Assessment of the feasible CTA windows for efficient spacing with energy-neutral CDO

Continuous descent operations (CDO) with con- trolled times of arrival (CTA) at one or several metering fixes could enable environmentally friendly procedures at the same time that terminal airspace capacity is not compromised. This paper focuses on CTA updates once the descent has been already initiated, assessing the feasible CTA window (and associated fuel consumption) of CDO requiring neither thrust nor speed-brake usage along the whole descent (i.e. energy modulation through elevator control is used to achieve different times of arrival at the metering fixes). A multiphase optimal control problem is formulated and solved by means of numerical methods. The minimum and maximum times of arrival at the initial approach fix (IAF) and final approach point (FAP) of an hypothetical scenario are computed for an Airbus A320 descent and starting from a wide range of initial conditions. Results show CTA windows up to 4 minutes at the IAF and 70 seconds at the FAP. It has been also found that the feasible CTA window is affected by many factors, such as a previous CTA or the position of the top of descent. Moreover, minimum fuel trajectories almost correspond to those trajectories that minimise the time of arrival at the metering fix for the given initial conditionPeer ReviewedPostprint (published version

Multi-objective optimisation of aircraft flight trajectories in the ATM and avionics context

The continuous increase of air transport demand worldwide and the push for a more economically viable and environmentally sustainable aviation are driving significant evolutions of aircraft, airspace and airport systems design and operations. Although extensive research has been performed on the optimisation of aircraft trajectories and very efficient algorithms were widely adopted for the optimisation of vertical flight profiles, it is only in the last few years that higher levels of automation were proposed for integrated flight planning and re-routing functionalities of innovative Communication Navigation and Surveillance/Air Traffic Management (CNS/ATM) and Avionics (CNS+A) systems. In this context, the implementation of additional environmental targets and of multiple operational constraints introduces the need to efficiently deal with multiple objectives as part of the trajectory optimisation algorithm. This article provides a comprehensive review of Multi-Objective Trajectory Optimisation (MOTO) techniques for transport aircraft flight operations, with a special focus on the recent advances introduced in the CNS+A research context. In the first section, a brief introduction is given, together with an overview of the main international research initiatives where this topic has been studied, and the problem statement is provided. The second section introduces the mathematical formulation and the third section reviews the numerical solution techniques, including discretisation and optimisation methods for the specific problem formulated. The fourth section summarises the strategies to articulate the preferences and to select optimal trajectories when multiple conflicting objectives are introduced. The fifth section introduces a number of models defining the optimality criteria and constraints typically adopted in MOTO studies, including fuel consumption, air pollutant and noise emissions, operational costs, condensation trails, airspace and airport operations

An integrated framework for trajectory optimisation, prediction and parameter estimation for advanced aircraft separation concepts

