Particle swarm optimization (PSO) is a well-known stochastic population-based search algorithm, originally developed by Kennedy and Eberhart in 1995. Given PSO's success at solving numerous real world problems, a large number of PSO variants have been proposed. However, unlike the original PSO, most variants currently have little to no existing theoretical results. This lack of a theoretical underpinning makes it difficult, if not impossible, for practitioners to make informed decisions about the algorithmic setup. This thesis focuses on the criteria needed for particle stability, or as it is often refereed to as, particle convergence. While new PSO variants are proposed at a rapid rate, the theoretical analysis often takes substantially longer to emerge, if at all. In some situation the theoretical analysis is not performed as the mathematical models needed to actually represent the PSO variants become too complex or contain intractable subproblems. It is for this reason that a rapid means of determining approximate stability criteria that does not require complex mathematical modeling is needed. This thesis presents an empirical approach for determining the stability criteria for PSO variants. This approach is designed to provide a real world depiction of particle stability by imposing absolutely no simplifying assumption on the underlying PSO variant being investigated. This approach is utilized to identify a number of previously unknown stability criteria. This thesis also contains novel theoretical derivations of the stability criteria for both the fully informed PSO and the unified PSO. The theoretical models are then empirically validated utilizing the aforementioned empirical approach in an assumption free context. The thesis closes with a substantial theoretical extension of current PSO stability research. It is common practice within the existing theoretical PSO research to assume that, in the simplest case, the personal and neighborhood best positions are stagnant. However, in this thesis, stability criteria are derived under a mathematical model where by the personal best and neighborhood best positions are treated as convergent sequences of random variables. It is also proved that, in order to derive stability criteria, no weaker assumption on the behavior of the personal and neighborhood best positions can be made. The theoretical extension presented caters for a large range of PSO variants. / Thesis (PhD)--University of Pretoria, 2017. / Computer Science / PhD / Unrestricted

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<p>Different techniques have been employed through the years to predict hydrodynamic instabilities on high speed liquid jets. In this work, a local linear stability analysis (LSA) has been chosen to estimate streamwise wavelengths on the jet surface near the jet exit.  Data for 0.24 to 0.5 diameters downstream in a high speed water jet issuing into air, given by Reynolds number based momentum thickness between 240 and 600, for validation of the method.  </p> <p>The hypothesis is: near the exit of the jet nozzle, for high speed liquid jets, the local velocity profile evolves based on the momentum thickness and, because of large inertia effects, the flow may be considered as inviscid for instability purposes. Therefore, the approach in this work is based on the Rayleigh equation and with the momentum thickness scaling, both non-dimensional and dimensional values of the most unstable wavelengths are obtained.</p> <p>The key aspect of the  approach is the relevance of the momentum thickness as the scaling factor for calculation purposes on dimensional values of wavelengths.</p> <p>Also, a hyperbolic tangent velocity profile is assumed for the Linear Stability Analysis based on the Rayleigh equation. Numerical restrictions and comparisons, using the Riccati transformation, are specified and described in detail to generalize this approach.</p> <p>Results show that analytical estimates of the most unstable streamwise wavelengths are close to the experimental measurements published by Portillo et al. in 2011.  The agreement using this new approach is often within the experimental uncertainty.</p> <p><br></p>

This thesis investigates large scale flow rotation in two configurations. In the first, the effect of flow rotation on a laminar flame is investigated. The flame is anchored in the wake of a cylindrical bluff body. The flow rotation is introduced by turning the cylinder along its axis. It is shown by Direct Numerical Simulation (DNS), that the cylinder rotation breaks the symmetry of both flame branches. Flame Transfer Function (FTF) measurements performed by the Wiener-Hopf Inversion suggest, that low rotation rates lead to deep gaps in the gain and the flame becomes almost insensitive to acoustic perturbation at a specific frequency. It furthermore is demonstrated that this decrease in gain of the FTF is due to destructive interference of the heat release signals caused by the two flame branches. The frequency at which the gain becomes almost zero can be adjusted by tuning the cylinder rotation rate. The study suggests that controlling the symmetry of the flame could be a tool of open-loop control of thermoacoustic instabilities.

