Tree structure guided graph neural networks for soft sensing and anomaly regulation

Abstract Graph neural networks (GNNs) have emerged as powerful tools for industrial soft sensing, offering the ability to model complex relationships among process variables. However, existing GNN-based soft sensors suffer from two critical limitations: (i) they lack hierarchical modeling capabilities to reflect the multi-level structure of industrial processes, and (ii) their black-box nature hinders interpretability, making it difficult to evaluate the influence of process variables on key performance indicators. These limitations reduce the reliability of GNNs in safety-critical industrial processes. To address these challenges, this paper proposes a tree structure guided GNN framework that integrates a data-driven adjacency matrix with a tree-based process representation derived from prior knowledge, enabling hierarchical feature aggregation and clearer correlation modeling. Based on this, a tree structure guided graph information bottleneck (GIB) method is developed to extract critical subtrees that preserve predictive information while suppressing task-irrelevant redundancies, thereby enhancing interpretability. Furthermore, an intrinsic counterfactual explanation module is introduced to generate actionable anomaly regulation suggestions by identifying minimal and interpretable process adjustments needed to restore key performance indicators to safe operating ranges. Experimental results on simulation and real-world industrial datasets demonstrate that the proposed framework achieves superior predictive accuracy, interpretability, and practical effectiveness in anomaly regulation.