A robustness and reliability based multidisciplinary analysis and optimization framework for aircraft design is presented. Robust design optimization and Reliability Based Design Optimization are merged into a uni ed formulation which streamlines the setup of optimization problems and aims at preventing foreseeable implementation issues in uncertainty based design. Surrogate models are evaluated to circumvent the intensive computations resulting from using direct evaluation in nondeterministic optimization. Three types of models are implemented in the framework: quadratic interpolation, regression Kriging and artificial neural networks. Regression Kriging presents the best compromise between performance and accuracy in deterministic wing design problems. The performance of the simultaneous implementation of robustness and reliability is evaluated using simple analytic problems and more complex wing design problems, revealing that performance benefits can still be achieved while satisfying probabilistic constraints rather than the simpler (and not as computationally intensive) robust constraints. The latter are proven to to be unable to follow a reliability constraint as uncertainty in the input variables increases. The computational effort of the reliability analysis is further reduced through the implementation of a coordinate change in the respective optimization sub-problem. The computational tool developed is a standalone application and it presents a user-friendly graphical user interface. The multidisciplinary analysis and design optimization tool includes modules for aerodynamics, structural, aeroelastic and cost analysis, that can be used either individually or coupled.

Variability has become one of the vital challenges that the designers of integrated circuits encounter. variability becomes increasingly important. Imperfect manufacturing process manifest itself as variations in the design parameters. These variations and those in the operating environment of VLSI circuits result in unexpected changes in the timing, power, and reliability of the circuits. With scaling transistor dimensions, process and environmental variations become significantly important in the modern VLSI design. A smaller feature size means that the physical characteristics of a device are more prone to these unaccounted-for changes. To achieve a robust design, the random and systematic fluctuations in the manufacturing process and the variations in the environmental parameters should be analyzed and the impact on the parametric yield should be addressed. This thesis studies the challenges and comprises solutions for designing robust VLSI systems in the presence of variations. Initially, to get some insight into the system design under variability, the parametric yield is examined for a small circuit. Understanding the impact of variations on the yield at the circuit level is vital to accurately estimate and optimize the yield at the system granularity. Motivated by the observations and results, found at the circuit level, statistical analyses are performed, and solutions are proposed, at the system level of abstraction, to reduce the impact of the variations and increase the parametric yield. At the circuit level, the impact of the supply and threshold voltage variations on the parametric yield is discussed. Here, a design centering methodology is proposed to maximize the parametric yield and optimize the power-performance trade-off under variations. In addition, the scaling trend in the yield loss is studied. Also, some considerations for design centering in the current and future CMOS technologies are explored. The investigation, at the circuit level, suggests that the operating temperature significantly affects the parametric yield. In addition, the yield is very sensitive to the magnitude of the variations in supply and threshold voltage. Therefore, the spatial variations in process and environmental variations make it necessary to analyze the yield at a higher granularity. Here, temperature and voltage variations are mapped across the chip to accurately estimate the yield loss at the system level. At the system level, initially the impact of process-induced temperature variations on the power grid design is analyzed. Also, an efficient verification method is provided that ensures the robustness of the power grid in the presence of variations. Then, a statistical analysis of the timing yield is conducted, by taking into account both the process and environmental variations. By considering the statistical profile of the temperature and supply voltage, the process variations are mapped to the delay variations across a die. This ensures an accurate estimation of the timing yield. In addition, a method is proposed to accurately estimate the power yield considering process-induced temperature and supply voltage variations. This helps check the robustness of the circuits early in the design process. Lastly, design solutions are presented to reduce the power consumption and increase the timing yield under the variations. In the first solution, a guideline for floorplaning optimization in the presence of temperature variations is offered. Non-uniformity in the thermal profiles of integrated circuits is an issue that impacts the parametric yield and threatens chip reliability. Therefore, the correlation between the total power consumption and the temperature variations across a chip is examined. As a result, floorplanning guidelines are proposed that uses the correlation to efficiently optimize the chip's total power and takes into account the thermal uniformity. The second design solution provides an optimization methodology for assigning the power supply pads across the chip for maximizing the timing yield. A mixed-integer nonlinear programming (MINLP) optimization problem, subject to voltage drop and current constraint, is efficiently solved to find the optimum number and location of the pads.

