发表机构
South Dakota State University（南达科他州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出图论框架，利用延迟嵌入动态模式分解从视频测量构建振动梁的图，以图拓扑特征（如连通性）作为损伤敏感度量，实验与数值研究验证了随裂纹深度增加连通性单调下降，为视觉结构损伤识别提供新基础。
AI 中文摘要
本研究提出了一种图论框架，用于从非接触式视频测量中表征振动悬臂梁动力学中损伤引起的变化。在该方法中，首先使用延迟嵌入动态模式分解（DMD）对健康状态及裂纹深度分别为5、10和13毫米的损伤状态下梁的动力学进行建模，数据来源于基于视觉的测量。由DMD得到的模态矩阵被用于构建该振动梁系统的图的邻接矩阵，并评估其拓扑特征，如图连通性、中心性、双星统计量和二元配置，作为损伤敏感度量。此外，还评估了不同的基于DMD的谱和模态度量，以支持图论损伤评估。结果表明，随着裂纹深度的增加，图的连通性、节点可达性和局部组织呈单调下降趋势。一项参数化数值研究进一步验证了实验观察到的连通性下降趋势。结果表明，由DMD模态矩阵导出的图的拓扑特征为梁动力学中损伤引起的变化提供了可解释的表征，并为基于视觉的结构损伤识别提供了有前景的基础。
英文摘要
This study presents a graph theoretic framework for characterizing damage-induced changes in the dynamics of a vibrating cantilever beam from non-contact video measurements. Within this approach, dynamics of the beam under healthy and damaged conditions with crack depths of 5, 10, and 13 mm are initially modeled using delay-embedded dynamic mode decomposition (DMD) from vision-based measurements. The resulting mode matrix from DMD is used to construct the adjacency matrix of a graph for this vibrating beam system, and its topological features such as graph connectivity, centrality, two-star statistics, and dyadic configurations are evaluated as damage-sensitive measures. Additionally, different DMD-based spectral and modal measures are evaluated to support the graph theoretic damage assessment. The results show a monotonic reduction in graph connectivity, nodal accessibility, and local organization of the graph with increasing crack depth. A parametric numerical study further validates the decreasing connectivity trend observed experimentally. The results demonstrate that the topological features of the graph derived from the DMD mode matrix provide an interpretable representation of damage-induced changes in the beam dynamics and offer a promising basis for vision-based structural damage identification.
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