Adaptive Soft Sensor Development Based on Online Ensemble Gaussian Process Regression for Nonlinear Time-Varying Batch Processes

Traditional soft sensors may be ill-suited for batch processes because they cannot efficiently handle process nonlinearity and/or time-varying changes as well as provide the prediction uncertainty. Therefore, a novel adaptive soft sensor, referred to as online ensemble Gaussian process regression (OEGPR), is proposed for nonlinear time-varying batch processes. The batch process is first divided into multiple local domains using a just-in-time localization procedure, which is equipped with a probabilistic analysis mechanism to detect and remove the redundant local domains. Then the localized GPR models and probabilistic data descriptors (PDD) are built for all isolated domains. Using Bayesian inference, the posterior probabilities of any test sample with respect to different local domains are estimated and set as the adaptive mixture weights of local predictions. Further, the overall mean and variance of the predictive distribution of the target variable are estimated via the finite mixture mechanism. Additionally, the OEGPR method performs adaptation at two levels to handle time-varying behavior: (i) local GPR and PDD models; and (ii) the mixture weights. The effectiveness of the OEGPR approach is demonstrated through a simulated fed-batch penicillin fermentation process as well as an industrial fed-batch chlortetracycline fermentation process.