## 6 Conclusions  
Precise estimation of BI is necessary for any ground excavation project, and this issue requires the application of appropriate prediction models. With this in view, several advanced ML methods, including LGP, BRT, LWLR, and KStar models, were proposed to estimate BI. In this regard, a database collected from a tunneling project in Pahang state, Malaysia, was used, using four input parameters (V\({}_{\text{p}}\), I\({}_{\text{s50}}\), D, and R\({}_{\text{n}}\)) and BI as the output parameter. In the modeling processes, 64 and 21 datasets, respectively, were used for training and testing phases. Finally, the models' accuracy was compared using several statistical criteria such as R and RSME. The findings of this study can be summarized as follows:  
1. Based on the results, all developed models' performance capacity was suitable and acceptable. Accordingly, all proposed models can be used with confidence for future research on predictions of other issues in the field of rock mechanics.
2. Among the proposed models, the KStar (R = 0.9984 and RMSE = 0.0865) model predicted BI with the best performance in the training phase, while the best performance for the testing phase was achieved by the LGP (R = 0.9529 and RMSE = 0.4838) model. In addition, both LWLR (R = 0.9490 and RMSE = 0.6607) and BRT (R = 0.9433 and RMSE = 0.6875), ranking second and third, respectively, lead to desired results for modeling BI values.  
Figure 12: The influence input variables ranking for estimation of BI value.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metric** & **All-R\({}_{\text{n}}\)** & **All-V\({}_{\text{p}}\)** & **All-Dry Density** & **All-I\({}_{\text{s50}}\)** & **All** \\ \hline R & 0.9273 & 0.9163 & 0.9081 & 0.9169 & 0.9433 \\ RMSE & 0.6959 & 0.7944 & 0.8027 & 0.7861 & 0.6875 \\ MAPE & 4.4592 & 5.1695 & 5.4642 & 5.0433 & 4.3884 \\ SI & 0.0560 & 0.0639 & 0.0646 & 0.0633 & 0.0553 \\ I\({}_{\text{A}}\) & 0.9318 & 0.9018 & 0.9004 & 0.9049 & 0.9324 \\ St.D & 1.6277 & 1.6277 & 1.6277 & 1.6277 & 1.6277 \\ Rank & 4.0000 & 3.0000 & 1.0000 & 2.0000 & - \\ \hline \hline \end{tabular}
\end{table}
Table 5: The sensitivity analysis results for all possible situations.  
The authors recommend increasing the accuracy of BI modeling as a possible future study, examining the ensemble of stacked models to integrate the advantages of standalone data-driven models.
* Sensitivity analysis demonstrated that dry density (\(D\)) was the most influential parameter with respect to BI.  
Conceptualization, M.H. and A.S.M.; methodology, M.J., I.A., M.M.S.S. and M.K.; validation, M.J. and I.A.; investigation, A.S.M. and M.K.; writing--original draft, M.H., A.S.M., M.J., I.A., M.M.S.S. and M.K., writing--review and editing, M.H., A.S.M., M.J., I.A., M.M.S.S. and M.K.; supervision, M.H.; funding acquisition, M.M.S.S. All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by the Ministry of Science and Higher Education of the Russian Federation, under the strategic academic leadership program 'Priority 2030' (Agreement 075-15-2021-1333, dated 30 September 2021).  
Not applicable.  
The authors declare no conflict of interest.