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Uncertainty in weather forecasts increases the complexity of aircraft trajectory optimization and makes trajectory prediction uncertain as well. The resulting 4D-trajectory uncertainty subsequently leads to congestion and capacity reduction of airspace and causes delays. Moreover, it also complicates Air Traffic Control’s (ATC’s) inter-aircraft separation management in an arrival sequence. As weather forecast uncertainty affects both individual trajectories and the associated arrival sequence, both aspects should be considered simultaneously in optimization. However, stochastic aircraft trajectory optimization has never been tackled with multiple aircraft, while stochastic arrival sequence optimization has never considered the trajectories of the sequenced aircraft. Furthermore, research works that integrated trajectories and the arrival sequence in optimization have only been carried out in a deterministic framework. To address these research gaps, this doctoral research develops a stochastic optimization method to simultaneously optimize descent/approach trajectories and the associated arrival sequence, while ensuring inter-aircraft separations under uncertain weather forecasts. We formulate a multi-phase Optimal Control (OC)-based robust trajectory optimization problem for descending/approaching aircraft. The ensemble approach is employed to model the effect of weather forecast uncertainty on a trajectory. We also introduce the ensemble approach into sequence optimization to bring robustness to arrival sequencing. The trajectory and arrival sequence optimizations are integrated into a single robust optimization framework called the integrated robust Trajectory & Sequence (T&S) optimization. This novel optimization method enables simultaneous optimization of trajectories and the arrival sequence in terms of statistical performances of fuel burn, fight time, and airspace throughput. It also allows for limiting the 4D-trajectory uncertainty of each aircraft to below a desired level. The developed optimization method is tested in illustrative operational use cases. The optimized robust trajectories mitigate the unwanted increase of operational costs due to the uncertain weather forecast such as an increase of fuel burn or change of speed, while always respecting operational constraints. The robust arrival sequences always ensure inter-aircraft separations under 4D-trajectory uncertainties. The proposed method can also quantify the operational costs each aircraft must owe to establish the optimal trajectory and sequence. The proposed method has the potential to realize a next-generation Arrival Manager (AMAN) by supporting better coordination between individual aircraft intents and ATC’s traffic management and enabling robust decision-making against weather forecast uncertainty.

<p dir="ltr">Supersonic transport has been an active field of aviation research since the 1950s, and its commercialization culminated in the Anglo-French airliner, the Concorde. Due to unsustainable operation costs and the sonic booms emanating along the path, supersonic transports have retreated from the forefront of research since the Concorde’s decommission. The annoyance caused by sonic booms further prompted the FAA to prohibit all overland civil flights over Mach 1. However, recent resurgence in SST projects such as NASA’s QueSST project and its experimental aircraft X-59 is set to employ a boom-minimization configuration and to re-evaluate the prospects of overland supersonic flights. In light of this advancement, a trajectory optimization framework that minimizes perceived boom along the path, tailored to supersonic in-land flights, is developed. An optimal control problem combining a sonic boom propagation model, the population distribution of the continental U.S., and a noise measure based on Perceived Level decibels is formulated and solved numerically via GPOPS-II. Two trajectories over the continental U.S. based on this framework are illustrated and aim to provide insights into future supersonic transport design, regulations, as well as air-traffic management.</p>

There is a need for a fuel-optimal required time of arrival (RTA) mode for aircraft flight management systems capable of enabling controlled time of arrival functionality in the presence of wind speed forecast uncertainty. A computationally tractable two-stage stochastic algorithm utilizing a data-driven, location-specific forecast uncertainty model to generate forecast uncertainty scenarios is proposed as a solution. Three years of Aircraft Communications Addressing and Reporting Systems (ACARS) wind speed reports are used in conjunction with corresponding wind speed forecasts from the Rapid Update Cycle (RUC) forecast product to construct an inhomogeneous Markov model quantifying forecast uncertainty characteristics along specific route through the national airspace system. The forecast uncertainty modeling methodology addresses previously unanswered questions regarding the regional uncertainty characteristics of the RUC model, and realizations of the model demonstrate a clear tendency of the RUC product to be positively biased along routes following the normal contours of the jet stream. A two-stage stochastic algorithm is then developed to calculate the fuel optimal stage one cruise speed given a required time of arrival at a destination waypoint and wind forecast uncertainty scenarios generated using the inhomogeneous Markov model. The algorithm utilizes a quadratic approximation of aircraft fuel flow rate as a function of cruising Mach number to quickly search for the fuel-minimum stage one cruise speed while keeping computational footprint small and ensuring RTA adherence. Compared to standard approaches to the problem utilizing large scale linear programming approximations, the algorithm performs significantly better from a computational complexity standpoint, providing solutions in fractional power time while maintaining computational tractability in on-board systems.

