# Experimental Validation of Non-Marker Simple Image Displacement Measurements for Railway Bridges
## 4 Verification Results by Model Bridge  
### Measurement Results  
Figure 9 shows the displacement responses obtained by non-marker image measurement and contact measurement when the midspan was vibrated at 35 Hz. Here, subset A was set for the model bridge web with a few measurement surface patterns such that the conditions were the strictest. Because the vibration applied was close to the resonance frequency in the primary deflection mode, the displacement amplitude was the highest at Ch3 in the midspan, and smaller at Ch0 and Ch6 near the supports. The maximum displacement amplitude was \(\pm\)50 \(\upmu\)m at Ch3 and the minimum was \(\pm\)25 \(\upmu\)m at Ch0 based on the measured values of the contact displacement meter. Therefore, on the measured image, the Ch3 measurement was a maximum of \(\pm\)0.035 pixels, whereas the Ch0 measurement was a minimum of \(\pm\)0.017 pixels.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Measurement Methods** & **Measurement Principles** & **Specifications** \\ \hline Self-vibration correction laser & & \\ Doppler velocimeter & & \\ (laser measurement) & & \\ \hline Displacement is calculated & Non-contact \\ by integrating the & With reflective marker \\ vibration velocity & Sampling rate: 500 Hz \\ measured with a laser & Measurement distance: \\ Doppler velocimeter & & 0.1–100 m \\ \hline Reflective marker, Doppler meter & & \\ \hline \hline \end{tabular} \
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{Non-marker image measurement A} & \multicolumn{1}{c}{Resolution:} \\ \multicolumn{1}{c}{} & 4096 \(\times\) 2160 pixels \\ Displacement is calculated & Camera: Flare \\ from images by DIC & 4M180-MCX \\ (Section 3.1) & Sampling rate: 200 fps \\ Lens: wide-angle or & standard \\ PC-controlled industrial camera & & \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{Non-marker image measurement B} \\ \hline Displacement is calculated & Resolution: \\ from images by DIC & 2048 \(\times\) 1088 pixel \\ Camera: DSC-RX1004M \\ Sampling rate: 60 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._The displacement responses obtained by non-marker image measurement and contact displacement measurement were similar at all measurement points. However, a long periodic error was confirmed, such that the maximum amplitude fluctuated in the non-marker image measurement. These errors may be attributed to the vibration transmitted through the laboratory floor, which shook the tripod or camera. Moreover, the responses of Ch2, Ch4, and Ch5 of non-marker image measurement were mediated by random noise; the conversion of these errors from the maximum amplitude was \(\sim\)20 \(\upmu\)m. In Ch6, the displacement amplitude of the non-marker image measurement was smaller than that of the contact measurement, and random noise was observed.  
To examine the effect of lens aberration and position in the image on these measurement errors, the number of pixels at each measurement position was converted from the I-digit height at each measurement point; however, the error due to aberration did not exist at all points. Thus, the error was not attributed to the position of the object in the image. Furthermore, as in the case of Ch6, Ch0 is located at the edge of the image, and has a small measurement error. This confirms that the error is not specific to the object position in the image. Another effect is that the brightness distribution in the measurement area is biased toward a certain value and does not have sufficient variance. In particular, Ch6 appears to be white in Figure 6, and so-called overexposure occurred. Therefore, when estimating the displacement amount, its measurement error is considered to be high because of the characteristics of the overexposed part due to reflection, in addition to the surface pattern peculiar to the structure. Thus, in practical application, it is necessary to predict the overexposed areas in advance, exclude them from the measurement points, and perform interpolation using the peripheral measurement points.