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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

Yıl 2021, Sayı: 27, 303 - 310, 30.11.2021
https://doi.org/10.31590/ejosat.913286

Öz

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.

Kaynakça

  • Afzal, P. (2018). Comparing ordinary kriging and advanced inverse distance squared methods based on estimating coal deposits; case study: East-Parvadeh deposit, central Iran. Journal of Mining and Environment, 9(3), 753–760.
  • Bargawa, W. S., Nugroho, S. P., Hariyanto, R., Lusantono, O. W., & Bramida, R. F. (2020). Geostatistical Modeling of Ore Grade In A Laterite Nickel Deposit. LPPM UPN “Veteran” Yogyakarta Conference Series Proceeding on Engineering and Science Series (ESS), 1(1), 301–310.
  • Bargawa, W. S., & Tobing, R. F. (2020). Iron ore resource modeling and estimation using geostatistics. AIP Conference Proceedings, 2245(1), 70016.
  • Cornell, R. M., & Schwertmann, U. (2003). The iron oxides: structure, properties, reactions, occurrences and uses. John Wiley & Sons.
  • Dag, A., & Ozdemir, A. C. (2013). A comparative study for 3D surface modeling of coal deposit by spatial interpolation approaches. Resource Geology, 63(4), 394–403.
  • De-Vitry, C., Vann, J., & Arvidson, H. (2007). A guide to selecting the optimal method of resource estimation for multivariate iron ore deposits. Proceedings of the Iron Ore Conference, 67–77.
  • Elevli, B., Demirci, A., Dogan, A., & Onal, G. (2018). Resource and reserve analysis of Hasancelebi Iron Ore deposit, Turkey. Mine Planning and Equipment Selection 2000, 199.
  • Gül, Y., & Küçükkarasu, O. (2020). Resource estimation for Alpagut-Dodurga coal field and determination of spatial distribution of coal quality parameters. Turkish Journal of Earth Sciences, 29(3), 521–537 . Gusman, M., Muchtar, B., Syah, N., Akbar, M. D., & Deni, A. V. (2019). Estimations of limestone resources using three dimension block kriging method, a case study: limestone sediment at PT Semen Padang. IOP Conference Series: Earth and Environmental Science, 314(1), 12069.
  • Hatton, W., & Fardell, A. (2012). New discoveries of coal in Mozambique—Development of the coal resource estimation methodology for International Resource Reporting Standards. International Journal of Coal Geology, 89, 2–12.
  • Jeuken, R., Xu, C., & Dowd, P. (2020). Improving Coal Quality Estimations with Geostatistics and Geophysical Logs. Natural Resources Research, 1–18.
  • Journel, A. G., & Huijbregts, C. J. (1978). Mining geostatistics (C. 600). Academic press London.
  • Marwanza, I., Nas, C., Azizi, M. A., & Simamora, J. H. (2019). Comparison between moving windows statistical method and kriging method in coal resource estimation. Journal of Physics: Conference Series, 1402(3), 33016.
  • Matheron, G. (1963). Principles of geostatistics. Economic geology, 58(8), 1246–1266.
  • Myers, D. E. (1992). Kriging, cokriging, radial basis functions and the role of positive definiteness. Computers & Mathematics with Applications, 24(12), 139–148.
  • Nielsen, S. H. H., Partington, G. A., Franey, D., & Dwight, T. (2019). 3D mineral potential modelling of gold distribution at the Tampia gold deposit. Ore Geology Reviews, 109, 276–289.
  • Rossi, M. E., & Deutsch, C. V. (2013). Mineral resource estimation. Springer Science & Business Media.
  • Samanta, B. (2010). Radial basis function network for ore grade estimation. Natural resources research, 19(2), 91–102.
