The Effect of Towed Array Orientation on the 3D
Acoustic Picture for Sound Sources and the
Vertical Ambient Noise Profile
by
ARCHIVES
kSSACI4UFTTS INSTrTUTE
OF FECHNOLOLOY
JUL 3 0 2015
Arthur Anderson
LIBRARIES
B.S., The Pennsylvania State University (2006)
S.M., Massachusetts Institute of Technology (2013)
Naval Engineer, Massachusetts Institute of Technology (2013)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
Massachusetts Institute of Technology 2015. All rights reserved.
A uthor...................
Signature redacted
Department of M
Certified by..
Signature redacted
al Engineering
May 18, 2015
rof Henrik Schmidt
Professor of Mechanical and Ocean Engineering
Thesi Supervisor
Accepted by........
Signature redacted....
David E. Hardt
Chairman, Department Committee on Graduate Students
2
The Effect of Towed Array Orientation on the 3D Acoustic
Picture for Sound Sources and the Vertical Ambient Noise
Profile
by
Arthur Anderson
Submitted to the Department of Mechanical Engineering
on May 18, 2015, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Mechanical Engineering
Abstract
The three dimensional (3D) acoustic arrival structure of the undersea ambient noise
field is important for many reasons, and can give us significant insights into the Arctic
environment. For example, the anthropomorphic sound of the ice cracking along the
ice edge could be used to track the location of the ice edge as it advances and retracts
throughout the seasons. The noise sources could also be used as a noise source to
acoustically map the bathymetry of the largely unexplored Arctic seabed. In addition,
vertical arrival structure of the ambient noise field could give hints and clues that
allow for improvements in both acoustic communications and target tracking. In this
research, we will examine the ability of an autonomous underwater vehicle (AUV)
equipped with a towed array in a virtual environment to develop an accurate 3D
acoustic picture of the undersea environment. While prior towed array experiments
are generally limited to the arrays being towed in a horizontal manner, here a "yoyo"
maneuver is introduced. In a yoyo maneuver, the vehicle moves up and down in
the water column as it traverses in order to break up the ambiguity of the measured
vertical arrival structure. This thesis presents a method to measure the "verticalness"
introduced into the towed array by this maneuver, and quantifies how this improves
the quality of the 3D arrival structure.
The results conclude that within the vehicle maneuvering limits of a Bluefin-21
AUV, a fully pitched yoyo pattern vs. a constant depth pattern results in a relative
increase in the maximum beam response of a source by approximately 6.5 dB, and
also decreases the 3-dB down bandwidth in the vertical direction by approximately
120. This is done without any significant losses for the bandwidth in the horizontal
direction. When using a towed array to characterize a horizontally isotropic noise
field, we find that within the AUV's maneuvering limits, the 3D beam response patterns are not sufficient to produce an accurate acoustic picture. To measure these
fields, a vertical array is the most appropriate.
3
Thesis Supervisor: Prof. Henrik Schmidt
Title: Professor of Mechanical and Ocean Engineering
4
Acknowledgments
This research has been the culmination of a lot of work form a lot of different people
that I'd like to thank. First of all, I'd like to thank my family, who has been there
to support me over and over again over the last 5 years I've spent here at MIT. An
especially important thank you to my mom, who despite not having an engineering
background, has read my thesis from cover to cover to help me edit out my spelling
and grammar mistakes.
Next, I'd like to thank all of the members of my thesis committee. The inputs
I've received from each of you have been especially invaluable. To Michael Benjamin
- your work in autonomy and support of me has really inspired me to pursue further
work in the field. I've learned so much about autonomy and robots through the many
experiences we've shared, and I will take that with me for the rest of my career. To
Franz Hover - thank you for always keeping a critical eye to my work, and pointing out
how I could take it to that next step, and make the product better. To John Leonard
- you're dedication to helping students succeed, despite your very busy schedule, is
unparalleled. Finally, a big thank you to my thesis adviser, Henrik Schmidt. Henrik,
your guidance throughout this entire endeavor has gotten this work to where it is
now. Your vision was the inspiration for this work, and your insights and experience
in the acoustic and autonomous communities have been invaluable to me throughout
this process. Thank you.
A final thank you to all my LAMSS lab mates. A big thank you to Stephanie Fried,
who introduced me into 3D acoustic processing and wrote many of the preliminary
versions of the code I use. Thank you Ian Katz for being there at the beginning,
when I was still trying to make sense of all the LAMSS repositories. To Alon - I've so
much enjoyed spending time with you and tinkering with robots, particularly during
RobotX. I always knew the longer I spent time with you the more knowledge I'd get.
Also thank you to Thom, Tom, Erin, Sheida, Stephanie. I know I've gotten help in
so many different ways from each of you throughout the years. Being with you all
and a part of this distinguished lab has been an absolute pleasure.
5
6
Contents
17
Introduction
Thesis Objectives and Original Contributions
. . . . . . . . . . . .
19
1.2
Thesis Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
.
1.1
.
1
2 Background
The Arctic Environment . . . . . . . . . . . . . . . . . . . . . . . .
23
2.2
Studying the Arctic . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3
The Arctic Acoustic Environment . . . . . . . . . . . . . . . . . . .
28
2.4
IC E X 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.5
A Sample 3D Image
. . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.6
Types of AUVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.7
The Bluefin-21
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
.
.
.
.
.
.
.
2.1
General Specifications
. . . . . . . . . . . . . . . . . . . . .
36
2.7.2
Equipped Acoustic Array - DURIP . . . . . . . . . . . . . .
38
.
.
2.7.1
41
3.2
.
41
41
Virtual Environment . . . . . .
MOOS-IvP and LAMSS
3.1.2
Vehicle Behaviors . . . .
43
3.1.3
Building a Virtual Acoustic Environment
44
3.1.4
Modeling Array Shape .
47
3D Acoustic Pictures . . . . . .
49
3.2.1
49
.
3.1.1
.
3.1
.
Overview of Methods
.
3
23
2D Beamforming.....
7
Creating the 3D Beam Response
. .
. . . . . . . . . .
51
Beam Response Patterns . . . . . . . . . . .
. . . . . . . . . .
53
3.3.1
Deconvolving the Noise Field
. . . .
. . . . . . . . . .
55
3.3.2
Modeling the Noise Field . . . . . . .
. . . . . . . . . .
56
3.3.3
Iteratively Solving for the Noise Field
. . . . . . . . . .
57
3.3.4
Statistical Convergence . . . . . . . .
. . . . . . . . . .
59
. . . . . .
. . . . . . . . . .
60
3.4.1
Instantaneous Verticalness . . . . . .
. . . . . . . . . .
61
3.4.2
Tracking Verticalness over Time . . .
. . . . . . . . . .
62
3.4.3
uVertScoreKeeper . . . . . . . . . . .
. . . . . . . . . .
62
.
.
.
.
.
.
.
3.2.3
.
.
Measuring Vertical Directionality
Noise Field with a Point Source
. . . . . . . . . . . . . .
65
4.1.1
Experimental Setup . . . . . . . . .
. . . . . . . . . . . . . .
65
4.1.2
Noise Field Results . . . . . . . . .
. . . . . . . . . . . . . .
67
Experimental Testing on a Simple Source .
. . . . . . . . . . . . . .
74
4.2.1
Experimental Setup . . . . . . . . .
. . . . . . . . . . . . . .
74
4.2.2
Results and Discussion........
.. .. .. .. ... .. .
78
.
.
.
Quantifying Resolution . . . . . . . . . . .
.
4.2
65
.
4.1
Convergence of a Noise Field . . . . . . . .
. . . . . . . . . . . . . .
80
4.4
Range Finding on a Source . . . . . . . . .
. . . . . . . . . . . . . .
84
4.4.1
Experimental Setup . . . . . . . . .
. . . . . . . . . . . . . .
84
4.4.2
Range Finding Calculation . . . . .
. . . . . . . . . . . . . .
85
4.4.3
Results and Discussion . . . . . . .
. . . . . . . . . . . . . .
86
.
.
.
.
.
4.3
Horizontally Isotropic Vertical Noise Fields
91
M otivation . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .
91
5.2
Experimental Setup . . . . . . . . . . . . .
. . . . . . . . . . . . . .
92
5.3
Initial Results . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .
94
5.4
Exploring a One-Sided Vertical Noise Profile . . . . . . . . . . . . . .
97
5.5
Revisiting the Notch Profile with Fixed Arrays
.
5.1
.
.
5
50
.
4
. . . . . . . . . .
.
3.4
Extension to 3D Beamforming . . . .
.
3.3
3.2.2
8
100
5.6
6
Beam Responses for a Vertical Notch . . . . . . . . . . . . . . . . .1
100
Future work and Conclusions
107
6.1
Real World Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
6.1.1
O bjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
6.1.2
Identifying the Notch . . . . . . . . . . . . . . . . . . . . . . .
112
6.1.3
Proposed Experiments . . . . . . . . . . . . . . . . . . . . . .
112
6.2
Better Ranging Algorithms . . . . . . . . . . . . . . . . . . . . . . . .
114
6.3
Ice Cracking Research
. . . . . . . . . . . . . . . . . . . . . . . . . .
116
6.4
Autonomy Solutions
. . . . . . . . . . . . . . . . . . . . . . . . . . .
116
6.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117
A Modeling the Pressure Field
A .1
119
R ay Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
A.2 Finding the Phase Difference . . . . . . . . . . . . . . . . . . . . . . . 122
A.3 Calculating Ray Pressures . . . . . . . . . . . . . . . . . . . . . . . .
123
A.4 Finding the Total Pressure . . . . . . . . . . . . . . . . . . . . . . . .
125
B Bellhop Inputs
127
C Modeling of a Towed Array
129
C.1 Modeling of an Array . . . . . . . . . . . . . . . . . . . . . . . . . . .
129
D Spherical to Conical Transformation
133
E 3D Acoustic Pictures for a Simple Source
137
F 3D Acoustic Pictures for Noise Notch
143
G Noise Code
151
9
10
List of Figures
The Yoyo Pattern Producing a 3D Picture
18
2-1
Receding Sea Ice and Arctic Routes . . . . . . . . . . . . .
24
2-2
Arctic Sea Route Navigability . . . . . . . . . . . . . . . .
25
2-3
NOAA/NASA Pathfinder Satellite
. . . . . . . . . . . . .
26
2-4
T-AGOS-20 USNS Able
. . . . . . . . . . . . . . . . . . .
27
2-5
Ambient Noise Levels in the Arctic for Different Frequencies
29
2-6
Ice Noise Measured as Individual Hotspots . . . . . . . .
30
2-7
ICEX 2016 Graphic . . . . . . . . . . . . . . . . . . . . .
32
2-8
Example of a 3D Acoustic Noise Profile in Shallow Water
33
2-9
Bluefin G lider . . . . . . . . . . . . . . . . . . . . . . . .
35
2-10 B luefin 21 . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2-11 DURIP Array Schematic . . . . . . . . . . . . . .. . . . .
39
2-12 DURIP Array Photograph . . . . . . . . . . . . . . . . .
39
.
.
.
.
.
.
.
.
.
.
.
1-1
MOOS Database Tree
. . . . . . . . . . . . . . . . . . .
42
3-2
IvP Helm Structure . . . . . . . . . . . . . . . . . . . . .
43
3-3
The Simulation Autonomy Code Architecture
. . . . . .
45
3-4
pMarineViewer from a MOOS-IvP Simulated Environment
47
3-5
2D Array Direction . . . . . . . . . . . . . . . . . . . . .
50
3-6
3D Conical Angle . . . . . . . . . . . . . . . . . . . . . .
51
3-7
2D vs. 3D Beamforming . . . . . . . . . . . . . . . . . .
52
3-8
Distance Vector . . . . . . . . . . . . . . . . . . . . . . .
53
3-9
3D Beam Examples . .
.
.
.
.
.
.
.
3-1
.
. . . . . . . . . . . .
11
54
3-10 Iterative Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3-11 Iteration Process Diagram . . . . . . . . . . . . . . . . . . . . . . . .
58
3-12 Verticalness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
3-13 uVertScoreKeeper Output . . . . . . . . . . . . . . . . . . . . . . . .
63
4-1
Simple Source Experimental Setup
. . . . . . . . . . . . . . . . . . .
67
4-2
Simple Source Results for Period 300 . . . . . . . . . . . . . . . . . .
68
4-3
Simple Source Results for Period 1000
. . . . . . . . . . . . . . . . .
70
4-4
Simple Source Results for a Constant Depth . . . . . . . . . . . . . .
70
4-5
Path Plots for Yoyo vs. Constant Depth Maneuvers . . . . . . . . . .
71
4-6
Vertical Noise Profiles at the Source Location for Multiple Levels of
Array Verticalness
4-7
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
Horizontal Noise Profiles for Multiple Levels of Array Verticalness
Looking at a Simple Source
. . . . . . . . . . . . . . . . . . . . . . .
73
4-8
Path Distance Geometry . . . . . . . . . . . . . . . . . . . . . . . . .
75
4-9
Relationships of Verticality to Acoustic Picture Resolution . . . . . .
78
4-10 Series of Snapshots of the Generated Noise Field with Increasing Amounts
of D ata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4-11 Correlations of the Noise Field Generated as a Function of Time . . .
83
4-12 Range Finding Experimental Setup . . . . . .... . . . . . . . . . . .
84
4-13 Range Finding Geometry . . . . . . . . . . . . . . . . . . . . . . . . .
86
4-14 Range Finding Acoustic Picture - Yoyo Pattern . . . . . . . . . . . .
87
4-15 Range Finding Acoustic Picture - Constant Depth . . . . . . . . . . .
87
4-16 Range Estimation - Vertical Arrival Structure Comparison . . . . . .
88
4-17 Range Finding - Experimental Range Measurements and Uncertainty
89
5-1
Vertical Notch Graphic . . . . . . . . . . . . . . . . . . . . . . . . . .
92
5-2
Vertical Notch Graphic . . . . . . . . . . . . . . . . . . . . . . . . . .
93
5-3
Noise Notch as Measured by a Vertical Array
94
5-4
3D Acoustic Pictures by a Towed Array of the Vertical Notch
. . . .
95
5-5
Vertical Notch as Measured by 3 Towed Array Experiments . . . . . .
96
12
. . . . . . . . . . . . .
5-6
Zoomed View of Vertical Profile for 3 Towed Array Experiments.. .
97
5-7
One Sided Ambient Noise Profile as Measured by a Vertical Array
98
5-8
One Sided Ambient Noise Profile as Measured by a Towed and Two
.
Fixed Diagonal Arrays . . . . . . . . . . . . . . . . . . . . . . . . . .
