## 2 Collation and Analysis of Measured Data of Temperature and Wind
### Probability Model Fitting of Wind Speed and Direction
#### 2.3.2 Sampling and Fitting of Wind Speed and Direction  
The statistical data are collected from the daily data of the bridge site from February 2023 to February 2024. Maximum wind speed refers to the maximum average wind speed in a certain period within 10 min at 10 m elevation. After calculation, the daily average wind speed is lower than the daily maximum wind speed, which is due to the longer action time of low wind speed and the shorter action time of high wind speed. However, high wind speed is the main reason for the fatigue damage of the structure. So, this section adopts the method of stage extremum to sample to determine the wind speed sample. The sample of average wind speed is divided into several sub-samples according to a certain time interval, and the extreme value of each sub-sample is taken as the sample point. Under normal circumstances, the sampling time can be 1 day [20], 4 days [21] or 30 days [22]. However, due to the short sampling time, in order to obtain more samples, the time interval of 1 day (the daily maximum 10 min average wind speed during the observation period) is taken as the time interval for the extreme value.  
According to the specification [23], the 360\({}^{\circ}\) wind direction is divided into 16 wind directions with the interval of 22.5\({}^{\circ}\). The wind direction statistics are carried out on the wind data sampled at intervals of 1 day, and the wind rose diagram representing the distribution frequency in each wind direction can be obtained, as shown in Figure 4.  
It is not difficult to see from the rose diagram of wind direction that the wind direction in this area is mainly SSE, S and SW, followed by SE, SSW and NNE, and the frequency of other wind directions is low. Taking the maximum wind speed as the sample, the number of samples is too small, and the number of samples appearing in each wind direction is uneven, which leads to a small number of samples in some wind directions. According to Formulas (3)-(5), the distribution curves of wind speed probability density function under all wind directions are fitted with parameters under different probability distributions. Then, the probability density function of wind speed under each wind direction is fitted according to the wind speed distribution under discrete wind direction. Table 1 gives the parameter fitting values and correlation coefficients of wind speed probability distribution under discrete wind direction and full wind direction under three probability models.  
In Table 1, \(A\) is the scale parameter, \(B\) is the position parameter, and \(C\) is the shape parameter. \(\sum\) means all wind direction. r is the correlation coefficient, and the closer the value is to 1, the better the fitting effect.  
Figure 4: Rose diagram of wind direction.  
For the correlation coefficient under each wind direction, the correlation coefficient under the fitting of Gumbel distribution and Weibull distribution is generally higher. However, for the all-wind direction, the correlation coefficient under the Gumbel distribution fitting is closer to 1 than the Weibull distribution, and the goodness is the best. Therefore, the calculation of basic wind speed in this study adopts the result of Gumbel distribution fitting. When the correlation coefficient is higher than 0.6, it is usually considered that there is a strong linear relationship, and the Gumbel distribution can be considered for fitting.