# 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  
Given that the HT method was sensitive to errors during spectral analysis, the accuracy of Hilbert spectrum analysis could be improved to some extent if the quality of the original observation data were improved by appropriate data preprocessing methods. Therefore, the \"clean\" monitoring sequence after denoising that served as the input data was vital for the identification of the main vibration frequency of the bridge structure, which was why noise reduction pre-processing of the dynamic observation data was performed in Section 4.1. In this section, the Hilbert spectrum analysis is performed on the observed data sequence after denoising, and the vibration frequencies of the bridge  
Figure 10: Comparison of denoising results from the four methods in the frequency domain: (a) horizontal direction and (b) vertical direction. structure in the horizontal and vertical directions are identified. Meanwhile, the identification value in this study and the empirical calculation value must be compared to determine the health and structural safety status of the bridge, which would verify the reliability and accuracy of the first natural frequency identification result. The EMD process was implemented on the original noise-containing observation sequence in the horizontal direction of the bridge, then on the denoised signal via the wavelet-EMD method. The purpose was to verify that the time-frequency analysis method based on wavelet threshold denoising and HHT could effectively extract the first natural frequency of the bridge structure under a noisy environment and that the dynamic characteristic analysis was feasible. Each IMF and the remainder in the time- and frequency-domains are shown in Figures 11 and 12 (S represents a noisy observation sequence in the horizontal direction and S(W-E) represents the denoised signal using the Wavelet-EMD method), and the correlation values of the respective IMF components were calculated simultaneously and shown in Figures 13 and 14. Figure 11: Decomposition result of the noisy observation sequence in the horizontal direction using EMD. Figure 12: Decomposition result of the denoised signal in the horizontal direction using EMD. A comparative analysis of Figures 11 and 13 indicates that the frequencies of IMF1 and IMF2 components obtained from the EMD method before denoising were distributed in a disorderly manner, and the correlation value of the component was low. IMF1 and IMF2 were high-frequency noise components according to the global and high distribution of the accidental error. Figure 12 shows that the high-frequency noise in the original observation sequence was suppressed effectively via wavelet-EMD denoising, and the number of decomposition layers of EMD was decreased. Given that the natural frequency of a long-span bridge structure is low, which is generally in the range of 0.1-1 Hz [29], the correlation values of the first three IMF components of the denoised signal were high, and those of the last two IMF components were low (Figure 14). Therefore, invalid trend components IMF4 and IMF5 may be removed from the denoised signal, and effective components IMF1-IMF3 were selected for reconstruction to obtain the vibration component of the bridge structure. The Hilbert time spectrum and the marginal spectrum of the bridge structure were obtained via Hilbert spectral transformation from the reconstructed vibration components and are shown in Figures 15 and 16, respectively. The results proved that the Hilbert marginal spectrum could accurately reflect the main frequency with the actual physical component. Similarly, multi-scale decomposition was performed on the observation data of the bridge in the vertical direction denoised by the wavelet-EMD method, and the correlation value was calculated. Then, the effective vibration components were selected for reconstruction.