Noise Abatement 3D Path Planning Using a Snake Algorithm

111 Pages·2015·7.29 MB·English

Noise Abatement 3D Path Planning
Using a Snake Algorithm
Msc. Thesis Report

H.A. Lazos Fernández
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Noise Abatement Path Planning
Using a Snake Algorithm
Thesis Report
Second Draft

for obtaining the degree of

Master of Science in Aerospace Engineering

Author
H.A. Lazos Fernández

Supervisor
Dr. ir. H.G. Visser

June 26th, 2015

Delft University of Technology Faculty of Aerospace Engineering
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Acknowledgements
This report presents the results of the improved Snake Model, which as far as the literature has
shown at the moment of the publication, is the first one to include a three dimensional snake
for navigational purposes.
Of the many people to whom I am grateful for competing this MSc thesis, I would like to begin
with my supervisors, dr. ir H.G. Vissser and dr. ir. S. Hartjes, since their support and guidance
was invaluable for developing this model. I would also wish to thank the Aerospace Engineering
staff from whom I received knowledge and guidance to obtain this degree, especially those
form C&S and ATO.
At the University level, I would like extend my gratitude to the staff of the Central Student
Administration, especially those of the International Office that so warmly welcomed me as an
international student provide me guidance during my stay at TU Delft.
At a personal level, I would like to thank my friends and programme colleagues, in particular
Victor and Hanif for their friendship and support, which I received almost upon arriving to Delft.
Finally, I would like to extend my infinite gratitude to my mother Maria Estela, who has never
stopped believing in me.
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Abstract
For several decades, the aviation industry has struggled with reducing the amount of noise
that aircraft generate, especially when flying close to communities. This effort has led to the
introduction of several technological novelties, both in new and retrofitted aircraft, especially
in the fields of aerodynamics and propulsion. Most recently, the focus has shifted towards the
operational side of the problem, where optimized takeoff procedures can be implemented to
effectively reduce noise nuisance. These procedures include specific departure trajectories,
together with noise abatement climb profiles .
In line with these operational efforts, the ATO section of the Delft University of Technology (TU
Delft) has developed a tool that makes use of dynamic optimization to define optimal Nosie
Abatement Procedures (NAP). Although the degree of precision of this computer model is high,
the nature of its calculations makes it unsuitable for online calculations, since it has a high
computational time.
In face of this situation, Kuijpers (2011) explored alternate solutions to generate NAP ground
trajectories, obtaining promising results especially with one method: the so called ‘snake
algorithm’. The objective of this research is to fully implement the Snake Method (SM) in a
noise abatement trajectory planner, augmenting the model developed by Kuijpers (2011).
In the context of trajectory planning, a snake is defined as a chain of masses, connected to
each other by a spring-damper system with its extremes fixed to a desired origin and
destination. When released, the springs will tend to reduce the distance between the masses
and create a straight trajectory between the two extremes. However, for this method to have
a practical use in the path planning context, a series of ‘obstacles’ are introduced in the vicinity
of the snake. These obstacles exert a repulsive virtual force towards the masses, pushing them
away from the obstacle center. When released, the system will eventually reach a minimum
kinetic energy equilibrium position, which represents an optimal trajectory.
In other fields, a snake avoids solid obstacles, however for the noise abatement problem, these
obstacles represent noise-affected population communities. Therefore, it is necessary to
implement a clustering mechanism that converts the scattered population data into groups
that can be interpreted by the snake as solid obstacles. One of the major additions of this
research to the model of Kuijpers (2011) is the implementation of the k-means algorithm,
which is a clustering methodology that has been found to be highly useful and computationally
efficient for clustering population data.
The snake model developed by Kuijpers (2011) has been considerably modified to work in a
three dimensional space and generate complete trajectories in the x, y and z axes. In addition,
the concept of ‘bending energy’ has been introduced to allow the snake to generate extremely
curved trajectories. Although the segments between masses remain straight, the bending
energy exerts a force on the masses, when their offset with respect to the previous and next
mass goes beyond a certain limit. This force, which is applied in the direction of the turn, will
allow the mass to have a greater offset, which will be represented in the final trajectory as a
curved segment.
After generating an optimal trajectory, the model presented in this research makes use of the
Integrated Noise Model (INM), which was explicitly designed to represent aviation acoustics.
The INM delivers a noise exposure calculation on the communities that are located in the
vicinity of the trajectory, graphically and numerically showing the impact of the trajectory on
the population.
Since as yet it has not been fully explored, the design and implementation of an online tool for
Noise Abatement Procedures (NAP) represents a significant innovation, and it has already
shown promising results. The results of this model have been compared to those of the
NOISHHH tool for two departures from Amsterdam Airport Schiphol: Spijkerboor and Arnhem.
This comparison has shown that the model is capable of generating accurate ground tracks
while creating an acceptable vertical profile with complete autonomy. Results show that he
model can generate trajectories in three dimensions and with sharp turns, although the
awakening levels increased compared to the NOISHHH model.
Although these results are promising, further research is recommended, especially for coupling
the aircraft performance capabilities with the snake algorithm. As for now, the model
calculates Speed and Thrust along the trajectory in an a-posteriori process that has no
influence on the snake algorithm results.
Even though further research is recommended to obtain more accurate results, this report
demonstrates the potential that the snake algorithm has for the development of aircraft that
can navigate under modern scenarios such as Performance Based Navigation (PBN).
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I. Table of Contents

