A fuzzy K-Means algorithm based on Fisher distribution for the identification of rock discontinuity sets
Rock discontinuities significantly impact the mechanical and hydraulic behavior of rock masses. A crucial aspect of rock engineering involves classifying discontinuities with similar orientations into groups. For this purpose, clustering algorithms, such as K-Means and Fuzzy K-Means (FKM), have been...
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| Vydáno v: | International journal of rock mechanics and mining sciences (Oxford, England : 1997) Ročník 182; s. 105879 |
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| Jazyk: | angličtina |
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Elsevier Ltd
01.10.2024
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| ISSN: | 1365-1609 |
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| Abstract | Rock discontinuities significantly impact the mechanical and hydraulic behavior of rock masses. A crucial aspect of rock engineering involves classifying discontinuities with similar orientations into groups. For this purpose, clustering algorithms, such as K-Means and Fuzzy K-Means (FKM), have been employed. However, the outcomes of these algorithms are influenced by the selection of initial cluster centers. This paper proposes an improved FKM algorithm to automatically identify rock discontinuity sets based on the Fisher distribution (FFKM). The algorithm uses the Fisher distribution to generate and select appropriate initial cluster centers. The performance of FFKM was initially validated using a published data set, and its results were compared with other clustering methods commonly used for grouping discontinuities. Results demonstrated the superior performance of FFKM over the FKM algorithm, comparable to other methods. Subsequently, the proposed algorithm was employed to analyze a fracture data set sampled at an open-pit iron mine. The FFKM facilitated identifying the correct number of sets and produced results consistent with the fracture sets observed in the field. Finally, the algorithm was verified using an artificial discontinuity data set, and the results demonstrated that the method correctly identified the number of sets and provided discontinuity sets similar to the original data set. The FFKM algorithm offers significant advantages: it maintains the essential characteristics of the FKM algorithm, effectively addresses the challenge of selecting suitable initial cluster centers, requires only the expected number of discontinuity sets as an input parameter, processes data within an acceptable computation time, serves as a tool for defining the number of discontinuity sets, and mitigates the drawbacks of the stereographic projection method.
•Mitigation of challenges associated with identifying discontinuity sets.•Accurate definition of the number of discontinuity sets.•The algorithm preserves the Fuzzy K-Means features.•Assistant tool in rock engineering and mining applications.•Determination of fracture sets in an open-pit iron mine. |
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| AbstractList | Rock discontinuities significantly impact the mechanical and hydraulic behavior of rock masses. A crucial aspect of rock engineering involves classifying discontinuities with similar orientations into groups. For this purpose, clustering algorithms, such as K-Means and Fuzzy K-Means (FKM), have been employed. However, the outcomes of these algorithms are influenced by the selection of initial cluster centers. This paper proposes an improved FKM algorithm to automatically identify rock discontinuity sets based on the Fisher distribution (FFKM). The algorithm uses the Fisher distribution to generate and select appropriate initial cluster centers. The performance of FFKM was initially validated using a published data set, and its results were compared with other clustering methods commonly used for grouping discontinuities. Results demonstrated the superior performance of FFKM over the FKM algorithm, comparable to other methods. Subsequently, the proposed algorithm was employed to analyze a fracture data set sampled at an open-pit iron mine. The FFKM facilitated identifying the correct number of sets and produced results consistent with the fracture sets observed in the field. Finally, the algorithm was verified using an artificial discontinuity data set, and the results demonstrated that the method correctly identified the number of sets and provided discontinuity sets similar to the original data set. The FFKM algorithm offers significant advantages: it maintains the essential characteristics of the FKM algorithm, effectively addresses the challenge of selecting suitable initial cluster centers, requires only the expected number of discontinuity sets as an input parameter, processes data within an acceptable computation time, serves as a tool for defining the number of discontinuity sets, and mitigates the drawbacks of the stereographic projection method.
