Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

Adaptive Processing as proposed in geometallurgy has to rely on spatially interpolated information on geometallurgical parameters like phase composition, size distributions of particles of different phases, grain shape parameters, and portions of value elements in different grains. Using the geostatistically predicted values for adaptive processing, e.g. for the selection of milling diameters, thresholds in physical separation, or choices on using an extra pre-separation step, is typically not optimal. Mathematically this effect is introduced by two forms of nonlinearities: 1) The nonlinear scales of compositions, distributions, and shapes have special properties with respect to geostatistics. Classical geostatistics creates some artefacts for these nonlinear scales. On the other hand, modern geostatistical procedures adapted to these scales do not provide unbiased results with respect to linear transformations of the data (e.g. biased block estimates). 2) Neither economic nor ecological effects (e.g. monetary gain) of processing decisions are linear in the interpolated geometallurgical parameters. These nonlinear transforms are not unbiasedly estimated by the likewise transformed unbiased geostatistical predictions of the geometallurgical parameters. Furthermore, we need to optimize the conditional expectation of the gain, rather than obtain an unbiased estimate. Standard geostatistics as such does not provide the "right sort" of estimates for adaptive processing. A nonlinear kriging procedure is needed to approximate the nonlinearities mentioned before.

We propose to solve these problems simultaneously using a nonlinear geostatistical technique for predicting the target function (the monetary gain), rather than to predict the geometallurgical parameters and compute the gain from them. The optimization can then be performed directly on this estimated function.
It can be shown that this optimization performed on the conditional expectations, not on unbiased predictions, would yield the best possible processing choice. We propose a procedure choosing the processing parameters on an approximation of the conditional expectation. The difficulties with the classical approach and the effectiveness of this new approach are illustrated by a simplified simulation example with a single processing parameter and a simple dependence on the microstructure.