This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.

Au cours des dernières années, s’est développé un intérêt tout particulier pour l’optimisation sans dérivée. Ce domaine de recherche se divise en deux catégories: une déterministe et l’autre stochastique. Bien qu’il s’agisse du même domaine, peu de liens ont déjà été établis entre ces deux branches. Cette thèse a pour objectif de combler cette lacune, en montrant comment les techniques issues de l’optimisation déterministe peuvent améliorer la performance des stratégies évolutionnaires, qui font partie des meilleures méthodes en optimisation stochastique. Sous certaines hypothèses, les modifications réalisées assurent une forme de convergence globale, c’est-à-dire une convergence vers un point stationnaire de premier ordre indépendamment du point de départ choisi. On propose ensuite d’adapter notre algorithme afin qu’il puisse traiter des problèmes avec des contraintes générales. On montrera également comment améliorer les performances numériques des stratégies évolutionnaires en incorporant un pas de recherche au début de chaque itération, dans laquelle on construira alors un modèle quadratique utilisant les points où la fonction coût a déjà été évaluée. Grâce aux récents progrès techniques dans le domaine du calcul parallèle, et à la nature parallélisable des stratégies évolutionnaires, on propose d’appliquer notre algorithme pour résoudre un problème inverse d’imagerie sismique. Les résultats obtenus ont permis d’améliorer la résolution de ce problème. / In recent years, there has been significant and growing interest in Derivative-Free Optimization (DFO). This field can be divided into two categories: deterministic and stochastic. Despite addressing the same problem domain, only few interactions between the two DFO categories were established in the existing literature. In this thesis, we attempt to bridge this gap by showing how ideas from deterministic DFO can improve the efficiency and the rigorousness of one of the most successful class of stochastic algorithms, known as Evolution Strategies (ES’s). We propose to equip a class of ES’s with known techniques from deterministic DFO. The modified ES’s achieve rigorously a form of global convergence under reasonable assumptions. By global convergence, we mean convergence to first-order stationary points independently of the starting point. The modified ES’s are extended to handle general constrained optimization problems. Furthermore, we show how to significantly improve the numerical performance of ES’s by incorporating a search step at the beginning of each iteration. In this step, we build a quadratic model using the points where the objective function has been previously evaluated. Motivated by the recent growth of high performance computing resources and the parallel nature of ES’s, an application of our modified ES’s to Earth imaging Geophysics problem is proposed. The obtained results provide a great improvement for the problem resolution.

Dans ces travaux, nous présentons des méthodes d'optimisation théoriques et numériques pour la conception optimale de circuits magnétiques pour propulseurs à effet Hall. Ces problèmes de conception sont des problèmes inverses très difficiles à résoudre que nous formulons sous forme de problèmes d'optimisation topologique. Les problèmes resultant sont non convexes avec des contraintes aux équations différentielles de Maxwell. Au cours de ces travaux, des approches originales ont été proposées afin de résoudre efficacement ces problèmes d'optimisation topologique. L'approche de densité de matériaux SIMP (Solid Isotropic Material with Penalization) qui est une variante de la méthode d'homogénéisation a été privilégiées. De plus, les travaux de ma thèse ont permis la mise en place de codes d'optimisation dénommé ATOP (Algorithm To Optimize Propulsion) utilisant en parallèle les logiciels de calculs scientifiques Matlab et d'élément finis FEMM (Finite Element Method Magnetics). Dans ATOP, nous utilisant à la fois des algorithmes d'optimisation locale de type descente basés sur une analyse de la sensibilité du problème et des algorithmes d'optimisation globale principalement de type Branch and Bound basés sur l'Arithmétique des Intervals. ATOP permettra d'optimiser à la fois la forme topologique des circuits magnétiques mais aussi le temps et le coût de production de nouvelles génération de propulseurs électriques. / In this work, we present theoretical and numerical optimization method for designing magnetic circuits for Hall effect thrusters. These design problems are very difficult inverse ones that we formulate under the form of topology optimization problems. Then, the obtained problems are non convex subject to Maxwell equations like constraints. Some original approaches have been proposed to solve efficiently these topology optimization problems. These approaches are based on the material density model called SIMP approach (Solid Isotropic Material with Penalization) which is a variante of the homogenization method. The results in my thesis allowed to provide optimization source code named ATOP (Algorithm To Optimize Propulsion) unsung in parallel two scientific computing softwares namely Matlab and FEMM (Finite Element Method Magnetics). In ATOP, we use both local optimization algorithms based on sensitivity analysis of the design problem; and global optimization algorithms mainly of type Branch and Bound based on Interval Arithmetic analysis. ATOP will help to optimize both the topological shape of the magnetic circuits and the time and cost of production (design process) of new generations of electrical thrusters.

