Damage identification using noisy frequency response functions based on topology optimization
Damage identification using noisy frequency response functions based on topology optimization
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DOI：
10.1016/j.jsv.2022.117412
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发表时间：
2022-11
影响因子：
4.7
通讯作者：
Akira Saito;Ryo Sugai;Zhongxu Wang;H. Saomoto
中科院分区：
文献类型：
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作者：
Akira Saito;Ryo Sugai;Zhongxu Wang;H. Saomoto
本文提出了一种使用噪声频率响应函数（FRF）和拓扑优化的鲁棒损伤识别方法。我们将损伤识别问题表述为根据测量的结构对给定外部动态载荷的动态响应生成结构损伤拓扑的逆问题。该方法基于目标函数的最小化，该目标函数表示通过实验模态分析获得的结构的测量频响函数与使用有限元分析通过谐波响应分析获得的结构的频响函数之间的误差。在最小化过程中，材料分布或结构的拓扑会发生变化，并且最佳损伤拓扑被确定为由于使用带惩罚的固体各向同性材料 (SIMP) 进行最小化而没有分配材料的区域。为了克服反问题的不适定性带来的问题，提出对原始目标函数应用最小绝对收缩和选择算子（Lasso）正则化，或者对设计变量的L1范数进行惩罚。通过应用 Lasso 正则化，该方法不仅可以消除虚假损坏区域，还可以最大限度地减少测量噪声的影响。本文首先介绍了所提出方法的数学背景及其数值实现。然后将该方法应用于悬臂板损伤的识别。频响函数是通过实验获得的，并应用了所提出的方法。结果表明，该方法成功识别了损伤。
This paper proposes a robust damage identification method using noisy frequency response functions (FRFs) and topology optimization. We formulate the damage identification problem as an inverse problem of generating the damage topology of the structure from measured dynamic responses of the structure to given external dynamic loading. The method is based on the minimization of the objective function representing errors between measured FRFs of the structure obtained by experimental modal analysis, and those obtained by harmonic response analysis using finite element analysis. In the minimization process, material distribution, or the topology of the structure is varied and the optimal damage topology is identified as regions with no material assigned as a result of the minimization using the solid isotropic material with penalization (SIMP). In order to overcome the problems caused by the ill-posedness of the inverse problem, it is proposed that the least absolute shrinkage and selection operator (Lasso) regularization, or the penalization to the L1 norm of the design variable be applied to the original objective function. By applying Lasso regularization, the method is expected not only to eliminate spurious damaged regions but also to minimize the effect of measurement noises. This paper first presents the mathematical background and its numerical implementation of the proposed methodology. The method is then applied to the identification of a damage of cantilevered plates. The FRFs were experimentally obtained and the proposed method is applied. It is shown that the method successfully identifies the damage.