Phase division and process monitoring for multiphase batch processes with transitions

In this paper, a new repeatability factor is introduced to achieve phase division for multiphase batch processes. Then a two-step feature vector selection based kernel variable correlation analysis (TSFVS-KVCA) method is proposed for batch processes with transitions monitoring. The TSFVS-KVCA method not only considers the within-phase nonlinear variable correlation but also between-phase one by extracting the common bases and the specific bases between two neighboring phases. The TSFVS method first selects feature vectors from each steady phase as within-phase subsets. Then between-phase subsets are selected from the within-phase subsets of two neighboring phases. These selected feature vectors have well capacity of description on original data so that they can substitute for original data in a feature space F. Thus the TSFVS method reduces the computational complexity and the instability of high-dimensional kernel in subsequent KVCA method. Moreover, each within-phase subset can be used as sub-bases in a feature space F, which simplify the objective function of KVCA method. In this way, the common bases can be extracted in an easier way. Based on the common bases, two neighboring steady phases can be separated into the common subspace and the specific subspace, in which nonlinear process monitoring method is carried out. Furthermore, an online monitoring method for transitions is proposed based on a just-in-time model. The model can be described by the common bases of two neighboring phases and specific bases of the dominant phase at current time interval. The dominant phase can be dynamically determined according to the correlation between current transition sample and neighboring phases. The results of simulation demonstrate effectiveness and superiority of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.