Parameter set selection for estimation of nonlinear dynamic systems

Abstract

Abstract A new approach is introduced for parameter set selection for nonlinear systems that takes nonlinearity of the parameter‐output sensitivity, the effect that uncertainties in the nominal values of the parameters have and the effect that inputs and initial conditions have on parameter selection into account. In a first step, a collection of (sub)optimal parameter sets is determined for the nominal values of the parameters using a genetic algorithm. These parameter sets are then further analyzed for uncertainty in the parameters and changes in the initial conditions and inputs using differential analysis as well as a sampling‐based approach to determine the key factors influencing sensitivity and the likelihood of a parameter set to be the optimal set under these varying conditions. The outcome of this procedure is a collection of parameter sets, which can be used for parameter estimation and additional information about how likely it is that a set is optimal for parameter estimation. Additionally, the size of the region in parameter space in which a certain set of parameters will remain optimal is determined. © 2007 American Institute of Chemical Engineers AIChE J, 2007