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Faculty of Engineering and Built Environment

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Subject: search.filters.subject.Mathematical models

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    Learning rate optimisation of an image processing deep convolutional neural network
    (2021) Buthelezi, Sibusiso Blessing; Reddy, Seren; Twala, Bhekisipho
    The major contribution of this dissertation is the proposal of the use of mathematical models to identify an optimal learning rate for an image processing deep convolutional neural network (DCNN). This model is derived from a nonlinear regression relationship between the learning rate and the accuracy of a test DCNN model. This relationship is meant to (A) resolve the problem of arbitrarily selecting the initial learning rate (B) reduce computational resource requirement and (C) reduce training instabilities. An algorithm is developed to analyse an inputted DCNN model and subsequently render output parameters that may be used to aid in the selection of an OLR. The benefit of an OLR includes improved training stability and reduced computational resources. The results rendered by the OLR algorithm proposes that an optimal learning rate improves model performance; this is described by the test model average accuracy of 91%. Furthermore, a model validation graph is also extrapolated. which will illustrate the mathematical model accuracy and the region of interest (ROI). The ROI defines the region in the learning rate spectrum with a positive effect on model performance.
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    Systems analysis of the transformation of South African cities
    (2017) Simelane, Thokozani Silas; Duffy, Kevin Jan; Pearce, Brian
    The need to quantify and model transformations that have taken place in the cities of South Africa is one of the grand challenges linked to country’s transition to Democracy. Given the complexities associated with different stages of city transformation, it is imperative that models used to unpack processes of city transformation are novel. In this study it emerged that statistical methods alone are not adequate to fully present, in a comprehensible way, all facets of drivers of city transformation. As a result, statistical methods have been combined with mathematical and system dynamics models. Results revealed that city transformations derive from a number of triggers. Underlining these are income, migration and houses. The empirical data collected through questionnaire survey that was later incorporated into mathematical models demonstrated that income is a primary driver that fuels city migration. System Dynamic Models demonstrated that the availability of houses or accommodation serve as constraints that keep the city population within the limits of the carrying capacity of a city. In addition it was further confirmed, through mathematical models that income has varying effects on the attractiveness of cities. This was found to be linked to the shape of the distribution of income in the city. A normally distributed income with a peak in the middle results in a city being more attractive than an evenly distributed income that peaks either at very low or high income levels. This observation brought forth a need to test heterogeneity when analyzing city transformation using income as an index. Mathematical Models that incorporated heterogeneity demonstrated the usefulness of systems analysis in unpacking the mechanism of city transformation, a component of city management that requires serious consideration for planning, budgeting and provision of limited resources like houses in the cities. Success of methods used in this study led to a conclusion that these can be enhanced through other techniques like agent based models. With this call, improvements on this study that can be attained through these techniques are recommended. This will enrich the understanding of the transformation and dynamics of cities under different conditions than those that exist in South Africa.