Flight Altitude Optimization Using Genetic Algorithms ...

Flight Altitude Optimization Using Genetic Algorithms Considering Climb and Descent Costs in Cruise with Flight Plan Information Alejandro Murrieta-Mendoza, Roberto S. Felix-Patron, Ruxandra Mihaela Botez Université du Québec – École de Technologie Supérieure - LARCASE Abstract Flight trajectory optimization algorithms reduce flight cost and fuel consumption, and therefore they diminish the polluting emissions released to the atmosphere. Ground teams and avionics equipment such as the Flight Management System evaluate different routes to minimize flight costs. The optimal trajectory represents the flight plan given to the crew. The resulting flight plan contains waypoints and weather information such as wind and temperature for each waypoint. The flight plan is normally introduced manually into the Flight Management System. In this paper, genetic algorithms were applied to the waypoints available in a flight plan to find the altitudes that minimize total fuel consumption, taking into account the cruise-climb and cruise-descent steps costs. The genetic algorithms consist of emulating the evolution process through a predefined number of generations. Here, an individual is defined as a set of altitudes, whose fitness depends on its ability to improve the flight cost. The most-fitted individuals are selected to reproduce and create a new generation of individuals. As new generations are created, the fitness of the individuals improves and therefore an optimal set of altitudes to reduce the flight cost is found. Aircraft fuel consumption in this algorithm was computed using a Performance Database, which was developed and validated by our industrial partner using experimental flight data. This differs from the Equations of Motion commonly used in the literature. Preliminary results showed n that the set of altitudes provided by the genetic algorithm improves the flight cost. This fuel reduction positively impacts the level of polluting emissions.

Definitions/Abbreviations Altitude

A given altitude for a waypoint.

ATM

Air Traffic Management

CDA/CDO

Continuous Descent Approach/Operations

CI

Cost Index

CLB Segment

Cost of a climb segment during cruise.

CO2

Carbon dioxide

CR Segment

Cost of a given cruise segment

DES Segment

Cost of a given descent segment during cruise.

EoM

Equations of Motion 1

FMS

Flight Management System

G

A given graph. The space grid.

Individual

A complete trajectory from ToC to ToD

LNAV

Lateral Navigation

NOx

Nitrogen Oxides

P

Path: Segment of edges between two different points.

PDB

Performance Database

RNAV

Area Navigation

RTA

Required Time of Arrival

sons

Vector defining the offspring between two individuals

ToC

Top of Climb

ToD

Top of Descent

TRL

Technical Readiness Level

V

Vertices. Nodes. The waypoints

W*

Edges weight. Cost between two waypoints.

WPT

Waypoint (Name, Altitude)

Introduction Many polluting particles such as Carbon dioxide (CO 2), Nitrogen Oxides (NOx) and hydrocarbons, among others, are released to the atmosphere due to fuel burn. CO2 is of special global concern due to its known effect on global warming. The CO2 released to the atmosphere by the aeronautical industry is estimated to be around 2 % of the total global share [1]. Flying is the aeronautical activity that pollutes the most due to the large fuel burn quantities needed to generate the required thrust. The efficiency improvements for the next generation aircraft will not be enough to reduce the pollution by the required amount, since the number of aircraft will continue to augment in the coming years. For this reason, not only has new technology focused on aerodynamics and aircraft design been considered, but also different alternatives such as economical measurements, the use of alternative fuel, and operational improvements, such as the airspace control upgrade. Airlines have changed their operations to reduce fuel burn even before flights are airborne, such as reducing auxiliary power unit use, engine washing and trajectory optimization. These changes have provided important savings [2]. Flight trajectory optimization has the advantage that the algorithms can be implemented for any aircraft, regardless of its technology. As long as avionics equipment is available while airborne to keep track of the flight being followed, and Air Traffic Management (ATM) authorizes the route to follow, fuel burn could be reduced. Fuel reduction, besides reducing emissions, may help airlines delay future economic measures related to pollution. The airborne equipment that keeps track of the flight route, and in some cases optimizes it, is the Flight Management System [3]. Other technologies are being developed, such as the Trajectory Aware Planner; software developed by 2

