The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Boundary shape optimization is a technique to search for an optimal shape by modifying the boundary of a device with a pre-specified topology. We consider boundary shape optimization of acoustic horns in loudspeakers and brass wind instruments. A horn is an interfacial device, situated between a source, such as a waveguide or a transducer, and surrounding space. Horns are used to control both the transmission properties from the source and the spatial power distribution in the far-field (directivity patterns). Transmission and directivity properties of a horn are sensitive to the shape of the horn flare. By changing the horn flare we design transmission efficient horns. However, it is difficult to achieve both controllability of directivity patterns and high transmission efficiency by using only changes in the horn flare. Therefore we use simultaneous shape and so-called topology optimization to design a horn/acoustic-lens combination to achieve high transmission efficiency and even directivity. We also design transmission efficient interfacial devices without imposing an upper constraint on the mouth diameter. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter. We optimize brasswind instruments with respect to its intonation properties. The instrument is modeled using a hybrid method between a one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a finite element model for the rapidly flaring part. An experimental study is carried out to verify the transmission properties of optimized horn. We produce a prototype of an optimized horn and then measure the input impedance of the horn. The measured values agree reasonably well with the predicted optimal values. The finite element method and the boundary element method are used as discretization methods in the thesis. Gradient-based optimization methods are used for optimization, in which the gradients are supplied by the adjoint methods.

Video editing and object recognition are two significant fields in computer vi- sion: the first has remarkably assisted digital production and post-production tasks of a digital video footage; the second is considered fundamental to image classification or image based search in large databases (e.g. the web). In this thesis, we address two problems, namely we present a novel formulation that tackles video editing tasks and we develop a mechanism that allows to generate more robust descriptors for objects in an image. Concerning the first problem, this thesis proposes two variational models to perform temporally coherent video editing. These models are applied to change an object’s (rigid or non-rigid) texture throughout a given video sequence. One model is based on propagating color information from a given frame (or be- tween two given frames) along the motion trajectories of the video; while the other is based on propagating gradient domain information. The models we present in this thesis require minimal user intervention and they automatically accommodate for illumination changes in the scene. Concerning the second problem, this thesis addresses the problem of affine invariance in object recognition. We introduce a way to generate geometric affine invariant quantities that are used in the construction of feature descrip- tors. We show that when these quantities are used they do indeed achieve a more robust recognition than the state of the art descriptors. i / La edición de vídeo y el reconocimiento de objetos son dos áreas fundamentales en el campo de la visión por computador: la primera es de gran utilidad en los procesos de producción y post-producción digital de vídeo; la segunda es esencial para la clasificación o búsqueda de imágenes en grandes bases de datos (por ejemplo, en la web). En esta tesis se acometen ambos problemas, en concreto, se presenta una nueva formulación que aborda las tareas de edición de vídeo y se desarrolla un mecanismo que permite generar descriptores más robustos para los objetos de la imagen. Con respecto al primer problema, en esta tesis se proponen dos modelos variacionales para llevar a cabo la edición de vídeo de forma coherente en el tiempo. Estos modelos se aplican para cambiar la textura de un objeto (rígido o no) a lo largo de una secuencia de vídeo dada. Uno de los modelos está basado en la propagación de la información de color desde un determinado cuadro de la secuencia de vídeo (o entre dos cuadros dados) a lo largo de las trayectorias de movimiento del vídeo. El otro modelo está basado en la propagación de la información en el dominio del gradiente. Ambos modelos requieren una intervención mínima por parte del usuario y se ajustan de manera automática a los cambios de iluminación de la escena. Con respecto al segundo problema, esta tesis aborda el problema de la invariancia afín en el reconocimiento de objetos. Se introduce un nuevo método para generar cantidades geométricas afines que se utilizan en la generación de descriptores de características. También se demuestra que el uso de dichas cantidades proporciona mayor robustez al reconocimiento que los descriptores existentes actualmente en el estado del arte.

