## 4 Results and Discussion
### Fluctuating Wind Characteristics
#### 4.2.5. Kurtosis, Skewness, and Probability Density Function  
Kurtosis and skewness are statistical measures that describe the shape and symmetry of the fluctuating wind speed distribution. When fluctuating wind speeds follow a Gaussian distribution, the kurtosis value is 3, and the skewness value is 0 [34]. The further these values deviate from the standard, the stronger the non-Gaussian characteristics of the wind speed. Additionally, kurtosis and skewness can reflect the probability of the occurrence of extreme wind speeds, which can aid in preventing bridge damage due to extreme wind loads. The kurtosis and skewness coefficients for the southwest bridge tower are presented in Figures 46 and 47. It can be observed that when the oncoming wind is uniform, both the kurtosis and skewness coefficients at the midpoint of the southwest tower are quite large. Particularly when the wind direction is 180\({}^{\circ}\), the kurtosis coefficient reaches as high as 60. This is due to the fact that the southwest tower is located on the leeward side of the mountain, making it very susceptible to the influence of extreme wind speeds, which leads to a higher kurtosis value in the 180\({}^{\circ}\) wind direction. Additionally, there is a clear trend of the kurtosis coefficient increasing with wind speed at the southwest tower, and the skewness coefficient also deviates significantly from the Gaussian value. When the oncoming flow is ABL inflow, the kurtosis and skewness values are generally close to those of the Gaussian distribution, indicating that the probability of extreme wind speeds occurring under ABL inflow is smaller. The kurtosis and skewness coefficients for the northeast bridge tower are shown in Figures 48 and 49. When the oncoming wind is uniform, both the kurtosis and skewness coefficients deviate more from the Gaussian values as the oncoming wind speed increases. The higher kurtosis and skewness values are observed at the midpoint of the tower. When the oncoming wind is ABL inflow, the 0\({}^{\circ}\) and 30\({}^{\circ}\) wind directions approximate a Gaussian distribution. However, when the oncoming wind direction is 180\({}^{\circ}\), owing to the obstruction of the mountain, both the kurtosis and skewness coefficients are higher, with the highest values still occurring at the midpoint of the bridge tower. Extra precautions should be taken at this location in engineering. Figure 47: Kurtosis and skewness coefficients of the southwest tower under ABL inflow with different wind speeds. Figure 48: Kurtosis and skewness coefficients of the northeast tower under uniform inflow with different wind speeds. The kurtosis and skewness coefficients for the main beam are shown in Figures 50 and 51. When the oncoming wind is uniform, the variation in the kurtosis and skewness coefficients along the main beam with wind speed follows the same pattern as that for the two towers. As the wind speed increases, the kurtosis coefficient gradually increases, and the skewness coefficient deviates more from the Gaussian value. Therefore, at higher wind speeds, the dynamic response of the bridge may be stronger due to the unsteadiness of fluctuating winds. When the oncoming wind is from ABL inflow, the kurtosis and skewness at the \(0^{\circ}\) and \(30^{\circ}\) wind directions basically conform to the Gaussian values. However, the skewness and kurtosis values at the \(180^{\circ}\) wind direction are significantly different from the Gaussian distribution, with the largest discrepancy observed at the midspan of the main beam. Consequently, the midspan is more susceptible to damage from strong gusts. To ensure structural integrity and safety under extreme wind conditions in engineering, special attention should be given to the design and maintenance of the main beam, particularly at the midspan. The probability density function displays an intuitive representation of the distribution of fluctuating wind speeds, as expressed in Equation (9) [35; 36].