Prediction of Copper Recovery from Geometallurgical Data using D-vine Copulas

"The accurate modelling of geometallurgical data can significantly improve decision-making and help optimize mining operations. This case study compares models for predicting copper recovery from three indirect test measurements that are typically available, to avoid the cost of direct measurement of recovery. Geometallurgical data from 930 drill core samples, with an average length of 19 m, from an orebody in South America have been analysed. The data includes copper recovery and the results of three other tests: Bond mill index test; resistance to abrasion and breakage index; and semi-autogenous grinding power index test. A genetic algorithm is used to impute missing data at some locations so as to make use of all 930 samples. The distribution of the variables is modelled with D-vine copula and predictions of copper recovery are compared with those from regressions fitted by ordinary least squares and generalized least squares. The D-vine copula model had the least mean absolute error. IntroductionIn this paper we compare the use of D-vine copula, generalized least squares (GLS), and ordinary least squares (OLS) for modelling geometallurgical data from an orebody in South America. The first objective is to construct models for predicting copper recovery (Rec) from the Bond mill index test (BWi); resistance to abrasion and breakage index (A*b); and semi-autogenous grinding (SAG) power index test (Spi). This involves fitting a D-vine copula and regression models fitted by OLS and GLS. The second objective is to investigate the performance of the fitted models for predicting Rec (Willmott and Matsuura 2005).Traditional resource model approaches either ignore the mineral processing characteristics of extracted tonnages or treat processing as an independent component of a mining operation. The net present value (or any other objective) can be truly optimized only by considering the mining operation as an integrated system in which net value is defined as the end-product that the company sells. This approach requires the resource model to be extended to include all relevant rock properties and processing responses."