## 6 Conclusions  
The prediction of MFS using AI-based techniques has practical implications in the mining industry, since it improves environmental and miners' safety while lowering costs. To model MFS prediction, this study employed three AI tree-based techniques coupled with the TPE optimization algorithm. Furthermore, this study utilized the SHAP technique to systematically evaluate the stability, robustness, and interpretability of the model. Lastly, an interactive web application was developed to facilitate the MFS predictions. The main conclusions of this study are as follows:  
1. Adding 3% noise to augment the dataset did not significantly distort the original dataset. Moreover, the large-scale database of 3740 samples provided deeper insights into the input and output parameters and thus enhanced the model's predictive capabilities;
2. The model evaluation results demonstrated that the TPE-ET model performed better than the other models in predicting MFS, achieving R\({}^{2}\), RMSE, MAE, and max error optimal values of 0.93, 0.04, 0.03, and 0.25 on the testing set;
3. The model interpretability results illustrated that rock parameters and geological conditions were the most significant parameters in predicting MFS. In this study, XB (m) and E (GPa) had the most significant impact and a positive contribution to the models' predictions.  
The tree-based algorithms utilized in this study produced outstanding predictions. However, there are still limitations, such as (1) the fact that this study used a small number of input parameters, which can limit the true precision of the model's prediction considering that there are many factors that influence MFS; (2) the fact that other powerful tree-based algorithms such as the histogram-based gradient boosting algorithm, extreme gradient boosting algorithm, and gradient boosting algorithm were not explored in the current study; and (3) the fact that noise addition during data augmentation reduced the data quality. Some of the recommendations for future research include the following: (1) employing ensemble methods may enhance the generalization capacities of the models, for example integrating tree-based models with other methods such as SVMs or ANNs; (2) integrating  
Figure 14: A scatter plot of BD and SHAP values with a LOWESS fit curve.  
physics-informed models with machine learning models would enhance the accuracy and reliability of this method, as machine learning models do not adhere to the physical laws governing the time-dependent dynamics of fragmentation systems; and (3) utilizing sensors to gather real-time fragmentation data and employing machine learning models for instantaneous predictions.  
Conceptualization: M.M., S.H. and C.L.; Methodology: M.M., C.L. and J.Z.; Investigation: M.M. and J.Z.; Writing--original draft preparation: M.M. and S.H.; Writing--review and editing: S.H., C.L. and J.Z.; Visualization: M.M., C.L. and J.Z.; Funding acquisition: J.Z. All authors have read and agreed to the published version of the manuscript.  
This research is partially supported by the Distinguished Youth Science Foundation of Hunan Province of China (2022 JJ10073).  
Not applicable.  
The data used in this study are from published research: [PERSON] et al. [55] ([PERSON], [PERSON] and [PERSON] Establishment of blasting design parameters influencing mean fragment size using state-of-art statistical tools and techniques. Measurement, 2017, 96: 34-51); [PERSON] et al. [57] ([PERSON], [PERSON] and [PERSON] Prediction of blast fragmentation using multivariate analysis procedures. Inter-national Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35: 1318-1333); [PERSON] and [PERSON] [58] ([PERSON] and [PERSON] Study on blasting fragmentation prediction model based on random forest regression method. Journal of Hydropower, 2020: 23-34.).  
The authors want to thank all the members who give us lots of help and co-operation.  
The authors declare no conflicts of interest.