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

Abstract

Soft sensor technology is increasingly crucial for quality control in modern industrial processes. However, as industrial systems grow more complex, they begin to exhibit intricate characteristics such as nonstationary, uncertainty, and dynamic. These complexities pose significant challenges to conventional data-driven soft sensor modelling approaches. In response, researchers have explored methods like stationary subspace analysis (SSA), probabilistic stationary subspace analysis (PSSA), and hidden Markov model (HMM) to handle nonstationary, uncertain, and dynamic process data. Nonetheless, each of these methods fails to fully capture these characteristics of complex industrial processes, which in turn limits their predictive performance. To overcome these limitations, this chapter introduces a probabilistic dynamic stationary subspace regression (PDSSR) soft sensor model tailored to nonstationary industrial processes. Specifically, the proposed model first decomposes the latent variables into quality-related and quality-unrelated components according to their relevance to the product quality variables. Next, within a stationary subspace analysis framework, the quality-related information is further partitioned into stationary and nonstationary components, thereby accurately capturing nonstationary characteristics. Moreover, during the online estimation process, a hidden Markov chain inference mechanism is incorporated to enhance the accuracy of parameter estimation by accounting for regime changes over time. Finally, Numerical example and a case study on a debutanizer distillation column demonstrate that the proposed method achieves high predictive accuracy in soft sensing for complex, nonstationary industrial processes.