Since the birth of commercial aviation, the applications and benefits of aircraft have grown immensely. This, in perfect synchrony with the average increase of purchasing power of the society, has rocketed the number of aircraft flying the skies. This increase comes at a cost, both in environmental and airspace capacity aspects. This thesis works towards the alleviation of the issues caused by the high number of flights, proposing concepts and mechanisms to safely increase the airspace capacity whilst minimising the environmental impact of aviation. This incredibly complex and neverending pursuit is omnipresent in the literature. One promising topic is the four dimensional (4D) trajectory optimisation with higher levels of automation. The research in this PhD thesis proposes an integrated framework for trajectory optimisation, trajectory prediction and parameter estimation, with which new air traffic management concepts can be assessed. This framework has the flexibility to optimise trajectories ranging from a free-flight to a very strict route structure, from a complete freedom at the vertical profile to a specific adherence to flight levels, etc. The 4D optimisation strategy results in a trajectory that complies with the scenario characteristics, which minimises a given functional objective such as the operational cost, time, fuel, etc. Furthermore, the same framework is used in a novel strategy to perform adaptive trajectory prediction (with conformance monitoring), and to estimate unknown parameters of an aircraft. To resolve this problem, an optimal control problem is formulated and converted into a non-linear programming (NLP) problem with direct collocation methods, and numerically resolved by an NLP solver. A comprehensive software architecture is presented, taking benefit from the best of two worlds to enable the flexibility and genericity of the developed optimisation framework: an object-oriented software coding language (C++) and a very powerful algebraic modelling language (GAMS). Based on this optimisation framework, the thesis produces operationally relevant results, demonstrating that the framework can cope with a variety of problems, and contributing to the ultimate goal of safely increasing airspace capacity and air traffic efficiency. Illustrative examples are presented focussed on the departure phase within a terminal manoeuvring area. First, an assessment of the efficiency of required times of arrival as a ways to increase air traffic capacity is presented, providing results on the cost in terms of fuel and time of imposing these time requirements within a TMA (which can get to surprisingly low figures), and its effectiveness for traffic separation. Second, the implementation of an aircraft separation methodology is presented, where an intruder trajectory is predicted and the ownship calculates its own optimal trajectory that deviates from it. A conformance monitoring strategy is implemented to ensure that the separation is maintained throughout the flight, acknowledging deviations, and reacting accordingly. Third, the prediction of the intruder trajectory is enhanced by the estimation of an equivalent mass using known past states. An impressive accuracy is achieved early after the beginning of the flight. Finally, the implementation of a multi-aircraft separation strategy is presented, where multiple aircraft are simultaneously optimised in the same optimisation problem, all whilst maintaining separation between them. The complexity of the alignment of aircraft coordinates for a fair comparison is tackled from a novel perspective. Conclusively, the different strategies for aircraft separation are compared, and quite surprisingly the best results for each strategy are quite similar. Indeed, the increase in operational cost that the different strategies present (when compared to the individual optimal trajectory) is negligible and alledgedly better than the current air traffic control separation paradigm.Des del naixement de l’aviació comercial, les aplicacions i beneficis dels avions han crescut immensament. Això, en perfecta sincronia amb l’augment mitjà del poder adquisitiu de la societat, ha augmentat el nombre d’avions que volen pel cel. Aquest augment comporta, tanmateix, un cost, tant en aspectes mediambientals com en la capacitat de l’espai aeri. Aquesta tesi és concebuda per treballar en l’alleujament dels problemes que resulten de l’elevat nombre de vols, proposant nous conceptes i mecanismes per augmentar la capacitat de l’espai aeri amb seguretat i alhora minimitzar l’impacte ambiental de l’aviació. Aquesta recerca, complexa però extremadament necessària, és la protagonista d’una gran quantitat de treballs científics publicats. Des de la propulsió, fins a les aerostructures i la gestió del transit aeri, avui en dia es dedica un gran esforç a la reducció de l’impacte ambiental, així com a l’augment de la seguretat i la capacitat de l’espai aeri. Un tema prometedor és la introducció de nous conceptes d’operació que aprofiten al màxim l’optimització de trajectòries en les quatre