Prediction and Uncertainty Propagation for Completion Time of Batch Processes Based on Data-Driven Modeling

Batch processes have been playing a crucial role for the flexibility in producing low-volume and high-value-added products. Due to the fluctuations of raw materials and operation conditions, the batch duration often varies. Prediction of batch completion time is important for the purpose of process scheduling and optimization. Existing studies of this subject have focused on the prediction accuracy, while the importance of the prediction uncertainty has been under-explored. When the key variable defining the completion time changes slowly toward the end of a batch, the prediction uncertainty tends to be large. Under such situations, we argue that the uncertainty should always be considered along with the mean prediction for practical use. To this end, two data-driven prediction methods using probabilistic principal component analysis and bootstrapping case-based reasoning are developed, followed by the uncertainty quantification in the probabilistic framework. Finally, two batch processes are used to demonstrate the importance of prediction uncertainty and the efficiency of the proposed schemes.