5-9
99
One Sided Ambient Noise Profile - Vertical Noise Picture Comparison
for 3 Experim ents . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
100
5-10 Towed Array and Fixed Diagonal Arrays in a One-Sided Horizontally
Isotropic Noise Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5-11 Beam Responses for a Horizontally Isotropic Vertical Noise Field at
Different Array Tilts . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5-12 Maximum Normalize Beam Response vs. Different Array Tilts for a
Horizontally Isotropic Vertical Noise Field . . . . . . . . . . . . . . . 103
5-13 Conical Beams measuring a a Horizontally Isotropic Noise Field
. . . 104
6-1
OASES Predicted Beam Pattern from Ice Cracking Noise . . . . . . . 110
6-2
Ranging Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . Il
6-3
Bottom Response Objective
6-4
Ranging Using Multiple Paths . . . . . . . . . . . . . . . . . . . . . . 115
6-5
Ice Cracking Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-6
Example Arctic Autonomy Utility Function
A-1
Snell's Law
. . . . . . . . . . . . . . . . . . . . . . . 112
116
. . . . . . . . . . . . . . 117
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
120
A-2 Ray Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
124
. . . . . .
131
C-1 Model of the Individual Forces on a Towed Array Element
D-1 Transformation from Spherical to Conical Coordinates
. . . . . . . . 134
E-1 Simple Source Results for Period 300 . . . . . . . . . . . . . . . . . .
138
E-2 Simple Source Results for Period 500 . . . . . . . . . . . . . . . . . .
138
E-3 Simple Source Results for Period 600 . . . . . . . . . . . . . . . . . .
139
E-4 Simple Source Results for Period 700 . . . . . . . . . . . . . . . . . .
139
E-5 Simple Source Results for Period 1000
13
. . . . . . . . . . . . . . . . . 140
. . . . . . . . .
140
E-7 Simple Source Results for Period 2000
. . . . . . . . .
.
141
.
141
.
E-6 Simple Source Results for Period 1500
E-8 Simple Source Results for Constant Depth . . . . . . .
. . . . . .
F-2 Vertical Ambient Noise Field Results for Period 300 . . .
. . . . . . 144
F-3 Vertical Ambient Noise Field Results for Period 500 . . .
. . . . . .
F-4 Vertical Ambient Noise Field Results for Period 600 . . .
. . . . . . 145
F-5 Vertical Ambient Noise Field Results for Period 700 . . .
. . . . . .
F-6 Vertical Ambient Noise Field Results for Period 1000 . .
. . . . . . 146
F-7 Vertical Ambient Noise Field Results for Period 1500 . .
. . . . . .
147
F-8 Vertical Ambient Noise Field Results for Period 2000 . .
. . . . . .
147
.
.
.
.
.
.
.
.
F-1 Vertical Ambient Noise Field Results for a Vertical Array
144
145
146
F-9 Vertical Ambient Noise Field Results for 450 Tilted Array. . . . . . . 148
F-10 Vertical Ambient Noise Field Results for 600 Tilted Array. . . . . . .
148
F-11 Vertical Ambient Noise Field Results for 75' Tilted Array.
149
14
List of Tables
A Brief Description of the Key Code Elements . . . . . . . . . . . .
46
4.1
Simple Source Experiments List . . . . . . . . . . . . . . . . . . . .
66
4.2
3D Acoustic Resolutions for Simple Source Experiments . . . . . . .
73
4.3
Experiments Conducted on Verticality
. . . . . . . . . . . . . . . .
77
4.4
Full Verticality Experimental Results . . . . . . . . . . . . . . . . .
79
5.1
Summary of Towed Array Experiments for Measuring a Vertical Notch
94
6.1
Objectives for the ICEX Experiment
.
.
.
.
.
3.1
.
. . . . . . . . .
C.1 Physical Variables used in Modeling the DURIP Array
15
. . . . . . . .
108
. . . . . . . .
132
16
Chapter 1
Introduction
For many reasons, the three-dimensional (3D) arrival structure of the undersea ambient noise field is important for research and development in the acoustic community.
Three dimensional arrival structures can be used to estimate the beam noise of an
array. This is important when estimating the performance of that array as a scientific
or Navy asset, and also there are clues in the vertical arrival structure that give hints
and clues as to the propagation paths for the noise. While the ideal measurement tool
to understand the 3D arrival structure would be a high-resolution volumetric array
sonar system, these systems are prohibitively expensive and generally not available.
While not ideal, towed arrays have been and can be used to estimate the 3D ambient
noise field [38].
In typical 2D beamforming on a line array, the azimuthal direction of a noise
source is by measuring the phase angle of the signal as it approaches each element.
But this doesn't present the whole picture. Rather than at angles relative to the array
on just the horizontal plane, the actual beam patterns are conically symmetric about
the axis of the array. It has been shown that even with small array tilts, a measured
3D noise field can be established using an iterative algorithm which deconvolves the
noise from the beam pattern. With the new technology of autonomous underwater
vehicles (AUVs), large towed arrays no longer need to be deployed from a ship, and
this gives the opportunity that towed array may be given verticalness, or array tilt,
introduced by an AUV maneuvering up and down in the water column in a "yoyo"
17
3
'R
3D Noise Rosette
*4,'
*%*
/
4,
I
*
i
I?
a
S
I
I
b
~*
Figure 1-1: A set of pictures that illustrates the new yoyo pattern taken by an AUV
vs. the traditional studies done using a horizontal path. The yoyo pattern helps to
rapidly break up the inherent ambiguity in the vertical arrival structure [32].
18
pattern as it moves also on the horizontal plane. In theory, this should allow for
rapidly breaking the vertical and horizontal angle ambiguity and present a shorter
time scale for noise statistics, thus allowing for better tracking of temporal events [32].
In this thesis we will study this idea in a virtual acoustic environment, and examine
the improvements to the 3D noise field that are introduced by these maneuvers.
1.1
Thesis Objectives and Original Contributions
In this thesis I explore the 3D "Sound Scape" produced for various environments using
a towed array that is towed not only in a circular pattern in the horizontal plane,
but also up and down in the water column in what we term a "yoyo" pattern. This
research is unique because while 3-dimensional beam forming has been performed on
arrays in the past, those arrays were only towed horizontally, and not in any sort of
vertical manner. This research is done in preparation for experiments planned in the
Arctic for the Spring of 2016. I will present here a method I've developed for both
quantifying the amount of "verticalness" in a towed array, as well as quantifying the
improvement in the resulting noise as a function of that verticalness. I do this by
leveraging existing acoustic and autonomy software to run experiments in a virtual
environment in order to characterize how verticalness affects a 3D acoustic picture.
In this thesis I make two other original contributions to the field. First, I demonstrate that using the vertical arrival structure of the noise field in a 3D acoustic picture
as measured by a towed array, one can estimate the range to that source. Second,
I examine in depth the ability of a towed array to measure a horizontally isotropic
ambient noise field. The motivations for measuring these types of fields are related
to the unique Arctic sound speed profile and discussed in Chapter 5. The original
contributions are summarized as follows:
Quantifying Verticalness vs. Noise Directionality Improvement.
In the course of this research I've developed a method to quantify the "verticalness" in a towed array over time, and used this as a metric to predict the signal
excess and resolution improvement of the resulting 3D noise directionality.
19
Ranging to a Source
By using the vertical arrival structure of sound from a source in a 3D acoustic
measurement, I demonstrate that it is feasible to estimate the range to a target
using ray tracing techniques.
Resolving Horizontally Isotropic Vertical Noise Fields
In this research I conduct an in depth study into the inherent ability of a towed
array, with and without verticality, to resolve a horizontally isotropic vertical
noise field.
1.2
Thesis Outline
Chapter 2 discusses the background of the project. This includes a background on the
Arctic environment, possible methods for studying it, and a literature review on the
Arctic's acoustic properties. In Chapter 2, I also discuss the upcoming experiment
that was the inspiration for this research (ICEX 2016) and the particular AUV and
array that will be used during this experiment.
Chapter 3 is an overview of the methods and processes used, covering 3 main
topics. The first of these is creation and structure of the virtual environment. This
includes a description of the software architecture used, and as well a discussion
on how we can simulate acoustic propagation.
The second topic is how I define
the verticalness of an array, and the third and final topic is a description of the
mathematics involved in 3D beams and beam response patterns, and how the noise
field can be deconvolved from those beam responses.
Chapter 4 deals with experiments involving a simple source, and covers the first
two of the three contributions listed in Section 1.1. It begins with a small series of
experiments in which the verticalness of an array is compared against the resolution
of the resulting noise field. Next, it expands into a larger design of experiments, where
a full range of experiments 'with different vertical scores are tested, compared, and
discussed. Also in this section, I show through experimentation the data requirements
for picture convergence, and the feasibility of determining the range to a source using
20
the vertical noise arrival structure.
Chapter 5 is the exploration into quantifying how a towed array's vertical score
will affect the 3D noise picture picture when measuring horizontally isotropic vertical
noise fields. This covers the third of the three contributions. At the beginning of the
chapter, I discuss the motivation for measuring these types of fields, and then discuss
a series of results of a number of experiments in measuring these types of ambient
noise fields. Finally, I take an in-depth look into why towed arrays are inherently poor
at resolving these types of fields by closely examining the beam response patterns.
Chapter 6 consists of suggestions for future work and conclusions. Included in the
future work is a list of objectives and experiments that can be used to test the results
presented here with real world experiments, as well as several other suggestions for
follow on work in different (but related) subject areas.
21
22
Chapter 2
Background
2.1
The Arctic Environment
The Arctic Ocean is comprised of nearly 5.4 million square miles, which is roughly 1.5
times the size of the United States. It is well known that the extent of the polar sea
ice in the arctic region is retreating from year to year. Over the coming decades, the
extent of multi-year Arctic sea ice extent is expected to recede. The region will become
increasingly more widely used, as commercial interests seek to use trade routes that
were previously inaccessible, and nations seek to assert their rights over the region's
abundant oil and gas resources. The increased activity will manifest itself in the form
of resource extraction, fishing, tourism, shipping, and Naval activity [10].
Figures 2-1 and 2-2 show the effect of the retreating sea ice on the commercial
routes through the region. The blue bars represent times for open water conditions,
or less than 10% ice coverage, while the yellow bars represent the shoulder season,
defined by less than 40% ice coverage. Currently, the Bering Strait only sees open
water conditions for approximately 145 days with a shoulder season of 40 days each
year. By the year 2030, that time is expected to increase to 190 open water days,
with 70 days of shoulder. Other routes will experience similar effects. The Northern
Sea Route, which currently only experiences 15 days of open water conditions and 40
days of shoulder, will see open water times on average of 50-60 days with 70 days of
shoulder season by 2030. The Northwest Passage and the Transpolar routes, which
23
Figure 2-1: This figure shows the anticipated future transit routes superimposed over
the expected sea ice yearly minimum (also called multi-year ice), projected to year
2030 as anticipated by the United States Navy [10].
24
Arctic Sea Route Navigability
Bering Strait (BS)
Transp
440 Vesel
zou
m
-aa..a
Ro te(TPR)
0 Vesses
20M0
2020
Northwest Pas
Northen Sea Route (NSR)
(5.225 HIM)
(4,7401NM)
44 Veselsesel
2012
2025
1
1
>
Ves
202S5
A
LM.0A44
LOU Oct
IA$"A
201
(NWP)
kMbdlee
saftoo
40% sea ice
Shoulder Season: 10-40% sea Ice
Open Water: < 10% sea Ice
Figure 2-2: Projected navigability of the Arctic transit routes projected to year 2030
as anticipated by the Office of Naval Intelligence [10].
as of 2012 do not even see shoulder seasons, could each experience on average 30-35
days of open water per year, both with a significant shoulder seasons.
The Arctic region also holds a vast amount of mineral resources with significant
wealth potential. Estimates for the hydrocarbon reserve exceed $1 trillion dollars.
The Alaskan Arctic alone is estimated to hold 29.9 billion barrels of oil, 221 trillion
cubic feet of natural gas, and 5.9 billion barrels of natural gas liquids [8]. In addition,
the Arctic environment may hold significant amounts of mineral resources, including
but not limited to iron ore, zinc, nickel, graphite, and palladium [10]. The new open
transit routes, along with the new potential for the extraction of resources, means
that the Arctic region has regained its importance since its decline at the end of the
Cold War.
2.2
Studying the Arctic
Because understanding the Arctic region is of critical importance, we must seek ways
to understand it. Important areas for research include persistent ice edge surveillance
25
Figure 2-3: The Pathfinder satellite is a joint project between NOAA and NASA [24].
It is equipped with an Advanced Very High Resolution Radiometer (AVHRR), which
allows it to measure sea surface temperatures and approximate sea ice thickness.
for the reasons of safe navigability, seabed mapping, discovering tools for resource
discovery, and fundamental climate change research. So the question arises, how do
we explore these areas, and what platforms could we use?
The first area, ice edge surveillance, is particularly important. Naval operations
are likely to expand with newly discovered resource competition, and other oceangoing vessels will use the North East and North West passages as regular shipping
lanes during more months of the year, increasing the likelihood of loss of life due to
collisions with floating icebergs and ice floes [29].
Persistent ice edge tracking, however, proves a difficult problem. Satellite or aerial
vehicle imagery would seem to be a good solution, however this proves difficult in
practice. Persistent monitoring aircraft are prohibitively expensive, and there are very
few satellites designed to pass over the arctic because geostationary satellites must be
located along the equator in order to remain in orbit. Another issue is that satellites
have difficulties measuring ice thickness. Some satellites have mounted altimeters, but
the accuracy of this data is fairly low, and generally only good for long time scales of a
month or longer. There are some satellites, such as the NOAA Pathfinder satellite [24]
(see Figure 2-3), that can measure ice thickness via an Advanced Very High Resolution
Radiometer (AVHRR) using knowledge of microwave emissivity. This, however only
26
Figure 2-4: The USNS Able, or T-AGOS-20 is a SURTASS ship in service to the US
Navy's Military Sealift Command [25]. Platforms such as this can deploy many different types of sensors to study the ocean environment, but are expensive to operate.
works when the satellite is overhead and no cloud cover [12] [40].
Finally, aerial
monitoring gives no hints as to the resources that lie in and below the Arctic seabed.
An alternative solution is deploy ships and submarines to monitor the area. Figure 2-4 shows a picture of the USNS Able, an oceanographic survey ship in the service
of the United States Navy's Military Sealift Command [25]. Able is equipped with
a number of different sensors, including a Surveillance Towed Array Sensor System
(SURTASS), a large towed array deployed from the back which can provide much
information about the environment, as well as other information in terms of seabed
mapping, resource discovery, and general climate change research. The presence of
ships and submarines in the Arctic however, even smaller ones, could be very costly.
Operating these platforms is not inexpensive, and neither are the personnel that man
them.
One last solution is research using autonomous underwater vehicles, or AUVs.
AUVs, like ships and submarines, can be equipped with a number sensors, including
acoustic arrays, that are all very useful in gathering information for Arctic research.
And precisely because they are unmanned, they could prove to be a persistent, rel27
atively inexpensive method for doing so. The main problem with AUVs however, is
that they represent a relatively new and risky technology, and much research about
them before they can be reliably deployed to measure the environment in a useful way.
