Vibration-based damage identification techniques have gained popularity immensely in the field of structural health monitoring (SHM). Frequency response function (FRF)-based damage quantification is mainly performed based on iterative model updating techniques. Most of these methods are time-consuming and erroneous in higher modes. Spectral element method (SEM) can overcome some of these limitations and can determine FRF expression directly for a broad class of civil structures. However, a closed-form expression for multiple damage severity is not proposed to date. In this study, an FRF-based formulation for quantifying damage has been proposed with the help of SEM in order to bypass the mode shape extraction for damage identification. To determine the effectiveness of the proposed formulation both numerical and experimental studies have been performed. A numerical simulation has been performed on a 14-storey shear building. Damage has been introduced by reducing the storey stiffness at intermediate and adjacent storeys. It has been perceived that damage severity at any storey can be estimated with only 3 sensors, one at the top storey and two others at the adjacent floors of the desired storey. To verify the effectiveness of the proposed expression, an experimental study has been carried out on a 9-storey miniature model. It has been observed that the first resonating peak amplitudes of the responses recorded simultaneously at desired locations of intact and damaged structures are sufficient to estimate the damage intensity. Thus, the proposed formulation is efficient as an output measurement-based approach. The novelty of this study lies in the proposed closed-form FRF-based multi-damage severity expression involving minimum number of sensors and without any information on the input excitation. The results obtained from both numerical and experimental study showcase the robustness, simplicity and applicability of the proposed formulation.

中文翻译：

---

基于频率响应函数的多损伤量化闭式表达及其在剪力建筑中的应用

基于振动的损伤识别技术在结构健康监测（SHM）领域得到了极大的普及。基于频率响应函数（FRF）的损伤量化主要基于迭代模型更新技术。这些方法中的大多数在较高模式下都是耗时且错误的。谱元法 (SEM) 可以克服其中一些限制，并可以直接确定各类土木结构的频响函数表达式。然而，迄今为止尚未提出多重损伤严重程度的封闭式表达式。在本研究中，在 SEM 的帮助下提出了一种基于 FRF 的损伤量化公式，以绕过损伤识别的振型提取。为了确定所提出的配方的有效性，已经进行了数值和实验研究。对一栋14层剪力建筑进行了数值模拟。由于降低中间层和相邻层的层刚度而造成损坏。据了解，只需 3 个传感器即可估计任何楼层的损坏严重程度，一个位于顶层，另外两个位于所需楼层的相邻楼层。为了验证该表达式的有效性，在9层微缩模型上进行了实验研究。据观察，在完整和受损结构的所需位置同时记录的响应的第一共振峰值幅度足以估计损坏强度。因此，所提出的公式作为基于输出测量的方法是有效的。这项研究的新颖之处在于提出的基于闭式 FRF 的多损伤严重程度表达式涉及最少数量的传感器，并且没有任何有关输入激励的信息。数值和实验研究获得的结果展示了所提出的公式的稳健性、简单性和适用性。