## 3 Weighted Least Square Support Vector Regression Model
### W-LSSVM for Icing Forecasting
Secondly, the relative errors in these models can be described from Figure 6. In the MLSM model, the maximum and minimum relative errors are 8.07% and 2.42%, respectively; and the fluctuating range of the RE curve is higher. In the BPNN model, the maximum error is 5.68% which is smaller than that of MLSM, and the minimum error is 1.47% which is smaller than that of MLSM; this demonstrates that the forecasting accuracy and the nonlinear fitting ability of BPNN is stronger than that of MLSM. In the single SVM model, the maximum and minimum errors are 4.7% and 1.09%; both values of SVMare superior to that of BPNN and MLRM, and the fluctuating range of the RE curves of the SVM is rather smaller. This again demonstrates the accuracy and the stability of SVM are higher than that of BPNN and MLRM in icing forecasting. In the proposed W-LSSVM-FA model, the maximum and minimum relative errors are 1.94% and 0.64%, respectively. Both of the values are the smallest among BPNN, SVM, and MLRM models. Moreover, the fluctuation of the curve is small, which is superior to the other models. Compared with the other three models, the proposed W-LSSVM-FA icing forecasting model has a higher accuracy and stability. Due to the fact that it performs a great pretreatment on the data with the input vectors weighted and that some redundant factors have been eliminated through the feature selection, the forecasting accuracy is improved, and the machine learning and training ability are relatively strengthened. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**BPNN**} & \multicolumn{2}{c}{**SVM**} & \multicolumn{2}{c}{**W-LSSVM-FA**} & \multicolumn{2}{c}{**MLRM**} \\ \cline{2-10}
**Time Point** & \begin{tabular}{c} **Actual** \\ **Value (mm)** \\ \end{tabular}  & \begin{tabular}{c} **Forecast** \\ **Value (mm)** \\ \end{tabular}  & \begin{tabular}{c} **Error** \\ **Error** \\ **Value (mm)** \\ \end{tabular}  & \begin{tabular}{c} **Forecast** \\ **Value (mm)** \\ \end{tabular}  & \begin{tabular}{c} **Error** \\ **Error** \\ **Value (mm)** \\ \end{tabular}  & \ \begin{tabular}{c} **Forecast** \\ **Value (mm)** \\ \end{tabular}  & \begin{tabular}{c} **Error** \\ **Error** \\ **Value (mm)** \\ \end{tabular}  \\ \hline T07-00 & 10.900 & 10.47 & \(-\)3.95\% & 10.67 & \(-\)2.11\% & 11.03 & 1.19  
Thirdly, the forecasting results can be evaluated by calculating the MAPE and RMSE. As the calculation results are shown, the MAPE values of the W-LSSVM-FA, SVM, BPNN, and MLRM models are 1.35%, 2.59%, 3.23%, and 4.06%, respectively. The proposed W-LSSVM-FA model has a lower error than the other models. The RMSE value is used to evaluate the discrete degree of whole forecasting values of each model. As we see in Table 2, the RMSE values of W-LSSVM-FA, SVM, BPNN, and MLRM are 1.38%, 2.68%, 3.31%, and 4.16%, respectively. The discrete degree of the W-LSSVM-FA icing forecasting model is the lowest; this demonstrates the proposed W-LSSVM-FA model is more stable for the prediction of icing thickness, and it can reduce the redundant influence of irrelevance factors through feature selection.