Bayesian Just-in-Time Learning and Its Application to Industrial Soft Sensing

Just-in-time learning (JITL), which can deal with both process nonlinearities and time-varying characteristics, has become a widely used tool for industrial soft sensing. High performance of JITL lies in selecting an accurate relevant sample set and developing a good base learner, which, however, still have some issues unresolved. In this article, a Bayesian JITL (BJTIL) is established to improve the performance of a JITL-based soft sensor in terms of relevant sample selection and base learner construction. The BJITL has dual implications. First, a semisupervised relevant sample selection strategy with a mixture of Mahalanobis distances based on the fully Bayesian Dirichlet process mixture model is proposed, such that both labeled and unlabeled samples can be exploited, and complicated non-Gaussian distributions (such as those with multipeaks or severe asymmetry) can be accounted for. Second, a weighted fully Bayesian Gaussian regression model with randomized mean and covariance is proposed as the base learner training algorithm so as to deal with the overfitting and numerical issues. Two real-world industrial processes are employed to evaluate the performance of the BJITL when it is applied to soft sensor development. The results demonstrate that the BJITL can achieve higher predictive accuracy in contrast with some state-of-the-art schemes for relevant sample selection and base learner construction. In addition, it is shown that the BJTIL can provide better predictive uncertainties.