## 3 Results
### Wind Speed State Fluctuation Results  
After data preprocessing, it is necessary to analyze the implied wind speed state fluctuation information from the global perspective. According to the intra-class compactness \(Var(U,c)\), inter-class separation \(Sep(U,c)\) and the Xie-Beni index, the number of wind speed state fluctuations is finally determined and the results are shown in Figure 4.  
As the number of clusters increases, the compactness tends to decrease. When the number of clusters is three the degree of change of compactness is the largest, and then it remains a gentle downward trend. It shows that when the number of clusters increases from two to three, the effect is the most obvious from the compactness level. When the number of clusters continues to grow from three, the compactness decreases slightly and the compactness has no significant effect on the clustering effect. The overall trend of separation decreases as the number of clusters increases. When the number of clusters is two, three, and four, it can be considered that the separation between different classes is more effective and there is a clear boundary between classes. When the number of clusters is more significant than four, the degree of separation is small. It changes slowly, indicating that the boundaries between categories are unclear and that the clustering effect is ineffective. When the number of clusters is three, the Xie-Beni index value is the smallest. That is to say, a cluster number of three is the best. Taken together, the optimal number of clusters is three. At a cluster number of three, the original data were clustered using the local regression FCM algorithm and the FCM algorithm, respectively, and the results were as follows:  
As seen in Figure 5a, the local regression FCM algorithm membership graph is smoother and the difference between different classes is more prominent. As seen in Figure 5b, the FCM membership graph shows the number of mutations related to the data set's outliers. When solving practical engineering problems, local regression FCM membership graph plots can be more intuitive in analyzing the problem. As can be seen from Figure 6, the local regression FCM algorithm divides the data into three categories. The first class has a clustering center of 4.979, which contains samples 302 to 442; the second class has a clustering center of 2.497, which includes samples 1 to 180, 209 to 301, and 442; and the third class has a clustering center of 0.998, which contains samples 181 to 208 and 443 to 500. Figure 4: Compactness versus cluster number. Figure 5: Comparison of the degree of membership graphs of the two methods: (**a**) Local regression FCM; (**b**) FCM. Figure 6: Comparison of the clustering centers of the two methods. This represents a certain number of fluctuations in wind speed around the three clustering centers of 4.979, 2.497, and 0.998 during this period. Samples belonging to each category do not necessarily appear in a concentrated manner, e.g., samples 181-208 and 443-500 are in the same class at the same time but occur in a very different order. This requires a judgment analysis of the samples in each cluster with the membership graph. The clustering centers obtained by the FCM algorithm are 4.986, 2.514, and 0.988, respectively, and the local regression FCM algorithm results are 4.4% lower than the FCM results. This is due to the outliers that increase the clustering centers during the iterations. These outliers are not average data and should be removed. Substituting the outliers into the calculation will affect the final result. All data are then rearranged by category to make a scatter diagram, as shown in Figure 7. The local regression FCM algorithm eliminates the outliers in the second clustering, which makes the clustering results more clear. There are some outliers at the junction of different classes, such as sample 141, which is determined by the algorithm characteristics of local regression FCM.