# Analysis of Wind Speed Characteristics Along a High-Speed Railway
## 3 Wind Speed Characteristics
### Wind Speed Distribution Characteristics  
The estimation of wind energy potential is made possible by the wind speed distribution [35]. Probability density functions (PDFs) are typically used to describe the distribution of wind speeds [36]. Additionally, it has the ability to describe how extreme wind speeds behave [37], which is advantageous for the high-wind circumstances that the high-speed train industry is concerned about. The frequency distribution of wind speed surrounding the HSR is represented in this study using four distribution models, including Weibull (Wei), generalized extreme value (GEV), gamma (Gam), and Rayleigh (Ray). The formulas for these four distribution models, which are used frequently and successfully throughout the world, are displayed in Table 2.  
While assessing the goodness-of-fit of the chosen PDFs using widely used statistical measures, we employed maximum likelihood estimation (ML) to calculate the parameters of each PDF. Table 3 provides definitions for the terms root mean square error (RMSE), correlation coefficient \(R^{2}\), chi-square error \(\chi^{2}\), and Kolmogorov-Smirnov test (K-S).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Probability Density Functions (PDF)** \\ \hline Wei & \(f(v,k,c)=\frac{k}{\sigma}\left(\frac{p}{\sigma}\right)^{k-1}\exp\left[-\left( \frac{p}{\sigma}\right)^{k}\right]\) \\ GEV & \(f(v,k,\sigma,\mu)=\frac{1}{\sigma}\left[1-\frac{k}{\sigma}(v-\mu)\right]^{ \frac{1}{k}-1}\exp\left\{-\left[1-\frac{k}{\sigma}(v-\mu)\right]^{\frac{1}{k} }\right\}\) \\ Gam & \(f(v,k,\sigma)=\frac{\sigma^{k}}{\Gamma(k)}v^{k-1}\exp(-\sigma v)\) \\ Ray & \(f(v,\sigma)=\frac{p}{\sigma^{k}}\exp\left(\frac{-p^{2}}{2\sigma^{k}}\right)\) \\ \hline \hline \end{tabular} Note: \(\sigma\) re represents scale parameter; \(k\) represents shape parameter.  
\end{table}
Table 2: Probability density function and parameters.  
Figure 4: Proportion of fluctuating wind speed amplitude \(>\)3 m/s.  
The probability distributions and histograms of the wind speed at stations K1005 and 58,237 at various time scales in February are shown in Figure 5. The distribution of wind speed at various time intervals can be essentially characterized by a distribution function, which has nothing to do with the wind speed's time scale. The statistical inaccuracy of the HSR station K1005 PDFs for February is shown in Appendix A. Wei's statistical error results are the best when compared to those of other distribution functions, suggesting that Wei can model the wind speed of K1005 at various time intervals. Wei, meanwhile, has proven to be a generally accepted model for wind speed modeling [38].  
To further investigate the variation in wind speed distribution between the WS and the high-speed train station on a 10 min time scale, Appendix B lists the assessment indicators for the probability distribution model of wind speed at all sites. Wei offers the least RMSE and K-S and biggest \(R^{2}\) for station K1005, and Wei can be utilized to fit the station's wind speed. The same outcome is also seen at the 58,237 station that is nearest K1005, suggesting some parallels in the wind field in this region. Ray has the best assessment index for stations K1066, K1245, and K1256, showing that Ray is more suited to match the wind speed distribution of these three stations. The WSs 58,242 and 58,352, as opposed to the HSR station, have the best GEV and statistical values that can properly indicate the wind  
Figure 5: Histogram and probability distribution of wind speed at different time scales at K1005 and 58237.  
speed. Additionally, we analyzed the wind speed distribution patterns above various RS thresholds and found that the Weibull distribution function consistently yielded the smallest criterion index for wind speeds above 5 m/s, 8 m/s, and 10 m/s. Therefore, the Weibull distribution should be prioritized in statistical modeling.