Non-convex sparse regularization via convex optimization for impact force identification

• Published in: Mechanical systems and signal processing 2023-05, Vol.191, p.110191, Article 110191
• Main Authors: Liu, Junjiang, Qiao, Baijie, Wang, Yanan, He, Weifeng, Chen, Xuefeng
• Format: Article
• Language: English
• Subjects: ADMM; Convex optimization; Impact force identification; Non-convex sparse regularization
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2023.110191

Instead of traditional Tikhonov regularization, sparse regularization methods like ℓ1 regularization have been a popular choice for impact force identification because it can encode sparse prior information into the inverse problem solving. However, ℓ1 regularization tends to have a limited ability to promote sparsity and underestimate high-amplitude components in the solution. Non-convex regularization holds the potential to promote sparsity more efficiently, and then further improves the accuracy of solutions. In this paper, we consider a family of non-convex regularizers with convexity-preserving characteristics to promote sparsity. By virtue of the non-convex regularizers, we propose a non-convex sparse regularization method to simultaneously localize and reconstruct impact events with a highly under-determined sensor setting. To avoid the inherent difficulties concerning non-convex optimization, we turn to the Alternating Direction Method of Multipliers(ADMM) algorithm. ADMM helps separate the primal non-convex problem into a sequence of convex sub-problems, each of which is easy-to-solve. The non-convex exponential penalty is chosen as the representative of this class of regularizers through theoretical analysis. Several simulations and experiments are conducted on a stiffened composite laminated panel to validate the proposed method. The proposed method outperforms the standard ℓ1 regularization in both localization accuracy and time-history reconstruction accuracy. •A novel non-convex sparse regularization model of impact force identification is built.•A non-convex ADMM solver is derived by virtue of convex optimization.•A generalized iterative thresholding operator is provided for the non-convex penalties.•The proposed method outperforms the standard ℓ1 regularization method.