## 3 Test Data Analysis
### Frequency Domain Analysis  
#### 3.2.1 FFT Analysis  
Time domain analysis can only describe the change of signal amplitude with time, while the frequency domain analysis allows us to more intuitively understand the composition of the signal as it reflects the essence of the signal [23]. Therefore, it is necessary to use the FFT method to transform the above vibration time domain signal, and plot the magnitude (RMS) spectrum, where the RMS value is the \"Root mean square\" of the signal and is used to characterize the amount of energy in the signal [24]. For calculating the RMS value from the time domain, the sum of the squares of all the amplitudes of the time series should be calculated, then divided by the total number of sample points, and, finally, the square root should be taken [25  
(1) According to Figure 13a, it can be seen that the rail acceleration spectrum distribution of the ordinary monolithic track and the steel-spring-floating slab track is significantly different. The peak points of the rail acceleration spectrum of the ordinary monolithic track are concentrated in the segment below 2000 Hz, and there are obvious peak points at 458.73 Hz and 1617.98 Hz. The amplitudes are 0.32 g and 0.28 g, respectively. The spectral peak points of the steel-spring-floating slab track are distributed in 0-3000 Hz, and the peak point density below 1000 Hz is greater than the rail acceleration of the ordinary monolithic track. Its two obvious peak points are located at 438.96 Hz and 2683.52 Hz, and their amplitudes are 0.35 g and 0.15 g, respectively. For the curved segment, as shown in Figure 13b, it can be seen that the amplitudes of each peak point are significantly larger than those of the straight-line segment. The maximum values of the ordinary monolithic track and the steel-spring-floating slab track are located at 1622.26 Hz and 693.99 Hz, respectively, and the amplitudes are 0.55 Hz and 0.53 Hz, respectively. (2) Comparing the waveform diagrams in Figures 13 and 14, it can be seen that the vibration acceleration waveform of the track bed is consistent with the waveform of the rail, where the position of the peak point is the same as the shape change law of the waveform, indicating that the transmission efficiency of the fastener for each frequency band of the rail acceleration is similar. However, the amplitude of the waveform of the steel- spring-floating slab track is significantly larger than that of the ordinary monolithic track. The reason is that the bottom of the steel-spring-floating slab track is suspended, and its constraints are less, and the stiffness of the vibration isolator is also maintained at a smaller value, with the result that the acceleration of the track bed of the steel-spring-floating slab track is significantly greater than that of the ordinary monolithic track. In Figure 14a, the maximum peak values of the acceleration amplitudes of the track bed of the ordinary monolithic track and the steel-spring-floating slab track are located at 1290.93 Hz and 432.79 Hz, respectively, and their amplitudes are 0.012 g and 0.097 g, respectively. In Figure 14b, the maximum peak values of the acceleration amplitudes of the track bed of the ordinary monolithic track and the steel-spring-floating slab track are located at 1249.33 Hz and 442.39 Hz, respectively, and their amplitudes are 0.015 g and 0.131 g, respectively. It can be seen that the peak positions of the acceleration spectrum of the track bed under different line conditions are very close, but the amplitude of the curved segment is larger than that of the straight line segment. (3) Since the acceleration amplitude of the tunnel wall reflects the impact of train vibration on the environment, it is also the key to evaluating the vibration damping effect of the track structure.