Persistent condensation trails are clouds, induced by the exhaust of an aircraft engine in a cold and ice-supersaturated environment. These artificial ice clouds can both cool and heat the atmosphere by scattering solar radiation and absorbing terrestrial radiation, respectively. The influence of condensation trails on the Earth-atmosphere energy balance and therewith the answer to the question of the dominating process had been mostly approximated on a global scale by treating the condensation trail as plane parallel layer with constant optical properties. Individual condensation trails and the influence of the solar angle had been analyzed, always using a course spatial grid and never under consideration of the aircraft performance, generating the condensation trail. For a trajectory optimization, highly precise results of the impact of condensation trails on the radiation budget and the influence of the aircraft performance on this impact is needed, so that future air traffic may consider the main factors of flight performance on the environmental impact of condensation trails. That’s why, a model is developed in this thesis to continuously estimate the scattering and absorption properties and their dependence on the aircraft performance. / Langlebige Kondensstreifen sind Eiswolken, welche durch Kondensation von Wasserdampf an Rußpartikeln in einer eisübersättigten Atmosphäre entstehen. Der Wasserdampf entstammt einerseits aus dem Triebwerkabgas und andererseits aus der Atmosphäre. Kondensstreifen können die Atmosphäre durch Rückstreuung solarer Strahlung kühlen und durch Rückstreuung und Absorption terrestrischer Strahlung erwärmen. Der Einfluss von Kondensstreifen auf den Wärmehaushalt der Atmosphäre und damit die Antwort auf die Frage nach dem dominierenden Effekt wurde bisher zumeist auf globaler Ebene ermittelt, wobei der Kondensstreifen als planparallele Schicht mit konstanten optischen Eigenschaften angenähert wurde. Individuelle Kondensstreifen und der Einfluss des Sonnenstandes wurden bisher nur mithilfe eines groben Rasters betrachtet und niemals unter Berücksichtigung der Flugleistung des Luftfahrzeuges, welches den Kondensstreifen generiert hat. Für eine Trajektorienoptimierung sind jedoch präzise Berechnungen des Strahlungseinflusses und eine gewissenhafte Berücksichtigung der Flugleistung notwendig. Nur so kann der zukünftige Luftverkehr die Haupteinflussfaktoren der Flugeigenschaften auf den Strahlungseinfluss der Kondensstreifen berücksichtigen. Aus diesem Grund wurde in dieser Arbeit ein Modell entwickelt, welches die Eigenschaften des Strahlungstransfers durch den Kondensstreifen kontinuierlich bestimmt und die aus der Flugleistung resultierenden Parameter berücksichtigt.

