Fuzzy Modeling for Reserve Estimation Based on Spatial Variability
- PDF / 367,553 Bytes
- 25 Pages / 441 x 666 pts Page_size
- 102 Downloads / 215 Views
Fuzzy Modeling for Reserve Estimation Based on Spatial Variability1 Bulent Tutmez,2 A. Erhan Tercan,3 and Uzay Kaymak4 This article addresses a new reserve estimation method which uses fuzzy modeling algorithms and estimates the reserve parameters based on spatial variability. The proposed fuzzy modeling approach has three stages: (1) Structure identification and preliminary clustering, (2) Variogram analysis, and (3) Clustering based rule system. A new clustering index approach and a new spatial measure function (point semimadogram) are proposed in the paper. The developed methodology uses spatial variability in each step and takes the fuzzy rules from input-output data. The model has been tested using both simulated and real data sets. The performance evaluation indicates that the new methodology can be applied in reserve estimation and similar modeling problems. KEY WORDS: reserve estimation, spatial variability, fuzzy modeling, variogram.
INTRODUCTION Ore reserve estimation, which includes the estimation of characteristics such as ore grade and ore thickness, has crucial importance for evaluation of mineral deposits. Estimated reserve is used in all phases of a mining project, including feasibility, mine planning and production scheduling. Traditional reserve estimation methods can be roughly classified into two main groups: geometric and geostatistical methods (Henley, 2000). Geometrical methods depend on geometrical relationships between sample points while geostatistical methods (Goovaerts, 1997; Henley, 2001) are based on random functions and consider spatial relationship of the sample data. Generally, geostatistical methods are more effective. Bardossy and Fodor (2004) have discussed the advantages and disadvantages of geostatistical methods for reserve estimation and they stressed that geostatistical 1Received
17 January 2006; accepted 19 June 2006; Published online: 21 February 2007. of Mining Engineering, Inonu University, Malatya 44280, Turkey; e-mail: [email protected]. 3Department of Mining Engineering, Hacettepe University, Ankara 06532, Turkey; e-mail: [email protected]. 4Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands; e-mail: [email protected]. 2Department
87 C 2007 International Association for Mathematical Geology 0882-8121/07/0100-0087/1
88
Tutmez, Tercan, and Kaymak
methods have some limitations. Geostatistical calculation needs suitable computer programs, and a considerable mathematical background. Further shortcomings of geostatistics were pointed out in detail by Diehl (1997). Integrating geostatistical concept with fuzzy set theory (Bardossy, Bogardi, and Kelly, 1990) is a novel direction, and the application of fuzzy modeling in reserve estimation is very limited. In the literature, Pham (1997) estimated the ore grades using a linguistic fuzzy model. Galatakis, Theodoridis, and Kouridou (2002) carried out a study for lignite quality estimation using a neural-fuzzy system. The main handicap of these works is that spa
Data Loading...