# Integration of Wavelet Denoising and HHT Applied to the Analysis of Bridge Dynamic Characteristics
## 4 Application Analysis
### Comparative Analysis of the Denoised Results  
Figure 8 shows the observation sequence of a monitoring point on the bridge in horizontal and vertical directions, but the vibration characteristics of the bridge structure cannot be determined visually. Under the interference of factors such as noise, the accuracy and effect of the identification of the first natural frequency of the bridge structure may be influenced if the original observation data were directly used for the dynamic characteristic analysis. Therefore, performing denoising pre-processing on the original observation sequence was necessary to improve the accuracy of identifying the first natural frequency. In the experiment, the wavelet-EMD denoising method based on wavelet threshold denoising and the EMD method were used to denoise the observation sequence in the horizontal and vertical directions in Figure 8. The results were compared with those of hard, soft, and semi-threshold wavelet denoising (the wavelet function selects the Sym wavelet, and the decomposition layer selected four layers; the wavelet-EMD method used the semi-threshold function). The results of the four denoising methods are shown in Figure 9, where H-Wavelet represents hard threshold denoising, S-Wavelet represents soft threshold denoising, I-Wavelet represents half threshold denoising, and WE represents wavelet-EMD denoising. Figure 9a shows the denoising results in the horizontal direction obtained using the four methods, and Figure 9b shows the denoising results in the vertical direction derived with the four methods. Figure 9 shows that the wavelet-EMD method obtained a large reduction in Gaussian white noise in the horizontal and vertical directions compared with the three other methods. The signal denoised by the wavelet-EMD method also filtered out most of the invalid IMF components, which could highlight the original signal information. The SNR and RMSE of the denoised signal and the linear correlation coefficient between the denoised signal and the original observation sequence were calculated to evaluate the denoising performance of the four methods quantitatively. Table 3 shows a comparison of the denoising performance of the four methods in the horizontal and vertical directions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Denoising Methods**} & \multicolumn{3}{c}{**Horizontal Direction**} & \multicolumn{3}{c}{**Vertical Direction**} \\ \cline{2-7}  & **SNR** & **RMSE (mm)** & **R** & **SNR** & **RMSE (mm)** & **R** \\ \hline
**H-Wavelet** & 8.434 & 3.609 & 0.938 & 8.704 & 0.689 & 0.928 \\
**S-Wavelet** & 8.856 & 3.019 & 0.951 & 8.387 & 0.784 & 0.920 \\
**I-Wavelet** & 10.082 & 2.169 & 0.962 & 9.186 & 0.369 & 0.953 \\
**Wavelet-EMD** & **11.134** & **1.904** & **0.971** & **10.246** & **0.365** & **0.965** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the four denoising methods in the horizontal and vertical directions. Figure 9: Comparison of denoising results from four methods in the time domain: (**a**) horizontal direction and (**b**) vertical direction. H-Wavelet represents hard threshold denoising, S-Wavelet represents soft threshold denoising, I-Wavelet represents half threshold denoising, and WE represents wavelet-EMD denoisingA comparative analysis of Figure 9 and Table 3 indicates that all four denoising methods played a certain denoising role, but the denoising effects differed slightly in different directions. In the comparison of the H-Wavelet and S-Wavelet methods, the three evaluation indexes indicated that the H-Wavelet method had a better denoising effect in the horizontal direction, whereas the S-Wavelet denoising method had a better denoising effect in the vertical direction. The wavelet-EMD method exerted a stable denoising effect in both directions. The method had a lower RMSE of the denoised signal and a higher SNR than the three methods, thus suppressing the noise effectively. This result proved that wavelet-EMD achieved the best denoising effect amongst the four methods.