# Optimizing Faulting Prediction for Rigid Pavements Using a Hybrid SHAP-TPE-CatBoost Model
## 3 Data Preparation
### Boruta-Based Feature Selection  
The Boruta algorithm, implemented using the boruta 0.3 library in Python, was employed for feature selection in this study. After 100 iterations, six key features were identified as the most influential factors in predicting faulting, as shown in Table 2. Additionally, statistical information for each feature is provided (see Table 3). The frequency distribution for each feature can be observed in Figure 1, where 'n' represents the frequency number indicating the number of samples within each variable's subinterval. When developing the faulting prediction model, it is crucial to examine the interdependence among the sample features to mitigate the issue of multicollinearity. By examining the Pearson correlation coefficient matrix of the features (see Figure 2), it can be observed that there is no significant issue of multicollinearity among the input variables. This can be evidenced by the absolute values of the correlation coefficients being far from 1.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Variable ID** & **Variable Type** & **Unit** & **Description** \\ \hline FLT & Output & mm & Average calculated edge faulting. \\ DWL & Structure & mm & The outer diameter of dowel bars. \\ PR & & / & Poisson’s ratio of concrete slab. \\ EM & & kPa & Modulus of elasticity of concrete slab. \\ CS & & kPa & Compressive strength of concrete slab. \\ TS & & kPa & Splitting tensile strength of concrete slab. \\ CTE & & mm/mm/deg C & Coefficient of Thermal Expansion value of concrete slab. \\ P10 & & \% & Percent subgrade passing sieve No. 10. \\ P40 & & \% & Percent subgrade passing sieve No. 40. \\ P200 & & \% & Percent subgrade passing sieve No. 200. \\ PI & & \% & Plasticity index. \\ BTH & & mm & Base thickness. \\ LTE & & \% & Load transfer efficiency. \\ PRC & Climate & mm & The annual precipitation. \\ FIN & / & Freezing index. \\ ESAL & Traffic & / & Estimated ESALs. \\ CESAL & / & Estimated Cumulative ESALs. \\ AGE & Age & year & The number of years that passed since the pavement was built. \\ \hline \end{tabular}
\end{table}
Table 1: Definition of all features and output variable.  
\begin{table}
\begin{tabular}{c c c} \hline
**Variable Type** & **Variable ID** & **Unit** \\ \hline Input & DWL & mm \\  & EM & kPa \\  & TS & kPa \\  & BTH & mm \\  & LTE & \% \\  & AGE & year \\ Output & FLT & mm \\ \hline \end{tabular}
\end{table}
Table 2: Feature selection results based on the Boruta algorithm.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Variables** & **Maximum Value** & **Minimum Value** & **Mean** & **Standard Deviation** \\ \hline FLT & 0 & 9.100 & 1.534 & 1.631 \\ DWL & 0 & 31.8 & 12.365 & 14.575 \\ EM & \(1.310\times 10^{7}\) & \(4.827\times 10^{7}\) & \(2.939\times 10^{7}\) & \(5.609\times 10^{6}\) \\ TS & 2916.585 & 6260.660 & 4204.700 & 688.453 \\ BTH & 22.900 & 589.300 & 146.754 & 84.890 \\ LTE & 19.462 & 93.550 & 70.238 & 15.295 \\ AGE & 2 & 32 & 15.981 & 6.153 \\ \hline \end{tabular}
\end{table}
Table 3: Statistics that provide fundamental information about variables.  
Figure 1: Distribution of variables: (**a**) DWL, (**b**) EM, (**c**) TS, (**d**) BTH, (**e**) LTE, and (**f**) AGE.