###### Abstract  
This paper proposes two approaches, Empirical Mode Decomposition (EMD) and Fourier Transform (FT), to correct the vibration signals measured by an Unmanned Aerial Vehicle (UAV), which overcomes the difficulty of selection of reference points used in other correction methods, such as homography transformation and three-dimensional reconstruction. In the method of this paper, a UAV is used to collect the video of a vibrated bridge, and the displacement signal of the bridge is obtained from the video by Kanade-Lucas-Tomasi (KLT) optical flow method, which contains false displacement caused by the ego-motion of the UAV during the measurement. The false displacement can be effectively eliminated by EMD and FT to obtain the real displacement signal. Finally, the displacement signal is processed by the Operational Modal Analysis (OMA) technique to obtain the bridge modal parameters. The performance of correcting vibration signals and extracting bridge modal parameters from the vibration signals based on EMD, FT, and Differential Filtering (DF) are compared by taking the fixed camera measurement as a reference (the accuracy of measuring bridge vibration with fixed cameras has been verified) in this paper, and it is demonstrated that EMD has better reliability in processing signal measured by UAVs, which is mainly due to the absence of random factors and too much noise in the signal processing process of EMD. umanned aerial vehicles; empirical mode decomposition; Fourier transform; differential filtering; operational modal analysis +
Footnote †: journal: Medical Imaging  
applications, Unmanned Aerial Vehicles (UAVs) [10; 11; 12] have become popular in bridge measurement [13; 14]. Due to the motion of UAVs during the measurement, false displacement is introduced in the measured displacement results [15]. Homography transformation [16] is a commonly used method to correct the displacement measured by UAVs. Four fixed reference points are used to calculate the homography matrix between the reference frame and other frames in this method, and the displacement of the target point on the bridge can be corrected by the homography transformation. However, this method requires the target points on the bridge and four fixed reference points to be in the same plane, and that is unrealistic in actual bridge measurement. The world coordinates of the target points on the bridge can be recovered by the three-dimensional reconstruction, and the displacement time-history curves of the target points can be obtained [17]. But the plane of target points and that of reference points are required to be parallel for this method, and the distance between two planes also needs to be known in advance, which is difficult to satisfy in the process of actual bridge measurement. As neural networks are developed, they are gradually applied to solve the problem of unstable shooting of UAVs. The characteristic relationship between the target points on the measured bridge and the reference points on the background can be learned by a Feedforward Neural Network (FNN), and true displacement of the target points can be predicted through the characteristic relationship by the trained FNN [18]. Although the false displacement caused by UAVs can be eliminated by this method, some fixed reference points on the background of the bridge are also required for this method, and that is difficult to realize in some cases (e.g., the background of the bridge is the boundless sea). The modal parameters of bridges can be obtained from the vibration signals measured by UAVs based on the Differential Filtering (DF) technique [19] without using any reference points [20]. In this method, the acceleration signal of the bridge can be obtained from original signal measured by UAVs by second-order differential filtering. However, the random signal caused by the UAV motion cannot be effectively eliminated by this method, which leads to the low accuracy of the obtained bridge modal parameters.