Feature Extraction of Constrained Dynamic Latent Variables

Feature extraction has become an essential prerequisite of developing data-based models, control and monitoring tools from massive industrial data. When the temporal correlation is significant, the latent feature is commonly described by a dynamic model, such as the state-space model. Industrial processes are widely subject to certain boundary constraints. However, most of the existing feature extraction methods have not considered the boundary constraints on the latent features. This study develops a learning approach with consideration of boundary constrained latent features. To retain dynamic behavior with a compact probability description, a novel state transition model is developed by using the Beta distribution for the constrained state. To learn the constrained dynamic feature from regularly observed data, a nonlinear observation function is incorporated, and the variational Bayesian inference is adopted for solving the problem. The effectiveness of the proposed method is demonstrated through numerical simulations along with industrial data sets.