# Several Tree-Based Solutions for Predicting Flyrock Distance Due to Mine Blasting
## 5 Results and Discussion  
Four tree-based methods were developed in this study, i.e., DT, RF, XGBoost, and AdaBoost, to predict flyrock due to blasting operations. The performance of each model was evaluated by four popular performance indices (i.e., R\({}^{2}\), RMSE, VAF, and the A-10 index). Table 9 shows the results of these tree-based models based on the training and testing phases. The accuracy of the developed models was compared using a ranking system introduced by [PERSON] et al. [97]. It is observed from Table 9 that although RF and DT achieved acceptable prediction accuracy, the AdaBoost model, which used the RF classifier in its core algorithm, yielded the best results, with a final rank of 32. Furthermore, XGBoost performed better in prediction than RF and DT; however, its performance compared to the AdaBoost model is poor. Although the datasets used in the current study have not been used in any other studies, the authors tried to compare the results with similar studies in the literature. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **Range** & **Value** \\ \hline Weak learner algorithm & Random Forest, Decision Tree & Random Forest Classifier \\ Tree depth & [2; 3; 4; 5; 6] & 3 \\ Algorithm & SAMME, SAMME.R & SAMME \\ criterion & Entropy, Gini & Entropy \\ Number of estimators & [50; 100; 200; 300] & 100 \\ Learning rate & [0.5, 1, 1.5, 2] & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The best AdaBoost model’s features in predicting flyrock. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**R\({}^{2}\)**} & \multicolumn{3}{c}{**RMSE**} & \multicolumn{3}{c}{**VAF**} & \multicolumn{3}{c}{**A10**} & **Final Rank** \\ \hline
**Model Name** & & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline AdaBoost & & 0.99 & 0.98 & 1.47 & 2.66 & 99.56 & 98.87 & 0.98 & 0.98 & \\ \multirow{2}{*}{XGBoost} & \multirow{2}{*}{Rank score} & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 4 & 32 \\  & & 0.97 & 0.92 & 2.91 & 4.85 & 97.33 & 91.99 & 0.97 & 0.94 & \\ \multirow{2}{*}{RF} & \multirow{2}{*}{Rank score} & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 3 & 24 \\  & & 0.93 & 0.91 & 4.32 & 4.86 & 92.96 & 92.12 & 0.96 & 0.91 & \\ \multirow{2}{*}{DT} & \multirow{2}{*}{Rank score} & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 2 & 16 \\  & & 0.89 & 0.84 & 5.72 & 6.58 & 89.39 & 84.81 & 0.89 & 0.84 & \\ \multirow{2}{*}{XGBoost} & \multirow{2}{*}{Rank score} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance indices of the developed models for flyrock prediction. Figure 9: Performance of SAMME and SAMME.R algorithms in AdaBoost model. [PERSON] et al. [23] modelled flyrock by GEP using the same input parameters used in the current study. The final results for the best GEP model were R2 train = 0.83 and R2 test = 0.91. [PERSON] and [PERSON] [98] developed another GEP model for flyrock prediction using the same inputs. They received R2 train = 0.91 and R2 test = 0.84 for their GEP model. In another study, [PERSON] et al. [99] developed a boosted regression tree (BRT) for flyrock estimation. The highest results for BRT are R2 train = 0.96 and R2 test = 0.84. In addition, by probing into some other studies that have been conducted in recent years [100, 101, 102, 103, 104, 105, 106]. It can be seen that the results of the AdaBoost and XGBoost models developed in the current study to predict flyrock distance are more accurate compared to similar investigations in the literature. Figure 10 presents the correlation between predicted and measured flyrock for the AdaBoost model's training and testing sets. A coloured shadow was applied to the plots to understand data concentration and distribution better. It is clear that AdaBoost is a powerful technique that is able to predict flyrock values that are very close to the measured ones. Figure 11 shows the model variables' importance results of four tree-based techniques, i.e., AdaBoost, XGBoost, RF, and DT.