A novel algorithm for solving multiplicative mixed-norm regularization problems. (October 2020)

• Record Type: Journal Article
• Authors: Aucejo, M.; De Smet, O.
• Is Part Of: Mechanical systems and signal processing. Volume 144(2020)
• Publication Date: 2020-10
• Subjects: Inverse problem -- Force reconstruction -- Multiplicative regularization -- Mixed-norm regularization; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2020.106887
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: A novel algorithm for solving mixed-norm regularization is introduced. The proposed algorithm is more robust than the algorithm originally implemented. A detailed comparison of both algorithms is conducted through a numerical experiment. Comparison with ordinary multiplicative regularization is also provided. Abstract: In a paper, recently published in Mechanical Systems and Signal Processing, a multiplicative mixed-norm regularization has been introduced for solving space-frequency force reconstruction problems. Originally, the solution is obtained from an Iteratively Reweighted Least-Squares (IRLS) algorithm. However, as shown in this communication, such an algorithm exhibits a lack of robustness regarding the measurement noise level. For this reason, a novel iterative resolution algorithm, based on the first-order optimality condition, is introduced. From a numerical experiment, it is shown that the proposed algorithm exhibits a better robustness than the IRLS algorithm initially implemented for solving force reconstruction problems in the frequency domain.