Integrating adaptive moving window and just-in-time learning paradigms for soft-sensor design

Most applications of soft sensors in process industries require learning from a stream of data, which may exhibit nonstationary dynamics, or concept drift. In this study, we develop a relevance vector machine (RVM) based novel adaptive learning algorithm called MW_Adp-JITL, to meet the demands of continuous processes. The resulting algorithm combines active and passive learning: A moving window (MW) algorithm, which adapts the window size against virtual/real concept drifts, is coupled with a just-in-time learning (JITL) model, constructed using an appropriate region of historical data, and the ensemble weights of the MW and JITL models are adjusted for each query point. Tests on four real industrial datasets and a synthetic data, comprising various concept drift scenarios, show that MW_Adp-JITL yields superior prediction accuracy and is generally more robust to changes in algorithm parameters compared to conventional adaptive learning methods and state-of-the-art algorithms from the literature. MW_Adp-JITL complies with time limits of online prediction, and is applicable for high dimensional processes under various types of concept drifts. It is seen that MW_Adp-JITL can successfully achieve a good balance in bias-variance tradeoff, justifying the use of only two exquisitely selected learners in ensemble learning.