# Train Speed Estimation from Track Structure Vibration Measurements  
[PERSON]  
1 School of Civil Engineering, Dalian University of Technology, Dalian 116024, China; [EMAIL_ADDRESS] (X.W.); [EMAIL_ADDRESS] (J.W.); [EMAIL_ADDRESS] (B.H.)  
[PERSON]  
2 School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China 2* 2  
and the geometrical parameters of the trains. The laser radar system [12], which is based on the Doppler effect, is used to obtain the coordinate value of the measured point in the scanning radar coordinate system. Then, the distance between two adjacent measurement cycles is determined by piecewise linear difference. The advantages and shortcomings of these methods are summarized in Table 1. Recently, some other researchers proposed to estimate train speed from ground vibration. The ground vibration frequency spectra were highly dependent on the train speed and carriages dimensions [13; 14]. Therefore, train speed could be calculated using the relationship between the train speed and the main frequency of vibration; meanwhile, this method has been proved to be robust [15; 16].  
In field track structural health monitoring, especially short-term monitoring, it is often hard to get the speed information from the traffic control center in real time due to the tough monitoring environment, communication difficulties, and complex administrative procedures [16]. In this case, it is necessary to measure train speed on the ground while monitoring. However, optical sensors, wheel counters, eddy current sensors, and radar systems are often too complex to be used in field track structural health monitoring. Considering that track structure vibration measurements are indispensable in monitoring, it is of great practical convenience to estimate train speed from track structure vibration measurements because there is no need for an additional train speed estimation module. Estimating train speed from track structure vibration measurements can meet the requirement of speed estimation in the short-term, multi-location, and tough environment of structural health monitoring.  
However, the vibration measurements are affected by many factors, such as train speeds, rail track structures, and structure health status. Such factors increase the difficulty of train speed estimation by traditional signal processing. Although many disturbances usually exist in the waveform images of rail track vibration measurements, there are still some unique features in waveform images. Therefore, the features in waveform images of vibration measurements can be abstract, employing image treatment techniques that endow computers with the functions of segmentation, classification, recognition, tracking, and decision-making, similar to human beings [17].  
This paper aims to provide a new train speed estimation method from displacement and acceleration measurements of the track structure. This method employed image treatment techniques, wavelet transform, and short-time Fourier transform to extract features of vibration measurements. 240 different measurements gotten from 20 trains measured by 12 sensors at speeds from 124.6 km/h to 227.2 km/h were applied to verify the stability and accuracy of the proposed method.