Phase and transition based batch process modeling and online monitoring

Multiple phases/stages with transitions from phase to phase are important characteristics of many batch processes. In order to model and monitor batch processes more accurately and efficiently, such process features are needed to be considered carefully. In this work, an index based on the angles between different principal component analysis (PCA) score spaces is developed to quantify the similarities between PCA models. Phase division algorithm is designed based on this new PCA similarity index, following by a statistical transition identification step. The steady phase ranges and transition ranges are then modeled separately. The transition models can be calculated by solving the optimization problems. Application examples show the advantages of the proposed method on both batch process modeling and online monitoring. (C) 2008 Elsevier Ltd. All rights reserved.