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.

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Data driven soft sensor design has recently gained immense popularity, due to advances in sensory devices, and a growing interest in data mining. While partial least squares (PLS) is traditionally used in the process literature for designing soft sensors, the statistical literature has focused on sparse learners, such as Lasso and relevance vector machine (RVM), to solve the high dimensional data problem. In the current study, predictive performances of three regression techniques, PLS, Lasso and RVM were assessed and compared under various offline and online soft sensing scenarios applied on datasets from five real industrial plants, and a simulated process. In offline learning, predictions of RVM and Lasso were found to be superior to those of PLS when a large number of time-lagged predictors were used. Online prediction results gave a slightly more complicated picture. It was found that the minimum prediction error achieved by PLS under moving window (MW), or just-in-time learning scheme was decreased up to ~5-10% using Lasso, or RVM. However, when a small MW si ze was used, or the optimum number of PLS components was as low as ~1, prediction performance of PLS surpassed RVM, which was found to yield occasional unstable predictions. PLS and Lasso models constructed via online parameter tuning generally did not yield better predictions compared to those constructed via offline tuning. We present evidence to suggest that retaining a large portion of the available process measurement data in the predictor matrix, instead of preselecting variables, would be more advantageous for sparse learners in increasing prediction accuracy. As a result, Lasso is recommended as a better substitute for PLS in soft sensors; while performance of RVM should be validated before online application.@en