# Optical Fibres for Condition Monitoring of Railway Infrastructure--Encouraging Data Source or
## 4 Measurements and Results
### Signal Pattern and Properties of Two Trains in the Same Composition at the Same Channels (Location)  
While the signal pattern differs for the same train journey among the channels, a question arises on whether the scattering process is similar for the same train composition at the same channel where the time difference between the two train rides is approximately one hour. The comparative analysis reveals a completely different scattering process taking place in all the channels displayed in Figure 5a-e. While the pattern seems to correlate for at least both the train journeys in the same train composition in the respective channel, it differed among the channels significantly even though the travelling speeds did not vary much. The scatterings shown in Figure 5a,c are almost congruent for both trains, showing that they had a similar impact on the signal. The same \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Raw Signal**} \\ \cline{2-6}  & **300** & **325** & **350** & **375** & **399** \\ \hline Min (a.u.) & 13,518 & 15,949 & 19,649 & 12,111 & 10,709 \\ Max (a.u.) & 24,915 & 23,556 & 24,561 & 24,473 & 24,768 \\ Mean (a.u.) & 23,281 & 19,283 & 22,411 & 21,465 & 22,791 \\ SD (a.u.) & 474 & 354 & 317 & 796 & 688 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical values of the measurement as a train passes through channels 300, 325, 350, 375 and 399. Figure 4: The backscattered intensity of the same train journey in 5 consecutive channels distributed equidistantly. also applies, in a diluted form, to the train journeys in Figure 5b,d,e, regardless of the contrasting signal pattern between the channels. Figure 5: Raw backscattered signal of two train rides in the same train composition on the same day in different channels (locations). (**a**) Channel 300; (**b**) Channel 325; (**c**) Channel 350; (**d**) Channel 375; (**e**) Channel 399. On analysis, the signal two circumstances are striking: (1) Channel 325 showed the least distinct scattering and, (2) while the values for the first four channels do not fall below zero, this was not true for Channel 399, where the smallest value was far below zero (\(-4552\)). The statistical values of both train rides are listed in Table 3.  
The results show that approaching trains, regardless of type, composition, speed and condition, have an immediate impact on the scattering process taking place in the fibre, resulting in a changed signal pattern in the time-domain. To determine whether the frequency response of the signal also changes due to the impact of a train, spectrograms were generated for a result visualisation using Matlab. In the first step, the signal was divided into overlapping segments and afterwards each segment was windowed with a Kaiser window (we used the default settings from Matlab). Subsequently, a short-time Fourier transform was computed, and the results were concatenated. The length of the segments (time resolution) and the amount of overlap between adjoining segments can be varied. In this case, we have chosen an overlap (specified as a percentage of the segment length) of 50%, with a time resolution of 78.4 ms. The frequency resolution was 32.7391 Hz. In basic terms, this is a histogram in a power-frequency space where a specific frequency appears brighter and \"hotter\" for as long as it persists in the signal while the signal is evolving. Based on the Nyquist theorem, the sampling rate of a signal must be at least twice the highest analogue frequency component. The utilised system had a sampling rate of 2500 samples per second, which meant that the highest detectable frequency was 1.25 kHz. Spectrograms were calculated for the same channels as in the figures below. On the left, the spectrogram of Train Journey 1 is depicted and on the right Train Journey 2 can be seen. The \(y\)-axis represents the frequency of the signal and the \(x\)-axis represents the time.