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.

Computational models and simulations are essential system design tools that allow for improved decision making and cost reductions during all phases of the design process. However, the most accurate models are often computationally expensive and can therefore only be used sporadically. Consequently, designers are often forced to choose between exploring many design alternatives with less accurate, inexpensive models and evaluating fewer alternatives with the most accurate models. To achieve both broad exploration of the alternatives and accurate determination of the best alternative with reasonable costs incurred, surrogate modeling and variable accuracy modeling are used widely. A surrogate model is a mathematically tractable approximation of a more expensive model based on a limited sampling of that model, while variable accuracy modeling involves a collection of different models of the same system with different accuracies and computational costs. As compared to using only very accurate and expensive models, designers can determine the best solutions more efficiently using surrogate and variable accuracy models because obviously poor solutions can be eliminated inexpensively using only the less expensive, less accurate models. The most accurate models are then reserved for discerning the best solution from the set of good solutions. In this thesis, a Value-Based Global Optimization (VGO) algorithm is introduced. The algorithm uses kriging-like surrogate models and a sequential sampling strategy based on Value of Information (VoI) to optimize an objective characterized by multiple analysis models with different accuracies. It builds on two primary research contributions. The first is a novel surrogate modeling method that accommodates data from any number of analysis models with different accuracies and costs. The second contribution is the use of Value of Information (VoI) as a new metric for guiding the sequential sampling process for global optimization. In this manner, the cost of further analysis is explicitly taken into account during the optimization process. Results characterizing the algorithm show that VGO outperforms Efficient Global Optimization (EGO), a similar global optimization algorithm that is considered to be the current state of the art. It is shown that when cost is taken into account in the final utility, VGO achieves a higher utility than EGO with statistical significance. In further experiments, it is shown that VGO can be successfully applied to higher dimensional problems as well as practical engineering design examples.

Improvements in performance, reliability and durability as well as reductions in production costs, remain critical prerequisites for the commercialization of proton exchange membrane fuel cells. In this thesis, a computational framework for fuel cell analysis and optimization is presented as an innovative alternative to the time consuming trial-and-error process currently used for fuel cell design. The framework is based on a two-dimensional through-the-channel isothermal, isobaric and single phase membrane electrode assembly (MEA) model. The model input parameters are the manufacturing parameters used to build the MEA: platinum loading, platinum to carbon ratio, electrolyte content and gas diffusion layer porosity. The governing equations of the fuel cell model are solved using Netwon's algorithm and an adaptive finite element method in order to achieve quadratic convergence and a mesh independent solution respectively. The analysis module is used to solve two optimization problems: i) maximize performance; and, ii) maximize performance while minimizing the production cost of the MEA. To solve these problems a gradient-based optimization algorithm is used in conjunction with analytical sensitivities. The presented computational framework is the first attempt in the literature to combine highly efficient analysis and optimization methods to perform optimization in order to tackle large-scale problems. The framework presented is capable of solving a complete MEA optimization problem with state-of-the-art electrode models in approximately 30 minutes. The optimization results show that it is possible to achieve Pt-specific power density for the optimized MEAs of 0.422 $g_{Pt}/kW$. This value is extremely close to the target of 0.4 $g_{Pt}/kW$ for large-scale implementation and demonstrate the potential of using numerical optimization for fuel cell design.

