Weighted Linear Dynamic System for Feature Representation and Soft Sensor Application in Nonlinear Dynamic Industrial Processes

TLDR

Industrial process plants use many redundant sensors, yet measured variables are often noisy, and existing probabilistic latent variable models are largely static linear, failing to account for process dynamics and nonlinearities. The study proposes a weighted linear dynamic system to uncover general data trends via latent variable modeling for soft sensor development. WLDS employs two weight types to locally linearize nonlinear state evolution and emission, and estimates parameters through a weighted log‑likelihood and EM algorithm. The method’s feasibility and effectiveness are shown through a numerical example and an industrial process application.

Abstract

Industrial process plants are instrumented with a large number of redundant sensors and the measured variables are often contaminated by random noises. Thus, it is significant to discover the general trends of data by latent variable models in the probabilistic framework before soft sensor modeling. However, traditional probabilistic latent variable models such as probabilistic principal component analysis are mostly static linear approaches. The process dynamics and nonlinearities have not been well considered. In this paper, a novel weighted linear dynamic system (WLDS) is proposed for nonlinear dynamic feature extraction. In WLDS, two kinds of weights are proposed for local linearization of the nonlinear state evolution and state emission relationships. In this way, a weighted log-likelihood function is designed and expectation-maximization algorithm is then used for parameter estimation. The feasibility and effectiveness of the proposed method is demonstrated with a numerical example and an industrial process application.