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.

翻译：本文提出了一种利用含噪声频响函数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一个反问题，即根据结构在给定外部动态荷载下的实测动力响应来生成结构的损伤拓扑。该方法基于最小化目标函数，该目标函数表示通过实验模态分析获得的结构实测频响函数与使用有限元分析进行谐响应分析获得的频响函数之间的误差。在最小化过程中，改变材料分布或结构拓扑，并通过使用固体各向同性材料惩罚法进行最小化，将未指定材料的区域识别为最优损伤拓扑。为了克服反问题不适定性带来的问题，建议对原始目标函数应用最小绝对收缩和选择算子正则化，即对设计变量的L1范数进行惩罚。通过应用Lasso正则化，该方法有望不仅消除虚假损伤区域，还能最小化测量噪声的影响。本文首先介绍了所提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识别。通过实验获取频响函数并应用所提方法。结果表明，该方法能够成功识别损伤。