1. Sparse Deconvolution for the Inverse Problem of Multiple-Impact Force Identification

The traditional regularization methods for impact force identification such as Tikhonov regularization and truncated singular value decomposition are to minimize the l ₂-norm of the desired force, commonly leading to a low accurate solution. In this paper, considering the inherent sparse nature of multiple impact forces, the idea of sparse deconvolution in signal/image processing is introduced to solve the ill-posed inverse problem of impact force identification. The primal-dual interior point method is applied to solve the convex optimization problem of the impact force deconvolution, where minimizing the l ₂-norm is replaced by minimizing the l ₁-norm. Experiments of two-input-two-output system is conducted on a shell structure to illustrate the advantage of the sparse deconvolution method. Due to the sparse regularization term, the elements of the sparse solution are nearly zeros in the unloading stage of impact force, where the small noise from the observed response is greatly inhibited. Compared with the traditional Tikhonov regularization method, the proposed sparse deconvolution method greatly improves the identification accuracy of the multiple-impact force.