Page 25 - 《振动工程学报》2025年第9期

第 38 卷第 9 期 振 动 工 程 学 报 Vol. 38 No. 9
2025 年 9 月 Journal of Vibration Engineering Sept. 2025

采 用 多 级 模 态 组 响 应 重 构 的 密 集 模 态 损 伤 识 别 方 法

邹云峰 ， 董欢枝 ， 卢玄东 ， 何旭辉 ， 蔡陈之 1,2
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（1. 中南大学土木工程学院，湖南 长沙 410075； 2. 轨道交通工程结构防灾减灾湖南省重点实验室，湖南 长沙 410075）
摘要：受限于常见的密集模态和庞大的结构维数，基于模态参数的损伤识别难以应用于土木结构中。为此，本文提出一种采
用多级模态组响应重构的密集模态损伤识别方法。针对密集模态的情况，将频率间隔小的几个模态归为一组，并提取整个模
态组响应作为损伤敏感特性。采用多级损伤识别和模型缩聚策略，在超单元级损伤定位中，通过模型缩聚将原结构转换为自
由度更少的超单元模型，再定义模态组响应应变能作为损伤指标求解最小化问题，实现损伤超单元的定位；在单元级损伤识
别中，将最小化问题表述为重构和实际的模态组响应的误差，从而实现损伤单元的定位和量化。通过数值模拟研究和试验验
证，阐述了该方法的运算过程，证明了其可行性。与传统方法对比的结果表明，该方法一方面通过多级识别策略和模型缩聚
提高了损伤识别的精度和效率，另一方面通过将模态组作为损伤敏感特性，弥补了基于模态识别的方法面对密集模态时无法
准确识别损伤的不足，无论密集模态存在与否都可基于结构的应力、应变、位移、加速度等多种动力响应进行损伤识别。

关键词： 模态组响应；密集模态；多级损伤识别；模型缩聚
中图分类号：TU17；O327 文献标志码：A DOI：10.16385/j.cnki.issn.1004-4523.202308014

Damage identification using multi-level modal group response reconstruction

in the presence of close spaced modes

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ZOU Yunfeng ，DONG Huanzhi ，LU Xuandong ，HE Xuhui ，CAI Chenzhi 1,2
（1.School of Civil Engineering，Central South University，Changsha 410075, China；2.Hunan Provincial Key Laboratory for Disaster
Prevention and Mitigation of Rail Transit Engineering Structure，Changsha 410075, China）
Abstract： Limited by common situations of closely spaced modes and large structural dimension， damage identification based on modal
parameter is difficult to perform in civil structures. A damage identification method based on multi-level modal group response reconstruction in
the presence of close spaced modes is proposed. Several modes with small intervals are grouped together，and response of the entire modal
group is extracted as damage sensitive characteristic. Based on the collected modal response，a multi-level damage identification strategy is
adopted. In the super element level damage location，the original structure is first converted into a super element model with fewer DOFs
through model reduction，and then the minimization problem is solved by defining the modal group response strain energy as a damage index
to achieve the location of damaged super elements；In element level damage identification，the minimization problem is expressed as the
discrepancy between reconstructed and actual modal group response to achieve elemental damage localization and quantification. A numerical
simulation study and the experimental verification were conducted to demonstrate the operational process and feasibility of this method.
Compared with traditional methods，the results show that the proposed method improves the accuracy and efficiency of damage identification
through multi-level identification strategies and model reduction，and on the other hand，improves the shortcomings of modal-analysis-based
methods that cannot accurately identify damage when faced with close spaced modes. Regardless of the presence or absence of close spaced
modes. Damage identification can be performed based on multiple dynamic responses such as stress，strain，displacement，and acceleration
of the structure.
Keywords：modal group response；close spaced mode；multi-level damage identification；model reduction

土木结构的性能不可避免地随着时间推移而下 甚至造成生命、经济和社会损失。因此，实时监测
降，从而影响结构的安全性和耐久性，若没有及时发 和预测结构性能、识别内部损伤位置与程度以及评
现结构的劣化并采取相应的措施，性能下降的结构 估剩余寿命，对提升结构运营效率和保障安全至关
可能无法承受原本的设计荷载，从而引发结构破坏， 重要。基于振动的损伤识别方法最为常用，即通过

收稿日期：2023-08-08；修订日期：2023-10-07
基金项目：国家自然科学基金资助项目（51925808，51508580）；湖南省杰出青年科学基金资助项目（2022JJ10082）