A Bayesian Framework for Optimal Experimental Design in Structural Dynamics

Abstract

A Bayesian framework for optimal experimental design in structural dynamics is presented. The optimal design is based on an expected utility function that measures the value of the information arising from alternative experimental designs and takes into account the uncertainties in model parameters and model prediction error. The evaluation of the expected utility function requires a large number of structural model simulations. Asymptotic techniques are used to simplify the expected utility functions under small model prediction error uncertainties, providing insight into the optimal design and drastically reducing the computation effort involved in the evaluation of the multi-dimensional integrals that arise. The framework is demonstrated using the design of sensors for modal identification and is applied to the design of a small number of reference sensors for experiments involving multiple sensor configuration setups accomplished with reference and moving sensors. In contrast to previous formulations, the Bayesian optimal experimental design overcomes the problem of the ill-conditioned Fisher information matrix for small number of reference sensors by exploiting the information in the prior distribution.