NASA and intended to be used in electronic flight bags to suggest optimal trajectories in real time. However, the FMS has been widely accepted by the industry, and is thus available in most commercial planes. Various studies have been performed to evaluate different FMS performance parameters [4-8]. Descent optimization has been of great interest to scientists and national airspace organizations due to its savings potential. Some programs were put in service to allow aircraft to follow the Continuous Descent Approach/Operations (CDA/CDO) [9-13]. The CDA/CDO is a procedure that allows an aircraft to descend through a constant slope instead of through a cruise-descend step fashion. This procedure has achieved important reductions in fuel consumption, pollution emission, and noise levels near populated areas. It is important to perform this procedure correctly in order to avoid the missed approach procedure, which is expensive in fuel burn and released emissions [14, 15]. Descent is the least expensive flight phase as the engines are at low power settings. Cruise, on the other hand, is the most expensive flight phase for long haul flights, so it is desirable to find the most economical cruise profile flight to provide important savings. There is now an important opportunity to improve aircraft trajectory prediction for the cruise phase. Studies performed with filtered radar data flights [16] during the cruise phase for different flights within the continental United States have shown that aircraft do not fly at their optimal speeds and altitudes [17, 18]. Providing these aircraft with their optimal profiles so they can propose those trajectories to ATM would represent an important pollution reduction and economic savings. Cruise can be optimized in two ways: utilizing the lateral and the vertical routes. Lateral Navigation (LNAV) refers to the set of waypoints to be followed. These waypoints are given in latitude and longitude coordinates. The vertical navigation (VNAV) can be defined as the altitudes and speed the aircraft has to respect following a given LNAV route. Research has been conducted on both navigation types. For the LNAV, graph search techniques have been implemented to find the most economic flight trajectory. For this navigation, optimizing a trajectory in the presence of obstacles has been of great interest, using graph search algorithms such as Dijsktra’s algorithm [19], A*[20] and metaheuristics such as tabu search [21, 22]. The VNAV trajectory has mostly been treated with Dynamic Programming. A technique called Moving Search Dynamic Programming was developed, which took into account the Required Time of Arrival (RTA) and non-fly zones [23]. Hagelauer implemented Dynamic Programming with Neuronal Networks, also considering the RTA [24]. This problem has been implemented using optimal control and considering different flight aspects, such as free flight, the RTA, city pairs, etc. [25-28]. Many algorithms solve for an aircraft’s Equations of Motion (EoM) to calculate flight dynamics and flight costs. Nevertheless, the FMS normally uses a Performance DataBases (PDB) instead of the EoM. Research has been conducted using a database to optimize the flight trajectory. The methodology to compute the flight cost using a PDB was presented in [29]. With a PDB, Dancila developed a fuel burn estimator for the cruise phase, with which the altitude was optimized for a given cruise [30, 31]. The golden section search was also implemented to optimize short flights [32, 33]. Gagne et al. [34] developed a reduced-exhaustive search algorithm to find the optimal flight profile. A search space reduction algorithm was developed and coupled with the lateral profile to obtain important flight cost reductions [35, 36]. Sibidé used dynamic programming to optimize the vertical profile [37]. Dijsktra’s algorithm was implemented to take advantage of winds and temperature to optimize a flight, changing its lateral route at a fixed altitude [38]. In this paper, the genetic algorithm technique was implemented to optimize the cruise phase. Genetic algorithms have been used to validate mathematical hypothesis in trajectory optimization [39]. They have also been used for more realistic optimization, searching for favorable winds at a fixed altitude to optimize the lateral trajectory. Genetic algorithms were applied to optimize a given flight in VNAV, LNAV, and by coupling the VNAV and the LNAV profiles [40-45].