  • Santos, T. C. dos, & Yamamoto, J. K. (2019). Ore resource estimation based on radial based functions-Case study on União Luiz and Morro do Carrapato Gold Deposits (Alta Floresta Gold Province). REM-International Engineering Journal, 72(3), 493–499.
  • Shahbeik, S., Afzal, P., Moarefvand, P., & Qumarsy, M. (2014). Comparison between ordinary kriging (OK) and inverse distance weighted (IDW) based on estimation error. Case study: Dardevey iron ore deposit, NE Iran. Arabian Journal of Geosciences, 7(9), 3693–3704.
  • Siddiqui, F. I., Pathan, A. G., Ünver, B., Tercan, A. E., Hindistan, M. A., Ertunç, G., Atalay, F., Ünal, S., & Kıllıoğlu, Y. (2015). Lignite resource estimations and seam modeling of Thar Field, Pakistan. International Journal of Coal Geology, 140, 84–96.
  • Skala, V., Karim, S. A. A., & Cervenka, M. (2020). Finding points of importance for radial basis function approximation of large scattered data. International Conference on Computational Science, 239–250.
  • Tercan, A. E., & Karayigit, A. I. (2001). Estimation of lignite reserve in the Kalburcayiri field, Kangal basin, Sivas, Turkey. International Journal of Coal Geology, 47(2), 91–100.
  • Tutmez, B., Dag, A., & Cengiz, A. K. (2009). Measuring dependence between calorific values of lignite and spatial positions by rank correlation method: A case study. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 32(1), 45–53.
  • Wadi, M., & Ivanik, O. (2019). Geospatıal Modellıng And Reserves Estımatıon Of Wadı Al Shatı Iron Ore Deposıt (Lıbya). Monitoring 2019, 2019(1), 1–5.
  • Wang, J., Zhao, H., Bi, L., & Wang, L. (2018). Implicit 3D modeling of ore body from geological boreholes data using hermite radial basis functions. Minerals, 8(10), 443.
  • Wang, S., Li, X., & Du, K. (2017). Grade distribution and orebody demarcation of bauxite seam based on coupled Interpolation. Arabian Journal for Science and Engineering, 42(9), 3963–3972.
  • Whateley, M. K. G., Inaner, H., Nakoman, E., & Mulcahy, S. (1997). Comparison of classical and geostatistical methods for coal resource estimation in the Turgut Deposits, Muğla-Yatağan, SW Turkey. European Coal Geology, Proceeding 3rd European Coal Conference, 559–572.
  • Wright, G. B. (2003). Radial basis function interpolation: numerical and analytical developments.
  • Yaylagul, C., & Tutmez, B. (2020). Learning distance effect on lignite quality variables at global and local scales. International Journal of Coal Science & Technology, 1–13.
  • Yünsel, T Y. (2007). Maden yataklarının jeoistatistiksel yöntemlerle analizi ve modellenmesi. ÇU Fen Bilimleri Enstitüsü, Maden Mühendisliği ABD, PhDr Tezi, Adana.
  • Yünsel, Tayfun Yusuf. (2019). In-situ coal quality variability analysis by combining Gaussian co-simulation and a JavaScript. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 41(21), 2631–2649.
  • Zerzour, O., Gadri, L., Hadji, R., Mebrouk, F., & Hamed, Y. (2021). Geostatistics-Based Method for Irregular Mineral Resource Estimation, in Ouenza Iron Mine, Northeastern Algeria. Geotechnical and Geological Engineering, 1–10.
  • Zhang, S. E., Nwaila, G. T., Tolmay, L., Frimmel, H. E., & Bourdeau, J. E. (2021). Integration of machine learning algorithms with Gompertz Curves and Kriging to estimate resources in gold deposits. Natural Resources Research, 30(1), 39–56.
  • Zhang, S. wen, Shen, C. yang, Chen, X. yang, Ye, H. chun, Huang, Y. fang, & Lai, S. (2013). Spatial Interpolation of Soil Texture Using Compositional Kriging and Regression Kriging with Consideration of the Characteristics of Compositional Data and Environment Variables. Journal of Integrative Agriculture, 12(9), 1673–1683. https://doi.org/10.1016/S2095-3119(13)60395-0

