Structural reinforcement layout optimization can be a very useful tool in the preliminary stages of design. In this research, sizing optimization techniques are used to generate results very similar to traditional layout optimization techniques with advantages in composite modeling and available strength and stability responses. Both linear and nonlinear sizing-to-design variable relationships are applied to a composite advanced sail design problem with high and low-complexity finite element models. An alternate methodology based on fractionalactorial-design and response surface modeling is also presented with promising results for finding the globally optimum reinforcement layout design. The stiffener layouts obtained from the different approaches are used to define an improved stiffener layout for sizing optimization for minimum weight. A weight savings of more than 19% is obtained over a baseline model using these methodologies.

Wind farm layout optimization can greatly improve wind farm performance. However, past wind farm design has been limited in several ways. Wind farm design usually assumes that all the turbines throughout the farm should be exactly the same. Oftentimes, the location of every turbine is optimized individually, which is computationally expensive. Furthermore, designers fail to consider turbine loads during layout optimization. This dissertation presents four studies which provide partial solutions to these limitations and greatly improve wind farm layout optimization. Two studies explore differing turbine designs in wind farms. In these studies, Wind farm layouts are optimized simultaneously with turbine design. We found that for small rotor diameters and closely spaced wind turbines, wind farms with different heights have a 5–10% reduction in cost of energy compared to farms with all the same turbine height. Coupled optimization of turbine layout and full turbine design results in an 2–5% reduction in cost of energy compared to optimizing sequentially for wind farms with turbine spacings of 8.5–11 rotor diameters. Wind farms with tighter spacing benefit even more from coupled optimization. Furthermore, we found that heterogeneous turbine design can produce up to an additional 10% cost of energy reduction compared to wind farms with identical turbines throughout the farm, especially when the wind turbines are closely spaced. The third study presents the boundary-grid parameterization method to reduce the computational expense of optimizing wind farms. This parameterization uses only five variables to define the layout of a wind farm with any number of turbines. For a 100 turbine wind farm, we show that optimizing the five variables of the boundary-grid method produces wind farms that perform just as well as farms where the location of each turbine is optimized individually, which requires 200 design variables. The presented method facilitates the study for both gradient-free and gradient-based optimization of large wind farms. The final study presents a model to calculate fatigue damage caused by partial waking on a wind turbine which is computationally efficient and can be included in wind farm layout optimization. Compared to high fidelity simulation data, the model accurately predicts the damage trends of various waking conditions. We also perform a wind farm layout optimization with the presented model in which we maximize the annual energy production of a wind farm while constraining the damage of each turbine. The results of the optimization show that the turbine damage can be constrained with only a very small sacrifice of less than 1% to the annual energy production.

To model dissipation of energy in vibrating civil structures, existence of viscous damping is commonly assumed primarily for mathematical convenience. In such a classical damper, the damping force is assumed to depend only on the velocity of deformation. Fluid viscous dampers that provide this type of damping have been manufactured to provide supplementary damping in civil and mechanical systems to enhance their performance. Some fluid dampers, however, exhibit stiffening characteristics at higher frequencies of deformation. The force deformation relationship of such dampers can be better represented by the Maxwell model of visco-elasticity. This model consists of a viscous dashpot in series with a spring, the latter element providing the stiffening characteristics. This study is concerned with the optimal utilization of such Maxwell dampers for seismic performance improvement of civil structures. The force deformation relationship of Maxwell dampers is described by a first order differential equation. Earlier studies dealing with these dampers, used an unsymmetric set of equations for combined structure and damper system. The solution of such equations for response analysis or for optimization calculation by a modal analysis approach would require the pair of the left and right eigenvectors. In this study, an auxiliary variable is introduced in the representation of a Maxwell damper to obtain symmetric equations of motion for combined structure and damper system. This eliminates the need for working with two sets of eigenvectors and their derivatives, required for optimal analysis. Since the main objective of installing these dampers is to reduce the structural response in an optimal manner, the optimization problem is defined in terms of the minimization of some response-based performance indices. To calculate the optimal parameters of dampers placed at different location in the structure, Rosen's gradient projection method is employed. For numerical illustration, a 24-story shear building is considered. Numerical results are obtained for seismic input defined by a spectral density function; however, the formulation permits direct utilization of response spectrum-based description of design earthquake. Three different performance indices -- inter story drift-based, floor acceleration-based, and base shear-based performance indices-- have been considered to calculate the numerical results. A computational scheme is presented to calculate the amount of total damping required to achieve a desired level of response reduction. The effect of ignoring the stiffening effect at higher frequencies in the Maxwell model on the optimal performance is evaluated by parametric variation of relaxation time coefficient. It is observed that the models with higher relaxation time parameter show a decreased response reducing damping effect. Thus ignoring the stiffening effect when it is, indeed, present would provide an unconservative estimation of the damping effect. The effect of brace flexibilities on different performance indices is also investigated. It is observed that flexibility in a brace reduces the effectiveness of the damper. / Master of Science

