Batch process monitoring based on multiple-phase online sorting principal component analysis

Existing phase-based batch or fed-batch process monitoring strategies generally have two problems: (1) phase number, which is difficult to determine, and (2) uneven length feature of data. In this study, a multiple-phase online sorting principal component analysis modeling strategy (MPOSPCA) is proposed to monitor multiple-phase batch processes online. Based on all batches of off-line normal data, a new multiple-phase partition algorithm is proposed, where k-means and a defined average Euclidean radius are employed to determine the multiple-phase data set and phase number. Principal component analysis is then applied to build the model in each phase, and all the components are retained. In online monitoring, the Euclidean distance is used to select the monitoring model. All the components undergo online sorting through a parameter defined by Bayesian inference (BI). The first several components are retained to calculate the T2 statistics. Finally, the respective probability indices of PT2 is obtained using BI as the moving average strategy. The feasibility and effectiveness of MPOSPCA are demonstrated through a simple numerical example and the fed-batch penicillin fermentation process.