dimensions (4D) i nivells d’automatització més elevats, tant per a sistemes de bord com de terra. Conceptes com ara operacions de perfil vertical continu són cada cop més utilitzats en el dia a dia. També, la reducció de la distancia recorreguda dels avions mitjançant rutes més directes esdevé una realitat com més va més evident. Per tal d’abastar un àmbit més ampli, els sistemes embarcats i de terra hauran d’esser actualitzats. És per això que s’hauria d’explorar minuciosament la quantificació dels beneficis esperats per als nou conceptes que es proposin, abans d’introduir-los a escala local o global. La investigació d’aquesta tesi doctoral proposa un sistema integrat per a l’optimització de trajectòries, la predicció, i l’estimació de paràmetres, amb el qual es poden avaluar nous conceptes de gestió del trànsit aeri. Aquest sistema té la flexibilitat d’optimitzar trajectòries que van des d’un vol lliure (free-flight) fins a una estructura de ruta molt estricta, des d’una llibertat completa al perfil vertical fins a una adhesió especifica als nivells de vol, etc. La definició d’escenaris és prou genèrica com per permetre una àmplia varietat de tipologies de vol, fases de vol, fases de rendiment, restriccions al llarg de la trajectòria, entre molts altres aspectes. L’estratègia d’optimització 4D d´ona com a resultat una trajectòria que no només compleix les característiques del vol (i de l’entorn configurat), sinó que també minimitza un objectiu funcional determinat, com ara el cost operatiu, el temps, el combustible, etc. I com ja s’ha mencionat breument, aquesta mateixa estratègia d’optimització s’adapta lleugerament per presentar una innovadora estratègia per realitzar prediccions de trajectòria adaptativa (amb monitoratge de conformitat) i per estimar paràmetres crucials inicialment desconeguts d’un avió. Per resoldre un problema tan complex, es formula un problema de control òptim i es converteix en un problema de programació no lineal (NLP) amb mètodes de col·locació directa. Aquest problema es resol numèricament mitjançant un programari de resolució de problemes NLP i se n’extreuen els resultats per a l’anàlisi. Es presenta una arquitectura de programari integral, aprofitant el millor de dos mons: un llenguatge de programació orientat a objectes (C++) i un llenguatge matemàtic algèbric molt potent (GAMS). La interacció entre aquests dos mons permet la flexibilitat i la genericitat del sistema d’optimització desenvolupat A partir d’aquest sistema d’optimització, els diferents capítols de la tesi produeixen resultats operatius rellevants. Això no només demostra que el sistema pot fer front a una gran varietat de problemes, sinó que també contribueix a l’objectiu final d’augmentar de forma segura la capacitat de l’espai aeri i l’eficiència del transit aeri. Es presenten diferents casos d’ ´ us i exemples il·lustratius centrats en enlairaments dins l’àrea de maniobra terminal (TMA). Concretament, quatre etapes formen aquesta part de la tesi. Primer, es presenta una avaluació de l’eficiència dels temps requerits d’arribada (RTA) com a forma d’augmentar la capacitat del transit aeri. Aquest estudi proporciona resultats sobre el cost en termes de combustible i temps d’imposar aquests requisits de temps dins d’una TMA (que pot arribar a xifres sorprenentment baixes). A més, mostra com d’efectiva pot ser aquesta estratègia per a la separació del transit. En segon lloc, es presenta la implementació d’una metodologia de separació d’avions mitjançant el sistema d’optimització. En ella, una aeronau (l’aeronau) genera una predicció de trajectòria d’un avio extern amb qui preveu tenir un conflicte proper (l’intrús). Seguidament, l’aeronau calcula la seva pròpia trajectòria òptima que es desvia d’aquella predita de l’intrús. S’implementa una estratègia de control de la conformitat per assegurar que la separació es mantingui durant tot el vol, reconeixent les desviacions i reaccionant en conseqüència. En tercer lloc, la predicció de la trajectòria intrusa es veu millorada per l’estimació d’una massa equivalent mitjançant estats passats coneguts (el deixant). Com era d’esperar, com més llarg sigui aquest deixant, millor serà l’estimació de la massa. Tanmateix, s’aconsegueix una precisió impressionant molt poc després de l’inici del vol. Finalment, es presenta la implementació d’una estratègia de separació de múltiples aeronaus. En aquesta formulació, s’optimitzen simultàniament les trajectòries de diversos avions dins el mateix problema d’optimització, mantenint la separació entre ells. La complexitat de l’alineació temporal de les coordenades d’avions per a una comparació justa s’aborda des d’una perspectiva innovadora. En conclusió, es comparen les diferents estratègies de separació d’avions i, sorprenentment, els millors resultats de cada estratègia són força similars. De fet, l’augment del cost operatiu que presenten les diferents estratègies (en comparació amb la trajectòria òptima individual) és insignificant i sempre millor que el paradigma actual de separació del control de trànsit aeri.Postprint (published version

