Parallel Interaction Spatiotemporal Constrained Variational Autoencoder for Soft Sensor Modeling

Data-driven soft sensors have been widely used in industrial processes for over two decades. Industrial processes often exhibit nonlinear and time-varying behavior due to complex physical and chemical mechanisms, feedback control, and dynamic noise. Lately, variational autoencoder (VAE) has arisen as one of the most prevalent methods for unsupervised learning of intricate distributions. Despite being successful in deep feature extraction and uncertain data modeling, it still suffers from instability and reconstruction error due to random sampling in the latent subspace representation of original input space. In this article, to deal with those limitations, constrained VAE (CVAE) is proposed by utilizing input sample information. Enthused by parallel interaction mechanism between the ventral and dorsal stream of the human brain in object recognition, parallel interaction spatial-temporal CVAE (PIST-CVAE) is proposed to extract spatial and temporal features from input samples. Lower dimensional nonlinear features extracted from PIST-CVAE are used to build the soft sensor. The effectiveness of CVAE and PIST-CVAE is demonstrated in an industrial case study, a polyester polymerization process. The obtained results demonstrate that CVAE is able to reconstruct inputs with higher accuracy and the proposed PIST-CVAE-based soft sensor yields more accurate estimations for the melt viscosity index of the polymerization process.