Identification of Rock Mass Discontinuity Sets Based on Density Peak Algorithm and Fuzzy C-Means Algorithm

Partitioning discontinuities into subsets is a crucial foundation for assessing the stability of rock masses in engineering. However, the conventional fuzzy C-means clustering algorithm (FCM) is sensitive to outliers and initial cluster centers, requires a predetermined cluster number, and tends to...

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Vydané v:	Rock mechanics and rock engineering Ročník 58; číslo 9; s. 10777 - 10793
Hlavní autori:	Wu, Qiong, Kang, Qianqian, Tang, Huiming, Zhang, Wen, Liu, Qiang, Qin, Yue, Zhang, Chenxi, Liu, Zhiqi, Zhang, Bo, Lin, Zhiwei
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Vienna Springer Vienna 01.09.2025 Springer Nature B.V
Predmet:	Accuracy Algorithms Civil Engineering Cluster analysis Clustering Datasets Density Discontinuity Earth and Environmental Science Earth Sciences Effectiveness Geology Geophysics/Geodesy Global optimization Methods Optimization Original Paper Outliers (landforms) Outliers (statistics) Partitioning Regional development Robustness (mathematics) Rock Rock masses Rocks Stability analysis Tectonics Fuzzy C-means clustering algorithm (FCM) Density peak clustering algorithm (DPC) Orientation analysis Rock mass discontinuity sets
ISSN:	0723-2632, 1434-453X
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Abstract	Partitioning discontinuities into subsets is a crucial foundation for assessing the stability of rock masses in engineering. However, the conventional fuzzy C-means clustering algorithm (FCM) is sensitive to outliers and initial cluster centers, requires a predetermined cluster number, and tends to converge to local optima. To overcome these limitations, this paper introduces an optimized fuzzy C-means clustering algorithm based on the density peak clustering algorithm (DPC-FCM) for partitioning rock mass discontinuity sets. The DPC-FCM algorithm leverages global density peak points as potential initial cluster centers, which not only indicates cluster number but also eliminates the randomness in selecting initial centers. This process keeps the FCM algorithm from falling into local optima, achieving global optimization and obviously enhancing the overall robustness of the method. Additionally, by treating points with low local density and far from other high-density points as outliers, the algorithm reduces the impact of outliers and enhances clustering accuracy. The DPC-FCM method was validated using an artificial data set and the San Manual copper mine data set. Comparison results of four widely-accepted methods and three commonly-used clustering validity indexes verified that the DPC-FCM method demonstrated superior rationality and clustering accuracy. Finally, the DPC-FCM method was applied to the separation of discontinuity sets and stability assessments of a deformed rock slope in Mindu Township, China. Combined with the analysis of the geological origin and regional tectonic development history, the method demonstrated its practical effectiveness. The DPC-FCM method is feasible and efficient, enhancing the accuracy and robustness of grouping. It provides a dependable foundation for the 3D discontinuity network model and stability assessment in rock engineering, demonstrating potential for engineering applications. Highlights An optimized fuzzy C means algorithm based on density peak algorithm was presented to partition rock mass discontinuity sets. The key advantage of this method is its ability to accurately determine the initial cluster centers and achieve global optimization. Comparative results with existing methods validate effectiveness and high robustness of the method. The proposed method eliminates the requirement for a predetermined number of clusters. The proposed method effectively identifies and eliminates outliers.
AbstractList	Partitioning discontinuities into subsets is a crucial foundation for assessing the stability of rock masses in engineering. However, the conventional fuzzy C-means clustering algorithm (FCM) is sensitive to outliers and initial cluster centers, requires a predetermined cluster number, and tends to converge to local optima. To overcome these limitations, this paper introduces an optimized fuzzy C-means clustering algorithm based on the density peak clustering algorithm (DPC-FCM) for partitioning rock mass discontinuity sets. The DPC-FCM algorithm leverages global density peak points as potential initial cluster centers, which not only indicates cluster number but also eliminates the randomness in selecting initial centers. This process keeps the FCM algorithm from falling into local optima, achieving global optimization and obviously enhancing the overall robustness of the method. Additionally, by treating points with low local density and far from other high-density points as outliers, the algorithm reduces the impact of outliers and enhances clustering accuracy. The DPC-FCM method was validated using an artificial data set and the San Manual copper mine data set. Comparison results of four widely-accepted methods and three commonly-used clustering validity indexes verified that the DPC-FCM method demonstrated superior rationality and clustering accuracy. Finally, the DPC-FCM method was applied to the separation of discontinuity sets and stability assessments of a deformed rock slope in Mindu Township, China. Combined with the analysis of the geological origin and regional tectonic development history, the method demonstrated its practical effectiveness. The DPC-FCM method is feasible and