Plusieurs machines actuellement utilisées, moteurs à combustion interne en automobile ou centrales thermiques dans l’énergie, rejettent de grandes quantités de chaleur. Généralement cette chaleur est dissipée dans l’atmosphère et son énergie perdue. Nous nous sommes donc intéressés aux moteurs à apport de chaleur externe dont l’énergie primaire est de l’énergie thermique, et plus particulièrement aux moteurs Stirling. L’une de ses principales caractéristiques est d’utiliser de la chaleur produite extérieurement comme source d’énergie. Ceci lui permet d’être multi-carburant et même d’utiliser de l’énergie thermique naturelle.L’étude menée comporte deux parties. Tout d’abord un modèle numérique zéro dimension, trois zones en temps fini a été développé. Il prend en compte les échanges thermiques aux parois et les pertes de charge, mais ne préjuge ni des dimensions moteur, ni des conditions de fonctionnement. Ceci lui permet de rester flexible pour s’adapter à l’architecture spécifique du moteur à simuler. Ensuite nous avons réalisé des mesures expérimentales sur deux moteurs de taille et puissance différentes (quelques watts et 1 kW). Ces résultats ont permis de valider le modèle. Au final nous avons obtenu un modèle numérique traduisant l’influence de paramètres dimensionnels et fonctionnels sur la puissance du moteur Stirling.Un outil d’aide à la conception de moteur Stirling a été développé en ajoutant au modèle un algorithme d’optimisation. Il permet une ébauche des caractéristiques d’un moteur Stirling. En fonction de l’application souhaitée et des contraintes s’y appliquant, il agit sur les caractéristiques choisies par l’utilisateur pour maximiser les performances. / Several machines currently used, internal combustion engines for the car industry or thermal power plants in energy, exhaust a considerable amount of heat. Generally this heat is dispersed in the atmosphere and its energy lost. So we took a special interest in external heat engines which primary energy is heat energy, and more particularly in Stirling engines. One of its main characteristics is the used of energy from heat produced externally like energy source. This allows Stirling engines to be multi-fuel and even to use natural heat energy.The study carried out is made up of two parts. First, a three zones zero dimensional finite-time thermodynamic model has been developed. It takes into account the heat transfer from the walls and the pressure drop, but does not prejudge the dimensions of the engine nor the conditions of its functioning. It is thus able to remain flexible and to adjust to the specific architecture of the engine that should be simulated. Afterwards, we have realized a series of experimental measures thanks to two engines different in size and power (a few Watt and 1 kW). These results allowed us to validate the model. In the end, we got a numerical model representing the influence of dimensional and functional parameters on the power of a Stirling engine.Eventually, a tool to assist in designing Stirling engines was developed adding an optimization algorithm to the model. It allows to sketch out a preliminary draft of the characteristics of a Stirling engine. Depending on the desired application and on the constraints exerted on the engine, the tool created will act on the characteristics of the engine chosen by the user to maximize its performances.

