Process industry key quality variable prediction method based on causal space-time diagram convolution

Abstract

The invention relates to a process industry key quality variable prediction method based on causal space-time diagram convolution. The method comprises the following steps: constructing a first causal relationship between process variables in an industrial production process of a target process; based on the causal time convolution and the attention mechanism, obtaining a second causal relationship between the process variables; then constructing a space-time diagram convolution model, and training the space-time diagram convolution model by using the training set and the test set based on a second causal relationship between process variables to obtain a key quality variable prediction model of the target process industry; and finally, inputting real-time data of the target process industrial production process into the prediction model, and outputting a prediction result of the target process industrial key quality variables. Compared with the prior art, the method has the advantages of improving the accuracy, robustness, interpretability and the like of overall prediction.

Description

Technical Field

[0001] This invention relates to the field of variable prediction technology, and in particular to a method for predicting key quality variables in the process industry based on causal spatiotemporal graph convolution. Background Technology

[0002] As the scale and complexity of process industries continue to increase, accurate prediction and monitoring of key quality variables have become an important requirement for the development of intelligent industry. Soft measurement technology, as a method for estimating difficult or unmeasurable quality variables using easily measurable variables, has been widely used in process industries such as chemical, energy, and metallurgy.

[0003] Existing soft measurement modeling methods mainly fall into three categories: multivariate statistical modeling methods, such as the mixed probability local least squares model proposed in reference 1, which can extract the linear relationship of key variables, but is difficult to effectively capture complex nonlinear features; machine learning modeling methods, such as the support vector regression model proposed in reference 2, which can describe nonlinearity to some extent, but has limited generalization ability and interpretability; and deep learning modeling methods, such as the bidirectional long short-term memory neural network proposed in reference 3, which has strong feature extraction and modeling capabilities, but often exhibits "black box" characteristics, lacks physical consistency and interpretability, and is prone to insufficient reliability of prediction results.

[0004] To overcome the aforementioned shortcomings, researchers have recently attempted to incorporate physical knowledge into data-driven models. Reference 4 proposes a physical information neural network, and Reference 5 proposes how to design such a network based on physical knowledge to improve model reliability and robustness. However, in actual process industries, physical knowledge often involves complex partial differential equations and a large number of difficult-to-obtain parameters, posing significant challenges to the application of such methods.

[0005] Compared to complete physical laws, causal relationships are easier to acquire as qualitative knowledge. Causal structures can reveal the mechanisms of interaction between process variables and can be represented by graph structures, where nodes represent variables and edges represent causal relationships. Based on this, Graph Neural Networks (GNNs) have gradually demonstrated their application value in industrial modeling. Reference 6 used a GNN to develop a soft measurement model for the steelmaking process to predict elemental mass, and Reference 7 used a GNN to implement a soft measurement task for the food waste digestion process. However, the above methods did not explicitly introduce causal relationships to improve the reliability and solvability of the models. To explicitly introduce causal relationships, Reference 8 analyzed the causal relationships between variables using conditional Granger causality and used it as the adjacency matrix of a graph convolutional neural network, improving the prediction accuracy of penicillin concentration in the penicillin fermentation process, but only considered the spatial relationships between variables. Reference 9 uses knowledge and data to guide the reinforcement learning process to discover spatiotemporal causal relationships between variables and uses these relationships to improve the prediction accuracy of graph neural networks. However, as the number of variables increases, the computational cost of training and graph structure search in the reinforcement learning process increases rapidly. In addition, the use of knowledge as a reward item, which is often “incomplete and not entirely accurate”, may mislead the reinforcement learning process.

[0006] As mentioned above, many studies have demonstrated the effectiveness of graph neural network models in predicting key quality variables in the process industry. However, when introducing causal relationships to improve model performance and reliability, the complexity of the algorithm and the spatiotemporal causal relationships between variables are not considered simultaneously. How to integrate causal knowledge with data-driven methods to construct a spatiotemporal graph convolutional modeling framework for the process industry, in the absence of a complete mechanistic model, to improve the accuracy, robustness, and interpretability of predictions, has become a technical problem that needs to be solved.

