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This paper describes an optimization algorithm that provides an economical Vertical Navigation profile planning by finding the combinations of climb, cruise and descent speeds, as well as the altitudes for an aircraft to minimize flight costs. The computational algorithm profits from a space search reduction algorithm to reduce the initial number o...
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... stated above, interpolations are done for temperatures (ISA DEV) followed by interpolations in aircraft weight as shown in Figure 1. The word "limit" in Figure 1 refers to the interpolation discrete value taken from the PDB that contains the desired value to interpolate. The desired outputs are normally the fuel consumption and the horizontal traveled distance, for climb and descent phases. Fuel burned is reduced from the total weight every 1,000 ft to improve calculations accuracy during climb and descent phases. For the cruise phase, only fuel flow is obtained from the PDB. During this flight phase fuel burned is reduced from aircraft weight every 25 nautical miles to improve computation accuracy. During cruise phase, the algorithm evaluates if performing step climbs could help reducing flight ...
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... stated above, interpolations are done for temperatures (ISA DEV) followed by interpolations in aircraft weight as shown in Figure 1. The word "limit" in Figure 1 refers to the interpolation discrete value taken from the PDB that contains the desired value to interpolate. The desired outputs are normally the fuel consumption and the horizontal traveled distance, for climb and descent phases. Fuel burned is reduced from the total weight every 1,000 ft to improve calculations accuracy during climb and descent phases. For the cruise phase, only fuel flow is obtained from the PDB. During this flight phase fuel burned is reduced from aircraft weight every 25 nautical miles to improve computation accuracy. During cruise phase, the algorithm evaluates if performing step climbs could help reducing flight ...
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... perform the trajectory optimization evaluation, a flight was selected one of the flight trajectories presented in the last Sub- Section which was the YUL -YVR flight. The YUL -YVR flight trajectory was optimized for different CI using the algorithm described in this paper. The same flight using the same conditions was optimized using the commercial FMS. The solution of the trajectories delivered by the new algorithm and the FMS were computed, and the cost differences are shown in Figure 10. As seen in all cases, the solution provided by the optimization algorithm developed in this paper was better than the solution provided by the commercial FMS of reference. This is due to a better selection of speeds and altitudes by the new ...
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Citations
... Fuel costs have become an increasingly important component of airline operating costs in recent years. There are a variety of techniques that can be used to control fuel consumption, among which flight trajectory optimization has the advantages of short time and low cost [1]. The objective function of the flight trajectory problem is complex and involves the processing of a large number of different information. ...
To reduce the cost of a flight, a calculation method is proposed in this paper, which takes the shortest distance as the goal and avoids the obstacle zone, and controls the turning angle as a constraint. Firstly, the Maklink diagram is used to build the obstacle zone model and establish the relationship between the obstacle zones. Then Dijkstra algorithm is used to construct the initial flight path to form a suboptimal path. Then the genetic ant colony algorithm is used to optimize the obtained suboptimal path. When there is a conflict risk between the two planned paths, the flight altitude of the aircraft on one path is adjusted, and the constraints are checked to form the optimal path. The simulation results show that the method can realize flight path optimization and verify the feasibility of the method.
... Many aerial control tasks are processed by avionics systems. Such tasks might include aircraft trajectory optimization [2] and its application into flight management systems [3], which aim to reduce operational costs [4], fuel consumption, and adverse environmental side effects [5]. A variety of algorithms, such as genetic algorithm (GA) [6], particle swarm optimization (PSO) [7], ant colony [8], bee colony [9], beam search [10], and harmony search [11] have been employed to solve aircraft trajectory optimization problems. ...
Two main factors, including regression accuracy and adversarial attack robustness, of six trajectory prediction models are measured in this paper using the traffic flow management system (TFMS) public dataset of fixed-wing aircraft trajectories in a specific route provided by the Federal Aviation Administration. Six data-driven regressors with their desired architectures, from basic conventional to advanced deep learning, are explored in terms of the accuracy and reliability of their predicted trajectories. The main contribution of the paper is that the existence of adversarial samples was characterized for an aircraft trajectory problem, which is recast as a regression task in this paper. In other words, although data-driven algorithms are currently the best regressors, it is shown that they can be attacked by adversarial samples. Adversarial samples are similar to training samples; however, they can cause finely trained regressors to make incorrect predictions, which poses a security concern for learning-based trajectory prediction algorithms. It is shown that although deep-learning-based algorithms (e.g., long short-term memory (LSTM)) have higher regression accuracy with respect to conventional classifiers (e.g., support vector regression (SVR)), they are more sensitive to crafted states, which can be carefully manipulated even to redirect their predicted states towards incorrect states. This fact poses a real security issue for aircraft as adversarial attacks can result in intentional and purposely designed collisions of built-in systems that can include any type of learning-based trajectory predictor.
... Using hybrid optimal control, Franco and Rivas [39] optimized the trajectory by taking into account different phases of flight such as climb, cruise and descent over a pre-defined ground track. Murrieta et al. [40,41] used a beam search algorithm to find the optimal trajectory by taking also into account climb, cruise and descent phases. ...
