Application of Improved Density Peak Clustering Algorithm in Dominant Grouping of Rock Discontinuities

doi:10.12068/j.issn.1005-3026.2025.20230259

Abstract

Abstract:

The stability evaluation of rock mass relies on reasonable rock discontinuities grouping. However， traditional methods are susceptible to boundary and outlier points. To address this issue， an improved density peak clustering algorithm was proposed for rock discontinuities grouping. Firstly， the rock discontinuities orientations were converted into spatial coordinates， and the squared sine of the angle between unit normal vectors was used as a similarity metric. Then， an objective function was constructed based on validity evaluation indices， and the cutoff distance was optimized using the crow algorithm to obtain the optimal grouping results. Validation with simulated datasets demonstrates that the proposed algorithm effectively reduces human intervention， avoids interference from outliers， and ensures more reliable and reasonable clustering outcomes. The results show that the proposed method not only maintains good consistency with traditional methods but also exhibits higher applicability， providing a reliable reference for dominant joint grouping in engineering applications.

Key words: density peak clustering, crow algorithm, validity evaluation indices, rock discontinuities, dominant grouping

CLC Number:

TU 45

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.

Figures/Tables 12

Fig. 1 DPC algorithm flow

Table 1 Two-dimensional normal distribution parameters of rock discontinuities orientation

组号	倾向		倾角		结构面条数
组号	平均值/（°）	方差	平均值/（°）	方差	结构面条数
1	166	30	56	8	80
2	326	50	41	8	60
3	31	10	65	10	30
4	90	12	76	10	40

Fig. 2 Simulated pole plot

Fig. 3 Comparison of rock discontinuities clustering results

Table 2 Comparison of rock discontinuities clustering results

组号	本文方法			K均值聚类
组号	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
组号	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

Table 3 Each clustering result evaluation index

算法类型	S	$V x b$
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

Table 3 Each clustering result evaluation index

算法类型	S	$V x b$
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

Fig. 4 Pole map of the measured rock discontinuity orientation

Fig. 5 Contour plot of measured rock discontinuity

Fig. 6 Rose diagram of measured rock discontinuity trend

Fig. 7 Comparison of measured rock discontinuities clustering results

Table 4 Clustering results of measured

组号	倾向/（°）	倾角/（°）	样本个数	S	$V x b$
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

Table 4 Clustering results of measured

组号	倾向/（°）	倾角/（°）	样本个数	S	$V x b$
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

Table 5 Test for the effectiveness of clustering of

分组方法	评价指标
分组方法	S	$V x b$
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

Table 5 Test for the effectiveness of clustering of

分组方法	评价指标
分组方法	S	$V x b$
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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