Os sistemas de transporte público por ônibus têm sido cada vez mais relevantes para o desenvolvimento das cidades. Técnicas para melhorar o planejamento e o controle da operação diária dos serviços de ônibus apresentaram melhorias significativas ao longo dos anos, e a previsão do tempo de viagem desempenha um importante papel no planejamento e nas estratégias da operação diária. A antecipação dos tempos de viagem ajuda os planejadores e controladores a evitar os vários problemas que surgem durante a operação diária da linha de ônibus. Ela também permite manter os usuários informados para que eles possam planejar com antecedência a sua viagem. Vários estudos relacionados à previsão do tempo de viagem podem ser encontrados na literatura. Devido a sua dificuldade intrínseca, o problema foi abordado por diferentes técnicas. Resultados numéricos de estudos demonstram o potencial uso de redes neurais em relação a outras técnicas. No entanto, a literatura não apresenta aplicações que incorporem uma retroalimentação das informações contidas em séries temporais, como é feito por redes neuronais recorrentes. A maioria dos estudos na literatura tem sido realizada com dados de cidades específicas e com linhas de ônibus com paradas fixas. A situação que surge em linhas de ônibus sem paradas fixas operadas com micro-ônibus apresenta uma dinâmica diferente dos estudos de caso da literatura Além disso, os estudos existentes não usam o gráfico de marcha como um instrumento de apoio para a previsão do tempo de viagem em ônibus. Nesta tese, estuda-se o problema da previsão do tempo de viagem para linhas de micro-ônibus sem paradas fixas, utilizando as informações básicas do gráfico de marcha. O modelo proposto é baseado em redes neurais recorrentes. Os dados de entrada incluem: (i) a hora de início da viagem do ônibus, (ii) sua posição atual em coordenadas GPS, (iii) o tempo atual e (iv) a distância percorrida após um minuto. As redes são treinadas com dados de uma linha de micro-ônibus da cidade de Porto Alegre, Brasil. Os dados correspondem ao ano de 2015. Os modelos fornecem previsões para a distância percorrida minuto a minuto e para uma janela de tempo de 30 minutos. O modelo desenvolvido foi treinado com um conjunto abrangente de dados de dias úteis, incluindo períodos de pico e fora de pico. Os dados de treinamento não desconsideraram informações de qualquer dia devido à ocorrência de eventos especiais. Concluiu-se que os modelos de redes neurais recorrentes desenvolvidos são capazes de absorver a dinâmica do movimento dos micro-ônibus. A informação produzida apresenta um nível adequado de precisão a ser utilizado para informar os usuários. Também é adequada para planejadores e controladores da operação, pois pode ajudar a identificar situações problemáticas em janelas de tempo futuras. / Public transport systems by bus have been increasingly relevant for the development of cities. Techniques to improve planning and control of daily operation of bus services presented significant improvements along the years, and travel time forecast plays an important hole in both planning and daily operation strategies. Travel times anticipation helps planners and controllers to anticipate the various issues that arise during the daily bus line operation. It also allows keeping users informed, so they can plan in advance for their trip. Several studies related to travel time prediction can be found in the literature. Due to its intrinsic difficulty, the problem has been addressed by different techniques. Numerical results from studies demonstrate the potential use of neural networks in relation to other techniques. However, the literature does not present applications that incorporate a feedback of the information contained in time series as it is done by recurrent neural networks. Most of the studies in the literature have been conducted with data from specific cities and buses lines with fixed stops. The situation that arises in bus lines without fixed stops operated with microbuses present a different dynamics from the literature case studies. In addition, existing studies do not use time-space trajectories as a supporting instrument for bus travel time prediction. In this thesis we study the problem of travel time prediction for microbus lines without fixed stops using the basic information of the time-space trajectories The proposed model is based on recurrent neural networks. The input data includes: (i) the start time of the bus trip, (ii) its current position in GPS coordinates, (iii) the current time and (iv) distance travelled after one minute. The networks are trained with data from a microbus line from the city of Porto Alegre, Brazil. Data corresponds to the year 2015. The model provide forecasts for distance travelled minute by minute, and for a time window of 30 minutes. The developed models were trained with a comprehensive set of data from working days including peak and off-peak periods. The training data did not disregard information from any day due to occurrence of special events. It was concluded that the recurrent neural network model developed is capable of absorbing the dynamics of the microbuses movement. The information produced present an adequate level of precision to be used for users information. It is also adequate for planners and operation controllers as it can help to identify problematic situations in future time windows.