Aircrafts require a large amount of fuel in order to generate enough power to perform a flight. That consumption causes the emission of polluting particles such as carbon dioxide, which is implicated in global warming. This paper proposes an algorithm which can provide the 3D reference trajectory that minimizes the flight costs and the fuel consumption. The proposed algorithm was conceived using the Floyd–Warshall methodology as a reference. Weather was taken into account by using forecasts provided by Weather Canada. The search space was modeled as a directional weighted graph. Fuel burn was computed using the Base of Aircraft DAta (BADA) model developed by Eurocontrol. The trajectories delivered by the developed algorithm were compared to long-haul flight plans computed by a European airliner and to as-flown trajectories obtained from Flightradar24®. The results reveal that up to 2000 kg of fuel can be reduced per flight, and flight time can be also reduced by up to 11 min.
... The vertical reference trajectory for all flight phases has been optimized by using the Golden Search Section algorithm and step climbs [24], search space reduction algorithms [25,26], flight cost estimators [27], and the beam search algorithm [28]. The latter two algorithms have been coupled to reduce the computation time [29]. The vertical and the lateral reference trajectories have been optimized by determining the optimal ground track and then finding the most economical waypoints to execute step climbs [30]. ...
... Reference source not found.. While the algorithms mentioned above allow for execution of the "step climb" function, they mostly rely on different strategies, such as distance [47], flight time [29], or a pre-computed weight-altitude relationship [46]. Another strategy is to evaluate each waypoint to determine if at that waypoint it is worthwhile to perform the step climb. ...
Aircraft require significant quantities of fuel in order to generate the power required to sustain a flight. Burning this fuel causes the release of polluting particles to the atmosphere and constitutes a direct cost attributed to fuel consumption. The optimization of various aircraft operations in different flight phases such as cruise and descent, as well as terminal area movements, have been identified as a way to reduce fuel requirements, thus reducing pollution. The goal of this chapter is to briefly explain and apply different metaheuristic optimization algorithms to improve the cruise flight phase cost in terms of fuel burn. Another goal is to present an overview of the most popular commercial aircraft models. The algorithms implemented for different optimization strategies are genetic algorithms, the artificial bee colony, and the ant colony algorithm. The fuel burn aircraft model used here is in the form of a Performance Database. A methodology to create this model using a Level D aircraft research flight simulator is briefly explained. Weather plays an important role in flight optimization, and so this work explains a method for incorporating open source weather. The results obtained for the optimization algorithms show that every optimization algorithm was able to reduce the flight consumption, thereby reducing the pollution emissions and contributing to airlines’ profit margins.
... Reducing the search space to find the optimal trajectory was explored in [45,46] and very good results were obtained. A Branch and Bound variation was also used to reduce the search space and find the optimal trajectory [47,48]. The Golden Section Search algorithm in short flights, and step climbs in long flights were implemented in [49]. ...
Fuel burn releases polluting particles to the atmosphere. Aeronautical operations have been estimated as being responsible for 2% of the total amount of carbon dioxide liberated to the atmosphere each year. Fuel is also one of the major expenses for airlines. Reducing the amount of fuel required to power flights brings benefits to both the environmental and economic aspects of the aeronautical industry. This paper aims to develop a new optimization algorithm that computes fuel-efficient aircraft reference trajectories inspired by the artificial bee’s colony and based on a numerical performance model. The flight trajectory is optimized in terms of speeds, altitudes, and geographical positions, while respecting the required time of arrival constraint. The optimal trajectory is composed of waypoints placed in each of the available dimensions (coordinates, altitudes, and speeds). Winds and temperatures are taken into account. These trajectories will be improved by taking all of the dimensions into consideration simultaneously, instead of improving them one after the other. Results have shown that, when flying under the free-flight concept and fulfilling the required time of arrival constraint, the algorithm saved around 5% of the fuel burn with respect to as-flown flights.
... An algorithm based on branch & bound was developed in [23] to compute the vertical reference trajectory for a complete flight. Search space reduction techniques and a branch and bound approximation were developed in [24] to reduce the computation time while providing good reference trajectories. Genetic Algorithms were implemented for the same purpose in [25], and later used to find the most convenient waypoints at which to execute the step-climbs or step-descents were executed [26]. ...
A methodology of aircraft reference trajectory optimization inspired by the ant colony optimization is used in this paper to find the most efficient trajectory in terms of fuel burn and flight cost during the cruise phase. Weather conditions are taken into account in computing the most economical trajectory. The algorithm is designed in two consecutive stages. First, the reference trajectory is optimized in three dimensions. Then, the most economical combination of Mach numbers that fulfills the required time of arrival constraint over that three-dimensional trajectory is found, creating a four-dimensional reference trajectory. Different simulation tests consisted of trajectories following a fixed altitude geodesic trajectory, as well as of real as-flown flights. Simulations revealed that the ant colony algorithm was able to find the most efficient trajectory and the flight cost was 6.82% more economical than the geodesic reference trajectory. Moreover, tests showed that the ant colony algorithm was able to find a four-dimensional trajectory close to the real flight plan trajectory, providing an optimization average of 0.91%. Studies showed that making a three-dimensional trajectory fulfilling the required time of arrival constraint led to an important loss of 2.4% of optimization due to the Mach number changes.