3

The most economical altitude is weight-dependent. The optimal altitude changes as the aircraft’s weight is decreased by fuel burn, which is even more evident for long haul flights. Changes in altitude (or step climbs) have been reported to reduce fuel consumption, as discussed by Lovegren [46]. Step climbs are used to emulate the optimal climb-cruise flight. Due to ATM constraints, a flight has to follow fixed altitudes. A change in altitude during cruise can be executed only after ATM authorization. The objective of the algorithm described in this paper is to find the altitudes for a given constant Mach cruise that minimize the flight cost. The cruise information was taken from a flown flight plan provided by a European airline. Algorithms in the literature normally use arbitrary trajectories, radar data, or sources such as FlightAware® to have an LNAV of reference where the takeoff weight and weather information are unknown to compare against real flights. The flight plan is a document filled out by the airline (or airline representative) and delivered to ATM authorities to request a computed trajectory. The goal of the flight plan is to allow ATM to calculate and assure the required separation between aircraft to guarantee safety. It also helps emergency teams to easily locate aircraft in case of distress [47]. Flight plans are normally computed before an aircraft is airborne, and if authorized by ATM may be loaded into the FMS. Flight plans may change during flight due to weather or unplanned events. This paper is organized as follows: Firstly, the PDB that provides the fuel burn is described in the first section. Secondly, the flight cost computation during cruise, considering changes in altitude is explained. Thirdly, the problem is formally defined. Fourthly, how the waypoints were used as a graph is described. Fifthly, the genetic algorithm and its application were explained. Finally, the results and conclusions are discussed in the last section.

Methodology The algorithm developed in this paper creates different trajectories by changing the altitudes at different waypoints while keeping the same Mach. The aircraft can climb or descend to a different altitude, or keep the same altitude. The fuel burn consumption is obtained from a PDB provided by our industrial partner. The flight waypoints’ locations as well as the weather at each waypoint were obtained from a real flight plan provided by an airline. The altitudes selection that provided the optimal flight, which is defined as the most economical cost, was obtained through a genetic algorithm. The cruise cost analysis begins at the Top of Climb (ToC) and ends at the Top of Descent (ToD).

The Performance Database (PDB) The PDB was created and validated using experimental flight data. The database is divided into different tables, depending on the flight phase. Since the flight phase optimized in this paper is the cruise, allowing step climbs and step descends, the required tables are the cruise, the climb and the descent. These tables are considered as black boxes as shown in Figure 1. All the inputs must be present to obtain the desired output.

The Flight Cost Computation The PDB inputs are discrete values, which mean that only limited profile combinations are known. Altitudes are given in 1,000 ft, which respects current ATM constraints of flying at 1,000-ft steps. No altitude interpolations were made, as only the speeds available at the PDB are considered by our industrial partner’s recommendations. On the other hand, weight and temperature change all throughout a flight to values not available as exact input values. For this reason interpolations are required to compute the flight costs. The general interpolation schema is shown in Figure 2. The word “limits” stands for the PDB upper and lower input bounds where the desired value to interpolate is located.

4

Altitude (ft) Mach Weight (kg) Temperature (C)

Climb Mach

Altitude (ft) Mach Weight (kg) Temperature (C)

Descent Mach

Altitude (ft) Mach Weight (kg) Temperature (C)

Cruise

Fuel Burn(kg) Distance (nm)

Fuel Burn(kg) Distance (nm)

Fuel Flow (kg/hr)

Figure 1.Performance Database

ISA DEV limit 1 from PDB

ISA DEV to interpolate

Interpolation for ISA DEV using PDB Weight limit 1 ISA DEV limit 2 from PDB

Weight to interpolate ISA DEV limit 1 from PDB

Weight limit 1 from PDB Interpolation for weight using ISA DEV interpolations

Desired Output

Weight limit 2 from PDB ISA DEV to interpolate

Interpolation for ISA DEV using PDB Weight limit 2 ISA DEV limit 2 from PDB

Figure 2. Interpolation schema

Notice in Figure 1 how for the climb and the descent two outputs are provided: required fuel to arrive at the desired altitude from the first altitude available in the PDB, and the horizontal distance traveled required to attain the desirable altitude. The flight computation begins at the ToC in the cruise database; if a climb or descent is identified; the database is changed when it is required. Once the climb or the descent is calculated, the database is set to cruise for the rest of a given segment. The fuel burn and distance traveled outputs for the current altitude are obtained. The same is done for the altitude at which is desirable to climb. For the cruise, only the fuel flow (kg/hr) is available, and so a segment distance and the ground speed (knots) are required to compute the flight time (hr). The flight path is divided in segments which were arbitrarily selected to be a maximum of 25 nm. This means that the distance between two waypoints is divided into segments with a maximum length of 25 nm. The ground speed is computed, taking into account the wind data provided by the flight plan. ro nd peed

r e ir peed

ind peed

(1)

