## 3 Case Study and Results Analysis
### Case Study 2  
\"Fusha-I-xian\", which is a representative 500 kV transmission line between Fuxing and Shapin of Hunan province, is chosen to prove the robustness and stability of the proposed QFA-w-SVM facing forecasting model. The sample data of \"Fusha-I-xian\" are also predicted by the five models and the results of five models are also used to make a comparison.  
Figure 10 shows the iteration trend of the QFA-w-SVM searching of optimization parameters. As can be seen from Figure 3, the convergence can be seen in generation 39 with the optimal MSE value of 0.1124, and the parameters of w-SVM are obtained with \(C=23.68\), \(\sigma=0.1526\), respectively.  
Figure 9: Values of mean absolute percentage error (MAPE), mean square error (MSE) and average absolute error (AAE).  
In FA-w-SVM model, the convergence can be seen in generation 53 with the optimal MSE value of 0.1307, and the parameters of w-SVM are obtained with \(C=31.58\), \(\sigma=0.0496\). In the PSO-SVM model, the convergence can be seen in generation 58 with the optimal MSE value of 0.1324, and the parameters of SVM are obtained with \(C=19.48\), \(\sigma=0.5962\). This proves that the proposed QFA-w-SVM model can find the global optimal value with the faster convergence compared with FA-w-SVM and PSO-SVM models. This also validates the stability of the proposed icing forecasting model.  
Figure 11 shows the forecasting results of the five models. The forecasting errors of the five models are shown in Figure 12. It can be seen from the comparison of the forecasting curve and the actual value that the forecasting results of ice thickness of those five models have approximation to actual curve. Among them, the proposed QFA-w-SVM has the best fitting learning and fitting ability, and 44 forecasting points mean that almost 94% of points are in the scope of [\(-\)3,\(+\)3]; only three forecasting points are out of this scope. In FA-w-SVM model, 27 forecasting points means that nearly 57% points are in the range [\(-\)3,\(+\)3], and 20 points fall out this scope. In PSO-SVM model, 20 forecasting points means that nearly 43% of points are in the scope, and 27 points are out of the range. In SVM model, only 2 points are in this range, and the rest of the forecasting points are not in this scope. In MLR model, none of points are in this scope. This reveals that QFA-w-SVM model has a higher forecasting accuracy than other mentioned models, and it also has stronger robustness and nonlinear fitting ability.  
Figure 11: Forecasting results of the five models.  
Figure 10: The convergence curves of algorithms.  
The values of MAPE, MSE, AAE of the five models in icing forecasting of \"Fusha-I-xian\" are shown in Figure 13. It can be seen that the proposed QFA-w-SVM model still has the smallest MAPE, MSE and AAE values, which are 1.9%, 0.026 and 0.018, respectively. This again reveals that the proposed QFA-w-SVM model has the best performance in the icing forecasting results. In addition, the MAPE, MSE and AAE values of FA-w-SVM are 3.01%, 0.063 and 0.028, respectively, which are both larger than that of QFA-w-SVM, but smaller than the rest of three models. In PSO-SVM, the MAPE, MSE and AAE values are 3.45%, 0.099 and 0.034, respectively, which are smaller than those of SVM and MLR models. That proves that the combined algorithms have better forecasting performance and the optimization algorithms can help single regression model to achieve a better accuracy through finding better parameters. This result agrees with the one presented in Section 3.3.