A multiplicative regularization for force reconstruction. (15th February 2017) - Aucejo, M.; De Smet, O.
Abstract: Additive regularizations, such as Tikhonov-like approaches, are certainly the most popular methods for reconstructing forces acting on a structure. These approaches require, however, the knowledge of a regularization parameter, that can be numerically computed using specific procedures. Unfortunately, these procedures are generally computationally intensive. For this particular reason, it could be of primary interest to propose a method able to proceed without defining any regularization parameter beforehand. In this paper, a multiplicative regularization is introduced for this purpose. By construction, the regularized solution has to be calculated in an iterative manner. In doing so, the amount of regularization is automatically adjusted throughout the resolution process. Validations using synthetic and experimental data highlight the ability of the proposed approach in providing consistent reconstructions. Abstract : Highlights: A multiplicative regularization for force reconstruction problem is presented. The formulation is highly flexible to describe prior knowledge of the sources. The method is validated numerically and experimentally. The multiplicative regularization is faster than Tikhonov-like (additive) regularization.