Bayesian-Based Causal Structure Inference With a Domain Knowledge Prior for Stable and Interpretable Soft Sensing

Due to the high-stakes nature of industrial processes, there is an immediate and pressing need on soft sensors for stability and interpretability. In this regard, causality-inspired modeling aims to learn causal features corresponding to the direct causes of quality variables, exhibiting great potential in terms of both stability and interpretability. However, most existing causality-inspired methods overlook temporal modeling and domain knowledge integration, which hinders their real-world application in industrial soft sensing. To this end, this article proposes a novel causality-inspired stable long short-term memory (Stable-LSTM), which leverages Bayesian-based causal structure inference and incorporates domain knowledge as a prior to enhance the performance stability and physical interpretability of soft sensors. After extracting temporal features via long short-term memory (LSTM), a Bayesian-based causal structure inference approach is developed by leveraging variational inference to learn the underlying hidden causal structure within the industrial processes. Through a hidden explanation of domain knowledge, a prior distribution is placed on the hidden causal structure, which will greatly enhance the physical interpretability and facilitate the exploration for true causality. Moreover, we also introduce a global sample reweighting strategy to remove spurious correlations and reveal causal effects between time series hidden features and quality variables. Finally, the performance stability and physical interpretability of the proposed Stable-LSTM are verified using a three-phase flow facility and a m-phenylenediamine distillation process. The results show that the Stable-LSTM achieves the highest soft sensing accuracy under distribution shift, and the inferred causal structure exhibits the greatest consistency with the domain knowledge, when compared with the seven existing methods.