## 3 Comparative Study
### Results and Discussions  
It is worth mentioning that in this research, the variation in arrival time has been neglected by integrating the arrival time so that the waveforms are aligned to compare their shapes. Significant attenuation in signal amplitude for both FBG and AE data, due to the damage incurred on the rail, is observed as shown in Figure 7. This observed attenuation is because the propagation of UGWs is interfered with causing some waves  
Figure 6: The sensors arrangement for (**a**) the intact condition; (**b**) the damaged condition with an artificial crack; (**c**) the damaged condition covered with blu-tack adhesives. to reflect or refract into the damaged area. For the FBG data, when a single artificial crack exists, the amplitude of the received signals is compromised by approximately 30%; when the area is covered by blu-tack adhesives the amplitude drops sharply till it reaches only half of that in the intact case, mainly because the large volume of blu-tack has absorbed much of the energy of the UGWs. Although FBG and AE data in the time domain have similar shapes to the waveforms, the amplitude decline can be less notable for the AE time-domain data. Moreover, it is noted that the first arrival waves for FBG data are more distinguishable compared to AE data. After the first arrival waves, the reflected waves can also be recognized. However, due to the complexity of the railway shape the sources of the reflective waves after the first arrival waves are untraceable. The noise level of AE sensors interfered the receiving quality. Thus, it is fair to conclude that FBGs have higher sensitivity in the time domain of detecting the existence of damage, while blu-tack adhesives and cracks have a similar effect on the propagation of the UGWs. The normalized signals shown in Figure 8 are obtained by FBGs, demonstrating the variation in time-domain characteristics caused by the crack and the bump on the railway surface. Due to the existence of the damage, the first arriving wave packet has shown obvious delay; as for the later arriving packet possibly because of the reflections, a significant difference was observed when compared to each other. It can also be seen that the effects caused by cracks and bumps are quite similar, both resulting in the guided wave arrival delay and amplitude decay. The spectrums of both the FBG and AE signals are obtained through Fast Fourier Transform (FFT). Only slightly visible variations have been observed in the spectrums obtained from the experiments (Figure 9). The central frequency is approximately 250 kHz, which indicates that the UGW receiving quality is eligible. Due to the presence of the damage, the oscillation amplitude of the spectral amplitude shows a visible decline. However, the artificial crack and the blu-tack adhesives have dispersed the central frequencies, resulting in wider bandwidths of frequencies. Additionally, the noise level of FBG data is slightly higher than that of AE data, mainly caused by the fluctuations of the emitting laser wavelength which is mostly inevitable due to the limitation of the instrument precision. Figure 7: The time-domain signals under different conditions acquired by: (**a**) FBG sensors and (**b**) AE sensors; (**c**) Waveform comparison between FBG and AE signals under the intact condition. Nevertheless, some low-frequency noise would not severely disrupt the subsequent analysis in this case. The spectrum amplitude has seen a slight drop in 'Cracked' and 'Bump' conditions, mainly because the waveform energy has reduced because of the defects on the propagation route. Figure 8: The UGW signals obtained by FBGs under different rail conditions. Figure 9: The frequency-domain plotting of the experimental data: (**a**) FBG data; (**b**) AE data. Through the analysis in this section, it can be concluded that the defects on the rail will affect the UGW signals in time and frequency domains. With such observations, various damage indices have been proposed, such as waveform-distortion-based and energy-based indices [1].