## 4 Experimental Results and Analysis
### Comparison of EMD, FT, and DF  
The processing effects of EMD, FT and DF techniques on the UAV measurement displacement signal and the effect of modal parameter extraction from the vibration signal are compared in this section. The true displacement of the bridge model can be decomposed from the original displacement signal by EMD (Figure 12a). The original signal contains seven IMFs and a remainder. The first IMF is the real displacement signal of the bridge model, which has obvious characteristics of free vibration attenuation. The decomposed remainder is monotonic, which is the condition to terminate the process of EMD. The signals shown in Figure 12a are processed by FT to obtain the corresponding spectrum diagrams (Figure 12b), which indicates that only the first IMF contain the structural vibration (frequency close to 3 Hz), which further indicates that IMF 1 is the real vibration signal of the structure. The decomposed components except IMF 1 are combined into a composite signal, which is the false displacement caused by the UAV measurement (Figure 13). The components of the original signal decomposed by EMD are reconstructed into a new signal. The standard deviation of the error curve between the new signal and the original signal is \(3.687\times 10^{-15}\), indicating that the error of the EMD process is very small and negligible. Figure 12: The results of EMD: (**a**) components of the original signal; (**b**) spectrum diagrams of the components. Since the signal measured by the UAV and corrected by DF is an acceleration signal, in order to facilitate comparison, the displacement signal measured by the fixed camera and the UAV displacement signal corrected by EMD and FT are processed by the second-order differential filtering, as shown in Figure 14. It shows that the curves of four cases are similar. In this section, the processing effects of three techniques are compared with three indexes. The locally weighted regression (LOWESS [41]) can be used to smooth the original displacement signal to obtain the ideal displacement curve \(x^{\prime}(t)\). The burr degree of the time-history curve can be reflected by the average value of the error curve between \(x(t)\) and \(x^{\prime}(t)\), which is defined as ECA in this paper. The higher the ECA, the more burr's the  
Figure 14: Acceleration signals of four cases: (**a**) fixed camera; (**b**) EMD; (**c**) FT; (**d**) DF. Figure 13: Original signal, IMF 1 and composite signal. curve has. The average ECA of the six nodes of the model with larger vibration amplitude (Nodes 14, 15, and 16 and 42, 43, and 44) are shown in Table 1 (the subsequent ECAs mentioned in this paper are the average ECA values of the six nodes). It shows that the ECA of EMD is the lowest, followed by FT, which are 24.897 and 25.310, respectively; while, the ECA of DF is the highest, which is 26.456. The TRAC between the corrected signals obtained by the three methods and the measurement results of the fixed camera are shown in Table 1. The TRAC of FT is the highest, which is 0.942, followed by EMD, which is 0.941, while the relative error of them is only 0.106%; the TRAC of DF is the lowest, which is 0.918. The signals of a stationary point on the model background measured by the UAV and corrected by three methods are shown in Figure 15. Theoretically, the curves are straight lines, so the Standard Deviation (STD) reflects the accuracy of correction. The average STD values of six static points are shown in Table 1 (the subsequent STDs mentioned in this paper are the average STD values of six static points). It demonstrates that the STD of EMD is the lowest, followed by that of FT, and they are 98.604 and 99.914, respectively. The STD of DF is the highest, which is 106.508. Figure 16 illustrates the PSD curves of the signals shown in Figure 14. According to the principle of OMA, the peak of the PSD curves corresponds to the modal natural frequency.