## 3 Experimental Verifications
### Vibration Analysis of the Noise Barrier  
A noise barrier is an exterior structure designed to protect inhabitants of sensitive land use areas from noise pollution. The noise barriers are installed on both sides of the CRHtrain railway bridge to mitigate noise from the railway when a train is passing by. These platy structures usually suffer from strong suction induced by the CRH train under practical working conditions. Wind pressure when a high-speed train passes by can cause harmful vibrations to the noise barriers and decrease the designed service life. Figure 8 shows the experimental setups of the noise barrier vibration test. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Model 1** & **Model 2** & **Model 3** & **Model 4** \\ \hline
**Theoretical \(\left(\mathrm{Hz}\right)\)** & 6.41 & 40.17 & 112.43 & 220.31 \\
**Proposed Method \(\left(\mathrm{Hz}\right)\)** & 6.37 & 40.16 & 113.60 & 221.60 \\
**Laplacian Kernel \(\left(\sigma\right)\)** & - & 2.20 & 0.79 & 0.40 \\
**Amplification Factor \(\left(\alpha\right)\)** & - & 8 & 10 & 12 \\ \hline \end{tabular}
\end{table} 
Table 1: Identified modal frequencies and analysis parameters in the beam test. Figure 7: Vibration signals and their frequency spectrums extracted from the original video (blue line) and the magnified video (red line) along the jagged edge of the saw blade. The field test was conducted near the KunShan railway station, which is an important railway hub in East China. The height of the viaduct is about 12 m, and traditional contact sensors are difficult to install. Vision-based vibration extraction is considered a suitable alternative to analyze the dynamic responses of the noise barrier when a high-speed train passes by. The high-speed camera (Mode-5 KF04M, Agile Device Inc.) was placed below the viaduct at a distance of about 28 m, and the distance between the camera head and the target was set to 30 m. The tilt angle was estimated to be 26\({}^{\circ}\), and the error rate caused by the tilt angle was approximately 0.6%\(\sim\)0.8% [34]. The filming was begun shortly before the high-speed train arrived. The frame rate of the video was set to 232 fps, and the resolution of the image was 660 \(\times\) 880 pixels during the experiment. We selected two analysis areas of which the dimensions were 100 \(\times\) 500 pixels in the video for further vibration analysis. The first smooth area in the blue rectangle is a clean edge without any textures, and the edge in the red rectangle contains visible textures. The colorization optimization algorithm of [PERSON] et al. was employed to remove noise from textures on the boundary before deviation extraction. As shown in Figure 9, the colorization optimization [35] can help remove noise edge variations due to textures and satisfy the constant edge profile assumption. The employed Laplacian kernels in motion magnification were calculated by using finite element analysis [36]. The frequency spectra of the extracted waveforms before and after acceleration  
Figure 8: Noise barrier experiment setups: (**a**) the experiment environment; (**b**) experimental setup; (**c**) image captured by the high-speed camera and selected analysis areas. Figure 9: Selected textured edge and edge after colorization optimization. magnification are compared in Figures 10 and 11. The SVD results indicate that the first two decomposed components took over 92% of the energy in the analysis matrices, so the rest of the singular values were zeroed in the final low-rank approximation signals. The waveforms extracted from the magnified videos contained high-frequency vibrations. Three obvious peaks (10.42 Hz, 21.07 Hz, and 45.77 Hz) were found in the magnified smooth clean edge and the textured edge. Higher order peaks (21.07 Hz and 45.77 Hz) were not clearly found in the signals extracted from the original video files. The used Laplacian kernels and magnification factors are given in Table 2. The results confirm the successful enhancement of low-level vibration signals in the magnified videos.