The feasibility of using AUVs and associated technology to evaluate the environment
is one of the main focuses for this research.
2.3
The Arctic Acoustic Environment
The primary focus in this research is studying the Arctic through the use of acoustics
as measured by AUVs, and in particular, the three-dimensional (3D) soundscape,
which will be discussed later. There are two important differences from most other
ocean environments that present themselves in the Arctic. The first is the unique
sound speed profile that is the result of salinity changes near the surface, and the
second is the ice cracking noise at the ice edge. There have been some studies that
give us hints as to the noise content we will see. The biggest area of interest is along
the arctic ice edge, because there is constant moving and cracking which creates a
significant amount of noise. This is noted in Diachok's paper [11], where he measured
the ambient noise levels at distances away from the marginal ice zone (MIZ) to see
the effects of the acoustic environment at different frequencies. His results can be
seen in Figure 2-5.
We can see from this figure that the spectrum levels for the different frequencies
increase significantly at and near the MIZ, for the frequencies of 100 Hz, 315 Hz, and
1000 Hz. At these frequencies, Diachok observed ambient noise levels up to 20 dB (re
(1ptbar) 2 /Hz ) higher than noise levels far under the ice field, and 12 dB higher than
noise levels in the open water. For a diffuse ice edge, these numbers are somewhat
less. These effects can be observed for long distances, especially at lower frequencies
such as 100 Hz, where we see the effects extend more than 50 km. Diachok concluded
that the noise mechanisms were probably related to wave and swell interactions with
individual ice floes, in a continuous distribution along the ice edge.
Further studies however, have indicated that this is not necessarily the case. In
28
A
A-0I
1%
400
-
%im1q0
IM*d
b
-30
/Ao
-
A
YAA
00VO
dip
-40 1-
-I-
-s0-
-o'
i
it0
I
s0
I
I
I
I
I
IOMCE
I
I
I
40
0
40
I
MET)
Figure 2-5: A measure of the ambient noise levels in the Arctic for different frequencies
at different distances from the ice edge, as measured in Diachok's paper [11].
29
30'
DiSTANT ICE
EDGE DOECTON
10'
C
40'
v0
*8
11.
Figure 2-6: Yang's experiments [39] showed that the ice edge noise, rather than being
a continuous line source, is actually the result of separate ice cracking "hot-spots",
which can be easily resolved at distances of 15 km away.
30
1983, a ship with a towed array of 64 hydrophone elements and an aperture of 290m,
listened to the noise field over a 24 hour period north of Jan Mayen Island. The ship
tracks, as well as some of the results of the experiment, are illustrated in Figure 26
[39].
While it was expected that the noise from an ice field came from a continuous
line source across the ice front, this experiment showed that the noise was actually
arising from a few localized individual ice cracking "hot-spots" along the ice edge,
which persisted for nearly 1 day, with a nominal separation of 50 km. The arrowed
lines in this figure represent the track of the ship, while the ice edge is represented
by the solid black lines. The points labeled A, B and C represent the separate areas
where ice cracking noise could be observed.
2.4
ICEX 2016
In the Spring of 2016, the US Navy is planning an ICe EXercise (ICEX), to which
it has invited MIT to participate for research with AUVs. This invitation represents
a renewal in funding for research in the Arctic Environment. During this exercise,
a team from the Laboratory for Autonomous Marine Sensing Systems (LAMSS) will
set up an ice camp somewhere on the polar ice cap above the Alaskan peninsula.
From there, they will deploy an AUV equipped with an acoustic towed array to learn
what sort of information can be learned about the environment through the use of
acoustics, or in particular the three-dimensional (3D) soundscape.
The lessons that could be learned from this experiment could prove significant.
Natural noise from the ice cracking could be used as a natural sound source. This
sound could not only be potentially utilized to track the ice edge, but for all significant
areas of research. The noise bouncing off the bottom could give hints as to the depth of
the arctic seabed, and also possibly the resources below. One method for imaging the
acoustic environment, will be the use of 3D acoustic pictures, or the 3D soundscape.
While currently no analysis on the soundscape exists for the Arctic, we have learned
information from the acoustic picture in other environments. The next section will
give just such an example.
31
Marginal Ice Zone
(MIZ)
Open Water
Figure 2-7: During the ICEX 2016 experiment with the US Navy, MIT will launch
an AUV equipped with a passive towed array in order to study the Arctic acoustic
environment. The goal is to use anthropomorphic ice cracking noise as a natural
source to obtain information to include bathymetry data, sub-seabed composition,
and ice edge location.
2.5
A Sample 3D Image
Using the array's information during ICEX 2016, the team from LAMSS hopes to
create a number of acoustic "pictures" which can give information about the surrounding environment.
Figure 2-8 is an example of one such image.
In 1993 the
SACLANT Undersea Research Center (SACLANTCEN) ran a number of towed array experiments listening to the ambient noise in shallow water areas using their ship
(R/V Alliance) as a towing platform. R.A. Wagstaff, in a paper [38], looked at several
of these experiments, and used an algorithm to develop a series of 3D acoustic images
using the methods that will be described later in this thesis (see Section 3.3.1). The
array in this case had an angle relative to the horizontal plane of approximately 1-2',
and the image was developed using a processing frequency of 100 Hz.
The image shows the full sound picture, with vertical angle on the y-axis and
azimuthal angle on the x-axis. A lot of information can be gained from this image by
comparing to the surroundings to the image. For example, the noise arriving at near
0' vertical angle and approximately 1500 azimuthal comes from a major northern
32
Distant
Shipping
Nearby Island
Island
Blockage
Noise
-
I
I
Noise
go
60
1
-30
-490
0
4
lei
I
so
Upslope
propagation
paths, allowed
by bathymetry
1351|180
225
I
S
AZ~r9WM4iE
(dbg)
I7 I
270
315
I- -- o
am0
Major Northern
Access for
coastal
steamers
Figure 2-8: An 3D acoustic picture analysis of a shallow water area from Wagstaff
and Newcomb's 1997 paper [38].
33
access for coastal steamers to a nearby port. From azimuthal angles 160' to 185', the
sound is mostly blocked by a series of small islands and relatively shallow bathymetry.
From azimuth's 245' to 330', the noise is arriving from a chain of nearby islands and
shipping which is bouncing off the sea bottom and the surface many times, which
gives rise to the vertical noise seen coming from these directions. Lastly, we can see
more noise from coastal steamers from the azimuths of approximately 25' to 60',
where the verticalness of the noise seen from the bathymetry from that direction is
indicative of the significant upslope propagation paths in that direction.
2.6
Types of AUVs
Here we will discuss the different types of AUVs available for general research today,
their capabilities, and a discussion on the appropriate vehicle choice for the ICEX
experiment. While there are many different models of AUVs available both commercially and militarily, the AUVs can generally be divided into three categories:
(1) gliders, (2) torpedo shaped AUVs, (3) and non-torpedo shaped AUVs. A glider
is an AUV that uses small changes in buoyancy in conjunction with a set of wings to
convert its vertical motion into horizontal motion. Examples of these include:
e The Webb Research Corporation's Slocum glider (named after the first person
to sail around the world solo)[35],
e The University of Washington's Applied Research Laboratory's "Seaglider" [1]
9 The Scripps Institution of Oceanography "Spray" [27] (Joshua Slocum's boat
when he sailed around the world, see Figure 2-9), which is sold by the Bluefin
Corporation
Gliders are advantageous in many ways to other AUVs in that they require very
little power to propel themselves through the water. They use very small changes in
buoyancy in conjunction with their wings to convert vertical motion to horizontal.
34
Figure 2-9: A Picture of a Bluefin "Spray" Glider[9]
The result is that they can conduct very long endurance missions, although they
are less maneuverable. Some, such as the Slocum Glider, can travel at 0.4 m/s and
operate in the water for 4-12 months. However, because of their slow speed and
generally small design size (they are typically designed to be handled by 1-3 people)
they cannot handle a particularly large payload, and therefore are limited on the types
of sensors they can carry. They operate at a variety of designed max depths (200 m
to 6000 m depending on the type). Another advantage is that they are generally less
expensive than other types of AUVs. For long term surveillance in the Arctic these
types of AUVs could prove to be the most useful.
The second type of AUVs are actively propelled and torpedo shaped. Examples
of these AUVs are:
" Bluefin 9", 12", and 21" from Bluefin Robotics [6].
" Remote Environmental Monitoring UnitS (REMUS) 100, 600, 3000, and 6000
from the Wood Hole Oceanographic Institute (WHOI) [18].
" Gavia - in types of (1) Offshore Surveyor, (2) Defense, (3) and Scientific classes [13].
These types of AUVs right now are considered the work horses of the community,
and are probably the most common type of AUV. One disadvantage is that they tend
to have shorter endurance ranges (on the order of hours or days) than the gliders,
however this can be extended if power saving methods are used, such as limiting
propulsion use and keeping the computing power to a minimum. They use active
35
propulsion generally by means of a propeller and a small fin, and the option to carry
larger payloads and more sensors than a glider, such as a towed array is an advantage.
These sorts of AUVs are particularly good for experiments that occur on the order
of hour or days, and can be deployed from a mother ship when doing so.
The last type of AUV is non-torpedo shaped AUVs. For a variety of reasons,
AUVs may be designed to a different shape. This may be for the purpose of carrying
unique payloads, such solar panels, or so that they can use more control surfaces or
propellers for increased maneuverability. These types of AUVs are typically only used
when their payloads require. Examples of non-torpedo shaped AUVs include:
9 The Autonomous Benthic Explorer (ABE) at WHOI [17]
e Solar AUV (SAUV II) [14]
9 Hovering Autonomous Underwater Vehicle (HAUV) [28]
2.7
The Bluefin-21
This research will focus on the Bluefin-21 torpedo shaped AUV because of its ability
to haul a towed array, it is actively propelled, and it is best suited for the ICEX experiment. Named for its 21" diameter hull, the Bluefin-21 has been used for many types
of missions, including offshore surveying, search and salvage, archaeology and exploration, oceanography, mine countermeasures, and handling unexploded ordnance [5].
The Bluefin-21 that will be used for the ICEX is maintained by LAMSS and is named
"Macrura".
2.7.1
General Specifications
Macrura is approximately 5 m long, weighs 785 lbs (dry), and contains nine lithium
polymer batteries which power its propulsion system. The top speed of the vehicle
is 4.5 knots, with an endurance time of 25 hours at 3 knots. Launch and recovery
of the vehicle is fairly straightforward: the launching platform must be equipped
36
Figure 2-10: A Picture of a Bluefin-21 on deck during a transit [6]. This is the vehicle
that will be used for the ICEX experiment, and an example of an actively propelled,
torpedo-shaped AUV.
with an A-frame, which launches the vehicle from a lift point mid-frame on the body.
Included in the on board navigational sensors are an Inertial Navigation System (INS),
a Doppler Velocity Log (DVL), Sound Velocity Sensors (SVS), and for when surfaced,
a Global Positioning Satellite (GPS) system. These sensors together allow the vehicle
to maintain real-time circular area probable (CEP) 50 accuracy of <0.1% of distance
traveled (DT) [5]. This means that 50% of the time the vehicle's navigation systems
will be accurate within a circular range of 0.1% of DT.
The primary form of communication while the vehicle is underwater is via underwater acoustics. While the AUV is underwater, the ship or controlling platform for
the AUV receives data and updates every couple minutes for near real-time information updates. Acoustic communication, or accoms, is handled by a system developed
by MIT under the open source software project Gobysoft.org [33]. In this communications paradigm, the transmissions of each node of an acoustic communications
network (such as VLA buoys, controlling ship, or the AUV), are given time windows in
which they can send their data. The data is encoded on the sending side and decoded
on the receiving side in order to reduce bandwidth, because the data transfer rate is
limited to about 1800 bps [30]. The reason for this is that acoustic communications
must use lower frequency ranges so that the signal does not attenuate after just a
37
few meters, even though the bandwidth at those frequencies is limited. While on the
surface, the Bluefin-21 is able to communicate through the RF or iridium antennas
on board for much higher data transfer rates [5].
Equipped Acoustic Array - DURIP
2.7.2
The array to be used in the ICEX experiment, as well as the one modeled in this research, is the Defense University Research Instrumentation Program (DURIP) array.
The DURIP array has a total of 32 hydrophones, with a total acoustic aperture of
30 m. 21 of the hydrophones are spaced at 1.5 m apart, while the remaining 11 are
nested in the center, as shown in Figure 2-11. The hydrophones have a sensitivity of
-176 dB/V/pPa, with a sensitivity tolerance of +/- 1 dB [26]. The optimal frequencies are measured when the acoustic wavelength is equal to half the spacing d of the
array, such that:
d= 2
A = c/f
2
(2.1)
where A is the wavelength of the acoustic wave, c is the speed of sound in the water,
and
f
is the optimal frequency for the array spacing. Using these equations, we can
calculate the optimal frequency for an array spacing of d as:
ft
C
=
(2.2)
In our acoustic array, we essentially have two arrays with a spacing of 0.75 m and
1.5 m. Using a sound speed c
=
1500 m/s, this array can be operated for frequencies
up to 1000 Hz and 500 Hz, respectively for the two apertures. Lower frequencies can
also be measured by choosing elements that are spaced further apart, however, the
resolution on your aperture decreases. This is why larger arrays are needed to resolve
lower frequencies. We can say the array has a bandwidth of approximate 100 Hz to
1000 Hz. Above 1000 Hz, we can expect to see aliasing, as the wavelength will become
significantly smaller than the array spacing, and the noise directionality becomes less
reliable.
38
DURIP Array
20 m
36 m
20 m
*
0
30 m
Aft
Compass
Aft Depth
Sensor
Forward
Compass
32 Pressure Sensor Elements
*
Drogue
1.5m spacing
1.5m spacing
0.75m spacing
Tow Line
Data
Acquisition
System
(DAS)
macrura
Figure 2-11: A general schematic of each of the DURIP array. Beginning at the
attach point of the AUV and working from right to left, the full array consists of
a 20 m tow line, a data acquisition system (DAS), a forward compass, 32 pressure
elements, an aft compass, an aft pressure sensor, and finally a 20 m drogue. The part
of the array that contains the actual elements is what's called a "nested" array, and
has two spacing sizes, 0.75 m and 1.5 m. These spacings allow it to cover a frequency
range anywhere from 100 to 1200 Hz.
Figure 2-12: The complete DURIP array at LAMSS [7], which will be used in the
ICEX experiment in the spring of 2016, and modeled for simulation in this research.
39
Each of the hydrophones are sampled at a rate 12 kHz, and data is collected
on each hydrophone in 2 second intervals. The array also has some other features
- on both the forward and aft ends a compass is mounted to help determine array
positions, and another pressure sensor is located just aft of the acoustic portion of
the array. The pressure and compass readings are sampled at a lower data rate than
the hydrophones [26]. Figure 2-12 shows a photo of the array.
