Application of partial least square regression in uncertainty study area

The aim of this work is to show how partial least squares (PLS) regression when combined with two other techniques Karhunen-Loeve (KL) expansion and Markov chain Monte Carlo (MCMC) can be efficient and effective at addressing parameter uncertainties that affect the predictive ability of a model for critical applications such as monitoring and control. We introduce a combination of PLS regression and KL to develop a reduced-order model (ROM) that captures the uncertain parameters effect on the model outputs, and the combination of PLS regression and MCMC for efficient updates of the uncertain parameter distributions. Two examples, a tubular reactor and an oil producing reservoir are presented to demonstrate these concepts.