When designing a ship, a designer often begins with "an idea" of what the ship might look like and what specifications the ship should meet. The multidisciplinary design optimization model is a tool that combines an analysis and an optimization process and uses a measure of merit to obtain what it infers to be the best design. All that the designer has to know is the range of values of certain design variables that confine the design within a lower and an upper bound. The designer then feeds the MDO model with any arbitrary design within the bounds and the model searches for the best design that minimizes or maximizes a measure of merit and also meets a set of structural and stability requirements. The model is multidisciplinary because the analysis process, which calculates the measure of merit and other performance parameters, can be a combination of sub-processes used in various fields of engineering. The optimization process can also be a variety of mathematical programming techniques depending on the type of the design problem. The container ship design problem is a combination of discreet and continuous sub-problems. But to avail the advantages of gradient-based optimization algorithms, the design problem is molded into a fully continuous problem. The efficiency and effectiveness with which an optimization process achieves the best design depends on how well the design problem is posed for the optimizer and how well that particular optimization algorithm tackles the type of design problems posed before it. This led the author to investigate the details of the analysis and the optimization process within the MDO model and make modifications to each of the processes, so that the two become more compatible towards achieving a better final design. Modifications made within the optimization algorithm were then used to develop a generalized modification method that can be used to improve any gradient-based optimization algorithm. / Master of Science

No / This paper describes a novel approach to the fusion of multidimensional images for colour displays. The goal of the method is to generate an output image whose gradient matches that of the input as closely as possible. It achieves this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is subsequently reintegrated to generate an output. Constraints on the output colours are provided by an initial RGB rendering to produce ‘naturalistic’ colours: we provide a theorem for projecting higher-D contrast onto the initial colour gradients such that they remain close to the original gradients whilst maintaining exact high-D contrast. The solution to this constrained optimisation is closed-form, allowing for a very simple and hence fast and efficient algorithm. Our approach is generic in that it can map any N-D image data to any M-D output, and can be used in a variety of applications using the same basic algorithm. In this paper we focus on the problem of mapping N-D inputs to 3-D colour outputs. We present results in three applications: hyperspectral remote sensing, fusion of colour and near-infrared images, and colour visualisation of MRI Diffusion-Tensor imaging.

The sparse coding is approximation/representation of signals with the minimum number of coefficients using an overcomplete set of elementary functions. This kind of approximations/ representations has found numerous applications in source separation, denoising, coding and compressed sensing. The adaptation of the sparse approximation framework to the coding problem of signals is investigated in this thesis. Open problems are the selection of appropriate models and their orders, coefficient quantization and sparse approximation method. Some of these questions are addressed in this thesis and novel methods developed. Because almost all recent communication and storage systems are digital, an easy method to compute quantized sparse approximations is introduced in the first part. The model selection problem is investigated next. The linear model can be adapted to better fit a given signal class. It can also be designed based on some a priori information about the model. Two novel dictionary selection methods are separately presented in the second part of the thesis. The proposed model adaption algorithm, called Dictionary Learning with the Majorization Method (DLMM), is much more general than current methods. This generality allowes it to be used with different constraints on the model. Particularly, two important cases have been considered in this thesis for the first time, Parsimonious Dictionary Learning (PDL) and Compressible Dictionary Learning (CDL). When the generative model order is not given, PDL not only adapts the dictionary to the given class of signals, but also reduces the model order redundancies. When a fast dictionary is needed, the CDL framework helps us to find a dictionary which is adapted to the given signal class without increasing the computation cost so much. Sometimes a priori information about the linear generative model is given in format of a parametric function. Parametric Dictionary Design (PDD) generates a suitable dictionary for sparse coding using the parametric function. Basically PDD finds a parametric dictionary with a minimal dictionary coherence, which has been shown to be suitable for sparse approximation and exact sparse recovery. Theoretical analyzes are accompanied by experiments to validate the analyzes. This research was primarily used for audio applications, as audio can be shown to have sparse structures. Therefore, most of the experiments are done using audio signals.

