Input Variable Relation and Importance Learning for Industrial Process Soft Sensing with Spatial-Temporal Graph Neural Networks

In soft sensor modeling, spatial correlations among variables within industrial processes are often overlooked by conventional data-driven methods, leading to a missed opportunity to enhance model accuracy and interpretability. This paper addresses this gap by proposing a variable structure learning graph convolutional network (VSL-STGCN) model that leverages the spatial correlations of variables for improved forecasting. The model employs an adjacency matrix self-learning approach, which does not rely on prior knowledge and learns the graph structure through end-to-end gradient descent, making it suitable for the complex and dynamic nature of industrial processes. Moreover, through utilizing feature importance analysis method based on Shapley value, researchers can gain insights into the decision-making process, leading to increased trust in the model predictions. The integration of Shapley values into the GNN model provides a robust interpretability framework, allowing for the quantification of each variable contribution to the model output. This enhances the transparency and credibility for soft sensing model, particularly for key indicators in industrial processes, and facilitates targeted monitoring and control in real-world applications.