# Boosting Model Interpretability for Transparent ML in TBM Tunneling
## 4 Results
### Model Development and Results in Penetration Rate Prediction  
The dataset was split 80-20 for training and testing, reserving 20% of the training set for validation. The XGB model underwent hyperparameter tuning using GridSearchCV, while the ANN model adopted a simple architecture (15 \(\times\) 64 \(\times\) 32 \(\times\) 1) with a ReLU activation function (except in the output layer) and Adam optimizer (initial learning rate: 0.001). Techniques like a custom learning rate scheduler and EarlyStopping were employed to enhance convergence and prevent overfitting. While Huber loss was considered for its robustness against outliers, the MSE was chosen as the loss function for better alignment with regression objectives. The ANN was trained for 500 epochs with close monitoring of validation metrics. Results, as summarized in Table 7, indicate both models performed well. The Wasserstein distance (earth mover's distance, EMD) [25], was calculated to compare the distribution of predictions to the target distribution. The ANN achieved an EMD of 0.337 and the XGBoost model achieved 0.309, indicating a close match between predicted and actual distributions (Figure 10). The slightly lower EMD for XGBoost suggests it replicates the target distribution marginally better than the ANN model.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**TBM Operational Parameters** & **Min** & **Max** & **Mean** & **Std.** \\ \hline TORQUE CW [M\(\mathrm{N}\)m] & 4.30 & 13.50 & 9.77 & 1.47 \\ \hline WORKING PRESSURE CW [bar] & 53.00 & 169.00 & 122.35 & 18.27 \\ \hline TOTAL FORCE TC [kN] & 5930.00 & 26,118.00 & 17,903.09 & 2869.86 \\ \hline SPEED TC [mm/min] & 8.00 & 24.00 & 17.17 & 2.19 \\ \hline TORQUE SC [kNm] & 0.00 & 122.00 & 78.47 & 14.74 \\ \hline WORKING\_PRESSURE SC [bar] & 0.00 & 154.00 & 98.96 & 18.65 \\ \hline PRESSURE GI [bar] & 0.02 & 3.55 & 1.97 & 0.53 \\ \hline TOTAL GROUT A [L] & 1011.00 & 8817.00 & 6333.44 & 500.90 \\ \hline TOTAL GROUT B [L] & 107.00 & 621.00 & 476.27 & 43.75 \\ \hline A/B VOLUME & 2.14 & 17.67 & 13.36 & 1.16 \\ \hline EXCAVATING [t/h] & 29.00 & 252.00 & 182.44 & 32.06 \\ \hline FACE PRESSURE EP [bar] & 0.00 & 1.97 & 1.29 & 0.28 \\ \hline AD PERCENTAGE & 0.10 & 0.80 & 0.61 & 0.09 \\ \hline RING PERCENTAGE & 0.12 & 0.58 & 0.30 & 0.06 \\ \hline STOP PERCENTAGE & 0.00 & 0.55 & 0.09 & 0.10 \\ \hline \end{tabular}
\end{table}
Table 6: Description table of the model’s input parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Models** & **MSE (mm/min)** & **RMSE (mm/min)** & **Wasserstein Distance** \\ \hline  & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline XGB & 0.38 & 1.90 & 0.62 & 1.38 & 0.33 & 0.42 \\ \hline ANN & 1.06 & 2.26 & 1.03 & 1.50 & 0.30 & 0.40 \\ \hline \end{tabular}
\end{table}
Table 7: Metrics for the training and testing process for the two models.  
While EMD highlights the models' ability to preserve statistical characteristics like mean, variance, and skewness, pointwise accuracy metrics such as the RMSE and MAE are necessary for evaluating individual prediction errors. Low values in these metrics would further validate the models' accuracy.  
The distribution plots (Figure 11) compare the ANN and XGBoost predictions against actual values, highlighting good alignment for both models. While ANN predictions show slight deviations in the tails, XGBoost predictions exhibit closer overlap with the actual distribution, as evidenced by its smaller Wasserstein distance. Both models display similar statistical properties, with XGBoost demonstrating marginally better accuracy in capturing the overall distribution.  
The small Wasserstein distances reflect strong model performance, with XGBoost slightly outperforming the ANN. However, selecting the \"better\" model should also consider factors like computational efficiency, robustness, interpretability, and pointwise accuracy, alongside Wasserstein distance.  
In Figure 12, a comparison of the models is depicted, showcasing their ability to accurately track the actual target trend (generalization).