Cai Xin, Wang Yunmin, Zhao Yihan, Chen Liye, Wang Peiyu, Wang Zhongkang, Li Jianguo
Sinosteel Maanshan General Institute of Mining Research Co., Ltd., Maanshan 243000, China.
School of Resources and Safety Engineering, Central South University, Changsha 410083, China.
Materials (Basel). 2025 Jun 27;18(13):3054. doi: 10.3390/ma18133054.
Accurate prediction of the dynamic compressive strength of brittle engineering materials is of significant theoretical and engineering importance for underground engineering design, safety assessment, and dynamic hazard prevention. To enhance prediction accuracy and model interpretability, this study proposes a novel framework integrating stacking ensemble learning with SHapley Additive exPlanations (SHAP) for dynamic strength prediction. Leveraging multidimensional input variables, including static strength, strain rate, P-wave velocity, bulk density, and specimen geometry parameters, we constructed six machine learning regression models: K-Nearest Neighbors (KNN), Random Forest (RF), Gradient Boosting Decision Tree (GBDT), LightGBM, XGBoost, and Multilayer Perceptron Neural Network (MLPNN). Through comparative performance evaluation, optimal base models were selected for stacking ensemble training. Results demonstrate that the proposed stacking model outperforms individual models in prediction accuracy, stability, and generalization capability. Further SHAP-based interpretability analysis reveals that strain rate dominates the prediction outcomes, with its SHAP values exhibiting a characteristic nonlinear response trend. Additionally, structural and mechanical variables such as static strength, P-wave velocity, and bulk density demonstrate significant positive contributions to model outputs. This framework provides a robust tool for intelligent prediction and mechanistic interpretation of the dynamic strength of brittle materials.
准确预测脆性工程材料的动态抗压强度对于地下工程设计、安全评估和动态灾害预防具有重要的理论和工程意义。为了提高预测精度和模型可解释性，本研究提出了一种将堆叠集成学习与SHapley加性解释（SHAP）相结合的新颖框架，用于动态强度预测。利用包括静态强度、应变率、纵波速度、体积密度和试样几何参数在内的多维输入变量，我们构建了六个机器学习回归模型：K近邻（KNN）、随机森林（RF）、梯度提升决策树（GBDT）、LightGBM、XGBoost和多层感知器神经网络（MLPNN）。通过比较性能评估，选择了最优的基础模型进行堆叠集成训练。结果表明，所提出的堆叠模型在预测精度、稳定性和泛化能力方面优于单个模型。进一步基于SHAP的可解释性分析表明，应变率主导预测结果，其SHAP值呈现出特征性的非线性响应趋势。此外，静态强度、纵波速度和体积密度等结构和力学变量对模型输出显示出显著的正向贡献。该框架为脆性材料动态强度的智能预测和机理解释提供了一个强大的工具。