•Mitigation of challenges associated with identifying discontinuity sets.•Accurate definition of the number of discontinuity sets.•The algorithm preserves the Fuzzy K-Means features.•Assistant tool in rock engineering and mining applications.•Determination of fracture sets in an open-pit iron mine. |
| ArticleNumber | 105879 |
| Author | Klen, André Monteiro Bonduà, Stefano Lana, Milene Sabino Kasmaeeyazdi, Sara Menezes, Danielle Aparecida de Carvalho, Pedro Gabriel de |
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| Keywords | Fuzzy K-Means algorithm Open-pit iron mine Orientation analysis Rock discontinuity sets Rock mass characterization |
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| References | Klen, Lana (bib3) 2014; 67 Yi, Feng, Wu, Zhou, Dong (bib16) 2023; 56 Jimenez-Rodriguez, Sitar (bib2) 2006; 43 Fisher (bib21) 1993 Hammah, Curran (bib6) 1998; 35 Wu, Feng, Yi, Zhao, Zhou (bib14) 2024 Zhou, Chen, Li (bib11) 2024; 173 Cui, Yan (bib7) 2020; 126 Cui, Yan (bib10) 2020; 24 Golzari Oskouei, Balafar, Motamed (bib12) 2021; 153 Xie, Beni (bib18) 1991; 13 Jimenez (bib8) 2008; 41 Menezes (bib24) 2014 Shanley, Mahtab (bib22) 1976; 8 Gao, Chen, Zhou, Niu, Liu (bib15) 2019; 23 Zheng, Deng, Yang, Wei, Zheng, Cui (bib20) 2014; 61 Fernandes, Roncato, Sérgio de Paula (bib23) 2023; 123 Xu, Chen, Wang, Zhou (bib1) 2013; 46 Li, Wang, Chen, Xu, Song (bib4) 2015; 48 Liu, Zhao, Xu (bib9) 2017; 94 Zhang, Wu, Liu, Xie, Zhou, Zhu (bib13) 2024; 57 Yong, Wang, Ye, Du, Luo (bib17) 2023 Celebi, Kingravi, Vela (bib19) 2013; 40 Song, Wang, Chen, Li, Zhang, Ruan (bib5) 2017; 21 Klen (10.1016/j.ijrmms.2024.105879_bib3) 2014; 67 Fisher (10.1016/j.ijrmms.2024.105879_bib21) 1993 Xu (10.1016/j.ijrmms.2024.105879_bib1) 2013; 46 Shanley (10.1016/j.ijrmms.2024.105879_bib22) 1976; 8 Cui (10.1016/j.ijrmms.2024.105879_bib10) 2020; 24 Jimenez (10.1016/j.ijrmms.2024.105879_bib8) 2008; 41 Jimenez-Rodriguez (10.1016/j.ijrmms.2024.105879_bib2) 2006; 43 Wu (10.1016/j.ijrmms.2024.105879_bib14) 2024 Gao (10.1016/j.ijrmms.2024.105879_bib15) 2019; 23 Yi (10.1016/j.ijrmms.2024.105879_bib16) 2023; 56 Zhang (10.1016/j.ijrmms.2024.105879_bib13) 2024; 57 Li (10.1016/j.ijrmms.2024.105879_bib4) 2015; 48 Song (10.1016/j.ijrmms.2024.105879_bib5) 2017; 21 Zhou (10.1016/j.ijrmms.2024.105879_bib11) 2024; 173 Celebi (10.1016/j.ijrmms.2024.105879_bib19) 2013; 40 Menezes (10.1016/j.ijrmms.2024.105879_bib24) 2014 Hammah (10.1016/j.ijrmms.2024.105879_bib6) 1998; 35 Cui (10.1016/j.ijrmms.2024.105879_bib7) 2020; 126 Xie (10.1016/j.ijrmms.2024.105879_bib18) 1991; 13 Golzari Oskouei (10.1016/j.ijrmms.2024.105879_bib12) 2021; 153 Fernandes (10.1016/j.ijrmms.2024.105879_bib23) 2023; 123 Liu (10.1016/j.ijrmms.2024.105879_bib9) 2017; 94 Zheng (10.1016/j.ijrmms.2024.105879_bib20) 2014; 61 Yong (10.1016/j.ijrmms.2024.105879_bib17) 2023 |
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Rock Eng doi: 10.1007/s00603-012-0244-z |
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| SubjectTerms | Fuzzy K-Means algorithm Open-pit iron mine Orientation analysis Rock discontinuity sets Rock mass characterization |
| Title | A fuzzy K-Means algorithm based on Fisher distribution for the identification of rock discontinuity sets |
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