4DT generator and guidance system

This thesis describes a 4D Trajectories Generator and Guidance system. 4D trajectory is a concept that will improve the capacity, efficiency and safety of airspace. First a 4D trajectories synthetizer design is proposed. A flight plan composed by a set of waypoints, aircraft dynamics model and a set of limits and constraints are assembled into an optimal control problem. Optimal solution is found by making use of an optimal control solver which uses pseudo spectral parametrization together with a generic nonlinear programming solver. A 4D Trajectories generator is implemented as a stand-alone application and combined with a graphic user interface to give rise to 4D Trajectories Research Software (4DT RS) capable to generate, compare and test optimal trajectories. A basic Tracking & Guidance system with proportional navigation concept is developed. The system is implemented as a complementary module for the 4D trajectories research software. Simulation tests have been carried out to demonstrate the functionalities and capabilities of the 4DT RS software and guidance system. Tests cases are based on fuel and time optimization on a high-traffic commercial route. A standard departure procedure is optimized in order to reduce the noise perceived by village’s population situated near airport. The tracking & guidance module is tested with a commercial flight simulator for demonstrating the performance of the optimal trajectories generated by the 4DT RS software

Spline parameterization based nonlinear trajectory optimization along 4D waypoints

Flight trajectory optimization has become an important factor not only to reduce the operational costs (e.g.,, fuel and time related costs) of the airliners but also to reduce the environmental impact (e.g.,, emissions, contrails and noise etc.) caused by the airliners. So far, these factors have been dealt with in the context of 2D and 3D trajectory optimization, which are no longer efficient. Presently, the 4D trajectory optimization is required in order to cope with the current air traffic management (ATM). This study deals with a cubic spline approximation method for solving 4D trajectory optimization problem (TOP). The state vector, its time derivative and control vector are parameterized using cubic spline interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into nonlinear programming problem (NLP). The proposed method is successfully applied to the generation of a minimum length optimal trajectories along 4D waypoints, where the method generated smooth 4D optimal trajectories with very accurate results.info:eu-repo/semantics/publishedVersio

Development of a battery of tests for a numerical optimal control library

One of the two objectives of this bachelor thesis is the development of a set of problems to be solved with an optimal control numerical method and evaluate the obtained results. The problems to be solved have been selected from the literature, which from now on are going to be named ’canonical problems’. These problems are used by authors in the field of optimal control in order to compare their results between them and assess the strength of the optimization method they are using. The second objective of this thesis is the development of four problems, related with climb, cruise and descend performance of a general twin turbofan airliner, applying the numerical method in question, and evaluating the results. This is then a manner to apply optimal control into more common problems in the aerospace field.Ingeniería Aeroespacia

