Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization

• Published in: Mechanical systems and signal processing 2018-01, Vol.98, p.32-49
• Main Authors: Pan, Chu-Dong, Yu, Ling, Liu, Huan-Lin, Chen, Ze-Peng, Luo, Wen-Feng
• Format: Article
• Language: English
• Subjects: Moving force identification; Redundant concatenated dictionary; Structural health monitoring (SHM); Weighted l1-norm regularization
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.04.032

•A hybrid methodology is proposed for moving force identification (MFI).•Redundant concatenated dictionary and weighted l1-norm regularization are used.•Moving force features of slowly-varying and local impact are considered.•Unknown moving forces are identified accurately by the proposed method.•The proposed method is better than either Tikhonov or l1-norm regularization. Moving force identification (MFI) is an important inverse problem in the field of bridge structural health monitoring (SHM). Reasonable signal structures of moving forces are rarely considered in the existing MFI methods. Interaction forces are complex because they contain both slowly-varying harmonic and impact signals due to bridge vibration and bumps on a bridge deck, respectively. Therefore, the interaction forces are usually hard to be expressed completely and sparsely by using a single basis function set. Based on the redundant concatenated dictionary and weighted l1-norm regularization method, a hybrid method is proposed for MFI in this study. The redundant dictionary consists of both trigonometric functions and rectangular functions used for matching the harmonic and impact signal features of unknown moving forces. The weighted l1-norm regularization method is introduced for formulation of MFI equation, so that the signal features of moving forces can be accurately extracted. The fast iterative shrinkage-thresholding algorithm (FISTA) is used for solving the MFI problem. The optimal regularization parameter is appropriately chosen by the Bayesian information criterion (BIC) method. In order to assess the accuracy and the feasibility of the proposed method, a simply-supported beam bridge subjected to a moving force is taken as an example for numerical simulations. Finally, a series of experimental studies on MFI of a steel beam are performed in laboratory. Both numerical and experimental results show that the proposed method can accurately identify the moving forces with a strong robustness, and it has a better performance than the Tikhonov regularization method. Some related issues are discussed as well.