[0007] Document 1: "YANG X, LIU X, XU C. Robust Mixture Probabilistic PartialLeast Squares Model for Soft Sensing With Multivariate Laplace Distribution[J / OL]. IEEE Transactions on Instrumentation and Measurement, 2021"; Document 2: "Soft-sensor development for fed-batch bioreactors using support vector regression[J / OL]. Biochemical Engineering Journal, 2006"; Reference 3: "LUI C F, LIU Y, XIE M. A Supervised Bidirectional Long Short-Term Memory Network for Data-Driven Dynamic Soft Sensor Modeling[J / OL]. IEEETransactions on Instrumentation and Measurement, 2022"; Reference 4: "KARNIADAKIS G E, KEVREKIDIS I G, LU L, et al. Physics-informedmachine learning[J / OL]. Nature Reviews Physics, 2021"; Reference 5: "Physics-guided neural networks with engineering domainknowledge for hybrid process modeling[J / OL]. Computers & ChemicalEngineering, 2023"; Reference 6: "FENG L, ZHAO C, LI Y, et al. Multichannel Diffusion GraphConvolutional Network for the Prediction of Endpoint Composition in theConverter Steelmaking Process[J / OL]. IEEE Transactions on Instrumentation andMeasurement, 2021"; Reference 7: "WANG Y, YAN P, GAI M. Dynamic Soft Sensor for AnaerobicDigestion of Kitchen Waste Based on SGSTGAT[J / OL]. IEEE Sensors Journal,2021"; Document 8: "LIU Y, JIA M, XU D, et al. Physics-guided graph learning softsensor for chemical processes[J / OL]. Chemometrics and Intelligent LaboratorySystems, 2024"; Document 9: "ZHANG In summary, many studies have demonstrated the effectiveness of graph neural network models in predicting key quality variables in the process industry. However, when introducing causal relationships to improve model performance and reliability, the complexity of the algorithm and the spatiotemporal causal relationships between variables were not considered simultaneously. The accuracy, robustness, and interpretability of the predictions all need improvement. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method for predicting key quality variables in the process industry based on causal spatiotemporal graph convolution.

[0009] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a method for predicting key quality variables in process industries based on causal spatiotemporal graph convolution is provided, the method comprising the following steps: S1. Obtain historical data of the target process industrial production process and divide the historical data into training set and test set; S2. Construct the first causal relationship between process variables in the target industrial production process; S3. Based on causal temporal convolution and attention mechanism, construct causal relationship discovery model, use the first causal relationship to guide the causal discovery model, and obtain the second causal relationship between process variables; S4. Construct a spatiotemporal graph convolutional model. Based on the second causal relationship between process variables, train the spatiotemporal graph convolutional model using the training set and test set to obtain a prediction model for key quality variables of the target process industry. S5. Obtain real-time data input to the prediction model of the target process industry's production process, and output the prediction results of key quality variables of the target process industry.

[0010] As a preferred technical solution, the first causal relationship in S2 is specifically a knowledge matrix constructed based on domain knowledge; the domain knowledge includes four categories: causal influence between variables, no causal influence between variables, input variables are not affected by other variables, and output variables do not affect other variables; the specific formula of the knowledge matrix is: in, , which is the knowledge matrix; The number of variables; Representative variable Unaffected Influence, and Edges are not allowed between them; Representative variable by Influence, and An edge needs to be established between them; in all In the case of, if , then represents It is an input variable and is not affected by other variables; in all In the case of, if , then represents It is an output variable and does not affect other variables; if and If there is no prior knowledge between them, then .

[0011] As a preferred technical solution, the specific process of S3 includes: The time series data of each variable is processed by multiple different temporal convolutional networks to obtain the time series embedding of each variable; Time-series embeddings are used to generate attention logs and context embeddings; The attention logarithm is converted into an attention score using the SoftMax function; The aggregation of contextual embeddings is calculated based on the attention score; Based on contextual embedding aggregation, the causal relationship model performs regression prediction on time series embeddings, generates prediction results, calculates the prediction error through a loss function, and then updates the causal relationship model. Extract the model parameters of the updated causal relationship model to obtain the second causal relationship.

[0012] As a preferred technical solution, the second causal relationship is a causal relationship matrix, which consists of a Granger causal relationship matrix, a knowledge matrix, and an identity matrix. Its specific formula is as follows: in, This is the Granger causality matrix; This is the knowledge matrix, i.e., the first causal relationship; It is an identity matrix.

