## 4 Explanation of the Prediction Models Using Explainable AI
### Analysis of the Prediction Models  
In this chapter, the authors employ the feature importance and SHAP summary plot results to illustrate the predictive models derived in each case. Figure 14 displays the importance of the features in each case, quantifying the impact of each feature on the predictive model. Specifically, Figure 14a showcases the impacts of independent features on the predictive models derived by the RF, XGB, and LightGBM algorithms in case 1. For the best-performing LightGBM, the settlement exhibits the highest impact at 43.17%, followed by P\({}_{Z}\) and P\({}_{\mathrm{L}}\) at 9.94%, T\({}_{\mathrm{F}}\) at 6.44%, O\({}_{\mathrm{H}}\) at 6.00%, O\({}_{\mathrm{V}}\) at 5.92%, P\({}_{\mathrm{P}}\) at 5.40%, P\({}_{\mathrm{CTC}}\) at 5.24%, EG at 3.44%, P\({}_{\mathrm{D}}\) at 2.55%, and P\({}_{\mathrm{N}}\) at 1.95%; B\({}_{\mathrm{R}}\) does not affect the prediction model at all. The feature importance in case 2 is illustrated in Figure 14b, where P\({}_{\mathrm{L}}\) has the highest impact at 22.02%, followed by P\({}_{\mathrm{CTC}}\) at 15.26%, P\({}_{\mathrm{P}}\) at 11.42%, E\({}_{\mathrm{G}}\) at 10.09%, P\({}_{\mathrm{D}}\) at 10.04%, P\({}_{\mathrm{Z}}\) at 8.27%, T\({}_{\mathrm{F}}\) at 6.62%, P\({}_{\mathrm{N}}\) at 6.55%, and O\({}_{\mathrm{V}}\) and O\({}_{\mathrm{H}}\) at 4.40% and 3.99%, respectively; B\({}_{\mathrm{R}}\) has a negligible impact at 1.35%. Case 3 is summarized in Figure 14c, where the settlement has the highest impact at 42.01%, followed by P\({}_{\mathrm{Z}}\) at 10.92%, P\({}_{\mathrm{L}}\)/P\({}_{\mathrm{D}}\) at 8.87%, T\({}_{\mathrm{F}}\) at 6.99%, P at 5.74%, O\({}_{\mathrm{V}}\) at 5.60%, P\({}_{\mathrm{CTC}}\) at 5.92%, O\({}_{\mathrm{H}}\) at 5.55%, AP\({}_{\mathrm{H}LE}\)/A\({}_{\mathrm{RAFT}}\) at 5.09%, and EG at 3.30%. Figure 14d shows the feature importance in case 4, where P\({}_{\mathrm{CTC}}\) has the highest impact at 19.02%, followed by AP\({}_{\mathrm{P}LE}\)/A\({}_{\mathrm{RAFT}}\) at 16.03%, P\({}_{\mathrm{P}}\) at 15.53%, P\({}_{\mathrm{Z}}\) at 14.54%, T\({}_{\mathrm{F}}\) at 9.29%, E\({}_{\mathrm{G}}\) at 8.07%, P\({}_{\mathrm{L}}\)/P\({}_{\mathrm{D}}\) at 7.96%, and O\({}_{\mathrm{H}}\) and O\({}_{\mathrm{V}}\) at 4.81% and 4.75%, respectively. Figure 14: _Cont._  
Figure 14: Cont. The analysis of the feature importance reveals that settlement is of significant importance in cases 1 and 3, where it is included as an independent variable. Meanwhile, PCTC has the highest feature importance in cases 2 and 4, where settlement is not considered. However, while the feature importance results can quantify the impacts of features on the predictive value of a target feature, they do not provide insight into whether the prediction value increases or decreases as the number of features increases. Therefore, the impact of each feature on the prediction model, as measured by the SHAP value, is analyzed in the summary plot presented in Figure 15.  
In the summary plot, a large absolute value of the SHAP value indicates a large contribution to the predicted value. A positive SHAP value indicates that as the feature value increases, the prediction value also increases, and as the feature value decreases, the prediction value decreases. Figure 15a illustrates the contributions of the features in the model derived by the best-performing LightGBM algorithm in case 1 as a function of the SHAP value, with the predicted values shown in order of magnitude. The feature with the largest contribution is P\({}_{\rm L}\), with the SHAP value increasing as the feature value increases. This trend indicates that the pile axial stress increases with the length of the pile, likely due to the larger allowable load of long piles compared with short piles. Next is P\({}_{\rm Z}\), which demonstrates that the pile axial stress increases as the feature value decreases, meaning that the pile axial stress is greater at the top of the pile.