Impact load identification using overlapping group sparsity

Impact force identification, known as an inverse problem, tends to be a challenging task due to its ill-posedness. Recently, the sparsity of impact forces in time domain is taken into account as a priori, and the classic `<sub>1</sub>-norm regularization is generally utilized to obtain the sparse estimation of impact forces. However, the underestimation of solutions often occurs while using `₁-norm regularization to tackle impact force identification problems. In this paper, a novel sparse regularization method for impact force identification based on overlapping group sparsity(OGS) is proposed. The OGS penalty considers not only the sparsity but the group sparsity structure of impact forces in time domain. Stronger prioris are added into the OGS penalty, thus leading to better identification performance. A new algorithm derived under the Majorize-Minimization(MM) principle is employed to minimize the objective function of impact force identification. Experiments on a stiffened composite structure are conducted to validate the proposed method. Corresponding results are compared with counterparts of `<sub>2</sub>-norm and `₁-norm regularization method, and the OGS method can yield more accurate results.