Title: Selection of optimal parameter set using estimability analysis and MSE-based model-selection criterion

Authors: Shaohua Wu; Kevin A.P. McLean; Thomas J. Harris; Kimberley B. McAuley

Addresses: Honeywell Aerospace Canada, Mississauga, ON, L5L 3S6, Canada. ' Department of Chemical Engineering, Queen's University, Kingston, Ontario, K7L 3N6, Canada. ' Department of Chemical Engineering, Queen's University, Kingston, Ontario, K7L 3N6, Canada. ' Department of Chemical Engineering, Queen's University, Kingston, Ontario, K7L 3N6, Canada

Abstract: Parameter estimation in complex mathematical models is difficult, especially when there are too many unknown parameters to estimate, and the available data for parameter estimation are limited. Estimability analysis ranks parameters from most estimable to least estimable based on the model structure, uncertainties in initial parameter guesses, measurement uncertainties, and experimental settings. Difficulties associated with poor numerical conditioning are avoided by only estimating those parameters that are most estimable. The remaining parameters are left at their initial values or can be removed from the model via simplification. In this paper, a mean squared error (MSE)-based model-selection criterion is used to determine the optimal number of parameters to estimate from the ranked parameter list, so that the most reliable model predictions can be obtained. This methodology is illustrated using a dynamic chemical reactor model.

Keywords: mathematical modelling; parameter estimation; parameter subset selection; optimal parameter sets; mean squared error; MSE; MSE-based criterion; model selection criterion; estimability analysis; model prediction; nonlinear dynamic modelling; parameter ranking; model simplification.

DOI: 10.1504/IJAMECHS.2011.042615

International Journal of Advanced Mechatronic Systems, 2011 Vol.3 No.3, pp.188 - 197

Published online: 19 Sep 2011 *

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