Two-directional concurrent strategy of mode identification and sequential phase division for multimode and multiphase batch process monitoring with uneven lengths

In general, batch processes cover two-directional dynamics, in which the batch-wise dynamics are related to different operation modes, while the time-wise variations correspond to different phases within each batch. The problem of unevenness is common as a result of various factors, particularly in multimode batch processes. In order to address these issues, this paper proposes a two-directional concurrent strategy of mode identification and sequential phase division for multimode and multiphase batch process monitoring with the uneven problem. Firstly, pseudo time-slices are constructed in order to describe the process characteristics regarding the sample concerned, which can preserve the local neighborhood information within a constrained searching range and effectively prevent the synchronizing problem caused by uneven lengths. Secondly, mode identification is conducted along the batch direction and the phase affiliation is sequentially determined along time direction by determining the changes in variable correlations. The two-directional steps are implemented alternatively in order to identify the mode and phase information, which can also guarantee the time sequence within each mode. Thirdly, for online monitoring, the mode information and phase affiliation are simultaneously judged in real time for each new sample, from which the fault status is distinguished from the phase shift. The division results can indicate the critical-to-mode phases from which a certain mode begins to be separated into different sub-modes. In order to illustrate the feasibility and effectiveness of the proposed algorithm, it is applied to a multimode and multiphase batch process (namely an injection molding process) with the uneven problem.