Derivative pricing, model calibration, and sensitivity analysis are the three main problems in financial modeling. The purpose of this study is to present an algorithm to improve the pricing process, the calibration process, and the sensitivity analysis of the double Heston model, in the sense of accuracy and efficiency. Using the optimized caching technique, our study reduces the pricing computation time by about 15%. Another contribution of this thesis is: a novel application of the Automatic Differentiation (AD) algorithms in order to achieve a more stable, more accurate, and faster sensitivity analysis for the double Heston model (compared to the classical finite difference methods). This thesis also presents a novel hybrid model by combing the heuristic method Differentiation Evolution, and the gradient method Levenberg--Marquardt algorithm. Our new hybrid model significantly accelerates the calibration process.

A hybrid design optimization method combining the stochastic method based on simultaneous perturbation stochastic approximation (SPSA) and the deterministic method of Broydon-Fletcher-Goldfarb-Shanno (BFGS) is developed in order to take advantage of the high efficiency of the gradient based methods and the global search capabilities of SPSA for applications in the optimal aerodynamic shape design of a three dimensional elliptic nozzle. The performance of this hybrid method is compared with that of SPSA, simulated annealing (SA) and gradient based BFGS method. The objective functions which are minimized are estimated by numerically solving the 3D Euler and Navier-Stokes equations using a TVD approach and a LU implicit scheme. Computed results show that the hybrid optimization method proposed in this study shows a promise of high computational efficiency and global search capabilities. / Singapore-MIT Alliance (SMA)

The construction equipment industry is developing at a fast pace, increasing the expectation on the next-generation machines. Wheel loaders and backhoe loaders are part of this evolution and all subsystems in those machines need to be developed to meet the high demands in energy eciency and productivity. One of the most important parts of the wheel loader is the loading unit. This is traditionally designed using highly experienced engineers and CAD software. To simplify the early stages of this process was an optimization tool developed to generate a design outlay. The optimization will minimize the mass of the linkage since unnecessary weight will lower the eciency. The minimum can be found by moving the joints and adjusting the shape of the device. The optimization will also include constraints to assure the correct performance of the linkage. Since there are a high number of design variables, a gradient-based optimization method was used. A finite element solver was also implemented to calculate the forces and stresses in the linkage. The linkages studied in this report are one from a typical wheel loader and one from a backhoe loader. Since these machines are extremely versatile, and used formany diferent tasks, two sets of constraints are compiled. One of the constraint sets yields a linkage suitable for machines only equipped with bucket, while the other results in an all-round linkage suitable for most tools and applications. The optimized linkages are compared to existing devices. The results show that there are some improvements possible and that the software could be used to help designers. However, the optimization problem is hard to solve due to non-smooth constraints functions and numerical instabilities. This issue could be overcome by diferent means, like using automatic diferentiation, a non-gradient based optimization method, decreasing the number of constraints or decreasing the number of design variables. / Utvecklingen av anlaggningsmaskiner sker i snabb takt och detta ökar förväntningarna på framtidens maskiner. En stor andel av alla anläggningsmaskiner är hjullastare och traktorgrävare och alla delsystem på dessa maskiner måste följa med i utvecklingen. En av de viktigaste delarna pa en hjullastare ar lastaggregatet. Det designas traditionellt med hjälp av CAD mjukvara och mycket erfarna konstruktörer. För att underlätta denna process har en optimeringsrutin utvecklats, som generarar ett designförslag. Optimeringen minskar länkagets massa genom att fytta lagringspositioner och ändra delarnas dimensioner. Detta ökar efektiviteten hos maskinen eftersom den slipper köra runt på onödig vikt. Optimeringen innehåller även villkor för att säkerställa god prestanda hos det optimerade aggregatet. Eftersom det ingår väldigt många designvariabler i optimeringen används en gradientbaserad metod. En finita element approximation används for att beräkna krafter och spänningar i länkaget. De länkage som undersöks i detta projekt är ett typsikt hjullastaraggregat och ett typiskt traktorgrävaraggregat. Eftersom dessa maskiner ar väldigt mångsidiga sammanställdes två olika uppsättningar av villkor. Den ena uppsättningen används för att optimera ett aggregat som endast ska användas med skopa, medan den andra uppsättningen används för att ta fram ett mer mångsidigt aggregat avsätt for att kunna klara av de flesta situationer och verktyg. De optimerade lastaggregaten är jämförda med produktionsaggregat och det visar sig att vissa förbättringar är möjliga. Slutsattsen är att optimeringsrutinen kan bli ett bra hjälpmedel for konstruktörer men att den behöver lite mer veriering. Villkorsfunktionen som optimeringen måste lösa är inte helt slät vilket är ett problem för en gradientbaserade metod och dessutom finns vissa numeriska instabiliteter. Dessa svårigheter kan undkommas pa olika sätt, t.ex. genom att använda automatisk derivering,byta optimeringsalgoritm, minska antalet villkor eller minska antalet variabler.

