Quality assessment of a variance estimator for Partial Least Squares prediction of batch-end quality

Abstract

This paper studies batch-end quality prediction using Partial Least Squares (PLS). The applicability of the zeroth-order approximation of Faber and Kowalski (1997) for estimation of the PLS prediction variance is critically assessed. The estimator was originally developed for spectroscopy calibration and its derivation involves a local linearization under specific assumptions, followed by a further approximation. Although the assumptions do not hold for batch process monitoring in general, they are not violated for the selected case study. Based on extensive Monte Carlo simulations, the influence of noise variance, number of components and number of training batches on the bias and variability of the variance estimation is investigated. The results indicate that the zeroth-order approximation is too restrictive for batch process data. The development of a variance estimator based on a full local linearization is required to obtain more reliable variance estimations for the development of prediction intervals.