Design for model parameter uncertainty using nonlinear confidence regions

An accurate method presented accounts for uncertain model parameters ill no nlinear process optimization problems. The model representation is consider ed in terms of algebraic equations. Uncertain quantity parameters are often discretized into a number of finite values that are then used in multiperi od optimization problems. These discrete values usually range between some lower and upper bound that call be derived from individual confidence inter vals. Frequently, more than one uncertain parameter is estimated at a time from a single set of experiments. Thus, using simple lower and upper bounds to describe these parameters may not be accurate, since it assumes the par ameters are uncorrelated. In 1999 Rooney, and Biegler showed the importance of including parameter correlation in design problems by, using elliptical joint confidence regions to describe the correlation among the Uncertain m odel parameters. In chemical engineering systems, however; the parameter es timation problem is often highly, nonlinear, and the elliptical confidence regions, derived from these problems may not be accurate enough to capture the actual model parameter uncertainty. In this work, the description of mo del parameter uncertainty is improved by, using confidence regions derived from the likelihood ratio test. It captures the nonlinearities efficiently and accurately, in the parameter estimation problem. Several examples solve d show the importance of accurately capturing the actual model parameter un certainty at the design stage.