# Integration of Wavelet Denoising and HHT Applied to the Analysis of Bridge Dynamic Characteristics
## 4 Application Analysis  
Sutong Bridge, which is in the lower reaches of Yangtze River, is a steel box girder cable-stayed bridge with double towers and double cables. Its main span is 1088 m long, and its main tower is 300.4 m high. Sutong Bridge ranked second amongst similar-type bridges in the world at the time of its completion. Evaluating the stage line shape, force, and safety of the bridge structure and determining the safety status of the bridge structure under environmental excitation conditions are vital. An all-weather dynamic geometric monitoring system based on GNSS technology had been established to monitor the geometry and structural state of towers and beams continuously and in real-time, to analyze the construction status, and to avoid unfavorable construction conditions [16]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Denoising Methods**} & \multicolumn{2}{c}{**Blocks Signal**} & \multicolumn{2}{c}{**Bumps Signal**} & \multicolumn{2}{c}{**Doppler Signal**} & \multicolumn{2}{c}{**Heavy Signal**} \\ \cline{2-9}  & **SNR** & **RMSE** & **SNR** & **RMSE** & **SNR** & **RMSE** & **SNR** & **RMSE** \\ \hline \multirow{4}{*}{**0** **6 dB**} & Noisy signal & 15.573 & - & 15.467 & - & 13.403 & - & 12.357 & - \\  & Wavelet denoising & 19.038 & 0.578 & 16.872 & 0.655 & 15.896 & 0.454 & 14.156 & 0.558 \\  & EMD denoising & **21.372** & **0.316** & 17.538 & 0.888 & 16.017 & 0.316 & 15.354 & 0.491 \\  & Wavelet-EMD & 20.819 & 0.376 & **18.147** & **0.369** & **17.643** & **0.202** & **16.069** & **0.343** \\ \hline \multirow{4}{*}{**2** **dB**} & Noisy signal & 6.593 & - & 5.855 & - & 4.403 & - & 4.357 & - \\  & Wavelet denoising & 11.168 & 0.555 & 10.364 & 0.462 & 9.764 & 0.409 & **9.156** & **0.306** \\  & EMD denoising & 12.083 & 0.413 & 10.905 & 0.491 & 10.375 & 0.438 & 7.874 & 0.492 \\  & Wavelet-EMD & **13.575** & **0.362** & **12.643** & **0.359** & **12.871** & **0.252** & 9.018 & 0.330 \\ \hline \multirow{4}{*}{**-2** **dB**} & Noisy signal & \(-2.451\) & - & \(-3.855\) & - & \(-4.313\) & - & \(-5.357\) & - \\  & Wavelet denoising & 5.035 & 0.455 & 6.872 & 0.563 & 6.831 & 0.684 & 3.876 & 0.678 \\ \cline{1-1}  & EMD denoising & 6.362 & 0.417 & 5.828 & 0.431 & 7.707 & 0.586 & 4.321 & 0.529 \\ \cline{1-1}  & Wavelet-EMD & **7.352** & **0.335** & **8.847** & **0.369** & **9.353** & **0.309** & **6.963** & **0.338** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Denoising results from the different methods on signals with different SNR. The GNSS monitoring points were set synchronously according to the needs of construction control and monitoring during the installation process of the steel box girder. The overall layout of the monitoring points is shown in Figure 7.  
The experimental data were obtained from the monitoring of a point on Sutong Bridge under a normal construction environment on 1 May 2007; the weather condition was good; the altitude cut-off angle of the satellites was set to 15\({}^{\circ}\); and the continuous observation in the dynamic observation mode lasted for approximately 3 h. Given that the natural frequency of long-span bridges usually falls within the range of 0-2 Hz, the monitoring sequence with the frequency range of 0-5 Hz could be identified when the sampling frequency of the GPS receiver was set to 10 Hz according to the Nyquist sampling theorem of signal processing. This identified range satisfied the requirements of first natural frequency identification. The GNSS dynamic observation data included the vibration signal of the bridge structure under environmental excitation and accidental errors, such as the multipath effect, because of the influence of the construction and the natural environment. Therefore, the rich bridge structure health information embedded in GNSS monitoring signals must be mined.