Electrical and Electronic Engineering - Theses
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ItemA Block Coordinate Descent approach for solving Graph SLAM( 2021)Simultaneous Localisation and Mapping (SLAM) refers to the problem of estimating the position of a mobile robot navigating in an unknown environment while simultaneously constructing a map of it, using measurements collected by sensors mounted on the robot, such as cameras, lasers, radars, or inertial sensors. SLAM is of particular interest when there is no prior knowledge of the environment nor external sources of localisation (compass, GPS). In this sense, SLAM aims for autonomy of robot motion and environment discovery. The graph-based formulation of the SLAM problem, also commonly referred to as Graph SLAM, maximum a posteriori estimation, factor graph optimisation or smoothing and mapping (SAM), is considered the current de-facto standard formulation for SLAM. This approach defines the SLAM problem as a nonlinear least squares minimisation problem, commonly solved via successive linearisation methods such as Gauss-Newton. However, iterative line search methods have limitations in terms of convergence guarantees and scalability, which suggest the research potential for alternative optimisation algorithms. In our research, we study an alternative numerical method for solving the Graph SLAM problem: the Block Coordinate Descent method. By partitioning the problem into a series of optimisation subproblems, this approach may offer comparatively better performance than iterative linearisation algorithms, such as lower per-iteration computational complexity, scalability and parallel processing capabilities. Importantly, this method is not dependant on linearisation, and under certain conditions, may offer convergence guarantees towards stationary points. We present our Block Coordinate Descent approach by systematically analysing the attributes of the optimisation subproblems originating from the use of this numerical method on a Graph SLAM problem formulation based on particular inertial, bearing and range measurement models: the Affine Motion Model, the Affine Bearing Model and the Squared Range Model. We verify the resulting optimisation subproblems satisfy conditions that offer convergence guarantees and scalability properties. Additionally, we evaluate our Block Coordinate Descent approach by implementing the resulting algorithm in a simulated environment using real-world datasets, comparing its performance to the Gauss-Newton line search method.
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ItemAdversarial Robustness in High-Dimensional Deep Learning( 2021)As applications of deep learning continue to be discovered and implemented, the problem of robustness becomes increasingly important. It is well established that deep learning models have a serious vulnerability against adversarial attacks. Malicious attackers targeting learning models can generate so-called "adversarial examples'' that are able to deceive the models. These adversarial examples can be generated from real data by adding small perturbations in specific directions. This thesis focuses on the problem of explaining vulnerability (of neural networks) to adversarial examples, an open problem which has been addressed from various angles in the literature. The problem is approached geometrically, by considering adversarial examples as points which lie close to the decision boundary in a high-dimensional feature space. By invoking results from high-dimensional geometry, it is argued that adversarial robustness is impacted by high data dimensionality. Specifically, an upper bound on robustness which decreases with dimension is derived, subject to a few mathematical assumptions. To test this idea that adversarial robustness is affected by dimensionality, we perform experiments where robustness metrics are compared after training neural network classifiers on various dimension-reduced datasets. We use MNIST and two cognitive radio datasets for our experiments, and we compute the attack-based empirical robustness and attack-agnostic CLEVER score, both of which are approximations of true robustness. These experiments show correlations between adversarial robustness and dimension in certain cases.
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ItemAssessing the Impacts of DER on Customer Voltages Using Smart Meter-Driven Low Voltage Line Models( 2020)The rapid adoption of distributed energy resources (DER) in low voltage (LV) networks is driving the need for distribution companies to assess their impacts on customer voltages in any demand/generation condition (also known as what-if analyses). Although this can be done by running conventional power flow analyses, there are two main challenges. The first one is that LV line models (three-phase LV feeder lines and single-phase service lines) are needed. However, the corresponding impedances are often poorly recorded by distribution companies. In other words, the information is incomplete or not available. The second challenge is that, if such studies are needed for operational purposes (calculations in near real-time), then implementing power flows to be run for hundreds of LV feeders can be a complex task for distribution companies. Several studies have attempted to solve the challenges of impedance estimation and simplified voltage calculations, but there are still some gaps. Given the rollout of smart meters in many places, several works have exploited smart meter measurements to estimate impedances of LV line models. However, in most cases, the three-phase nature of LV feeders (i.e. the phase couplings) is not adequately considered; and thus, such approaches cannot cater for the needs of inherently unbalanced LV networks. For the voltage calculations, existing simplified methods are based on the single-phase voltage drop equations and an additional ‘unbalanced factor’. Given that the ‘unbalanced factor’ is determined either empirically or using data-driven techniques that require large amounts of data, such methods cannot be precise or practical enough for their actual implementation by distribution companies. This thesis proposes a practical approach to determine customer voltages (in what-if analyses) using smart meter-driven LV line models that adequately capture the effects among the three phases. Firstly, impedances (three-phase LV feeder lines and single-phase service lines) are estimated using linearised voltage drop equations and a regression technique. This process exploits historical time-series measurements from smart meters and at the head of the LV feeder and assumes that the customer connectivity and customer phase connection are known. Then, using the linearised voltage drop equations and the estimated impedances, simplified calculations of customer voltages can be carried out for what-if analyses (any demand/generation condition). The proposed approach is demonstrated on realistic LV networks from Australia and the UK. Impedances are estimated considering realistic weekly historical meter measurements (i.e. active power, reactive power, and voltage magnitudes) with a 15-minute resolution (672 time steps). Voltage calculations (what-if analyses) consider weekly demand and generation profiles with 1-minute resolution (10,080 time steps). Results show a very good accuracy for most of the estimated impedances. More importantly, the calculated voltages are not only highly accurate but are also obtained much faster than with a power flow engine. Consequently, the findings suggest that the proposed approach is accurate and practical enough for its use by distribution companies.