# Dynamic Response Analysis of Overpass Ramp Based on Grey System Theory Model
## 5 Conclusions  
This study used the MIDAS CIVIL NX finite element analysis software to model and conduct numerical simulations on the ramp bridge of the Fuxing Interchange Bridge. Reasonable loading methods and conditions were determined. Based on this, experimental research on the ramp bridge's displacement, strain, and acceleration was conducted. Finally, the grey prediction model was used to predict the maximum dynamic deflection, maximum dynamic strain, and vibration acceleration at a speed of 60 km/h. The following conclusions were drawn:  
By comparing the maximum dynamic deflection, acceleration, and dynamic strain when passing through the monitoring section at different speeds, the dynamic strain and dynamic deflection caused by vehicle excitation were generally minor. As the vehicle speed gradually increased, there was a clear trend of increasing dynamic deflection, dynamic strain, and vibration acceleration at the midpoint measurement point. Under the action of moving vehicle loads, the bridge's maximum vertical displacement value, strain, and vibration acceleration all met the design requirements specified in the relevant codes.  
Figure 14: Comparison of predicted values and simulated values: (**a**) comparison of maximum dynamic deflections; (**b**) comparison of maximum dynamic strains; and (**c**) comparison of vibration accelerations.  
An analysis of the impact coefficient test results under different vehicle speeds and excitations revealed that the higher the vehicle speed, the greater the impact coefficient. When the vehicle's driving radius R increased from 265 m to 275 m, the vertical deflection impact coefficient at the midpoint of the side span was approximately symmetrical. When the driving radius was smaller, the impact coefficient was the largest. The experimental data indicate that driving on the inside of the bridge has the greatest impact on the vertical deflection impact coefficient.  
Considering the speed limit on the ramp, the maximum dynamic deflection, maximum dynamic strain, and vibration acceleration at the monitoring section were predicted using a grey prediction model when the vehicle speed ranged from 20 to 60 km/h. Subsequently, finite element software was utilized to simulate the maximum dynamic deflection, maximum dynamic strain, and vibration acceleration at the mid-span measurement point as a loaded vehicle passed through at 30 to 60 km/h speeds. The difference between the grey prediction and finite element simulation values was relatively small, indicating a good prediction result.  
Conceptualization, Y.J. and G.L.; methodology, G.L.; software, G.L.; validation, G.L., Y.J., and W.X.; formal analysis, Y.J.; investigation, Y.J.; resources, Y.J.; data curation, G.L.; writing--original draft preparation, Y.J.; writing--review and editing, Y.J.; visualization, Y.J.; supervision, W.X.; project administration, Y.J.; funding acquisition, Y.J. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Fundamental Research Funds for the Central Universities (2572023 CT17-05) and the Department of Transportation of Heilongjiang Province (HJK2023B008-2).  
Not applicable.  
Our data came from the civil engineering intelligent monitoring cloud network platform provided by Changsha Yijian Information Technology Co., Ltd.  
Thanks are extended to [PERSON] for helping to complete the dynamic load test process, and to [PERSON] for reviewing the writing.  
The authors declare no conflicts of interest. The funders collected and interpreted the data in the study design.