A Selective Migration-Based Improved GPR Modeling Method for Batch Process

Model-based control plays an important role in batch process control. With more data collected online, real-time model updates using Gaussian process regression (GPR) are becoming increasingly practical for improving the performance of model-based control strategies. However, in batch processes, process configurations are often adjusted, which can be costly if a new model has to be identified from scratch each time. Although several GPR migration methods exist, they are primarily designed for static models and are not well-suited for dynamic system modeling for control purposes. Therefore, we propose a selective migration-based online GPR identification method that enables the dynamic model for batch process control to learn selectively from the previously identified old process model as needed. In our method, we present selective migration strategies for two types of GPR model parameters: 1) hyperparameters and 2) data points. Additionally, we provide a complete algorithm for online dynamic model identification. Beyond that, for data point parameters selective migration, we propose a fast migration dataset-seeking method for a smaller computational cost and a mixed integer programming migration dataset-seeking method for a smaller prediction loss. Theoretical analysis of the framework reveals the initial improvement and final convergence. Finally, we provide two illustrative numerical examples to show the effectiveness of the proposed methods.