# Bridge Damping Extraction Method from Vehicle-Bridge Interaction System Using Double-Beam Model
## 1 Introduction  
Vehicle-bridge interaction (VBI) has been extensively studied in the field of structural health monitoring (SHM) [1]. Numerous studies have shown that the dynamic characteristics of VBI systems differ from those of bridges, and this difference often cannot be ignored [2; 3; 4; 5]. Traffic loads, as an important load in bridge operation, cause such differences in dynamic characteristics that have important impacts on the condition assessment of bridges. The influence of the vehicle-bridge coupling effect on bridge frequency has been extensively studied. [PERSON] [5] used a spring mass model to simulate a vehicle, in which the closed-form solutions of the VBI system for a vehicle traveling over a bridge were calculated when the first-order modal of the bridge was considered without damping. [PERSON] [6] proposed a method to extract the frequencies of a VBI system using the synchroextracting transform technique. Numerical studies have demonstrated the effectiveness of the method, and the frequency identification results are in general agreement with the theoretical solution proposed by [PERSON] [5]. [PERSON] [7] used a Bayesian time-frequency analysis method toidentify the change of frequency when a train crosses a bridge. This method was also shown to be good at extracting the time-varying frequency characteristics of a VBI system. [PERSON] [8] conducted an experiment to measure the evolution of the modal properties of a bridge as a vehicle drives across it. Vehicle and modal frequency were analyzed at different bridge locations using a simplified vehicle model with a spring mass. The study found that the spring mass vehicle model was able to accurately explain the phenomena in the experiment. A vehicle suspension system is similar to an additional damper that absorbs and reduces bridge vibrations [7]. This process causes the damping of a VBI system to be greater than the damping of the bridge. Therefore, the vehicle-bridge coupling effect has an impact on the damping identification results of a bridge. In bridge health monitoring, the damping identified by monitoring data often has a large dispersion problem [9; 10]. The presence of traffic on a bridge usually causes the damping identified using bridge monitoring data to be that of the VBI system, which is an important reason for the large dispersion of damping identification results. However, in the field of SHM, a large amount of research has focused on developing damping identification algorithms to improve the accuracy of results, and few studies have analyzed the dispersion of damping identification results from the perspective of vehicle-bridge coupling effects. [PERSON] [11] proposed using a dynamic displacement reconstruction algorithm to suppress the higher-order modal components and then using the Natural Excitation Technique combined with the Eigensystem Realization Algorithm (NExT-ERA) to identify the damping ratio of a reconstructed displacement. [PERSON] [12] used the random decrement technique (RDT) and wavelet transformation (WT) to identify the damping ratio of Sutong Bridge during a typhoon. [PERSON] [13] proposed using an amplitude-modulation function to pre-process the measured data and then used the operational modal analysis (OMA) method to identify the damping ratio. [PERSON] [9] used 2.5 years of bridge monitoring data to analyze the variation pattern of a damping ratio with a displacement reconstruction algorithm, but the identification results still showed relatively large fluctuations. Therefore, it is important to study the effect of the vehicle-bridge coupling effect on bridge damping identification and extract the bridge damping ratio from a VBI system to improve the accuracy of bridge damping ratio identification results. In recent years, there have been reports of abnormal vibrations on two bridges in China that have attracted widespread attention in society. One of the bridges was the Humen Bridge in Guangdong. A change in the dynamic characteristics of the bridge is suspected to be one of the causes of this incident.