The efficient optimisation of vehicle suspension systems is of increasing interest for vehicle manufacturers. The main aim of this thesis is to develop a methodology for efficiently optimising an off-road vehicle’s suspension for both ride comfort and handling, using gradient based optimisation. Good ride comfort of a vehicle traditionally requires a soft suspension setup, while good handling requires a hard suspension setup. The suspension system being optimised is a semi-active suspension system that has the ability to switch between a ride comfort and a handling setting. This optimisation is performed using the gradient-based optimisation algorithm Dynamic-Q. In order to perform the optimisation, the vehicle had to be accurately modelled in a multi-body dynamics package. This model, although very accurate, exhibited a high degree of non-linearity, resulting in a computationally expensive model that exhibited severe numerical noise. In order to perform handling optimisation, a novel closed loop driver model was developed that made use of the Magic Formula to describe the gain parameter for the single point driver model’s steering gain. This non-linear gain allowed the successful implementation of a single point preview driver model for the closed loop double lane change manoeuvre, close to the vehicle’s handling limit. Due to the high levels of numerical noise present in the simulation model’s objective and constraint functions, the use of central finite differencing for the determination of gradient information was investigated, and found to improve the optimisation convergence history. The full simulation model, however, had to be used for the determination of this gradient information, making the optimisation process prohibitively expensive, when many design variables are considered. The use of carefully chosen simplified two-dimensional non-linear models were investigated for the determination of this gradient information. It was found that this substantially reduced the total number of expensive full simulation evaluations required, thereby speeding up the optimisation time. It was, however, found that as more design variables were considered, some variables exhibited a lower level of sensitivity than the other design variables resulting in the optimisation algorithm terminating at sub-optimal points in the design space. A novel automatic scaling procedure is proposed for scaling the design variables when Dynamic-Q is used. This scaling methodology attempts to make the n-dimensional design space more spherical in nature, ensuring the better performance of Dynamic-Q, which makes spherical approximations of the optimisation problem at each iteration step. The results of this study indicate that gradient-based mathematical optimisation methods may indeed be successfully integrated with a multibody dynamics analysis computer program for the optimisation of a vehicle’s suspension system. Methods for avoiding the negative effects of numerical noise in the optimisation process have been proposed and successfully implemented, resulting in an improved methodology for gradient-based optimisation of vehicle suspension systems. / Thesis (PhD)--University of Pretoria, 2008. / Mechanical and Aeronautical Engineering / unrestricted