基于改进遗传算法的岩体结构面产状聚类分析
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摘要
根据产状对结构面进行分组是研究岩体结构的重要环节。传统分组方法通常需要依靠地质经验,缺乏客观性,而现有的聚类方法也存在一些缺陷。基于变长度字符串遗传算法,提出了一种改进的K均值算法,实现了岩体结构面产状的自动聚类。该方法的核心思想是使用遗传算法为K均值算法选择恰当的聚类中心,克服了K均值(K-means)算法受初始聚类中心影响,易收敛于局部最优解的缺陷。由于使用了变长度字符串,该方法能够在聚类过程中自动确定最佳结构面组数,同时提供最优的分组结果。针对产状数据,提出了一种新的变异方法,该方法利用C++语言实现,并被应用于浙江省某地下水封洞库结构面产状数据的分析,得到较为合理的分组结果,证明了该方法的有效性。
Grouping structural planes based on their occurrences is an important way in analyzing the structure characteristics of rock mass. Traditional classification methods usually greatly rely on geological experience of researchers, which is lack of objectivity. The powerful clustering methods, however, also have drawbacks. In this paper, based on variable length string genetic algorithm, an improved K-means clustering method was proposed, making the automatic clustering of discontinuity occurrence of rock mass available. The essence of the proposed method is to select appropriate initial cluster centers for K-means algorithm applying the genetic algorithm. It overcomes the limitation that the K-means algorithm is usually affected by the initial cluster center and easily converges to the local optimal solution. The application of variable length strings in the improved algorithm of classification, however,can not only automatically determine the number of the optimal structural plane groups during the clustering process, but also provide optimal grouping results. In addition, a new mutation algorithm is proposed based on the occurrence data. It is realized in C++ and is applied in analyzing the occurrence of structural planes in an underground water-sealing rock caverns located at Zhejiang province,China. Reasonable classification results are achieved, proving the applicability of the proposed approach in this paper.
Grouping structural planes based on their occurrences is an important way in analyzing the structure characteristics of rock mass. Traditional classification methods usually greatly rely on geological experience of researchers, which is lack of objectivity. The powerful clustering methods, however, also have drawbacks. In this paper, based on variable length string genetic algorithm, an improved K-means clustering method was proposed, making the automatic clustering of discontinuity occurrence of rock mass available. The essence of the proposed method is to select appropriate initial cluster centers for K-means algorithm applying the genetic algorithm. It overcomes the limitation that the K-means algorithm is usually affected by the initial cluster center and easily converges to the local optimal solution. The application of variable length strings in the improved algorithm of classification, however,can not only automatically determine the number of the optimal structural plane groups during the clustering process, but also provide optimal grouping results. In addition, a new mutation algorithm is proposed based on the occurrence data. It is realized in C++ and is applied in analyzing the occurrence of structural planes in an underground water-sealing rock caverns located at Zhejiang province,China. Reasonable classification results are achieved, proving the applicability of the proposed approach in this paper.
引文
[1]周玉新,周志芳,孙其国.岩体结构面产状的综合模糊聚类分析[J].岩石力学与工程学报, 2005, 24(13):2283-2287.ZHOU Yu-xin, ZHOU Zhi-fang, SUN Qi-guo.Synthetical fuzzy clustering analysis for joints occurrence of rock mass[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(13):2283-2287.
[2] DUNCAN C W, CHRISTOPHER W M. Rock slope engineering:Civil and mining(4th ed.)[M]. New York:Spon Press, 2004.
[3] ISRM. International society for rock mechanics commission on standardization of laboratory and field tests:Suggested methods for the quantitative description of discontinuities in rock masses[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1978, 15(6):319-368.
[4]蔡美峰,王鹏,赵奎,等.基于遗传算法的岩体结构面的模糊C均值聚类方法[J].岩石力学与工程学报,2005, 24(3):371-376.CAI Mei-feng, WANG Peng, ZHAO Kui, et a1. Fuzzy C-means cluster analysis based on genetic algorithm for automatic identification of joint sets[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(3):371-376.
[5]范雷,王亮清,唐辉明.节理岩体结构面产状的动态聚类分析[J].岩土力学, 2007, 28(11):2405-2408.FAN Lei, WANG Liang-qing, TANG Hui-ming.Dynamic cluster analysis of discontinuity orientations of jointed rock mass[J]. Rock and Soil Mechanics, 2007,28(11):2405-2408.