Dans cette Thèse, la conception robuste avec un modèle incertain d'un système électromécanique avec vibro-impact est fait. Le système électromécanique est constitué d'un chariot, dont le mouvement est excité par un moteur à courant continu et un marteau embarqué dans ce chariot. Le marteau est relié au chariot par un ressort non linéaire et par un amortisseur linéaire, de façon qu'un mouvement relatif existe entre eux. Une barrière flexible linéaire, placé à l'extérieur du chariot limite les mouvements de marteau. En raison du mouvement relatif entre le marteau et la barrière, impacts peuvent se produire entre ces deux éléments. Le modèle du système développé prend en compte l'influence du courant continu moteur dans le comportement dynamique du système. Certains paramètres du système sont incertains, tels comme les coefficients de rigidité et d'amortissement de la barrière flexible. L'objectif de la Thèse est de réaliser une optimisation de ce système électromécanique par rapport aux paramètres de conception afin de maximiser l'impact puissance sous la contrainte que la puissance électrique consommée par le moteur à courant continu est inférieure à une valeur maximale. Pour choisir les paramètres de conception dans le problème d'optimisation, une analyse de sensibilité a été réalisée afin de définir les paramètres du système les plus sensibles. L'optimisation est formulée dans le cadre de la conception robuste en raison de la présence d'incertitudes dans le modèle. Les lois de probabilités liées aux variables aléatoires du problème sont construites en utilisant le Principe du Maximum l'Entropie et les statistiques de la réponse stochastique du système sont calculées en utilisant la méthode de Monte Carlo. L'ensemble d'équations non linéaires sont présentés, et un solveur temporel adapté est développé. Le problème d'optimisation non linéaire stochastique est résolu pour différents niveaux d'incertitudes, et aussi pour le cas déterministe. Les résultats sont différents, ce qui montre l'importance de la modélisation stochastique / In this Thesis, the robust design with an uncertain model of a vibro-impact electromechanical system is done. The electromechanical system is composed of a cart, whose motion is excited by a DC motor (motor with continuous current), and an embarked hammer into this cart. The hammer is connected to the cart by a nonlinear spring component and by a linear damper, so that a relative motion exists between them. A linear flexible barrier, placed outside of the cart, constrains the hammer movements. Due to the relative movement between the hammer and the barrier, impacts can occur between these two elements. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. Some system parameters are uncertain, such as the stiffness and the damping coefficients of the flexible barrier. The objective of the Thesis is to perform an optimization of this electromechanical system with respect to design parameters in order to maximize the impact power under the constraint that the electric power consumed by the DC motor is lower than a maximum value. To chose the design parameters in the optimization problem, an sensitivity analysis was performed in order to define the most sensitive system parameters. The optimization is formulated in the framework of robust design due to the presence of uncertainties in the model. The probability distributions of random variables are constructed using the Maximum Entropy Principle and statistics of the stochastic response of the system are computed using the Monte Carlo method. The set of nonlinear equations are presented, and an adapted time domain solver is developed. The stochastic nonlinear constrained design optimization problem is solved for different levels of uncertainties, and also for the deterministic case. The results are different and this show the importance of the stochastic modeling

Formulations of optimization under uncertainty (OUU) commonly used in aerospace design—those based on treating statistical moments of the quantity of interest (QOI) as separate objectives—can result in stochastically dominated designs. A stochastically dominated design is undesirable, because it is less likely than another design to achieve a QOI at least as good as a given value, for any given value. As a remedy to this limitation for the multi-objective formulation of moments, a novel OUU formulation is proposed—dominance optimization. This formulation seeks a set of solutions and makes use of global optimizers, so is useful for early stages of the design process when exploration of design space is important. Similarly, to address this limitation for the single-objective formulation of moments (combining moments via a weighted sum), a second novel formulation is proposed—horsetail matching. This formulation can make use of gradient- based local optimizers, so is useful for later stages of the design process when exploitation of a region of design space is important. Additionally, horsetail matching extends straightforwardly to different representations of uncertainty, and is flexible enough to emulate several existing OUU formulations. Existing multi-fidelity methods for OUU are not compatible with these novel formulations, so one such method—information reuse—is generalized to be compatible with these and other formulations. The proposed formulations, along with generalized information reuse, are compared to their most comparable equivalent in the current state-of-the-art on practical design problems: transonic aerofoil design, coupled aero-structural wing design, high-fidelity 3D wing design, and acoustic horn shape design. Finally, the two novel formulations are combined in a two-step design process, which is used to obtain a robust design in a challenging version of the acoustic horn design problem. Dominance optimization is given half the computational budget for exploration; then horsetail matching is given the other half for exploitation. Using exactly the same computational budget as a moment-based approach, the design obtained using the novel formulations is 95% more likely to achieve a better QOI than the best value achievable by the moment-based design.

