Measurement noise influence on statistical properties of batch-end quality predictions1

In this paper, an extensive Monte Carlo simulation is performed to investigate the influence of output measurement noise on Multiway Partial Least Squares (MPLS) batch-end quality predictions. MPLS models are well suited for monitoring (bio)chemical batch processes, but the lack of insight in noise influence leaves companies reluctant to accept the technique. Simplified relations between prediction variance and measurement noise exist for spectroscopy calibration problems, but are based on assumptions that do not necessarily hold for batch process modelling. The non-linear properties of the PLS predictor and the lack of knowledge about its statistical distribution make the derivation of an analytical relation extremely difficult.Based on an extensive case study of a penicillin production process, MPLS predictions of final batch quality are shown to outperform offline quality measurements. Even at very high noise levels, the models capture the important information in the measurements and discard most of the noise. Prediction bias and variance are studied and found to behave inversely with respect to the model order. This inverse behaviour has important consequences for model order selection, which becomes a trade-off between bias and variance. In this light, several crossvalidation-based techniques for selection of the optimal number of principal components are compared. An adjusted Wold's R criterion proves to be slightly favorable to the minimum MSE and general Wold's R criterion.