Stable soft sensor modeling based on causality analysis

Data-driven soft sensors, aiming to estimate and predict hard-to-measure quality variables using easy-to-measure process variables, have now become the key foundation for monitoring the stable and safe operation of industrial processes. However, traditional machine-learning methods usually make an assumption that training data and test data share the same probability distribution or the probability distribution of test data is known, which is impractical in the fact that test data come from multi-unknown operating modes. Based on causality analysis and stable learning, soft sensors for stable prediction, namely stable soft sensors, are proposed in this paper. To address this problem, three stable soft sensor frameworks based on causal variables, unsupervised causal features, and supervised causal features are designed. By introducing causality in soft sensor modeling, the interpretability is enhanced and the prediction results in different operating modes get stable. The effectiveness of the proposed method is shown through case studies in the benchmark Tennessee Eastman process.