Robust aircraft trajectory optimization under meteorological uncertainty

Mención Internacional en el título de doctorThe Air Traffic Management (ATM) system in the busiest airspaces in the world is currently being overhauled to deal with multiple capacity, socioeconomic, and environmental challenges. One major pillar of this process is the shift towards a concept of operations centered on aircraft trajectories (called Trajectory-Based Operations or TBO in Europe) instead of rigid airspace structures. However, its successful implementation (and, thus, the realization of the associated improvements in ATM performance) rests on appropriate understanding and management of uncertainty. Due to its complex socio-technical structure, the design and operations of the ATM system are heavily impacted by uncertainty, proceeding from multiple sources and propagating through the interconnections between its subsystems. One major source of ATM uncertainty is weather. Due to its nonlinear and chaotic nature, a number of meteorological phenomena of interest cannot be forecasted with complete accuracy at arbitrary lead times, which leads to uncertainty or disruption in individual air and ground operations that propagates to all ATM processes. Therefore, in order to achieve the goals of SESAR and similar programs, it is necessary to deal with meteorological uncertainty at multiple scales, from the trajectory prediction and planning processes to flow and traffic management operations. This thesis addresses the problem of single-aircraft flight planning considering two important sources of meteorological uncertainty: wind prediction error and convective activity. As the actual wind field deviates from its forecast, the actual trajectory will diverge in time from the planned trajectory, generating uncertainty in arrival times, sector entry and exit times, and fuel burn. Convective activity also impacts trajectory predictability, as it leads pilots to deviate from their planned route, creating challenging situations for controllers. In this work, we aim to develop algorithms and methods for aircraft trajectory optimization that are able to integrate information about the uncertainty in these meteorological phenomena into the flight planning process at both pre-tactical (before departure) and tactical horizons (while the aircraft is airborne), in order to generate more efficient and predictable trajectories. To that end, we frame flight planning as an optimal control problem, modeling the motion of the aircraft with a point-mass model and the BADA performance model. Optimal control methods represent a flexible and general approach that has a long history of success in the aerospace field. As a numerical scheme, we use direct methods, which can deal with nonlinear systems of moderate and high-dimensional state spaces in a computationally manageable way. Nevertheless, while this framework is well-developed in the context of deterministic problems, the techniques for the solution of practical optimal control problems under uncertainty are not as mature, and the methods proposed in the literature are not applicable to the flight planning problem as it is now understood. The first contribution of this thesis addresses this challenge by introducing a framework for the solution of general nonlinear optimal control problems under parametric uncertainty. It is based on an ensemble trajectory scheme, where the trajectories of the system under multiple scenarios are considered simultaneously within the same dynamical system and the uncertain optimal control problem is turned into a large conventional optimal control problem that can be then solved by standard, well-studied direct methods in optimal control. We then employ this approach to solve the robust flight plan optimization problem at the planning horizon. In order to model uncertainty in the wind and estimating the probability of convective conditions, we employ Ensemble Prediction System (EPS) forecasts, which are composed by multiple predictions instead of a single deterministic one. The resulting method can be used to optimize flight plans for maximum expected efficiency according to the cost structure of the airline; additionally, predictability and exposure to convection can be incorporated as additional objectives. The inherent tradeoffs between these objectives can be assessed with this methodology. The second part of this thesis presents a solution for the rerouting of aircraft in uncertain convective weather scenarios at the tactical horizon. The uncertain motion of convective weather cells is represented with a stochastic model that has been developed from the output of a deterministic satellite-based nowcast product, Rapidly Developing Thunderstorms (RDT). A numerical optimal control framework, based on the pointmass model with the addition of turn dynamics, is employed for optimizing efficiency and predictability of the proposed trajectories in the presence of uncertainty about the future evolution of the storm. Finally, the optimization process is initialized by a randomized heuristic procedure that generates multiple starting points. The combined framework is able to explore and as exploit the space of solution trajectories in order to provide the pilot or the air traffic controller with a set of different suggested avoidance trajectories, as well as information about their expected cost and risk. The proposed methods are tested on example scenarios based on real data, showing how different user priorities lead to different flight plans and what tradeoffs are then present. These examples demonstrate that the solutions described in this thesis are adequate for the problems that have been formulated. In this way, the flight planning process can be enhanced to increase the efficiency and predictability of individual aircraft trajectories, which would lead to higher predictability levels of the ATM system and thus improvements in multiple performance indicators.El sistema de gestión del tráfico aéreo (Air Traffic Management, ATM) en los espacios aéreos más congestionados del mundo está siendo reformado para lidiar con múltiples desafíos socioeconómicos, medioambientales y de capacidad. Un pilar de este proceso es el gradual reemplazo