Parameter Set Selection for Estimation for Nonlinear Dynamic Systems

This paper introduces a new approach 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.