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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

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Designing products and processes is a fundamental aspect of engineering that significantly impacts society and the world. Chemical process design aims to create more efficient and sustainable production processes that consume fewer resources and emit less pollution. Mathematical models that accurately describe process behavior are necessary to make informed and responsible decisions. However, as processes become more complex, purely symbolic formulations may be inadequate, and simulations using tailored computer code become necessary. The decision‐making process in optimal design requires a procedure for choosing the best option while complying with the system’s constraints, for which task optimization approaches are well suited. This doctoral thesis focuses on black‐box optimization problems that arise when using process simulators in optimal process design tasks and assesses the potential of derivative‐free, metaheuristics, and surrogate‐based optimization approaches. The optimal design of natural gas liquefaction processes is the case study of this research. To overcome numerical issues from black‐box problems, the first work of this doctoral thesis consisted of using the globally convergent Nelder‐Mead simplex method to the optimal process design problem. The second work introduced surrogate models to assist the search towards the global optimum of the black‐box problem and an adaptive sampling scheme comprising the optimization of an acquisition function with metaheuristics. Kriging as surrogate models to the simulation‐optimization problems are computationally cheaper and effective predictors suitable for global search. The third work aims to overcome the limitations of acquisition function optimization and the use of metaheuristics. The proposed comprehensive mathematical notation of the surrogate optimization problem was readily implementable in algebraic modeling language software. The presented framework includes kriging models of the objective and constraint functions, an adaptive sampling procedure, a heuristic for stopping criteria, and a readily solvable surrogate optimization problem with mathematical programming. The success of the surrogate‐based optimization framework relies on the kriging models’ prediction accuracy regarding the underlying, simulation‐based functions. The fourth publication extends the previous work to multi‐objective black‐box optimization problems. It applies the ε constraint method to transform the multi‐objective surrogate optimization problem into a sequence of single‐objective ones. The ε‐constrained surrogate optimization problems are implemented automatically in algebraic modeling language software and solved using a gradient‐based, state‐of‐the‐art solver. The fifth publication is application-driven and focuses on identifying the most suitable mixed‐refrigerant refrigeration technology for natural gas liquefaction in terms of energy consumption and costs. The study investigates five natural gas liquefaction processes using particle swarm optimization and concludes that there are flaws in the expected relationships between process complexity, energy consumption, and total annualized costs. In conclusion, the research conducted in this doctoral thesis demonstrates the importance and capabilities of using optimization to process simulators. The work presented here highlights the potential of surrogate‐based optimization approaches to significantly reduce the computational cost and guide the search in black‐box optimization problems with chemical process simulators embedded. Overall, this doctoral thesis contributes to developing optimization strategies for complex chemical processes that are essential for addressing some of the current most pressing environmental and social challenges. The methods and insights presented in this work can help engineers and scientists design more sustainable and efficient processes, contributing to a better future for all.

Complex mathematical models are often built to describe a physical process that would otherwise be extremely difficult, too costly or sometimes impossible to analyze. Generally, these models require solutions to many partial differential equations. As a result, the computer codes may take a considerable amount of time to complete a single evaluation. A time tested method of analysis for such models is Monte Carlo simulation. These simulations, however, often require many model evaluations, making this approach too computationally expensive. To limit the number of experimental runs, it is common practice to model the departure as a Gaussian stochastic process (GaSP) to develop an emulator of the computer model. One advantage for using an emulator is that once a GaSP is fit to realized outcomes, the computer model is easy to predict in unsampled regions of the input space. This is an attempt to 'characterize' the overall model of the computer code. Most of the historical work on design and analysis of computer experiments focus on the characterization of the computer model over a large region of interest. However, many practitioners seek other objectives, such as input screening (Welch et al., 1992), mapping a response surface, or optimization (Jones et al., 1998). Only recently have researchers begun to consider these topics in the design and analysis of computer experiments. In this dissertation, we explore a more traditional response surface approach (Myers, Montgomery and Anderson-Cook, 2009) in conjunction with traditional computer experiment methods to search for the optimum response of a process. For global optimization, Jones, Schonlau, and Welch's (1998) Efficient Global Optimization (EGO) algorithm remains a benchmark for subsequent research of computer experiments. We compare the proposed method in this paper to this leading benchmark. Our goal is to show that response surface methods can be effective means towards estimating an optimum response in the computer experiment framework. / Ph. D.

A study was performed to compare two different methods for generating surrogate models for the analysis and design of airfoils. Initial research was performed to compare the accuracy of surrogate models for predicting the lift and drag of an airfoil with data collected from highidelity simulations using a modern CFD code along with lower-order models using a panel code. This was followed by an evaluation of the Class Shape Trans- formation (CST) method for parameterizing airfoil geometries as a prelude to the use of surrogate models for airfoil design optimization and the implementation of software to use CST to modify airfoil shapes as part of the airfoil design process. Optimization routines were coupled with surrogate modeling techniques to study the accuracy and efficiency of the surrogate models to produce optimal airfoil shapes. Finally, the results of the current research are summarized, and suggestions are made for future research.

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