5

The flight cost for a given segment is computed by taking into account fuel and time. Time is converted into fuel cost by means of a variable called the Cost Index (CI). The CI is calculated by the airlines, considering flight timerelated costs such as maintenance and crew salary. egment ost

el

rn

light ime

(2)

The total flight cost can then be calculated by adding all the segments as shown in Equation 3, where CR refers to cruise, CLB to climb and DES to descent. ∑

∑

∑

(3)

Considering the climb, cruise and descent tables, the flight cost computation can be summarized as indicated in the flowchart in Figure 3, where the algorithm determines if the computation requires a sub-database change. Start

Next Waypoint Different Altitude?

Yes

Climb?

Yes

Descent

Climb

Cruise

ToD?

Yes End

Figure 3. Sub-databases change in trajectory calculations

Problem Definition Having defined the PDB, the flight cost and its computations, the problem can be formally defined as indicated in the following paragraphs. Given an open weighted directed graph, defined as G(V,E,W*) where V is the finite vertices (or nodes) available, E is the edges connecting two vertices, and W* is the weight (cost) of each edge, find the combinations of (V,E) that minimize the flight cost for two different vertices V contained in G. A given path P from A to B can be defined as the sequence of edges of a given graph that conducts from A to B. Since weights define the cost, weights are ultimately of interest, as shown in Equation 4. (

)

(

)

(

)

(

)

(4)

Thus the optimization problem can be defined as: ( ( )

)

∑

(5) (6) 6

( )

(7)

For the problem in this paper, the graph is represented by the grid described in the next section, where point A is the ToC and point B is the ToD, V is the set (WPT, Altitude), E is the segments connecting the different waypoints, and. Weight W* is the cost associated for each edge depending on the state of the preceding node. In other words, W* changes depending on the decisions taken before arriving at the current node. The Weight is the cost given in Equation 2. The path P is a given individual, as described in the “ enetic Algorithm” Section.

The Flight Plan and the Grid The flight plan provides the waypoints that the aircraft has to follow, the Mach speed, and the altitude to fly at for each waypoint. Weather information is provided for each waypoint, but only for limited altitudes. These altitudes are not necessarily the same for each waypoint. For example, if the aircraft is at 34,000 ft at WPT 1, and weather for WPT 2 is available only for altitudes from 33,000 ft to 36,000 ft, the aircraft can either descend to 33,000 ft, keep its current altitude or climb to a maximum of 36,000 ft. WPT 3 may have altitudes from 35,000 ft to 39,000 ft. The search space for the genetic algorithms is created in the form of a 2D grid (distance and altitude). This grid contains all the waypoints available at the flight plan. For each waypoint, only those altitudes where weather information is available are taken into account. A graphical grid description is provided in Figure 4, where the red nodes are the ones that do not have weather information, and the blue nodes are the waypoints that have weather information, i.e., are the nodes where the aircraft can fly to. Alt5

Alt4

Alt3

A

B

Alt2

Alt1 ToC

WPT1

WPT2

WPT3

WPTn-3

WPTn-2

WPTn-1

ToD

Figure 4.VNAV Flight Graph defined by waypoints

From each waypoint the aircraft can fly to any of the altitudes available in the next waypoint. As the number of waypoints increases, the total trajectories number increases as well. For the flight trajectory studied in this paper, more than 50 waypoints are taken into account, with at least 3 possible altitudes per waypoint. With these conditions, the number of available trajectories would be too large, which would make any optimization algorithm very time consuming and thus undesirable. Therefore, not all the waypoints of the grid are selected as points to change altitude. Instead, only those waypoints where altitude was changed in the original flight plan and waypoints in-between when the distance was longer than 200 nm are considered as decision waypoints where altitude can be changed. This distance was selected arbitrarily since it as was considered that ATM would not allow many altitudes changes in a short-distance segment.