This thesis provides a numerical and theoretical investigation of transitional and turbulent enclosed rotating flows, with a focus on the formation of macroscopic coherent flow structures. The underlying processes are strongly threedimensional due to the presence of boundary layers on the discs and on the walls of the outer (resp. inner) cylindrical shroud (resp. shaft). The complexity of these flows poses a great challenge in fundamental research however the present work is also of importance for industrial rotating machinery, from hard-drives to space engines turbopumps - the design issues of the latter being behind the motivation for this thesis. The present work consists of two major investigations. First, industrial cavities are modeled by smooth rotor/stator cavities and therein the dominant flow dynamics is investigated. For the experimental campaigns on industrial machinery revealed dangerous unsteady phenomena within the cavities, the emphasis is put on the reproduction and monitoring of unsteady pressure fluctuations within the smooth cavities. Then, the LES of three configurations of real industrial turbines are conducted to study in situ the pressure fluctuations and apply the diagnostics already vetted on academic problems.

This work details the development and implementation of a numerical model capable of solving strongly-coupled fluid-structure interaction problems involving long thin structures, which are common multi-physics problems encountered in many applications. In most fluid-structure interaction problems the deformation of the slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal decomposition technique for linear structural analysis, the governing equations and boundary conditions are updated to account for the leading-order non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. Two computational fluid-structure interaction approaches are then implemented in a partitioned manner: a finite volume method for discretisation of both the fluid and solid domains and the quadratic modal formulation for the structure coupled with a finite volume fluid solver. Strong-coupling is achieved by means of a fixed-point solver with dynamic relaxation. The fluid-structure interaction approaches are validated and compared on benchmark problems of increasing complexity and strength of coupling between the fluid and solid domains. Fluid-structure interaction systems may become unstable due to the interaction between the fluid-induced pressure and structural rigidity. A thorough stability analysis of finite elastic plates in uniform flow is conducted by varying the structural length and flow velocity showing that these are critical parameters. Validation of the results with those from analytical methods is done. An analysis of the dynamic interactions between multiple finite plates in various configurations is also conducted.

We consider the boundary control problem to stabilize the power of a signal and a pump propagating down a Raman amplifier. This is essentially an initial-boundary value problem (IBVP) of a hyperbolic system with Lotka-Volterra type nonlinearities. We treat the system as a control problem with states in the function space and use Lyapunov-based analysis to demonstrate asymptotic stability in the C_0 and the L_2-sense. The stability conditions are derived for closed-loop systems with a proportional controller and a dynamic controller, and confirmed by simulations in MATLAB.

We consider the boundary control problem to stabilize the power of a signal and a pump propagating down a Raman amplifier. This is essentially an initial-boundary value problem (IBVP) of a hyperbolic system with Lotka-Volterra type nonlinearities. We treat the system as a control problem with states in the function space and use Lyapunov-based analysis to demonstrate asymptotic stability in the C_0 and the L_2-sense. The stability conditions are derived for closed-loop systems with a proportional controller and a dynamic controller, and confirmed by simulations in MATLAB.

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Autonomous mobile sensor networks consist of a number of autonomous mobile robots equipped with various sensors and tasked with a common mission. This thesis considers the topology control of such an ad hoc mobile sensor network. In particular, I studied the problem of controlling the size, with respect to a distance metric, of the network for general interactive forcing among agents. Developed is a stability result, allowing one to design force laws to control the spread of the network. Many of the current results assume a known and/or fixed topology of the graph representing the communication between the nodes, i.e. the graph laplacian is assumed constant. They also assume fixed and known force-laws. Hence, the results are limited to time-invariant dynamics. The research considers stability analysis of sensor networks, unconstrained by specific forcing functions or algorithms, and communication topologies. Since the graph topologies are allowed to change as the agents move about, the system dynamics become discontinuous in nature. Filippov’s calculus of differential equations with discontinuous right hand sides is used to formally characterize the multi-agent system with the above attributes. Lyapunov’s Stability Theory, applied to discontinuous systems, is then used to derive bounds on the norm of the system states given bounds on its initial states and input. The above derived stability results lend themselves to the derivation of methods for the design of algorithms or force-laws for mobile sensor networks. The efficacy of the derived results is illustrated through several examples where it is shown how they may be used for synthesizing a topology managing strategy. Examples are given of designing force-laws that limit the network in a desired area.