# Study on Fluctuating Wind Characteristics and Non-Stationarity at U-Shaped Canyon Bridge Site
## 3 Analysis of Fluctuating Wind Characteristics
### Characteristics of Fluctuating Wind Under Stationarity Assumption  
Turbulence intensity quantifies the relative strength of pulsating wind. It is defined as the ratio of the standard deviation of wind speed fluctuations to the mean maximum wind speed over a 10 min interval:  
\[I_{u}=\frac{\sigma_{u}}{U} \tag{4}\]  
In the formula, \(I_{a}\) denotes the turbulence intensity in three directions, where the subscript \(\alpha\) represents \(u\), \(v\) and \(w\), respectively. \(\sigma_{\alpha}\) represents the standard deviation of wind speed fluctuations, and \(U\) represents the mean wind speed.  
Additionally, wind pulsation intensity can also be expressed using the gust factor, typically defined as the ratio of the maximum mean wind speed over a gust duration (\(t_{g}=3\)) to the mean maximum wind speed over a 10 min interval.  
\[G_{u}(t_{g})=1+\frac{\max\left[\overline{u}(t_{g})\right]}{U} \tag{5}\]  
Based on data preprocessing, wind speeds exceeding 4 m/s were selected for pulsating wind calculations. The calculations of turbulence intensity and gust factor are presented in  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Distribution** & \multicolumn{2}{c}{**Shape**} & \multicolumn{2}{c}{**Scale**} & \multicolumn{2}{c}{**Shape**} & \multicolumn{2}{c}{**Scale**} & \multicolumn{2}{c}{**Weighting**} \\
**Strict** & **Parameter 1** & **Parameter 1** & **Parameter 2** & **Parameter 2** & **Parameter 2** & **Factor of** & **R2** \\ \hline Weibull & 1.498 & 4.033 & \(\backslash\) & \(\backslash\) & 1 & 0.804 \\ Gamma & 1.699 & 2.28 & \(\backslash\) & \(\backslash\) & 1 & 0.772 \\ Weibull-Weibull & 4.666 & 3.392 & 1.297 & 1.817 & 0.681 & 0.996 \\ Weibull-Gamma & 4.724 & 3.545 & 2.494 & 0.522 & 0.649 & 0.998 \\ Gamma-Gamma & 2.134 & 0.792 & 13.948 & 0.333 & 0.465 & 0.994 \\ \hline \hline \end{tabular}  
* Take the Weibull-Gamma mixture model as an example. In this model, shape parameter 1 (\(\lambda\)) and scale parameter 1 (\(\delta\)) are the parameters of the first Weibull distribution, while shape parameter 2 (\(\alpha\)) and scale parameter 2 (\(\beta\)) are those of the Gamma distribution, and \(\omega\) is the weighting factor of the first Weibull distribution, determining its contribution to the overall mixture.  
\end{table}
Table 1: Wind speed probability density distribution fitting results.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Distribution** & \multicolumn{2}{c}{**Probability Density Function (PDF)**} \\ \hline Weibull & \(f(x;\lambda,k)=\frac{1}{\left(\frac{\delta}{k}\right)^{-1}}exp\left[-\left( \frac{\delta}{k}\right)^{\frac{1}{k}}\right]\) \\ Gamma & \(f(x;\alpha,\beta)=\frac{\alpha^{-1}}{\left(\frac{\delta}{k_{1}}\right)^{-1}}exp \left(-\frac{\delta}{k}\right)\) \\ Weibull-Weibull & \(f(x;\lambda,k_{1},k_{1},\lambda_{2},k_{2},\omega)=\alpha\frac{1}{\alpha_{1}} \left(\frac{\delta}{k_{1}}\right)^{\frac{1}{k_{1}-1}}exp\left[-\left(\frac{ \delta}{k_{1}}\right)^{\frac{1}{k}}\right]+(1-\omega)\frac{1\alpha_{1}}{\alpha _{1}}\left(\frac{\delta}{k_{2}}\right)^{\frac{1}{k_{2}-1}}exp\left[-\left( \frac{\delta}{k_Figures 3 and 4. Turbulence intensity was primarily distributed in the range of 0.05-0.30 and exhibited an overall decreasing trend with increasing wind speed. Due to significant data dispersion, the linear fitting results were poor.  
Gust factors corresponding to turbulence intensity were primarily distributed in the range of 1.0-2.0. The gust factors exhibited an overall upward trend with increasing turbulence intensity, showing strong linear correlation with an R\({}^{2}\) value of 0.85.