# Three-Dimensional Reconstruction-Based Vibration Measurement of Bridge Model Using UAVs
###### Abstract
It is, however, difficult to find an ideal place to deploy cameras for some bridges across rivers and valleys. Consequently, many scholars use UAVs carrying high-resolution cameras instead of fixed-position cameras for SHM of bridges [25; 26; 27]. UAVs have been widely used in structural crack detection [28], safety inspections [29], and displacement measurement [30]. Moreover, UAVs have been used for 3D geometry reconstruction to obtain accurate numerical models (e.g., FEM models) [31]. Nevertheless, due to UAV ego-motion, the tracked displacement is the combination of the absolute displacement of bridges and false displacement induced by UAV motion [30]. Hence, the methods to eliminate the false displacement induced by the UAV motion have been proposed [26; 30; 32; 33]. The camera parameters of each UAV video frame are calculated using triangulation [34], so that the world coordinates of the structure can be restored, and the absolute displacement can be obtained [30]. The absolute displacement is estimated by subtracting the UAV movement, which derived from an embedded Inertial Measuring Unit (IMU) [33]. The false displacement is regarded as the low-frequency noise caused by the UAV hovering, which can be filtered away by the high-pass filter method [26]. The planar homography transformation between the images before and after the UAV motion can be determined by direct linear transformation based on at least four sets of 2D-to-2D (two-dimensional) point correspondences [35; 36]; according to this algorithm, the false displacement induced by the UAV motion can be corrected [32]. However, this method has a restriction that the reference points on the fixed object plane must be coplanar with the target points, that is, the selected fixed reference objects on the background should be close enough to the measured bridge; otherwise, there will be a significant error. To select reference points far from the target bridge in field measurements, it is necessary to find a way to overcome the above limitation. In this paper, an improved correction algorithm is developed for eliminating the false displacement induced by the UAV motion by using 3D reconstruction. First, a video of bridge model vibration is captured by a UAV and analyzed by the DIC. Then, the projection matrices of each UAV motion are obtained by camera calibration, and the 3D coordinates of the target points on the bridge model are derived by the projection matrices. Then, the real displacement can be obtained by subtracting the coordinates of the target points on the first frame. The displacement time-histories of the target point are analyzed by the OMA; then, the natural frequencies can be extracted [37]. Finally, the results obtained from the homography-based method and 3D reconstruction method are compared. This work integrates [PERSON]'s calibration method [38] with a drone to provide a measurement method for bridge vibration. The outcome from this investigation demonstrates the efficacy of the proposed approach for obtaining dynamic displacement of bridges that are inaccessible to fixed-position cameras or sensors.