Future ambitious solar system exploration missions are likely to require ever larger propulsion capabilities and involve innovative interplanetary trajectories in order to accommodate the increasingly complex mission scenarios. Two recent advances in trajectory design can be exploited to meet those new requirements: the use of low-thrust propulsion which enables larger cumulative momentum exchange relative to chemical propulsion; and the consideration of low-energy transfers relying on full multi-body dynamics. Yet the resulting optimal control problems are hypersensitive, time-consuming and extremely difficult to tackle with current optimization tools. Therefore, the goal of the thesis is to develop a methodology that facilitates and simplifies the solution finding process of low-thrust optimization problems in multi-body environments. Emphasis is placed on robust techniques to produce good solutions for a wide range of cases despite the strong nonlinearities of the problems. The complete trajectory is broken down into different component phases, which facilitates the modeling of the effects of multiple bodies and makes the process less sensitive to the initial guess. A unified optimization framework is created to solve the resulting multi-phase optimal control problems. Interfaces to state-of-the-art solvers SNOPT and IPOPT are included. In addition, a new, robust Hybrid Differential Dynamic Programming (HDDP) algorithm is developed. HDDP is based on differential dynamic programming, a proven robust second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. HDDP also incorporates nonlinear mathematical programming techniques to increase efficiency, and decouples the optimization from the dynamics using first- and second-order state transition matrices. Crucial to this optimization procedure is the generation of the sensitivities with respect to the variables of the system. In the context of trajectory optimization, these derivatives are often tedious and cumbersome to estimate analytically, especially when complex multi-body dynamics are considered. To produce a solution with minimal effort, an new approach is derived that computes automatically first- and high-order derivatives via multicomplex numbers. Another important aspect of the methodology is the representation of low-thrust trajectories by different dynamical models with varying degrees of fidelity. Emphasis is given on analytical expressions to speed up the optimization process. In particular, one novelty of the framework is the derivation and implementation of analytic expressions for motion subjected to Newtonian gravitation plus an additional constant inertial force. Example applications include low-thrust asteroid tour design, multiple flyby trajectories, and planetary inter-moon transfers. In the latter case, we generate good initial guesses using dynamical systems theory to exploit the chaotic nature of these multi-body systems. The developed optimization framework is then used to generate low-energy, inter-moon trajectories with multiple resonant gravity assists.

This study focuses on the Sun's influence on the motion near the triangular libration points of the Earth-Moon system. It is known that there exists a very strong resonant perturbation near those points that produces large deviations from the libration points, with an amplitude of about 250,000 km and a period of 1,500 days. However, it has been shown that it is possible to find initial conditions that negate the effects of that perturbation, even resulting in stable, although very large, periodic orbits. Using two different models, the goal of this research is to determine the initial configurations of the Earth-Moon-Sun system that produce minimal deviations from the libration points, and to provide a better understanding of the dynamics of this highly nonlinear problem. First, the Bicircular Problem (BCP) is considered, which is an idealized model of the Earth-Moon-Sun System. The impact of the initial configuration of the Earth-Moon-Sun system is studied for various propagation times and it is found that there exist two initial configurations that produce minimal deviations from L₄ or L₅. The resulting trajectories are very sensitive to the initial configuration, as the mean deviation from the libration points can decrease by 30,000 km with less than a degree change in the initial configuration. Two critical initial configurations of the system were identified that could allow a particle to remain within 30,000 km of the libration points for as long as desired. A more realistic model, based on JPL ephemerides, is also used, and the influence of the initial epoch on the motion near the triangular points is studied. Through the year 2007, 51 epochs are found that produce apparently stable librational motion near L₄, and 60 near L₅. But the motion observed depends greatly on the initial epoch. Some epochs are even found to significantly reduce the deviation from L₄ and L₅, with the spacecraft remaining within at most 90,000 km from the triangular points for upwards of 3,000 days. Similarly to what was observed in the BCP, these trajectories are found to be extremely sensitive to the initial epoch. / text

Challenging science requirements and complex space missions are driving the need for fast and robust space trajectory design and simulation tools. The main aim of this thesis is to develop new and improved high performance algorithms and solution techniques for commonly encountered problems in astrodynamics. Five major problems are considered and their state-of-the art algorithms are systematically improved. Theoretical and methodological improvements are combined with modern computational techniques, resulting in increased algorithm robustness and faster runtime performance. The five selected problems are 1) Multiple revolution Lambert problem, 2) High-fidelity geopotential (gravity field) computation, 3) Ephemeris computation, 4) Fast and accurate sensitivity computation, and 5) High-fidelity multiple spacecraft simulation. The work being presented enjoys applications in a variety of fields like preliminary mission design, high-fidelity trajectory simulation, orbit estimation and numerical optimization. Other fields like space and environmental science to chemical and electrical engineering also stand to benefit.