Genetic Algorithm The genetic algorithms mimic Darwin’s theory of natural selection, where the most capable individuals survive and reproduce to create offspring that evolve in the process. This phenomena is reproduced in this paper as follows. Within an initial population, the most fitted individuals are selected to reproduce and create a new generation. A population consisting of parents and their offspring is then created and evaluated, where the least fitted individuals are discarded and new ones are randomly added to create a new generation. From this new generation, again the 7

most fitted individuals are selected and another set of offspring is created. This process is repeated until a predetermined number of generations is reached. In the next sections, genetic algorithms’ particularities to the vertical navigation problem are defined. Initial Population The initial population consists of a pre-determined number of randomly generated trajectories, which represent the individuals. The initial population size should be a small fraction of the total possible trajectories. Each available trajectory is an individual. An individual is defined as given in Equation 8, where i represents each waypoint (WPT) available in the flight plan. Altitude is a valid altitude for that waypoint. (8)

Evaluation The individuals must be evaluated. This evaluation involves computing each individual cost using the PDB and Equations 2 and 3. The fittest individual is the one that offers the lowest cost. Selection In nature, the most-fitted individual tends to survive and create offspring. However, for different reasons, individuals that are not as fit also survive. These less-fitted individuals are important for evolution since they provide diversity. In the algorithm terminology, as the most fitted individuals (trajectories) are selected, the solution begins to converge toward an optimal or suboptimal result. There is no practical way of knowing if this convergence is towards the global optimal. The selection of a few less-fitted individuals serves to explore more random search space areas and thus look for other potential optimal solutions. There are different methods for selecting which individuals survive and reproduce. Rank selection sorts individuals by cost; only the most fitted are selected and can reproduce. This method presents a quick convergence, but with the risk that the solution might not be the global optimal. The roulette method assigns a surviving chance percentage to each individual, providing the most capable individual the highest survival opportunities. When the roulette is turned, the most capable individuals have more chances to be selected, but the least fitted individuals are not automatically discarded as in the rank selection. This method is slower to converge but is better at avoiding suboptimal solutions. Another method is the uniform method where all individuals reproduce – which is quite expensive in computation time. For this application, the tournament method was selected. The individuals face each other randomly and the most fitted in each pairing survives. The individuals are randomly assigned in the tournament brackets. This way, the best ones have more chances to survive while allowing the less fortunate some opportunities to be selected and reproduce. After the tournament, half of the population is eliminated. This method offers rapid convergence and adequate diversity. Reproduction The surviving individuals reproduce to create a new generation which will be combined with its parents, creating a new population. Ideally the new generation should be more fitted than the last since they were created from the best parents available. The reproduction is performed by the crossover method. Let i and j be two different individuals (parents) composed of n even waypoints. The son is generated by taking the first half of parent i and the second half of parent j. The son can then be expressed as shown in Figure 5.

8

Figure 5. Offspring Creation From Two Parents

After all of the sons have been created, they are evaluated. The individuals are sorted; the most economical one is defined as the optimal for that generation. For the next generation, the individuals that did not survive the tournament are discarded and replaced by randomly generated individuals. This step increases the diversity, avoiding local sub-optima. A new tournament is then performed. This process is repeated until the pre-defined number of generations is reached. The algorithm’s process is shown in Figure 6. START Generate Initial Population Cost Evaluation and Sorting

Tournament

Reproduction

Sons Cost Evaluation All Population Sorting Reduce 20% weakest population Generate Random Individuals Population Evaluation & Sorting Optimal Determination

Last Generation?

