Complex Orebody 3D Modeling Using Radial Basis Function Surface Incorporating Stacking Integration Strategy
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摘要: 建立三维矿体模型是数字矿山、智慧矿山的基础.针对经典径向基函数曲面重建算法在原始数据稀疏时出现曲面边界自拟合及模型不连续现象，提出了一种集成多种机器学习模型的径向基函数曲面复杂矿体三维建模方法.该方法利用Stacking模型学习矿体轮廓线离散化点云数据的分布特征，建立表征矿体模型几何信息的有向点集；在此基础上提取边界点及法向量，通过Hermite型径向基函数建立隐式场，最后基于行进四面体算法建立三维矿体模型.与轮廓线拼接法、经典径向基函数曲面重建算法、简单克里金插值法相比，该方法能够有效减少曲面边界自拟合现象，减少模型多余孔洞，提高模型的连续性；建立的模型所切轮廓线与原始轮廓线相似度达75.14%，与人工干预程度较高的显式模型相当；在体积表征上与显式模型的差距达到最低.Abstract: Establishing a 3D orebody model is the foundation of digital mine and smart mine. In response to the phenomenon that the classical radial basis function surface reconstruction algorithm leads to surface boundary self-fitting and model discontinuity when the original data is sparse, this paper proposes a method of implicit automatic modeling of complex orebody with radial basis function incorporating multiple machine learning. This method uses the Stacking model to learn the distribution characteristics of the discrete point cloud data of the orebody contour lines to build a directed point set characterizing the geometric information of the orebody model. On this basis, the boundary points and normal vectors are extracted, the implicit field is established by the Hermite radial basis function, and finally the 3D orebody model is visualized based on the marching tetrahedron algorithm. The analysis was compared with the contour line splicing method, the classical radial basis function surface reconstruction algorithm, and the simple kriging interpolation method. The method can effectively reduce the phenomenon of self-fitting of surface boundaries, reduce redundant holes in the model, and improve the continuity of the model; the similarity between the contour lines cut by the established model and the original contour lines reaches 75.14%, which is comparable to the explicit model with a high degree of manual intervention; the gap between the model and the explicit model in volume characterization reaches the lowest.
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图 2 基于Stacking集成策略的隐式三维地质建模流程
Fig. 2. Implicit 3D geological modeling process based on Stacking integration strategy
图 12 不同方法所建矿体模型
（1）为本文所建模型，（2）为HRBF法所建模型，（3）为轮廓线拼接法所建模型，（4）为简单克里金插值法所建模型
Fig. 12. Orebody models constructed by different methods
图 13 模型所切轮廓线与原始轮廓线相似度
Fig. 13. Similarity between the contour line cut by the model and the original contour line
图 14 矿体模型体积对比
差值百分比计算公式：（轮廓线拼接法模型和其他模型体积之差/轮廓线拼接法模型体积）×100%（保留1位小数）；（1）为本文所建模型，（2）为HRBF法所建模型，（3）为轮廓线拼接法所建模型，（4）为简单克里金插值法所建模型
Fig. 14. Orebody model volume comparison chart
表 1 Stacking集成策略各分类器超参数信息
Table 1. Stacking integration strategy hyperparameter information for each classifier
分类器 超参数 参数值 搜索范围 Stage 1 RF max_depth 15 [1, 50] Criterion ‘gini’ - n_estimators 300 [200, 300, 400] KNN n_neighbors 3 [1, 11] Weight ‘uniform’ [‘uniform’, ‘distance’] Algorithm ‘auto’ - XGBoost learning_rate 0.3 [0.1, 1] max_depth 6 [1, 10] n_estimators 100 [50, 100, 150, 200] Stage 2 XGBoost learning_rate 0.3 [0.1, 1] max_depth 6 [1, 10] n_estimators 100 [50, 100, 150, 200] 
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表 2 各分类器F1-score对比情况
Table 2. Comparison of F1-score of each classifier
类别 度量 RF KNN XGBoost Stacking 矿体 Precision 0.92 0.82 0.84 0.88 Recall 0.64 0.79 0.62 0.79 F1-score 0.75 0.80 0.72 0.83 岩石 Precision 0.87 0.92 0.86 0.92 Recall 0.98 0.93 0.95 0.96 F1-score 0.92 0.92 0.90 0.94
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