Force localization and reconstruction using a two-step iterative approach

In this paper, we propose a two-step iterative approach to both localize and reconstruct a single point force acting on a structure. Since force reconstruction problems are typically ill-posed, regularization techniques are generally called for. However, for the considered localization-and-reconstruction problem, traditional parameter selection criteria become time-consuming and easily fail. So we propose the stabilization diagram of identified locations to determine the appropriate regularization range and the true force location. The consistency of identified locations under different regularization levels indicates the rationality of corresponding parameters. After the construction of the stabilization diagram, the problem can be transformed to a reconstruction-only one and solved by classic methods. We also adopted a two-phase version of complex method to accelerate the localization process on complex-shaped structures. The approach is validated by simulations of a cantilever beam, an impacted table, and an experiment of an impacted beam. The results show that the force can be well localized and reconstructed from only the responses of structures by the proposed approach.