Os sistemas de transporte público por ônibus têm sido cada vez mais relevantes para o desenvolvimento das cidades. Técnicas para melhorar o planejamento e o controle da operação diária dos serviços de ônibus apresentaram melhorias significativas ao longo dos anos, e a previsão do tempo de viagem desempenha um importante papel no planejamento e nas estratégias da operação diária. A antecipação dos tempos de viagem ajuda os planejadores e controladores a evitar os vários problemas que surgem durante a operação diária da linha de ônibus. Ela também permite manter os usuários informados para que eles possam planejar com antecedência a sua viagem. Vários estudos relacionados à previsão do tempo de viagem podem ser encontrados na literatura. Devido a sua dificuldade intrínseca, o problema foi abordado por diferentes técnicas. Resultados numéricos de estudos demonstram o potencial uso de redes neurais em relação a outras técnicas. No entanto, a literatura não apresenta aplicações que incorporem uma retroalimentação das informações contidas em séries temporais, como é feito por redes neuronais recorrentes. A maioria dos estudos na literatura tem sido realizada com dados de cidades específicas e com linhas de ônibus com paradas fixas. A situação que surge em linhas de ônibus sem paradas fixas operadas com micro-ônibus apresenta uma dinâmica diferente dos estudos de caso da literatura Além disso, os estudos existentes não usam o gráfico de marcha como um instrumento de apoio para a previsão do tempo de viagem em ônibus. Nesta tese, estuda-se o problema da previsão do tempo de viagem para linhas de micro-ônibus sem paradas fixas, utilizando as informações básicas do gráfico de marcha. O modelo proposto é baseado em redes neurais recorrentes. Os dados de entrada incluem: (i) a hora de início da viagem do ônibus, (ii) sua posição atual em coordenadas GPS, (iii) o tempo atual e (iv) a distância percorrida após um minuto. As redes são treinadas com dados de uma linha de micro-ônibus da cidade de Porto Alegre, Brasil. Os dados correspondem ao ano de 2015. Os modelos fornecem previsões para a distância percorrida minuto a minuto e para uma janela de tempo de 30 minutos. O modelo desenvolvido foi treinado com um conjunto abrangente de dados de dias úteis, incluindo períodos de pico e fora de pico. Os dados de treinamento não desconsideraram informações de qualquer dia devido à ocorrência de eventos especiais. Concluiu-se que os modelos de redes neurais recorrentes desenvolvidos são capazes de absorver a dinâmica do movimento dos micro-ônibus. A informação produzida apresenta um nível adequado de precisão a ser utilizado para informar os usuários. Também é adequada para planejadores e controladores da operação, pois pode ajudar a identificar situações problemáticas em janelas de tempo futuras. / Public transport systems by bus have been increasingly relevant for the development of cities. Techniques to improve planning and control of daily operation of bus services presented significant improvements along the years, and travel time forecast plays an important hole in both planning and daily operation strategies. Travel times anticipation helps planners and controllers to anticipate the various issues that arise during the daily bus line operation. It also allows keeping users informed, so they can plan in advance for their trip. Several studies related to travel time prediction can be found in the literature. Due to its intrinsic difficulty, the problem has been addressed by different techniques. Numerical results from studies demonstrate the potential use of neural networks in relation to other techniques. However, the literature does not present applications that incorporate a feedback of the information contained in time series as it is done by recurrent neural networks. Most of the studies in the literature have been conducted with data from specific cities and buses lines with fixed stops. The situation that arises in bus lines without fixed stops operated with microbuses present a different dynamics from the literature case studies. In addition, existing studies do not use time-space trajectories as a supporting instrument for bus travel time prediction. In this thesis we study the problem of travel time prediction for microbus lines without fixed stops using the basic information of the time-space trajectories The proposed model is based on recurrent neural networks. The input data includes: (i) the start time of the bus trip, (ii) its current position in GPS coordinates, (iii) the current time and (iv) distance travelled after one minute. The networks are trained with data from a microbus line from the city of Porto Alegre, Brazil. Data corresponds to the year 2015. The model provide forecasts for distance travelled minute by minute, and for a time window of 30 minutes. The developed models were trained with a comprehensive set of data from working days including peak and off-peak periods. The training data did not disregard information from any day due to occurrence of special events. It was concluded that the recurrent neural network model developed is capable of absorbing the dynamics of the microbuses movement. The information produced present an adequate level of precision to be used for users information. It is also adequate for planners and operation controllers as it can help to identify problematic situations in future time windows.

