Fitting Mixtures of Kent Distributions to Aid in Joint Set Identification

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planes can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation–maximization algorithm is used to fit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

[1]  M. A. Stephens.  TECHNIQUES FOR DIRECTIONAL DATA , 1969 .

[2]  K. Mardia.  Statistics of Directional Data , 1972 .

[3]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[4]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[5]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[6]  J. Kent.  The Fisher‐Bingham Distribution on the Sphere , 1982 .

[7]  H. Schaeben.  A new cluster algorithm for orientation data , 1984 .

[8]  A. Palmstrøm.  The volumetric joint count as a measure of rock mass jointing , 1986 .

[9]  Yu-Sheng Hsu,et al.  A stepwise method for determining the number of component distributions in a mixture , 1986 .

[10]  Nicholas I. Fisher,et al.  Statistical Analysis of Spherical Data. , 1987 .

[11]  G. McLachlan.  On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture , 1987 .

[12]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .

[13]  S. Priest.  Discontinuity Analysis for Rock Engineering , 1992 .

[14]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[15]  M. P. Windham,et al.  Information-Based Validity Functionals for Mixture Analysis , 1994 .

[16]  P. Pal Roy.  Breakage assessment through cluster analysis of joint set orientations of exposed benches of opencast mines , 1995 .

[17]  I P Webber,et al.  A NEW CORE ORIENTATION DEVICE , 1996 .

[18]  G. Celeux,et al.  An entropy criterion for assessing the number of clusters in a mixture model , 1996 .

[19]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[20]  Marcel Arnould,et al.  Measurement of the fragmentation efficiency of rock mass blasting and its mining applications , 1996 .

[21]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[22]  Adrian E. Raftery,et al.  Linear flaw detection in woven textiles using model-based clustering , 1997, Pattern Recognit. Lett..

[23]  R. E. Hammah,et al.  Fuzzy cluster algorithm for the automatic identification of joint sets , 1998 .

[24]  Adrian E. Raftery,et al.  How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis , 1998, Comput. J..