40
Chapter 3
Overview of Methods
This chapter discusses the methods used to create the virtual environment, and in
particular the tools used to process the resulting data from that environment. This
includes beamforming techniques in two and three dimensions, how a noise field is
modeled, and how we can extract a pseudo-stationary noise field from the beam
response patterns. This section also discusses how I quantify the "verticalness" in
the array.
3.1
3.1.1
Virtual Environment
MOOS-IvP and LAMSS
There are many different autonomy middlewares that are used for robotic applications. Of these, some of the more common middlewares include Mission Oriented Operating Suite (MOOS) [2] [3], Robot Operating System (ROS) [15], and Lightweight
Communications and Marshalling (LCM) [23]. The code architecture used in this
research is based on the open source project MOOS-IvP, from the MOOS autonomy
middleware.
Launched originally at MIT in 2005, MOOS-IvP includes more than 150,000 lines
of code and 30+ core applications dedicated to controlling marine vehicles, mission
planning, debugging, and post-mission analysis. The software has been run on more
41
MOGS Appkedon
Figure 3-1: A MOOS community is a collection of applications, each publishing and
subscribing to variables published to a central MOOS database. A MOOS community typically operates on a single vehicle or computer. Image courtesy of Mike
Benjamin [4].
than a dozen different platforms and is being used at the Office of Naval Research
(ONR), the Defense Advanced Research Projects Agency (DARPA), and the National Science Foundation programs at MIT. MOOS-IvP can be used for a simulated
environment, or for fielding the vehicles in a real environment.
MOOS contains a core set of modules that provide a middleware capability based
on a publish-subscribe mailing architecture. Processes in the MOOS database are
defined by what messages they write (publishing), and what messages they consume
(subscribing).
The key idea for MOOS is that it allows for applications that are
mostly independent, and that any application can be easily replaced or upgraded
with an improved version. The only requirement for the improved application is that
only its interface matches [4]. Figure 3-1 shows a MOOS community, which typically
runs on a single machine, and the structure of processes. MOOS communities set-up
on on multiple platforms are also capable of communicating with one another.
On top of the MOOS-IvP architecture, there is another architecture known as
the LAMSS environment - where LAMSS stands for the Laboratory for Autonomous
Marine Sensing Systems. The LAMSS repository is an additional build of MOOS
modules that have been structured to allow easy transfer between simulation of an
autonomy system on a vehicle and moving that autonomy system to an actual experiment. In simulation, LAMSS already has a set of tools that allow a use to simulate
42
1vP Function
1vP Function
Informiation|
Decision
Figure 3-2: The IvP helm is a single MOOS application. It uses a behavior-based
architecture, in which a mode structure is used to determine which behaviors are
active. Each of the active behaviors are then reconciled using a multi-objective optimization solver, or the IvP solver. The resulting decision is then published to the
MOOS database. Image courtesy of Mike Benjamin [4].
an acoustic environment. Many of these simulations have been leveraged for the ideas
presented in this research.
3.1.2
Vehicle Behaviors
IvP (Interval Programming) is a single application that runs inside the MOOSDB.
IvP uses a behavior-based architecture for implementing autonomy. These behaviors
are distinct modules, each of which are dedicated to a specific aspect of autonomy,
such as following a set of waypoints or for collision avoidance. If multiple behaviors
are active, the IvP uses a solver to reconcile the desires of each behavior using an
objective function [4]. Figure 3-2 shows how the IvP system is structured.
There are two relatively simple behaviors to control the vehicle in this research.
The first behavior, BHViLoiter, directs the vehicle to move along the points of a
polygon. These points can be specified individually, or as a collection of points with
a center and a radius. To create a circular pattern using this behavior, one simply
increases the number of points in the loiter polygon so that it approximates a circle.
The second behavior, BHVSmartYoyo, is used to control depth. This is a behavior
43
available inside the LAMSS repository, and by specifying a yoyo length period in
meters, the AUV is directed to move up and down in the water column between two
specified depths. By controlling the period of the yoyo pattern, we can control the
pitch of the path taken by the AUV, and of the towed array behind it.
In a real world experiment, many other behaviors would need to be utilized to
control the vehicle safely, specifically including such behaviors as an emergency surface
behavior, a minimum altitude behavior so that the vehicle doesn't ground, a travel to
waypoint behavior, and a set of behaviors for vehicle recovery. Fortunately, many of
these behaviors exist in the standard MOOS-IvP and LAMSS repositories, and they
have been tried and tested in both simulation and real world experiments.
3.1.3
Building a Virtual Acoustic Environment
As discussed in the previous section, the code base used in this research utilizes
existing code built in the MOOS-IvP and LAMSS repositories. Figure 3-3, shows
the key tools and programs used to generate the virtual acoustic environment in this
thesis.
The crux of the data processing happens in a piece of code called uSimPassiveSonar. uSimPassiveSonar takes in elements from several other applications that define
the environment, and ultimately outputs the pressure sensor data for the elements
of the simulated array. The other utilities and processes provide interfaces, inputs,
and do calculations that allow uSimPassiveSonar to operate. The application uses a
ray-tracing model, which simulates ambient noise, noise from sources, and also allows
for specifications of the vertical noise directionality.
The model for the system is
discussed in Appendix A.
uSimPassiveSonar relies on two other processes - uSimNoiseCovariance, which
develops the noise covariance matrix required for producing the pressure patterns,
and iBellhop, which provides a MOOS interface to an acoustic modeling program
called Bellhop.
This program is a Gaussian/finite element beam code written in
Fortran, and is part of a larger acoustic toolbox available online from the Ocean
Acoustics Library [22].
44
pGen~ealce
uSimNoise ce
uSiMptarge
UsimCTm
uSimBathy
-
--
-
uSIMIassive or
IBeffhop
uSimTowedArray
Figure 3-3: The MOOS-IvP Autonomy Code Architecture for the experiments run in
this research. The purple blocks represent the building blocks for the acoustic picture
during the simulation in real time, and the blue block is the resulting data, including the time, array position, and pressure readings, recorded in real time. Lastly,
the orange block is the 3D acoustic noise code, generated after the experiment is
completed.
45
Code
pGenSealce
uSimTargets
uSimCTD
uSimPassiveSonar
uSimNoiseCovariance
iBellhop
Description
Defines the characteristics of the noise
source(s) being used in the experiment and
provides visual cues in the simulation environment, including source strength, location,
depth, and frequency range
Takes definitions from pGenSealce and produces the sources in a format that can be
consumed by uSimPassiveSonar
Gives inputs for temperature, salinity, and
pressure that ultimately define the sound
speed profile
Provides bathymetry (sea bottom) data for
the environment
Provides array element positions using a dynamic cable model for the array
Coordinates inputs from other various modules to produce the pressure and array location data used for post-simulation processing
Builds the covariance matrix based on the
environmental inputs and vehicle location to
produce the acoustic data
A MOOS interface to the Bellhop program
which performs the ray tracing calculations
needed to provide accurate noise data
Table 3.1: A brief description of each of the key code modules used to build the
virtual acoustic environment.
46
Figure 3-4: A snapshot from the display of a simulated acoustic environment. The
ice edge and hot-spot visuals are created by pGenSealce, while the IvP helm controls
the AUV Macrura with a series of behaviors.
There are other pieces of code that feed inputs into uSimPassiveSonar. pGenSealce
defines the noise source sources, including source frequencies, location, and depth.
pGenSealce also then publishes these definitions as messages to the MOOSDB, which
is subscribed to by uSimTargets. uSimTargets then generates the information and
data necessary to simulate the noise source, and feeds this data into uSimPassiveSonar for processing. uSimCTD and uSimBathy each describe different parts of the
environment. uSimCTD simulated the acoustic environment in terms of the salinity,
temperature, and pressure in order to develop a sound speed profile which is used
in the passive sonar processing. uSimBathy provides data on the bathymetry of the
acoustic environment. Finally, uSimTowedArray gives the position of each of the elements on the array based on the vehicles position using non-linear cable mechanics.
Table 3.1 gives a brief description of each of the processes involved, and Figure 3-4
shows a snapshot of the simulation in progress.
3.1.4
Modeling Array Shape
The shaping of an array is a crucial part of acoustic processing, and therefore so
is the program uSimTowedArray. uSimTowedArray provides those positions using a
47
nonlinear dynamic cable model to describe the motion through the water, and the
background for these mechanics are discussed in Appendix C. The exact positions
of the array are known and calculated, and used both for receiving the signal in the
simulated acoustic environment, and for processing afterwards.
In real world experiments, however, the actual array position that receives the
signal will not necessarily match the assumed element positions used for signal processing. Convention tells us that if the position of the elements is known to within
10% of the wavelength, the signal will still be reasonably accurate. For the frequency
used in this research, that means the position of the elements must be known to be
within approximately 17 cm:
PositionError<= (0.10)- ~ 17cm
(3.1)
This metric can be achieved in a number of different ways. Arrays that deal with
higher frequencies
(
10+ kHz) can be made at much shorter lengths to achieve the
same aperture as an array designed for lower frequencies. These smaller arrays can
be held in a rigid fixed line, such as off the nose of an AUV. However, this proves
impractical when using larger arrays that necessitate the use of towed line.
Another solution is modeling with constraints. Based on the position of the vehicle, the model used to simulate the array position in this research could be used
to estimate the actual position. Also, recall that the DURIP array has several other
sensor inputs apart from the arrays - two compasses and a pressure sensor on the
aft portion of the array. Using the model subject these constraints could achieve the
desired accuracy, however, more testing on this subject would need to be done.
There are methods in real world experiments such as the use of high frequency
transponders or Ultra Short Baselines (USBLs) [34], which are used to actively track
accurate distances to different locations along the array. These USBLs can be fairly
accurate - one such USBL available commercially is the iXBlue fourth generation
GAP, which advertises a 0.06% accuracy at ranges of up to 4,000 m [19]. Since the
farther element on the array would be approximately 53 m, by these standards we
48
could see positional accuracy to within ~3 cm. This USBL is not equipped to be
installed on a Bluefin-21, however, the technology for measuring the elements within
the required accuracy is available.
3.2
3.2.1
3D Acoustic Pictures
2D Beamforming
The purpose of beamforming is to find the angle of incidence from an array to a
noise source (or a noise field created by a number of sources) by measuring the phase
differences of the arriving acoustic waves between a series of pressure sensors along
that array. To begin understanding three-dimensional (3D) beamforming, it helps to
begin with standard 2D beamforming.
Let z be the direction of a straight array of i = 1 : N elements on a horizontal
plane, at the locations d, = [0, s, 2s, 3s, . . , Ns], where s is the spacing of the array. If
we are observing at frequency
f, we can calculate the wave
number to be: k = 27rf /c,
and describe the wave number k in terms of the azimuthal direction 0 as:
kZ =eik cos O
(3.2)
where 0 is the angle away from perpendicular to the array in the domain of 100 1800],
as shown in Figure 3-5. This wave number can be used to calculate the beam for that
direction for this array orientation:
N
b(0) = N
eikdi
(3.3)
i=1
To get the phase information from the array, we take the Fourier Transform of a
snapshot of pressure data pi at frequency
f to
get the signal delay vector in complex
space for each array element i where i = 1 : N:
Vi = TT(pi, f)
49
(3.4)
0
kZ
Pressure
wave
fronts
Figure 3-5: The "look" direction 0 in 2 dimensions (typically on the horizontal plane)
away from perpendicular to the array.
Finally, the beam pattern response is generated by multiplying the delay vector of
the signal by the beam for each direction 0:
N
B(6) = N
vi b()
(3.5)
i=1
This beam response gives the picture of the noise directionality seen by the array.
It is known as Bartlett beamforming [20]. The ambiguities of this sort of beamforming
are that positive and negative angles (6's) cannot be distinguished from one another.
For example, if the direction of the wave number k. was 0 = 30', the noise directionality calculated by Equation 3.5 would not be able to distinguish that direction from
0 = -30'.
3.2.2
Extension to 3D Beamforming
3D beamforming is similar to 2D beamforming, except that we realize the fact that
noise is not just ambiguous for 0 vs. -6, but for a whole cone of directionality with
an axis along the array. In the case of a line array as described in Section 3.2.1,
the direction 9 actually describes a conical angle /3 in three dimensions, as shown
in Figure 3-6. In conventional 2D beamforming, this concept is lost. Noise sources
coming from above or below the horizontal plane will be spread over many azimuthal
directions, giving a false representation of the actual noise field. It therefore follows
that a 3D method will in fact give a more accurate picture.
Figure 3-7 shows an example of a simple broadside beam response pattern rep50
#
Figure 3-6: The noise coming onto a straight array from the beam formed at angle
is coming from all the directions of the cone projected onto a sphere.
resented in two and three dimensions. 0 represents the azimuthal bearing, where 00
is directly North and 1800 is directly South, and
#
represents the vertical direction,
where 90' is directly up from the horizontal plane and -90' is directly below. In the
3D noise picture at the bottom of Figure 3-7, 0 is on the horizontal axis, 0 is on
the vertical, and the beam response is represented by the color on a scale where red
is the maximum beam response and blue is the minimum. The figure represents a
three dimensional pattern of a 10-element horizontal array with its ends aligned from
0 = -900
to 0 = 900 with a source at 0 = 0' corresponding to 3 = 90'. In the 3D
representation, note that the maximum of the pattern is on the area represented by
the cone defined by j = 90'. This illustrates that not only does the beam pattern
max out at 0 = 0 and 0 = 180', but also from directly above and below, as we would
expect. In the following sections, we will explore a few other beam patterns, as well
as the mathematical process for producing them.
3.2.3
Creating the 3D Beam Response
Let the x, y, and z positions of the array in three dimensional space be represented by
the vectors xn, yn, and zn for the nth array element of N array elements. Using these
numbers, we define a distance vector dn(0, #), which represents the distance from the
nth element to a sphere in the far field. The location of the center of the coordinate
system is unimportant, because it is only the relative distances from each direction
(0,0) that are needed to measure the phase difference of the arrival pressure waves.
d,,(0,
#)
can be calculated by the following equation based on the geometry presented
in Figure 3-8:
51
I
0.8
-\
0.6
0.4
0.2
0
50
100
150
200
250
300
350
M 5
CU
iznt
IUU
r
MU
_Iuu
horizontal (azimuthal) bearing, degrees
Figure 3-7: A comparison of the beam pattern response for a horizontal array broadside to a source in 2D and 3D.
d,(0, 0) = -(x, sin 0 + y, cos 0) cos
#-
z, sin 0
(3.6)
Once the distance vector is calculated for each element, and the wave number
k = 2wrf/c is found, the beam pattern for the array orientation can be calculated,
similar to the way it is calculated in 2D beamforming:
b,(0, 0)= e ikdn
(3.7)
Finally, the 3D beam response r(O, #) is calculated by summing the product of
the delay vector (Equation 3.4) and the calculated beam (Equation 3.7) over each
element, and dividing by the total number of elements:
N
r(o,
=V'Cikd,,(0,<0)
1)
(3.8)
n=1
This picture is generic for any array orientation, and any shape, including curved
52
z
d.(OO)
00A
Figure 3-8: The distance vector da(O, #) represents the distance from the x, y, z
position of the array element to a sphere located in the far field that represents the 0
and # directions.
arrays, as long as the positions of the individual elements are known. Note, however,
that the conical ambiguities discussed in Section 3.2.2, will only apply if the array is
configured straight.
