期刊
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
卷 191, 期 -, 页码 -出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ymssp.2023.110191
关键词
Impact force identification; Non-convex sparse regularization; Convex optimization; ADMM
In this paper, a non-convex sparse regularization method is proposed to promote sparsity and improve solution accuracy. The Alternating Direction Method of Multipliers (ADMM) algorithm is used to solve the non-convex optimization problem. The proposed method outperforms the standard e'1 regularization in both localization accuracy and time-history reconstruction accuracy.
Instead of traditional Tikhonov regularization, sparse regularization methods like e'1 regulariza-tion have been a popular choice for impact force identification because it can encode sparse prior information into the inverse problem solving. However, e'1 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 e'1 regularization in both localization accuracy and time-history reconstruction accuracy.
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