Comparison of Radial Basis Function and Ordinary Kriging Estimations in an Iron Ore Deposit parison of Radial Basis Function and Ordinary Kriging Estimations in an Iron Ore Deposit

Abstract

While in the near past nearest neighbor and inverse distance methods have been used in mineral resource estimation, recently kriging became the dominant method. These days, new mineral resource estimation techniques are developed as alternatives to kriging. One of the alternative techniques developed is Radial Basis Functions (RBF). RBF can be defined as a real-valued function with the value of  is used as input and this value is equal to radial kernel value. Interpolation can be performed by using these functions. While the use of the radial basis function is widely applied in many diverse areas, its usage in the mining industry is limited. Additionally, in the studies on mineral resources, RBF were either used solely or compared with kriging in a specialized form. In this study, estimations with RBF and kriging are compared in an iron ore deposit. For comparison, firstly, ore grade estimations are performed with kriging. For this purpose, variograms are calculated and block estimations are performed. Later, estimations are performed by using RBF. Gaussian kernel function is used for estimations and α value is selected as 2.6. Finally, summary statistics of the results were compared in terms of visual and trend analyses.

Keywords

• Kriging
• radial basis functions
• iron ore

Bir Demir Yatağında Radyal Temelli Fonksiyon ve Ortalamasız Krigleme Kestirimlerinin Karşılaştırılması

Abstract

Yakın geçmişte maden kaynaklarının kestirimi için ters uzaklık, en yakın komşu gibi yöntemler kullanılmakla birlikte, son dönemde maden yataklarının kestiriminde genellikle krigleme yöntemi kullanılmaktadır. Günümüzde kaynak kestiriminde kriglemeye alternatif yöntemler de gelişmektedir. Gelişmekte olan yöntemlerden birisi de Radyal Temelli Fonksiyon (RTF) ile kestirimdir. RTF gerçel değer alan bir ’nın değerinin bir girdi ve sabit noktaya göre değerinin radyal çekirdek değerine eşit olduğu fonksiyonlar olarak tanımlanırlar. Bu fonksiyonlar kullanılarak interpolasyon yapılabilir. RTF’ler ile interpolasyon birçok alanda kullanılmakla birlikte madencilikte henüz yaygın olarak kullanılmamaktadır. Ayrıca maden yatakları ile ilgili yapılan çalışmalarda ya RTF tek başına kullanılmış ya da RTF’nin özelleşmiş formları, krigleme ile karşılaştırılmıştır. Bu çalışmada, bir demir yatağında RTF kestirimleri ile krigleme kestirimleri karşılaştırılmıştır. Karşılaştırma amacı ile yataktaki demir tenörünün dağılımı öncelikle krigleme ile kestirilmiştir. Bu amaçla, variogramlar hesaplanmış ve bloklar üzerinden kestirimler yapılmıştır. Sonrasında ise RTF ile kestirim yapılmıştır. Kestirimde çekirdek fonksiyon olarak Gauss fonksiyonu tercih edilmiş ve fonksiyon α parametresi olarak 2,6 değeri kullanılmıştır. Elde edilen sonuçlar kestirimlerin özet istatistikleri, görsel ve trend analizleri yapılarak karşılaştırılmıştır.

Keywords

• krigleme
• radyal temelli fonksiyon
• demir cevheri

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