Abstract
The reconstruction of mechanical sources from vibration measurements is known to be an ill-posed inverse problem. A classical solution to overcome this difficulty consists in including prior information on the spatial distribution of the sources to constrain the space of solutions. Among all the methods developed to this end, the Tikhonov regularization is certainly the most popular. However, it assumes a global a priori on the spatial distribution of sources. Incidentally, poor results can be obtained if a structure is subjected to localized and distributed sources. This paper aims at providing an identification methodology able to take advantage of prior local information on both the nature and location of excitation sources. For this purpose, the Bayesian framework is well adapted, since it offers a rigorous probabilistic approach to exploit our a priori knowledge on the sources to identify. The proposed Bayesian formulation is based on the use of generalized Gaussian priors, which provide a flexible way to introduce local a priori information. Practically, the resulting optimization problem is solved from a Generalized Iteratively Reweighted Least-Squares algorithm. The validity of the proposed methodology is illustrated numerically. It is especially shown that local information improves drastically the quality of the source identification.
Mathieu Aucejo
Associate Professor
My research interests include inverse problems, vibration control and vibro-acoustics.