Enhancing interpretable soft sensing with embedded hybrid modeling: the GraphTrans approach for industrial processes

High-level optimization and control demand highly accurate process models. However, existing modeling strategies often struggle to achieve a reasonable balance between accuracy and interpretability, thus limiting their industrial applicability. We propose an interpretable embedded hybrid modeling framework to address this challenge and introduce GraphTrans, a novel data-driven model architecture. GraphTrans integrates graph convolutional networks to capture local correlations among process variables, employs graph-masked multi-head attention to model structured global dependencies, and uses a kernel projection module to enhance feature representation under incomplete observations. By embedding GraphTrans into the mechanism model to generate sample-level dynamic mechanism parameters, the proposed framework enables accurate and interpretable soft sensing of key process indicators while maintaining physically constrained mechanism-parameter outputs. Simulation experiments were performed on three reactor datasets from the zinc purification process, a representative industrial scenario, with a total of 3079 samples. Compared with the best condition-based mechanism modeling strategy, GraphTrans-EMM reduced the mean absolute error by 35.90% and improved R² by 31.43% on average across the three datasets. Comparative experiments with representative deep learning baseline models further confirmed the superior predictive accuracy of the proposed framework while preserving a mechanism-based interpretation path. In addition, the identified mechanism parameters remained within physically meaningful ranges and provided interpretable insights into reaction-state variations, including atypical samples. Ablation studies validate the model architecture's rationality, with each module contributing to improved predictive performance. The perception and localization of atypical samples through abnormal parameter deviations further highlight the framework's potential for fault diagnosis and other industrial applications.