# Predicting Putting Development of Pavement with Flexible Overlay Using Artificial Neural Network
## 3 Rutting Prediction
### Sensitivity Analysis of Parameters  
Unimportant variables can reduce the computational efficiency and increase the risk of overfitting. The inputs fed into ANN models should be factors that affect the output. Before being fed into ANN models, the dataset, such as the test section number and some redundant indicators, should be eliminated. Moreover, the input variables should not be correlated with each other. Feature importance can help to screen features. In this study, random forest, an integrated algorithm, was used to compute the impurity-based feature importance. A random forest is composed of many decision trees, and in this algorithm, the tree grows when the feature can make the variance of a target decrease the most [33]. The more a feature minimizes the error, the more important it is to the target. Feature importance analysis based on the random forest was carried out in this study, and the result is presented in Figure 4. The explanations of the variables in the graph are shown in Table 2.  
According to the ranking results of the importance of the variables shown in Figure 3, the average annual number of freeze-thaw cycles and historical average daily temperature gradient have a great influence on rutting, in addition to the ESALs and service years. In addition, the structure of the surface layer and the material of the surface layer play important roles in rutting, especially the asphalt surface thickness and voids in mineral aggregate (VMA). The cumulative rut damage (PRIOR) of the original pavement also has a great impact on the pavement performance after repair. If the surface layer is not properly treated before paving, then it will provide an uneven underlayer structure to the renovated pavement. Thus, it is necessary to conduct a thickness milling treatment for the original road before overlay repair.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistic Name** & **Training Set** & **Test Set** \\ \hline Sample distribution (4829) & 3394 & 1435 \\ Distribution of sample proportion & 0.703 & 0.297 \\ Relative error of left rut depth (RUT\_RD\_IWP) & 0.116 & 0.132 \\ Relative error of right rut depth (RUT\_RD\_OWP) & 0.141 & 0.139 \\ Relative error of left wheel track band width & 0.296 & 0.291 \\ Relative error of right wheel track band width & 0.289 & 0.298 \\ (RUT\_RW\_OWP) & & \\ Relative error of cross-section positive area & 0.274 & 0.279 \\ (RUT\_POS\_AREAS) & & \\ Relative error of cross-section negative area & 0.159 & 0.182 \\ Relative error of cross-section fill area & & \\ (RUT\_FILL\_AREAS) & & \\ Average overall relative error & 0.201 & 0.218 \\ (L(\(\
u,\hat{y}\))) & 2392.743 & 1139.270 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Reliability analysis of rut model.  
According to the above parameter sensitivity analysis, it is considered that the rutting of the repaired pavement is closely related to the cumulative damage of the original pavement and the repair treatment scheme, in addition to traffic and other environmental conditions.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Variable** & **Description** \\ \hline T\_ESAL\_TOTAL & Equivalent uniaxial loads after repair \\ YEAR\_TOTAL & Service year after repair \\ HIST\_ANNUAL\_AIR\_FREEZE\_CYCLES & Annual freeze–thaw cycles \\ HIST\_TEMP\_GRADIENT & Average daily temperature difference \\ ORIG\_SPEC\_GRAV & Specific gravity of original surface mixture \\ PRIOR\_NEG\_AREAS & Area characteristics of original pavement \\  & cross-section \\ PRIOR\_FILL\_AREAS & Filling area of original pavement cross-section \\ SUBBASE\_T & Base thickness \\ LANE\_WIDTH & Lane width \\ ORIG\_VMA & VMA of original surface mixture \\ PRIOR\_RD\_OWP & Putting of raw pavement right wheel track \\ YEAR\_OVER & Repair year \\ OVER\_VMA & Overlay VMA \\ SUBBASE\_DENSITY & Compaction density of subbase \\ PAV\_OVER\_T & Overlay thickness \\ OVER\_MS & Marshall stability overlay \\ \hline \hline \end{tabular}
\end{table}
Table 2: Explanations of variables.  
Figure 4: Importance analysis based on random forest.