Transfer Learning for Dynamic Feature Extraction Using Variational Bayesian Inference

Data-driven methods have been extensively utilized in establishing predictive models from historical data for process monitoring and prediction of quality variables. However, most data-driven approaches assume that training data and testing data come from steady-state operating regions and follow the same distribution, which may not be the case when it comes to complex industrial processes. To avoid these restrictive assumptions and account for practical implementation, a novel online transfer learning technique is proposed to dynamically learn cross-domain features based on the variational Bayesian inference in this work. Stemming from the probabilistic slow feature analysis, a transfer slow feature analysis (TSFA) technique is presented to transfer dynamic models learned from different source processes to enhance prediction performance in the target process. In particular, two weighting functions associated with transition and emission equations are introduced and updated dynamically to quantify the transferability from source domains to the target domain at each time instant. Instead of point estimation, a variational Bayesian inference scheme is designed to learn the parameters under probability distributions accounting for corresponding uncertainties. The effectiveness of the proposed technique with applications to soft sensor modelling is demonstrated by a simulation example, a public dataset and an industrial case study.