An Evaluation of Multi-point Stochastic approaches for Uncertainty Assessment in Ore Grade Estimation

Abstract

Minerals and energy resources are the lifelines for the development and prosperity of a nation. In India, majority of the deposits are lying deep in earth, and it throws challenges to mining, engineers, and geologist to extract them safely and economically without compromising the environment. Ore grade estimation is one of the vital stages of each and every mining project. It plays the dominant role in the decision-making process for investment and development of various mining projects and hence become an important and crucial stage. The thesis focuses on the development of machine learning (ML) based non-linear regression models and pattern based multipoint stochastic (MPS) simulation algorithm for uncertainty assessment in ore grade estimation. In this thesis ML-based estimators and pattern based MPS simulation were developed and subsequently applied to two case study mines (a limestone and an iron ore deposit) in the Indian scenario.
Distinct ML based nonlinear regression architectures such as Multilayer Perceptron Neural Network (MLP NN), General Regression Neural Network (GRNN), Support Vector Regression (SVR) are developed to improve the grade estimation. The multiple lithological units are incorporated as auxiliary information with spatial coordinates into the ML-based models. These models do not require any preliminary geological study and are free from any statistical assumption on the raw data.
For iron ore deposit, set of input variable consists of three-dimensional (3-D) spatial coordinates and their ten underlying lithologies, and an iron grade is the only output variable. However, for limestone deposit 3-D spatial coordinates with four distinct lithology form the set of input variables. The set of output variables consists of four constituents of limestone deposit as calcium oxide (CaO), alumina (AI2O3), ferrous oxide (Fe2O3), and silica (SiO2). The ML architectures with appropriate training capture the inherent spatial variability of assay values and their underlying rock types. The best design with the lowest root mean square error (RMSE) and the highest correlation coefficient (R) is selected for the construction of grade map. The GRNN network was found to be more suitable as compared to all other models regarding generalization capability for both limestone and iron ore deposit. The dissertation also aims at developing pattern based multipoint stochastic simulation algorithm using contourlet transformation named as contoursim for uncertainty assessment in grade estimation. The idea of contoursim is motivated by the wavesim existing in the recent literatures.
The algorithm is developed for the simulation of spatially correlated variables such as ore grade and their underlying lithology. The major steps involved in the contoursim is same as that of other MPS based scheme, but the use of separable filter bank structure allows them to identify the complex structure such as curve linearity present in the geological deposit. The CT with their separated filter bank structure capture the complex spatial interaction among several attributes with sparse coefficients. In this thesis, dimension reduction of the pattern database is achieved by contourlet decomposition of each pattern with appropriate scale. The reduced pattern database is further classified into several clusters by coarsest scale coefficients. The algorithm captures the existing trend and continuity of the ore deposit and thus reproduced the available intrinsic patterns of the training image into their several realizations. Multiple realizations of the iron and limestone allow for an assessment of spatial uncertainty in grade estimation. Further ensemble map of ten different realizations have been obtained. The histogram of the training image and their realizations also confirms the capability of contourlet transform to capture the spatial heterogeneity and anisotropy inherent in the complex geological phenomena.
The algorithm is verified by two dimensional unconditional simulation using categorical binary channel training image and continuous mineralization of CaO. The sensitivity analysis of the algorithm with respect to its several influential parameters is explored. The study revealed that the algorithm is sensitive to the number of clusters, number of contourlet coefficients, and number of directional sub-bands from coarser to fine level of decomposition.