Os sistemas de transporte público por ônibus têm sido cada vez mais relevantes para o desenvolvimento das cidades. Técnicas para melhorar o planejamento e o controle da operação diária dos serviços de ônibus apresentaram melhorias significativas ao longo dos anos, e a previsão do tempo de viagem desempenha um importante papel no planejamento e nas estratégias da operação diária. A antecipação dos tempos de viagem ajuda os planejadores e controladores a evitar os vários problemas que surgem durante a operação diária da linha de ônibus. Ela também permite manter os usuários informados para que eles possam planejar com antecedência a sua viagem. Vários estudos relacionados à previsão do tempo de viagem podem ser encontrados na literatura. Devido a sua dificuldade intrínseca, o problema foi abordado por diferentes técnicas. Resultados numéricos de estudos demonstram o potencial uso de redes neurais em relação a outras técnicas. No entanto, a literatura não apresenta aplicações que incorporem uma retroalimentação das informações contidas em séries temporais, como é feito por redes neuronais recorrentes. A maioria dos estudos na literatura tem sido realizada com dados de cidades específicas e com linhas de ônibus com paradas fixas. A situação que surge em linhas de ônibus sem paradas fixas operadas com micro-ônibus apresenta uma dinâmica diferente dos estudos de caso da literatura Além disso, os estudos existentes não usam o gráfico de marcha como um instrumento de apoio para a previsão do tempo de viagem em ônibus. Nesta tese, estuda-se o problema da previsão do tempo de viagem para linhas de micro-ônibus sem paradas fixas, utilizando as informações básicas do gráfico de marcha. O modelo proposto é baseado em redes neurais recorrentes. Os dados de entrada incluem: (i) a hora de início da viagem do ônibus, (ii) sua posição atual em coordenadas GPS, (iii) o tempo atual e (iv) a distância percorrida após um minuto. As redes são treinadas com dados de uma linha de micro-ônibus da cidade de Porto Alegre, Brasil. Os dados correspondem ao ano de 2015. Os modelos fornecem previsões para a distância percorrida minuto a minuto e para uma janela de tempo de 30 minutos. O modelo desenvolvido foi treinado com um conjunto abrangente de dados de dias úteis, incluindo períodos de pico e fora de pico. Os dados de treinamento não desconsideraram informações de qualquer dia devido à ocorrência de eventos especiais. Concluiu-se que os modelos de redes neurais recorrentes desenvolvidos são capazes de absorver a dinâmica do movimento dos micro-ônibus. A informação produzida apresenta um nível adequado de precisão a ser utilizado para informar os usuários. Também é adequada para planejadores e controladores da operação, pois pode ajudar a identificar situações problemáticas em janelas de tempo futuras. / Public transport systems by bus have been increasingly relevant for the development of cities. Techniques to improve planning and control of daily operation of bus services presented significant improvements along the years, and travel time forecast plays an important hole in both planning and daily operation strategies. Travel times anticipation helps planners and controllers to anticipate the various issues that arise during the daily bus line operation. It also allows keeping users informed, so they can plan in advance for their trip. Several studies related to travel time prediction can be found in the literature. Due to its intrinsic difficulty, the problem has been addressed by different techniques. Numerical results from studies demonstrate the potential use of neural networks in relation to other techniques. However, the literature does not present applications that incorporate a feedback of the information contained in time series as it is done by recurrent neural networks. Most of the studies in the literature have been conducted with data from specific cities and buses lines with fixed stops. The situation that arises in bus lines without fixed stops operated with microbuses present a different dynamics from the literature case studies. In addition, existing studies do not use time-space trajectories as a supporting instrument for bus travel time prediction. In this thesis we study the problem of travel time prediction for microbus lines without fixed stops using the basic information of the time-space trajectories The proposed model is based on recurrent neural networks. The input data includes: (i) the start time of the bus trip, (ii) its current position in GPS coordinates, (iii) the current time and (iv) distance travelled after one minute. The networks are trained with data from a microbus line from the city of Porto Alegre, Brazil. Data corresponds to the year 2015. The model provide forecasts for distance travelled minute by minute, and for a time window of 30 minutes. The developed models were trained with a comprehensive set of data from working days including peak and off-peak periods. The training data did not disregard information from any day due to occurrence of special events. It was concluded that the recurrent neural network model developed is capable of absorbing the dynamics of the microbuses movement. The information produced present an adequate level of precision to be used for users information. It is also adequate for planners and operation controllers as it can help to identify problematic situations in future time windows.