Bir Demir Yatağında Radyal Temelli Fonksiyon ve Ortalamasız Krigleme Kestirimlerinin Karşılaştırılması

Yıl 2021, Sayı: 27, 303 - 310, 30.11.2021
https://doi.org/10.31590/ejosat.913286

Öz

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.

Kaynakça

  • Afzal, P. (2018). Comparing ordinary kriging and advanced inverse distance squared methods based on estimating coal deposits; case study: East-Parvadeh deposit, central Iran. Journal of Mining and Environment, 9(3), 753–760.
  • Bargawa, W. S., Nugroho, S. P., Hariyanto, R., Lusantono, O. W., & Bramida, R. F. (2020). Geostatistical Modeling of Ore Grade In A Laterite Nickel Deposit. LPPM UPN “Veteran” Yogyakarta Conference Series Proceeding on Engineering and Science Series (ESS), 1(1), 301–310.
  • Bargawa, W. S., & Tobing, R. F. (2020). Iron ore resource modeling and estimation using geostatistics. AIP Conference Proceedings, 2245(1), 70016.
  • Cornell, R. M., & Schwertmann, U. (2003). The iron oxides: structure, properties, reactions, occurrences and uses. John Wiley & Sons.
  • Dag, A., & Ozdemir, A. C. (2013). A comparative study for 3D surface modeling of coal deposit by spatial interpolation approaches. Resource Geology, 63(4), 394–403.
  • De-Vitry, C., Vann, J., & Arvidson, H. (2007). A guide to selecting the optimal method of resource estimation for multivariate iron ore deposits. Proceedings of the Iron Ore Conference, 67–77.
  • Elevli, B., Demirci, A., Dogan, A., & Onal, G. (2018). Resource and reserve analysis of Hasancelebi Iron Ore deposit, Turkey. Mine Planning and Equipment Selection 2000, 199.
  • Gül, Y., & Küçükkarasu, O. (2020). Resource estimation for Alpagut-Dodurga coal field and determination of spatial distribution of coal quality parameters. Turkish Journal of Earth Sciences, 29(3), 521–537 . Gusman, M., Muchtar, B., Syah, N., Akbar, M. D., & Deni, A. V. (2019). Estimations of limestone resources using three dimension block kriging method, a case study: limestone sediment at PT Semen Padang. IOP Conference Series: Earth and Environmental Science, 314(1), 12069.
  • Hatton, W., & Fardell, A. (2012). New discoveries of coal in Mozambique—Development of the coal resource estimation methodology for International Resource Reporting Standards. International Journal of Coal Geology, 89, 2–12.
  • Jeuken, R., Xu, C., & Dowd, P. (2020). Improving Coal Quality Estimations with Geostatistics and Geophysical Logs. Natural Resources Research, 1–18.
  • Journel, A. G., & Huijbregts, C. J. (1978). Mining geostatistics (C. 600). Academic press London.
  • Marwanza, I., Nas, C., Azizi, M. A., & Simamora, J. H. (2019). Comparison between moving windows statistical method and kriging method in coal resource estimation. Journal of Physics: Conference Series, 1402(3), 33016.
  • Matheron, G. (1963). Principles of geostatistics. Economic geology, 58(8), 1246–1266.
  • Myers, D. E. (1992). Kriging, cokriging, radial basis functions and the role of positive definiteness. Computers & Mathematics with Applications, 24(12), 139–148.
  • Nielsen, S. H. H., Partington, G. A., Franey, D., & Dwight, T. (2019). 3D mineral potential modelling of gold distribution at the Tampia gold deposit. Ore Geology Reviews, 109, 276–289.
  • Rossi, M. E., & Deutsch, C. V. (2013). Mineral resource estimation. Springer Science & Business Media.
  • Samanta, B. (2010). Radial basis function network for ore grade estimation. Natural resources research, 19(2), 91–102.
  • Santos, T. C. dos, & Yamamoto, J. K. (2019). Ore resource estimation based on radial based functions-Case study on União Luiz and Morro do Carrapato Gold Deposits (Alta Floresta Gold Province). REM-International Engineering Journal, 72(3), 493–499.
  • Shahbeik, S., Afzal, P., Moarefvand, P., & Qumarsy, M. (2014). Comparison between ordinary kriging (OK) and inverse distance weighted (IDW) based on estimation error. Case study: Dardevey iron ore deposit, NE Iran. Arabian Journal of Geosciences, 7(9), 3693–3704.
