# Optimizing Faulting Prediction for Rigid Pavements Using a Hybrid SHAP-TPE-CatBoost Model
## 4 Model Construction
### SHAP-Based Feature Interpretation  
One of the primary obstacles in implementing machine learning in practical business domains is the challenge of conveying the key indicators involved to operators, unlike linear regression, where this is relatively straightforward. Although the results obtained from machine learning are considered reliable, the process itself often lacks transparency and interpretability [31; 32]. Therefore, its effectiveness and reliability need to be reviewed and validated. To solve this issue, this paper proposes the application of the SHAP interpretation method to improve model interpretability. According to Table 7, the variable rankings based on SHAP values remain consistent in both the training and testing datasets, except for LTE and EM, which swapped positions. This indicates that the variable ranking is robust. Among all the variables, AGE has the greatest impact on faulting values, exerting over 1.5 times the influence of other significant \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **R Square** & **MAE** & **RMSE** \\ \hline TPE-RF & 0.755 & 0.500 & 0.928 \\ TPE-AdaBoost & 0.721 & 0.717 & 0.990 \\ TPE-GDBT & 0.867 & 0.387 & 0.684 \\ TPE-LightGBM & 0.865 & 0.483 & 0.688 \\ TPE-CatBoost & 0.906 & 0.346 & 0.573 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparing the performance of five models. Figure 7: Performance comparison among four benchmarked models: (**a**) RF model, (**b**) AdaBoost model, (**c**) GDBT model, and (**d**) LightGBM model. features. The variables LTE, DWL, and EM have a moderate level of impact on faulting values. Additionally, the variables TS and BTH have a relatively less significant impact on faulting values. Figure 8 shows the feature density scatter plot computed using the SHAP method. The scatter plot displays a decreasing trend in feature importance, with colors ranging from blue to red representing smaller to larger feature values. Each point represents the SHAP value of a sample, which reflects the contribution of that feature to an individual prediction, and the collection of points demonstrates the overall direction and magnitude of the feature's influence on the prediction. According to the results presented in Figure 8, the analysis suggests that AGE is the most influential factor affecting the model's predictions. As the pavement ages, both the SHAP values and faulting predictions increase. This is because over time, pavements experience prolonged load and climate conditions, resulting in accumulated displacement and frequent deformation, which is typically considered normal. Inadequate load transfer between adjacent slabs is a significant contributor to pavement faulting [33]. Hence, the load transfer efficiency (LTE) and dowel diameter (DWL) exhibit a negative correlation with faulting values. Moreover, the material properties of the pavement slabs, specifically the TS values, also exhibit a negative correlation with faulting. However, the study surprisingly finds a positive correlation between the elastic modulus (EM) and faulting values, contrary to common understanding. Typically, when the slabs possess higher stiffness (higher EM), critical stresses are reduced, and this helps resist faulting. One possible explanation for this positive correlation is that the EM is positively correlated with slab faulting while also negatively correlated with dowel diameter. Since dowel diameter is a primary factor in causing faulting, its impact might overshadow the influence of the elastic modulus on faulting [34]. Lastly, it is important to note that the pavement base layer also significantly affects the occurrence of faulting. The thickness of the pavement base layer, represented by BTH, shows a notable influence on faulting.