A Bayesian framework for real‐time identification of locally weighted partial least squares

Abstract

Just‐in‐time (JIT) learning methods are widely used in dealing with nonlinear and multimode behavior of industrial processes. The locally weighted partial least squares (LW‐PLS) method is among the most commonly used JIT methods. The performance of LW‐PLS model depends on parameters of the similarity function as well as the structure and parameters of the local PLS model. However, the regular LW‐PLS algorithm assumes that the parameters of the similarity function and structure of the local PLS model are known and do not fully utilize available knowledge to estimate the model parameters. A Bayesian framework is proposed to provide a systematic way for real‐time parameterization of the similarity function, selection of the local PLS model structure, and estimation of the corresponding model parameters. By applying the Bayes' theorem, the proposed framework incorporates the prior knowledge into the identification process and takes into account the different contribution of measurement noises. Furthermore, Bayesian model structure selection can automatically deal with the model complexity problem to avoid the overfitting issue. The advantages of this new approach are highlighted through two case studies based on the real‐world near infrared data. © 2014 American Institute of Chemical Engineers AIChE J, 61: 518–529, 2015