Relative sub-PCA modeling algorithm using iterative within-phase relative analysis for multiphase batch process monitoring

For multiphase batch processes, sub-phase modeling method assumes the underlying process characteristics stay similar within the same phase and represented by one unified phase model. However, the time-varying process variation within each phase has not been addressed. In the present work, relative analysis is iteratively conducted for time-slices within the same phase to capture the relative changes of process variation along time direction. Thus, for each time slice within the same phase, two systematic subspaces are separated, revealing time-independent variation and time-dependent variation respectively. Only the time-independent variation which stays similar with the same phase can be described by a unified phase model. The time-dependent variation reflects time-varying characteristics within each phase which has to be described by different models. For online monitoring, different types of variations can be supervised respectively in which the changes of process variation can be well tracked, providing reliable fault detection performance as well as enhanced process understanding. It is illustrated with a typical multiphase batch process.