# Experimental Validation of Non-Marker Simple Image Displacement Measurements for Railway Bridges
## 3 Processing and Test Methods
### Field Measurements Method  
In this study, two railway bridges with different properties were investigated. Table 3 and Figure 5 show the outline of bridge A of the local low-speed railway that was measured for confirmation in this study. It comprises two steel I girders with a 20 m span length and a 1.4 m girder height. For the main girder, two steel I girders with a length of 10 m are connected with bolts at the midspan. Wooden sleepers are directly laid on the upper flanges of the girder. In the field test, the accuracy of non-marker image measurement was confirmed by comparing it with the existing displacement measurement system using a laser Doppler velocimeter, as explained below. The train speed was \(<\)100 km/h and the contribution of the dynamic response was insignificant compared with that of the high-speed railway bridge; the bridge has a single track and is simply supported, and the behavior of train passage is relatively simple. Moreover, a steel bridge constructed by connecting several members has a clear subset texture (surface pattern), thus making it relatively easy to ensure accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Equipment** & **Product Models** & **Companies** & **Specifications** \\ \hline \multirow{2}{*}{Contact displacement gauge} & \multirow{2}{*}{CFP-10} & Tokyo Sokki & Range: 10 mm \\  & & (Shinagawa, Tokyo, Japan) & Output:5 mV/V \\ \hline \multirow{2}{*}{Data recording} & Ni cDAQ-9172 & National Instruments & \\  & Ni9220 & Japan & Sampling rate: 2000 Hz \\  & LabVIEW & (Minato, Tokyo, Japan) & \\ \hline \multirow{2}{*}{Camera} & \multirow{2}{*}{Flare 4M180-MCX} & IO industries & \\  & & (Hamamatsu, Shizuoka, Japan) & Resolution: 2048 \(\times\) 800 \\ \hline \multirow{2}{*}{Recorder} & DVR Express & IO industries & \\  & CORE2 & (Hamamatsu, Shizuoka, Japan) & Sampling rate: 350 Hz \\ \hline \multirow{2}{*}{Lens} & \multirow{2}{*}{LM8 XC2} & Kowa Company. Ltd. & \\  & & (Nagoya, Aichi, Japan) & Focal length: 8.5 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of the measuring equipment. Figure 4: Layout of the measuring equipment: (**a**) 35 Hz excitation, (**b**) 120 Hz excitation. Table 4 and Figure 6 show the specifications and pictures of the high-speed railway bridge B that was measured. Bridge B is a two-span continuous prestressed concrete rigid frame bridge whose dynamic behavior under train passage is relatively complicated; the length of the measured span is 89.2 m. Because it is a concrete box girder bridge, there are few clear textures on the bridge taken by non-marker image measurement. Therefore, it is difficult to ensure the displacement estimation accuracy by DIC. Moreover, the maximum speed of bridge B is 260 km/h, the frequency at which displacement occurs is higher than that of bridge A, and a contribution of the dynamic response is anticipated [26; 27]. For bridge B, the point 34.5 m from the starting point was set as the target point for deflection measurement. The height from the ground to the bottom of the girder is 5.7 m, and other measurement devices that require space were placed beneath the girder. Table 5 shows the specifications of the measuring equipment on bridge A, and Figure 7 shows the installation status of each measuring device. In addition to the suggested \begin{table}
\begin{tabular}{c c} \hline \hline
**Types** & **Simply Supported Bridge** \\ \hline Maximum speed & 260 km/h \\ Span length & 89.2 m + 77.2 m \\ Girder height & 1.5–3.2 m \\ Girder type & Concrete box \\ Track & Ballastless double track \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Specifications of bridge B.  
Figure 5: Outline of bridge A: (**a**) bridge span and sketch, (**b**) view of bridge A.