Monitoring Uneven Multistage/Multiphase Batch Processes using Trajectory-Based Fuzzy Phase Partition and Hybrid MPCA Models

Batch processes often have the traits of multiple operation stages/phases and uneven batch durations. These two traits bring difficulties to batch process modelling and monitoring. In this paper, a trajectory-based fuzzy phase partition (TBFPP) method and hybrid multiway PCA (MPCA) models are developed for monitoring multistage/multiphase batch processes with uneven durations. The TBFPP method divides each batch into several fuzzy operation phases by clustering trajectory data of phase-sensitive process variables using the sequence-constraint fuzzy c-means (SCFCM) clustering algorithm. This TBFPP method not only solves the uneven duration problem of batches, but also can identify transition regions between neighbouring operation phases. Fuzzy operation phases are further divided into "steady" and "transition" operation phases according to the membership degrees of samples. Hybrid modelling methods, consisting of phase-based (global) modelling and just-in-time (local) modelling, are used to cope with different process characteristics of the "steady" and "transition" operation phases. Offline phase-based MPCA models are built for "steady" operation phases to describe the steady process characteristics. Online just-in-time MPCA models are built for "transition" operation phases to handle the time-varying process characteristics. Based on the hybrid MPCA models, an online process monitoring method is proposed. The efficacy of the proposed methods is demonstrated through a simulation study of a fed-batch fermentation process.