[0013] As a preferred technical solution, the spatiotemporal graph convolution model in S4 is specifically constructed based on temporal convolutional neural networks, graph convolutional neural networks, and gated recurrent units.

[0014] As a preferred technical solution, the specific process of constructing a spatiotemporal graph convolutional model in S4 includes: S41. Preprocess the training and test data using the time window method to obtain the preprocessed dataset; S42. Using a temporal convolutional neural network based on the preprocessed dataset, extract the temporal features of the input variables and establish time series dependencies through a gated recurrent unit. S43. Based on the second causal relationship, considering the local time relationship between process variables, a local spatiotemporal adjacency matrix is ​​introduced. S44, in conjunction with the local spatiotemporal adjacency matrix Hidden state Transform into input hidden state This leads to a local spatiotemporal graph convolutional neural network that incorporates causal relationships. The number of variables; T is the number of time steps; S45, Based on Local Spatiotemporal Adjacency Matrix A causal spatiotemporal graph convolutional model is constructed; feature fusion and prediction output are achieved by the causal spatiotemporal graph convolutional model through a fully connected layer.

[0015] As a preferred technical solution, the specific process of extracting the temporal features of input variables and establishing time series dependencies in S42 is as follows: in, , which is the hidden state at the current time step t; Input data for spatiotemporal context; Update the gate for GRU; Reset the gate for GRU; This is a GRU candidate hidden state; It is the input at the current time step t after preprocessing; , , , , and These are the parameters to be learned; , and This is the corresponding bias to be learned; This indicates the hidden state of the previous time step; and For activation functions; It represents the Hadamardi (or Hadama) stack.

[0016] As a preferred technical solution, the specific formula for the local spatiotemporal adjacency matrix in S43 is as follows: in, , is the local spatiotemporal adjacency matrix; This indicates a local time causal relationship between variables; It is a zero matrix; during training... It is defined as a trainable matrix; This represents the second causal relationship, which is the causal relationship matrix.

[0017] As a preferred technical solution, the specific representation of the local spatiotemporal graph convolutional neural network that introduces causal relationships in S44 is as follows: in, To introduce local spatiotemporal graph convolutional neural networks for causal relationships; The input is hidden. for The degree matrix; These are the parameters to be learned.

[0018] As a preferred technical solution, when training the spatiotemporal graph convolutional model in S4, a loss function containing a root mean square error term and an entropy function term is used, and its specific formula is as follows: in, For loss; The actual value; This is a predicted value; For hyperparameters; It is the entropy function of the local spatiotemporal adjacency matrix.

[0019] According to another aspect of the present invention, a prediction system for key quality variables in the process industry based on causal spatiotemporal graph convolution is provided. The system includes a data acquisition and partitioning module, an initial causal relationship construction module, a causal relationship optimization module, a prediction model training module, and a real-time prediction module. The data acquisition and segmentation module is used to acquire historical data of the target process industry's production process and to divide the historical data into training and testing sets. The initial causal relationship building module is used to construct the first causal relationships between process variables in the target process industrial production process; The causal relationship optimization module is used to build a causal relationship discovery model based on causal temporal convolution and attention mechanism, and to guide the causal relationship discovery model with the first causal relationship to obtain the second causal relationship between process variables; The prediction model training module is used to construct a spatiotemporal graph convolutional model. Based on the second causal relationship between process variables, the spatiotemporal graph convolutional model is trained using training and test sets to obtain a prediction model for key quality variables of the target process industry. The real-time prediction module is used to input real-time data of the target process industry's production process into the prediction model and output the prediction results of the key quality variables of the target process industry.

[0020] Compared with the prior art, the present invention has the following beneficial effects: 1. In this invention, by constructing a first causal relationship and a second causal relationship, and using these causal relationships to guide the training of a spatiotemporal graph convolutional model, a prediction model for key quality variables in the target process industry is obtained. This achieves the integration of causal knowledge and data-driven methods in the absence of a complete mechanistic model, constructing a spatiotemporal graph convolutional modeling framework for the process industry. Through knowledge matrix constraints and attention mechanisms, the model output is ensured to be consistent with the mechanistic logic of the industrial process. Simultaneously, the causal graph and attention matrix provide a visual explanation of the prediction results, enhancing the model's interpretability and engineering acceptability; and improving the overall accuracy, robustness, and interpretability of the prediction.

