| Global Optimization for Parameter Estimation in Dynamic Systems | ||
| Youdong Lin, Chemical and Biomolecular Engineering, University of Notre Dame, 181 Fitzpatrick Hall, Notre Dame, IN 46556 and Mark A. Stadtherr, University of Notre Dame, Department of Chemical and Biomolecular Engineering, 182 Fitzpatrick Hall, Notre Dame, IN 46556 Parameter estimation is a key step in the development of mathematical models of physical phenomena, and is well studied [1]. In many problems, especially in chemical engineering, the systems are nonlinear in nature and described by ordinary differential equations (ODEs), or by differential-algebraic equations (DAEs). These factors lead to the important issue of multiplicity of local solutions in the parameter estimation [2,3]. In this study, we present a deterministic global optimization approach for parameter estimation in dynamic systems. The approach is based on an interval-Newton approach [4,5]. Validated solution methods [6-8] for ODEs (initial value problems) are used to produce bounds that are guaranteed to contain the true solutions of a dynamic system with uncertainty in parameters, as well as the first- and second-order sensitivities of the states with respect to parameters. Computational details and results will be presented through application to several problems involving reaction kinetics. [1] Bard, Y. Nonlinear Parameter Estimation; Academic Press: New York, 1974. [2] Stewart, W. E.; Caracotsios, M.; Sorensen, J. P. Parameter Estimation from Multiresponse Data. AIChE J. 1992, 38(5), 641. [3] Esposito, W. R.; Floudas, C. A. Global Optimization for the Parameter Estimation of Differential-Algebraic Systems. Ind. Eng. Chem. Res. 2000, 39, 1291. [4] Hanson, E.; Walster, G. W. Global Optimization Using Interval Analysis; Marcel Dekker, New York, NY, 2004. [5] Lin, Y.; Stadtherr, M. A. LP Strategy for Interval-Newton Method in Deterministic Global Optimization. Ind. Eng. Chem. Res. 2004, 43, 3741. [6] Moore, R. E.; Interval Analysis; Prentice-Hall, Englewood Cliffs, NJ, 1966. [7] Berz, M.; Makino, K. Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-order Taylor Models, Reliable Computing 1998, 4, 361. [8] Nedialkov, N. S.; Jackson, K. R. An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary differential Equation. Reliable Computing 1999, 5, 289.
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