knowledge in the chemical process, and construct a variable topology graph according to the relationships between variables;

[0068] Step 2.2: Use a data-driven method to find potential key variable relationships. Taking a data set of n training data samples and m feature variables as an example, use mutual information MI to measure each feature variable in the data set Based on the strength of the relationship between the training data label y, the variables are sorted in descending order of MI, and the top 20% of the variables are selected to complete feature selection. The calculation formula of MI is as follows:

[0069]

[0070] where P(x,y) is the joint probability distribution between the random variables x and y;

[0071] Step 2.3: Calculate the mutual information MI between the variables after screening, select the top 50% of the variable relationships as the basis for supplementary graph construction, and complete the construction of the variable topology graph.

[0072] 3) Modeling and training

[0073] Build a temporal graph convolutional TGCN model to train the training data set, and at the same time establish other comparison models for model training.

[0074] Step 3.1: Establish a TGCN model, input the constructed complete variable topology graph in the form of an adjacency matrix into the TGCN, input the divided training data set into the model, and use the TGCN to extract the variable correlation and temporal correlation of the variables. The temporal graph convolutional layer TGCL is composed of a graph convolutional network and a gated recurrent unit, as Figure 1 shown

[0075]

[0076] where A represents the input adjacency matrix, D = ∑ j A j represents the degree matrix of the adjacency matrix, H is the feature vector of the current layer, represents the number of layers, σ represents the ReLU(·) activation function, and W represents the trainable parameter;

[0077] As Figure 2 shown, the gated recurrent unit is an algorithm that determines the future state of a certain unit in the network through the current input and the state at the past moment, expressed as:

[0078] u t = σ(W u [h t-1 , x t )

[0079] r t = σ(W r [h t-1 , x t )

[0080] c t = tanh(W c [r t *h t-1 , xt )

[0081] h t = u t * h t-1 +(1 - u t )* c t

[0082] where u t represents the result of the update gate, r t represents the result of the reset gate, c t represents the result of the current memory cell, h t and h t-1 represent the module output results at time t and t - 1 respectively, W u , W r and W c represent the trainable weights corresponding to the update gate, reset gate, and memory cell respectively,

[0083] Input the input data X t and the adjacency matrix A into the graph convolutional network to obtain the feature X' extracted after graph convolution t , take X' t and the output h t-1 at the previous time step as the input of the GRU, and obtain the hidden state h t and the prediction result Y t at the current time step through the gated recurrent mechanism. Predict the target variable by stacking TGCL,

[0084] The calculation process of TGCL is expressed by the following formula, where GC(·) represents the graph convolution mechanism, GC u , GC r and GC c represent graph convolution mechanisms with different learnable weight matrices W u , W r and W c respectively, b u , b r and b c are biases, and tanh(·) is the activation function,

[0085] u t = σ(W u [GC u (A, X), h t-1 + b u )

[0086] r t = σ(W r [GC r (A, X), h t-1 + b r )

[0087] c t = tanh(W c [GC c (A, X), (r t *h t-1 ) + b c )

[0088] h t = u t *h t-1 + (1 - u t )*c t

[0089] Step 3.2: Use the fully connected layer FCL to output the prediction result, which is expressed by the following formula:

[0090] Y'_FCL(h t )

[0091] where Y' represents the prediction result of the model at time t;

[0092] Step 3.3: Train the model by optimizing the loss function composed of the prediction result and the label of the training dataset. The formula of the loss function is expressed by the following formula:

[0093]

[0094]

[0095] where Y represents the label data, γ represents the regularization hyperparameter term, and L reg is the regression term used to avoid overfitting, and W train represents all the trainable weight parameters during the training process of the TGCN model;

[0096] Step 3.4: Input the training dataset into the contrast model for training.

[0097] 4) Model testing

[0098] Make predictions on the test dataset,

[0099] Step 4.1: Input the test dataset into the trained TGCN model for testing, and at the same time use the trained contrast model to test the test dataset;

[0100] Step 4.2: Compare the test results of the TGCN model and other contrast models.

[0101] Summarize the above steps to obtain the structure diagram of the soft sensor model based on temporal graph convolution, as shown in Figure 3 .

[0102] Example

[0103] (1) Obtain the dataset of the styrene free radical polymerization process as follows:

[0104] Step 1.1: Use the styrene free radical polymerization MWD simulation program to simulate and generate process data under 40 different experimental operating conditions, with 100 samples for each experimental operating condition label data.

[0105] Step 1.2: Randomly shuffle the 40 batches of data and divide the dataset into 20 batches of training set and 20 batches of test set according to the ratio of 1:1.

[0106] Step 1.3: Apply medium noise (5% Gaussian noise) to the data in the styrene free radical polymerization MWD experiment.

[0107] Step 1.4: Normalize the data after applying the noise.

