A novel fuzzy phase partition method and a hybrid modeling strategy are proposed for quality prediction and process monitoring in batch processes with multiple operation phases. The fuzzy phase partition method is proposed on the basis of a sequence-constrained fuzzy c-means (SCFCM) clustering algorithm. It divides the batch process into several fuzzy operation phases by performing the SCFCM algorithm on trajectory data of phase-sensitive process variables. This SCFCM-based partition method not only has high computation efficiency and good partition accuracy but also is easy to implement and popularize. In addition, it generates “soft” partition results, where a “transition” phase exists between two adjacent “steady” operation phases. A hybrid modeling strategy is developed to build appropriate models for all operation phases according to their own characteristics. Phase-based multiway PLS models are built for regular steady phases that have longer durations and stable process behaviors. Just-in-time PLS models are built for those phases with shorter durations but time-varying or nonlinear process behaviors, including all transition phases and several irregular steady phases. This hybrid modeling strategy significantly enhances the modeling accuracy, resulting in better quality prediction and process monitoring performance. Advantages of proposed methods are illustrated by case studies in a fed-batch penicillin fermentation process.

Integrated phase partition, online phase identification, and phase-based monitoring methods are proposed for multiphase batch processes with uneven durations. A new phase partition method is developed based on the warped K-means (WKM) clustering algorithm, which divides the entire batch into several operation phases by clustering the trajectory data of phase-sensitive process variables. This WKM-based phase partition method can efficiently cope with the sequentiality of batch data and, thus, ensures a reasonable phase partition result. Besides, because only phase-sensitive variables are used for phase partition, the phase partition accuracy is improved. An online phase identification method is proposed to identify the corresponding operation phase of a new sample according to a phase identification combination index (PICI). PICI quantifies the correlation of a new sample with each operation phase by calculating distance and time difference between the sample and the phase center. The PARAFAC2 and unfolded principal component analysis (uPCA) methods are applied to build monitoring models from the uneven-length batch data in each phase. T 2 and SPE statistics are constructed for fault detection. The contribution plot of T 2 statistic is used for fault diagnosis. The effectiveness and advantages of proposed methods are illustrated by the case study in a fed-batch penicillin fermentation process.

A novel process monitoring method is proposed based on sparse principal component analysis (SpPCA). To reveal meaningful variable correlations from process data, the SpPCA is developed to sequentially extract a set of sparse loading vectors from process data. To build a high-performance monitoring model, a fault detectability matrix is applied to select the sparse loading vectors used for process modeling from all sparse loading vectors obtained by SpPCA. The fault detectability matrix ensures that the faults related to any monitored process variable are detectable in the principal component subspace and no overlapped (or redundant) loading vectors are involved in the monitoring model. Moreover, the selected sparse loading vectors classify all process variables into nonoverlapping groups according to variable correlations. Two-level contribution plots, which consist of group-wise and group-variable-wise contribution plots, are used for fault diagnosis. The first-level group-wise contribution plot describes the individual contribution of each variable group to the fault. The second-level group-variable-wise contribution plot reflects the individual contribution of each process variable to the fault. The two-level contribution plots not only utilize meaningful correlations between process variables in the same group, but also effectively remove the interference from process variables in other groups. Therefore, the fault diagnosis reliability and accuracy are significantly improved. The implementation, performance, and advantages of the proposed methods are illustrated with an industrial case study.

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