Modelling and diagnostics of batch processes and analogous kinetic experiments

In chemical kinetics and batch processes K variables are measured on the ba tches at regular time intervals. This gives a J x K matrix for each batch ( J time points times K variables). Consequently, a set of N normal batches g ives a three-way matrix of dimension (N x J x K). The case when batches hav e different length is also discussed. In a typical industrial application o f batch modelling, the purpose is to diagnose an evolving batch as normal o r not, and to obtain indications of variables that together behave abnormal ly in batch process upsets. Other applications giving the same form of data include pharmaco-kinetics, clinical and pharmacological trials where patie nts (or mice) are followed over time, material stability testing and other kinetic investigations. A new approach to the multivariate modelling of thr ee-way kinetic and batch process data is presented. This approach is based on an initial PLS analysis of the ((N x J) x K) unfolded matrix ((batch x t ime) x variables) with 'local time' used as a single y-variable. This is fo llowed by a simple statistical analysis of the resulting scores and results in multivariate control charts suitable for monitoring the kinetics of new experiments or batches. 'Upsets' are effectively diagnosed in these charts , and variables contributing to the upsets are indicated in contribution pl ots. In addition, the degree of 'maturity' of the batch can be as predicted vs. observed local time. The analysis of batch data with respect to variou s questions is discussed with respect to typical objectives, overview and s ummary, classification, and quantitative modelling. This is illustrated by an industrial example of yeast production. (C) 1998 Elsevier Science B.V. A ll rights reserved.