[0021] 2. In this invention, by constructing a first causal relationship between process variables, using the causal relationship to discover a second causal relationship, and training a spatiotemporal graph convolutional model based on the second causal relationship, and since the first causal relationship is a knowledge matrix constructed based on domain knowledge, only a small amount of domain knowledge, such as qualitatively clarifying whether there is a causal influence between variables and the attributes of input and output variables, is required. Compared to physical information neural network methods that rely on partial differential equations, this invention can directly handle complex causal relationships such as variable interactions, equipment coupling, and control loops commonly found in process industries. This method does not require complete mechanistic equations; only a small amount of available qualitative causal knowledge is needed to guide modeling, making it more practically feasible and scalable.

[0022] 3. In this invention, by constructing a knowledge matrix of qualitative constraints based on domain knowledge, the four types of boundaries of causal relationships between variables are clarified, avoiding unfounded false associations, providing clear guidance for subsequent causal discovery, reducing the model search space, and improving the efficiency and rationality of causal modeling.

[0023] 4. In this invention, a local spatiotemporal graph convolutional neural network that introduces causal relationships is constructed based on the second causal relationship. The second causal relationship is a causal relationship matrix, which is composed of a Granger causal relationship matrix, a knowledge matrix, and an identity matrix. This allows the spatiotemporal graph convolutional neural network guided by causal knowledge to combine domain knowledge with Granger causal relationships, guide the construction of the adjacency matrix, and effectively avoid misjudgments caused by relying solely on correlation analysis.

[0024] 5. In this invention, multiple different temporal convolutional networks are used to process the time-series data of each variable, resulting in time-series embeddings. Attention mechanisms and regression prediction are used to capture the causal relationships of variables in the time dimension. Time-series dependencies are established through gated recurrent units, linking the hidden state of the current time step with the hidden state of the previous time step through update and reset gates to characterize dynamic lag relationships. Furthermore, by fusing the causal influence of the time dimension in spatiotemporal graph convolution using a local spatiotemporal adjacency matrix, a causal delay detection mechanism is introduced into the spatiotemporal graph convolution framework. This enables the method to identify dynamic lag relationships between variables, thereby enhancing the modeling capability of temporal features. This improvement allows the model to not only capture spatial topological dependencies but also effectively characterize causal influences across time, further improving prediction performance.

[0025] 6. The loss function in this invention includes both a prediction error term and an adjacency matrix entropy function term. While minimizing the prediction bias, it guides the local spatiotemporal adjacency matrix to maintain reasonable sparsity and causal consistency, avoids model overfitting, and improves the model's generalization ability and reliability under different industrial conditions. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the steps in the method for predicting key quality variables in the process industry based on causal spatiotemporal graph convolution in this invention. Figure 2 This is a schematic diagram of the method's execution architecture process; Figure 3 This is a flow chart of the sulfur recovery process for sulfur-containing materials in the embodiments; Figure 4 This is a schematic diagram comparing the predicted output of the comparison model with the actual value in the embodiment. Figure 5a This is a diagram showing the real-time prediction results of the CNN model applied in the embodiment; Figure 5b The image shows the real-time prediction results of the LSTM model applied in this embodiment. Figure 5c The image shows the real-time prediction results of the STA-LSTM model applied in this embodiment. Figure 5d This is a graph showing the real-time prediction results of the GMCE model applied in the embodiment. Figure 5e This is a graph showing the real-time prediction results of the STGCN model applied in the embodiment. Figure 5f The image shows the real-time prediction results of the STCG-GAT model used in this embodiment. Figure 6 This is a schematic diagram of the spatiotemporal causal matrix in the embodiment. Detailed Implementation

[0027] 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, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0028] Example 1 In this embodiment, a method for predicting key quality variables in the process industry based on causal spatiotemporal graph convolution is adopted. The method steps are as follows: Figure 1 As shown, it specifically includes: S1. Obtain historical data of the target process industrial production process and divide the historical data into training set and test set; S2. Construct the first causal relationship between process variables in the target industrial production process; S3. Based on causal temporal convolution and attention mechanism, construct causal relationship discovery model, use the first causal relationship to guide the causal discovery model, and obtain the second causal relationship between process variables; S4. Construct a spatiotemporal graph convolutional model. Based on the second causal relationship between process variables, train the spatiotemporal graph convolutional model using the training set and test set to obtain a prediction model for key quality variables of the target process industry. S5. Input the real-time data of the target process industry's production process into the prediction model, and output the prediction results of the key quality variables of the target process industry.

