Bayesian optimal experimental design for parameter estimation and response predictions in complex dynamical systems

Abstract

A Bayesian optimal experimental design (OED) framework is revisited and applied to a number of structural dynamics problems. The objective is to optimize the design of the experiment such that the most informative data are obtained for either for parameter estimation or response predictions. The Bayesian OED is based on maximizing the expected utility function taken as the Kullback-Leibler divergence between the prior and posterior distribution of the model parameters. Asymptotic approximations for the multi-dimensional integrals arising in the formulation of the expected utility function are proposed, valid for large number of data and small prediction errors. The OED based on these approximations are shown to be equivalent to the OED based on the robust information entropy introduced in the past for structural dynamics applications. Analytical expressions are developed to point out the effect of the variances of Bayesian Gaussian priors on the optimal design. The design variables may include the location of sensors, location of actuators or characteristics of the excitation such as amplitude variation and frequency content characteristics. A stochastic optimization algorithm is conveniently used to solve the optimization problem in the continuous physical domain of variation of the design variables. The proposed framework is applicable to complex linear and nonlinear dynamical systems. The asymptotic results are compared to the results obtained from accurate but computationally expensive sampling algorithms and are shown to be adequate for experimental design purposes. Two optimal experimental design problems illustrate the proposed methodology: 1) optimal sensor placement for load identification in nonlinear beam models, 2) optimal sensor placement for modal identification of bridges using complex FE models. © 2017 The Authors. Published by Elsevier Ltd.