Bayesian optimal sensor placement for parameter estimation under modeling and input uncertainties

Abstract

A Bayesian optimal sensor placement (OSP) framework for parameter estimation in nonlinear structural dynamics models is proposed, based on maximizing a utility function built from appropriate measures of information contained in the input–output response time history data. The information gain is quantified using Kullback–Leibler divergence (KL-div) between the prior and posterior distribution of the model parameters. The design variables may include the type and location of sensors. Asymptotic approximations, valid for large number of data, provide valuable insight into the measure of information. Robustness to uncertainties in nuisance (non-updatable) parameters associated with modeling and excitation uncertainties is considered by maximizing the expected information gain over all possible values of the nuisance parameters. In particular, the framework handles the case where the excitation time history is measured by installed sensors but remains unknown at the experimental design phase. Introducing stochastic excitation models, the expected information gain is taken over the large number of uncertain parameters used to model the random variability in the input time histories. Monte Carlo or sparse grid methods estimate the multidimensional probability integrals arising in the formulation. Heuristic algorithms are used to solve the optimization problem. The effectiveness of the method is demonstrated for a multi-degree of freedom (DOF) spring–mass chain system with restoring elements that exhibit hysteretic nonlinearities.