A Bayesian Robust Observation Design Approach for Systems with (Large) Parametric Uncertainties

Abstract

Classical optimal experimental design (OED) methods have not been fully exploited in modeling of complex systems, due to the brittle design results generated based on prior models and computational burden in the optimization scheme. In this work, a novel method for robust experimental design (RED) of combined measurement set selection and sampling time scheduling has been proposed for systems with large parameter uncertainties. A Bayesian design framework is employed, involving Gaussian quadrature formula (GQF) approximation of the expected performance of the posterior distribution over uncertain parameter domain. The robust Bayesian experimental design (BED) has been relaxed to a semi-definite programming (SDP) problem which can be solved as a convex optimization problem. The proposed method has been examined by simulation studies on a lab-scale enzymatic biodiesel production system, with results compared to OED and uniform sampling under two design scenarios.