A Bayesian Method for Estimating Uncertainty in Excavated Material

Abstract: This paper proposes a method to probabilistically quantify the moments (mean and variance) of excavated material during excavation by aggregating the prior moments of the grade blocks around the given bucket dig location. By modelling the moments as random probability density functions (pdf) at sampled locations, a formulation of the sums of Gaussian based uncertainty estimation is presented that jointly estimates the location pdfs, as well as the prior values for uncertainty coming from ore body knowledge (obk) sub block models. The moments calculated at each random location is a single Gaussian and they are the components of Gaussian mixture distribution. The overall uncertainty of the excavated material at the given bucket location is represented by the Gaussian Mixture Model (GMM) and therefore moment matching method is proposed to estimate the moments of the reduced GMM. The method was tested in a region at a Pilbara iron ore deposit situated in the Brockman Iron Formation of the Hamersley Province, Western Australia, and suggests a frame work to quantify the uncertainty in the excavated material that hasn't been studied anywhere in the literature yet.