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This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The control problem is solved both on an open track and while safely driving no closer than a fixed distance behind another locomotive. In contrast to other research in the field, this thesis achieves a real-time capable and embeddable closed-loop optimization with advanced modeling and numerical solving techniques with a non-linear optimal control problem. This controller is first formulated as a non-convex control problem and then converted to an advanced convex second-order cone problem with the intent of using a simple numerical solver, ensuring global optimality, and improving control robustness. Convex and non-convex numerical methods of solving the control problem are investigated and closed-loop performance results with a simulated vehicle are presented under realistic modeling conditions on advanced tracks both on desktop and embedded computer architectures. It is observed that the controller is capable of robust vehicle driving in cases both with and without modeling uncertainty. The benefits of pairing the optimal controller with a parameter estimator are demonstrated for cases where very large mismatches exists between the controller model and the simulated vehicle. Stopping performance is consistently within 25cm of target stations, and the worst case closed-loop optimization time was within 100ms for the computation of a 1000 point control horizon on an i7-6700 machine. / Thesis / Master of Applied Science (MASc) / This research formulates and implements a novel closed-loop optimal control system that drives a train between two stations in an optimal time, energy efficient, or mixed objective manner. It is deployed on a commuter vehicle and directly manages the motoring and braking systems. The optimal controller uses sensor feedback from the train and in real-time computes the most efficient control decision for the train to follow given knowledge of the track profile ahead of the train, speed restrictions and required arrival time windows. The final control implementation is capable of safe, high accuracy and optimal driving all while computing fast enough to reliably deploy on a rail vehicle.

La plupart des patients infectés par le VIH ont une charge virale qui peut être rendue indétectable par des combinaisons antirétrovirales hautement actives (cART); cependant, il existe des effets secondaires aux traitements. L'utilisation des modèles mécanistes dynamiques basés sur des équations différentielles ordinaires (ODE) a considérablement amélioré les connaissances de la dynamique HIV-système immunitaire et permet d'envisager une personnalisation du traitement. L'objectif de ces travaux de thèse est d'améliorer les techniques statistiques d'estimation de paramètres dans les modèles mécanistes dynamiques afin de proposer des stratégies de surveillance et d'optimisation des traitements. Après avoir introduit NIMROD un algorithme d'estimation bayésienne basé sur une maximisation de la vraisemblance pénalisée, nous montrons la puissance des approches mécanistes dynamiques pour l'évaluation des effets traitements par rapport aux méthodes descriptives d'analyse des trajectoires des biomarqueurs. Puis, nous définissons le « modèle à cellules cibles », un système ODE décrivant la dynamique du VIH et des CD4. Nous montrons qu'il possède de bonnes capacités prédictives. Nous proposons une preuve de concept de la possibilité de contrôler individuellement la dose de traitement. Cette stratégie adaptative réajuste la dose du patient en fonction de sa réaction à la dose précédente par une procédure bayésienne. Pour finir, nous introduisons la possibilité de l’'individualisation des changements de cART. Ce travail passe par la quantification in vivo d'effets de cART en utilisant des indicateurs d'activité antivirale in vitro. Nous discutons la validité des résultats et les étapes méthodologiques nécessaires pour l'intégration de ces méthodes dans les pratiques cliniques. / Most HIV-infected patients viral loads can be made undetectable by highly active combination of antiretroviral therapy (cART), but there are side effects of treatments. The use of dynamic mechanistic models based on ordinary differential equations (ODE) has greatly improved the knowledge of the dynamics of HIV and of the immune system and can be considered for personalization of treatment. The aim of these PhD works is to improve the statistical techniques for estimating parameters in dynamic mechanistic models so as to elaborate strategies for monitoring and optimizing treatments. We present an algorithm and program called NIMROD using Bayesian inference based on the maximization of the penalized likelihood. Then, we show the power of dynamic mechanistic approaches for the evaluation of treatment effects compared to methods based on the descriptive analysis of the biomarkers trajectories. Next, we build the “target cells model “, an ODE system of the dynamics between the HIV and CD4. We demonstrate it has good predictive capabilities. We build a proof of concept for drug dose individualization. It consists in tuning the dose of the patient based on his reaction to the previous doses using a Bayesian update procedure. Finally, we introduce the possibility of designing an individualized change of cART. This work involves the quantification of in vivo effects of cART using in vitro antiviral activity indicators. We discuss the validity of the results and the further steps needed for the integration of these methods in clinical practice.

