# Three-Dimensional Reconstruction-Based Vibration Measurement of Bridge Model Using UAVs
###### Abstract  
This paper presents a measurement method of bridge vibration based on three-dimensional (3D) reconstruction. A video of bridge model vibration is recorded by an unmanned aerial vehicle (UAV), and the displacement of target points on the bridge model is tracked by the digital image correlation (DIC) method. Due to the UAV motion, the DIC-tracked displacement of the bridge model includes the absolute displacement caused by the excitation and the false displacement induced by the UAV motion. Therefore, the UAV motion must be corrected to measure the real displacement. Using four corner points on a fixed object plane as the reference points, the projection matrix for each frame of images can be estimated by the UAV camera calibration, and then the 3D world coordinates of the target points on the bridge model can be recovered. After that, the real displacement of the target points can be obtained. To verify the correctness of the results, the operational modal analysis (OMA) method is used to extract the natural frequencies of the bridge model. The results show that the first natural frequency obtained from the proposed method is consistent with the one obtained from the homography-based method. By further comparing with the homography-based correction method, it is found that the 3D reconstruction method can effectively overcome the limitation of the homography-based method that the fixed reference points and the target points must be coplanar. b 2021 27 May  
deployed. Therefore, some non-contact measurement methods, such as the global positioning system (GPS) [9], and laser doppler vibrometer (LDV) [10], have been used to measure structural dynamic displacement under these situations. As the measurement accuracy and sampling frequency of GPS is low, it is generally used for bridges with large vibration amplitude [11]. Though the LDV system can be utilized to collect the vibration response of bridges at various locations, it is costly and time-consuming to measure vibration in practical applications [12]; moreover, it is not suitable for long-term bridge monitoring because it needs to be deployed on the ground underneath the bridge and supervised at all times [13]. With the rapid development of computer technology and image processing technology, the vision-based measurement methods [14; 15; 16] have been widely used as they are accurate, non-contact, and full-field. Compared with contact methods, the vision-based methods provide the possibility for displacement measurement of a bridge at a distance. Through the motion magnification analyses, the vision-based methods can identify modal parameters for SHM without providing displacement measurement [17]. In addition, it is more accurate and applicable than other non-contact methods, e.g., GPS. Moreover, the emergence of low-price and high-resolution cameras makes these methods more and more popular. Among the vision-based methods, the digital image correlation (DIC) [18; 19] has been commonly used to measure the deformation and displacement of engineering structures. By calculating the correlation of gray-scale values between the reference subset and the target subset of a series of images, the deformation information of the region of interest (ROI) on the measured surface can be obtained [20]. Therefore, it is extensively applied in the motion tracking of the target points on bridges to obtain their displacement [21; 22; 23]. To ensure the measurement accuracy and efficacy, sufficient image stability, contrast for an optimal choice and track of target points should be considered. In addition, in an outdoor environment, the weather and lighting conditions (e.g., fog interference and illumination change, etc.) may also influence the measurement results, and a subpixel level method can be utilized to handle these negative factors [24]. In the vision-based measurement, cameras need to be fixed in a position with sufficient light and keep an appropriate distance from the measured bridge.