# Evaluation of High-Speed Railway Bridges Based on a Nondestructive Monitoring System
## 3 Evaluation of the Bridge Condition Using SHM Monitoring Data
### Evaluation of the Bridge Gorder Vibration Behavior
Furthermore, the Bessel filter cut-off frequency of 30 Hz is applied to remove the noise measurements of the accelerometer [21]. It is noticed that the maximum acceleration occurred at points 1 and 5 for the passage and opposite directions at 406 km/h speed, respectively, with values within the design limits as shown in Table 1. While there is no high relative change at points 2 to 4, the RMS of the 360 km/h is smaller than that of the 406 km/h on passage way, while _vice versa_ in the opposite way except for point 5. The maximum torsion occurred at point 5 at a speed of 406 km/h with a value very close to the design value (Table 1). Thus, it is recommended to limit the train speed to 400 km/h only. In addition, the effective torsion test should be assessed at the end points of the bridge (point of maximum torsion). [PERSON] _et al._[3; 17] concluded that the quadratic linear fitting for the maximum and RMS are calculated for the acceleration measurements can be used to detect the performance of high-speed railway bridges based on one span monitoring. Herein, this method is applied to detect and check the performance of the bridge due to different speeds on the two ways of the track. The maximum and RMS of 150 acceleration of the original measurements are shown in Figure 7. The quadratic linear fitting is suitable for the maximum acceleration (Figure 7a), while the RMS shows no correlation between the passage and opposite ways. Therefore, the maximum acceleration fitting can be used to check the safety of the bridge. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multicolumn{4}{c}{**Acceleration (m/s\({}^{2}\))**} & \multicolumn{4}{c}{**RMS (m/s\({}^{2}\))**} & \multicolumn{4}{c}{**Max Torsion**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Passage**} & \multicolumn{2}{c}{**Opposite**} & \multicolumn{2}{c}{**Passage**} & \multicolumn{2}{c}{**Opposite**} & \multicolumn{2}{c}{**(rad/s\({}^{2}\))**} \\ \cline{2-10}  & **360** & **406** & **360** & **406** & **360** & **406** & **360** & **406** & **360** & **406** \\ \hline
1 & 0.104 & 1.251 & 0.196 & 0.079 & 0.006 & 0.035 & 0.008 & 0.004 & 0.059 & 0.191 \\
2 & 0.169 & 0.183 & 0.231 & 0.088 & 0.008 & 0.009 & 0.011 & 0.006 & 0.072 & 0.191 \\
3 & 0.244 & 0.319 & 0.279 & 0.146 & 0.010 & 0.012 & 0.013 & 0.007 & 0.079 & 0.037 \\
4 & 0.569 & 0.622 & 0.252 & 0.239 & 0.014 & 0.016 & 0.012 & 0.008 & 0.244 & 0.055 \\
5 & - & 0.401 & 0.169 & 2.497 & - & 0.013 & 0.008 & 0.035 & - & 0.343 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum acceleration, root mean square (RMS) and torsional acceleration for the filtration of vibration measurements. Figure 7: Cross-correlation between the passage and opposite way responses for 360 km/h. (**a**) cross-correlation maximum acceleration; (**b**) cross-correlation route mean square (RMS) acceleration. In this case, the fitting equation is used to predict the opposite way measurements for the 400 and 406 km/h, as shown in Figure 8. The correlation coefficient of the measured maximum values and predicted values with 400 and 406 km/h is 0.999 and 0.998 for opposite accelerations, respectively. The results indicate that good cross-correlation exists between the maximum values of the opposite way at the two train speeds. Herein, the control chart can be used to monitor the changes in the vertical accelerations caused by deterioration of the vibration behavior. Firstly, the condition index \(e\) (\(e\) = Max (measurements) \(-\) Max (prediction)) for early warning of abnormal vibration behavior is defined as the difference between the measured and predicted maximum values of the accelerations in the opposite way. Then, a mean value control chart is employed to monitor the time series of \(e\) with regard to the opposite accelerations. For online monitoring, the controlling parameter is chosen so that, when the structural vibration is in good condition, all observation samples fall between the control limits.