东北大学学报(自然科学版) ›› 2025, Vol. 46 ›› Issue (3): 130-137.DOI: 10.12068/j.issn.1005-3026.2025.20230259
收稿日期:
2023-09-04
出版日期:
2025-03-15
发布日期:
2025-05-29
通讯作者:
高晨翔
作者简介:
王述红(1969―),男,江苏泰州人,东北大学教授,博士生导师.
基金资助:
Shu-hong WANG, Chen-xiang GAO(), Qin-kuan HOU
Received:
2023-09-04
Online:
2025-03-15
Published:
2025-05-29
Contact:
Chen-xiang GAO
摘要:
岩体稳定性评价依赖于合理的结构面分组,但传统方法存在易受边缘点与异常点影响的弊端.为此,提出一种改进的密度峰值聚类算法用于结构面优势分组.首先,将结构面产状转换为空间坐标,并以单位法向量夹角正弦值的平方作为相似性度量.随后,基于有效性评价指标构建目标函数,并利用乌鸦算法优化截断距离以获取最佳分组结果.通过模拟数据集验证了该算法能够有效减少人为干预,避免异常点干扰,确保聚类结果更加可靠和合理.结果表明,所提方法不仅与传统方法一致性良好,还具有更高的适用性,为工程中结构面优势分组提供了可靠的参考.
中图分类号:
王述红, 高晨翔, 侯钦宽. 改进的密度峰值聚类算法在岩体结构面优势分组中的应用[J]. 东北大学学报(自然科学版), 2025, 46(3): 130-137.
Shu-hong WANG, Chen-xiang GAO, Qin-kuan HOU. Application of Improved Density Peak Clustering Algorithm in Dominant Grouping of Rock Discontinuities[J]. Journal of Northeastern University(Natural Science), 2025, 46(3): 130-137.
组号 | 倾向 | 倾角 | 结构面条数 | ||
---|---|---|---|---|---|
平均值/(°) | 方差 | 平均值/(°) | 方差 | ||
1 | 166 | 30 | 56 | 8 | 80 |
2 | 326 | 50 | 41 | 8 | 60 |
3 | 31 | 10 | 65 | 10 | 30 |
4 | 90 | 12 | 76 | 10 | 40 |
表1 结构面产状的二维正态分布参数
Table 1 Two-dimensional normal distribution parameters of rock discontinuities orientation
组号 | 倾向 | 倾角 | 结构面条数 | ||
---|---|---|---|---|---|
平均值/(°) | 方差 | 平均值/(°) | 方差 | ||
1 | 166 | 30 | 56 | 8 | 80 |
2 | 326 | 50 | 41 | 8 | 60 |
3 | 31 | 10 | 65 | 10 | 30 |
4 | 90 | 12 | 76 | 10 | 40 |
组号 | 本文方法 | K均值聚类 | ||||
---|---|---|---|---|---|---|
倾向/(°) | 倾角/(°) | 样本个数 | 倾向/(°) | 倾角/(°) | 样本个数 | |
1 | 165.87 | 55.08 | 82 | 171.53 | 54.54 | 73 |
2 | 316.05 | 42.14 | 60 | 316.05 | 42.14 | 60 |
3 | 27.87 | 66.33 | 30 | 27.87 | 66.33 | 30 |
4 | 83.58 | 75.00 | 38 | 90.77 | 71.50 | 47 |
组号 | DPC聚类 | FCM聚类 | ||||
倾向/(°) | 倾角/(°) | 样本个数 | 倾向/(°) | 倾角/(°) | 样本个数 | |
1 | 162.93 | 55.73 | 86 | 170.22 | 54.72 | 75 |
2 | 311.11 | 42.37 | 61 | 313.01 | 42.14 | 55 |
3 | 32.74 | 66.74 | 29 | 30.51 | 62.87 | 35 |
4 | 81.31 | 75.39 | 34 | 91.97 | 72.50 | 45 |
表2 结构面聚类结果对比
Table 2 Comparison of rock discontinuities clustering results
组号 | 本文方法 | K均值聚类 | ||||
---|---|---|---|---|---|---|
倾向/(°) | 倾角/(°) | 样本个数 | 倾向/(°) | 倾角/(°) | 样本个数 | |
1 | 165.87 | 55.08 | 82 | 171.53 | 54.54 | 73 |
2 | 316.05 | 42.14 | 60 | 316.05 | 42.14 | 60 |
3 | 27.87 | 66.33 | 30 | 27.87 | 66.33 | 30 |
4 | 83.58 | 75.00 | 38 | 90.77 | 71.50 | 47 |
组号 | DPC聚类 | FCM聚类 | ||||
倾向/(°) | 倾角/(°) | 样本个数 | 倾向/(°) | 倾角/(°) | 样本个数 | |
1 | 162.93 | 55.73 | 86 | 170.22 | 54.72 | 75 |
2 | 311.11 | 42.37 | 61 | 313.01 | 42.14 | 55 |
3 | 32.74 | 66.74 | 29 | 30.51 | 62.87 | 35 |
4 | 81.31 | 75.39 | 34 | 91.97 | 72.50 | 45 |
算法类型 | S | |
---|---|---|
本文方法 | 0.711 | 26.41 |
K均值聚类 | 0.700 | 26.88 |
DPC聚类 | 0.679 | 27.44 |
FCM聚类 | 0.694 | 27.50 |
表3 各聚类结果评价指标
Table 3 Each clustering result evaluation index
算法类型 | S | |
---|---|---|
本文方法 | 0.711 | 26.41 |
K均值聚类 | 0.700 | 26.88 |
DPC聚类 | 0.679 | 27.44 |
FCM聚类 | 0.694 | 27.50 |
组号 | 倾向/(°) | 倾角/(°) | 样本 个数 | S | |
---|---|---|---|---|---|
1 | 265.29 | 61.21 | 38 | 0.52 | 24.09 |
2 | 198.41 | 36.78 | 37 | ||
3 | 205.34 | 71.22 | 32 | ||
4 | 62.73 | 60.91 | 11 |
表4 实测结构面聚类结果 (rock discontinuities)
Table 4 Clustering results of measured
组号 | 倾向/(°) | 倾角/(°) | 样本 个数 | S | |
---|---|---|---|---|---|
1 | 265.29 | 61.21 | 38 | 0.52 | 24.09 |
2 | 198.41 | 36.78 | 37 | ||
3 | 205.34 | 71.22 | 32 | ||
4 | 62.73 | 60.91 | 11 |
分组方法 | 评价指标 | |
---|---|---|
S | ||
本文方法 | 0.52 | 24.09 |
K均值聚类 | 0.46 | 34.11 |
DPC聚类 | 0.36 | 29.76 |
FCM聚类 | 0.50 | 29.61 |
表5 实测结构面聚类有效性检验 (measured rock discontinuities)
Table 5 Test for the effectiveness of clustering of
分组方法 | 评价指标 | |
---|---|---|
S | ||
本文方法 | 0.52 | 24.09 |
K均值聚类 | 0.46 | 34.11 |
DPC聚类 | 0.36 | 29.76 |
FCM聚类 | 0.50 | 29.61 |
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