A research report submitted in partial fulfillment of the requirements for the degree of Master of Science in School of Computer Science and Applied Mathematics to the Faculty of Science University of Witwatersrand, 2019 / Learning-based methods have recently become popular in control engineering, achieving good performance on a number of challenging tasks. However, in complex environments where data efficiency and safety are critical, current methods remain unsatisfactory. As a step toward addressing these shortcomings, we propose a learning-based approach that combines Gaussian process regression with model predictive control. Using sparse spectrum Gaussian processes, we extend previous work by learning a model of the dynamics incrementally from a stream ofsensory data. Utilizinglearned dynamics and model uncertainty, we develop a controller that can learn and plan in real-time under non-linear constraints. We test our approach on pendulum and cartpole swing up problems and demonstrate the benefits of learning on a challenging autonomous racing task. Additionally, we show that learned dynamics models can be transferred to new tasks without any additional training. / TL (2020)

A research project report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Masters of Science in Engineering, 2017 / The assessment of local and spatial uncertainty associated with a regionalised variable such as nickel grade at Hunters Road magmatic sulphide deposit is one of the critical elements in the resource estimation. The study focused on the application of Multiple Indicator Kriging (MIK) and Sequential Gaussian Simulation (SGS) in the estimation of recoverable resources and the assessment of grade uncertainty at Hunters Road’s Western orebody. The Hunters Road Western orebody was divided into two domains namely the Eastern and the Western domains and was evaluated based on 172 drill holes. MIK and SGS were performed using Datamine Studio RM module. The combined Mineral Resources estimate for the Western orebody at a cut-off grade of 0.40%Ni is 32.30Mt at an average grade of 0.57%Ni, equivalent to 183kt of contained nickel metal. SGS results indicated low uncertainty associated with Hunters Road nickel project with 90% probability of an average true grade above cut-off, lying within +/-3% of the estimated block grade. The estimate of the mean based on SGS was 0.55%Ni and 0.57% Ni for the Western and Eastern domains respectively. MIK results were highly comparable with SGS E-type estimates while the most recent Ordinary Kriging (OK) based estimates by BNC dated May 2006, overstated the resources tonnage and underestimated the grade compared to the MIK estimates. It was concluded that MIK produced better estimates of recoverable resources than OK. However, since only E-type estimates were produced by MIK, post processing of “composite” conditional cumulative distribution function (ccdf) results using a relevant change of support algorithm such as affine correction is recommended. Although SGS produced a good measure of uncertainty around nickel grades, post processing of realisations using a different software such as Isatis has been recommended together with combined simulation of both grade and tonnage. / XL2018

A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2016 / It is of great importance to minimize misclassification of ore and waste during grade control for a mine operation. This research report compares two recoverable reserve estimation techniques for ore classification for Kayelekera Uranium Mine. The research was performed on two data sets taken from the pit with different grade distributions. The two techniques evaluated were Sequential Gaussian Simulation and Ordinary Kriging. A comparison of the estimates from these techniques was done to investigate which method gives more accurate estimates. Based on the results from profits and loss, grade tonnage curves the difference between the techniques is very low. It was concluded that similarity in the estimates were due to Sequential Gaussian Simulation estimates were from an average of 100 simulation which turned out to be similar to Ordinary Kriging. Additionally, similarities in the estimates were due to the close spaced intervals of the blast hole/sample data used. Whilst OK generally produced acceptable results like SGS, the local variability of grades was not adequately reproduced by the technique. Subsequently, if variability is not much of a concern, like if large blocks were to be mined, then either technique can be used and yield similar results. / M T 2016