L’objectif de cette étude est d’améliorer l’extension du logiciel de programmation hors-ligne RobotStudio™ existante et de développer une nouvelle stratégie pour générer la trajectoire du robot par rapport aux paramètres essentiels de projection thermique. Notamment, l’historique de la température par rapport à la trajectoire générée est prise en compte dans cette étude.L’extension logicielle Thermal Spray Toolkit (TST) intégrée dans le cadre de RobotStudio™ est spécialement développée pour générer la trajectoire du robot en projection thermique. L’amélioration de l’extension TST dans la nouvelle version de RobotStudio™ est mise au point sur deux modules principaux :PathKit : génération de la trajectoire sur des pièces complexes.ProfileKit : modélisation du cordon singulier du dépôt et prédiction de son épaisseur en fonction des paramètres opératoires.Les déficiences existantes de l’extension TST impliquent de mettre en œuvre une méthode plus avancée qui permettra de générer la trajectoire du robot en utilisant le maillage pour le calcul d’élément finis. Ainsi, l’opération de projection thermique pourra être menée. Dans cette étude, la méthodologie de maillage est introduite afin de fournir une stratégie de choix de points de trajectoire et l’obtention d’orientations de ces points de trajectoire sur la surface à revêtir. Un module dit MeshKit est donc ajouté dans l’extension TST afin de lui apporter ces fonctionnalités nécessaires.Un couplage entre la trajectoire du robot et la répartition de chaleur du substrat a été développé, ce qui permet d’étudier l’évolution de température pendent le processus de projection thermique. / The objective of this study is to improve the add-in package of off-line programming software RobotStudio™ and to develop a new strategy for generating the robot trajectory according to the kinematic parameters of thermal spraying. The computed temperature evolution relative to the generated robot trajectory on the coating surface is also considered in this study.The add-in package Thermal Spray Toolkit (TST) integrated in RobotStudio™ is developed to generate the robot trajectory for thermal spraying. The improved TST for new version of RobotStudio™ is composed of two principle modules:PathKit: generation of robot trajectory on the free-form coating surface.ProfileKit: modeling the coating profile and prediction the coating thickness based on kinematic parameters.The existing deficiency of TST leads to the development of an advanced robot trajectory generation methodology. In this study, the new approach implements the robotic trajectory planning in an interactive manner between RobotStudio™ and the finite element analysis software (FES). It allows rearranging the imported node created on the surface of workpiece by FES and in turns generating the thermal spraying needed robot trajectories.A coupling between the robot trajectory and the heat distribution on the substrate has been developed, which allows analyzing the temperature evolution during the thermal spray process, it helps to minimize thermal variations on the substrate and to select the appropriate execution sequence of trajectory.

The work presented in this thesis aims to make contribution to the understanding and application of six-legged statically stable walking machines in both theoretical and practical levels. In this thesis five pieces of work, performed with and for the three-joint six-legged Robot-EA308, are presented: 1) Standard gaits, which include the well-known wave gaits, are defined and a stability analysis, in the sense of static stable walking, is performed on an analytical level. Various definitions are given / theorems are stated and proved. 2) A free gait generation algorithm with reinforcement learning is developed. Its facilities of stability improvement, smooth speed changes, and adaptation in case of a rear-leg deficiency with learning of five-legged walking are experimented in real-time on the Robot-EA308. 3) Trajectory optimization and controller design is performed for the protraction movement of a three-joint leg. The trajectory generated by the controller is demonstrated with the Robot-EA308. 4) The full kinematic-dynamic formulation of a three-joint six-legged robot is performed with the joint-torques being the primary variables. It is demonstrated that the proposed torque distribution scheme, rather than the conventional force distribution, results in an efficient distribution of required forces and moments to the supporting legs. 5) An analysis of energy efficiency is performed for wave gaits. The established strategies for determination of gait parameters for an efficient walk are justified using the Robot-EA308.