[6] SHANLEY R J, MAHTAB M A. Delineation and analysis of clusters in orientation data[J]. Mathematical Geology, 1976, 8(1):9-23.
[7] MAHTAB M A, YEGULALP T M. A rejection criterion for definition of clusters in orientation data[C]//Proceedings of the 22nd Symposium on Rock Mechanics.New York:[s. n.], 1982:116-123.
[8] HAMMAH R E, CURRAN J H. Fuzzy cluster algorithm for the automatic identification of joint sets[J].International Journal of Rock Mechanics and Mining Sciences, 1998, 35(7):889-905.
[9] BEZDEK J C. Pattern recognition with fuzzy objective function algorithms[M]. New York:Plenum, 1981.
[10] JIMENEZ-RODRIGUEZ R, SITAR N. A spectral method for clustering of rock discontinuity sets[J]. International Journal of Rock Mechanics and Mining Sciences, 2006,43(7):1052-1061.
[11]徐黎明,陈剑平,王清.多参数岩体结构面优势分组方法研究[J].岩土力学, 2013, 34(1):189-195.XU Li-ming, CHEN Jian-ping, WANG Qing. Study of method for multivariate parameter dominant partitioning of discontinuities of rock mass[J]. Rock and Soil Mechanics, 2013, 34(1):189-195.
[12] LI Yan-yan, WANG Qing, CHEN Jian-ping, et al.K-means algorithm based on particle swarm optimization for the identification of rock discontinuity sets[J]. Rock Mechanics and Rock Engineering, 2015, 48(1):375-385
[13] MAULIK U, BANDYOPADHYAY S. Fuzzy partitioning using a real-coded variable-length genetic algorithm for pixel classification[J]. IEEE Transactions on Geoscience and Remote Sensing, 2003, 41(5):1075-1081.
[14] HRUSCHKA E R, CAMPELLO R J G B, CASTRO L N D. Evolving clusters in gene-expression data[J].Information Sciences, 2006, 176(13):1898-1927.
[15] MAULIK U, BANDYOPADHYAY S, MUKHOPADHYAY A. Multiobjective genetic algorithms for clustering[M].Berlin:Springer, 2011.
[16] JAIN A K, MURTY M N, FLYNN P J. Data clustering:A review[J]. ACM Computing Surveys, 1999, 31(3):264-323.
[17] HAMMAH R E, CURRAN J H. On distance measures for the fuzzy K-means algorithm for joint data[J]. Rock Mechanics and Rock Engineering, 1999, 32(1):1-27.
[18] MARKLAND J. The analysis of principal components of orientation data[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1974, 11(5):157-163.
[19]谢全敏,夏元友.基于遗传算法的边坡稳定性评价的动态聚类法[J].岩土力学, 2002, 23(2):170-172.XIE Quan-min, XIA Yuan-you. A dynamic clustering method for evaluation of slope stability based on genetic algorithms[J]. Rock and Soil Mechanics, 2002, 23(2):170-172.
[20] BANDYOPADHYAY S, MAULIK U. Genetic clustering for automatic evolution of clusters and application to image classification[J]. Pattern Recognition, 2002, 35(6):1197-1208.
[21] HRUSCHKA E R, EBECKEN N F F. A genetic algorithm for cluster analysis[J]. Intelligent Data Analysis, 2003, 7(1):15-25.
[22] DAVIES D L, BOULDIN D W. A cluster separation measure[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1979, PAMI-1(2):224-227.
[23] MURTHY C A, CHOWDHURY N. In search of optimal clustersusinggeneticalgorithms[J].Pattern Recognition Letters, 1996, 17(8):825-832.
[2] DUNCAN C W, CHRISTOPHER W M. Rock slope engineering:Civil and mining(4th ed.)[M]. New York:Spon Press, 2004.
[3] ISRM. International society for rock mechanics commission on standardization of laboratory and field tests:Suggested methods for the quantitative description of discontinuities in rock masses[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1978, 15(6):319-368.
