# Prediction Model for Shield Tunneling Roll Angle and Pitch Angle: A PCA-PSO-LGBM Approach
## 4 Result and Discussion
### Comparison of Prediction Results of Different Models  
To verify the superiority of the PCA-PSO-LGBM model, this paper introduced the Bayesian optimization algorithm [31] and three machine learning models: Random Forest [32], Support Vector Regression [33], and K-nearest neighbors [34] as comparisons. The PCA-Bayesian-LGBM, PCA-LGBM, PCA-PSO-RF, PCA-PSO-SVR, and PCA-PSO-KNN prediction models were constructed to examine their predictive performance on shield roll angle and pitch angle, with the results shown in Figures 14 and 15. On one hand, by comparing the prediction indicators of the three models--PCA-PSO-LGBM, PCA-Bayesian-LGBM, and PCA-LGBM--it is evident that the PCA-LGBM model had the worst predictive performance, with an \(MAE\) of \(0.088^{\circ}\) for roll angle and \(0.073^{\circ}\) for pitch angle, and \(R^{2}\) of \(0.968\) and \(0.965\), respectively. This indicates that relying solely on the manual random selection of LGBM hyperparameters cannot achieve the highest prediction accuracy. Although the PCA-Bayesian-LGBM model shows better predictive performance than the PCA-LGBM model, with an \(MAE\) of \(0.077^{\circ}\) for roll angle and \(0.051^{\circ}\) for pitch angle, and \(R^{2}\) values of \(0.974\) and \(0.983\), respectively, it still falls short of the PCA-PSO-LGBM \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Hyperparameters** & **Colsample\_Bytes** & **Learning\_Rate** & **Max\_Depth** & **Min\_Child\_Samples** & **n\_Estimators** & **Num\_Leaves** & **Reg\_Alpha** & **Reg\_Lambda** & **Subsample** \\ \hline Roll angle & 1 & 0.0680 & 5 & 3 & 2796 & 17 & 0.1 & 0.0269 & 0.2479 \\ Pitch.angle & 1 & 0.0868 & 7 & 7 & 1258 & 19 & 0.1 & 0.001 & 0.7544 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of hyperparameter optimization for the roll and pitch angle prediction model. Figure 12: Pitch angle prediction results: (**a**) prediction performance on the training, validating, and testing set; (**b**) comparison between actual and predicted values in the testing set. Figure 13: Statistics of absolute error values in the test set: (**a**) roll angle; (**b**) pitch angle. model. This is because Bayesian optimization relies on probabilistic models (such as Gaussian processes), constructing surrogate models to approximate the objective function and using acquisition functions (such as expected improvement) to select the next evaluation point. Theoretically, this method can more effectively explore and exploit the search space, but in practice, due to potential inaccuracies in the surrogate model, the selected evaluation points may not be optimal, thereby affecting the final predictive performance. Especially when facing an LGBM model with a high-dimensional hyperparameter space, Bayesian optimization may suffer from the \"curse of dimensionality\", where the required number of sampling points increases exponentially with the dimension, potentially leading to insufficient exploration during optimization. While particle swarm optimization is also affected by dimensionality, its characteristic of swarm searching can alleviate this issue to some extent. Figure 14: Comparison of \(MAE\) for prediction results from different models. Figure 15: Comparison of \(R^{2}\) for prediction results from different models. On the other hand, by comparing the prediction metrics of the four models--PCA-PSO-LGBM, PCA-PSO-RF, PCA-PSO-SVR, and PCA-PSO-KNN--it is evident that the PCA-PSO-RF model has an \(MAE\) of 0.102\({}^{\circ}\) for shield roll angle and 0.048\({}^{\circ}\) for pitch angle, with the \(R^{2}\) values of 0.924 and 0.980, respectively. The prediction performance for the roll angle is not as good as that of the PCA-PSO-LGBM model, while the prediction performance for the pitch angle is comparable to that of the PCA-PSO-LGBM model. However, since each decision tree in the RF model requires independent computation during prediction, this increases computational complexity and results in a slower prediction speed compared to the LGBM model.