## 4 Analysis and Discussion
### Time-Frequency-Domain Analysis for Multi-Feature Extraction and Assessment
Figure 15: IMFs of a typical response of Segment 1. Further, the CAC values among the first six IMFs of Segment 1 and those of Segment 2 were calculated by using Equation (9) in Section 3.3. The CAC values of Segment 1 and Segment 2 in the current stage of monitoring are shown in Figure 20. The CAC represents the degree of correlation between two IMFs. When the track structure is in a state of interlayer debonding, the wheel-rail vibration signal waveform will definitely change. The change in signal leads to a change in IMF and, therefore, a change in CAC mode. Compared to the normal state of the track structure, interlayer debonding results in more reflective surfaces in the propagation path of the vibration, and thus the vibration signal is complicated. As can be seen by comparing Figure 20a,b, the interlayer debonding led to a complex CAC pattern. By comparing Figure 20a,b, it was found that the CAC pattern of Segment 2 obviously deviated from that of Segment 1, which is accordant to the fact that Segment 2 is in a debonding state while Segment 1 is in a normal state. The CAC pattern (the group of 36 CAC values) is also debonding-sensitive. In time-frequency-domain feature extraction, the CAC deviation from diagonal matrix was more sensitive to interlayer debonding defect because of neglecting the higher diagonal, which is named as active CAC instead of CAC as time-frequency-domain feature. The maximum ones among the local peaks and local energies in different frequency bands in Table 6 and this group of CAC values were used in the subsequent analysis of Section 4.5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Working** & **Frequency** & \multirow{2}{*}{**Local Peak**} & **Local Energy** & **Maximum** & **Maximum** \\  & **Conditions** & **Band** & & & **Local Energy** & **Local Energy** \\ \hline \multirow{4}{*}{Sensor 1} & Segment 1 & 0–11 & 28.99 & 1.88 & \multirow{2}{*}{28.99} & \multirow{2}{*}{4.64} \\  & Segment 11–80 & 8.55 & 4.64 & & & \\ \cline{1-1} \cline{2-6}  & Segment 2 & 0–35 & 439.70 & 115.00 & & \\ \cline{1-1} \cline{2-6}  & Segment 2 & 35–60 & 131.70 & 23.00 & 439.70 & 115.00 \\ \cline{1-1} \cline{2-6}  & Segment & 60–80 & 89.20 & 45.30 & & \\ \hline \multirow{4}{*}{Sensor 2} & Segment 1 & 0–25 & 41.00 & 8.96 & \multirow{2}{*}{88.55} & \multirow{2}{*}{33.70} \\  & Segment 25–80 & 88.55 & 33.70 & & & \\ \cline{1-1} \cline{2-6}  & Segment 2 & 36–80 & 445.00 & 125.00 & 445.00 & 125.00 \\ \hline \multirow{4}{*}{Sensor 3} & Segment 1 & 0–34 & 28.92 & 6.36 & \multirow{2}{*}{28.92} & \multirow{2}{*}{6.36} \\  & Segment 34–80 & 8.50 & 5.66 & & & \\ \cline{1-1} \cline{2-6}  & Segment & 0–4 & 434.70 & 12.70 & \multirow{2}{*}{434.70} & \multirow{2}{*}{99.70} \\ \cline{1-1} \cline{2-6}  & Segment 2 & 8–74 & 231.40 & 99.70 & & \\ \cline{1-1} \cline{2-6}  & & 74–80 & 74.32 & 22.80 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Local peak and energy in different frequency bands and maximum local peaks and energies. Figure 20: **(a)** The CAC values of Segment 1 in the current monitoring stage. **(b)** The CAC values of Segment 2 in the current monitoring stage.