[4]蔡美峰,王鹏,赵奎,等.基于遗传算法的岩体结构面的模糊C均值聚类方法[J].岩石力学与工程学报,2005, 24(3):371-376.CAI Mei-feng, WANG Peng, ZHAO Kui, et a1. Fuzzy C-means cluster analysis based on genetic algorithm for automatic identification of joint sets[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(3):371-376.
[5]范雷,王亮清,唐辉明.节理岩体结构面产状的动态聚类分析[J].岩土力学, 2007, 28(11):2405-2408.FAN Lei, WANG Liang-qing, TANG Hui-ming.Dynamic cluster analysis of discontinuity orientations of jointed rock mass[J]. Rock and Soil Mechanics, 2007,28(11):2405-2408.
[6] SHANLEY R J, MAHTAB M A. Delineation and analysis of clusters in orientation data[J]. Mathematical Geology, 1976, 8(1):9-23.
[7] MAHTAB M A, YEGULALP T M. A rejection criterion for definition of clusters in orientation data[C]//Proceedings of the 22nd Symposium on Rock Mechanics.New York:[s. n.], 1982:116-123.
[8] HAMMAH R E, CURRAN J H. Fuzzy cluster algorithm for the automatic identification of joint sets[J].International Journal of Rock Mechanics and Mining Sciences, 1998, 35(7):889-905.
[9] BEZDEK J C. Pattern recognition with fuzzy objective function algorithms[M]. New York:Plenum, 1981.
[10] JIMENEZ-RODRIGUEZ R, SITAR N. A spectral method for clustering of rock discontinuity sets[J]. International Journal of Rock Mechanics and Mining Sciences, 2006,43(7):1052-1061.
[11]徐黎明,陈剑平,王清.多参数岩体结构面优势分组方法研究[J].岩土力学, 2013, 34(1):189-195.XU Li-ming, CHEN Jian-ping, WANG Qing. Study of method for multivariate parameter dominant partitioning of discontinuities of rock mass[J]. Rock and Soil Mechanics, 2013, 34(1):189-195.
[12] LI Yan-yan, WANG Qing, CHEN Jian-ping, et al.K-means algorithm based on particle swarm optimization for the identification of rock discontinuity sets[J]. Rock Mechanics and Rock Engineering, 2015, 48(1):375-385
[13] MAULIK U, BANDYOPADHYAY S. Fuzzy partitioning using a real-coded variable-length genetic algorithm for pixel classification[J]. IEEE Transactions on Geoscience and Remote Sensing, 2003, 41(5):1075-1081.
[14] HRUSCHKA E R, CAMPELLO R J G B, CASTRO L N D. Evolving clusters in gene-expression data[J].Information Sciences, 2006, 176(13):1898-1927.
[15] MAULIK U, BANDYOPADHYAY S, MUKHOPADHYAY A. Multiobjective genetic algorithms for clustering[M].Berlin:Springer, 2011.
[16] JAIN A K, MURTY M N, FLYNN P J. Data clustering:A review[J]. ACM Computing Surveys, 1999, 31(3):264-323.
[17] HAMMAH R E, CURRAN J H. On distance measures for the fuzzy K-means algorithm for joint data[J]. Rock Mechanics and Rock Engineering, 1999, 32(1):1-27.
[18] MARKLAND J. The analysis of principal components of orientation data[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1974, 11(5):157-163.
[19]谢全敏,夏元友.基于遗传算法的边坡稳定性评价的动态聚类法[J].岩土力学, 2002, 23(2):170-172.XIE Quan-min, XIA Yuan-you. A dynamic clustering method for evaluation of slope stability based on genetic algorithms[J]. Rock and Soil Mechanics, 2002, 23(2):170-172.
[20] BANDYOPADHYAY S, MAULIK U. Genetic clustering for automatic evolution of clusters and application to image classification[J]. Pattern Recognition, 2002, 35(6):1197-1208.
[21] HRUSCHKA E R, EBECKEN N F F. A genetic algorithm for cluster analysis[J]. Intelligent Data Analysis, 2003, 7(1):15-25.
[22] DAVIES D L, BOULDIN D W. A cluster separation measure[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1979, PAMI-1(2):224-227.
[23] MURTHY C A, CHOWDHURY N. In search of optimal clustersusinggeneticalgorithms[J].Pattern Recognition Letters, 1996, 17(8):825-832.