# Integration of Wavelet Denoising and HHT Applied to the Analysis of Bridge Dynamic Characteristics
## 4 Application Analysis
### First Natural Frequency Identification from the Denoised Results
Finally, the Hilbert time spectrum and marginal spectrum of the bridge structure in the vertical direction were calculated and shown in Figures 17 and 18, respectively. Figures 15 and 17 show the time-frequency spectrum of the vibration component of the bridge structure in the horizontal and vertical directions, respectively. A clear line existed between 0 and 0.2 Hz in each figure, and the maximum dominant frequencies were 0.153 and 0.139 Hz, respectively. Figures 16 and 18 show the marginal spectrum of the vibration component of the bridge structure in the horizontal and vertical directions, respectively. An amplitude extremum existed in each marginal spectrum image, and 0.153 and 0.139 Hz corresponded to the two main frequency lines in Figures 15 and 17, respectively. Comparison and analysis of the four graphs indicated that the vibration frequencies of the bridge in the horizontal and vertical directions were 0.153 and 0.139 Hz, respectively. Figure 14: Correlation values of respective IMF components from the denoised signal. Figure 13: Correlation values of respective IMF components from the noisy observation sequence. Figure 16: Hilbert marginal spectrum of the denoised observation sequence in the horizontal direction. Figure 17: Hilbert time spectrum of the denoised observation sequence in the vertical direction. Figure 18: Hilbert marginal spectrum of the denoised observation sequence in the vertical direction. Figure 15: Hilbert time spectrum of the denoised observation sequence in the horizontal direction. However, the reliability and precision of the first natural frequency identification results based on time-frequency analysis methods are often difficult to ensure in practical applications. The parameter values identified in this study must be compared with those of other different methods. The theoretical calculation value of the bending natural vibration frequency of Sutong Bridge in the horizontal direction was 0.145 Hz according to the theoretical and empirical calculation methods of the dynamic characteristics of long-span bridges [34; 35; 36], and the value of the vertical direction was 0.133 Hz. A comparison of the identification results with the theoretical calculations showed that the relative errors of the bridge structure in horizontal and vertical directions were 5.52% and 4.67%, respectively, and the statistical results are shown in Table 4.  
Table 4 shows that the amplitude of the main frequency of the bridge in the horizontal direction (4.50 mm) was significantly larger than that in the longitudinal direction (1.02 mm), and the main frequency in the vertical direction of the bridge was not as prominent as the horizontal one. This result indicated that under environment excitation conditions, the loads, such as the construction environment and wind, exerted a larger influence on the longitudinal direction of the bridge. Similarly, analysis of the observation data from the monitoring points in other periods indicated that the first natural frequency was the same in horizontal and vertical directions, except for a slight difference in amplitude. This result indicated that the wavelet-EMD method was used to denoise the original observation data firstly. Then, Hilbert spectrum analysis was performed on the denoised data to obtain the accurate first natural frequency of the bridge structure. This scheme had high identification accuracy and could be used for dynamic characteristic extraction of bridge structures.