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

• Published in: Journal of sound and vibration Vol. 563; p. 117844
• Main Authors: Ercan, Tulay, Papadimitriou, Costas
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 27.10.2023
• Subjects: Bayesian learning; Information entropy; Kullback–Leibler divergence; Nonlinear models; Optimal experimental design; Structural dynamics; Structural dynamics; Optimal experimental design; Kullback–Leibler divergence; Nonlinear models; Information entropy; Bayesian learning
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2023.117844

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. •Modeling and input uncertainties are incorporated in sensor placement design.•Kullback–Leibler divergence quantifies sensor network information under uncertainty.•Asymptotic approximations provide valuable insight into sensor placement design.•Realizations of stochastic input models are useful to perform sensor placement.•Accuracy and computational efficiency are maintained using single input realization.