Impact force reconstruction and localization using nonconvex overlapping group sparsity

Although extensively studied, impact force identification is still a challenging task. When the location of the impact force is unknown, an under-determined problem is usually required to be tackled. In this paper, a novel impact force identification method based on the nonconvex overlapping group sparsity(NOGS) is proposed, allowing to localize the impact and recover its time history simultaneously from quite limited measurements(i.e., the number of responses is less than the number of potential impact locations). The NOGS not only enriches the prior information by taking the group sparsity structure of impact forces into consideration, but enhances the sparsity and the accuracy of estimated amplitude via its nonconvexity. A new algorithm, named fast nonconvex overlapping group sparsity algorithm(FaNogSa), derived in the light of the Majorize-Minimization(MM) principle is utilized to minimize the nonconvex objective function. Simulations and experiments are both implemented systematically on a stiffened composite structure to validate the proposed method, and two strain gauges are utilized to monitor 54 potential impacts. The corresponding results, comparing to the plain nonconvex(atan) regularization and the standard ℓ₁-norm regularization, say that the proposed method is able to localize the impact and at the same time recover its time history accurately, while under the same measuring conditions the nonconvex(atan) method and the ℓ₁-norm method usually fail.