TRANSACTION PAPER

 

An algorithm for quantifying regionalized ore grades

 

 

B. Tutmez^I; A.E. Tercan^II; U. Kaymak^III

^IInonu University, Department of Mining Engineering, Malatya, Turkey
^IIHacettepe University, Department of Mining Engineering, Ankara, Turkey
^IIIErasmus University Rotterdam, Econometric Institute, Rotterdam, The Netherlands

 

 

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SYNOPSIS

We present a novel hybrid algorithm for quantifying the ore grade variability that has central importance in ore reserve estimation. The proposed algorithm has three stages: (1) fuzzy clustering, (2) similarity measure, and (3) grade estimation. The method first considers data clustering, and then uses the clustering information for quantifying the ore grades by means of a cumulative point semimadogram function. The method provides a measure of similarity and gives an indication of the regional heterogeneity. In addition, grade estimations can be obtained at different levels of similarity using a weighting function, which is the standard regional dependence function (SRDF).

Keywords: Grade, fuzzy clustering, similarity measure, point madogram, weighting function

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References

1. ŞEN, Z. Cumulative semivariogram model of regionalized variables. Mathematical Geology, vol. 21, 1989. pp. 891-903.         [ Links ]

2. JOURNEL, A.G. and HUIJBREGTS, Ch.J. Mining Geostatistics. Academic Press, 1981.         [ Links ]

3. ŞEN, Z. Point cumulative semivariogram for identification of heterogeneities in regional seismicity of Turkey. Mathematical Geology, vol. 30, no. 7, 1988. pp. 767-787.         [ Links ]

4. OZTOPAL, A. Artificial neural network approach to spatial estimation of wind velocity data. Energy Conversion and Management, vol. 47, no. 4, 2006. pp. 395-406.         [ Links ]

5. TUTMEZ, B. and HATIPOGLU, Z. Spatial estimation model of porosity. Computers & Geosciences, vol. 33, 2007. pp. 465-475.         [ Links ]

6. TUTMEZ, B., TERCAN, A.E., and KAYMAK, U. Fuzzy modeling for reserve estimation based on spatial variability. Mathematical Geology, vol. 39, no. 1, 2007. pp. 87-111.         [ Links ]

7. GOOVAERTS, P. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York, 1997.         [ Links ]

8. BEZDEK, J.C., EHRLICH, R., and FULL, W. FCM: The fuzzy c-means clustering algorithm, Computers & Geosciences, vol. 10, nos. 2-3, 1984. pp. 191-203.         [ Links ]

9. BABUSKA, R. Fuzzy Modelling for Control. Kluwer Academic, 1998.         [ Links ]

10. SOUSA, J.M.C. and KAYMAK, U. Fuzzy Decision Making in Modelling and Control, World Scientific, Singapore, 2002.         [ Links ]

11. XIE, X.L. and BENI, G.A. A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell, vol. 13, no. 8, 1991. pp. 841-847.         [ Links ]

12. KAYMAK, U. and BABUSKA, R. Compatible cluster merging for fuzzy modelling. Proc. FUZZ-IEEE/IFES '95, Yokohama, 1995. pp. 897-904.         [ Links ]

13. KAYMAK, U. and SETNES, M. Extended fuzzy clustering algorithms. ERIM report series Research in Management, Erasmus University Rotterdam, ERS-2000-51-LIS. 2000.         [ Links ]

14. DEUTSCH, C.V. and JOURNEL, A.G. GSLIB: Geostatistical Software Library and User's Guide. 2nd edn. Oxford University Press, New York, 1998.         [ Links ]

15. TARAWNEH, A.D. and ŞAHIN, A.D. Regional wind energy assessment technique with applications, Energy Conversion & Management, vol. 44, no. 9, 2003. pp. 1563-1574.         [ Links ]

16. HÖPPNER, F., KLAWONN, F., KRUSE, R., and RUNKLER, T. Fuzzy Cluster Analysis, John Wiley & Sons, Chichester, 1999.         [ Links ]

17. WELLMER, F.-W. Statistical Evaluations in Exploration for Mineral Deposits, Springer, Heidelberg, 1998.         [ Links ]

 

 

Paper received Dec. 2006
Revised paper received Jan. 2008