## 5 Discussion  
The discussion is mainly divided into three parts:  
1. From the above experimental results, it can be known EMD has the best effect on the correction of displacement signal measured by the UAV. With respect of the acceleration signals, the effect of EMD and FT is better than DF, and the reason is as follows: the signals of EMD and FT are processed by second-order differential filtering on the basis of the corrected signals, while DF directly applies a differential filter to the original signal, which contains random signal caused by UAV measurement, so the signal after DF is poor. Figure 18 shows the EMD corrected displacement signal and its second-order differential. The figure shows that the burr of the signal increases significantly after DF, which shows the noise can be introduced by DF. Moreover, the true displacement signal of the bridge model cannot be obtained through DF, and therefore, EMD and FT are obviously more reliable for the processing of displacement signal measured by the UAV.  
Figure 16: PSD curves of four cases: (**a**) fixed camera; (**b**) EMD; (**c**) FT; (**d**) DF.  
Figure 17: The mode shape identified by four methods.  
The comparisons of correction effect of EMD and FT based on the displacement signals are shown in Table 2. It can be seen that EMD is better than FT, mainly because the high time resolution (the minimum time interval on the time axis) and the high frequency resolution (the minimum frequency interval on the frequency axis) cannot be obtained by FT at the same time, and the conversion between time domain signal and frequency domain signal is not accurate enough. In addition, with FT correction technique, it is not easy to find the optimal value of \(F\) without knowing the natural frequency of the structure in advance, so EMD is more generally applicable than FT.  
In addition to the above three techniques for signal measured by the UAV, Average Filtering (AF) [43] technique can also be used to correct the displacement signal measured by the UAV (see the Appendix A for more details). In the first step of AF correction technique, the signal of structural vibration is filtered out from the original signal, and the obtained displacement signal is the false displacement. In the second step, the filtered structural vibration signal can be obtained by subtracting the false displacement from the original signal. The correction effect of AF depends on \(N\) (see the Appendix A for more details). The optimal effect of AF technique (\(N=8\), it is verified by numerical experiment) and the correction effects of EMD and FT are compared in Table 2 (the results are based on the displacement signals). The table shows that the effect of AF technique is between EMD and FT. Therefore, using AF to correct the displacement measured by UAVs is also a considerable method.  
During the processing of AF, partial false displacement signals may be filtered or partial structural vibration signals are not filtered cleanly, which may lead to poor correction effect. In addition, the value of \(N\) is different for different data, so AF technique is not as applicable as EMD.  
3. The above conclusion is based on the bridge model. In follow-up research, the methods used in this paper will be applied to the measurement results of actual bridges.