Cette thèse porte sur les problèmes d'optimisation robustes et fiables avec l'incertitude d'entrée.Tout d'abord, les différentes catégories de méthodes d'optimisation stochastique pour traiter l'incertitude sont présentées. Ces méthodes visent à trouver une solution plus robuste et fiable en minimisant la variance de l'objectif et/ou en réduisant la probabilité de violer les contraintes en différentes manières. Chaque catégorie a diverses approches et après la comparaison, les plus efficaces sont sélectionnées.Cependant, comme ces méthodes augmentent le nombre d'évaluations par rapport à l'optimisation déterministe et nécessitent l'information de gradient qui peut être bruyante fournie par des modèles lourds comme les modèles d'éléments finis, elles ne conviennent pas aux modèles qui prennent du temps. Des stratégies de méta-modèles basées sur le krigeage sont proposées dans ce manuscrit car elles pourraient utiliser la détermination d'une petite taille d’échantillons pour approcher des fonctions complexes et donner des dérivés précis. La fonction objectif initiale et les contraintes sont progressivement remplacées par des méta-modèles de krigeage utilisant le critère d’enrichissement pour ajouter des échantillons dans le processus d'optimisation. Différentes stratégies compris le choix du critère et le positionnement de l'enrichissement de l'échantillon pour chaque catégorie sont comparées et mettent en évidence les plus efficaces.Ensuite, les approches d'optimisation développées dans ce travail de recherche sont appliquées aux modèles analytiques et aux éléments finis d'un transformateur pour résoudre des problèmes d'optimisation électromagnétique. / This PhD thesis deals with the robust and reliability-based optimization problems under input uncertainty.First, the different categories of stochastic optimization methods to treat the uncertainty are presented. These methods aim to find a more robust and/or reliable solution by minimize the variance of objective and reducing the probability to violate the constraints in different ways. Each categories has various approaches and after comparison, the most effective ones are selected.However, as these methods increase the number of evaluation than deterministic optimization and need the gradient information which may be noisy provided by time-consuming models like finite element models, they are not suitable for the heavy models. So kriging-based meta-model strategies are proposed in this manuscript as it could use the determination of small size sample to approach complex functions and give accurate derivatives. The original objective function and constraints are progressively replaced by kriging meta-models using infill sampling criterion to add samples in the process of optimization. Different strategies including the choice of the criterion and the positioning of sample enrichment for each categories are compared and highlight the most effective ones.Then the optimization approaches developed within this research work are applied to the analytic and finite element models of a transformer for solving an electromagnetic optimization problems.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-28T12:37:32Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese_Doutorado_EngCivil_FMGF_2016_[digital].pdf: 9767217 bytes, checksum: e33d3971801fd7f7f68b85fc05826ba3 (MD5) / Made available in DSpace on 2016-07-28T12:37:32Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese_Doutorado_EngCivil_FMGF_2016_[digital].pdf: 9767217 bytes, checksum: e33d3971801fd7f7f68b85fc05826ba3 (MD5) Previous issue date: 2016-01-29 / Ao esgotar as reservas de hidrocarbonetos em terra e águas rasas, a indústria vem explorando e produzindo petróleo em águas profundas e ultraprofundas. No entanto, a verificação hidrodinâmica de novos sistemas flutuantes de produção continua usando as metodologias consagradas, especialmente os ensaios em tanques oceânicos de laboratório. A utilização de modelos em escala reduzida vem sendo adotada desde os primeiros projetos em águas rasas e continua até hoje nos projetos em águas ultraprofundas. No entanto, os ensaios em profundidades superiores a 1.500m necessitam de um fator de escala muito elevado, com diversos problemas associados, dentre eles as dificuldades de acomodar as linhas de ancoragem e as incertezas relacionadas a modelos muito pequenos. Dentre as soluções possíveis, os ensaios híbridos (numérico-experimental) se apresentam como a solução mais viável para verificação experimental em águas ultraprofundas, em especial o ensaio híbrido passivo. Esse tipo de ensaio é organizado em etapas, sendo a primeira