[0029] The first causal relationship in S2 is specifically a knowledge matrix constructed based on domain knowledge; domain knowledge includes four categories: causal influence between variables, no causal influence between variables, input variables are not affected by other variables, and output variables do not affect other variables.

[0030] The specific process of S3 includes: The time series data of each variable is processed by multiple different temporal convolutional networks to obtain the time series embedding of each variable; Time-series embeddings are used to generate attention logs and context embeddings; The attention logarithm is converted into an attention score using the SoftMax function; The aggregation of contextual embeddings is calculated based on the attention score; Based on contextual embedding aggregation, the causal relationship model performs regression prediction on time series embeddings, generates prediction results, calculates the prediction error through a loss function, and then updates the causal relationship model. Extract the model parameters of the updated causal relationship model to obtain the second causal relationship.

[0031] The spatiotemporal graph convolutional model in S4 is specifically built upon temporal convolutional neural networks, graph convolutional neural networks, and gated recurrent units.

[0032] The specific process of constructing a spatiotemporal graph convolutional model in S4 includes: S41. Preprocess the training and test data using the time window method to obtain the preprocessed dataset; S42. Using a temporal convolutional neural network based on the preprocessed dataset, extract the temporal features of the input variables and establish time series dependencies through a gated recurrent unit. S43. Based on the second causal relationship, considering the local time relationship between process variables, a local spatiotemporal adjacency matrix is ​​introduced. S44, in conjunction with the local spatiotemporal adjacency matrix Hidden state Transform into input hidden state This leads to a local spatiotemporal graph convolutional neural network that incorporates causal relationships. The number of variables; T is the number of time steps; S45, Based on Local Spatiotemporal Adjacency Matrix A causal spatiotemporal graph convolutional model is constructed; feature fusion and prediction output are achieved by the causal spatiotemporal graph convolutional model through a fully connected layer.

[0033] In this embodiment, the specific operational architecture of the method is as follows: Figure 2 As shown, the specific implementation process includes: 1) Obtain historical data of the target process industry's production process and divide it into training and testing sets; 2) Construct preliminary causal relationships between process variables using domain knowledge; 3) Based on causal temporal convolution and attention mechanisms, a causal relationship discovery model is constructed, and preliminary causal relationships are used to guide the causal discovery model to obtain the causal relationships between process variables; 4) Based on temporal convolutional neural networks, graph convolutional neural networks, and gated recurrent units, a spatiotemporal graph convolutional model is constructed. The model is trained on the training set and validated on the test set to obtain a prediction model for key quality variables of the target process industry. 5) Obtain actual real-time data to input into the prediction model and obtain the prediction results of key quality variables of the target process industry.

[0034] In this embodiment, the preliminary causal relationship is the first causal relationship, and the causal relationship between process variables is the second causal relationship.

[0035] In 1), the sulfur recovery unit operates (e.g.) Figure 3 The historical data of the process (shown) is 10068×6 in size after removing some invalid physical quantities. Each data point contains 6 physical quantities, including MEA gas flow rate and SWS gas flow rate. 50% of the historical data is used for training, and the remaining 50% is used for real-time testing.

[0036] Figure 3 A flowchart of a sulfur recovery process for sulfur-containing materials is provided. The core of this process is the conversion of sulfur-containing raw materials into sulfur and a byproduct (Maxisulf). Detailed explanations of the materials, equipment, and process flow are as follows: I. Meaning of Materials MEA: Ethanolamine, is a commonly used absorbent for sulfur-containing materials in desulfurization processes; ATM: Sulfur-containing feed gas, which is the sulfur-containing feed gas in the process; SWS: Sulfur washing solution, used as an auxiliary treatment for sulfur-containing materials; Sulfur: sulfur, a core product of the process; Maxisulf: A sulfur-containing product (or sulfur-containing byproduct) that is the final output of the process.

[0037] II. Equipment Definition F101: Mixing / Reaction Vessel, responsible for the initial mixing and reaction of MEA, ATM, and SWS feeds; R101 / R102: Reactors used to promote the reaction of sulfur-containing materials and enhance the efficiency of sulfur generation. The materials will circulate between the reactor and the heat exchanger. E101 / E102 / E103: Heat exchangers, which regulate the temperature of materials through heat exchange, and are also sulfur precipitation units; D104: Separator, used to separate the final material to obtain the byproduct Maxisulf.

