## 5 Conclusions  
The wind-resistant robustness of bridges is defined as the ability of a bridge to resist the maximum wind speed that is unforeseen or unusual. The return period of the maximum wind speed that a bridge can resist was used to represent the wind-resistant robustness index. Aiming at the problem of flutter robustness evaluation, a stochastic model of the flutter safety domain determined by four random variables was established. Flutter robustness analysis of eight existing long-span suspension bridges and two long-span suspension bridges to be built was carried out. The robustness evaluation results showed that 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. The flutter robustness of the two bridges to be built was relatively low, and the return periods of the maximum wind speed they could resist were between 239 and 247 years. Flutter safety problems may occur if these two bridges encounter a strong wind with a return period of 300 years. As for the problem of aerostatic torsional stability robustness evaluation, a stochastic model of the aerostatic torsional stability safety domain represented by two random variables was proposed. The coefficients of variation of these two random variables varied within a reasonable range. By comparing the calculation results of the aerostatic torsional stability robustness index under different coefficients of variation, the influence of the coefficient of variation on the evaluation of aerostatic torsional stability robustness was analyzed. The shortest return periods of the reference wind speed that Jiangyin Yangtze River Bridge and Nansha Bridge could resist, not only at the initial wind attack angle of 0\({}^{\circ}\) but also at a relatively unfavorable initial wind attack angle of +3\({}^{\circ}\), were beyond 1000 years. These two bridges possess the ability to resist the maximum wind speed that is unforeseen or unusual. The shortest return period of the reference wind speed that Xihoumen Bridge \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(\delta_{b}\)} & \multicolumn{2}{c}{\(\delta_{t}\) = 0.05} & \multicolumn{2}{c}{\(\delta_{t}\) = 0.075} & \multicolumn{2}{c}{\(\delta_{t}\) = 0.1} \\ \cline{2-7}  & \(\beta\) & \(T_{m}\) **(Year)** & \(\beta\) & \(T_{m}\) **(Year)** & \(\beta\) & \(T_{m}\) **(Year)** \\ \hline \(\delta_{b}=0.12\) & 4.5558 & 383,240 & 4.4004 & 185,097 & 4.2051 & 76,638 \\ \(\delta_{b}=0.14\) & 4.3896 & 176,119 & 4.2577 & 96,833 & 4.0909 & 46,544 \\ \(\delta_{b}=0.16\) & 4.2547 & 95,543 & 4.14 & 57,586 & 3.994 & 30,784 \\ \(\delta_{b}=0.18\) & 4.1453 & 58,933 & 4.0436 & 37,996 & 3.9135 & 21,986 \\ \(\delta_{b}=0.20\) & 4.055 & 39,893 & 3.9633 & 27,056 & 3.8455 & 16,624 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Results of aerostatic torsional stability robustness evaluation of Nansha Bridge at 0\({}^{\circ}\) initial wind attack angle. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\delta_{t}\) = 0.05} & \multicolumn{2}{c}{\(\delta_{t}\) = 0.075} & \multicolumn{2}{c}{\(\delta_{t}\) = 0.1} \\ \cline{2-7} \(\delta_{b}\) & \(\beta\) & \(T_{m}\) **(Year)** & \(\beta\) & \(T_{m}\) **(Year)** & \(\beta\) & \(T_{m}\) **(Year)** \\ \hline \(\delta_{b}=0.12\) & 4.3023 & 118,319 & 4.1544 & 61,323 & 3.9677 & 27,560 \\ \(\delta_{b}=0.14\) & 4.153 & 60,949 & 4.0278 & 35,523 & 3.8687 & 18,279 \\ \(\delta_{b}=0.16\) & 4.0316 & 36,102 & 3.923 & 22,869 & 3.7842 & 12,970 \\ \(\delta_{b}=0.18\) & 3.9334 & 23,880 & 3.8372 & 16,071 & 3.7137 & 9792 \\ \(\delta_{b}=0.20\) & 3.8523 & 17,092 & 3.7657 & 12,042 & 3.6541 & 7749 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Results of aerostatic torsional stability robustness evaluation of Nansha Bridge at +3\({}^{\circ}\) initial wind attack angle.