Fault diagnosis based on concurrent phase partition and analysis of relative changes with limited fault batches

For batch processes, if sufficient fault batches are available, fault characteristics can be analyzed in deep. However, it is in general difficult and may be impractical to get sufficient batches for every fault case. Thus, how to derive reliable fault information based on limited batches has been an important question for fault diagnosis, which, however, has not been addressed yet. Starting from limited fault batches, this article proposes a fault diagnosis strategy for multiphase batch processes. Two important modeling procedures, concurrent phase partition and analysis of relative changes, are developed to make full use of limited fault batches. First, for each fault case, a generalized time-slice is constructed by combining several consecutive time-slices. The time-varying characteristics of normal and fault statuses are then jointly analyzed. Then, in each phase, the reference monitoring models are developed from normal case with sufficient batches and each fault case is related with normal case to explore the relative changes (i.e., the fault effects). Comprehensive subspace decomposition is implemented and used to develop fault reconstruction models. Starting from limited batches, the proposed algorithm can offer reliable fault diagnosis performance. It is illustrated with a typical multiphase batch process, including one normal case and three fault cases with limited batches.