I. TABLE OF CONTENTS ................................................................................................................................. I
II. LIST OF ACRONYMS ................................................................................................................................. V
III. NOMENCLATURE ................................................................................................................................... VII
LATIN SYMBOLS ...................................................................................................................................................... VII
GREEK SYMBOLS .................................................................................................................................................... VIII
SUBSCRIPTS .......................................................................................................................................................... VIII
HYPERSCRIPTS ......................................................................................................................................................... IX
IV. LIST OF FIGURES ................................................................................................................................. XI
V. LIST OF TABLES....................................................................................................................................... XV
1 INTRODUCTION ....................................................................................................................................... 1
1.1 BACKGROUND ............................................................................................................................................ 1
1.2 RESEARCH DEFINITION ................................................................................................................................. 3
1.2.1 Objectives .......................................................................................................................................... 4
1.2.2 Research Questions ........................................................................................................................... 4
1.3 STRUCTURE OF THE REPORT .......................................................................................................................... 5
2 STATE OF THE ART ................................................................................................................................... 7
2.1 SNAKE ALGORITHM ..................................................................................................................................... 7
2.1.1 Initialization ....................................................................................................................................... 8
2.1.2 Snake Definition ................................................................................................................................ 9
2.1.3 Energy Minimization ......................................................................................................................... 9
2.1.4 Bending energy................................................................................................................................ 13
2.2 K-MEANS CLUSTERING .............................................................................................................................. 16
2.3 AVIATION ACOUSTICS ................................................................................................................................ 19
2.3.1 Relevant Concepts ........................................................................................................................... 19
2.3.2 Noise Modelling ............................................................................................................................... 25
2.4 THE INTEGRATED NOISE MODEL .................................................................................................................. 26
2.4.1 Flight Path Information ................................................................................................................... 27

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2.4.2 Acoustic Computation ..................................................................................................................... 28
2.5 TERMINAL PROCEDURES FOR NOISE ABATEMENT ............................................................................................ 29
2.5.1 ICAO Nosie Abatement Recommendations ..................................................................................... 30
2.5.2 NADP ............................................................................................................................................... 31
3 PREVIOUS VERSION OF THE SNAKE ALGORITHM FOR NAP .................................................................... 33
3.1 BACKGROUND .......................................................................................................................................... 33
3.2 SNAKE CONCEPT ....................................................................................................................................... 34
3.3 RESULTS ................................................................................................................................................. 35
3.4 ANALYSIS AND RECOMMENDATIONS ............................................................................................................. 36
4 TRAJECTORY PLANNER ........................................................................................................................... 37
4.1 MODEL ARCHITECTURE .............................................................................................................................. 38
4.2 SPATIAL SYSTEM OF REFERENCE .................................................................................................................. 39
4.3 K-MEANS CLUSTERING ............................................................................................................................... 40
4.4 SNAKE ALGORITHM ................................................................................................................................... 41
4.4.1 Obstacle Force ................................................................................................................................. 41
4.4.2 Bending Force .................................................................................................................................. 43
4.4.3 Height force ..................................................................................................................................... 44
4.4.4 Total force and displacement of each mass .................................................................................... 46
4.5 NOISE EXPOSURE CALCULATION .................................................................................................................. 47
4.5.1 Autopilot tracking for determining V and T..................................................................................... 47
4.5.2 Noise Model .................................................................................................................................... 51
4.6 PLOTTING ............................................................................................................................................... 53
5 MODEL CALIBRATION ............................................................................................................................ 55
5.1 SNAKE ALGORITHM ................................................................................................................................... 55
5.1.1 Spring and Damping Coefficients ................................................................................................... 55
5.1.2 Obstacle repulsive coefficient .......................................................................................................... 56
5.1.3 Bending Energy ............................................................................................................................... 57
5.1.4 Height Force .................................................................................................................................... 58
5.1.5 Artificial Obstacles ........................................................................................................................... 59
5.2 K-MEANS CLUSTERING ............................................................................................................................... 61
5.2.1 Maximum Number of Iterations (𝑵𝒊𝒕) ............................................................................................ 62
5.2.2 Number of Clusters (𝑵𝒄) ................................................................................................................. 62
5.2.3 Cluster Radius .................................................................................................................................. 63
5.2.4 Number of replications (𝑵𝒓) ........................................................................................................... 65
5.2.5 Trajectory Envelope ......................................................................................................................... 66
5.3 NOISE EXPOSURE ...................................................................................................................................... 67
5.3.1 Thrust and Speed Determination .................................................................................................... 67
5.4 FINAL CALIBRATION PARAMETERS ................................................................................................................ 68
6 RESULTS AND VALIDATION .................................................................................................................... 69
6.1 MODEL RESULTS FOR SPY .......................................................................................................................... 70
6.1.1 Tracked Speed and Thrust ............................................................................................................... 73
6.2 MODEL RESULTS FOR ARNEM .................................................................................................................... 74
6.3 ANALYSIS OF THE 3D PROPERTIES OF THE MODEL ............................................................................................ 77
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