Optimal Experimental Design for Probabilistic Model Discrimination Using Polynomial Chaos

Abstract

Building dynamic models is important in many applications including model-based design, optimization, and control. When multiple hypothesized models have predictions that are consistent with the measurements, experimental design is used to discriminate between the models. This task is particularly challenging for nonlinear systems subject to uncertainties. An optimal experimental design method for model discrimination for polynomial uncertain systems is presented that can be used to discriminate models based on dissimilarity of the probability densities of the model outputs. Generalized polynomial chaos theory in conjunction with Galerkin projection is used to derive an extended set of ordinary differential equations. Simulation of the extended system enables prediction of the propagation of probabilistic uncertainties associated with the model parameters and initial conditions, and to obtain the output probability densities. The simulation of the hypothetical models is embedded in a nonlinear optimization problem to determine an optimal input sequence that maximizes model dissimilarity. The experimental design method is demonstrated using a numerical example.