On-line monitoring of batch processes using multiway independent component analysis

Batch processes play an important role in the production of low-volume, high-value products such as polymers, pharmaceuticals, and biochemical products. Multiway principal component analysis (MPCA), a multivariate projection method, has been widely used to monitor batch processes. But in-control data of non-stationary processes in fact contain inherent non-Gaussian distributed data due to ramp changes, step changes, and even weak levels of autocorrelation. Monitoring charts obtained by applying MPCA to such non-Gaussian data may contain nonrandom patterns corresponding to the data characteristics. To obtain better monitoring performance in a batch process with non-Gaussian data, on-line batch monitoring method with multiway independent component analysis (MICA) is developed in this paper. MICA is based on a recently developed feature extraction method, called independent component analysis (ICA), whereas PCA looks for Gaussian components, whereas ICA searches for non-Gaussian components. MICA projects the multivariate data into a low-dimensional space defined by independent components (ICs). When the measured variables have non-Guassian distributions, MICA provides more meaningful statistical analysis and on-line monitoring compared to MPCA because MICA assumes that the latent variables are not Gaussian distributed. The proposed method was applied to the on-line monitoring of a fed-batch penicillin production. The simulation results demonstrate the power and advantages of MICA.