On-line monitoring of batch processes using a PARAFAC representation

Abstract

For assured through-batch process performance monitoring, a number of established bilinear and trilinear modelling techniques require data to be available for the entire duration of the batch to realize the on-line application of the nominal model. Various strategies have been proposed for the in-filling of those yet unknown values. A methodology is presented where the unknown observations are calculated as a weighted combination of the scores up to the current time point in the new batch and those previously computed from a reference data set. This approach is investigated for the trilinear technique of parallel factor analysis (PARAFAC). Modified confidence limits are then proposed for the bivariate scores plot for on-line monitoring with a PARAFAC model. The identification of those variables indicative of causing changes in process operation has been accomplished through the application of contribution plots. Based on such plots, a methodology, with associated confidence limits, is proposed for the location of those variables whose behaviour differs from that encapsulated within the reference data set. The approach is demonstrated and compared with existing techniques on a benchmark simulation of a semi-batch emulsion polymerization that has been used in similar studies. Copyright © 2003 John Wiley & Sons, Ltd.