## 4 Analysis and Discussion
### Frequency-Domain Analysis for Multi-Feature Extraction and Assessment  
Previous studies have shown that the vibration frequency spectrum of the ballastless track of HSR changes when it is damaged [18; 59]. In this section, the frequency spectrums of Segment 1 and Segment 2 are studied. Fourier transform was used to extract spectrum characteristics. The frequency-domain responses of Segment 1 and Segment 2 are shown in Figure 13, in which the blue line represents the spectrum of Segment 1, and the orange line stands for that of Segment 2. As the measurement positions at cross-sections 1-1  
Figure 11: Scatter plot of peak acceleration of Segment 1 in the current monitoring stage. Figure 12: Scatter plot of peak acceleration of Segment 2 in the current monitoring stage. Figure 10: Typical vertical acceleration of Segment 2 in the current monitoring stage. and 3-3 were symmetrical regarding the measurement position at cross-section 2-2, the spectrums of sensor No. 1 and sensor No. 3 were similar. As shown in Figure 13, the horizontal coordinate adopted a logarithmic scale, and the vibration energy was distributed in the frequency bands of 0-30 Hz, 30-60 Hz, and 60-90 Hz. The responses in 0-30 Hz accounted for the dominant proportion of energy, and the details of responses in 30-60 Hz and 60-90 Hz are also displayed in Figure 13a,i. Similar to the findings in Section 4.2, the vibration level of Segment 2 was considerably larger than that of Segment 1, which is consistent with the fact that Segment 2 had a distinct debonding defect. Vibration is the cause of waves, and waves are the result of vibration. The low-frequency vibration in the manuscript is the wheel-track vibration wave reaching the cable trough after attenuation, and the frequency of the wheel-track vibration wave can reach 5 kHz [60], which is also a high-frequency wave like GWs [61]. The monitoring object is the China Railway Track System (CRTS)-II-slab ballastless track structure, which has a complex layer structure. The high-frequency wheel-rail vibration wave is attenuated through the CA mortar layer, which has the effect of vibration and noise reduction [3] to reach the cable trough to a low-frequency vibration wave. Further, the frequency of the vibration signal in the cable trough is concentrated within 100 Hz, as shown in Figure 13 and Table 4. This means that the wave used in this manuscript was also a high-frequency vibration wave. However, the ballastless track structure attenuates the high-frequency vibration wave to a low-frequency vibration wave. The authors in [62] conducted an  
Figure 13: Frequency-domain responses of Segment 1 and Segment 2.  
in-depth study of damage detection of ballastless track structures by using low-frequency and high-frequency waves, respectively, and showed that high-frequency vibration waves with frequencies of 1-20 kHz are attenuated to 500 Hz when they pass through the track structure and reach the detection point. This is more consistent with the results of this manuscript and shows that the method proposed in this paper is reliable. The peak frequencies and peak amplitudes of Segment 1 and Segment 2, marked by the blue circles in Figure 13a-c, are respectively listed in Table 4. The relative differences of peak frequencies and amplitudes between the two track segments are listed in the last column of these two tables. The peak frequencies of Segment 2 were slightly lower than those of Segment 1, and the peak amplitudes of Segment 2 were significantly higher than those of Segment 1. The reason for this phenomenon is that the stiffness of the ballastless track structure decreases due to the creation of interlayer debonding. As a result, the peak frequencies of the track structure decrease, and when subjected to the transient impact of passing-by trains, the vibration level of this track segment increases. These findings are coincident with the descriptions in [56]. The differences among the three graphs in Figure 13 may be ascribed to the longitudinal non-uniformity of the interlayer debonding thickness.