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To identify mechanical sources acting on a structure, Tikhonov-like regularizations are generally used. These approaches, however, only provide point estimates, meaning that the uncertainty about the regularized solution is not quantified. In practice, such information is essential to guarantee the quality of reconstructed sources. In this contribution, three possible Bayesian formulations of the source identification problem are presented and their limitations discussed. To assess the posterior uncertainty on the parameters appearing in each formulation given a simulated vibration field and a mechanical model, a Gibbs sampler is implemented. The proposed numerical validations highlight the practical interest of these formulations in terms of parameters estimations and posterior uncertainty quantification.

BAYESIAN FORMULATIONS FOR FORCE RECONSTRUCTION PROBLEMS