## 3 Results and Discussion
### Influence of Roller Parameters and Subgrade Properties  
Figure 8 shows the regression importance of roller parameters and subgrade properties (collectively called influence factors) obtained by RF algorithms. It could be seen that, in the regression of ICMV and ISMV, the importance of subgrade property was more significant than that of roller parameter while all of them should not be neglected. Particularly, when the regression target was compaction degree, the importance of \(w\) became apparent, even exceeded the importance of CMV and CCV. Figure 7: Monadic linear regression results between different ICMV and ISMV, (**a**) CMV/CCV vs. \(E_{\text{LWD}}\), (**b**) \(E_{\text{vib}}\) vs. \(E_{\text{LWD}}\), (**c**) CMV/CCV vs. compaction degree, (**d**) \(E_{\text{vib}}\) vs. compaction degree. Note: \(D\) represents the compaction degree in the legend. In order to further explore the impacts of influence factors on the correlations between ICMV and ISMV, bivariate multiple-power regressions among ICMV, ISMV and influence factors were established (the independent variables are ICMV and influence factors while the dependent variable is ISMV). It should be noted that (a) only one influence factor was introduced in each regression analysis, as the influence regularity of factor could be revealed more adequately; (b) the power number of ICMV was set to 1 constantly because the nonlinear influence analysis of ICMV was not the focus of this section; (c) the power number of influence factors was set to be less than 4 because the fitting of higher power was lack of practical significance; (d) though the nonlinear influence could be revealed by other methods such as exponential and logarithmic regressions, he results of them were not exhibited here for simplicity. Determination coefficient R\({}^{2}\) was used to characterize the effects of bivariate multiple-power regression. The results are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type of ISMV**} & \multirow{2}{*}{**Type of ICMV**} & \multirow{2}{*}{**Influence Factor**} & \multicolumn{3}{c}{**R\({}^{2}\) of Different Power Number of Influence Factor**} \\ \cline{3-6}  & & & **Power Number = 1** & **Power Number = 2** & **Power Number = 3** \\ \hline \multirow{6}{*}{\(E_{\text{LWD}}\)} & & \(w\) & 0.5991 & 0.6341 & 0.6766 \\ \cline{3-6}  & & \(v\) & 0.6007 & 0.6470 & 0.6862 \\ \cline{3-6}  & & Am & 0.6011 & 0.6014 & 0.6024 \\ \cline{3-6}  & & \(k_{\text{u}}\) & 0.6089 & 0.6091 & 0.6094 \\ \cline{3-6}  & & \(w\) & 0.4399 & 0.4753 & 0.4950 \\ \cline{3-6}  & & \(v\) & 0.4364 & 0.4682 & 0.4981 \\ \cline{3-6}  & & Am & 0.4314 & 0.4320 & 0.4335 \\ \cline{3-6}  & & \(k_{\text{u}}\) & 0.4306 & 0.4309 & 0.4314 \\ \hline \multirow{6}{*}{\(E_{\text{vib}}\)} & & \(w\) & 0.6617 & 0.6931 & 0.7535 \\ \cline{3-6}  & & \(v\) & 0.6662 & 0.7081 & 0.7746 \\ \cline{1-1} \cline{2-6}  & & Am & 0.6548 & 0.6563 & 0.6583 \\ \cline{1-1} \cline{2-6}  & & \(k_{\text{u}}\) & 0.6489 & 0.6504 & 0.6512 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of bivariate multiple-power regressions. Figure 8: Feature importance obtained by RF. In Table 4, the fitting equation is a linear function when the power number of influence factor equal to 1 whereas the fitting equation is a nonlinear function of higher order when the power number is higher than 1. It can be observed that R\({}^{2}\) values increased as the power number of \(w\) and \(v\) increased whereas the power number of Am and \(k_{\text{u}}\) had almost no effect on R\({}^{2}\) values. Therefore, it can be considered that the influence of \(w\) and \(v\) on correlations between ICMV and ISMV are nonlinear whereas that of Am and \(k_{\text{u}}\) are linear. Especially, considering the existence of optimal moisture content (OMC), the analysis data were divided into three zones with \(w\) to further study the influence of \(w\): optimum zone (OMC \(\pm\) 2%, i.e., \(w\) = 8.5-12.5%), dry zone (\(w\) < 8.5%) and wet zone (\(w\) > 12.5%).