Adaptive batch monitoring using hierarchical PCA

A new approach to monitoring batch processes using the process variable trajectories is presented. It was developed to overcome the need in the approach of Nomikos and MacGregor [P. Nomikos, J.F. MacGregor, Monitoring of batch processes using multi-way principal components analysis, Am. Inst. Chem. Eng. J. 40 (1994) 1361–1375; P. Nomikos, J.F. MacGregor, Multivariate SPC charts for batch processes, Technometrics 37 (1995) 41–59; P. Nomikos, J.F. MacGregor, Multi-way partial least squares in monitoring batch processes, Chemometrics Intell. Lab. Syst. 30 (1995) 97–108] for estimating or filling in the unknown part of the process variable trajectory deviations from the current time until the end of the batch. The approach is based on a recursive multi-block (hierarchical) PCA/PLS method which processes the data in a sequential and adaptive manner. The rate of adaptation is easily controlled with a parameter which controls the weighting of past data in an exponential manner. The algorithm is evaluated on industrial batch polymerization process data and is compared to the multi-way PCA/PLS approaches of Nomikos and MacGregor. The approach may have significant benefits when monitoring multi-stage batch processes where the latent variable structure can change at several points during the batch.