## 3 Results and Discussion
### Probability Characteristics of Extreme Pressure Coefficients
#### 3.1.2 Probability Distribution Modelling of Extreme Pressure Coefficient  
(1) The probability distribution model of the area-averaged extreme pressure coefficient for different areas for a typical wind angle. Probability distribution fitting is conducted for the extreme area-averaged wind pressure coefficients in a swarmed area. Figure 4 shows the probability distributions of the area average extreme pressure coefficients of 2 m\({}^{2}\), 10 m\({}^{2}\), 25 m\({}^{2}\), and 72 m\({}^{2}\) (full scale) in the swarmed area of the west facade at 0\({}^{\circ}\) wind direction angle. It can be seen from Figure 4 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Distribution** & **Form** & **Condition** \\ \hline Extreme value Type I distribution: & \(F(x)=\exp\{-\exp[-(x-u)/a]\}\) & \(x\in R\) \\ \hline Extreme value Type II distribution: & \(F(x)=0\) & \(x\leq u\) \\ Frechet distribution & \(F(x)=\exp\left[-(x-u)/a\right]^{-1/k}\) & \(x>u\), \(k>0\) \\ \hline Extreme value Type III distribution: & \(F(x)=\exp\left[-(x-u)/a\right]^{-1/k}\) & \(x<u\), \(k<0\) \\ Weibull distribution & \(F(x)=0\) & \(x\geq u\) \\ \hline \hline \end{tabular} Note: The three extreme value distributions can be expressed in a unified form GEV distribution:\(F(x)=\exp\Bigl{\{}-[1+k(x-u)/a]^{-1/k}\Bigr{\}}\), where \(u\) is the position parameter; \(a\) is the scale parameter; and \(k\) is the shape parameter. When \(k=0\): extreme value Type I distribution; when \(k>0\): extreme value Type II distribution; when \(k<0\): extreme value Type III distribution.  
\end{table} 
Table 1: Extreme value probability models. that the area-averaged extreme pressure coefficients for different areas in the swarmed area have good fitting performance using the GEV distribution, and the \(k\) is less than zero, which is best fitted with the extreme value Type III distribution. As for Gumbel distribution, there is an obvious deviation in some areas. Figure 4: _Cont._  
The Kolmogorov-Smirnov (K-S) test is applied to see whether the Gumbel or GEV distribution is preferred. The K-S test expression for the two attempts is as follows:  
\[D_{K}=\max\lvert Fe(x)-F(x)\rvert \tag{5}\]  
where \(Fe\left(x\right)\) is the hypothetical probability distribution, \(F\left(x\right)\) is the cumulative probability distribution of the sample itself, and the standard evaluation formula \(\mathrm{D_{K}}<\mathrm{D_{K}}\alpha\). The samples obtained by the wind tunnel test are considered to follow this probability distribution. \(\alpha\) is a significant level, and \(\mathrm{D_{K}}\alpha\) is above the critical value. The Akaike information criterion (AIC) can also be used to test the fitting goodness of the extreme value probability distribution [22]. The AIC method is expressed as  
\[\mathrm{AIC}=2n-2\ln L \tag{6}\]  
where \(n\) represents the number of free parameters of the considered model, and L represents the maximum likelihood of the model. Figure 5 shows the results of the K-S test method and the AIC test method for the probability distribution fitting of the minimum wind pressure coefficients in the swarmed area for different areas. The results indicate that the use of the GEV distribution is preferred for the probability distribution fitting of the extreme pressure coefficient for all kinds of area sizes. Figure 4: The probability distribution fitting for the area-averaged extreme pressure coefficients for different areas: (**a**) 2 m\({}^{2}\), (**b**) 10 m\({}^{2}\), (**c**) 25 m\({}^{2}\), (**d**) 72 m\({}^{2}\). Figure 5: Examination of probability distribution fitting goodness of extreme pressure coefficients. (**a**) D\({}_{\mathrm{K}}\) value in swarmed area. (**b**) AIC value in swarmed area. (2) Effect of wind direction on the probability distribution model for peak pressure coefficients.