A Sparse adaptive Bayesian filter for input estimation problems

Julian Ghibaudo (1) , Mathieu Aucejo (1) , Olivier de Smet (1)

1 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés

The present paper introduces a novel Bayesian filter for estimating mechanical excitation sources in the time domain from a set of vibration measurements. The proposed filter is derived from a very general Bayesian formulation, unifying most of the state-of-the-art recursive filters developed in the last decade for solving input-state estimation problems. More specifically, the proposed Bayesian filter allows promoting the spatial sparsity of the estimated input vector, by assuming that the predicted input vector is a random vector with independent and identically distributed components following a generalized Gaussian distribution. To properly estimate the most probable parameters of the latter probability distribution, a nested Bayesian optimization is implemented. The validity of the proposed approach, called Sparse adaptive Bayesian Filter, is assessed both numerically and experimentally. In particular, the comparisons performed with some state-of-the-art filters show that the proposed strategy outperforms the existing filters in terms of input estimation accuracy and avoids the so-called drift effect.

Mots clés: Linear inverse problem; Force localization; Space-time

Domaines: Acoustique [physics.class-ph]; Mécanique [physics.med-ph]; Vibrations [physics.class-ph]; Mécanique des structures [physics.class-ph]

Julian Ghibaudo, Mathieu Aucejo, Olivier de Smet. A Sparse adaptive Bayesian filter for input estimation problems. Mechanical Systems and Signal Processing, 2022, ⟨10.1016/j.ymssp.2022.109416⟩. ⟨hal-03700301⟩