# Experimental Validation of Non-Marker Simple Image Displacement Measurements for Railway Bridges
## 5 Verification Results of Field Tests  
### Measurement Results of Bridge A  
For bridge A, the bridge midspan during the passage of six- and two-car trains was obtained by non-marker image and laser measurements. As per the estimation results, it is difficult to apply the non-marker image measurement to some bridges with a camera distance of 16.5 m.  
Figure 19 shows the measured displacement responses during the train passage. The maximum amounts of deflection were \(\sim\)5.5 and 7.2 mm when the six- and two-car trains passed, respectively. The measuring distance in this environment was \(\sim\)9.2 mm  
Figure 18: Difference in measurement accuracy due to turning the LED light on and off (standard deviation of contact type and non-marker image measurement responses).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Situation** & **Time** & **Illuminance (klx)** & **Applicability** \\ \hline \multirow{4}{*}{Outdoor/Sunny} & Noon & 100 & \(\Circuit\) \\  & 10 AM & 65 & \(\Circuit\) \\  & 3 PM & 35 & \(\Circuit\) \\  & 1 h before sunset & 1 & \(\Circuit\) \\ \hline \multirow{4}{*}{Outdoor/Cloudy} & Noon & 32 & \(\Circuit\) \\  & 10 AM & 25 & \(\Circuit\) \\ \cline{1-1}  & 1 h after sunrise & 2 & \(\Circuit\) \\ \cline{1-1}  & Surrise/sunset & 0.3 & \(\times\) \\ \hline Under the street light & Night & 0.05-0.1 & \(\times\) \\ \hline Moonlight & Night & 0.0005–0.001 & \(\times\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Guideline for general illuminance and brightness [29].  
per pixel. Thus, the maximum displacement corresponds to 0.6-0.8 pixels, and sufficient displacement occurs compared with the measurement limit accuracy (0.03 pixels in total amplitude). The results of the non-marker image measurement correlate with those of the laser measurement.  
Table 9 shows the maximum displacements obtained by each measurement system during the two tests. Moreover, the error of the maximum displacement of the non-marker image measurement, using the laser measurement as the correct value, is shown. The error of the maximum displacement when the train passed was \(\sim\)3% or less relative to the laser measurement. Therefore, under the current measurement conditions, it can be confirmed that the maximum deflection can be sufficiently evaluated by non-marker image measurement.  
Figure 20 shows examples of calculating the deflection shape of bridge A during the train passage by taking advantage of the non-marker image measurement. Here, 44 measurement points were placed in the longitudinal direction of the bridge, and the deflection at the time of the train passage was calculated at each measurement point. The deflection shape varies based on the bogie position of the passing vehicle. Because the texture of the measurement surface is relatively clear at all points on the steel bridge, the dynamic behavior of the girder can be spatially captured by calculating the deflection shape in this manner. Since the bridge is a simple support girder on which the train runs at a relatively low speed, the bending behavior when the train passes is relatively simple, and depends only on the bogie position. These applications may be useful for understanding the dynamic behavior of continuous girders and cable-stayed bridges having more complex structural forms.  
Figure 19: Comparison of displacement measurement results of bridge A during train passage: (a) six-car train and (b) two-car train.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Tests** & \
\begin{tabular}{c} **Maximum Displacements** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Errors** \\ **(\%)** \\ \end{tabular} \\ \hline Laser measurement & & 5.47 & - \\ \hline non-marker image measurement & & 5.64 & 3.1 \\ \hline Laser measurement & & 7.16 & - \\ \hline non-marker image measurement & & 7.06 & 1.4 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Maximum displacements of bridge A.