Robust Supervised Probabilistic Factor Analysis and Its Application to Industrial Soft Sensor Modeling

Data-driven soft sensors have recently drawn considerable and increasing research interest in process industries. To achieve good performance, data analytics algorithms usually have to address complex characteristics presented by industrial datasets. Outlying data samples, which result in heavy-tailed distributions, is particularly challenging to deal with, as they can significantly distort the estimation of model parameters. In order to resolve such issue, this paper proposes a robust supervised probabilistic factor analysis model (RSPFA), including the model structure and the expectation-maximization-based training algorithm. Unlike the conventional assumption of Gaussian distributed dataset, the RSPFA exploits the Student's t distribution, and enhances the robustness by the means of the immunity of the Student's t distribution. Besides, to adapt the RSPFA to nonlinear industrial processes, a locally weighted RSPFA (LW-RSPFA) is further developed using the philosophy of `divide and conquer'. The proposed methods are evaluated with three cases including one synthetic case and two real-world industrial cases, through which the effectiveness and applicability of the RSPFA and LW-RSPFA are verified.