# 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 Girders' Train Responses  
The measured vertical strain histories of the monitoring points of the passage way for the train speeds 290 and 406 km/h are presented in Figure 9a,b. The vertical strain of the mid-span point of passage and opposite ways for different train speeds are compared in Figure 9c,d. As the train speeds increase to 290, 360, 400 and 406 km/h, the strain responses (\(dt\)) decrease to 2.1, 1.93, 1.64 and 1.61 s, respectively. This shows that the time of static strain responses decreases by 23.33% when the speed changes from 290 and 406 km/h. In addition, the maximum strain response in the passage and opposite ways occurred at a speed of 290 km/h. The results as such show that the static and dynamic behavior of the bridge is higher with low train speeds. In addition, the strain measurements of the bridge points are highly correlated (0.95) with each speed change. This means that the strain measurement of the mid span point can be used to detect the performance of the whole bridge. This situation will decrease the cost of the monitoring system due to the use of one monitoring point only. The high correlation (0.99) of strain response for the passage and opposite ways occurred at 400 and 406 km/h. It means that the strain response of the two speeds is approximately equal in the static response. However, to show clearly the relationship between dynamic and static response of the bridge, the dynamic increment factor should be calculated and analyzed. The Savitzky-Golay finite impulse response(FIR) smoothing filter is applied to detect the static strain of the bridge. The first polynomial order with 101 frame size is utilized in this study. Figure 10a shows the strain measurements and filter data of the mid span of  
Figure 8: Predicting the effect of cross-correlation between maximum values of accelerations by using quadratic polynomials. (**a**) 400 km/h; (**b**) 406 km/h. passage direction with a train speed of 406 km/h. Therefore, the dynamic increment factor (DF) can be calculated as follows [22; 23]:  
\[\mathrm{DF}=1+\left(\frac{\mathrm{A_{dyn}}}{\mathrm{A_{stc}}}\right) \tag{2}\]  
where \(\mathrm{A_{dyn}}\) and \(\mathrm{A_{stc}}\) are the maximum absolute of dynamic and static amplitude of the strain, as shown in Figure 10a. The dynamic factors of passage (P) and opposite (O) directions for the monitored points are illustrated in Figure 10b. The dynamic factor calculation shows that the DF of 290 km/h train is higher than other train speeds at the passage and opposite directions. Furthermore, the DF of the opposite direction is higher than the passage direction with all train speeds except point (P3) with speeds of 400 and 406 km/h. From Figure 10b, it can be seen that the DFs for the development speeds are less than two. It means that the dominant performance of the bridge is static with speeds of 360, 400 and 406 km/h at all  
Figure 10: Measured static strain and dynamic factor of the strain. (**a**) measured and filtered static strain; (**b**) dynamic factor of the monitoring points. Figure 9: Strain measurements of the main girder induced by high-speed train. (**a**) passing response points for 290 km/h; (**b**) passing response points for 406 km/h; (**c**) passage response mid span points; (**d**) opposite response mid span points. monitoring points, while the dynamic performance occurred at the opposite monitoring direction with train speed 290 km/h and point (O1) with train speed 400 km/h. These results indicate that the static behavior increases with increased train speeds. Therefore, the fatigue and frequency behavior should be studied to investigate the safety of the bridge under high train speed effect. Herein, the cross-correlation evaluation is used to predict the dynamic behavior of strain contents. The same conditions used in the acceleration analysis are used in this part. Figure 11 presents the cross-correlation and the cubic fitting of the maximum dynamic of strain measurements.