YES END

Figure 6. Genetic Algorithm Flow Chart

9

Results In this section, the flight cost provided by the genetic algorithm developed in this paper is compared to the real flight cost. The flight analyzed in this Section was provided by our partner airline. Our industrial partner arbitrary selected one flight and it was used as the reference flight to explore the potential of Genetic Algorithms The examined flight is the cruise of a Bucharest to Canary Island flight, flown at a Take Off weight of 130 tons, Mach 0.8, and a Cost Index of 50 for a long haul 2 turbofan aircraft. For the altitude change decision, 14 waypoints were considered as altitude change decision points. Figure 7 shows the waypoints to follow and identifies the ones where altitude changes can be performed (cyan colored waypoints in Figure 7).

46

44

42

40

Lattiude (DEG)

38

36

34

32

30

28

26 -15

-10

-5

0

5 Longitude (DEG)

10

15

20

25

Figure 7. Flight Plan waypoints, identifying the waypoints where step climbs can be executed

The vertical profiles flown by the real flight and the flight proposed by the genetic algorithm are shown in Figure 8. The real flight (blue) shows climbs, and descents along its trajectory. Our partner airline did not comment the reason of this changes, so it is assumed it was either due to weather conditions, ATM constrains, or it was the optimal trajectory computed by the airline. 4

x 10

4

Real Flight Optimal Flight

3.9 3.8

Altitude (ft)

3.7 3.6 3.5 3.4 3.3 3.2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Horizontal Traveled Distance (nm)

Figure 8. VNAV Profile comparison

10

Table 1.Flights Costs Comparison

Flight

Flown Flight

Optimized Flight

Difference

Fuel Burn (kg)

32256.74

30709.69

1547 (5.04%)

From the selection of climb, descent and cruise segments, and in accordance with Table 1, the algorithm optimizes the flight by 5% more savings in terms of fuel. This fuel reduction can easily be translated into emissions not released to the atmosphere. This reduction is due to improved altitude selection identified by the genetic algorithm that offer better fuel economy than the altitudes provided by the flight plan. The solution presented by Genetic Algorithms suggested that their implementation can improve trajectories optimization, which would represent important fuel savings. However, more flight tests are required to validate this algorithm, as well as it comparison against different algorithms to measure its performance.

Conclusion A genetic algorithm was implemented as a means to find the altitudes that would result in the most economical flight plan in terms of fuel burn reduction. The climb and descent added on have improved the new trajectory results by comparing results against the flown flight. The flight cost was computed using a PDB instead of the EoM widely used in the literature. The use of a PDBs increase the TRL of our findings. The waypoints and the weather information were provided using a real flown flight plan. ATM restrictions such as flying at a constant Mach and flying at constant-level segments and following an airway were respected. The optimization was obtained using a better selection of altitudes than those available in the original flight plan. Assumptions were made that ATM would allow all the flight level changes proposed by the algorithm. The 5% in fuel savings represents an important CO2 reduction considering the number of flights per month performed by any airline. As future work, evaluating additional flight plans would be desirable to have a better perspective of the quality of the solutions provided by the algorithm. It would also be desirable to consider other flight phases, such as “initial climb”, and “descent to approach” in order to obtain a more complete solution. It is important to develop different optimization algorithms s ch as Dijsktra’s algorithm, rtificial nt olony, and exhaustive algorithms to validate the solutions provided by the Genetic Algorithms, and to measure its performance. Real time restrictions would be desired as well, as a means to implement a 4D optimization algorithm. Finally, exploring alternate lateral routes would be desirable, which could be used also in conjunction with more info, and weather.

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Contact Information To contact the authors for more information please visit the LARCASE laboratory at http://larcase.etsmtl.ca.

Acknowledgments This Research was conducted at The Research Laboratory in Active Controls, Avionics and Aeroservoelasticity (LARCASE) for the global project “Optimized Descent and r ise” with f nds from the the Business-led Network of Centers of Excellence Green Aviation Research & Development Network (GARDN). The authors would like to thank Mr. Rex Haygate, Dominique Labour and Yvan Blondeau from CMC-Electronics – Esterline, and Oscar Carranza from LARCASE. A special thanks for the airline that provided the flight plan that chose to be kept as anonymous. Alejandro Murrieta-Mendoza would like to thank CONACYT and the FQRNT. 13