L'imagerie par résonance magnétique (IRM) est l'une des modalités d'imagerie les plus puissantes et les plus sures pour examiner le corps humain. L'IRM de haute résolution devrait aider à la compréhension et le diagnostic de nombreuses pathologies impliquant des lésions submillimétriques ou des maladies telles que la maladie d'Alzheimer et la sclérose en plaque. Bien que les systèmes à haut champ magnétique soient capables de fournir un rapport signal-sur-bruit permettant d'augmenter la résolution spatiale, le long temps d'acquisition et la sensibilité au mouvement continuent d'entraver l'utilisation de l'IRM de haute résolution. Malgré le développement de méthodes de correction du mouvement et du bruit physiologique, le long temps d'acquisition reste un obstacle majeur à l'IRM de haute résolution, en particulier dans les applications cliniques.Au cours de la dernière décennie, la nouvelle théorie du compressed sensing (CS) a proposé une solution prometteuse pour réduire le temps d'examen en IRM. Après avoir expliqué la théorie du compressed sensing, ce projet de thèse propose une étude empirique et quantitative du facteur de sous-échantillonnage maximum réalisable grâce au CS pour l'imagerie pondérée en T ₂ *.En outre, l'application de CS en IRM repose généralement sur l'utilisation de courbes d'échantillonnage simples telles que les lignes droites, spirales ou des légères variations de ces formes élémentaires qui ne tirent pas pleinement parti des degrés de liberté offerts par le hardware et ne peuvent être facilement adaptées à une distribution d'échantillonnage arbitraire. Dans cette thèse, j'ai introduit une méthode appelée SPARKLING, qui permet de surmonter ces limitations en adoptant une approche radicalement nouvelle de la conception de l'échantillonnage de l'espace-k. L'acronyme SPARKLING signifie Spreading Projection Algorithm for Rapid K-space sampLING. C'est une méthode flexible inspirée des techniques de stippling qui génère automatiquement, grâce à un algorithme d'optimisation, des courbes d'échantillonnage non-cartésiennes optimisées et compatibles avec les contraintes hardware de l'IRM en termes d'amplitude de gradient maximale et d'accélération maximale. Ces courbes d'échantillonnage sont conçues pour répondre à des critères clés pour un échantillonnage optimal : une distribution contrôlée des échantillons et une couverture de l'espace-k localement uniforme. Avant de s'engager dans des acquisitions, nous avons vérifié que notre système de gradient était bien capable d'exécuter ces trajectoires complexes. Nous avons implémenté une méthode de mesure de phase et avons observé une très bonne adéquation entre trajectoires prescrites et mesurées.Enfin, en alliant une efficacité d'échantillonnage avec le compressed sensing et l'imagerie parallèle, les trajectoires SPARKLING ont permis de réduire jusqu'à 20 fois le temps d'acquisition d'un examen IRM T ₂ * par rapport aux acquisitions cartésiennes de référence, sans détérioration de la qualité d'image. Ces résultats expérimentaux ont été obtenus à 7 Tesla pour de l'imagerie cérébrale in vivo. Par rapport aux stratégies d'échantillonnage non-cartésiennes usuelles (spirale et radiale), la technique proposée a également permis d'obtenir une qualité d'image supérieure. Enfin, l'approche proposée a été étendue à l'imagerie 3D et appliquée à 3 Tesla pour laquelle des résultats préliminaires ex vivo à une résolution isotrope de 0.6 mm suggèrent la possibilité d'atteindre des facteurs d'accélération très élevés jusqu'à 60 pour la pondération T ₂ * et l'imagerie pondérée en susceptibilité. / Magnetic resonance imaging (MRI) is one of the most powerful and safest imaging modalities for examining the human body. High-resolution MRI is expected to aid in the understanding and diagnosis of many neurodegenerative pathologies involving submillimetric lesions or morphological alterations, such as Alzheimer’s disease and multiple sclerosis. Although high-magnetic-field systems can deliver a sufficient signal-to-noise ratio (SNR) to increase spatial resolution, long scan times and motion