Nonparametric Identification Based on Multi-inherited Gaussian Process Regression for Batch Process

This study presents a multi-inherited Gaussian process regression (GPR)-based nonparametric identification method for batch process. In the GPR framework, the impulse response of each time point consists of two parts: one is the inheritance part for utilizing the model information of previous time points, in which a Gaussian prior is imposed over the unknown inheritance weight, and the other is the residual impulse response, which is interpreted as a zero-mean Gaussian process. Following the empirical Bayes approach, we derive the joint estimation of the inheritance weight and the residual impulse response. The hyperparameters are determined by maximizing the marginal likelihood. As the correlation of process dynamics at adjacent time points is considered by model inheritance, the proposed method can effectively improve the estimation accuracy. Finally, we demonstrate the superiority of the proposed identification method in two case studies.