3.3
Beam Response Patterns
To get an understanding of different types of beam response patterns, it is important
to look at a few examples of the beam pattern responses for different source locations
and array orientations, as shown in Figure 3-9. For these examples, all the data was
normalized, and the array held in a straight line at different orientations to a point
source.
The top left picture illustrates the resulting beam pattern for a source broadside
to the array. This clearly shows that the ambiguities exist at elevation
+/-
90 , and
also in the azimuthal direction 1800 degrees away from the source. If we think about
it as a conical pattern around the array, the pattern is the cone defined by 0 = 90', or
a circle in a plane perpendicular to and centered on the array. In the example in the
top right corner of Figure 3-9, we see the beam response with the array tilt still set to
0 , but now the source is closer to endfire. This would be the projection of the cone
specified by 3 = 150 for a horizontal array. Note that when the source is closer to the
endfire of the array as opposed to broadside, the beamwidth of the response is much
larger, resulting in an increase in the uncertainty of our directionality measurements.
In the bottom two pictures of Figure 3-9, we introduce tilt into the array. The
53
Source ?eer Endfire
80
GO. tilt
I
.
-
--
1
0.9
60
4C
0.7
41
20
0.6
2'
03
0.4
-2C
-4(
-2
0.3
0.2
-6(
0.1
-8C
50
100
uu
250
200
150
Azimuthal Bearing
>
100
150
200
Azimuthal Bearing
'CUU
Azimuthal Bearing
au
uv
as
I
028
0,7
0.6
0.5
04
013
0.2
0.1
Off-horlhantal Source
Tilted Arry
A..
-... A-m .. nea
111U
0.9
I
I
I
0.9
0.8
0.7
0.6
0.5
0.4
03
02
0.1
>:
Azimuthal Bearing
I
1
0.9
0.8
0.7
0.6
05
0A
0.3
02
0.1
Figure 3-9: Beam response patterns for multiple array orientations and source locations. Top Left: A horizontal array broadside beam response. Top Right: A horizontal
array with the source near endfire. Bottom Left: Source broadside to a tilted array.
Bottom Right: Tilted array with a source not at broadside.
54
picture on the bottom left represents an array with 300 tilt and a source placed
broadside, and again with the conical "circle" defined by
#
the circle is tilted. This removes the ambiguity away from
= 90'. This time, however,
+/-
90' elevation. In the
final picture, we see a more complicated beam pattern, with 100 tilt in the array and
the source off broadside.
In general, if the location of the source is known and the array is assumed to be
straight, we can calculate the angle / by the following equation [38]:
cos--
cos # cos 0 cos a + sin[cos -- (cos # cos 0)]
x sin a sin tan
-1
sin
(cosqs
cos 0 sin0
#
#
f
where a is the tilt of the array. The full geometric derivation for calculating this
angle is available in Appendix D [36].
3.3.1
Deconvolving the Noise Field
The method we chose to deconvolve the noise field was that originally proposed by
Wagstaff to use 3D directionality principles to increase the quality of the 2D noise
rosette.
The first inclination when trying to understand a noise field, is to run the vehicle
in as many directions as possible, and then take average of all the beams produced
from the different directions. This method however presents problems, particularly
due to the presence of sidelobes, which will be included in the picture, but don't
actually make a part of it. Instead we use a method for extracting a noise field
originally proposed by Wagstaff [37]. Wagstaff uses a model of the 3D noise field
that includes the beam of the array, and then uses an iterative method to extract
the pseudo-stationary noise field from it. Pseudo-stationary means that the measurements assume the noise field does not change over all the positions of the array from
which the measurements are taken, and also does not change over the span of time
55
Figure 3-10: The technique used for deconvolving the noise field. On the left side
the data and the shape of the array are used to produce a measured beam response,
or "directional measure", and on the right hand side, the beam of the array and a
noise field estimate is used to create an estimated beam response, or "directional
estimate". The estimate and response are then compared, and a new noise field
estimate is generated so that the process can be repeated.
during which the measurements are taken.
Here I will present the method used to extract the noise field. This method is
slightly different than the one Wagstaff presented because Wagstaff calculated all his
beams in advance, converted them to 2D using Equation 3.9, and then compared
those to the measured 2D beam patterns of the array to produce the noise field. This
conversion was necessary because at the time, calculating the 3D beam patterns was
computationally expensive.
However, now we can now simply calculate the beam
response for each set of data in real time for each iteration, and then compare it to
the 3D estimated noise field for each iteration. This has the added benefit that curved
arrays can now be measured, as the 2D conversion can only be applied to straight
arrays. The full iterative technique for this process is illustrated in Figure 3-11.
3.3.2
Modeling the Noise Field
In Wagstaff's 1997 paper, he presented an iterative method for developing the noise
field based on a model [38]. To begin, we assume that the noise field is developed
with Equation 3.10:
rij
=
-
- dtj
T 0 27T
2
0
,r
nitotai(, 4,t)bj (6,1)
-do
2
cos # do
(3.10)
_,/2
In the above equation, rij is the 3D beam response for the ith beam (a (0,
#)
combination), and the jth array orientation (or data sample). t is time over the total
56
#
time T of the measurement, 0 is the azimuthal angle in the horizontal plane, and
is the vertical angle in elevation. bj(0,
#)
is the beam response pattern for the jth
array orientation (or data sampling), as calculated for that particular array position
in Equation 3.7, and nrtoti (0, q, t) is the complete, time dependent noise field. This
equation assumes that the range of positions of the array are all small compared to
the overall size of the noise field in such a way that the noise field doesn't change
based on array position.
Now, let us take a look at the overall noise field as a sum of components:
ntotal(O, q, t) = n(O, 9) + ((0, 0, t) + E(0, #, t)
In Equation 3.11, nrtotal (0,
n(0,
#, t)
#) is the pseudo-stationary
(3.11)
is the overall time-dependent measured noisefield.
noise in the environment, ((0,
9, t) is the time-dependent
component of the noise field due to fluctuations in the acoustic propagation, noise
source movement, changes in noise source, etc., and c(0,
#5, t)
is the error induced by
tow ship noise, flow noise, array position error, etc. In simulation as well as in real
time testing, we can consider ((0,
E(O,
9, t)
9, t)
to be negligible with temporal averaging, and
to be small enough to be negligible by using noise reduction techniques and
array grooming
[38].
With these assumptions, we can re-model the noise field as:
ntotai(O, #, t)
r n(0, 9)
(3.12)
Using this approximation we can reduce Equation 3.10 to the following:
ri
=
4x 0
in(O, #)bj (0,9 ) cos #d#
dO
(3.13)
-_r/2
This is the model we use to solve for the noise field.
3.3.3
Iteratively Solving for the Noise Field
Equation 3.13 has three main components. The first, the 3D beam response rij (9
5),
can be calculated from the array positions as in Section 3.2.3. The second component
57
Assume a Constant
Noise Field
Calculate the Delay
Vector
Calculate Difference
between current and last
Pooled Std. Devs.
Calculate the Estimated
Beam Response s
Find the Pooled Standard
Deviation
Find the Difference
between the Estimate and
Measured
Output NoiseField
Divide by two, add the
lp
average difference to
Estimated Noise Field
Figure 3-11: A Process Diagram for the iterative process used to deconvolve the noise
field from the beam response patterns.
is the beam for each array orientation b-(9, 0), which can also be calculated using
Equation 3.7. The remaining component, n(O, 0), is the last unknown, and what
we are trying to solve for.
This is done with the iterative process prescribed by
Wagstaff [38], where we begin with an estimate for the noise field, use it to calculate
the estimated beam pattern response, compare it to the actual response, and then
based on the difference make a new guess for n(O, #). This process is repeated until
the noise field settles on a certain position. This is illustrated in a process diagram
in Figure 3-11. The following paragraphs describe this process in greater detail.
The process begins with an initial estimation for the noise field in dB Nk=o, which
we set to any constant C, which could just be an approximation of the ambient noise
field. The choice doesn't really matter as the end result is relatively insensitive to the
initial estimate. This guess is taken and converted to the pressure intensity domain:
Nk=0(0, 0) = C
hnk(0, ) 10Nk/10
-
(314)
where rik is the estimated noise field in the pressure intensity domain for kth iteration
in the process. In general, upper case letters will be used to describe fields in the dB
58
2
)
domain, while lower case letters will be used to describe fields in the intensity (p|
domain. Based on the noise field, we now want to find the estimated beam response
pattern. This is done by calculating the signal noise delay vector for each element:
7/2
Vi,j,k,n
j
/27r7r/2 (O,
jO)e ikdi,j' cos
k
OdfdO
(3.15)
_
where
Vi,j,k,n
is the delay vector for the ith direction of I total directions, the jth
array orientation or data sample of J total data samples, the kth iteration, and the
nth array element of N total elements. With the delay vector, the estimated beam
response is calculated and then converted back to dB space:
ik
i,j,k,feikdi,jn
ij,k
10 log1 0 ij,k)
(3.16)
n=1
The final step in the iterative process is to find the difference between the estimated
field response and the measured one, divide by 2, and then add the result to the
estimated noise field from the previous iteration:
Ai,j,k =
Rij -
Ni,j,k
1 (0, 0) +
-k+
I
Ai~~
2
J
(3.17)
j=1
This process is then repeated until the standard deviation of the solution converges, as described in Section 3.3.4.
3.3.4
Statistical Convergence
To determine when the process has been repeated enough times and has stabilized
on a noise field, we measure the standard deviation of the estimated beam responses
relative to the actual beam responses. A quantitative measure can be derived by
calculating the pooled standard deviation o-, of the differences between the measured
beam response and calculated guessed response [37].
1
J
(= j)
E
j=1
59
1/2
(3.18)
where the standard deviation o- for the jth array orientation or data sample is:
[
j) 1/2
~~
I
=1_ (Rij . i_1
-
I-1
-
(3.19)
RJ)-1R1/2
and Rj is the mean difference for the jth array orientation:
-
Rj =
1'
(Ni,j - Ri,)
(3.20)
i-1
After each iteration, Equation 3.18 is used to calculate the pooled standard deviation op. This value in general becomes smaller and smaller as the estimation for the
noise field becomes more accurate. For each iteration, we can track the change 6 p in
ap.
6
p,k = Up,k - Up,k-1
(3.21)
Finally the iteration process is discontinued when 6p,k reaches some pre-determined
arbitrarily small threshold. At this point, the resulting h(O, q) is accepted as the final
estimate for n(O, q).
3.4
Measuring Vertical Directionality
One of the key components for understanding the quality of the 3D picture, as we will
see in Chapter 4, is in understanding how adding "verticalness" into a towed array
as it is given tilt in the water column will affect the 3D acoustic picture. Quantifying
how much "verticalness" one can have in a towed array for a period of different array
orientations and tilts is crucial.
There are many ways to get verticalness into an array. The yoyo pattern used here
is one of those ways. However, the vehicle could also be maneuvering through the
depth column for a specific purpose, such as to establish acoustic communications,
or to rise to the surface. Because of this, we need a way to quantify the amount of
verticalness we find in an array over time that works in all situations. This section
60
L
h
Figure 3-12: The measurements for finding the verticalness of an array by its elements.
h represents the height of the array, from the lowest z-direction element to the highest
element, where L represents the maximum distance between any two elements on the
array projected on to the x-y plane, which is typically the horizontal distance between
the first and last element.
shows how we can quantify verticalness so that it can be used as a benchmark to test
how to achieve the best 3D acoustic picture.
3.4.1
Instantaneous Verticalness
At any instant in time, we are able to measure the amount of verticalness we have
in our array. This is done by measuring the height of the array as compared to the
length, and using the following equation:
w(t) =
2
-
wr
sin
1
h
(--)
L
(3.22)
where w(t) is the verticalness of the array, h is the height from the lowest element to
the highest element, and L is the total length of the array, as show in Figure 3-12.
In this method, if an array is perfectly horizontal, its verticalness is w(t) = 0, and
similarly if it's perfectly vertical, its verticalness is w(t) = 1. In this way, we can
track the verticalness of an array at a given instant time.
61
3.4.2
Tracking Verticalness over Time
Creating a single 3-dimensional picture involves measuring the values over a length
of time, something on the order of minutes or longer. Therefore, it's not the instantaneous verticalness in the array that's important, but the amount of verticalness that
has been seen over the most recent amount of time. This section shows a method
to do this, using the instantaneous verticalness measurements and applying it to an
impulse response model. If we keep track of the verticalness of the array over time
with Equation 3-12, we can keep track of a "vertical score", which I'll call v(x), with
the following equation:
e-(tx-)/w(x)dx
v(t) =
(3.23)
Jt
In the above equation,
T,
is a decay constant, t is the current time and to is the
time the measurements began. Verticalness more recently in the array becomes more
important than verticalness a longer time ago, using an exponential decay. Figure 313 shows an example of one of the experiments conducted by showing vehicle depth,
the measured array verticalness, and finally the vertical score. For this example and
all the experiments, the value r, = 100 was used.
3.4.3
uVertScoreKeeper
In order to keep track of the vertical score, a matlab program call uVertScoreKeeper
was created to run in along with the vehicle to keep track of the verticalness of
the array. Using iMatlab as an interface, it provides real time tracking and visual
representation of the ship position, array positioning, the instantaneous verticalness,
and the vertical score. In addition, it saves all the information so that it can be used
for processing and analysis after the virtual experiment is completed.
shows an example output running in simulation.
62
Figure 3-13
XY Position
1000 r
800-
Array Visualization
0-
Hot Spot 1
SL = 120
TL = 65.036
SE = 14.964
-100
-100
-60
-80
600-
-40
0
-20
Verticalness of Array
UU
0.2-
Verticalness = 0.21006
.
0.1
400-
0
200-
500
2000
1500
1000
Time(t)
Vertical Score
-
cu 0.3
0
Vertical Score
0.2
acrura
0
=
0.18652
0.1
-600
-400
-200
0
200
400
0
600
500
1000
1500
2000
Time(t)
Figure 3-13: An example of the real time tracking provided by uVertScoreKeeper.
The left window shows the path taken by the AUV in the x-y plane of the AUV,
the top right shows the depth of the AUV along with a visualization of the array
projected behind the vehicle, the middle right window is a graph of the instantaneous
verticalness, and the bottom right window is a measure of the vertical score. The
vertical score measured at the end is the overall vertical score for the run.
