# Wavelet Time-Frequency Analysis on Bridge Resonance in Train-Track-Bridge Interactive System
## 1 Introduction  
The operation of a high-speed train has high requirements for the smoothness and stability of the track, which leads to the dependence on bridge construction, especially in areas with high population density, poor geological conditions and limited land resources. Different from the stationary situation, when the train crosses the bridge at a certain speed, the train and bridge will also vibrate and the system will produce inertial force. The vibration response of the bridge will aggravate the fatigue of its structural members to some extent, resulting in the reduction in its own strength and structural stability [1]. In particular, when the loading frequency corresponding to the train speed is close to the natural vibration frequency of the bridge, the bridge vibration response amplitude will be increased, which may cause damage to itself and endanger driving safety in extreme cases. Therefore, a comprehensive study on resonant response to ensure the dynamic performance of the bridge and the safety of vehicle operation is conducted at home and abroad to meet the engineering need of railway bridge research and design. [PERSON] and [PERSON] [2] studied the dynamic response of a girder bridge under high-speed trains, with an emphasis on the resonant vibration, and found that the sum of free-vibration response components generated by each moving load acting successively on the bridge results in the resonance, and if the number of vehicles is very small, resonance may not occur. [PERSON] et al. [3]proposed a low-cost multi-sensor data acquisition system (DAQ) for detecting various faults in 3D-printed products by using an Arduino micro-controller that collects real-time multi-sensor signals using vibration, current, and sound sensors, which is prospective to the study on scaled resonant bridge models. [PERSON] and [PERSON] [4] investigated the resonant characteristics of three-dimensional bridges when high-speed trains pass them and pointed out that to avoid resonance, the dominated train frequencies and the bridge natural frequencies should be as different as possible, especially for the first dominated train frequency and the first bridge natural frequency in each direction. The resonance mechanism and the conditions of the train-bridge system were investigated by [PERSON] et al. [5] through theoretical derivations, numerical simulations and experimental data analysis. [PERSON] and [PERSON] [6] illustrated the influence of these variations on the train-bridge resonance of this particular bridge by means of a nonlinear single degree of freedom system, based on the previously mentioned experimental results. The results indicate that the influence of the increasing damping ratio leads to a considerable decrease in the resonant amplitude whilst the decreasing natural frequency decreases the critical train speed at which resonance occurs. Considering that the acquisition and transport of sensor data could suffer interference in the train's environment due to electromagnetic noise from various sources, [PERSON] et al. [7] presented an architecture for data acquisition of analog data from a train's environment, drawn to perform data acquisition with various noise sources, which is meaningful for withdrawing the bridge response data from the trains. The Railway Technology Research Centre (CITEF) [8] has developed a new data acquisition system (DAS) based on Odroid which consists of a main box that is compact and easy to transport and will be greatly useful for monitoring comfort and safety in railways during the resonant bridge condition. [PERSON] et al. [9] developed a novel drive-by system for high-speed railways to detect resonant bridges; the difference between two track irregularities at the same position using devices mounted on the first and last vehicles of a train was measured. With the development of time-analysis theory, an increasing number of applications concerning wavelet transform on train-track-bridge interactive dynamics investigations have been conducted at home and abroad. [PERSON] et al.