Traditionally, the design of complex aerospace systems requires iteration among segregated disciplines such as aerodynamic modeling and trajectory optimization. Multidisciplinary design optimization algorithms have been developed to efficiently orchestrate the interaction among these disciplines during the design process. For example, vehicle capability is generally obtained through sequential iteration among vehicle shape, aerodynamic performance, and trajectory optimization routines in which aerodynamic performance is obtained from large pre-computed tables that are a function of angle of attack, sideslip, and flight conditions. This numerical approach segregates advancements in vehicle shape design from advancements in trajectory optimization. This investigation advances the state-of-the-art in conceptual hypersonic aerodynamic analysis and trajectory optimization by removing the source of iteration between aerodynamic and trajectory analyses and capitalizing on fundamental linkages across hypersonic solutions. Analytic aerodynamic relations, like those derived in this investigation, are possible in any flow regime in which the flowfield can be accurately described analytically. These relations eliminate the large aerodynamic tables that contribute to the segregation of disciplinary advancements. Within the limits of Newtonian flow theory, many of the analytic expressions derived in this investigation provide exact solutions that eliminate the computational error of approximate methods widely used today while simultaneously improving computational performance. To address the mathematical limit of analytic solutions, additional relations are developed that fundamentally alter the manner in which Newtonian aerodynamics are calculated. The resulting aerodynamic expressions provide an analytic mapping of vehicle shape to trajectory performance. This analytic mapping collapses the traditional, segregated design environment into a single, unified, mathematical framework which enables fast, specialized trajectory optimization methods to be extended to also include vehicle shape. A rapid trajectory optimization methodology suitable for this new, mathematically integrated design environment is also developed by relying on the continuation of solutions found via indirect methods. Examples demonstrate that families of optimal hypersonic trajectories can be quickly constructed for varying trajectory parameters, vehicle shapes, atmospheric properties, and gravity models to support design space exploration, trade studies, and vehicle requirements definition. These results validate the hypothesis that many hypersonic trajectory solutions are connected through fast indirect optimization methods. The extension of this trajectory optimization methodology to include vehicle shape through the development of analytic hypersonic aerodynamic relations enables the construction of a unified mathematical framework to perform rapid, simultaneous hypersonic aerodynamic and trajectory optimization. Performance comparisons relative to state-of-the-art methodologies illustrate the computational advantages of this new, unified design environment.

The transportation sector has been identified as one of many sources of today's energetic and environmental problems. With constantly increasing numbers of vehicles on the road, non-renewable fossil fuels are becoming scarce and expensive. In addition, due to the pollutant emissions of internal combustion engines, the transportation sector is a major producer of greenhouse gas emissions. To resolve these problems researcher are looking for technological solutions, such as more efficient components and alternative drive train technologies, on one hand. On the other hand, work is being done to ensure the most efficient utilization of available technological resources. Eco driving is one way to immediately reduce a driver's energy consumption. In this thesis the potential gains of eco driving for passenger vehicles will be discussed. The main objective of this work is to, first, identify and compare drive train specific, optimal vehicle operation. Secondly, the effect of real-life constraints on potential gains of eco driving is evaluated. In addition, an approach to integrate mathematical optimization algorithms in an advanced driver assist system for eco driving is proposed. Physical vehicle models are developed for three representative vehicles: the conventional, electric and power-split hybrid vehicle. Using real-life and standard drive cycles a baseline mission is defined by specifying trip and road constraint. Applying the dynamic programming algorithms the trajectory optimization problem is solved, minimizing energy consumption for the trip. The effect of traffic on potential gains of eco driving is discussed, considering a vehicle following situation. Integrating emission constraints in the optimization algorithm the environmental advantages of eco driving are discussed. Finally, the developed algorithms were integrated in a driver assist system. Experimental tests on a driving simulator were used to verify the effectiveness of the system, as well as driver acceptance.