Cette thèse est dédiée à la conception optimale de la machine synchrone à rotor bobiné modulaire sans balais pour les systèmes embarqués. Cette machine est basée sur une structure POKIPOKITM développée par Mitsubishi Electric Coopération avec les convertisseurs de puissance intégrée pour augmenter la capacité de tolérance aux défauts. L'analyse électromagnétique est utilisée pour étudier les différentes machines synchrones à rotor bobiné et donc, pour sélectionner la structure qui offre la meilleure tolérance aux défauts et les performances les plus élevées. D’abord, le choix des nombres de phases, d’encoches et de pôles est un point critique. Ensuite, quelques machines sont analysées et comparées selon les critères tels que la densité de couple, le rendement, l'ondulation de couple. La machine avec 7 phases, 7 encoches et 6 pôles est alors choisie. Cette machine est ensuite comparée à la machine synchrone à aimant permanent monté en surface. Le résultat démontre que la machine synchrone à rotor bobiné modulaire sans balais possède le potentiel de remplacer la machine synchrone à aimant permanent dans notre application parce qu’elle présente des performances similaires avec une capacité de tolérance aux défauts élevée. Dans un second temps, une fois la structure 7phases/7encoches/6pôles choisie, cette machine est optimisée en utilisant NOMAD (qui est un logiciel d'optimisation de boîte noire) afin de minimiser le volume externe sous les contraintes électromagnétiques, thermiques et mécaniques. Comme ce problème d'optimisation est extrêmement difficile à résoudre, quelques relaxations ont été effectuées pour tester les différents algorithmes d'optimisation : fmincon (de Matlab) et NOMAD. Nous remarquons que NOMAD est plus efficace que fmincon pour trouver des solutions à ce problème de conception où certaines contraintes sont calculées par des simulations numériques (ANSYS Maxwell ; code éléments finis). En utilisant la méthode NOMAD basée sur l’algorithme Mesh Adaptive Direct Search, nous obtenons des résultats optimaux qui satisfont toutes les contraintes proposées. Il est nécessaire de valider ce design optimisé en vérifiant toutes les contraintes par des simulations électromagnétiques et thermiques en 3D. Les résultats montrent que le couple moyen obtenu par la simulation en 3D est inférieur à la valeur souhaitée. Par conséquent, en augmentant la longueur de la machine, une nouvelle machine corrigée est ainsi obtenue. Nous observons que les pertes de fer obtenues en 3D sont plus élevées qu'en 2D en raison du flux de fuite dans la tête de bobinage. En prenant les valeurs des pertes analysées par la simulation en 3D, la température de surface de la nouvelle machine analysée par la méthode Computational Fluid Dynamics est plus élevée que celle calculée dans l’optimisation. Enfin, un prototype de machine est construit et quelques tests expérimentaux est réalisés. Le résultat montre que la force électromotrice à vide a une forme d'onde similaire par rapport à la prédiction numérique en 3D et la différence de couple statique maximum entre les tests expérimentaux et les simulations par éléments finis en 3D est faible. / This thesis is dedicated to the design and the optimization of modular brushless wound rotor synchronous machine for embedded systems. This machine is constructed based on POKIPOKITM structure with integrated drive electronics. Finite element analysis based optimization becomes more popular in the field of electrical machine design because analytical equations are not easily formalized for the machines which have complicate structures. Using electromagnetic analysis to comparatively study different modular brushless wound rotor synchronous machines and therefore, to select the structure which offers the best fault tolerant capability and the highest output performances. Firstly, the fundamental winding factor calculated by using the method based on voltage phasors is considered as a significant criterion in order to select the numbers of phases, stator slots and poles. After that, 2D finite element numerical simulations are carried out for a set of 15 machines to analyze their performances. The simulation results are then compared to find an appropriate machine according to torque density, torque ripple and machine efficiency. The 7phase/7-slot/6-pole machine is chosen and compared with a reference design surfacemounted permanent magnet synchronous machine in order to evaluate the interesting performance features of the wound rotor synchronous machine. In the second design stage, this machine is optimized by using derivative-free optimization. The objective is to minimize external volume under electromagnetic, thermal and mechanical constraints. Given that an accurate finite element analysis for machine performance takes a long time. Moreover, considering that the average torque can be obtained by simulating the model with only four rotor positions instead of one electric period, optimization strategy is proposed to reduce computational time and therefore, obtain a fast convergence ability by defining relaxed problems which enable minimizing the external volume of the machine under only several constraints such as average torque, torque ripple and copper losses. By testing relaxed problems, two different optimization methods (NOMAD and fmincon) are compared in order to select an appropriate method for our optimization problem. Using NOMAD method based on Mesh Adaptive Direct Search, we achieve optimal results which satisfy all of the constraints proposed. In the third design stage, all constraints are validated by 3D electromagnetic and thermal simulations using finite element and computational fluid dynamics methods. The 3D results show that the average torque obtained is lower than the desired value. By increasing the length of the machine, a new corrected machine is thus obtained. It can be observed that the iron losses obtained in 3D are higher than that in 2D due to the leakage flux in the end-winding. Then, the machine temperature is analyzed by using ANSYS Fluent. Note that the surface temperature is higher than that calculated in the optimization and the coil temperature is 8.48°C higher than the desired value (105°C). However, some dissipation by the shaft and the bearings of the machine are expected to reduce the machine temperature. Finally, a machine prototype is built and some experimental tests are carried out. The results show that the electromotive force has a similar waveform compared to 3D prediction and the difference of the measured and predicted maximum static torques is small.

