A fully Bayesian approach based on Bernoulli–Gaussian prior for the identification of sparse vibratory sources from displacement measurements

Abstract

This paper introduces a fully Bayesian approach to the Force Analysis Technique (FAT), which aims at identifying sparse vibratory sources from displacement measurements. Being based on the local equation of motion of a structure, the FAT allows for the estimation of vibratory sources without the need of specifying boundary conditions. Nevertheless, since it involves the calculation of higher-order spatial derivatives of the measured displacements, it is highly sensitive to noise perturbations and thus requires careful regularization. Besides, although sparse excitations are commonplace in structural vibrations, standard regularization strategies tend to over-smooth them in the reconstruction process. This paper shows how to reconcile the two goals of regularization and sparsity enforcement in the FAT by setting up a hierarchical Bayesian model rooted on a Bernoulli–Gaussian prior. Inference of all the parameters in the model is achieved with a Gibbs sampler whose convergence is efficiently accelerated with a partial collapsing strategy.