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.

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.

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.

Design optimization is a method that can be used to automate the design process to obtain better results. When applied to aeroelastic structures, design optimization often leads to the creation of highly flexible aeroelastic structures. There are, however, a number of conventional design procedures that must be modified when dealing with highly flexible aeroelastic structures. First, the deformed geometry must be the baseline for weight, structural, and stability analyses. Second, potential couplings between aeroelasticity and rigid-body dynamics must be considered. Third, dynamic analyses must be modified to handle large nonlinear displacements. These modifications to the conventional design process significantly increase the difficulty of developing an optimization framework appropriate for highly flexible aeroelastic structures. As a result, when designing these structures, often either gradient-free optimization is performed (which limits the optimization to relatively few design variables) or optimization is simply omitted from the design process. Both options significantly decrease the design exploration capabilities of a designer compared to a scenario in which gradient-based optimization is used. This dissertation therefore presents various contributions that allow gradient-based optimization to be more easily used to optimize highly flexible aeroelastic structures. One of our primary motivations for developing these capabilities is to accurately capture the design constraints of solar-regenerative high-altitude long-endurance (SR-HALE) aircraft. In this dissertation, we therefore present a SR-HALE aircraft optimization framework which accounts for the peculiarities of structurally flexible aircraft while remaining suitable for use with gradient-based optimization. These aircraft tend to be extremely large and light, which often leads to significant amounts of structural flexibility. Using this optimization framework, we design an aircraft that is capable of flying year-round at \SI{35}{\degree} latitude at \SI{18}{\kilo\meter} above sea level. We subject this aircraft to a number of constraints including energy capture, energy storage, material failure, local buckling, stall, static stability, and dynamic stability constraints. Critically, these constraints were designed to accurately model the actual design requirements of SR-HALE aircraft, rather than to provide a rough approximation of them. To demonstrate the design exploration capabilities of this framework, we also performed several parameters sweeps to determine optimal design sensitivities to altitude, latitude, battery specific energy, solar efficiency, avionics and payload power requirements, and minimum design velocity. Through this optimization framework, we demonstrate both the potential of gradient-based optimization applied to highly flexible aeroelastic structures and the challenges associated with it. One challenge associated with the gradient-based optimization of highly flexible aeroelastic structures, is the ability to accurately, efficiently, and reliably model the large deflections of these structures in gradient-based optimization frameworks. To enable large-scale optimization involving structural models with large deflections to be performed more easily, we present a finite-element implementation of geometrically exact beam theory which is designed specifically for gradient-based optimization. A key feature of this implementation of geometrically exact beam theory is its compatibility with forward and reverse-mode automatic differentiation, which allows accurate design sensitivities to be obtained with minimal development effort. Another key feature is its native support for unsteady adjoint sensitivity analysis, which allows design sensitivities to be obtained efficiently from time-marching simulations. Other features are also presented that build upon previous implementations of geometrically exact beam theory, including a singularity-free rotation parameterization based on Wiener-Milenkovi\'c parameters, an implementation of stiffness-proportional structural damping using a discretized form of the compatibility equations, and a reformulation of the equations of motion for geometrically exact beam theory from a fully implicit index-1 differential algebraic equation to a semi-explicit index-1 differential algebraic equation. Several examples are presented which verify the utility and validity of each of these features. Another challenge associated with the gradient-based optimization of highly flexible aeroelastic structures is the ability to reliably track and constrain individual dynamic stability modes across the design iterations of an optimization framework. To facilitate the development of mode-specific dynamic stability constraints in gradient-based optimization frameworks we develop a mode tracking method that uses an adaptive step size in order to maintain an arbitrarily high degree of confidence in mode correlations. This mode tracking method is then applied to track the modes of a linear two-dimensional aeroelastic system and a nonlinear three-dimensional aeroelastic system as velocity is increased. When used in a gradient-based optimization framework, this mode tracking method has the potential to allow continuous dynamic stability constraints to be constructed without constraint aggregation. It also has the potential to allow the stability and shape of specific modes to be constrained independently. Finally, to facilitate the development and use of highly flexible aeroelastic systems for use in gradient-based optimization frameworks, we introduce a general methodology for coupling aerodynamic and structural models together to form modular monolithic aeroelastic systems. We also propose efficient methods for computing the Jacobians of these coupled systems without significantly increasing the amount of time necessary to construct these systems. For completeness we also discuss how to ensure that the resulting system of equations constitutes a set of first-order index-1 differential algebraic equations. We then derive direct and adjoint sensitivities for these systems which are compatible with automatic differentiation so that derivatives for gradient-based optimization can be obtained with minimal development effort.

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.

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.

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.