delas responsável pela definição do sistema truncado. Se essa etapa não for executada de forma satisfatória, o sucesso do ensaio pode ser comprometido. Assim, a fim de minimizar essa questão, propõe-se nesta tese de doutorado uma forma sistemática para encontrar sistemas truncado equivalentes, considerando os efeitos estáticos e dinâmicos, através da utilização de ferramentas de otimização. Nesse sentido, a abordagem adotada utiliza um simulador para análise estática e dinâmica de estruturas offshore denominado Dynasim e um algoritmo de otimização baseado em gradiente através do sistema Dakota. Também é utilizada a metodologia de planejamento de experimentos para identificar os fatores que influenciam as respostas estática e dinâmica do problema, evitando o uso de variáveis de projeto irrelevantes no estudo da otimização. Ressalta-se que essa metodologia não foi aplicada em outros trabalhos no contexto de sistemas de ancoragem truncado, segundo nosso conhecimento. Além disso, analisa-se o projeto ótimo do sistema truncado em várias condições ambientais, cujo interesse é verificar a concordância dele com o sistema de ancoragem na profundidade completa. Devido ao elevado custo computacional envolvido nessa verificação, utiliza-se a computação de alto desempenho, com processamento paralelo, para viabilizar a realização dessas análises. Como é demonstrado neste trabalho, a metodologia proposta facilita a busca de sistemas de ancoragem truncado equivalente preservando as características estáticas e dinâmicas do sistema de ancoragem completo. São apresentados e discutidos quatro casos, os dois primeiros se referem a casos simplificados, o terceiro é baseado na literatura e o quarto é baseado em um cenário real. Os resultados obtidos nos casos estudados mostram que os sistemas truncados equivalentes encontrados conseguem reproduzir o comportamento dos sistemas completos para as condições verificadas. / With the depletion of onshore and offshore shallow-water reserves, the industry has exploited and produced oil in deep water and ultra-deepwater. However, the hydrodynamic verification of new floating production systems continues using the established methodologies, especially by carrying out tests on ocean basin laboratories. Small-scale model tests have been used since the first projects in shallow water and continue today in the projects in ultra-deepwater. However, tests in depths above 1,500m require a very high scale factor, which poses several complications, among them the difficulties to accommodate the mooring lines and the small models related uncertainties. Among the possible solutions, the hybrid testing (numerical and experimental) are the most feasible solution to experimental verification in ultra-deepwater, especially the hybrid passive systems test. Such test is divided into steps, the first one responsible for the definition of the truncated system. If this step is not performed satisfactorily, the success of the test may be compromised. Thus, in order to minimize this issue, a systematic way to find equivalent truncated systems, considering the static and dynamic effects through the use of the optimization tools is proposed in this doctoral thesis. Accordingly, the approach adopted uses a numerical simulator, called Dynasim, for static and dynamic analysis of offshore structures, and a gradient based optimization algorithm, given in Dakota computational system. Additionally, the design of experiments methodology is used to identify the factors that influence the static and dynamic responses of the problem, avoiding the use of irrelevant design variables in the optimization process. It has to be emphasized that this methodology has not been used in other works in the context of truncated mooring systems, to our knowledge. Furthermore, the optimal design of the truncated system is analyzed for several environmental conditions. The aim is to verify the agreement of the truncated mooring system with system in the full-depth. Due to the high computational cost involved in the verification, we use the high-performance computing, with parallel computation, to perform the analyzes. As shown in this work, the proposed methodology easy the search for equivalent truncated mooring systems preserving the static and dynamic characteristics of full-depth mooring systems. Four case studies are presented and discussed. The first two refer to simplified cases; the third is based on the literature and the fourth is based on a real scenario. The results in each case show that the truncated equivalent system found can reproduce the behavior of full-depth system for the verified conditions.