de las estructuras rígidas de navegación, basadas en aerovías y waypoints, hacia las operaciones basadas en trayectorias. No obstante, la implementación exitosa de este concepto y la realización de las ganancias esperadas en rendimiento ATM requiere entender y gestionar apropiadamente la incertidumbre. Debido a su compleja estructura socio-técnica, el diseño y operaciones del sistema ATM se encuentran marcadamente influidos por la incertidumbre, que procede de múltiples fuentes y se propaga por las interacciones entre subsistemas y operadores humanos. Uno de los principales focos de incertidumbre en ATM es la meteorología. Debido a su naturaleza no-linear y caótica, muchos fenómenos de interés no pueden ser pronosticados con completa precisión en cualquier horizonte temporal, lo que crea disrupción en las operaciones en aire y tierra que se propaga a otros procesos de ATM. Por lo tanto, para lograr los objetivos de SESAR e iniciativas análogas, es imprescindible tener en cuenta la incertidumbre en múltiples escalas espaciotemporales, desde la predicción de trayectorias hasta la planificación de flujos y tráfico. Esta tesis aborda el problema de la planificación de vuelo de aeronaves individuales considerando dos fuentes importantes de incertidumbre meteorológica: el error en la predicción del viento y la actividad convectiva. Conforme la realización del viento se desvía de su previsión, la trayectoria real se desviará temporalmente de la planificada, lo que implica incertidumbre en tiempos de llegada a sectores y aeropuertos y en consumo de combustible. La actividad convectiva también tiene un impacto en la predictibilidad de las trayectorias, puesto que obliga a los pilotos a desviarse de sus planes de vuelo para evitarla, cambiado así la situación de tráfico. En este trabajo, buscamos desarrollar métodos y algoritmos para la optimización de trayectorias que puedan integrar información sobre la incertidumbre en estos fenómenos meteorológicos en el proceso de diseño de planes de vuelo en horizontes de planificación (antes del despegue) y tácticos (durante el vuelo), con el objetivo de generar trayectorias más eficientes y predecibles. Con este fin, formulamos la planificación de vuelo como un problema de control óptimo, modelando la dinámica del avión con un modelo de masa puntual y el modelo de rendimiento BADA. El control óptimo es un marco flexible y general con un largo historial de éxito en el campo de la ingeniería aeroespacial. Como método numérico, empleamos métodos directos, que son capaces de manejar sistemas dinámicos de alta dimensión con costes computacionales moderados. No obstante, si bien esta metodología es madura en contextos deterministas, la solución de problemas prácticas de control óptimo bajo incertidumbre en la literatura no está tan desarrollada, y los métodos propuestos en la literatura no son aplicables al problema de interés. La primera contribución de esta tesis hace frente a este reto mediante la introducción de un marco numérico para la resolución de problemas generales de control óptimo no-lineal bajo incertidumbre paramétrica. El núcleo de este método es un esquema de conjunto de trayectorias, en el que las trayectorias del sistema dinámico bajo múltiples escenarios son consideradas de forma simultánea, y el problema de control óptimo bajo incertidumbre es así transformado en un problema convencional que puede ser tratado mediante métodos existentes en control óptimo. A continuación, empleamos este método para resolver el problema de la planificación de vuelo robusta. La incertidumbre en el viento y la probabilidad de ocurrencia de condiciones convectivas son modeladas mediante el uso de previsiones de conjunto o ensemble, compuestas por múltiples predicciones en lugar de una única previsión determinista. Este método puede ser empleado para maximizar la eficiencia esperada de los planes de vuelo de acuerdo a la estructura de costes de la aerolínea; además, la predictibilidad de la trayectoria y la exposición a la convección pueden ser incorporadas como objetivos adicionales. El trade-off entre estos objetivos puede ser evaluado mediante la metodología propuesta. La segunda parte de la tesis presenta una solución para reconducir aviones en escenarios tormentosos en un horizonte táctico. La evolución de las células convectivas es representada con un modelo estocástico basado en las proyecciones de Rapidly Developing Thunderstorms (RDT), un sistema determinista basado en imágenes de satélite. Este modelo es empleado por un método de control óptimo numérico, basado en un modelo de masa puntual en el que se modela la dinámica de viraje, con el objetivo de maximizar la eficiencia y predictibilidad de la trayectoria en presencia de incertidumbre sobre la evolución futura de las tormentas. Finalmente, el proceso de optimizatión es inicializado por un método heurístico aleatorizado que genera múltiples puntos de inicio para las iteraciones del optimizador. Esta combinación permite explorar y explotar el espacio de trayectorias solución para proporcionar al piloto o al controlador un conjunto de trayectorias propuestas, así como información útil sobre su coste y el riesgo asociado. Los métodos propuestos son probados en escenarios de ejemplo basados en datos reales, ilustrando las diferentes opciones disponibles de acuerdo a las prioridades del planificador y demostrando que las soluciones descritas en esta tesis son adecuadas para los problemas que se han formulado. De este modo, es posible enriquecer el proceso de planificación de vuelo para incrementar la eficiencia y predictibilidad de las trayectorias individuales, lo que contribuiría a mejoras en el rendimiento del sistema ATM.These works have been financially supported by Universidad Carlos III de Madrid through a PIF scholarship; by Eurocontrol, through the HALA! Research Network grant 10-220210-C2; by the Spanish Ministry of Economy and Competitiveness (MINECO)'s R&D program, through the OptMet project (TRA2014-58413-C2-2-R); and by the European Commission's SESAR Horizon 2020 program, through the TBO-Met project (grant number 699294).Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira iPresidente: Damián Rivas Rivas.- Secretario: Xavier Prats Menéndez.- Vocal: Benavar Sridha

