# Integration of Wavelet Denoising and HHT Applied to the Analysis of Bridge Dynamic Characteristics
## 1 Introduction  
Affected by ambient excitation and traffic loads, the complex structure of long-span bridges may have internal and non-linear responses that influence the health of bridge structures. The analysis of the dynamic characteristics of bridge structures under various conditions through the health monitoring of large bridges is essential to the construction and safe operation of bridges. As an important parameter reflecting the dynamic characteristics of bridge structures, the main vibration frequency has become the focus of attention in bridge monitoring. Many studies have showed that the modal frequencies of different structures and their changes reflect the health state of a bridge structure [1; 2; 3; 4; 5; 6; 7; 8]. The accelerometers, optical fibers, piezoelectric sensors, and intelligent materials attached to important components of a bridge structure can monitor their local natural frequency characteristics [1; 2; 3; 4; 5; 6; 7; 8]. However, the displacement deformation characteristics are difficult to determine [9; 10; 11]. Although total station (even robotic total station), 3D laser scanners, close-range photogrammetry equipment, and theGlobal Navigation Satellite System (GNSS) have been adopted to monitor the deformation information of bridges, their respective shortcomings limit their wider application [10; 11; 12; 13]. [PERSON] [14] used GNSS technology in 1998 to monitor the dynamic deformation of a suspension bridge with a main span of 720 m and verified that the vibration displacement and main frequency of the main beam under wind load were consistent with the results of the wind tunnel experiments and finite element calculations. Given that GNSS monitoring can provide long-term, continuous, high-frequency, and dynamic displacement information and extract dynamic frequencies from it, GNSS technology has become an important means of bridge health monitoring and is widely used in the safety monitoring of bridge structures [15; 16; 17; 18; 19]. GNSS dynamic observation data often contain considerable noise due to the interference of external environmental factors, such as multipath effects, and noise-containing GNSS signals usually exhibit nonlinearity and non-stationarity. Thus, exploring the abundant structural health information hidden in GNSS monitoring signals is crucial. Domestic and foreign scholars have conducted studies on non-stationary signal processing methods, such as short-time Fourier transform, wavelet transform, and the Wigner-Ville distribution [20; 21; 22; 23; 24]. Although short-time Fourier and wavelet transform can analyze the time-frequency characteristics of non-stationary noise-containing signals, these methods on non-stationary signals may lead to the phenomenon of false components due to the limitation imposed by the uncertainty principle. In addition, the selection of the Fourier window and wavelet basis functions entails high subjectivity, which limits the utilization scope of the two methods to some extent [25]. Hilbert-Huang transform (HHT) is an adaptive local time-frequency analysis method proposed by [PERSON] et al. in 1998; HHT is composed of empirical mode decomposition (EMD) and the Hilbert transform (HT) [26]. The method carries out blind adaptive decomposition in accordance with the signal itself and separates the non-stationary signal into several intrinsic mode functions (IMF) according to the frequency content (from high to low frequency). On this basis, HT is implemented on each IMF component to explore its spectral characteristics [26]. However, due to the influence of noise and signal discontinuity, the mode-mixing problem often occurs when EMD is applied to the decomposition of non-stationary noise-containing signals. This may result in interference on the EMD decomposition results and the subsequent results of Hilbert spectrum analysis; consequently, effective physical information may not be accurately determined [27; 28]. [PERSON] et al.