Bayesian force reconstruction with an uncertain model

This paper presents a Bayesian approach for force reconstruction which can deal with both measurement noise and model uncertainty. In particular, an uncertain model is considered for inversion in the form of a matrix of frequency response functions whose modal parameters originate from either measurements or a finite element model. The model uncertainty and the regularization parameter are jointly determined with the unknown force through Monte Carlo Markov chain methods. Bayesian credible intervals of the force are built from its posterior probability density function by taking into account the quantified model uncertainty and measurement noise. The proposed approach is illustrated and validated on numerical and experimental examples.