## 2 Materials
### Multicollinearity Processing  
In regression analysis, there is a high correlation between multiple independent variables, that is, multicollinearity, which leads to instability in model estimates and a decline in predictive effectiveness. The VIF is a common method to detect multicollinearity. The classical linear regression model is expressed as:  
\[Y=\beta_{0}+\beta_{1}X_{1}+\beta_{2}X_{2}+...+\beta_{k}X_{k}+e \tag{2}\]  
where detailed variable definitions are provided in Table A3 in Appendix A. For each independent variable \(X_{i}\), the VIF value is calculated as follows:  
\[VIF_{i}=\frac{1}{1-R_{i}^{2}} \tag{3}\]  
where \(R_{i}^{2}\) is the coefficient of determination between the \(i\) influence factor and the other influence factors. The larger \(VIF_{i}\) is, the larger the \(R_{i}^{2}\) is, indicating that the fit is better and the degree of collinearity between the \(i\) explanatory variable and the other explanatory variables is higher. It is generally believed that when \(VIF>5\), there is an obvious collinearity problem between the \(i\) explanatory variable and other explanatory variables, and when \begin{table}
\begin{tabular}{c c c} \hline
**Feature Name** & **Description** & **Source LTPP Data Sheet** \\ \hline MAINTENANCE & Road section repair and maintenance times & TST\_L05B \\ GB\_THICKNESS & Average thickness of unbonded (granular) base (GB) & TST\_L05B \\ SUBGRADE\_MATL & & TST\_L05B \\ AC\_THICKNESS & Average thickness of asphalt concrete layer (AC) & TST\_L05B \\ DRIANINAGE\_TYPE & Type of underground drainage & SECTION\_DRIANINAGE\_TYPE \\ PRECIPITATION & Annual precipitation & MERRA\_PRECIP\_YEAR \\ TEMP & Annual average temperature & MERRA\_TEMP\_YEAR \\ FREEZE\_INDEX & Freezing index & MERRA\_TEMP\_YEAR \\ FREEZE\_THAW & Number of freeze–thaw cycles & MERRA\_TEMP\_YEAR \\ WIND & Wind speed & MERRA\_WIND\_YEAR \\ HUMIDTY & Mean annual humidity & MERRA\_HUMIDY\_YEAR \\ CLOUD\_COVER & Average hourly cloud coverage & MERRA\_HUMID\_YEAR \\ SHORTWAVE\_SURFACE & Mean duration of surface incident shortwave radiation & MERRA\_SOLAR\_YEAR \\ ESAL & The equivalent number of actions of a standard axle load & TRF\_TREND \\ MRI & Average IRI values of left and right wheel tracks & ANALYSIS\_IRI \\ \hline \end{tabular}
\end{table} 
Table 1: Description and source of features. \begin{table}
\begin{tabular}{c c c} \hline
**Classified Variable** & **Original Sort Code** & **Code** \\ \hline SUBGRADE\_MATL & 101–148 & 1 (fine-grained soil) \\  & 202–207, 252–257 & 2 (poorly graded coarse-grained soil) \\  & 201, 209–217, 259–267 & 3 (well-graded coarse-grained soil) \\  & 282, 287 & 4 (rock) \\ \hline DRAINAGE\_TYPE & 1 & 1 (no underground drainage) \\  & 2–7 & 2 (underground drainage) \\ \hline \end{tabular}
\end{table} 
Table 2: The principle of recoding. \(VIF\geq 10\), it means that there is a serious multicollinearity between the explanatory variables. The VIF values of the independent variables are shown in Figure 3.  
As can be seen in Figure 3, the VIF values of the variables CLOUD_COVER and SHORTWAVE_SURFACE in the dataset of this study are greater than 10, indicating a serious multicollinearity problem. CLOUD_COVER significantly influences the amount of solar shortwave radiation reaching the surface, where high cloud cover reduces shortwave radiation, thus creating a strong correlation between these two variables. To solve the problem of multicollinearity, the variable SHORTWAVE_SURFACE with a high VIF value was first removed, and the VIF value was recalculated. The new VIF values are shown in Table 3. After removing SHORTWAVE_SURFACE, the multicollinearity problem was sufficiently mitigated, as the VIF value of CLOUD_COVER dropped below the threshold of 10. This reduction occurred because the primary source of its multicollinearity was eliminated, reducing the \(R^{2}\) value when regressing CLOUD_COVER on the remaining variables. The number of independent variables in the dataset after multicollinearity treatment is 13.