An interpretable deep learning model for the accurate prediction of mean fragmentation size in blasting operations

Fragmentation size is an important indicator for evaluating blasting effectiveness. To address the limitations of conventional blasting fragmentation size prediction methods in terms of prediction accuracy and applicability, this study proposes an NRBO-CNN-LSSVM model for predicting mean fragmentation size, which integrates Convolutional Neural Networks (CNN), Least Squares Support Vector Machines (LSSVM), and the Newton-Raphson Optimizer (NRBO). The study is based on a database containing 105 samples derived from both previous research and field collection. Additionally, several machine learning prediction models, including CNN-LSSVM, CNN, LSSVM, Support Vector Machine (SVM), and Support Vector Regression (SVR), are developed for comparative analysis. The results showed that the NRBO-CNN-LSSVM model achieved remarkable prediction accuracy on the training dataset, with a coefficient of determination (R²) as high as 0.9717 and a root mean square error (RMSE) as low as 0.0285. On the test set, the model maintained high prediction accuracy, with an R² value of 0.9105 and an RMSE of 0.0403. SHapley Additive exPlanations (SHAP) analysis revealed that the modulus of elasticity (E) was a key variable influencing the prediction of mean fragmentation size. Partial Dependence Plots (PDP) analysis further disclosed a significant positive correlation between the modulus of elasticity (E) and mean fragmentation size. In contrast, a distinct negative correlation was observed between the powder factor (P_f) and mean fragmentation size. To enhance the convenience of the model in practical applications, we developed an interactive Graphical User Interface (GUI), allowing users to input relevant variables and obtain instant prediction results.