... Algorithms aiming to reduce the search space to improve the aircraft's convergence as in [17]. Beam search, a variation of branch and cut, was suggested in [18], and it was later improved to reduce the computation time [19] finding the global optimal solution. An algorithm able to find the optimal altitude for a fixed altitude cruise and a fuel burn estimator was studied in [20]. ...
The consumption of fossil fuels in order to power flights leads to undesirable pollution particles to be released to the atmosphere. Fuel also represents an important expense for airlines. For these reasons, it is of interest to reduce fuel burn for a given flight. In this article, the altitudes followed by a commercial aircraft during the cruise phase of a flight, also called vertical reference trajectory, were optimized in terms of fuel burn. The airspace was modelled under the form of a unidirectional graph. Fuel burn was computed using a numerical performance model. The weather forecast was obtained from the model delivered by Environment Canada. The selection of waypoints where to execute the changes in altitudes that provided the most economical flight cost in terms of fuel burn was determined using the particle swarm optimisation (PSO) algorithm. The trajectories provided by the algorithm developed in this paper were compared against simple geodesic trajectories to validate its optimization potential, and against as flown trajectories. Results have showed that up to 6.5% of fuel burn can be saved comparing against simple trajectories, and up to 3.1% was optimized comparing against as flown trajectories.
... Due to the high number of solutions available, to solve the vertical reference trajectory, more common methodologies such as branch and cut (Murrieta- Mendoza and Botez, 2015) and genetic algorithms (Felix Patron et al., 2013) have been explored. ...
Cruise is normally the longest and most expensive phase in a long-haul flight. Taking advantage of winds to reduce flight time using a constant mach number is of real interest to the aeronautical industry. Reducing flight time will reduce time related costs, help passengers to catch their connections, and reduce fuel consumption. Saving fuel also leads to fewer polluting emissions released to the atmosphere. The “free-flight” concept is adopted here, with the search space area modeled as a graph in which the weather information at each vertex is obtained from predictions from Environment Canada. The Floyd-Warshall optimization algorithm was implemented to allow the flight reference trajectory optimization to have automatic decision making capacities to deliver the shortest path trajectory between departure and destination airports. Simulations showed that flight time savings as high as 19 minutes could be obtained, representing (roughly estimated) a savings of 1.2 tons of fuel.
... In (Sidibe and Botez, 2013) dynamic programming was implemented to optimize the speeds and altitudes while executing stepclimbs . A branch and cut variation coupled with a search space reduction algorithm was developed in (Mendoza and Botez, 2015a). The lateral reference trajectory has been optimized using the A* algorithm while avoiding objects (Dicheva and Bestaoui, 2014). ...
Fuel required to power flights releases polluting particles such as carbon dioxide (CO 2) and Nitrogen Oxides (NOx). Reducing the fuel consumption to power a given flight brings as a consequence a reduction of the pollution released to the atmosphere and a reduction in flight costs. Trajectory optimization has been seen as an alternative to reduce fuel consumption by guiding aircraft to zones where they can have a better performance in terms of fuel consumption. In this paper, the Dijkstra's algorithm was implemented to identify the waypoints where to perform the change of altitudes to reduce the fuel consumption taking into account the aircraft performance and weather conditions. The aircraft performance was obtained from a numerical database obtained from experimental flight test data and the weather information was obtained from the forecast provided by Weather Canada. The deterministic Dijkstra's algorithm was selected because the methodology developed in this paper is aimed to be loaded in a Flight Management System. The search space was modeled as a graph in 2 dimensions: altitude and distance. Simulations results comparing different trajectories have shown savings of over 4.33 % in a flight such as Vancouver to Madrid.
... In (Sidibe and Botez, 2013) dynamic programming was implemented to optimize the speeds and altitudes while executing stepclimbs. A branch and cut variation coupled with a search space reduction algorithm was developed in (Murrieta- Mendoza and Botez, 2015a). ...
Fuel required to power flights releases polluting particles such as carbon dioxide (CO 2) and Nitrogen Oxides (NOx). Reducing the fuel consumption to power a given flight brings as a consequence a reduction of the pollution released to the atmosphere and a reduction in flight costs. Trajectory optimization has been seen as an alternative to reduce fuel consumption by guiding aircraft to zones where they can have a better performance in terms of fuel consumption. In this paper, the Dijkstra's algorithm was implemented to identify the waypoints where to perform the change of altitudes to reduce the fuel consumption taking into account the aircraft performance and weather conditions. The aircraft performance was obtained from a numerical database obtained from experimental flight test data and the weather information was obtained from the forecast provided by Weather Canada. The deterministic Dijkstra's algorithm was selected because the methodology developed in this paper is aimed to be loaded in a Flight Management System. The search space was modeled as a graph in 2 dimensions: altitude and distance. Simulations results comparing different trajectories have shown savings of over 4.33 % in a flight such as Vancouver to Madrid.