Persistent condensation trails are clouds, induced by the exhaust of an aircraft engine in a cold and ice-supersaturated environment. These artificial ice clouds can both cool and heat the atmosphere by scattering solar radiation and absorbing terrestrial radiation, respectively. The influence of condensation trails on the Earth-atmosphere energy balance and therewith the answer to the question of the dominating process had been mostly approximated on a global scale by treating the condensation trail as plane parallel layer with constant optical properties. Individual condensation trails and the influence of the solar angle had been analyzed, always using a course spatial grid and never under consideration of the aircraft performance, generating the condensation trail. For a trajectory optimization, highly precise results of the impact of condensation trails on the radiation budget and the influence of the aircraft performance on this impact is needed, so that future air traffic may consider the main factors of flight performance on the environmental impact of condensation trails. That’s why, a model is developed in this thesis to continuously estimate the scattering and absorption properties and their dependence on the aircraft performance.:1 Introduction 3 1.1 Motivation 3 1.2 State of the art 5 1.3 Approach 6 2 Theoretical background 9 2.1 The Earth’s atmosphere 9 2.1.1 The mean vertical structure of the atmosphere 12 2.1.2 Standard atmospheres 14 2.2 Radiation 15 2.2.1 Nature of radiation 15 2.2.2 Important metrics describing radiation 17 2.2.3 Relevant spectra and principles of radiation 19 2.2.4 Solar radiation 20 2.2.5 Terrestrial radiation 21 2.2.6 Radiative transfer and extinction 22 2.2.7 Radiative transfer equation 30 2.2.8 Energy budget of the Earth-atmosphere system 32 2.3 Thermodynamics 33 2.3.1 Atmospheric stability 33 2.3.2 Turbulence 36 2.3.3 Conditions of contrail formation 41 3 Development of a radiative forcing model 45 3.1 Model atmosphere 45 3.2 Flight performance model 46 3.3 Atmospheric radiative transfer model 49 3.3.1 Two Stream Approximation 51 3.3.2 Discrete ordinate radiative transfer solver 52 3.3.3 Methods to calculate broadband radiances and irradiances 53 3.4 Contrail life cycle model 57 3.4.1 Dissipation regime 58 3.4.2 Diffusion regime 63 3.5 Contrail radiative forcing model 74 3.5.1 Consideration of multiple scattering using a Monte Carlo simulation 74 3.5.2 Geometry of the Monte Carlo simulation 75 3.5.3 Interpretation of Beer’s law 76 3.5.4 Procedure of the Monte Carlo simulation 79 3.5.5 The extinguished power per unit length contrail 87 3.5.6 Scattering and absorption efficiencies Qs, Qa and asymmetry parameters gHG 89 3.5.7 Calibration of the Monte Carlo simulation 94 4 Calculations 99 4.1 Contrail properties 99 4.1.1 Conditions of contrail formation 100 4.1.2 Initial dimensions at the end of the dissipation regime 101 4.1.3 Microphysical properties during the diffusion regime 103 4.2 Radiative transport up to the contrail 105 4.2.1 Solar direct and diffuse radiance 106 4.2.2 Terrestrial irradiance 107 4.3 Scattering and absorption properties of radiation within the contrail 109 4.3.1 Monte Carlo simulation for solar radiation 109 4.3.2 Monte Carlo simulation for terrestrial irradiances 112 4.3.3 Relevance of multiple scattering 116 4.4 Radiative extinction 116 4.4.1 Solar zenith and azimuthal angle 118 4.4.2 Flightpath 120 4.4.3 Contrail evolution 122 4.4.4 Turbulence 126 4.4.5 Wavelength specific extinction 129 4.5 Terrestrial energy forcing of a contrail 133 4.6 Verification 135 5 Conclusion and outlook 141 5.1 Conclusion 141 5.2 Outlook 144 List of Figures 147 List of Tables 151 Abbreviations and Symbols 153 Glossary 161 Bibliography 169 Acknowledgements 183 / Langlebige Kondensstreifen sind Eiswolken, welche durch Kondensation von Wasserdampf an Rußpartikeln in