For gas turbines, the demand for high-performance, more efficient and longer-life turbine blades is increasing. This is especially so, now that there is a need for high-power and low-weight aircraft gas turbines. Thus, the search for improved design methodologies for the optimisation of combustor exit temperature profiles enjoys high priority. Traditional experimental methods are found to be too time-consuming and costly, and they do not always achieve near-optimal designs. In addition to the above deficiencies, methods based on semi-empirical correlations are found to be lacking in performing three-dimensional analyses and these methods cannot be used for parametric design optimisation. Computational fluid dynamics has established itself as a viable alternative to reduce the amount of experimentation needed, resulting in a reduction in the time scales and costs of the design process. Furthermore, computational fluid dynamics provides more insight into the flow process, which is not available through experimentation only. However, the fact remains that, because of the trial-and-error nature of adjusting the parameters of the traditional optimisation techniques used in this field, the designs reached cannot be called “optimum”. The trial-and-error process depends a great deal on the skill and experience of the designer. Also, the above technologies inhibit the improvement of the gas turbine power output by limiting the highest exit temperature possible, putting more pressure on turbine blade cooling technologies. This limitation to technology can be overcome by implementing a search algorithm capable of finding optimal design parameters. Such an algorithm will perform an optimum search prior to computational fluid dynamics analysis and rig testing. In this thesis, an efficient methodology is proposed for the design optimisation of a gas turbine combustor exit temperature profile. The methodology involves the combination of computational fluid dynamics with a gradient-based mathematical optimiser, using successive objective and constraint function approximations (Dynamic-Q) to obtain the optimum design. The methodology is tested on three cases, namely: (a) The first case involves the optimisation of the combustor exit temperature profile with two design variables related to the dilution holes, which is a common procedure. The combustor exit temperature profile was optimised, and the pattern factor improved, but pressure drop was very high. (b) The second case involves the optimisation of the combustor exit temperature profile with four design variables, one equality constraint and one inequality constraint based on pressure loss. The combustor exit temperature profile was also optimised within the constraints of pressure. Both the combustor exit temperature profile and pattern factor were improved. (c) The third case involves the optimisation of the combustor exit temperature profile with five design variables. The swirler angle and primary hole parameters were included in order to allow for the effect of the central toroidal recirculation zone on the combustor exit temperature profile. Pressure loss was also constrained to a certain maximum. The three cases show that a relatively recent mathematical optimiser (Dynamic-Q), combined with computational fluid dynamics, can be considered a strong alternative to the design optimisation of a gas turbine combustor exit temperature profile. This is due to the fact that the proposed methodology provides designs that can be called near-optimal, when compared with that yielded by traditional methods and computational fluid dynamics alone. / Thesis (PhD)--University of Pretoria, 2009. / Mechanical and Aeronautical Engineering / unrestricted

This thesis introduces a topology optimization approach to design, from scratch, efficient microwave devices, such as antennas and waveguide transitions. The design of these devices is formulated as a general optimization problem that aims to build the whole layout of the device in order to extremize a chosen objective function. The objective function quantifies some required performance and is evaluated using numerical solutions to the 3D~Maxwell's equations by the finite-difference time-domain (FDTD) method. The design variables are the local conductivity at each Yee~edge in a given design domain, and a gradient-based optimization method is used to solve the optimization problem. In all design problems, objective function gradients are computed based on solutions to adjoint-field problems, which are also FDTD discretization of Maxwell's equations but solved with different source excitations. For any number of design variables, the computation of the objective function gradient requires one solution to the original field problem and one solution to the associated adjoint-field problem. The optimization problem is solved iteratively using the globally convergent Method of Moving Asymptotes (GCMMA). By the proposed approach, various design problems, including tens of thousands of design variables, are formulated and solved in a few hundred iterations. Examples of solved design problems are the design of wideband antennas, dual-band microstrip antennas, wideband directive antennas, and wideband coaxial-to-waveguide transitions. The fact that the proposed approach allows a fine-grained control over the whole layout of such devices results in novel devices with favourable performance. The optimization results are successfully verified with a commercial software package. Moreover, some devices are fabricated and their performance is successfully validated by experiments.

This thesis deals with problem of experimental identification using principles of artificial intelligence and development of nonlinear models. It shows how to estimate parameters of nonlinear models and it compares different types of nonlinear models based on analytical analysis which were developed from measured data in simulation and real system motors with flexible component.

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Noise has become a main nuisance in urban areas to the point that according to the World Health Organization 40% of the European population is exposed to excessive noise levels, mainly due to ground transportation. There is therefore a need to find new ways to mitigate noise in urban areas. In this work, a possible device to achieve this goal is studied: a low-height noise barrier. It consists of a barrier typically less than one meter high placed close to a source, designed to decrease the noise level for nearby pedestrians and cyclists. This type of device is studied both numerically and experimentally. Tramway noise barriers are especially studied since the noise sources are in this case very close to the ground and can therefore be attenuated efficiently. The shape and the surface treatment of the barrier are optimized using a gradient-based method coupled to a 2D boundary element method (BEM). The optimization variables are the node coordinates of a control mesh and the parameters describing the surface impedance. Sensitivities are calculated efficiently using the adjoint state approach. Numerical results show that the shapes generated by the optimization algorithm tend to be quite irregular but provide a significant improvement of more than 5 dB(A) compared to simpler shapes. Utilizing an absorbing treatment on the source side of the barrier is shown to be efficient as well. This second point has been con firmed by scale model measurements. In addition, a full scale low height noise barrier prototype has been built and tested in situ close to a tramway track in Grenoble. Measurements show that the device provides more than 10 dB(A) of attenuation for a close receiver located at the typical height of human ears. These results therefore seem to con rm the applicability of such protections to efficiently decrease noise exposure in urban areas.