[0038] III. Process Flow The feed (MEA+ATM+SWS) enters F101 to complete the initial mixing and reaction; The material enters E101 from F101, while the material in R101 is recycled to E101, where sulfur is precipitated. The material in E101 flows into E102, and the material in R102 is recycled to E102, where sulfur is released again. The material from E102 enters E103, where sulfur is precipitated and then flows into D104, where it is finally separated to obtain the byproduct Maxisulf.

[0039] 2) In this step, preliminary causal relationships between process variables are constructed using domain knowledge. The specific implementation steps are as follows: 201) Based on the characteristics of the process industry, domain knowledge is divided into four categories: the first category is where there is a causal relationship between variables; the second category is where there is no causal relationship between variables; the third category is where input variables are not affected by other variables; and the fourth category is where output variables do not affect other variables. 202) A knowledge matrix can be defined based on the classification. : in, Represents the number of variables. Representative variable Unaffected Influence, and Edges are not allowed between them; Representative variable by Influence, and An edge needs to be established between them; in all In the case of, if ,represent It is an input variable and is not affected by other variables; in all In the case of, if ,represent It is an output variable and does not affect other variables; if and If there is no prior knowledge between them, then .

[0040] 203) will This serves as a preliminary causal relationship between process variables constructed through domain knowledge.

[0041] In step 3), a causal relationship discovery model is constructed based on causal temporal convolution and attention mechanisms. Preliminary causal relationships are used to guide the causal discovery model to obtain the causal relationships between process variables. The specific implementation steps are as follows: 301) Use Each time series data variable is processed by a different Temporal Convolutional Network (TCN) to obtain the embedding of each time series. 302) Use the obtained time series embeddings to generate attention logs and context embeddings; 303) Use the SoftMax function to log the attention. Converted into attention scores; 304) Calculate the aggregation of contextual embeddings based on attention scores; 305) Context-based aggregation ,right Perform regression prediction and calculate the loss function; 306) The final causal relationship matrix is ​​obtained after training. : in, Represents the Granger causality matrix, Represents knowledge matrix, Represents the identity matrix.

[0042] Furthermore, 302) specifically refers to: attention logarithm and context embedding for: Among them, context embedding attention logarithm ; Furthermore, the attention score is: Among them, attention score This represents the weights of the input variables used for prediction; Furthermore, aggregation of context embeddings for: in, Allows for cross-variable mixing of features; 4) Based on temporal convolutional neural networks, graph convolutional neural networks, and gated recurrent units, a spatiotemporal graph convolutional model is constructed. The model is trained on a training set and validated on a test set to obtain a prediction model for key quality variables in the target process industry. The specific implementation steps are as follows: 401) Preprocess historical data using the time window method; 402) Temporal features of input variables are extracted using a Temporal Convolutional Neural Network (TCN), and time series dependencies are established using a Gated Recurrent Unit (GRU), as shown below: in, It is the input at the current time step t after preprocessing. , , , , and These are the parameters to be learned. , and This is the corresponding bias to be learned. This indicates the hidden state of the previous time step. This represents the hidden state at time t. It represents the Hadamardi (or Hadama) stack; 403) Considering the local time relationships between process variables, a local spatiotemporal adjacency matrix is ​​introduced. : in, This represents a local temporal causal relationship between variables during training. It is defined as a trainable matrix; 404) In conjunction with the local spatiotemporal adjacency matrix Hidden state Transform into ; 405) Based on local spatiotemporal adjacency matrix Construct a causal spatiotemporal graph convolution model: in, for The degree matrix, These are the parameters to be learned. For activation functions; 406) Feature fusion and prediction output are achieved through fully connected layers. in, and The parameters to be learned and Bias to be learned; 407) Choose the root mean square error and entropy function as the loss function: in, This refers to the actual value. This refers to the predicted value. For hyperparameters, This represents the entropy function.

[0043] In step 5), real-time data is input into the prediction model to obtain the predicted sulfur dioxide concentration.

[0044] like Figure 4 The image shows the sulfur dioxide concentration prediction results of the causal spatiotemporal graph convolution model in this scheme. The blue line represents the predicted value, and the red line represents the actual value. The root mean square error (RMSE) between the predicted and actual values ​​is 0.0197. =0.8162.

