A Self-Interpretable Deep Learning Soft Sensor Based on Spatio-Temporal Causal Discovery Graph

As the complexity of industrial system and process data increases, deep learning has demonstrated performance beyond traditional methods in the soft sensor domain. However, deep learning's black-box design restricts the models' interpretability, which could produce inaccurate prediction outcomes. Using a temporal attention mechanism and a gated recurrent unit, this study presents a novel spatio-temporal self-interpretative causal discovery (STCD) model that resolves this problem by generating a self-interpretative soft sensor that can identify spatio-temporal causality in time-series data. By minimizing the maximum mean difference loss function, the model can simulate the distribution of real data and improve the prediction accuracy. Using real industrial data, spatio-temporal causality maps were constructed and the model learning results were analyzed to determine the spatio-temporal causality between variables. The direction of spatio-temporal causality was determined by comparing the effective model complexity, and a spatio-temporal causal directed graph was plotted while generating soft sensors to visualize the relationship between variables. The application to a rotating air pre-heater thermal deformation dataset verifies the validity of the self-interpretation capability of the STCD method, which offers advantages in terms of performance and causal resolution capability over existing soft sensor and causal discovery methods. This work not only provides a new soft sensor approach for understanding and predicting time series data, but also provides new insights for exploring causal mechanisms between variables in industrial processes.