## 3 The Application Results and Discussion
### Comparison and Analysis of Accuracy  
Figure 5 illustrates the different scatter plots of the train set and test set for the prediction value of four models and the true value of the measured icing time.In the figure, the \(y=x\) line is plotted to represent the best performance, and a confidence zone is formed by 15% and \(-\)15% error line. It shows that fewer data points fall beyond the confidence zone ranging from \(-\)15% to 15% for both train set and test set after SVR is improved by RSM or PSO. RSM-SVR shows better performance compared with PSO-SVR, for which 52 data points are in the train set and 25 data points are included in the confidence zone. In RSM-SVR, the value of \(R^{2}\) for train set and test set is, respectively, 0.9258 and 0.8771, which sees an enhancement of 2.73% and 1.74% compared with PSO-SVR. It is concluded that the calibration of input variables by RSM will outperform the effect of PSO if the parameter combination, \(\sigma\) and \(C\), is already approximated to the optimal solution.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{5}{c}{**Data Set**} \\ \cline{2-6}  & **1** & **2** & **3** & **\%** & **188** \\ \hline Icing time (min) & 43 & 40 & 45 & \% & 16 \\ Pavement initial & \(-\)2 & \(-\)1.31 & \(-\)1.68 & \% & \(-\)4.5 \\ temperature & \(-\)0.75 & \(-\)0.71 & \(-\)1.09 & \% & \(-\)3.52 \\ Environment average & \(-\)3.27 & \(-\)2.49 & \(-\)2.24 & \% & \(-\)8.4 \\ temperature & \(58.25\%\) & 60.24\% & 60.78\% & \% & 62.06\% \\ Radiation & 0 & 0 & 0 & \% & 0 \\ Wind speed & 0 & 0 & 0 & \% & 0.39 \\ Water film thickness (cm) & 1 & 0.8 & 2.4 & \% & 1.8 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pavement icing information.  
Moreover, the combination of two methodologies appears to demonstrate best optimization effects with 61 in train set and 31 in test set, and the \(R^{2}\) are, respectively, 0.9655 and 0.9318. It indicates the availability of coupling these two methods for optimization.  
In Figure 6, the four models are compared for \(MAE\), \(MAPE\), and \(RMSE\). The original \(MAE\), \(MAPE\), and \(RMSE\) for SVR are, respectively, 10.7087, 2.6735, and 0.2116 in training and 9.8709, 2.5748, and 0.2038. After the application of RSM or PSO, the three items all see an enhancement, which indicates the effectiveness of the two methodologies in improving SVR. This trend is similar to the results in past research [27; 31]. It suggests that RSM and PSO can both contribute to the improvement of prediction accuracy of SVR, while RSM demonstrates better performance than PSO, for which the three indexes are, respectively, 7.4895, 2.2990, and 0.1833 in training and 8.2087, 2.2472, and 0.1642 in testing. This demonstrates that the optimization of input variables can achieve better performance in enhancing the prediction capability of SVR compared with optimizing the SVR parameters. In addition, the combination of two methodologies obtains the best optimization result with 3.4849, 1.3437, and 0.1032 in training and 4.5519, 1.7646, and 0.1233 in testing. More details are shown in Table 3.  
Figure 7 displays the predictive value of four models and the true value in the test set. According to the ratio set in CV method, 38 sets of data are used in this section to verify the capability of four models established in this paper. The comparison demonstrates that predictive value of hybrid improved SVR, PSO-SVR, and RSM-SVR is more approximated to the true value than the original SVR. The data points of PSO-SVR are more deviated from the true value in contrast to RSM-SVR, while the result is further improved as the two optimization methodologies, RSM and PSO, are combined to optimize SVR. This corresponds to the results in Figure 5 and Table 3.  
Figure 5: The correlation coefficient.