A indústria aeronáutica vem promovendo avanços tecnológicos em velocidades crescentes, para sobreviver em mercados extremamente competitivos. Neste cenário, torna-se imprescindível o uso de ferramentas de projeto que agilizem o desenvolvimento de novas aeronaves. Os atuais recursos computacionais permitiram um grande aumento no número de ferramentas que auxiliam o trabalho de projetistas e engenheiros. O projeto de uma aeronave é uma tarefa multidisciplinar por essência, o que logo incentivou o desenvolvimento de ferramentas computacionais que trabalhem com várias áreas ao mesmo tempo. Entre elas se destaca a otimização multidisciplinar em projeto, que une métodos de otimização à modelos matemáticos de áreas distintas de um projeto para encontrar soluções de compromisso. O presente trabalho introduz a otimização multidisciplinar em projeto (Multidisciplinary Design Optimization - MDO) e discorre sobre algumas aplicações possíveis desta metodologia. Foi realizada a implementação de um sistema de MDO para o projeto de asas flexíveis, considerando restrições de aeroelasticidade dinâmica e massa estrutural. Como meta, deseja-se encontrar distribuições ideais de rigidezes flexional e torcional da estrutura da asa, para maximizar a velocidade crítica de flutter e minimizar a massa estrutural. Para tanto, foram utilizados um modelo dinâmico-estrutural baseado no método dos elementos finitos, um modelo aerodinâmico não-estacionário baseado na teoria das faixas e nas soluções bidimensionais de Theodorsen, um modelo de previsão de flutter que utiliza o método K e, por fim, um otimizador baseado no método de algoritmos genéticos (AGs). São apresentados os detalhes empregados em cada modelo, as restrições aplicadas e a maneira como eles interagem ao longo da otimização. É feita uma análise para a escolha dos parâmetros de otimização por AG e em seguida a avaliação de dois casos, para verificação da funcionalidade do sistema implementado. Os resultados obtidos demonstram uma metodologia eficiente, que é capaz de buscar soluções ótimas para problemas propostos, que com devidos ajustes pode ter enorme valor para acelerar o desenvolvimento de novas aeronaves. / The aeronautical industry is always trying to speed up technological advances in order to survive in extremely competitive markets. In this scenario, the use of design tools to accelerate the development of new aircraft becomes essential. Current computational resources allow greater increase in the number of design tools to assist the work of aeronautical engineers. In essence, the design of an aircraft is a multidisciplinary task, which stimulates the development of computational tools that work with different areas at the same time. Among them, the multidisciplinary design optimization (MDO) can be distinguished, which combines optimization methods to mathematical models of distinct areas of a design to find compromise solutions. The present work introduces MDO and discourses on some possible applications of this methodology. The implementation of a MDO system for the design of flexible wings, considering dynamic aeroelasticity restrictions and the structural mass, was carried out. As goal, it is desired to find ideal flexional and torsional stiffness distributions of the wing structure, that maximize the critical flutter speed and minimize the structural mass. To do so, it was employed a structural dynamics model based on the finite element method, a nonstationary aerodynamic model based on the strip theory and Theodorsen’s two-dimensional solutions, a flutter prediction model based on the K method and a genetic algorithm (GA). Details on the model, restrictions applied and the way the models interact to each other through the optimization are presented. It is made an analysis for choosing the GA optimization parameters and then, the evaluation of two cases to verify the functionality of the implemented system. The results obtained illustrate an efficient methodology, capable of searching optimal solutions for proposed problems, that with the right adjustments can be of great value to accelerate the development of new aircraft.