Optimal experimental design in stochastic structural dynamics

Abstract

This paper provides a methodology for optimal prediction of the response of randomly vibrating structures using information from a limited number of measurements. The objective is to optimize the locations of sensors for the purpose of making the most accurate predictions of the response at unmeasured locations in structural systems. The kriging method is used to find the response predictions and the corresponding mean-square errors at unmeasured locations. The mean-square errors in the predictions depend on the locations of sensors and the correlation characteristics of the response evaluated from the model of dynamics and the characteristics of the excitation. The response predictions depend also on the information contained in measurements. The optimal sensor locations are selected to minimize the total mean-square error of the response predictions at unmeasured points. This leads to a complicated non-convex optimization problem in which multiple local and global optima may exist. A hybrid optimization method based on evolution strategies is used to determine a global minimum. The optimal experimental design method presented in the paper is illustrated by designing the optimal sensor locations for an elastic beam and a plate subjected to a class of random stationary loads.