Automatic segmentation of dynamic and static models based on high order slow feature analysis and principal component analysis for multiphase batch monitoring

Most batch processing is complicated by having multiple stages and process steps. During each stage, the operating process is deliberately maintained at a fixed operating condition for a while before the new operating condition is changed to make sure that the process is uniformly stirred or the reactions are complete. This implies that there are several different dynamic and static behaviors during the changes in the different conditions in the operating batch process. In the past, slow feature analysis (SFA) has been used to describe the multiphase steady states and process dynamics. This single SFA certainly makes the model biased when SFA is used to fully describe the batch process. And it certainly limits the ability to monitor batch process variables. In this research, a monitoring model called multi-local models with high-order SFAs and principal component analysis models (PCAs) (ML-HOSFA-PCA) is proposed. The HOSFA model describes the dynamic process while the PCA model describes the static process. Based on the collected batch data, ML-HOSFA-PCA can automatically and self-iteratively cut out the dynamic stages and the static stages, and at the same time, the corresponding local dynamic and static models are obtained by solving nonlinear dynamic modeling problems. The numerical case is used to demonstrate the automatic partitioning results of the proposed method. The four phases can be accurately determined, and the fault detection rate is the highest (97.30%). In the industrial PVC synthesis batch process, two phases are partitioned and the fault detection rate can be 100% for the involved faults, showing significant advantages compared with the existing methods.