sensitivity continue hindering the utilization of high resolution MRI. Despite the development of corrections for bulk and physiological motion, lengthy acquisition times remain a major obstacle to high-resolution acquisition, especially in clinical applications.In the last decade, the newly developed theory of compressed sensing (CS) offered a promising solution for reducing the MRI scan time. After having explained the theory of compressed sensing, this PhD project proposes an empirical and quantitative analysis of the maximum undersampling factor achievable with CS for T ₂ *-weighted imaging.Furthermore, the application of CS to MRI commonly relies on simple sampling patterns such as straight lines, spirals or slight variations of these elementary shapes, which do not take full advantage of the degrees of freedom offered by the hardware and cannot be easily adapted to fit an arbitrary sampling distribution. In this PhD thesis, I have introduced a method called SPARKLING, that may overcome these limitations by taking a radically new approach to the design of k-space sampling. The acronym SPARKLING stands for Spreading Projection Algorithm for Rapid K-space sampLING. It is a versatile method inspired from stippling techniques that automatically generates optimized non-Cartesian sampling patterns compatible with MR hardware constraints on maximum gradient amplitude and slew rate. These sampling curves are designed to comply with key criteria for optimal sampling: a controlled distribution of samples and a locally uniform k-space coverage. Before engaging into experiments, we verified that our gradient system was capable of executing the complex gradient waveforms. We implemented a local phase measurement method and we observed a very good adequacy between prescribed and measured k-space trajectories.Finally, combining sampling efficiency with compressed sensing and parallel imaging, the SPARKLING sampling patterns allowed up to 20-fold reductions in MR scan time, compared to fully-sampled Cartesian acquisitions, for T ₂ *-weighted imaging without deterioration of image quality, as demonstrated by our experimental results at 7 Tesla on in vivo human brains. In comparison to existing non-Cartesian sampling strategies (spiral and radial), the proposed technique also yielded superior image quality. Finally, the proposed approach was also extended to 3D imaging and applied at 3 Tesla for which preliminary results on ex vivo phantoms at 0.8 mm isotropic resolution suggest the possibility to reach very high acceleration factors up to 60 for T ₂ *-weighting and susceptibility-weighted imaging.

The primary importance of trajectory reconstruction is to assess the accuracy of pre-flight predictions of the entry trajectory. While numerous entry systems have flown, often these systems are not adequately instrumented or the flight team not adequately funded to perform the statistical engineering reconstruction required to quantify performance and feed-forward lessons learned into future missions. As such, entry system performance and reliability levels remain unsubstantiated and improvement in aerothermodynamic and flight dynamics modeling remains data poor. The comparison is done in an effort to quantitatively and qualitatively compare Kalman filtering methods of reconstructing trajectories and atmospheric conditions from entry systems flight data. The first Kalman filter used is the extended Kalman filter. Extended Kalman filtering has been used extensively in trajectory reconstruction both for orbiting spacecraft and for planetary probes. The second Kalman filter is the unscented Kalman filter. Additionally, a technique for using collocation to reconstruct trajectories is formulated, and collocation's usefulness for trajectory simulation is demonstrated for entry, descent, and landing trajectories using a method developed here to deterministically find the state variables of the trajectory without nonlinear programming. Such an approach could allow one to utilize the same collocation trajectory design tools for the subsequent reconstruction.