Fitting a theoretical model to an experimental variogram is an important issue in geostatistical studiesbecause if the variogram model parameters are tainted with uncertainty, the latter will spread in the results of estimations and simulations. Although the most popular fitting method is fitting by eye, in some cases use is made of the automatic fitting method on the basis of putting together the geostatistical principles and optimization techniques to: 1) provide a basic model to improve fitting by eye, 2) fit a model to a large number of experimental variograms in a short time, and 3) incorporate the variogram related uncertainty in the model fitting. Effort has been made in this paper to improve the quality of the fitted model by improving the popular objective function (weighted least squares) in the automatic fitting. Also, since the variogram model function (£) and number of structures (m) too affect the model quality, a program has been provided in the MATLAB software that can present optimum nested variogram models using the simulated annealing method. Finally, to select the most desirable model from among the single/multi--structured fitted models, use has been made of the cross-validation method, and the best model has been introduced to the user as the output. In order to check the capability of the proposed objective function and the procedure, 3 case studies have been presented.
Keywords:Automatic variogram fitting, Geostatistics, Optimization, simulated annealing Dopasowanie modelu teoretycznego do eksperymentalnego wariogramu jest kluczowym zagadnieniem w badaniach geostatystycznych ponieważ jeśli parametry modelu wariogramu obarczone są niepewnością, to otrzymamy znaczny rozrzut wyników obliczeń i symulacji. Pomimo, że najpopularniejszą metoda dopasowania jest dopasowanie 'na oko', w niektórych przypadkach wykorzystuje się automatyczne metody dopasowania modelu oparte na zasadach geostatystyki i optymalizacji w celu: 1) dostarczenia podstawowego modelu do dopasowania 'na oko'; 2) dopasowania modelu do większej ilości eksperymentalnych wariogramów w krótkim okresie czasu; 3) uwzględnienia niepewności związanej z wariogramem w dopasowaniu modelu. W pracy podjęto próbę poprawy jakości dopasowania modelu poprzez wprowadzenie zmodyfikowanej popularnej funkcji celu (ważone najmniejsze kwadraty) do au-*
UNIVERSITY OF KASHAN, DEPARTMENT OF MINING ENGINEERING, KASHAN, IRANBrought to you by | MIT Libraries Authenticated Download Date | 5/12/18 9:41 PM 636 tomatycznego dopasowania. Ponadto, ponieważ funkcja modelu wariogramu (L) i ilość struktur (m) ma także wpływ na jakość modelu, opracowano program w środowisku MATLAB który podaje optymalne modele wariogramu w oparciu o metodę symulacji odprężania. W części końcowej wybrano najkorzystniejszy model spośród modeli dopasowania z wykorzystaniem metody walidacji krzyżowej i najlepszy model przedstawiany jest użytkownikowi. W celu zbadania możliwości stosowania proponowanej funkcji celu i przedstawionej procedury, zaprezentowano trzy studia przypadku.Słowa klu...
Over the life of a mine, it is often necessary to drill additional holes to address new, or changing, objectives. Most previous algorithms proposed for this purpose have aimed at reducing the block model uncertainty and enhancing the value of the drilling information as their objective functions, and have paid little or no attention to improving the accuracy of the ore/waste classification. In this paper, the authors have used the misclassification probability parameter to define an objective function for the optimisation of the location of additional drill holes. Using the simulated annealing method, the efficiency of the proposed objective function has been validated and proven in optimally locating additional drill holes for an application in a phosphate mine. An advantage of this objective function compared with the usual ones is that, in addition to having a direct relationship to the kriging variance, it depends highly on the estimated and cutoff grades; the greater the difference between these grades, the lesser the misclassification probability. Since these two grades remain unchanged as the number of the drill holes increases, the only way to reduce the misclassification probability is reducing the estimation variance by drilling the additional drill holes in appropriate locations.
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