BAYESIAN STRUCTURAL SOURCE IDENTIFICATION USING GENERALIZED GAUSSIAN PRIORS
Résumé
The reconstruction of mechanical sources from vibration measurements is known to be an ill-posed inverse problem. One of the most widespread method to overcome this difficulty is the Tikhonov regularization. Such an approach consists in including in the formulation of the inverse problem some prior information on the nature of the sources to constrain the space of solutions. However, the reconstructed sources are generally too smooth to properly deal with localized sources. This paper aims at providing an identification methodology able to take advantage of prior information on the nature of excitation sources. More particularly, we will focus on the identification of localized sources. For this purpose, the bayesian framework is well adapted, since it offers a rigourous probabilistic approach to exploit our a priori knowledge on the nature of the sources to identify. The proposed bayesian formulation is based on the use of generalized gaussian priors, which provide a flexible way to introduce a priori information. Usually one use standard gaussian priors for both uncertainties and source distributions. Because noise and sources are usually of different kind (e.g. white noise on measurement and sparsity of sources distribution), we propose to introduce two different priors. The first one tuned to deal with uncertainties and the second one adapted to the nature of the sources exciting the structure. Practically, the inverse problem is solved from a Generalized Iteratively Reweighted Least-Squares algorithm. The proposed methodology is illustrated on various numerical and experimental examples (i.e. for different sources distribution). It is shown that using priors depending on sources distribution nature are needed to improve drastically the quality of the source identification.
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