Probabilistic stationary subspace regression model for soft sensing of nonstationary industrial processes

Abstract

Benefitting from the development of industrial intelligence, data‐driven soft sensors have been widely applied in industrial processes in recent years. Driven by fluctuations in raw material quality, varying loads, and uncertain disturbances, industrial processes are often characterized by nonstationary properties. However, the nonstationary characteristics of the process are not considered in traditional data‐driven methods, leading to the poor prediction performance of soft sensors. Meanwhile, numerous nonstationary modelling methods have been proposed for process monitoring, with probabilistic stationary subspace analysis (PSSA) showing significant application potential. Unfortunately, PSSA has not yet been used to develop effective soft sensors for nonstationary processes. Therefore, the PSSA model is extended to the regression form (PSSR), and a corresponding soft sensing model is developed in this paper. Unlike previous approaches, the proposed PSSR can offer a suitable description of nonstationary processes and fully capture the mathematical correlation between input and output variables. Finally, the prediction performance of PSSR is verified through case studies on a numerical example and penicillin fermentation process. The experimental results indicate that PSSR can provide a superior solution for soft sensing modelling of nonstationary industrial processes.