einer eisübersättigten Atmosphäre entstehen. Der Wasserdampf entstammt einerseits aus dem Triebwerkabgas und andererseits aus der Atmosphäre. Kondensstreifen können die Atmosphäre durch Rückstreuung solarer Strahlung kühlen und durch Rückstreuung und Absorption terrestrischer Strahlung erwärmen. Der Einfluss von Kondensstreifen auf den Wärmehaushalt der Atmosphäre und damit die Antwort auf die Frage nach dem dominierenden Effekt wurde bisher zumeist auf globaler Ebene ermittelt, wobei der Kondensstreifen als planparallele Schicht mit konstanten optischen Eigenschaften angenähert wurde. Individuelle Kondensstreifen und der Einfluss des Sonnenstandes wurden bisher nur mithilfe eines groben Rasters betrachtet und niemals unter Berücksichtigung der Flugleistung des Luftfahrzeuges, welches den Kondensstreifen generiert hat. Für eine Trajektorienoptimierung sind jedoch präzise Berechnungen des Strahlungseinflusses und eine gewissenhafte Berücksichtigung der Flugleistung notwendig. Nur so kann der zukünftige Luftverkehr die Haupteinflussfaktoren der Flugeigenschaften auf den Strahlungseinfluss der Kondensstreifen berücksichtigen. Aus diesem Grund wurde in dieser Arbeit ein Modell entwickelt, welches die Eigenschaften des Strahlungstransfers durch den Kondensstreifen kontinuierlich bestimmt und die aus der Flugleistung resultierenden Parameter berücksichtigt.:1 Introduction 3 1.1 Motivation 3 1.2 State of the art 5 1.3 Approach 6 2 Theoretical background 9 2.1 The Earth’s atmosphere 9 2.1.1 The mean vertical structure of the atmosphere 12 2.1.2 Standard atmospheres 14 2.2 Radiation 15 2.2.1 Nature of radiation 15 2.2.2 Important metrics describing radiation 17 2.2.3 Relevant spectra and principles of radiation 19 2.2.4 Solar radiation 20 2.2.5 Terrestrial radiation 21 2.2.6 Radiative transfer and extinction 22 2.2.7 Radiative transfer equation 30 2.2.8 Energy budget of the Earth-atmosphere system 32 2.3 Thermodynamics 33 2.3.1 Atmospheric stability 33 2.3.2 Turbulence 36 2.3.3 Conditions of contrail formation 41 3 Development of a radiative forcing model 45 3.1 Model atmosphere 45 3.2 Flight performance model 46 3.3 Atmospheric radiative transfer model 49 3.3.1 Two Stream Approximation 51 3.3.2 Discrete ordinate radiative transfer solver 52 3.3.3 Methods to calculate broadband radiances and irradiances 53 3.4 Contrail life cycle model 57 3.4.1 Dissipation regime 58 3.4.2 Diffusion regime 63 3.5 Contrail radiative forcing model 74 3.5.1 Consideration of multiple scattering using a Monte Carlo simulation 74 3.5.2 Geometry of the Monte Carlo simulation 75 3.5.3 Interpretation of Beer’s law 76 3.5.4 Procedure of the Monte Carlo simulation 79 3.5.5 The extinguished power per unit length contrail 87 3.5.6 Scattering and absorption efficiencies Qs, Qa and asymmetry parameters gHG 89 3.5.7 Calibration of the Monte Carlo simulation 94 4 Calculations 99 4.1 Contrail properties 99 4.1.1 Conditions of contrail formation 100 4.1.2 Initial dimensions at the end of the dissipation regime 101 4.1.3 Microphysical properties during the diffusion regime 103 4.2 Radiative transport up to the contrail 105 4.2.1 Solar direct and diffuse radiance 106 4.2.2 Terrestrial irradiance 107 4.3 Scattering and absorption properties of radiation within the contrail 109 4.3.1 Monte Carlo simulation for solar radiation 109 4.3.2 Monte Carlo simulation for terrestrial irradiances 112 4.3.3 Relevance of multiple scattering 116 4.4 Radiative extinction 116 4.4.1 Solar zenith and azimuthal angle 118 4.4.2 Flightpath 120 4.4.3 Contrail evolution 122 4.4.4 Turbulence 126 4.4.5 Wavelength specific extinction 129 4.5 Terrestrial energy forcing of a contrail 133 4.6 Verification 135 5 Conclusion and outlook 141 5.1 Conclusion 141 5.2 Outlook 144 List of Figures 147 List of Tables 151 Abbreviations and Symbols 153 Glossary 161 Bibliography 169 Acknowledgements 183