Multivariate statistical monitoring of two-dimensional dynamic batch processes utilizing non-Gaussian information

Dynamics are inherent characteristics of batch processes, and they may exist not only within a particular batch, but also from batch to batch. To model and monitor such two-dimensional (2D) batch dynamics, two-dimensional dynamic principal component analysis (2D-DPCA) has been developed. However, the original 2D-DPCA calculates the monitoring control limits based on the multivariate Gaussian distribution assumption which may be invalid because of the existence of 2D dynamics. Moreover, the multiphase features of many batch processes may lead to more significant non-Gaussianity. In this paper, Gaussian mixture model (GMM) is integrated with 2D-DPCA to address the non-Gaussian issue in 2D dynamic batch process monitoring. Joint probability density functions (pdf) are estimated to summarize the information contained in 2D-DPCA subspaces. Consequently, for online monitoring, control limits can be calculated based on the joint pdf. A two-phase fed-batch fermentation process for penicillin production is used to verify the effectiveness of the proposed method.