  • Siddiqui, F. I., Pathan, A. G., Ünver, B., Tercan, A. E., Hindistan, M. A., Ertunç, G., Atalay, F., Ünal, S., & Kıllıoğlu, Y. (2015). Lignite resource estimations and seam modeling of Thar Field, Pakistan. International Journal of Coal Geology, 140, 84–96.
  • Skala, V., Karim, S. A. A., & Cervenka, M. (2020). Finding points of importance for radial basis function approximation of large scattered data. International Conference on Computational Science, 239–250.
  • Tercan, A. E., & Karayigit, A. I. (2001). Estimation of lignite reserve in the Kalburcayiri field, Kangal basin, Sivas, Turkey. International Journal of Coal Geology, 47(2), 91–100.
  • Tutmez, B., Dag, A., & Cengiz, A. K. (2009). Measuring dependence between calorific values of lignite and spatial positions by rank correlation method: A case study. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 32(1), 45–53.
  • Wadi, M., & Ivanik, O. (2019). Geospatıal Modellıng And Reserves Estımatıon Of Wadı Al Shatı Iron Ore Deposıt (Lıbya). Monitoring 2019, 2019(1), 1–5.
  • Wang, J., Zhao, H., Bi, L., & Wang, L. (2018). Implicit 3D modeling of ore body from geological boreholes data using hermite radial basis functions. Minerals, 8(10), 443.
  • Wang, S., Li, X., & Du, K. (2017). Grade distribution and orebody demarcation of bauxite seam based on coupled Interpolation. Arabian Journal for Science and Engineering, 42(9), 3963–3972.
  • Whateley, M. K. G., Inaner, H., Nakoman, E., & Mulcahy, S. (1997). Comparison of classical and geostatistical methods for coal resource estimation in the Turgut Deposits, Muğla-Yatağan, SW Turkey. European Coal Geology, Proceeding 3rd European Coal Conference, 559–572.
  • Wright, G. B. (2003). Radial basis function interpolation: numerical and analytical developments.
  • Yaylagul, C., & Tutmez, B. (2020). Learning distance effect on lignite quality variables at global and local scales. International Journal of Coal Science & Technology, 1–13.
  • Yünsel, T Y. (2007). Maden yataklarının jeoistatistiksel yöntemlerle analizi ve modellenmesi. ÇU Fen Bilimleri Enstitüsü, Maden Mühendisliği ABD, PhDr Tezi, Adana.
  • Yünsel, Tayfun Yusuf. (2019). In-situ coal quality variability analysis by combining Gaussian co-simulation and a JavaScript. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 41(21), 2631–2649.
  • Zerzour, O., Gadri, L., Hadji, R., Mebrouk, F., & Hamed, Y. (2021). Geostatistics-Based Method for Irregular Mineral Resource Estimation, in Ouenza Iron Mine, Northeastern Algeria. Geotechnical and Geological Engineering, 1–10.
  • Zhang, S. E., Nwaila, G. T., Tolmay, L., Frimmel, H. E., & Bourdeau, J. E. (2021). Integration of machine learning algorithms with Gompertz Curves and Kriging to estimate resources in gold deposits. Natural Resources Research, 30(1), 39–56.
  • Zhang, S. wen, Shen, C. yang, Chen, X. yang, Ye, H. chun, Huang, Y. fang, & Lai, S. (2013). Spatial Interpolation of Soil Texture Using Compositional Kriging and Regression Kriging with Consideration of the Characteristics of Compositional Data and Environment Variables. Journal of Integrative Agriculture, 12(9), 1673–1683. https://doi.org/10.1016/S2095-3119(13)60395-0
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Fırat Atalay 0000-0001-6349-7745

Mehmet Suphi Ünal 0000-0002-9993-8300

Süleyman Yasin Kıllıoğlu 0000-0003-2227-9834

Erken Görünüm Tarihi 29 Temmuz 2021
Yayımlanma Tarihi 30 Kasım 2021
Yayımlandığı Sayı Yıl 2021 Sayı: 27

Kaynak Göster

APA Atalay, F., Ünal, M. S., & Kıllıoğlu, S. Y. (2021). Bir Demir Yatağında Radyal Temelli Fonksiyon ve Ortalamasız Krigleme Kestirimlerinin Karşılaştırılması. Avrupa Bilim Ve Teknoloji Dergisi(27), 303-310. https://doi.org/10.31590/ejosat.913286