[0108] (2) Conduct TGCN model training

[0109] Step 2.1: Construct a prior topological subgraph according to part of the kinetic equations of the styrene free radical polymerization process.

[0110] Among them, part of the kinetic equations can be expressed by the following functional relationships:

[0111]

[0112] Among them, C i represents the concentration in the outlet initiator feed stream, F i represents the volumetric flow rate of the inlet initiator, C m represents the monomer concentration in the inlet monomer feed stream, T r is the reaction temperature, f(.) represents the kinetic functional relationship, and the functional relationship between variables can be regarded as a dependence relationship. The constructed prior subgraph is as Figure 4 shown.

[0113] Step 2.2: Eight process variables are obtained in the styrene free radical polymerization process, namely the flow rate of the inlet solvent (F i ), the flow rate of the inlet monomer (F m ), the flow rate of the inlet initiator (F s ), the monomer concentration in the inlet monomer feed stream (C m ), the solvent concentration in the solvent feed (C s ), the initiator concentration in the initiator feed stream (C i ), the inlet feed temperature (T i ) and the polymer concentration (d). Among them, the polymer concentration is the target variable of this experiment. Calculate the MI of each variable with the styrene free radical polymerization product concentration, as shown in Table 1.

[0114] MI values of each variable in Table 1 and the concentration of styrene free radical polymerization product

[0115] Styrene polymerization process variables MI Flow rate of inlet solvent 0.36 Flow rate of inlet monomer 0.46 Flow rate of inlet initiator 0.25 Monomer concentration in the inlet monomer feed stream 0.68 Solvent concentration in the solvent feed 0.34 Initiator concentration in the initiator feed stream 0.23 Inlet feed temperature 0.22

[0116] Step 2.3: According to Table 1, screen out the two variables with the largest MI, the inlet monomer flow rate (F m ), and the monomer concentration (C m ) in the inlet monomer feed stream. Calculate the MI of F m and C m with the variables represented by each node in the prior topological subgraph again. Calculate that the MI of F m and T i , F m and C i is relatively large. Based on this, determine the edge connection between nodes and supplement the prior subgraph to obtain the required causal topological graph, as shown in Figure 5 .

[0117] (3) Modeling and training

[0118] Step 3.1: Establish a TGCN model, input the constructed complete variable topological graph into the TGCN in the form of an adjacency matrix, input the divided training data set into the model, and use the TGCN to extract the variable correlation and time correlation of variables.

[0119] Step 3.2: Use the fully connected layer FCL to output the prediction result of the styrene free radical MWD.

[0120] Step 3.3: Train the model by optimizing the loss function composed of the prediction result and the label of the training data set.

[0121] (4) Model testing and comparison of the prediction performance of six soft sensing models

[0122] Step 4.1: Input the test data set into the trained TGCN model for testing, and at the same time use the trained comparison model to test the test data set;

[0123] Step 4.2: Compare the test results of the TGCN model and other comparison models.

[0124] This model uses the root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) as the evaluation criteria,

[0125] RMSE can be expressed as:

[0126]

[0127] MAE can be expressed as:

[0128]

[0129] R 2 can be expressed as:

[0130]

[0131] where y i and respectively represent the true value and the predicted value of the distributed output data at the i-th time step, T represents the time step length, represents the average value of the y i set,

[0132] According to the RMSE, MAE and R in Table 2 2 it can be seen that the proposed TGCN model has the best prediction effect. The Gaussian process regression model (GPR), support vector regression model (SVR), GCN and GRU are selected as the baseline models. Figure 6 are the visualization of the prediction results of TGCN, GPR, SVR, GCN and GRU for the last 2 batches. Compared with GPR and SVR, the RMSE of the TGCN model is reduced by 29.3% and 53.1% respectively. This is mainly because GPR and SVR cannot effectively reflect the time and space characteristics of the data. In addition, GRU, as a model for extracting time features, shows good prediction effects, but its neglect of variable correlation leads to a worse prediction effect than TGCN. GCN can effectively capture the variable correlation of process variables, but cannot well obtain the time features of the data. Therefore, in this experiment, the prediction effect of GCN is not as good as that of TGCN.

[0133] Table 2 Comparison of the prediction performance of six soft sensor models for the MWD of styrene radical polymerization

[0134] Model RMSE MAE <![CDATA[R 2 > GPR 8.70e-5 5.49e-5 0.849 SVR 1.31e-4 9.12e-5 0.652 GCN 1.21e-4 9.27e-5 0.719 GRU 8.31e-5 5.55e-5 0.870 TGCN 6.15e-5 4.09e-5 0.941

[0135] The time graph convolution modeling method proposed by the present invention has been fully verified on the MWD dataset of styrene radical polymerization, improving the prediction accuracy and enhancing the interpretability of the model, which has universality and generality.

