Multi-parameter multiplicative regularization: an application to force reconstruction problems

International audienceThis paper introduces a multi-parameter multiplicative regularization for force reconstruction problems. This approach allows exploiting the local prior information available on the sources to identify, while determining the related regularization parameters in an elegant and ecient manner. The aim of this paper is to assess the applicability of a multi-parameter regularization strategy compared to a single parameter formulation for reconstructing the external sources acting on a mechanical structure. A particular attention is also paid to the practical resolution of the regularization problem by implementing an original Iteratively Reweighted algorithm derived from the direct application of the rst-order optimality condition. The performance of the proposed algorithm in terms of solution accuracy is compared with a more classical implementation based on an Iteratively Reweighted Least-Squares procedure. The interest of the proposed multi-parameter strategy is assessed numerically. Obtained results demonstrates that consistent reconstructions are obtained for high and moderate measurement noise level whatever the formulation considered (i.e. single or multi-parameter) provided that the suitable resolution algorithm is implemented. For very and extremely noisy input data, the single parameter strategy is more robust than the multi-parameter approach