TwIST sparse regularization method using cubic B-spline dual scaling functions for impact force identification

For impact force identification, as a severe ill-posed inverse problem, the wavelet-transform method individually requires a large and accurate decomposition level to obtain a robust and accurate result. However, continuing to increase the number of cubic B-spline dual scaling functions will make the cost of calculation too expansive. To overcome the above mentioned difficulties of impact force identification, sparse regularization is used as a post-processing to solve the residual ill-posed problems. During the iteration process of sparse regularization, the two-step iterative shrinkage-thresholding algorithm (TwIST) algorithm is applied rather than the original iterative shrinkage-thresholding (IST) algorithm, which is more suitable for sparse solution. By combining cubic B-spline scaling functions as pre-processing and TwIST sparse regularization algorithm as post-processing, the proposed method TwIST-SpaR-CB can obtain better impact force identification accuracy with improved computational efficiency. The effectiveness and accuracy of the proposed method compared with the two individual method were verified by experimental and numerical results.