Weighted nonlinear dynamic system for deep extraction of nonlinear dynamic latent variables and industrial application

Soft sensor plays an increasingly important role in modern industrial processes for estimating key quality variables which are hard to measure. With the development of deep learning technologies, soft sensors based on the deep learning methods have drawn great attention. Aiming to predict key quality variables, a supervised weighted nonlinear dynamic system (WNDS) model aided by the maximal information coefficient (MIC) is proposed in this article. The variational autoencoder is employed into the system for extracting nonlinear dynamic features. The supervised WNDS model can simultaneously analyze the correlations between variables and the relationships between historical samples and present samples. Furthermore, the proposed method is extended to a semisupervised form, in order to handle the imbalanced numbers between routinely recorded process data and limited labeled quality data. The prediction performance is validated by an industrial case.