Nonlinear Geostatistics for Geometallurgical Optimisation

Adaptive mineral processing has to rely on spatially predicted information on primary geometallurgical parameters, like phase composition, size and shape distributions of grains from various phases, portions of value elements in different grain types. Naively, one would predict these parameters geostatistically and select an optimal processing for the predicted structure. This is suboptimal, due to various kinds of nonlinearities in the problem. First, some primary geometallurgical quantities themselves are measured in non-real scales, like compositional or stereologically distorted geometric information. Standard geostatistics has to be replaced by compositional and geometric geostatistics, involving complex transforms and restrictions. Further, only partial and uncertain information is available, introducing a stochastic character to the optimisation problem. Moreover, many response variables leading to costs, outcomes, and eventual effects of later processing depend nonlinearly on the primary geometallurgical parameters, which implies that the final monetary value is not estimated unbiasedly by kriging. Finally unbiased linear prediction (such as kriging) is not the best method of prediction for decision making. The conditional expectation of the monetary values is needed instead. The impact of these problems is explained in this paper with simplified examples and a first approach to a general solution is proposed.