Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction. (15th January 2017) - Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng
Abstract: Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l 2 -norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l 2 -norm is replaced by minimizing the l 1 -norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction. Highlights: Sparse deconvolution is introduced to the field of impact force reconstruction. PDIPM based on l 1 -norm is proposed to solve large-scale deconvolution problem. The performance of l 1 -norm regularization method is verified by two experiments. Both single and consecutive impact forces are accurately reconstructed by PDIPM. Compared with l 2 -norm regularization, PDIPM is highly accurate and efficient.