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Structural Engineering and Mechanics Volume 75, Number 4, August25 2020 , pages 477-485 DOI: https://doi.org/10.12989/sem.2020.75.4.477 |
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Anti-sparse representation for structural model updating using l∞ norm regularization |
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Ziwei Luo, Ling Yu, Huanlin Liu and Zexiang Chen
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| Abstract | ||
| Finite element (FE) model based structural damage detection (SDD) methods play vital roles in effectively locating and quantifying structural damages. Among these methods, structural model updating should be conducted before SDD to obtain benchmark models of real structures. However, the characteristics of updating parameters are not reasonably considered in existing studies. Inspired by the lll∞ norm regularization, a novel anti-sparse representation method is proposed for structural model updating in this study. Based on sensitivity analysis, both frequencies and mode shapes are used to define an objective function at first. Then, by adding l∞ norm penalty, an optimization problem is established for structural model updating. As a result, the optimization problem can be solved by the fast iterative shrinkage thresholding algorithm (FISTA). Moreover, comparative studies with classical regularization strategy, i.e. the l2 norm regularization method, are conducted as well. To intuitively illustrate the effectiveness of the proposed method, a 2-DOF spring-mass model is taken as an example in numerical simulations. The updating results show that the proposed method has a good robustness to measurement noises. Finally, to further verify the applicability of the proposed method, a six-storey aluminum alloy frame is designed and fabricated in laboratory. The added mass on each storey is taken as updating parameter. The updating results provide a good agreement with the true values, which indicates that the proposed method can effectively update the model parameters with a high accuracy. | ||
| Key Words | ||
| structural model updating; l∞ norm regularization; anti-sparse representation; sensitivity analysis | ||
| Address | ||
| MOE Key Laboratory of Disaster Forecast and Control in Engineering, School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, China | ||