An information theoretic framework for optimal experimental design

Abstract

An information theoretic framework for optimal experimental design is presented. The objective function is rooted in information theory, and is the expected Kullback-Leibler divergence between the prior and posterior pdf in a Bayesian framework. In this way we seek designs which will yield data that are most informative for model parameter inference. In general, the objective function has to be estimated by a Monte Carlo sum, which means that its evaluation requires a large number of model runs. Asymptotic approximations are introduced to significantly reduce these runs. The optimization of the objective function is performed using stochastic optimization methods such as CMA-ES to avoid premature convergence to local optimal usually manifested in optimal experimental design problems. The framework is demonstrated using applications from mechanics. Two optimal sensor placement problems are solved: 1) parameter estimation in non-linear model of simply supported beam under uncertain load, 2) modal identification. © 2017 Taylor & Francis Group, London.