Identification of full-field dynamic modes using continuous displacement response estimated from vibrating edge video

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.