efficient, enhancing the accuracy and robustness of grouping. It provides a dependable foundation for the 3D discontinuity network model and stability assessment in rock engineering, demonstrating potential for engineering applications. Highlights An optimized fuzzy C means algorithm based on density peak algorithm was presented to partition rock mass discontinuity sets. The key advantage of this method is its ability to accurately determine the initial cluster centers and achieve global optimization. Comparative results with existing methods validate effectiveness and high robustness of the method. The proposed method eliminates the requirement for a predetermined number of clusters. The proposed method effectively identifies and eliminates outliers. Partitioning discontinuities into subsets is a crucial foundation for assessing the stability of rock masses in engineering. However, the conventional fuzzy C-means clustering algorithm (FCM) is sensitive to outliers and initial cluster centers, requires a predetermined cluster number, and tends to converge to local optima. To overcome these limitations, this paper introduces an optimized fuzzy C-means clustering algorithm based on the density peak clustering algorithm (DPC-FCM) for partitioning rock mass discontinuity sets. The DPC-FCM algorithm leverages global density peak points as potential initial cluster centers, which not only indicates cluster number but also eliminates the randomness in selecting initial centers. This process keeps the FCM algorithm from falling into local optima, achieving global optimization and obviously enhancing the overall robustness of the method. Additionally, by treating points with low local density and far from other high-density points as outliers, the algorithm reduces the impact of outliers and enhances clustering accuracy. The DPC-FCM method was validated using an artificial data set and the San Manual copper mine data set. Comparison results of four widely-accepted methods and three commonly-used clustering validity indexes verified that the DPC-FCM method demonstrated superior rationality and clustering accuracy. Finally, the DPC-FCM method was applied to the separation of discontinuity sets and stability assessments of a deformed rock slope in Mindu Township, China. Combined with the analysis of the geological origin and regional tectonic development history, the method demonstrated its practical effectiveness. The DPC-FCM method is feasible and efficient, enhancing the accuracy and robustness of grouping. It provides a dependable foundation for the 3D discontinuity network model and stability assessment in rock engineering, demonstrating potential for engineering applications.HighlightsAn optimized fuzzy C means algorithm based on density peak algorithm was presented to partition rock mass discontinuity sets.The key advantage of this method is its ability to accurately determine the initial cluster centers and achieve global optimization.Comparative results with existing methods validate effectiveness and high robustness of the method.The proposed method eliminates the requirement for a predetermined number of clusters. The proposed method effectively identifies and eliminates outliers.
Author	Wu, Qiong Kang, Qianqian Qin, Yue Lin, Zhiwei Zhang, Bo Liu, Qiang Zhang, Chenxi Liu, Zhiqi Tang, Huiming Zhang, Wen
Author_xml	– sequence: 1 givenname: Qiong orcidid: 0000-0001-5029-5925 surname: Wu fullname: Wu, Qiong organization: Faculty of Engineering, China University of Geosciences – sequence: 2 givenname: Qianqian surname: Kang fullname: Kang, Qianqian organization: Faculty of Engineering, China University of Geosciences – sequence: 3 givenname: Huiming surname: Tang fullname: Tang, Huiming email: tanghm@cug.edu.cn organization: Faculty of Engineering, China University of Geosciences – sequence: 4 givenname: Wen surname: Zhang fullname: Zhang, Wen organization: College of Construction Engineering, Jilin University – sequence: 5 givenname: Qiang surname: Liu fullname: Liu, Qiang organization: Faculty of Engineering, China University of Geosciences – sequence: 6 givenname: Yue surname: Qin fullname: Qin, Yue organization: Faculty of Engineering, China University of Geosciences – sequence: 7 givenname: Chenxi surname: Zhang fullname: Zhang, Chenxi organization: Faculty of Engineering, China University of Geosciences – sequence: 8 givenname: Zhiqi surname: Liu fullname: Liu, Zhiqi organization: Faculty of Engineering, China University of Geosciences – sequence: 9 givenname: Bo surname: Zhang fullname: Zhang, Bo organization: Faculty of Engineering, China University of Geosciences – sequence: 10 givenname: Zhiwei surname: Lin fullname: Lin, Zhiwei organization: Faculty of Engineering, China University of Geosciences
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Snippet	Partitioning discontinuities into subsets is a crucial foundation for assessing the stability of rock masses in engineering. However, the conventional fuzzy...
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SubjectTerms	Accuracy Algorithms Civil Engineering Cluster analysis Clustering Datasets Density Discontinuity Earth and Environmental Science Earth Sciences Effectiveness Geology Geophysics/Geodesy Global optimization Methods Optimization Original Paper Outliers (landforms) Outliers (statistics) Partitioning Regional development Robustness (mathematics) Rock Rock masses Rocks Stability analysis Tectonics
Title	Identification of Rock Mass Discontinuity Sets Based on Density Peak Algorithm and Fuzzy C-Means Algorithm
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