# Open-Pit Bench Blasting Fragmentation Prediction Based on Stacking Integrated Strategy
## 5 Conclusion and Summary  
During the blasting process, numerous factors, including controllable and uncontrollable ones, affect the blasting results. Thus, it is challenging to use a single-fitting equation to comprehensively describe the relationship between various influencing factors and fragmentation size. Compared to traditional empirical equation prediction methods, artificial intelligence methods can effectively simulate the relationship between various input and output parameters. This study utilized a dataset containing 97 data samples and set seven input parameters to predict the fragmentation size \(X_{50}\). To improve prediction performance, the prediction effects of three single models--random forest, SVR, and XGBoost--were compared and selected. A stacking integrated strategy was employed, using random forest and XGBoost models as base learners to construct the fusion model. This method has been applied in engineering fields, but its application in predicting blasting fragmentation is still relatively limited. The predictive performance of the established models was evaluated using four mathematical indicators. The following conclusions can be drawn from this study:  
* The stacking integrated model outperformed the single models and had higher predictive accuracy. The model evaluation yielded an \(R^{2}\) value of 0.943, with MSE, RMSE, and MAE values of 0.00269, 0.05187, and 0.03320, respectively, on the training set; and 0.00197, 0.04435, and 0.03687, respectively, on the testing set;
* From the feature importance evaluation results of the two methods, it can be seen that in the process of constructing the model, the input feature \(E\) has the highest influence on the predicted fragmentation size, followed by \(T/B\) and \(X_{B}\);
* Compared with the prediction methods of other researchers, the prediction method established in this study better integrates the advantages of individual algorithms. The engineering verification results also demonstrated that the constructed algorithm has good predictive accuracy, and its prediction results can provide references for blasting design.  
Validation, Y.S.; formal analysis, Y.S., R.Z. and Z.Y.; investigation, Y.S.; methodology, Y.S.; writing--original draft preparation, Y.S.; writing--review and editing, Z.Z., R.Z., Z.Y. and Y.Z. All authors have read and agreed to the published version of the manuscript.  
Figure 12: Comparison of results from engineering validation.  
Funding: The research presented in this paper was funded by the National Natural Science Foundation of China (Grant Nos. 12072376 and 52274105). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations The following abbreviations are used in this manuscript: \(R^{2}\) Coefficient of Determination MSE Mean Square Error RMSE Root Mean Square Error MAE Mean Absolute Error KCO Kuznetsov-Cunningham-Ouchterlony BPNN Back Propagation Neural Network ANN Artificial Neural Network SVM Support Vector Machine ANFIS Adaptive Network-based Fuzzy Inference System PCA Principal Component Analysis GWO Grey Wolf Optimization CNN Convolutional Neural Network MLP Multilayer Perceptron PSO Particle Swarm Optimization SVR Support Vector Regression KNN K-Nearest Neighbor GP Gaussian Process RCS Rock Compressive Strength