Online monitoring of batch processes using multi-phase principal component analysis

Unfold Principal Component Analysis (u-PCA) has been successfully applied in the monitoring of batch processes. The traditional online monitoring strategy is based on the same unfolding procedure used for end-of-batch monitoring. This procedure may distort the interval where the process is out of normal operation, with delays in the detection of a fault or in the return to normal operation of a faulty batch. In this paper, a new strategy for the generation of a model specially suited for on-line monitoring is presented. This method is based on the combination of four ideas: mean trajectory subtraction and auto-scaling as preprocessing, variable-wise unfolding, addition of lagged variables to fit the dynamics and multi-phase modelling with multi-phase PCA. Evolving and local models have been included in the comparative analysis of the different approaches.