On a General Iteratively Reweighted Algorithm for Solving Force Reconstruction Problems

The multiplicative ℓq-regularization has been recently introduced in structural dynamics for solving force reconstruction problems. Practically, the resolution of this regularization strategy requires the implementation of an iterative procedure. To this end, an Iteratively Reweighted Least-Squares algorithm has been originally implemented. The core idea of this algorithm is to replace the direct resolution of the inverse problem by an equivalent iterative procedure having an explicit and unique solution at each iteration. However, the exploitation of this very general idea allows defining other Iteratively Reweighted schemes. The present paper aims at comparing the overall performances of three particular Iteratively Reweighted algorithms for solving force reconstruction problems derived from a more general and original iterative procedure. The numerical applications proposed in this contribution highlight the ability of the considered algorithms in providing consistent regularized solutions with respect to various parameters such as the measurement noise level or the tolerance chosen to stop the iterative process.