63
64
Chapter 4
Noise Field with a Point Source
4.1
Quantifying Resolution
One of the major points of this thesis is the exploration or the increase in the resolution
of a noise picture based on the the verticalness of the array. In this section, we will
run experiments that will demonstrate that increasing verticalness in the array can
significantly increase the resolution of the 3-dimensional acoustic picture. In addition,
we will see the time for convergence of a noise picture, and finally demonstrate the
feasibility of using 3D pictures to find the range to a target.
4.1.1
Experimental Setup
To explore the changes in quality of the noise picture, a simple experiment was devised. In this experiment, we set a simple source directly North of the vehicle, at a
distance of 5km and at 5 m depth, with a frequency of 900 Hz. The source level is
set to 120 dB. The frequency was chosen because that is similar to some of the noise
frequencies that have been seen previously in the Arctic. It was also chosen because
it matches well with the frequency range of the DURIP array. The noise source level
was chosen to be high enough such that the signal could be seen relatively well above
the ambient noise present. A lower source signal could be used, however, the goal is
to distinguish how the vertical directionality of the array affects the resolution, not
65
Experiment
1
2
3
4
5
6
7
8
Yoyo-Period
300
500
600
700
1000
1500
2000
N/A
Table 4.1: Different periods were used for the yoyo patterns for each experiment to
introduce different levels of vertical directionality into the array. For the 8th run, the
vehicle was held at a constant depth, and therefore has no period.
see the limits of can and can not be seen.
The AUV was run in a circular loiter pattern with a radius of 100m. The vehicle
was started at a depth of 50 m and allowed to run one full circular loiter pattern.
Figure 4-1 gives the general setup. For the constant depth run, the vehicle remains
at 50m, but for the other runs, the vehicle is commanded to perform different yoyo
pattern with different periods. The period specified is the distance the vehicle would
travel along its horizontal path before it completed a full up-down-up pattern. The
upper limit of the yoyo pattern is set to 20 m depth and the lower 100 m depth.
Shorter periods correspond to higher degrees of vertical directionality, while larger
periods correspond to lower. Table 4.1 gives a list of the different yoyo periods used
in the experiment.
The pixel resolution of the 3D acoustic images produced is 30 in the vertical
direction and 3' in the azimuthal. Higher pixel resolutions were not measured because
small changes in the pixel resolution lead to great changes in the time to calculate.
Also, because the algorithm uses large multi-dimensional matrices as opposed to
loops to make the calculations, the program runs faster but is susceptible to memory
clog-ups at higher resolutions.
Through trial and error experiments, the 3 0 -by-3'
resolution is good for data post-processing. For real-time measurements, a 5 0 -by-5'
resolution is more appropriate. The resolution of the azimuthal and vertical directions
do not necessarily need to be the same. When trying to get more information in one
direction over another, the resolution in that direction can be increased while the
66
Ice Edge
5km
1O0m
Loiter Pattem
Figure 4-1: The setup for the experiment involving a single simple source. The AUV
will conduct a loiter pattern with a 100 m radius, 5 km South of a noise "hot spot"
along the ice edge, simulated as a point source with a source level of 120 dB at 900
Hz.
other is decreased to maintain similar calculation speeds. This method is used in
Chapter 5.
4.1.2
Noise Field Results
Figure 4-2 shows the result of the experiment with a period of 300 m. The top left
graph in the figure shows the noise field estimate in decibels.
The bottom three
graphs, from left to right, show the path of the vehicle on the horizontal (x-y) plane,
the depth of the vehicle as a function of time, and the vertical score of the array
tracked over time. The figure to the right of the acoustic picture shows the vertical
noise profile. The black solid line corresponds to the average vertical noise profile
(averaged in the intensity domain, not dB), and the dashed blue line corresponds to
the vertical noise profile at the source location.
We can observe from the results that for this particular experiment, that the
vehicle did not have enough time to travel all the way between the depths of 20 m and
67
3D Noise Field - Period 300
80
80
80
75
60
a 40
7
70
20
.r
0,
65
0
60
-20
-40
60
40
20
0n
0
0
-20>
55
-40
50
-60
-80
45
Azimuthal Bearing, degrees
150
100
-
-'
-100-0
x (M)
100
=
0.20003
/
-60
-100
0.2Vert Score
-20 - - - - - - - - - - - - -- - - 40 -0.2
.50
0
-100
-150
0.3
3
0 -----------------------
0
100
50
Ambient Noise Level (dB)
0
100
-----------------200
300
Time (s)
400
0
0
100
200
300
Time (s)
400
Figure 4-2: The noise picture results from a yoyo period of 300 m. The top left graph
is the acoustic picture, with azimuthal angle 0 on the horizontal axis, and vertical
angle # on the vertical axis. The bottom left graph depicts the path of the vehicle in
the x-y plane, the bottom center is the depth of the vehicle as a function of time, and
the bottom right shows the vehicle's vertical score over time, as well as the ending
score. The graphic on the right shows the average vertical noise field (black line) and
the vertical noise field at the source location (blue dotted line), which is at 0 = 0'.
68
100 m. This is due to the physical limitations on the Bluefin-21 AUV's maneuvering,
set in the vehicle simulator uMVSBluefin. Therefore, a period of 300 m with the
depth limits set will correspond to approximately the maximum verticalness that can
be achieved in the array for the Bluefin-21. The vertical score achieved is v = 0.21.
We can also see that the vertical score tracks well with the depth profile. The vertical
score increases while the vehicle is on its up or down-slope paths, and tends to decrease
as soon as the vehicle makes a turn to go back in the other direction. This is a result
of the array leveling out at the peaks and troughs of the yoyo pattern.
In the measured noise field, we can see very clearly the horizontal and vertical
location of the source - at 0' azimuth and near 0' elevation. This corresponds well
with the placement of the source. To measure the resolution of the noise source (the
quality of the picture, not the number of pixels per degree), we measure the peak of
the response and the 3-dB down bandwidth. The peak is simply the maximum of
the beam response at the source location. The 3-dB down bandwidth of the response
is measured in both the horizontal and the vertical directions by taking the peak
response, subtracting 3, and finding where the beam pattern intersects on either side.
For this particular experiment, we can see a maximum dB level of 79.4 dB, and a
3-dB down bandwidth of approximately 10.5' in the vertical direction, and 4.5' in
the horizontal direction.
If we remove some of the vertical directionality from the array by increasing the
yoyo pattern period, we can see some degradation in the resolution of the picture.
Figure 4-3 shows the results for a yoyo period of 1000 m, with a resulting vertical
score of v = 0.123. This is a little more than half of the verticalness achieved by
the 300 m period yoyo experiment. The maximum response of the source is 3.1 dB
lower at 76.3 dB, and the vertical 3-dB down bandwidth at the source is 5.5' wider at
16'. However, if we look at the horizontal 3-dB bandwidth at the horizontal axis we
see no degradation, which is still at approximately 4.5'. This means that increasing
the verticalness from 0.123 to 0.21 does not degrade the horizontal arrival structure.
Eventually at some level of verticalness we would assume that adding verticalness will
degrade this direction, but it does not happen within the maneuvering limits of the
69
3D Noise Field - Period 1000
80
N 80
80
75
60
60
40
70
40
0
1
20
20
65
0
60
Ca2C
-- 20
0
-20 >
55
-60
-60
50
-80
-80
45
-15u
-IUU
-U
U
iuu
u
Azimuthal Bearing, degrees
-
--
-20
50
-
-
--- -
-
0.3
-
-
0
Vert Score= 0.12258
-
150
100
0.2
-40C
0
-50
80
40
60
Ambient Noise Level (dB)
Lau
-60
-80
-100
-1501
-100
0
x (m)
100
0
01
-
-100 ---------------
100
300
200
Time (s)
400
100
0
300
200
Time (s)
400
Figure 4-3: Results of the 3D acoustic picture for a horizontal circular pattern combined with a yoyo maneuver with a specified period of 1000 m.
3D Noise Field - Const depth
80
80
75
a
a
OE
a
60
40
70
65
OE
20
/
a
0
EU
60
.2
-20
(
a
55
a
-40
-
50
-60
-80
-100
-150
150
50
-10
-50
-60-
-100
-150
-80
-100- ---
-'
-100
0
x (m)
100
0
a
-100
300
400
Time (s)
Vert Score
80
40
60
Ambient Noise Level (dB)
=0.018588
0.1
_
0L
----------------200
45
150
0.3
0 -----------------------20 - - - - - - - - - - - - - - - - V
-4 0.2
-40-
100
..
100
50
0
-50
Azimuthal Bearing, degrees
0
100
300
Time (s)
200
400
Figure 4-4: Results of the 3D acoustic picture for a horizontal circular pattern with
no change in depth.
70
.
-
0
-
-
-
Yoyo Period 300
Yoyo Period 1000
Constant Depth
-20-1
~-40,-.
-1
-60
00
y-irection
-5-5
-100
-100
x-direction
Figure 4-5: A comparison of 3D path plots taken by the AUV for three different
experiments. The black dashed line is the vehicle path taken at constant depth,
the blue line is the vehicle path taken for the same loiter pattern, but with a yoyo
maneuver with a period of 300 m, and the red line is a yoyo pattern with a shallower
angle, corresponding to a period of 1000 m.
AUV.
Finally, Figure 4-4 shows the results where there is minimal vertical directionality, or where the vehicle was still run in the circular pattern, but without the yoyo
maneuver. Even when traveling at a constant depth, some vertical directionality still
exists because the array in the model is slightly buoyant, and the array rises slightly
in the water column behind the vehicle. This experiment achieved a vertical score of
v = 0.019. The measured noise field in this experiment is even less desirable than
what was observed from the two previously discussed experiments.
The peak dB
level of the response is significantly lower, at 71.3 dB, more than 8 dB lower than
the response from the experiment with the period of 300 m. In addition, the 3-dB
down vertical bandwidth at the source is larger - at approximately 21.5'. This is
more than double the bandwidth from the period 300 m yoyo pattern. And similar
71
80-
Veia -
0A1gl
70
---
65 --
Vert -0.123
Vr-0.5
460
0
75
0
30
0
6000
40er
00
0-420
t45
40
-60
-20
0
20
40
60
80
Vertical Angle
Figure 4-6: Vertical noise profiles at the source location for multiple levels of array verticalness. As the vertical score decreases, there is a clear pattern where the
bandwidth increases and noise peak decreases.
to the result we observed with the period 1000 m yoyo experiment, the 3 dB down
horizontal bandwidth still remains relatively constant at the same 4.5'. For 3D plot
path comparison of the constant depth path vs a period of 300 m vs. a period 1000
m, refer to Figure 4-5.
Let us now take a closer look at the comparison between all the experiments run
from Table 4.1. A full listing for the results from each of the pictures is listed on
Table 4.2.
Figure 4-6 shows the vertical profiles for each of the acoustic pictures
at the source location (0
=
0) side-by-side, while Figure 4-7 shows the horizontal
profile at the source location. 3D acoustic pictures for all the results can be found in
Appendix E.
We can see from observing the vertical ambient noise profiles that as the vertical
score increases, the resolution of the vertical arrival structure of the noise from the
source increases as well. This is both in the form of the bandwidth and the peak
response. Table 4.2 categorizes the results from the measurements.
While the limited pixel resolution of these pictures (3' in both the 0 and q5 directions), does remove some of the preciseness from the results, the general trends in the
data appear to be clear. With an increased verticalness, within the limitations of the
AUV's maneuvering capabilities, we see a general increase in the peak dB, a decrease
72
Experiment
Vertical Score
Peak dB
1
2
3
4
5
6
7
8
0.019
0.057
0.080
0.123
0.136
0.155
0.193
0.200
0
2.0
3.1
5.0
4.4
6.2
6.9
8.1
Vertical 3- Horizontal
on
dBrDown 33-dB Down
dB Down
21.80
6.80
6.20
27.4"
26.00
5.30
16.30
5.6
5.2"
15.60
13.80
4.50
4.20
12.50
10.30
5.90
Table 4.2: Vertical noise profile resolutions for experiments looking at a simple source
within the maneuvering limits of the Bluefin-21.
80
-_Vert =
75
-
70
0.200
0.193
Vert-0155
Vert 0.136
-_Vert-
Vert =0.123
-Veft-0.080
__Vert- 0D57
-Vert -0.019
65
60
0
10.55
CU
E 50
S45
40
35
30
-80
-60
-40
-20
0
20
Azimuthal Angle
40
60
80
Figure 4-7: Horizontal noise profiles for multiple levels of array verticalness looking
at a simple source. We can see from the graph that the 3-dB down bandwidth of the
noise field does not change considerably with increased vertical scores.
73
in the vertical 3-dB down bandwidth, and little to no change in the horizontal. In the
next section, we will test the verticalness of the array beyond the maneuvering limits
of the Bluefin-21 AUV, and define general relationships between the verticalness and
these three metrics which define the resolution.
4.2
Experimental Testing on a Simple Source
4.2.1
Experimental Setup
In examining the verticalness of the array within the maneuvering limits of the
Bluefin-21, we have learned that increasing the verticalness will increase the resolution of the picture as well as the vertical bandwidth of the response. But intuition
tells us that this will not necessarily be the case if we continue to make the array more
vertical. At some point, these measurements can no longer continue to get better,
and the horizontal bandwidth may suffer. We know that, for example, a perfectly
vertical array would have no horizontal information. And so the question arises, how
much verticality in a towed array is too much?
We can answer this question with a series of well-designed experiments. There are
many ways this could be set up though the use of constraints, and many ways this
could be tested. The goal of this research, however, is to test the improvement that
verticality would have on the picture. The constraints on the experimental process
were developed as follows:
1. The towing AUV will always conduct a full circle in the horizontal plane, and
a yoyo pattern in the vertical direction
2. The duration of time over which the measurements are made will remain constant
3. The speed of the vehicle will remain constant
4. The max depth and period of the AUV yoyo maneuver can be changed to
manipulate the verticality of the array, but the AUV must always remain in the
74
1theoreical
d
4
A/2
Figure 4-8: The geometry used to calculate the total path distance S taken by the
AUV as a function of the horizontal distance traveled X'.
surface duct so that the noise picture can remain pseudo-stationary
Using these constraints, we can design a series of experiments. We control the
verticalness of the experiment by changing the yoyo period and the minimum and
maximum depths of the behavior. To ensure that the vehicle always travels the same
distance, we calculate the radius of the circle in the horizontal plane that the AUV
will need to take using a few assumptions. These are: (1) the vehicle will always travel
in a straight line, (2) can instantly change pitch after each up-down leg of the yoyo
maneuver, and (3) maneuvers in a perfect circle in the horizontal direction. With
these assumptions, the radius of the circle can then be calculated using geometry.
