Optimal experiment design under parametric uncertainty: A comparison of a sensitivities based approach versus a polynomial chaos based stochastic approach

Abstract

In order to estimate parameters accurately in nonlinear dynamic systems, experiments that yield a maximum of information are invaluable. Such experiments can be obtained by exploiting model-based optimal experiment design techniques, which use the current guess for the parameters. This guess can differ from the actual system. Consequently, the experiment can result in a lower information content than expected and constraints are potentially violated. In this paper an efficient approach for stochastic optimal experiment design is exploited based on polynomial chaos expansion. This stochastic approach is compared with a sensitivities based approximate robust approach which aims to exploit (higher order) derivative information. Both approaches aim at a more conservative experiment design with respect to the information content and constraint violation. Based on two simulation case studies, practical guidelines are provided on which approach is best suited for robustness with respect to information content and robustness with respect to state constraints.