Multiphase two-dimensional time-slice dynamic system for batch process monitoring

In this work, a multiphase 2D time-slice dynamic system approach has been proposed to characterize the batch-wise and variable-wise dynamics of batch processes simultaneously. First, in each phase, the 2D latent representation has been developed for time slice matrices so as to extract informative features from both batch-wise and variable-wise variations. Afterward, the first-order Markov chains are introduced for capturing the underlying 2D latent dynamics across time-slice evolutions. In this way, batch process dynamic behaviors in each working phase can be captured from both single batch run and batch-to-batch evolutions, while process noise can also be explained in the probabilistic modeling framework. Last, in order to carry out online monitoring with the proposed 2D dynamic system, an effective 2D online-monitoring mechanism is established. The feasibility of the dynamic batch process monitoring method is validated on the fed-batch penicillin fermentation benchmark. (C) 2019 Elsevier Ltd. All rights reserved.