An iterative within-phase relative analysis algorithm for relative sub-phase modeling and process monitoring

•An iterative within-phase relative analysis algorithm is proposed.•The time-varying process characteristics within each phase are evaluated.•The within-phase similarity and dissimilarity are distinguished for modeling.•Different types of variations are decomposed for online monitoring separately.•It is demonstrated to work well for within-phase analysis and fault detection.

For multiphase batch processes, sub-phase modeling methods assumed that the underlying process characteristics stay similar within the same phase which thus can be represented by one unified phase model. However, despite the similarity, process characteristics may also be different more or less within the same phase, revealing a certain degree of within-phase dissimilarity. How to distinguish within-phase similarity and dissimilarity and separately model them for online monitoring are important questions, which, however, have not be addressed yet. In the present work, an iterative within-phase relative analysis algorithm is proposed to handle this problem. Instead of arbitrary similarity assumption, relative changes of process characteristics along time direction are analyzed for time-slices within the same phase. Thus, two systematic subspaces are separated at each time, revealing within-phase similar characteristics and within-phase dissimilar characteristics respectively. Only the within-phase similar part can be described by a unified phase model. In contrast, the within-phase dissimilar part reflects the time-varying characteristics even in the same phase and thus has to be described by different models. For online monitoring, different types of variations can be supervised respectively so that the changes of process variations can be more specifically tracked, providing reliable fault detection performance as well as enhanced process understanding. It is illustrated with a typical multiphase batch process.