Let us assume that X is the distance the vehicle has traveled in the horizontal plane
along the circumference of a circle. From the constraint that the vehicle must travel
in a full circle, we can calculate the full distance xO the AUV will travel in terms of
the radius of the circle:
= 27rr
-O
(4.1)
Now let us look at the maneuvering in the depth column. If the depth through
which the AUV travels before it turns to its next leg of the yoyo is d and the period is
75
A, then using the geometry presented in Figure 4-8, we can calculate the total distance
' the vehicle has traveled as a function of the distance traveled in the horizontal plane
() =
A
2
d2 + ()
2_
(4.2)
Now from the constraints that the vehicle travels over a fixed time at a fixed
velocity, to and vo, and that the total distance traveled is S' = tovo, we can rearrange
Equations 4.1 and 4.2 to solve for the radius:
r =v
Atov0
(4.3)
47r d 2 +(A)
This is the radius used in the experiment given the other parameters. Obviously,
even in the simulation, the vehicle cannot change pitch instantly. Also the vehicle
does not maneuver in a perfect circle all the time, particularly at higher pitches when
the azimuthal angle is difficult to control, and as such the vehicle may go a bit over
or under the circle in the fixed time allotted for each experiment. However, as we
will see in Section 4.3, the acoustic picture will tend to converge before that, and so
a little less or more will not affect the picture significantly.
Through a series of experiments we were able to test vertical scores of up to almost
0.54. Higher verticalities could not be tested for two reasons. The first is that even
inside of simulation, the vehicle was difficult to control at higher pitches.
Similar
to an actual in-water experiment, for an AUV at high pitches, small changes in the
rudder of an AUV result in large changes in the azimuthal direction of the vehicle,
which causes the simple PID controller designed to handle the azimuthal direction to
become unstable. With a redesign of the PID controller, this could be fixed, but they
are well outside the actual limits of the AUV, and are therefore not included in this
work. The second is the shape of the towed array with a yoyo maneuver. Each time
the AUV turns at the top or bottom of the yoyo pattern, the array becomes more or
less horizontal. So because of these direction changes, even with very high pitches in
76
Set Parameters
Time [s
[
l
Calculated Parameters
peed
Period [m]
Min Depth
Max Depth
[im]
Calculated
# Direction
Theoretical
[m]
Radius
Changes
Pitch
[m/s]
1
450
1.5
N/A
50
50
107.4
0.0
0.0
2
450
1.5
2000
20
100
107.1
1.0
4.6
3
450
1.5
1500
20
100
106.8
1.0
6.1
4
450
1.5
1000
20
100
106.1
2.0
9.1
5
450
1.5
800
20
100
105.3
2.0
11.3
6
450
1.5
600
20
100
103.8
3.0
14.9
7
450
1.5
500
20
100
102.3
3.0
17.7
8
450
1.5
400
20
100
99.7
4.0
21.8
9
450
1.5
500
20
140
96.9
3.0
25.6
10
450
1.5
500
20
170
92.1
3.0
31.0
11
450
1.5
500
20
200
87.2
3.0
35.8
12
450
1.5
450
20
200
83.9
3.0
38.7
13
450
1.5
350
20
200
74.9
3.0
45.8
Table 4.3: 13 Experiments conducted to test the verticality of the array. The parameters speed and time were fixed, and the period and min/max depths were varied in
order the control the vertical score. The radius of the horizontal loiter pattern was
calculated so that the vehicle always completes one full circle in the time allotted.
the middle of the yoyo legs, the overall vertical score will be lower.
The full design of experiments can be found in Table 4.3. The yoyo period and
the maximum depth were the parameters used to control the verticality. A general
sense of the verticality can be understood by the theoretical pitch and the number of
direction changes from the yoyo maneuver, also listed in the table. The theoretical
vertical angles are calculated using Figure 4-8 with the following equation:
-tan-
(jd2
(4.4)
)
Otheoretical
and the number of direction changes is simply
nchanges =
voto/(A/2) rounded up.
Higher theoretical tilt angles will correspond to higher vertical scores, and more direction changes will result in lower vertical scores.
77
Relative Max dB
3-dB Down Bandwidth
25
8-i
a
0
I
7
Ve rtical1
Horizontal
20
6-
~15
S0
al
0
0.1
0.2
tclScr
0.3
0.4
0.5
0
0.6
cr
etia
Ca
0.1
0.2
0.3
0.4
0.5
0.6
Vertical Score
Vertical Score
Figure 4-9: These graphs show the improvement trends in the resolution of the measured noise field for a range of vertical scores. The graph on the left shows the peak
DB of the noise field, while the graph on the right shows the trends in the bandwidth. On the right graph, the blue dots are the vertical 3-dB down bandwidth at
the azimuthal source location and the green dots are the horizontal 3-dB down bandwidth. The vertical dashed lines represent the approximate maneuvering limits of the
Bluefin-21 AUV.
4.2.2
Results and Discussion
The results from the experiments can be seen in Table 4.4, and the are graphed in
Figure 4-9. From these results we can devise a general set of conclusions about how
the vertical score of the array can affect the resolution of the picture. It should be
noted that the vertical and horizontal bandwidths are approximate. The actual pixel
resolution on the picture is only three degrees, and so a linear interpolation method
was used to calculate them.
Our observations of the range of vertical scores lead us to the following conclusions.
On the left graph, we can observe that increasing the vertical score will increase the
peak dB of the noise field, up to a point. The peak dB tends to increase until a vertical
score of approximately 0.25 or 0.3, and then tends to level off at approximately 6.5 dB
higher than what was measured in the constant depth experiment. From the right
graph, we can see the vertical (blue dots) and horizontal (green dots) 3-dB down
bandwidths measured. The 3-dB down vertical bandwidths tend to improve up until
a vertical score of about 0.3, and then level off to about 3'-5'. The set of points
78
#
1
2
3
4
5
6
7
8
9
10
11
12
13
Vert Score
Horizontal
Bandwidth
Vertical
Bandwidth
0.021
0.075
0.092
0.117
0.138
0.169
0.202
0.239
0.305
0.413
0.491
0.539
0.524
6.70
6.4*
6.30
5.50
4.60
5.00
4.1*
4.40
5.30
5.50
7.30
6.6*
7.00
20.80
22.40
17.80
15.40
17.80
14.10
11.20
10.00
4.80
3.50
3.70
3.00
2.70
Table 4.4: The results from the 13 Experiments tested over a full range of array
verticalness.
appears to generally follow a quadratic relationship. Lastly, over the entire range of
the horizontal bandwidth, there doesn't seem to be much loss over of the entire range
of vertical scores.
To draw general relationships in the domain of vertical scores tested, one can
take a look at the trend-lines developed.
With the peak dB, I've separated the
response generally into two domains, the first is a linearly increasing relationship,
and the second is a constant, generally level response.
There is some variation in
these results, particularly for the higher vertical scores where the peak dB deviates
from the average at that point. The equations with their constants and domains are
as follows:
peakdBrei
v 6 [0 , 0.24)
cV
(4.5)
v e [0.24 , 0.54]
C2
c 2 = 6.64
c = 30.0
Note that we've adjusted the dB scale to a relative scale, where 0 is the peak dB
response for a horizontally towed array (no yoyo maneuver), such that peakdBrei =
79
peak-dB - peak-dBconstant-depth. a 1 and a 2 are constants, and v is the vertical score
for the run.
We also have relationships for the bandwidths. For the horizontal bandwidth,
we'll assume that the bandwidth is constant over the full domain, and so we set our
trend line to the average:
Horizontal_Bandwidth= C3
C3
V E [0 , 0.54]
(4.6)
= 5.75
Finally, for the vertical bandwidth, we find that a quadratic relationship makes
the best fit. The following is the best fit line for the vertical bandwidth:
Vertical _Bandwidt h =
C4
4.3
=75.2
c4 v2 + c 5 v + c6
c5 =-82.1
v E [0 , 0.54]
(4.7)
c 6 = 25.1
Convergence of a Noise Field
When developing a 3D noise picture, the natural question arises: how much time,
data, and maneuvering is required for an AUV with a towed array to obtain a reliable
noise picture? It was clear from the previous experiments that a full rotation is in
fact enough data to converge on a noise field, but what about less? To study this, the
AUV was run in a full circle, while the estimated noise field was calculated different
points throughout along that run using the data that had been collected up to that
point. This field was then compared to the noise field measured after from the full
loiter pattern to test if it matches. These two pictures were compared via a correlation
factor, calculated by the following equation:
80
base(Oi, q5) - field(i, #5)
1
Correlation=
where
j
E n I
Z?- csQ5~ ~ mE>
is the jth noise field part in the
a
e2
cos(#5) E'
cos(5)(48
# direction of n total vertical directions,
(4.8)
i is the
ith potion of the noise field in the 0 direction of m total azimuthal directions, and a is
the standard deviation. In this way, each pixel of the acoustic noise field is measured
against and compared to the measured noise field, and given a value based on a
normal distribution curve. For this calculation, Correlation = 1 means the picture
matches the measured noise field, and Correlation - 0 would be several standard
deviations away. A standard deviation of o- = 3dB was chosen because in practice
this is what we tend to see when calculating up, which the pooled standard deviation
between the estimated and measured beam responses as described in Section 3.3.4.
The reason for the cos(#) term in Equation 4.8 is to take into account the fact
that not all the pixels in the noise picture are equal. The noise field as we display it is
actually a Mercator projection, or a flat cylindrical projection of a spherical field. The
cos(#) makes sure that pixels at high vertical angles are less significant than pixels at
or near the horizontal plane, because those pixels represent a smaller area from which
the noise arrives. Lastly, when calculating the signal, a minimum dB floor was set.
The reason for this is that we want to measure the correlation in the response (i.e.
the areas with higher dBs) and not the random differences of the noise. Therefore,
for the purposes of measuring the correlation, if a pixel of the noise picture fell below
the floor, it was set to that floor. The dB floor used here was set to 20 dB, which is
still well below the ambient noise level.
Figure 4-10 shows the noise field generated at certain points throughout the loiter
pattern circle. The last picture (bottom right) of the figure represents the noise field
generated after the full circle is complete, which took 402 seconds. The first (top left)
picture represents the noise field generated through the algorithm based after just a
single data sample was taken.
81
t=2s
t=13s
t=36s
t=80s
t=201 s
t=321 s
t=48s
t=402s
Figure 4-10: A series of snapshots of the noise fields generated after different points
of time as more and more data is gathered.
Clearly, we can see that one data sample is not enough for the algorithm to
generate a complete noise picture. The iteration technique converges on a field that
is not realistic and the beam response scattered in many directions. As more data is
collected, however, the picture does get better. In the t = 36 s picture, we can see a
smoother more realistic picture is starting to develop, although this is not necessarily
reliable yet. Later, at t = 48 s a mix of the data once again appears pixelated, with
high noise levels coming from directions that aren't the direction of the source. Note
the high noise content present near the bottom of the picture. As time moves on,
however, it becomes much more likely that the noise algorithm converges on the true
noise pattern. At t = 80 s, it is almost there, and all the pictures after that have
reasonable correlation with the full picture achieved after t = 402 s.
We can better understand the trends if we look at the correlation scores of the
noise fields as a function of time around the circle - this is shown in Figure 4-11. We
can see it three domains over which we see different behaviors of the algorithm. In
the first domain, from t = 0 s to about t = 40 s, we see no convergence of the picture,
the generated noise field is not going to work. In the second domain, from t = 40
s to about t = 120 s, we see intermittent convergence. Here, occasionally the noise
field iteration algorithm will converge on a picture which is relatively close to the
true noise field, however, it's not reliable. Finally, in the third domain, from about
82
Acoustic Picture Convergence
0.90.80.70.60
0
U
0.40.30.20.10
0
50
100
150
200
Time (s)
250
300
350
400
Figure 4-11: The correlations calculated based on Equation 4.8 for generated noise
fields with the available data up to that time.
t = 120 s and onward, we have fairly reliable convergence on the true noise field.
There are many other factors that play a roll in establishing the convergence of a
picture. First, it is important that the array turns and faces different azimuthal and
vertical directions relative to the source in order to reduce the overall noise ambiguity.
If the array always stays in the same orientation relative to the source, the resulting
noise picture will be poor, no matter how much time and data is gathered. Another
thing to consider is that each beam formed in the simulation is based off of 2 seconds
of data. For example, t = 60 s is also equivalent to evaluating 30 different beam
patterns being used in the iterative process, and this may also be more of a factor in
determining the time. In an effort to capture all this information, the following is a
list of the factors that should be taken into consideration when attempting to get an
accurate picture:
" The percent completion in which the array has turned
" The number of data samples taken
83
40 km
Water Edge
Source
2,000 m
Acoustic Ray
AUV
Figure 4-12: The experimental set up for the range finding experiments. Here, the
source was 40 km away, and the vehicle conducted its yoyo patterns at a depth of
approximately 2000 m. This depth was chosen so that the only noise directions
arrivals would be the result of the reliable acoustic path (RAP) ray.
o The time over which the data samples are taken
From our experiments, we observed that the picture converges after approximately
120 seconds, or 60 data samples, or about 30% of a circle.
4.4
4.4.1
Range Finding on a Source
Experimental Setup
In this experiment, we examine the feasibility of finding the range to a source using
the vertical arrival structure. Here, we want the AUV to be further away from the
source, and below the surface duct.
This is so the only sound arriving from the
source to the array is from the reliable acoustic path (RAP), whose direction is well
below the horizontal plane. For this experiment, the vehicle is set deeper at 2000
m, at a distance of 20 km South of the source. Based on these new depths, a series
of experiments was run, with same periods specified in Table 4.1. The source level
was raised to 140 dB so that the sound still comes through the water even with the
increased transmission loss associated with the additional distance. Figure 4-12, show
the general setup for this experiment. Before we examine the results, we will give a
short discussion on the calculations used to estimate the arrival of the rays.
84
4.4.2
Range Finding Calculation
A simple calculation for the range to a target can be made if some simplifying assumptions are made in the calculation. According to Snell's law, a ray of sound propagates
such that:
CosO(Z)= Const.
(4.9)
c(z)
Now, if we assume that sound speed is linear with depth, such that:
(4.10)
c(z) = c(0) + gz
where c(0) is the sound speed at the water surface (z = 0) and g is the sound speed
gradient, we can say that rays will travel in circular paths, where the center of the
circle will be where the sound speed goes to zero, or at the location:
z
(4.11)
C(0)
9
By the geometry shown in Figure 4-13, the radius of the circle given the arrival
angle of the ray 0 and the depth of the receiver d, is:
(4.12)
c(0)/g + d,
cos 0
,
Again, by the geometry of the problem, we can again calculate the variable a1
and similarly a 2 by the following equations, and ultimately find our range between
the source and receiver:
a,
=
r2 - (C() + d,)
a2
-
range = a, + a 2
r2 _
c() +
(4.13)
(4.14)
For the purposes of this particular calculation, we approximate the constant sound
speed gradient to be g = 0.022m/
m
and c(0) = 1440 m/s. In the measured sound
85
a,
a2
d,,
Figure 4-13: This figure shows the geometry used to calculate the range of the source
given the angle of arrival 0. For these calculations, the simplifying assumption that
the sound speed profile is linear was used.
speed profile, the gradient above z = 1000 m is g = 0.0196m/
and for below 1000m
is g = 0.024 m/s. The actual sound speed at the surface is c(0) = 1440m/s. For more
m
precise range measurements, one could build a piece-wise array based on ray-tracing
models currently in use [20]. However, for the purposes of this thesis only a simple
calculation to demonstrate the feasibility of ranging using the 3D acoustic picture.
