Deep Bayesian Slow Feature Extraction with Application to Industrial Inferential Modeling

Inferential modeling has been of significance for modern manufacturing in estimating the quality-related process variables. As an effective inferential model, probabilistic slow feature analysis (PSFA) has gained attention in regression tasks to interpret dynamic properties with a slowness preference. However, PSFA is often challenged by the nonlinear sequential data due to its linear state-space structure. In this article, a new nonlinear extension of PSFA is proposed under the deep learning framework to enhance the dynamic feature extraction with limited labels, incorporating variational inference and Monte Carlo inference to derive the objective function. The proposed model considers the relevance of inputs with outputs as the input weights to upgrade prediction performance. The proposed model is verified through an industrial hydrocracking process to predict diesel yield with missing labels ranged from 0% to 50%, and the root mean squared error is reduced by at least 8.78% compared to PSFA.