On the generation of environmentally efficient flight trajectories

To achieve a sustainable future for air transport, the International Civil Aviation Organization has proposed goals for reductions in community noise impact, local air quality and climate impacting emissions. The goals are intended to be achieved through advances in engine design, aircraft design and through improvements in aircraft operational procedures. This thesis focuses on operational procedures, and considers how trajectory generation methods can be used to support flight and airspace planners in the planning and delivery of environmentally efficient flight operations. The problem of planning environmentally efficient trajectories is treated as an optimal control problem that is solved through the application of a direct method of trajectory optimisation combined with a stochastic Non Linear Programming (NLP) solver. Solving the problem in this manner allows decision makers to explore the relationships between how aircraft are operated and the consequent environmental impacts of the flights. In particular, this thesis describes a multi-objective optimisation methodology intended to support the planning of environmentally efficient climb and descent procedures. The method combines environmental, trajectory and NLP methods to generate Pareto fronts between several competing objectives. It is shown how Pareto front information can then be used to allow decision makers to make informed decisions about potential tradeoffs between different environmental goals. The method is demonstrated through its application to a number of real world, many objective procedure optimisation studies. The method is shown to support in depth analysis of the case study problems and was used to identify best balance procedure characteristics and procedures in an objective, data driven approach not achievable through existing methods. Driven by operator specific goals to reduce CO2 emissions, work in this thesis also looks at trajectory based flight planning of CO2 efficient trajectories. The results are used to better understand the impacts of ATM constraints and recommended procedures on both the energy management and fuel efficiency of flights. Further to this, it is shown how trajectory optimisation methods can be applied to the analysis of conventional assumptions on fuel efficient aircraft operations. While the work within is intended to be directly relevant to the current air traffic management system, both consideration and discussion is given over to the evolution and continued relevance of the work to the Single European Sky trajectory based concept of operation

Probabilistic trajectory generation using uncertainty propagation model

This document establishes the basis for the work to be developed within Work Package 2 of the START project. The objective of this Work Package is to build a methodology that could allow for the obtainment of the probabilistic trajectories that would result from the propagation of the characterized micro-level uncertainties in the aircraft trajectory prediction process. This deliverable will be focused on implementing the models and processes required to capture the influence of the uncertainties that are present in the development of an aircraft trajectory. To this end, we will show how to propagate these uncertainties, using a stochastic trajectory predictor, that will allow us to obtain a set of probabilistic trajectories from an initial deterministic flight plan, which will encapsulate the effect of the inputs’ variability. First, an introduction to Polynomial Chaos Theory, which is the basis of the stochastic trajectory predictor developed in START, and our solution for introducing weather uncertainty into the trajectory prediction process will be exposed. Then, it will be presented how the integration of the advanced data assimilation models, introduced in the deliverable D2.1 [2], together with the stochastic trajectory predictor will lead to more robust airline operations. Additionally, the framework for the probabilistic trajectory generation will be introduced, showing how all different modules will be employed in START in a two-phase approach (first an off-line fitting phase to obtain the models for uncertainty propagation, and then an online phase where, making use of the fitted model, the probabilistic trajectories can be obtained from a deterministic flight plan). Finally, a study case will be presented, showing the application of the previously defined methodology to a specific scenario.Preprin