Integration of data uncertainty in linear regression and process optimization

Abstract

Data uncertainties provide important information that should be taken into account along with the actual data. In fact, with the development of measurement instrumentation methods and metrology, one is very often able to rigorously specify the uncertainty associated with each measured value. The use of this piece of information, together with raw measurements, should - in principle - lead to more sound ways of performing data analysis, empirical modeling, and subsequent decision making. In this paper, we address the issues of using data uncertainty in the task of model estimation and, when it is already available, we show how the integration of measurement and actuation uncertainty can be achieved in the context of process optimization. Within the scope of the first task (model estimation), we make reference to several methods designed to take into account data uncertainties in linear multivariate regression (multivariate least squares, maximum likelihood principal component regression), and others whose potential to deal with noisy data is well known (partial least squares, principal component regression, and ridge regression), as well as modifications of previous methods that we developed, and compare their performance. MLPCR2 tends to achieve better predictive performance than all the other tested methods. The potential benefits of including measurement and actuation uncertainties in process optimization are also illustrated. © 2005 American Institute of Chemical Engineers AIChE J, 2005