Multilevel component analysis and multilevel PLS of chemical process data

Principal component analysis (PCA) and partial least squares (PLS) are well-established techniques for analyzing multivariate process data. However, chemical processes often vary at different levels, due to, for instance, catalyst deactivation or fouling. In such cases, data from a time period that comprises multiple catalyst or fouling runs contain both variation within runs at the lower level and variation between runs at the higher level. In ordinary PCA and PLS models, these sources of variation are confounded. Multiway PCA and PLS are usually not appropriate either, because the runs in the data set can be very different, which means that the overall data set does not have a proper multiway structure. Multilevel component analysis (MLCA) and multilevel partial least squares (MLPLS) are proposed as better options for analyzing such process data. The models obtained with these techniques contain submodels for the different levels in the data, and thereby separate the within-run and between-run variation in the process variables W. In addition, MLPLS can use response variables (Y) to guide the projections into meaningful directions, and provide information on the sources of variation in Y and the relationship between X and Y. Extensions to more than two levels are straightforward, and can be used, for instance, for the comparison of runs from different plants. Copyright (C) 2006 John Wiley & Sons, Ltd.