## 5 Results and Discussion  
### Performance Comparison  
The variation in strength of bio-cemented sand directly relates to the design safety and engineering performance of overlying structures. The LARO-EnML proposed in this study effectively addresses nonlinearity and multi-factor coupling issues in MICP-treated sand strength assessment by integrating the advantages of multiple learning methods. To comprehensively evaluate LARO-EnML performance, this section conducts a systematic comparative analysis with various base learners to thoroughly analyse the effectiveness of the ensemble strategy. Table 1 presents the performance evaluation indicator comparison results for each model on the training set. As shown in the table, the LARO-XGBoost demonstrates the most excellent performance on the training set, with RMSE of 0.2694, MAE of 0.1673, R\({}^{2}\) reaching 0.9807, and OI value of 0.9818, with all indicators representing the best performance among all models. The LARO-EnML follows closely, with RMSE of 0.3018, MAE of 0.1484, R\({}^{2}\) of 0.9758, and OI value of 0.9784, ranking second among all models. Among base learners, LARO-optimised models generally outperform their original versions. Compared to the standard XGBoost, LARO-XGBoost shows significant improvement, with RMSE decreasing from 0.3262 to 0.2694 and R\({}^{2}\) increasing from 0.9717 to 0.9807, demonstrating the significant enhancement of the LARO method on model performance. Similarly, LARO-SVM exhibits obvious performance improvement compared to the standard SVM model, with RMSE substantially decreasing from 0.9323 to 0.5762 and R\({}^{2}\) increasing from 0.7688 to 0.9117. It should be noted that MLP serves as the meta-learner in architecture, with its role being to learn combination relationships among base learner outputs, resulting in relatively weaker performance on the training set. Beyond quantitative indicators, Figure 6 intuitively demonstrates the prediction performance differences of various models on the training set through visualisation. From the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model Name**} & \multicolumn{4}{c}{**Evaluation**} \\ \cline{2-5}  & **RMSE** & **MAE** & **R\({}^{2}\)** & **OI** \\ \hline XGBoost & 0.3262 & 0.2155 & 0.9717 & 0.9755 \\ LARO-XGBoost & 0.2694 & 0.1673 & 0.9807 & 0.9818 \\ SVM & 0.9323 & 0.4142 & 0.7688 & 0.8549 \\ LARO-SVM & 0.5762 & 0.2591 & 0.9117 & 0.9376 \\ MLP & 0.7244 & 0.3856 & 0.8604 & 0.9073 \\ LARO-EnML & 0.3018 & 0.1484 & 0.9758 & 0.9784 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison of ML models on the training set. scatter plots, it can be observed that prediction points from LARO-XGBoost and LARO-EnML models are most closely distributed around the ideal prediction line (dashed line), indicating their high prediction accuracy. Residual distribution histograms show that LARO-XGBoost has an average bias of 0.00 and LARO-EnML has an average bias of 0.02, with both models' residuals primarily concentrated around zero values, presenting favourable distribution characteristics. In contrast, other base learners exhibit relatively dispersed residual distributions, particularly MLP, with an average bias reaching 0.06. From the perspective of evaluating the actual application value of models, performance on test data serves as the key criterion for measuring model generalisation capability and engineering applicability. As shown in Table 2, the LARO-EnML demonstrates optimal performance on the test set. This model achieves an RMSE of 0.5449, MAE of 0.2853, R\({}^{2}\) of 0.9570, and OI value of 0.9597, with all indicators representing the best performance among all models, fully demonstrating the superiority of ensemble learning strategies in generalisation capability. Particularly noteworthy is the performance variation from training set to test set.