Uneven batch data alignment with application to the control of batch end-product quality.

Batch processes are commonly characterized by uneven trajectories due to the existence of batch-to-batch variations. The batch end-product quality is usually measured at the end of these uneven trajectories. It is necessary to align the time differences for both the measured trajectories and the batch end-product quality in order to implement statistical process monitoring and control schemes. Apart from synchronizing trajectories with variable lengths using an indicator variable or dynamic time warping, this paper proposes a novel approach to align uneven batch data by identifying short-window PCA&PLS models at first and then applying these identified models to extend shorter trajectories and predict future batch end-product quality. Furthermore, uneven batch data can also be aligned to be a specified batch length using moving window estimation. The proposed approach and its application to the control of batch end-product quality are demonstrated with a simulated example of fed-batch fermentation for penicillin production.