Deussen, Philipp; Galvanin, Federico; (2023) A joint model-based design of experiments approach for the identification of Kriging models in geological exploration. In: Kokossis, Antonios and Georgiadis, Michael and Pistikopoulos, Stratos, (eds.) Computer Aided Chemical Engineering. (pp. pp. 789-794). Elsevier: Athens, Greece.

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Abstract

When exploring prospective mining locations, a central task is modelling rock attributes in the subsurface. The drilling needed to sample these locations is costly, so efficient sampling and reliable interpolation methods are needed. Kriging models (Gaussian Processes) are thus used, with the kernel and its parameters determined from data analysis of preliminary samples and expert judgement. New samples iteratively update the model, targeting exploitation (high ore grades) and exploration (minimising prediction variance). The problem arises if the chosen kernel is incorrect or high uncertainty affects parameters. This paper thus suggests a joint model-based design of experiments (j-MBDoE) approach to target two objectives: maximising the distinguishability of candidate model predictions and reducing model uncertainty from parameter variance. Three different kernels in an Ordinary Kriging GP were used as candidate models. In-silico data was generated using one kernel and the optimal design strategy iteratively determined sampling locations to maximise model distinguishability with a constraint to ensure improved parameter estimates. Two models could be distinguished and the data approximated well with a limited number of drilling experiments while satisfactorily estimating kernel parameters.

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