[0045] Figure 5 shows a comparison between the predicted and actual values ​​of this other model. The blue line represents the predicted value, and the red line represents the actual value. Figure 5a The CNN (Convolutional Neural Network) model predicts values ​​that are close to the true values ​​in general, but there are deviations when there are local fluctuations, especially at the peaks where the fit is insufficient. Figure 5b The LSTM (Long Short-Term Memory) model, compared to CNN, models time dependencies better and the prediction curve is closer to the true value, but there is still a certain lag in areas with drastic fluctuations. Figure 5c By incorporating a spatiotemporal attention mechanism into the STA-LSTM model (Spatial-Temporal Attention Long Short-Term Memory network), the prediction results are further improved, and it is able to better capture the dynamic changes in SO2 concentration. Figure 5d The GMCE model (Graph-based Multi-scale Context Embedding Model) closely approximates the true values ​​and captures the relationships between variables, but errors still exist at some extreme points. Figure 5e The STGCN model (Spatial-Temporal Graph Convolutional Network) provides smoother predictions compared to the previous methods, and can better fit the real SO2 concentration, especially in terms of overall trend and fluctuation amplitude. Figure 5f The STCG-GAT model (Spatial-Temporal Causal Graph-Graph Attention Network) produces prediction curves that closely match the true values, capturing long-term trends and effectively tracking peaks and abrupt changes. Compared to CNNs and LSTMs, this approach significantly reduces lag and offset issues. Compared to STALSTM, GMCE, and STGCN, it better tracks abrupt changes at peaks. Compared to STCG-GAT, the predicted values ​​do not exhibit excessive oscillations at peaks, demonstrating better generalization performance.

[0046] Table 1 presents a quantitative description of the results comparing this scheme with other models, from RMSE and R... 2 From this perspective, the prediction performance of different models was compared. The results show that traditional deep learning-based global modeling methods (such as CNN and LSTM) still have large errors in predicting SO2 concentration, indicating that relying solely on single temporal or spatial features is insufficient to obtain ideal results. By introducing STALSTM and GMCE, the effectiveness of spatiotemporal attention mechanisms and variable co-embedding can be seen. Compared with simple time series modeling methods, the prediction accuracy is significantly improved. Further comparison of STGCN and STCG-GAT verifies the advantages of graph structure modeling and graph attention mechanisms, which continuously improve prediction performance. GC-STGCN (Graph Causal-Spatial Temporal Graph Convolutional Network), which introduces causal constraints into the spatiotemporal graph convolutional network, performs best in all metrics. Compared with STCG-GAT, it not only significantly improves prediction accuracy but also shows significant improvements in model interpretability and robustness.

[0047] like Figure 6 The diagram shows the local spatiotemporal adjacency matrix. Darker colors in the diagram represent larger values. This can be interpreted as the secondary airflow being controlled by the MEA airflow to ensure the correct stoichiometry. This can be explained by adding MEA overflow gas to maintain a constant input flow to the secondary combustion chamber if the SWS airflow is too low. Therefore, through comprehensive comparison, the effectiveness of the proposed quality prediction model has been verified.

[0048] Table 1. Quantitative description of the comparison results between this scheme and other models. In summary, this solution integrates causal knowledge with data-driven methods to construct a spatiotemporal graph convolutional modeling framework for process industries, even in the absence of a complete mechanistic model. Through knowledge matrix constraints and attention mechanisms, it ensures that the model output remains consistent with the mechanistic logic of the industrial process. Furthermore, the causal graph and attention matrix provide a visual explanation of the prediction results, enhancing the model's interpretability and engineering acceptability; thus improving the overall accuracy, robustness, and interpretability of the predictions.

[0049] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A process industry key quality variable prediction method based on causal spatio-temporal graph convolution, characterized in that, The method steps comprise: S1, obtaining historical data of a target process industrial production process, and dividing the historical data into a training set and a test set; S2, constructing a first causal relationship between process variables in the target process industrial production process; S3, constructing a causal relationship discovery model based on causal time convolution and attention mechanism, guiding the causal discovery model with the first causal relationship to obtain a second causal relationship between the process variables; S4, constructing a spatio-temporal graph convolution model, training the spatio-temporal graph convolution model based on the second causal relationship between the process variables using the training set and the test set to obtain a key quality variable prediction model of the target process industry; S5, inputting real-time data of the target process industrial production process into the prediction model to output a prediction result of the key quality variable of the target process industry.

2. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 1, characterized in that, The first causal relationship in S2 is a knowledge matrix constructed based on domain knowledge; the domain knowledge includes four categories: causal influence between variables, no causal influence between variables, input variables not affected by other variables, and output variables not affecting other variables; The specific formula of the knowledge matrix is: where, is the knowledge matrix; is the number of variables; represents a variable is not affected by , and , the edge between them should be forbidden; represents a variable is affected by , and , the edge between them should be established; in all cases, if , then the variable is an input variable and is not affected by other variables; in all cases, if , then the variable is an output variable and does not affect other variables; If and no prior knowledge between .

3. The causal spatio-temporal graph convolution based process industry key quality variable prediction method according to claim 1, characterized in that, The specific process of S3 comprises: using multiple different time convolution networks to process the time series data of each variable to obtain time series embedding of each variable; using the time series embedding to generate attention logarithm and context embedding; using a SoftMax function to convert the attention logarithm into an attention score; calculating the aggregation of the context embedding according to the attention score; based on the aggregation of the context embedding, the causal relationship model performs regression prediction on the time series embedding to generate a prediction result, and then calculates the prediction error through a loss function, and further updates the causal relationship model; extracting the model parameters of the updated causal relationship model to obtain the second causal relationship.

4. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 3, characterized in that, The second causal relationship is a causal relationship matrix composed of a Granger causal relationship matrix, a knowledge matrix and a unit matrix, and its specific formula is: wherein is the Granger causality matrix; is the knowledge matrix, i.e. the first causality; is the identity matrix.

5. The causal spatio-temporal graph convolution based process industry key quality variable prediction method according to claim 1, characterized in that, The spatio-temporal graph convolution model in S4 is constructed based on a time convolution neural network, a graph convolution neural network and a gated recurrent unit.

6. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 5, characterized in that, The specific process of constructing the spatio-temporal graph convolution model in S4 comprises: S41, preprocessing the training set and the test set data through a time window method to obtain a preprocessed data set; S42, extracting the time characteristics of the input variables based on the preprocessed data set through a time convolution neural network, and establishing time series dependence through a gated recurrent unit; S43, based on the second causal relationship, considering the local time relationship between the process variables, introducing a local spatio-temporal adjacency matrix; S44, cooperate with local spatio-temporal adjacency matrix , the hidden state is transformed into the input hidden state , the local spatio-temporal graph convolutional neural network introducing causality is obtained, is the number of variables; T is the number of time steps; S45, Based on Local Spatiotemporal Adjacency Matrix A causal spatiotemporal graph convolutional model is constructed; feature fusion and prediction output are achieved by the causal spatiotemporal graph convolutional model through a fully connected layer.

7. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 6, characterized in that, The specific process of extracting the time characteristics of the input variables and establishing the time series dependence in S42 is as follows: wherein, is the hidden state of the current time step t; is the spatio-temporal input data; is the GRU update gate; is the GRU reset gate; is the GRU candidate hidden state; is the input of the current time step t after pre-processing; , , , , and are parameters to be learned; , and are corresponding biases to be learned; denotes the hidden state of the previous time step; and are activation functions; denotes the Hadamard product.

8. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 7, characterized in that, The specific formula of the local spatio-temporal adjacency matrix in S43 is: wherein is a local spatio-temporal adjacency matrix; denotes a local temporal causal relationship between variables; is a zero matrix; during the training process is defined as a trainable matrix; is a second causal relationship, i.e. a causal relationship matrix.

9. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 8, characterized in that, The specific representation of the local spatio-temporal graph convolution neural network introducing the causal relationship in S44 is: wherein, is a local spatio-temporal graph convolutional neural network for introducing causality; is an input hidden state; is is a degree matrix; is a parameter to be learned.

10. The causal spatio-temporal graph convolution-based process industry key quality variable prediction method according to claim 9, characterized in that, When training the spatio-temporal graph convolution model in S4, a loss function containing a root mean square error term and an entropy function term is used, and its specific formula is: where, is the loss; is the true value; is the predicted value; is the hyperparameter; is the entropy function of the local spatio-temporal adjacency matrix.

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