# Integration of Wavelet Denoising and HHT Applied to the Analysis of Bridge Dynamic Characteristics
## 5 Conclusions  
With the GNSS dynamic monitoring data of Sutong Bridge as the study object and in consideration of the low precision of first natural frequency identification due to noise interference caused by HHT processing of non-stationary signals, this study proposed a time-frequency analysis method based on the combination of wavelet threshold denoising and HHT. This method was applied to the analysis of the dynamic characteristics of a bridge structure. The conclusions were as follows:  
1. The proposed wavelet-EMD method suppressed high-frequency noise effectively, decreased the decomposition layers of EMD, and reduced the margin effects on the quality of effective signal decomposition. The SNR and linear correlation coefficient of the denoised signal were the largest, and RMSE was the smallest. The method had a stable denoising effect in the horizontal and vertical directions.
2. The Hilbert spectrum analysis of the denoised data clearly reflected the spectral value of the bridge structure, and the numerical results agreed well with the theoretical calculations. The relative errors of the natural frequency identification in the horizontal and vertical directions were 5.52% and 4.67%, respectively, which meant that the natural vibration characteristics of the bridge structure were identified effectively.  
[PERSON] and [PERSON] participated in the design of this study, and they both performed the statistical analysis. [PERSON] carried out the study and collected important background information. [PERSON] and [PERSON] carried out the concepts, the design of data acquisition, the definition of the new algorithm, the literature search, the data analysis, and the manuscript preparation. [PERSON], [PERSON], [PERSON], and [PERSON] carried out the data acquisition, the literature search, and the manuscript editing. [PERSON], [PERSON], [PERSON], and [PERSON] performed the manuscript review. All authors read and approved the content of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Direction** & \
\begin{tabular}{c} **Measured** \\ **Frequency (Hz)** \\ \end{tabular} &
\begin{tabular}{c} **Theoretical** \\ **Calculation (Hz)** \\ \end{tabular} & **Relative Error (\%)** & **Amplitude (mm)** \\ \hline
**Horizontal** & 0.153 & 0.145 & 5.52 & 4.50 \\
**Vertical** & 0.139 & 0.133 & 4.67 & 1.02 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Horizontal and vertical frequencies of the bridge structure and its amplitude.  
**Funding:** This paper was supported by the National Natural Science Foundation of China under Grant 41274020 and also by Henan Polytechnic University's Key Laboratory of Mine Spatial Information Technologies of National Administration of Surveying, Mapping and Geo-information of China under Grant KLM201806.  
**Acknowledgments:** The authors would like to thank the National Natural Science Foundation of China and Henan Polytechnic University's Key Laboratory of Mine Spatial Information Technologies of National Administration of Surveying, Mapping and Geo-information of China for the financial support.  
**Conflicts of Interest:** The authors declare that they have no conflicts of interest.  
**Availability of Data and Materials:** The data contained in this manuscript were the result of experiments by the research group. Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study. Please contact the authors for data requests.