Made available in DSpace on 2016-08-17T14:53:21Z (GMT). No. of bitstreams: 1 Sergio Augusto.pdf: 2350058 bytes, checksum: 7c3c67925b0b27a77105c3cb0799c4e6 (MD5) Previous issue date: 2012-05-04 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This work provides a framework to obtain the optimal bidding strategy for a GENCO in long-term electricity auction. The tool is based on intelligent techniques for optimizing the proposed Utility Function. The goal is to find the optimal strategy that maximizes the expected payoff of GENCO and simultaneously minimize the risks. The risks are modeled by two classical metrics: the Variance (Portfolio Theory) and Value at Risk (VaR). The proposed methodology is applied to auctions for long-term forward contracts, such that used in the Brazilian power system for buying and selling energy in the regulated market. The Bidding Strategy is formed through a Supply Curve which relates the optimal amount of energy to different offer prices. Thus, it allows the GENCO define the best bid (offer) for a given offer price. The proposed approach is validated for three test cases: First, concerning the variation of generation and price of energy scenarios for evaluation of the bidding strategy and the GENCOS risk perception; The second, consider a cascade hydro-term system for evaluation of MRE; and The third, considers the northeastern Brazilian subsystem where the supply curve is formed for the CHESF company's power plants portfolio. The results show how the offer may be changed according the variation of the spot prices and physical generation and demonstrate the efficacy of meta-heuristics proposed to optimize the supply model. / Este trabalho apresenta uma ferramenta de auxílio e suporte à tomada de decisões na formação de estratégias de oferta para agentes geradores (GENCOS) participantes de leilões de eletricidade de longo-prazo. A ferramenta é baseada em técnicas inteligentes para a otimização da Função de Utilidade proposta média-risco . O objetivo é encontrar a Estratégia Ótima que maximize o retorno esperado da GENCO e, simultaneamente, minimize os riscos relacionados às incertezas no montante de energia produzida e no preço spot, modelados por duas métricas clássicas de risco: a Variância (teoria dos portfólios) e o Valor em Risco (VaR). A abordagem proposta é aplicada ao mercado brasileiro de eletricidade, especificamente, ao ambiente de Leilões de Energia Existente na categoria Quantidade de Energia, tais quais os leilões aplicados pelo órgão regulador brasileiro para compra e venda de energia no mercado regulado. Sugere-se aqui a formação de uma Curva de Oferta que relacione a quantidade de energia ótima para diferentes preços de oferta. E, deste modo, permita a GENCO definir qual o melhor lance (oferta) para dado preço de oferta durante o processo do leilão. Para a avaliação da abordagem foram utilizados três casos testes: O primeiro considera cenários de geração física e preço de energia a fim de avaliar a estratégia de oferta e a percepção ao risco de contratação da GENCO quanto à variação de tais cenários; o segundo, considera um sistema em cascata onde é possível observar o efeito do Mecanismo de Realocação de Energia (MRE) sobre a oferta das GENCOS; e o terceiro considera o subsistema nordeste brasileiro onde a curva de oferta é formada para o portfólio de usinas pertencentes à empresa CHESF. Os resultados demonstram como a oferta de energia pode ser alterada de acordo com cenários de oferta gerados e comprovam a eficiência da meta-heurística proposta para otimização do modelo de oferta.

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