# Brillouin Frequency Shift Sensing Technology Used in Railway Strain and Temperature Measurement
## 3 Methods of Test and Verification
### The Displacement Distribution and Changes over Time  
Based on the measurements of the distributed fiber optic sensing system that was used in this test, Figure 11 shows the strain data of the tested rail. The four areas of A, B, C, and D sustained strain, indicating that these places are more abnormal than others. The picture shows that the steel rail repeatedly experienced similar strain. The railway experienced greater strain at times where temperatures were higher (09:20-14:50) and lower strain when temperatures were lower. This explains the accumulation and release of the stress of the steel rail. The areas A, B, C, and D experienced high strain for long periods of time. Relevant railroad personnel should examine these abnormal spots.  
Figure 10: The strain distribution profile: the strain distribution varies because the restraining force is different in the unmovable area (on the right) and the movable area (on the left).  
In addition, with the large data calculation and combined analysis capabilities of the sensing system, we were able to calculate the measured strain difference (\(\Delta\varepsilon\)) in units of 0.5 m. Displacement was calculated by integrating the strain shown in Equation (6). Then, the simple rectangular rule was used to estimate values through Expression (7):  
\[D_{x}=\int\varepsilon_{x}dx+D_{0} \tag{6}\]  
\[D_{x}=0.5\cdot\sum\varepsilon_{x}+D_{0} \tag{7}\]  
where \(D_{x}\) is the displacement and \(\varepsilon_{x}\) is the strain difference at distance \(x\). Displacement already existed in the railway before installing the fiber. We focused on measuring the displacement change after installation, so there was no need to consider the previous displacement of the rail. In the calculation, the initial value of displacement was equal to zero, \(D_{0}=0\). Furthermore, the tested rail displacement was measured to be from \(-0.3\) to \(+0.4\) mm, as shown in Figure 12.  
Through the calculation of strain distribution data from Figure 11, we created Figure 12, which is easier to comprehend. This displacement distribution can be provided to railway management to assess abnormal railway data. In Figure 12, there are some significant regions--both the stretched (red) and compressed (blue) regions--that are different from other regions with zero displacement.  
We tried to study these abnormal regions in the context of the overall structure of the track. We know that the main function of the ballast and track bed is to maintain rail elasticity, disperse train loads, and absorb driving shock, but the measured results of our study showed that the rail's recovery elasticity is insufficient. In addition, our chosen verification field was a section where the operational line was recently converted from ground into an elevated section; during the verification days, the track adjustment and ballast compaction were still in progress at night. Therefore, we speculate that the abnormal displacement of the rail may have been due to the uncompleted compaction of the ballast or track slab. However, this inference needs further research and verification.  
Figure 11: The 48 h strain distribution: the strain distribution of the tested rail over a 48 h period, showing four abnormal areas of A, B, C and D.