Bayesian Learning for Dynamic Feature Extraction With Application in Soft Sensing

Data-driven techniques such as principal component analysis (PCA) have been widely used to derive predictive models from historical data and applied for quality prediction in industry. Motivated by reducing data collinearity and extracting informative driving forces behind data, latent variable models are explored to facilitate the prediction by regressing data on a set of extracted features. In this paper, a novel learning strategy is proposed to build dynamic features under a full Bayesian framework, incorporating data information and prior knowledge of process dynamics. Unlike the traditional PCA that extracts features based on variances explained, in this paper, the latent features are extracted with the guidance of preferred velocities of nominal variations. By applying Bayesian learning algorithms, parameters are estimated with probability distributions accounting for corresponding uncertainties, and the number of latent features can be automatically determined by the variational Bayesian inference algorithm. The effectiveness and practicability of this Bayesian dynamic feature regression are demonstrated through simulated examples as well as an industrial case study.