## 3 Prediction Model of Pile Axial Stress  
### Data Exploration and Preprocessing  
This study utilizes a variety of variables and algorithms to derive and optimize a model capable of predicting the axial stress of a pile during tunnel excavation adjacent to a piled raft. The numerical analysis is used to identify the variables, and the resulting settlement is used as input data for machine learning. However, the allowable load applied to the piled raft is excluded from the input data for machine learning because it is expected to have a significant impact on the prediction model and, therefore, to predict the axial stress change accordingly. In this study, the authors analyze the performance of the prediction models derived by varying the features of the input data. Table 3 shows that four cases are examined. In case 1, settlement is included as an independent feature among the variables applied to the numerical analysis, and in case 2, settlement is excluded from case 1 and applied to machine learning. In cases 3 and 4, the authors create new features by combining the variables considered in the numerical analysis. Specifically, \(\rm{A_{PLE}}/\rm{A_{RAFT}}\) is the cross-sectional area of the pile relative to the area of the raft in the piled raft, a variable created by combining \(\rm{P_{D}}\), \(\rm{P_{N}}\), and \(\rm{B_{R}}\) from Table 1. Additionally, \(\rm{P_{L}}/\rm{P_{D}}\) is the length-diameter ratio of the pile, while \(\rm{P_{P}}\) and \(\rm{P_{Z}}\) indicate the location at which the pile axial stress is measured, with \(\rm{P_{P}}\) divided into the left, center, and right based on the raft center and determined by applying the \(\rm{P_{CTC}}\) value. \(\rm{P_{Z}}\) is the depth at which the pile axial stress is measured. In case 3, the authors consider settlement as a feature for machine learning, whereas in case 4, settlement is excluded. Table 3 provides a summary of the features considered for machine learning in each case. Figure 7 shows that the null of the input data is missing in each case. To identify the presence of any outliers within the data, the distribution of the dependent variable was subjected to examination, as illustrated in Figure 8. The analysis confirmed that no outliers are present within the data. While it is common for data obtained from field measurements to contain outliers, the present study did not extensively investigate the handling of outliers and instead relied on the results derived from numerical analysis. \begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline
1 & \(\rm{E_{G}}\) & \(\rm{E_{G}}\) & \(\rm{E_{G}}\) & \(\rm{E_{G}}\) \\
2 & \(\rm{O_{H}}\) & \(\rm{O_{H}}\) & \(\rm{O_{H}}\) & \(\rm{O_{H}}\) \\
3 & \(\rm{O_{V}}\) & \(\rm{O_{V}}\) & \(\rm{O_{V}}\) & \(\rm{O_{V}}\) \\
4 & \(\rm{P_{D}}\) & \(\rm{P_{D}}\) & \(\rm{P_{L}}/\rm{P_{D}}\) & \(\rm{P_{L}}/\rm{P_{D}}\) \\
5 & \(\rm{P_{L}}\) & \(\rm{P_{L}}\) & \(\rm{A_{PLE}}/\rm{A_{RAFT}}\) & \(\rm{A_{PLE}}/\rm{A_{RAFT}}\) \\
6 & \(\rm{B_{R}}\) & \(\rm{B_{R}}\) & \(\rm{P_{CTC}}\) & \(\rm{P_{CTC}}\) \\
7 & \(\rm{P_{N}}\) & \(\rm{P_{N}}\) & \(\rm{T_{F}}\) & \(\rm{T_{F}}\) \\
8 & \(\rm{P_{CTC}}\) & \(\rm{P_{CTC}}\) & \(\rm{P_{P}}\) & \(\rm{P_{P}}\) \\
9 & \(\rm{T_{F}}\) & \(\rm{T_{F}}\) & \(\rm{P_{Z}}\) & \(\rm{P_{Z}}\) \\
10 & \(\rm{P_{P}}\) & \(\rm{P_{P}}\) & Settlement & \\
11 & \(\rm{P_{Z}}\) & \(\rm{P_{Z}}\) & & \\
12 & Settlement & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Features for machine learning in each case. Figure 7: _Cont._  
Figure 8: Distribution of raw data. Figure 7: Null checking of the input data: (**a**) case 1; (**b**) case 2; (**c**) case 3; (**d**) case 4. The results of the correlation analysis between the features in each case are presented in Figure 9. It is important to note that correlation does not necessarily imply causality between the features, but rather a statistical relationship.