Phase analysis and statistical modeling with limited batches for multimode and multiphase process monitoring

For multimode batch processes, the conventional modeling methods in general require that sufficient batches should be available for every mode, which, however, cannot be guaranteed in practice. It may be impractical to conduct enough trial runs and wait until sufficient batches are available before development of monitoring models for each mode. Starting from limited batches, how to derive reliable process information and develop monitoring models has been an important question for successful online multimode batch process monitoring. To address this problem, this article proposes a phase analysis and statistical modeling strategy with limited batches. One mode which has obtained sufficient batches is chosen as the reference mode while the other modes which can only get limited batches work as alternative modes. Starting from limited batches, the proposed algorithm addresses two issues, concurrent phase partition and analysis of between-mode relative changes. First, for each alternative mode, generalized time-slices are constructed by combining several consecutive time-slices within a short time region to explore local process correlations. The time-varying characteristics are then concurrently analyzed across modes so that multiple sequential phases are identified simultaneously for all modes. Then phase-representative data units are arranged by variable-unfolding the conventional time-slices for the reference mode and the generalized time-slices for each alternative mode respectively. Between-mode statistical analysis is performed within each phase where the relative changes from the reference mode to each alternative mode are analyzed. From the between-mode perspective, different types of relative variations in each alternative mode are separated and modeled for online monitoring. Starting from limited batches, online batch process monitoring can be conducted, providing reliable fault detection performance. The proposed algorithm is illustrated with a typical multiphase batch process with multiple modes. (C) 2014 Elsevier Ltd. All rights reserved.