## 3 Aerodynamic Flutter Stability Robustness Evaluation
### Robustness Calibration of Aerodynamic Flutter Stability  
#### 3.3.1 Flutter Robustness Analysis of Eight Completed Bridges  
Taking eight representative long-span suspension bridges as examples, including Nansha Bridge, Zhoushan Xhiounen Bridge, Runyang Yangtze River Bridge, Jiangyin Yangtze River Bridge, Tsing Ma Bridge, Huangpu Bridge, Humen Bridge, and Haicang Bridge, flutter robustness analysis and comparisons were carried out. The key design parameters and dynamic characteristics for the eight existing bridges are listed in Table 1. The mean values and standard deviations of the four fundamental random variables of these eight bridges are listed in Table 2.  
Based on the equivalent central point method and equivalent checking point method, the robustness evaluation of flutter stability for these eight bridges was conducted, and the calculation results are summarized in Tables 3 and 4. The return periods of the reference wind speed that the eight existing bridges could resist ranged from 584 years to 12,018 years, which were much longer than the service life. Therefore, these eight bridges all possessed the ability to resist the maximum wind speed that is unforeseen or unusual. Figure 1 shows the comparison of the reliability indices calculated using the equivalent central point method and equivalent checking point method. It can be seen from the figure that the relative calculation errors of the reliability index calculated using the equivalent central point method and equivalent checking point method were between 1.06% and 1.87%. The equivalent central point method could be adopted for the purpose of simplified calculations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Bridge** & **Main Span** & **Girder Type** & **Width of** & **Depth of** & **Vertical** & **Torsion** \\  & **(m)** & **Girder (m)** & **Girder (m)** & **Girder (m)** & **(Hz)** & **(Hz)** \\ \hline Nansha Bridge & 1688 & Box & 49.7 & 4.0 & 0.1018 & 0.2201 \\ Xihoumen Bridge & 1650 & Twin box & 36.0 & 3.5 & 0.1001 & 0.2323 \\ Runyang Yangtze River Bridge & 1490 & Box & 38.7 & 3.0 & 0.1241 & 0.2308 \\ Jiangyin Yangtze River Bridge & 1385 & Box & 36.9 & 3.0 & 0.1418 & 0.2625 \\ Ising Ma Bridge & 1377 & Truss & 41.0 & 7.6 & 0.1050 & 0.2680 \\ Huangpu Bridge & 1108 & Box & 41.7 & 3.5 & 0.1502 & 0.3180 \\ Human Bridge & 888 & Box & 35.6 & 3.0 & 0.1715 & 0.3612 \\ Haicang Bridge & 648 & Box & 36.6 & 3.0 & 0.1680 & 0.4570 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Key design parameters and fundamental frequencies of vertical bending and torsion modes for eight existing bridges. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Bridge** & \(\mu_{C_{f}}\) & \(\sigma_{C_{f}}\) & \(\mu\mu_{J}\) & \(\sigma_{U_{f}}\) & \(\mu_{C_{b}}\) & \(\sigma_{C_{b}}\) & \(\mu_{U_{b}}\) & \(\sigma_{U_{b}}\) \\ \hline Nansha Bridge & 1 & 0.05 & 70.7 & 5.30 & 1.16 & 0.08 & 27.04 & 5.41 \\ Xihoumen Bridge & 1 & 0.05 & 95.0 & 7.13 & 1.16 & 0.08 & 33.59 & 6.72 \\ Runyang Yangtze River Bridge & 1 & 0.05 & 55.1 & 4.13 & 1.16 & 0.08 & 23.05 & 4.61 \\ Jiangyin Yangtze River Bridge & 1 & 0.05 & 61.0 & 4.58 & 1.16 & 0.08 & 22.17 & 4.43 \\ Tsing Ma Bridge & 1 & 0.05 & 99.0 & 7.43 & 1.16 & 0.08 & 40.56 & 8.11 \\ Huangpu Bridge & 1 & 0.05 & 87.2 & 6.54 & 1.16 & 0.08 & 28.93 & 5.79 \\ Humen Bridge & 1 & 0.05 & 79.3 & 5.95 & 1.16 & 0.08 & 29.29 & 5.86 \\ Haicang Bridge & 1 & 0.05 & 95.0 & 7.13 & 1.18 & 0.08 & 31.39 & 6.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean values and standard deviations of fundamental random variables for eight existing bridges.