# Predicting Putting Development Using Machine Learning Methods Based on RIOCHTrack Data
## 2 Methodology
### Feature Selection  
The input variables, comprising internal and external factors, affect the rutting changes to some extent. The internal factors include pavement structure type and structural layer thickness, as well as modulus, asphalt, aggregate, and mixture properties, whereas the main external factors are the axle load and temperature. The temperature is taken as the daily average temperature during the vehicle loading period. Asphalt type, gradation, and porosity are important to control indicators in the asphalt mixture design process, which greatly affect the anti-rutting performance of the mixture [32]. The input variables after initial selection are listed as follows.  
Climate: daily average temperature.  
Cumulative axle load: ESALs.  
Figure 4: Axle load schematic of RIOHTRack.  
Figure 5: Cumulative action times of RIOHTRack.  
Asphal mixture upper/middle/lower layers: thickness, modulus, gradation, nominal maximum aggregate size, asphalt penetration, asphalt ductility, asphalt softening point, porosity, asphalt content, and bulk density of asphalt mixture.  
Base, subbase, and subgrade: thickness, material type, and modulus.  
Removing redundant features is crucial as they not only lead to increased computational costs but also affect the computational efficiency of the model and increase the risk of overfitting. Therefore, to improve the computational performance of the model, it is essential to calculate the importance of features and further screen the input variables before training the model. In this chapter, the importance of all variables is calculated using RF, as shown in Figure 6. Thereafter, variables with feature importance of 0 are eliminated, such as AC1 penetration_25, AC2 dynamic stability, AC3 VISC_135, and Subgrade Mr.  
Removing unimportant variables does not mean that the remaining variables can be directly used to train the model. It is also necessary to perform multicollinearity diagnosis on the remaining variables and subsequently eliminate any variables exhibiting multicollinearity. This study adopts the reverse elimination method. Reverse elimination is a feature selection method for multiple linear regression, where a significance level of \(\alpha=0.05\) is first defined, after which all variables are used to fit the model. Next, the variable with the highest \(p\)-value is selected and compared with \(\alpha\). If the \(p\)-value of the variable is greater than \(\alpha\), the variable is removed. The model is then refitted with the remaining variables, and the process is repeated until all variables are accounted for. The results after variable filtering are listed in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variables** & **Min** & **Max** & **Mean** & **Std** & **Skew** & **Kurt** \\ \hline AC1 Mr & 6481 & 8083 & 7789 & 428.7556 & \(-\)1.6424 & 2.2024 \\ AC1 passing 4.75 mm (\%) & 16.4 & 34.2 & 30.0 & 4.6198 & \(-\)1.3872 & 1.5642 \\ AC1 passing 0.075 mm (\%) & 2.2 & 9.7 & 7.1052 & 1.6269 & \(-\)0.7618 & 2.4100 \\ AC1D.P & 4.29 & 5.56 & 5.008 & 0.3621 & 0.1112 & \(-\)0.9678 \\ AC1 VV (\%) & 4.18 & 13.88 & 5.33 & 2.0875 & 3.5617 & 11.8116 \\ AC1 Gsb & 2.3025 & 2.4919 & 2.4546 & 0.0417 & \(-\)2.4832 & 6.4980 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical information of variables.  
Figure 6: Feature importance analysis based on RF.