# Dynamic Stability Assessment of High-Speed Railway Bridges Using Numerical Model Updating
## 4 Dynamic Stability Assessment for High-Speed Railway Bridges
### Dynamic Stability Assessment Using the Updated Numerical Models  
The dynamic stability of high-speed railway bridges is necessary in order to determine vibration serviceability and driving stability, and it is required by the high-speed railway design standards of Korea. In this study, dynamic stability assessment was conducted by using the updated numerical models in order to examine the effectiveness of the proposed numerical model updating method and updated numerical models. According to the high-speed railway design standards, dynamic stability is examined up to 1.1 times the design speed with a speed increment of 10 km/h [45]. In this study, however, moving load analysis was conducted for a speed of up to 430 km/h even though the design speed of the target bridges was 350 km/h. In the moving load analysis, the damping ratios estimated using the extended Kalman filter were used, and the speed was increased by 10 km/h in the 20 km/h to 430 km/h range. The maximum vertical displacement of the bridge, maximum vertical acceleration of the upper plate, and maximum vertical ir-regularity of the track according to the train speed were examined in the moving load analysis. Figure 8: Comparison of the measured and analyzed responses from the target bridges: (**a**) Imgi 2 nd Bridge; (**b**) Maeaji Bridge; (**c**) Hwalchun Bridge. In the field, an ambient vibration test was conducted by using a limited number of wireless sensors, and the measurement point roaming method was applied in order to measure the acceleration response at various points. The load conditions of high-speed railway bridges hardly changed due to the characteristics of high-speed trains. Therefore, responses at various points could be measured in the ambient vibration test of the high-speed railway bridges by using a limited number of sensors based on the measurement point roaming method, and the dynamic properties of the bridges could be estimated. The conclusions that can be obtained through the application of the proposed numerical model updating method for high-speed railway bridges are as follows:  
* It was confirmed that the method of updating the numerical model based on the iterative univariate search method enables numerical model updating through a small number of iterations without preparing separate differential functions. * The results of the moving load analysis that used the updated numerical model could obtain a response similar to the response in the time and frequency domains measured from high-speed railway bridges. * The results of the moving load analysis that used the updated numerical model showed that the field test of high-speed railway bridges can be replaced with numerical analysis. * It was confirmed that using the updated numerical model allows for the dynamic stability assessment of high-speed railway bridges. * It was found that the results of the field tests for high-speed railway bridges, which are difficult to conduct due to economic and physical limitations, can be predicted by using the proposed numerical model updating method. In this study, the applicability of the proposed numerical model updating method for various types of bridges needs to be further examined, as it was only examined for PSC box girder bridges. Furthermore, if further research on train-bridge interaction is conducted, the proposed method is expected to be useful in examining the maintenance and driving stability of high-speed railway bridges. Conceptualization, S.-W.K., D.-U.P. and S.-J.C.; Experimental test, S.-W.K., D.-U.P. and S.-J.C., Methodology, S.-W.K., D.-U.P. and J.-B.P. ; Software, S.-W.K., D.-U.P. and J.-B.P. ; Validation, S.-W.K., D.-U.P., S.-J.C. and J.-B.P. ; Visualization, S.-W.K., D.-W.Y. and D.-U.P. ; Investigation, S.-W.K., D.-W.Y., D.-U.P., S.-J.C. and J.-B.P. ; Writing-original draft, S.-W.K. and D.-U.P. ; Writing-review & editing, S.-W.K. and D.-U.P. ; Funding acquisition, S.-W.K. All authors have read and agreed to the published version of the manuscript.