Abstract The video of vibrating structure provides dense quantitative continuous spatial information that is harnessed using various computer vision algorithms in the past decade. Computer vision algorithms that implement sparse optical flow, have been successful in acquiring the Lagrangian representation of motion. Such vision-based measurement already proved its potential in replacing the need for a contact based vibration measurement sensors. In order to obtain full-field, spatially dense, vibrational modes, a large number of discrete sensors would be necessary throughout the specimen’s length, making it impractical. The phase-based video processing method is found to be successful in visualizing full-field operational mode shapes of a vibrating structure. However, the phase-based optical flow provides an Eulerian representation of the motion at every pixel of the image space, which does not acquire the full-field spatiotemporal Lagrangian displacement trajectory of the structure. Hence, there is a need to design a target-free, noncontact vision-based framework that can directly extract and quantify full-field dynamic modes of a real-life vibrating structural member from its video, by acquiring the trajectory of every particle on the structure at each frame of the video using optical flow. The continuous edge of a moving object is a rich optical feature whose motion perpendicular to its orientation can be tracked in Lagrangian coordinates using optical flow. In a recent paper by authors, the method of measuring full-field displacement response of a vibrating continuous edge of a structural member has been reported. In this paper, the full-field displacement response is acquired using the recently presented method and subsequently, its spatially dense dynamic modes are extracted from its video using the acquired full-field spatiotemporal displacement response of the vibrating structure. The full-field dynamic modes and modal parameters are extracted using the Hankel dynamic mode decomposition method, which is applicable both for linear, as well as nonlinear dynamical systems. Further, experimental validation of the proposed method is presented for two kinds of structures (1) a three-story steel frame, and (2) an aluminum cantilever beam, both undergoing free vibration. The results obtained using the proposed method is validated with the displacement measured using Laser Doppler Vibrometer at a particular point of the edge. The extracted modal properties using the proposed methodology compares satisfactorily with the results of the eigensystem realization algorithm applied to the discrete point accelerometer measurements attached at all three floors of the frame. Also, the numerically obtained mode shapes from the analytical model of the cantilever beam validate the estimated modal parameters and the full-field mode shapes. To validate the efficacy of the proposed method in real-world structures, part of the vibrating cable of Tacoma Narrows bridge is tracked from its video, moments before its collapse. The proposed method does successfully extract the dominating vibrational modes of the cables of the Tacoma Narrows bridge.

中文翻译：

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使用从振动边缘视频估计的连续位移响应识别全场动态模式

摘要 振动结构的视频提供了密集的定量连续空间信息，在过去十年中使用各种计算机视觉算法进行了利用。实现稀疏光流的计算机视觉算法已经成功地获得了运动的拉格朗日表示。这种基于视觉的测量已经证明其有潜力取代基于接触的振动测量传感器的需求。为了获得全场、空间密集、振动模式，需要在整个样本长度上安装大量离散传感器，这使其不切实际。发现基于相位的视频处理方法在可视化振动结构的全场工作模式形状方面是成功的。然而，基于相位的光流提供了图像空间每个像素的运动的欧拉表示，它不获取结构的全场时空拉格朗日位移轨迹。因此，需要设计一种无目标、非接触式视觉框架，通过获取每个粒子在其视频中的轨迹，直接从视频中提取和量化真实振动结构构件的全场动态模式。使用光流在视频的每一帧进行结构化。运动物体的连续边缘是一种丰富的光学特征，其垂直于其方向的运动可以使用光流在拉格朗日坐标中进行跟踪。在作者最近的一篇论文中，已经报道了测量结构构件振动连续边缘的全场位移响应的方法。在本文中，使用最近提出的方法获取全场位移响应，随后使用获得的振动结构的全场时空位移响应从其视频中提取其空间密集动态模式。使用 Hankel 动态模式分解方法提取全场动态模式和模态参数，该方法适用于线性和非线性动态系统。此外，针对两种结构（1）三层钢框架和（2）铝悬臂梁，都进行了自由振动，对所提出的方法进行了实验验证。使用所提出的方法获得的结果通过在边缘的特定点使用激光多普勒测振仪测量的位移进行验证。使用所提出的方法提取的模态属性与应用于框架所有三层的离散点加速度计测量的本征系统实现算法的结果进行了令人满意的比较。此外，从悬臂梁的分析模型中数值获得的模态振型验证了估计的模态参数和全场模态振型。为了验证所提出的方法在现实世界结构中的有效性，塔科马海峡大桥的部分振动电缆在其倒塌前一刻从其视频中进行跟踪。