# Experimental Validation of Non-Marker Simple Image Displacement Measurements for Railway Bridges
## 3 Processing and Test Methods
### Field Measurements Method
\begin{table}
\begin{tabular}{c c} \hline \hline
**Types** & **Simply Supported Bridge** \\ \hline Maximum speed & 100 km/h \\ Span length & 20 m \\ Girder height & 1.4 m \\ Grid type & I type steel girder \(\times\) 2 \\ Track & Wooden steeper single track (without slab) \\ Moment of inertia of area & 0.062 m\({}^{4}\) \\ Frequency & 13.03 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specifications of bridge A.  
Figure 6: Outline of bridge B: (**a**) bridge span and sketch, (**b**) view of bridge A.  
method, a laser Doppler velocimeter (referred to as laser measurement) [6] was used to measure the girder deflection during the train passage to verify the accuracy of the proposed non-marker image measurement. Laser measurement estimates the displacement by integrating the measurement response of a laser Doppler velocimeter. Furthermore, the laser Doppler velocimeter has a built-in acceleration sensor, making it possible to separate the vibration of the meter itself from the measurement response [6; 27]. For non-marker image measurement, a video camera was installed 16.5 m from the bridge such that the entire bridge could be seen on the screen. A single vertical pixel in the image taken under the measurement conditions corresponds to a 9.2 mm vertical distance at the bridge position. In the non-marker image measurement, the displacement at the midspan was measured for verification with a different measurement method, and the deflection shape of the girder was measured by taking advantage of the non-marker image measurement. In measuring the deflection shape of the girder, 44 points were set at equal intervals along the longitudinal direction of the girder as measurement points, and the displacement was calculated at each position. Two passing trains (6 cars at 45 km/h and 2 cars at 35 km/h) were involved. The measurement was performed between 11:00 and 15:00. The weather was cloudy and there was almost no wind. Figure 7: Installation status of each measuring device for bridge A. \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 & & \\ by integrating the & & Non-contact \\ vibration velocity & & With reflective marker \\ measured with a laser & & Sampling rate: 500 Hz \\ Doppler velocimeter & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Specifications of the measuring equipment on bridge A. Figure 8 shows the installation position of each method on bridge B, and Table 6 shows the equipment specifications and installation status of each displacement measurement method performed on the bridge. The bridge displacements for bridge B during the train passage were simultaneously measured by four measurement methods: a ring-type gauge, a laser [6], non-marker image measurement A (industrial camera), and non-marker image measurement B (compact digital camera). Non-marker image measurement B used the high-speed shooting function of a general compact digital camera. This is a scenario that assumes simple measurement using a digital camera carried on a portable structure. The ring-type gauge and laser measurements were undertaken by directly arranging the equipment under the measurement point. In the ring-type gauge, a jig was attached to the underside of the girder, and a piano wire was stretched between the gauge and the jig to measure the displacement when the train passed the gauge output. For non-marker image measurements A and B, cameras were installed 50 and 20 m from the girder measurement point, and the side surface of the girder was examined. The girder displacement was estimated by DIC using the existing contrast of the surface of the measurement point (side surface of the girder). The measurement sampling of the bridge displacement was 1 kHz for the ring-type gauge and the laser, 200 fps for the non-marker A (an industrial camera), and 60 fps for the non-marker B (digital camera).