## 3 Weighted Least Square Support Vector Regression Model
### Further Simulation  
To verify whether the W-LSSVM can bring better results, another representative 500 kV high voltage transmission line, called \"Fusha-I-xian\", was selected to make a comparison of the forecasting results by using the selected features (W-LSSVM-FA method) and original features (only W-LSSVM method). The sample data of \"Fusha-I-xian\" were also predicted by BPNN, SVM, MLRM and the results of the five models were also used to make a comparison. The data of \"Fusha-I-xian\" are from 12 January 2008 to 25 February 2008, which totally have 287 data groups. Also, part of the original data is shown in Figure 7. The former 247 data points are used as training sample, and the last 40 as testing sample. In the W-LSSVM-FA model, the FA model is used to select the features. First, initialize the parameters of the FA model: set the maximum iteration number \(Maxgen=500\), the number of initial fireworks \(PopNum=30\), the sparks number determination constant \(M=100\), the explosion radius determination constant \(\hat{R}=150\), and the upper and lower limits of the individual searching range of fireworks are \(V_{up}=512\) and \(V_{down}=-512\), respectively. Let the border of parameter \(\gamma\) be \([2^{-5},\ 2^{10}]\) and the border of parameter \(\sigma\) be \([2^{-5},\ 2^{5}]\), respectively. Also, the final selected features are temperature, humidity, wind speed, rainfall, load current, air pressure, and sunlight intensity, respectively. The iterative process curve of the fireworks algorithm for the sample data of \"Fusha-I-xian\" is shown in Figure 8. As we can see from Figure 8, the optimal fitness value is \(-0.916\), which is found by FA when the iterative number reaches 55. The final selected features for the sample are temperature, humidity, wind speed, wind direction, and sunlight intensity, respectively. The parameters of W-LSSVM-FA are obtained as follows: \(\gamma=56.7841\), \(\sigma=14.7715\). In the W-LSSVM  
Figure 6: The relative errors curve of each method. model, the original features are only temperature, humidity, and wind speed. With the method of cross validation, the parameters of W-LSSVM are obtained as follows: \(\gamma=38.9962\), \(\sigma=15.3720\). All forecasting results and the relative errors of the five models are shown in Figures 9 and 10, respectively. A part of the forecasting values and errors of five models is listed in Table 3.  
As is shown in Figure 9, the prediction values of W-LSSVM-FA are closest to the original values, this again proves the W-LSSVM-FA model has a higher forecasting accuracy and stability compared  
\begin{table} \begin{tabular}{c} **Error** \\ \end{tabular}  \\ \hline
1 & 11.67 & 11.84 & 1.46\% & 11.98 & 2.66\% & 11.29 & \(-\)3.26\% & 11.21 & \(-\)3.94\% & 11.28 & \(-\)3.34\% \\
2 & 12.49 & 12.23 & \(-\)2.08\% & 12.01 & \(-  
with the other four prediction models. The prediction results of W-LSSVM are closer to the original data than that of the SVM, BPNN, and MLRM models, this again reveals that it can improve the nonlinear mapping ability and strengthen the learning ability of the machine through the weighting process of LSSVM. The MAPE and RMSE values of the five models are shown in Table 3. It can be seen that the proposed W-LSSVM-FA model still has the smallest MAPE and RMSE values, which are 2.02% and 2.05%, respectively. This again reveals the proposed W-LSSVM-FA model has the best performance inicing thickness forecasting. Moreover, the MAPE and RMSE values of W-LSSVM are smaller than that of SVM, BPNN, and MLRM; this demonstrates the W-LSSVM has a higher prediction accuracy and better learning ability by using original features to forecast. The relative errors can be seen in Figure 10. We can see from the above computation that comparing with the W-LSSVM-FA and W-LSSVM method, the W-LSSVM-FA model has a higher forecast precision.