[0136] The content described in the embodiments of this specification is only a list of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms stated in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A distributed output process time graph convolution modeling method, characterized in that It includes the following steps: 1) Data acquisition and integration First, according to the actual operating conditions in the chemical production process, collect data with different characteristics, divide the data set into a training data set and a test training set, and perform normalization processing; 2) Topological graph construction First, construct a topological graph based on the prior knowledge in the actual chemical process, use a data-driven method to find potential variable relationships, and supplement the topological graph according to these variable relationships, so that a complete topological graph is constructed; 3) Modeling and training Construct a time graph convolutional TGCN model to train the training data set, and at the same time establish other comparison models for model training; 4) Model testing Make predictions on the test data set; The specific process of step 3) includes the following steps: Step 3.1: Establish a TGCN model, input the constructed complete variable topological graph into the TGCN in the form of an adjacency matrix, input the divided training data set into the model, and use the TGCN to extract the variable correlation and time correlation of the variables. The time graph convolutional layer TGCL is composed of a graph convolutional network and a gated recurrent unit. where A represents the input adjacency matrix, D = ∑ j A j represents the degree matrix of the adjacency matrix, H is the feature vector of the current layer, l represents the number of layers, σ represents the ReLU(·) activation function, and W represents the trainable parameters; the gated recurrent unit is an algorithm that determines the future state of a certain unit in the network through the current input and the state at the past moment, expressed as: u t = σ(W u [h t-1 , x t ) r t = σ(W r [h t-1 , x t ) c t = tanh(W c [r t *h t-1 , x t ) h t = u t * h t-1 + (1 - u t ) * c t Among them, u t represents the result of the update gate, r t represents the result of the reset gate, c t represents the result of the current memory cell, h t and h t-1 represent the output results of the module at time t and time t-1 respectively, W u , W r and W c represent the trainable weights corresponding to the update gate, reset gate, and memory cell respectively, Input the input data X t and the adjacency matrix A into the graph convolutional network to obtain the feature X' extracted after graph convolution t , take X' t and the output h at the previous moment t-1 as the input of the GRU, and obtain the hidden state h at the current moment after the gated recurrent mechanism t and the prediction result Y t , and stack the TGCL to achieve the prediction of the target variable The calculation process of TGCL is expressed by the following formula, where GC(·) represents the graph convolution mechanism, GC u , GC r and GC c respectively represent the graph convolution mechanisms with different learnable weight matrices W u , W r and W c , b u , b r and b c are biases, and tanh(·) is the activation function. u t = σ(W u [GC u (A, X), h t-1 + b u ) r t = σ(w r [GC r (A,c), h t-1 + b r ) c t = tanh(W c [GC c (A,X),(r t *h t-1 ) + b c ) h t = u t * h t-1 + (1 - u t ) * c t Step 3.2: Use the fully connected layer FCL to output the prediction result, which is expressed by the following formula: Y′ = FCL(h t ) where Y' represents the prediction result of the model at time t; Step 3.3: Train the model by optimizing the loss function composed of the prediction result and the label of the training data set. The formula of the loss function is expressed by the following formula: where Y represents the label data, γ represents the regularized hyperparameter term, and L reg is a regression term used to avoid overfitting, and W train represents all the trainable weight parameters during the training process of the TGCN model; Step 3.4: Input the training data set into the comparison model for training.

2. The method for distributed output process time graph convolution modeling according to claim 1, characterized in that The specific process of step 1) includes the following steps: Step 1.1: Divide the collected data set into a training data set and a test data set according to a ratio of 1:1; Step 1.2: Perform normalization processing on the training data set and the test data set. The data standardization formula is Among them, X' is the data after standardization processing, X is the original data without standardization processing, X min is the minimum value of the data, X max is the maximum value of the data.

3. The distributed output process time graph convolution modeling method according to claim 2, wherein The specific process of step 2) includes the following steps: Step 2.1: First, find the relationships between variables according to the prior knowledge in the chemical process, and construct a variable topological graph according to the relationships between variables; Step 2.2: Use the data-driven method to find potential key variable relationships. Take a dataset with n training data samples and m feature variables as an example. Use mutual information (MI) to measure the strength of the relationship between each feature variable in the dataset and the training data label y. Arrange the variables in descending order of MI and select the top 20% of the variables to complete feature selection. The calculation formula of MI is as follows: where P(x,y) is the joint probability distribution between the random variables x and y; Step 2.3: Calculate the mutual information MI between the variables after screening, select the top 50% of the variable relationships as the basis for supplementary graph construction, and complete the construction of the variable topological graph.

4. The distributed output process time graph convolutional modeling method according to claim 3, wherein The specific operation process of step 4) includes the following steps: Step 4.1: Input the test data set into the trained TGCN model for testing, and at the same time use the trained comparison model to test the test data set; Step 4.2: Compare the test results of the TGCN model and other comparison models.

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