## 4 Aerostatic Torsional Stability Robustness Evaluation
### Robustness Calibration of Aerostatic Torsional Stability
#### 4.3.1 Jiangyin Yangtze River Bridge  
The calculated reliability indices and return periods at 0\({}^{\circ}\) initial wind attack angle and +3\({}^{\circ}\) wind attack angle are listed in Tables 10 and 11, respectively. At the initial wind attack angle of 0\({}^{\circ}\), the maximum failure probability of Jiangyin Yangtze River Bridge was 8.66 \(\times\) 10\({}^{-6}\), and the shortest return period of the reference wind speed that the bridge could resist was 115,471 years. Even at a relatively unfavorable initial wind attack angle of +3\({}^{\circ}\), the maximum failure probability was 1.33 \(\times\) 10\({}^{-5}\), and the shortest return period could still reach 75,162 years, which was far beyond the design service life. Therefore, Jiangyin Yangtze River Bridge possesses the ability to resist the maximum wind speed that is unforeseen or unusual. It can be known from the results listed in Tables 10 and 11 that in different combinations of the coefficients of variation of \(U_{td}\) and \(U_{b}\), the relative errors of the reliability index were within 16.72% at the initial wind attack angle of 0\({}^{\circ}\) and 16.53% at the initial wind attack angle of +3\({}^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \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 \(\delta_{b}=0.12\) & 5.1593 & 8,068,588 & 4.9826 & 3,187,985 & 4.7643 & 1,055,351 \\ \(\delta_{b}=0.14\) & 4.9500 & 2,694,928 & 4.7997 & 1,258,626 & 4.6124 & 502,454 \\ \(\delta_{b}=0.16\) & 4.7832 & 1,159,243 & 4.6521 & 608,695 & 4.4875 & 277,532 \\ \(\delta_{b}=0.18\) & 4.6491 & 599,904 & 4.5323 & 342,789 & 4.3850 & 172,435 \\ \(\delta_{b}=0.20\) & 4.5361 & 349,016 & 4.4306 & 212,831 & 4.2969 & 115,471 \\ \hline \end{tabular}
\end{table}
Table 10: Results of aerostatic torsional stability robustness evaluation of Jiangyin Yangtze River Bridge at 0\({}^{\circ}\) initial wind attack angle.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Bridge**} & \multirow{2}{*}{**Initial Wind Attack Angle**} & \multirow{2}{*}{\(U_{td}\)} & \multicolumn{2}{c}{\(\sigma U_{td}\)} \\ \cline{3-5}  & & & \(\delta_{t}\) = 0.05 & \(\delta_{t}\) = 0.075 & \(\delta_{t}\) = 0.1 \\ \hline \multirow{2}{*}{Jiangyin Yangtze River Bridge} & 0\({}^{\circ}\) & 113 & 5.65 & 8.48 & 11.30 \\  & +3\({}^{\circ}\) & 110 & 5.50 & 8.25 & 11.00 \\ \hline \multirow{2}{*}{Xihounem Bridge} & 0\({}^{\circ}\) & 105 & 5.25 & 7.88 & 10.50 \\  & +3\({}^{\circ}\) & 95 & 4.75 & 7.13 & 9.50 \\ \hline \multirow{2}{*}{Nansha Bridge} & 0\({}^{\circ}\) & 114 & 5.70 & 8.55 & 11.40 \\  & +3\({}^{\circ}\) & 108 & 5.40 & 8.10 & 10.80 \\ \hline \end{tabular}
\end{table}
Table 8: Mean values and standard deviations of \(U_{td}\) for three existing bridges.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{\(\delta_{b}\)} & \multicolumn{2}{c}{**Jiangyin Yangtze River Bridge**} & \multicolumn{2}{c}{**Xihounem Bridge**} & \multicolumn{2}{c}{**Nansha Bridge**} \\ \cline{2-7}  & \(\mu_{U_{b}}\) & \(\sigma U_{b}\) & \(\mu_{U_{b}}\) & \(\sigma U_{b}\) & \(\mu_{U_{b}}\) & \(\sigma U_{b}\) \\ \hline \(\delta_{b}=0.2\) & 23.78 & 4.76 & 33.11 & 6.62 & 27.24 & 5.45 \\ \(\delta_{b}=0.18\) & 24.74 & 4.45 & 34.43 & 6.20 & 28.3