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Spatial–Temporal Clustering and Optimization of Aircraft Descent and Approach Trajectories

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Abstract

This study presents a procedure for the spatial–temporal clustering and optimization of aircraft descent and approach trajectories. First, the spatial–temporal similarity between two trajectories is defined. Clustering analysis are conducted to identify the prevailing trajectories. The clustering centers obtained based on spatial–temporal distance are compared with those obtained based on the traditional Euclidean distance. Second, a multi-objective optimization model is established to minimize fuel consumption, aircraft emission and noise impact considering flight constraints. The Pareto solution that has the highest similarity with the prevailing trajectories is selected as the final optimized trajectory. The performance indicators of the optimized trajectory are compared with the average values of historic trajectories. It is found that travel time, fuel consumption and noise impact for the optimized trajectory are reduced by 5.34%, 0.96% and 11.86%, respectively. The percentages are 0.96%, 1.32%, 9.18%, 3.54% and 4.00% for CO2, SOx, NOx, CO and HC, respectively. Also, the performance indicators for the two clustering centers based on spatial–temporal distance are generally closer to average performance of original trajectories, as well as those of the optimized trajectories, as compared with the two clustering centers based on Euclidean distance. The spatial–temporal clustering methods may help to discover the valuable information that lies in those indicators associated with features reflected in time dimension.

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Abbreviations

A FA :

The lowest altitude of the final approach

A FAobs :

The highest obstacle height in the main zone of the final approach plus 150 m

A IA :

Altitude of initial approach point

A IAobs :

The highest obstacle altitude in the main zone of the initial approach plus 300 m

A JR :

Minimum crossing altitude at the JR NDB station

A TP :

The lowest altitude at the starting turning point

A VYK :

Minimum crossing altitude at the VYK VOR/DME station

A WAIT :

Altitude at the waiting point

C Tdes, r :

Descent thrust coefficient of different altitudes

d :

Distance between engine and noise detection point

D(P):

Impacting distance of the engine thrust P at a specific noise level

dis(linkm, linkn):

Spatial–temporal distance between linkm and linkn

dis(tri,trj):

Space–time distance between the two trajectories

dst(p,q):

Euclidean distance between the closest track points between linkm and linkn

F :

Fuel consumption

FFi :

Fuel flow rate of the i-th phase

f ni :

Average fuel flow rate between the i-th and (i + 1)-th points in phase n

F obj :

Fuel consumption required for aircraft operation

FTi :

Duration of the i-th phase

GS:

Ground speed

H :

Height between aircraft and ground

H :

Humidity correction term

H p :

Barometric altitude

IAS:

Indicated air speed

k :

Number of clusters

L :

Specified noise level

L(d):

Noise level at distance d

L(P):

Noise level corresponding to the engine thrust P

LAmax :

Maximum sound level

L dn :

Night equivalent sound level

linkm :

The m-th part of a trajectory

M :

Mach

M obj :

Noise impact during approach

N :

Total amount of trajectories

N eng :

The number of engines

P :

Thrust of single engine

P amb :

Inlet environmental pressure (psia)

P e :

Dimensionless pollutant equivalent number

P ev :

Pollution equivalent value

P obj :

Total pollutant equivalent number

P sat :

Saturation vapour pressure

REICO:

Reference emission index value

REIHC:

Reference emission index value

REONOx :

Reference emission index value

RH:

Relative humidity

S :

Total emissions

SEL:

Sound exposure level

S ni :

Influencing area between the i-th and (i + 1)-th points in phase n

t :

Flight time

T ambc :

Temperature

TAS:

True air speed

Thrmax climb :

Maximum take-off thrust of the engine

t i :

The flight time

t m :

Timestamps of the starting points of linkm

t ni :

Flight time between the i-th and (i + 1)-th points in phase n

tri :

The i-th trajectory

v m :

Speeds of the starting points of linkm and linkn

w :

Specific humidity

W f :

Fuel flow rate

W ff,ref :

The corrected fuel flow rate factor during LTO phase

δ amb :

PAmb/14.696 psia

θ amb :

TAmb/518.67R

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Funding

This research was sponsored by the Fundamental Research Funds for the Central Universities (No. NS2020046) and the National Natural Science Foundation of China (51608268, U1933119, 71971112).

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Authors and Affiliations

  1. College of General Aviation and Flight, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Zhao Yang & Bing Wang

  2. College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Rong Tang & Yixin Chen

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  1. Zhao Yang
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  2. Rong Tang
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Correspondence to Zhao Yang.

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Yang, Z., Tang, R., Chen, Y. et al. Spatial–Temporal Clustering and Optimization of Aircraft Descent and Approach Trajectories. Int. J. Aeronaut. Space Sci. 22, 1512–1523 (2021). https://doi.org/10.1007/s42405-021-00401-y

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