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<p>Rock fragmentation size (X<sub>50</sub>) is a critical process indicator in mining production, directly influencing the efficiency and cost of downstream operations such as crushing, transportation, and mineral processing. Due to the coupled effects of geological conditions and blast design parameters, X<sub>50</sub> exhibits strong nonlinearity and interactive characteristics, making it difficult for traditional empirical or single data-driven models to simultaneously achieve high accuracy, robustness, and interpretability. This study introduces a novel ensemble method termed Convex Stacking with Guarded Calibration (CSGC), which integrates six base machine learning models (including KNN, RandomForest (RF), SVR, Light Gradient Boosting Machine (LGBM), XGBoost, and MLP) using stratified out-of-fold predictions, MAPE-friendly convex optimization, and guarded isotonic calibration. Based on a dataset of 91 field samples from 8 open-pit mines, models were evaluated using an 80/20 train–test split and 5-fold out-of-fold validation. The proposed CSGC framework is compared against individual models and classical stacking. Results show that CSGC achieves superior performance on the test set (R<sup>2</sup> = 0.928, RMSE = 0.039), showing better predictive accuracy than the best individual model(XGBoost: R<sup>2</sup> = 0.896, RMSE = 0.047). Global and local interpretability analyses via SHAP and LIME identify elastic modulus (E), stemming-to-burden ratio (T/B), bench height-to-burden ratio (H/B), in-situ block size (Xa), and powder factor (Pf) as the dominant factors driving X<sub>50</sub>, with notable nonlinear and interactive effects across value ranges. The study improves prediction accuracy and interpretability for fragmentation modeling that supports blast optimization and operational control in mining engineering.</p>

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An interpretable Convex Stacking with Guarded Calibration ensemble approach for predicting rock fragmentation in mine blasting

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月30日

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  • Chunping Lin,
  • Xiaolei Sun,
  • Junfeng Mai,
  • Bo Liu,
  • Peng Cheng

摘要

Rock fragmentation size (X50) is a critical process indicator in mining production, directly influencing the efficiency and cost of downstream operations such as crushing, transportation, and mineral processing. Due to the coupled effects of geological conditions and blast design parameters, X50 exhibits strong nonlinearity and interactive characteristics, making it difficult for traditional empirical or single data-driven models to simultaneously achieve high accuracy, robustness, and interpretability. This study introduces a novel ensemble method termed Convex Stacking with Guarded Calibration (CSGC), which integrates six base machine learning models (including KNN, RandomForest (RF), SVR, Light Gradient Boosting Machine (LGBM), XGBoost, and MLP) using stratified out-of-fold predictions, MAPE-friendly convex optimization, and guarded isotonic calibration. Based on a dataset of 91 field samples from 8 open-pit mines, models were evaluated using an 80/20 train–test split and 5-fold out-of-fold validation. The proposed CSGC framework is compared against individual models and classical stacking. Results show that CSGC achieves superior performance on the test set (R2 = 0.928, RMSE = 0.039), showing better predictive accuracy than the best individual model(XGBoost: R2 = 0.896, RMSE = 0.047). Global and local interpretability analyses via SHAP and LIME identify elastic modulus (E), stemming-to-burden ratio (T/B), bench height-to-burden ratio (H/B), in-situ block size (Xa), and powder factor (Pf) as the dominant factors driving X50, with notable nonlinear and interactive effects across value ranges. The study improves prediction accuracy and interpretability for fragmentation modeling that supports blast optimization and operational control in mining engineering.