4.4.3
Results and Discussion
To get a basic understanding of these properties, let us first compare two of the
experiments for this discussion: the first experiment is with the yoyo pattern with a
period of 300 m, and the second the experiment with no yoyo pattern. The results of
the noise field calculations can found in Figures 4-14 and 4-15.
We'll first discuss the difference between the two pictures. A comparison of the
vertical arrival structure at the source location can be found in Figure 4-16. We
can see clearly that the picture with the yoyo pattern better resolution in the vertical
direction (smaller 3-dB down bandwidths), as well as higher peak responses ( 2.5 dB).
The 3-dB down bandwidth can be a tool for measuring the uncertainty in the angle of
arrival measurement. Larger bandwidths would correspond to higher uncertainties,
and the uncertainty in the range can be calculated by finding the difference between
86
3D Noise Field - Period 300
75
80
80
60
70
60
40
40
65
20
20
60
0
C0
-20
-20
55
-40
-60
50
-60
-80
-80
45
0.3
Vert Score= 0.1953
-
150
100
50
E -2020
E0
-4r -2040
00.2
-2060.
-50
-150,
-100
0
Si0.1
-2080 -------2100'
0
100
--
-100
100
80
60
40
Ambient Noise Level (dB)
-50
0
50
Azimuthal Bearing, degrees
-1980
-2000 - - --- - - - - - - - - - -
x (m)
-
-
----
200
300
Time (s)
0
400
0
100
200
300
400
Time (s)
Figure 4-14: The resulting 3D acoustic pictu re from the range finding experiment
conducted with a yoyo period of 300 m.
3D Noise Field - Const depth
75
80
80
60
SI
4)
Ci
40
CU
20
40
65
20
60
0
'U
60
70
-20
-20>
55
Si
cy
00
-40
-40
-60
50
-60
-80
-80
45
Azimuthal Bearing, degrees
-1980
150
50
E
0i
-50
z -2040
a.
-2060
40
Ambient Noise Level (dB)
Vert
Score
=
0.021741
0 0.2
-2020
-
-100
-150,
60
0.3
-2000 --
100
80
-100
t
CU 0.1
--
-2080------------
-0
x (m)
100
-2100-
0
100
200
300
Time (s)
400
0-
0
100
200
300
Time (s)
400
Figure 4-15: The resulting 3D acoustic picture from the range finding experiment
conducted at constant depth.
87
Measured
angle of arrival
Suncertainty
Vert 0.195
Vert=0.022
70CO65
C 600
C.
55
-
c
E
5045
40
-80
-60
-40
-20
0
20
40
60
80
Vertical Angle
Figure 4-16: A comparison of the vertical noise arrival structures at the azimuthal
location of the sound source for two experiments. The blue line is the arrival structure
from the experiment with a yoyo pattern, and the red line is the same but without
the yoyo pattern. The peaks of the vertical noise profiles represent the measured
direction the reliable acoustic path (RAP) sound rays, which can be used to predict
the distance to a source.
the two distances that correspond the angles at the edges of the 3-dB down band.
We can also observe that even though we expect the rays to arrive only from a
negative elevation angle, there is very clearly a mirror image that can be seen above
the horizontal plane. That differential, however, is less apparent in the yoyo pattern
experiment.
Now let's compare the measured vertical angles, the calculated ranges, and the
uncertainties for all 8 experiments run.
The results are graphed in Figure 4-17.
We can see that for all the calculations, the range is approximately correct with
some variation.
The ranges for these experiments measure at 46.1 km, which is
approximately a 15% error from the actual distance of 40 km. Further observation
of the results shows that the distances fall into only 3 discrete values. Recall that
the pixel resolution of these pictures is only 3'. While linear approximation is used
for the 3-dB down bandwidth, the peaks will still always occur at a particular pixel,
resulting in discrete values for the range calculations. Finer resolutions (i.e. more
88
80
1
70
09
0.8
060.7
C 50
40
- - - - - -
vi
30
E
0.5
0.4
-
QJ
F
0.6
0.320
0
U
0.20.1
10 -
0
0.05
0.1
0.15
0
0.2
Vert Score
0.05
0.1
0.15
0.2
Vert Score
Figure 4-17: The graph on the left shows the results of the range measurements. Left:
The red squares represent the calculated range of the source based on the location of
the angle of arrival, while the vertical red lines represents the error range specified by
the 3-dB down uncertainty measurements. The dashed black line shows the actual
distance of the noise source. Right: The uncertainties, as compared to the vertical
score of the experiment. These values are simply the magnitudes of the red vertical
lines in the graph to the right.
computing power) would be needed for more varied results than the ones presented
here. It should also be noted that the results are also sensitive to the parameters
used, particularly the sound speed gradient, which, as mentioned in Section 4.4.2, is
only an approximation of the actual, more complicated sound speed profile.
Despite these difficulties, there are still some conclusions we can reach. The first
is that it is feasible to measure distance with a towed array using the vertical angle of
arrival structure, and that the angle of arrival is clearer, or has a higher signal excess,
when the yoyo pattern is used. The second is that the uncertainty in the measurement
is fairly large, with values ranging around 30% to 60% of the distance being measured.
Part of this is due to the relatively low resolution in the measurements, and the other
part is due to the fact that small changes in the angle of arrival mean large changes in
the distance estimation. By finding methods to increase the accuracy and precision
of this measurement, it may be possible to achieve better results. Finally, it does
appear that perhaps higher vertical scores correspond to better measurements and
smaller uncertainties, but with the limited data presented here, we cannot positively
89
state that this is the case. The work presented here shows that range finding is in
fact feasible, however, further study should be done to better understand the effects
of verticalness on the distance measurements.
90
Chapter 5
Horizontally Isotropic Vertical
Noise Fields
5.1
Motivation
In addition to just looking at simple sources, we will also take a look at the ability of
a towed array to evaluate horizontally isotropic vertical fields. One major motivation
for this research is related target to tracking. A unique characteristic of the Arctic
environment is the presence of a noise 'notch' in the vertical ambient noise profile,
where the ambient noise from that particular direction is much lower than the noise
from other vertical directions, as shown in Figure 5-1. This notch is the result of the
unique Arctic sound speed profile.
The reason for the noise notch is a unique result given the arctic sound speed
profile, where a bend in the gradient occurs. The bend causes some sound rays to
be trapped above and turn back, while others will bend down and move lower before
turning up - leaving a direction from which there is less ambient noise. The bend in
the sound speed profile and the presence of the notch are shown in Figure 5-2. This
noise notch is important in target tracking and acoustic communications, because it
could be exploited in order to increase the signal-to-noise ratio (SNR) of a signal,
which is directly related to the ability of a receiver to distinguish a signal, as per the
sonar equation [20]:
91
900
50
30
00
Ambient
Noise
Notch
-90
Figure 5-1: A simple illustration (not from real data) of what the vertical ambient
noise profile may look like.
SNR = SL - TL - N
(5.1)
where, SL is the source level, TL is the transmission loss, and N is the ambient noise
level. If a vehicle is trying to listen to a target or an acoustic communication signal,
the vehicle could maneuver in such a way that the vertical angle at which the signal
is coming from is the same as the direction of the vertical noise "notch". This will
result in a reduction in the noise level N, and thus a higher SNR. Thus, if the vertical
notch does exist, it could be useful if a towed array was able to identify it. In this
chapter, we discuss this possibility.
5.2
Experimental Setup
In this experiment, no noise sources were present. Using the existing LAMSS software,
a noise "notch" was created at an angle of -30' independent of depth, which is a
reduction in the ambient noise form that direction.
92
The vehicle was then run at a
BELLHOP- Arctic Environment, incoherent
0 -req900Hz
'*0
50
Bend in
the SSP
1000
60
1500-
65
2000 -
70
S2500-
75
3000-
80
3500
85
4000
90
4500-
95
50CC
1440
-
;
1460
140
500 1520
Sound Speed (mis)
1540
1500
0.5
1
1.5
2
2.5
Range (m)10
3
3.5
4
4.5
5
100
Figure 5-2: The presence of a "notch" is expected in the ambient noise profile given
the affects of the sound speed profile on the array paths taken.
number of different periods corresponding to different levels of vertical directionality,
so that they may be compared against one another. The different periods specified
are the same as those presented in Table 4.1, with the exception that a constant
depth experiment was not run. Because the primary direction we are concerned with
is vertical, the pixel resolution of the 3D pictures produced from these results was
changed to 1' degree increments in the vertical
# direction,
and 100 increments in the
azimuthal 0 direction.
In order to get a true picture, a virtual experiment wherein an AUV with a vertical
array of the same size as the DURIP array was used. The AUV with the vertical
array was run in the same pattern as the other experiments, with no change in the
depth column, and the same 3D algorithm was run. The base picture, against which
we compare the results from the other virtual experiments, is presented in Figure 53. The notch is exaggerated to what we would likely see in the environment for
experimental purposes, dropping -25 dB below the ambient noise level.
93
so
80
50
60
60
45
440
40
20
(0
0
20o
0
-20
-20
30
-40
-40
-60
-60
23
-80
-80
-150
-100
50
0
-50
Azimuthal Bearing, degrees
100
150
20
40
60
Noise Level (dB/deg)
Figure 5-3: The noise notch as measured by a vertical array.
Experiment
1
2
3
4
5
6
7
8
Period
2000
1500
1000
700
600
500
300
N/A
Vertical Score
0.059
0.082
0.123
0.139
0.155
0.190
0.206
1
Min Beam
42.4 dB
42.4 dB
42.6 dB
43.2 dB
41.9 dB
42.6 dB
41.6 dB
21.4 dB
Min Location
-4.0
-1.0
-1.0
-10.00
-25.00
-27.00
-22.50
-28.50
Table 5.1: A summary of the results for the towed array experiments in an attempt
to identify the vertical noise notch. While the minimum location does in fact change,
the minimum peak does not approach anywhere near to the minimum of the field
measured by a vertical array.
5.3
Initial Results
The results from 3 of the 8 experiments run can be seen in the measured field noise
pictures of Figure 5-4. Pictures for the results of all the experiments can be found
in Appendix F. The vertical average noise profiles plotted against each other can be
found found on Figure 5-5, and a summary comparing results of the experiments is
listed in Table 5.1.
The first and most obvious observation is that the measurement of the vertical
notch by the 3D algorithm was not particularly successful. We can see that the total
drop in decibels is very small compared to the drop that we see in the measured
vertical array. However, if we look more closely, there are some hints of the measured
94
Vueticalness
0.05
50
so
so5
60
v
40
10
cij 20
C 0
4S
40
-20>
0
0
35
U -40
.50
E -60
30
-80
2
-150
-100
5Sos25
150
-
0
ee
4
45
Noise Level (dB)
4^^-,
0-..4...
Verticalness
0
50
0
-50
0.12
80
60
so
50
404
20
.r
0
40
3545
00
Q
3
-20
-40
.So UJ
30
-60
-80
-150
50
0
-50
-100
100
ISO
25
A--
0-0-
Verticalness
*
0.21
45
so
s5
Noise Level (dB)
55
80
50
40
C
C
45
C
S20
40
0
9 -20
0 o
3
-.40-5
-80
-150
-100
A
-50
-,..
50
0
l
f
4%
100
..
,
150
25
So
48
46
Noise Level (dB)
Figure 5-4: The vertical notch noise field as measured by 3 towed array experiments.
The top experiment is the picture resulting from a yoyo period of 1500 m, the middle
with a period of 1000 m, and the bottom with a period of 300 m. While the pictures
really don't capture the actual notch, the towed array experiments above a vertical
score of approximately 0.1 seem to show some evidence of a notch. The actual location
of the notch is denoted by the dashed line on each of the pictures.
95
55
vs. Vertical Array
-Towed
-
40
z
45-
---
vert
-
-
0.026
0.10
___Vert
ert
0 12
30-
-
25
80
60
-40
-20
0
20
40
60
80
Vertical Angle
Figure 5-5: The vertical notch as measure by 3 towed array experiments. The yellow
line is the result for a yoyo maneuver with a period of 300 m, the red for 1000 m, and
the blue 1500 m. The towed array appears to give poor measurements of the presence
of a notch.
noise field present in the results. Figure 5-6 shows a zoomed version of the results for
the experiments running with vertical scores of 0.2, 0.12, and 0.08. In the experiment
with the highest vertical score, we can see some evidence that a notch is detected.
There is a gradual drop in dB across the entire vertical domain and we can see that
the minimum peak bottoms out at -27', which is very close to the actual bottom at
-30'. As the vertical score drops, that measured response minimum gradually moves
its way into the center. The experiment with a vertical score of 0.12 shows a minimum
at -22', and when we move and lower, to a vertical score of 0.08, the minimum moves
all the way to the center. Any vertical scores below -0.10 appear to have this same
behavior, where the notch cannot be detected at all.
Measuring the location of the minimum does not, however, mean that these noise
pictures make a good representation of the field. The 3D acoustic picture generated
by these experiments do not present themselves as a notch picture from the actual
noise field, but rather as a gradual descent to the minimum. Also, the drops to the
minimums are small, on the order of about -5 dB, about 20% of the actual drop.
Also that drop is spread over the entire vertical domain, rather than concentrated at
the actual location of the notch.
96
Towed vs. Vertical Array
52
Actual Location (-30*)
51
I
50
InI
nl
I
Vertert
47
46-II
45III
-80
-60
-40
-20
0
Vertical Ange
20
40
60
80
Figure 5-6: A zoomed view of the average measured vertical noise profile for 3 towed
array experiments and a vertical array. This zoomed view of Figure 5-5 shows that
there is some evidence of the location of the noise notch in the resulting noise field.
However, at the break between the periods of 1000 m and 1500 m, or at about a
vertical score of ~0.1, any evidence of the location of the notch disappears as the
minimum of the measured noise response moves to the horizontal plane.
5.4
Exploring a One-Sided Vertical Noise Profile
In an effort to better understand why the picture was not being generated, a stronger
one sided ambient noise profile was generated and the same experiments were run
again. This profile was measured by a vertical array in a method similar to that
discussed in Section 5.2. Figure 5-7 shows the noise picture as measured by a vertical
array.
In addition, several new experiments were run. While the limitations of the vehicle
only allow a vertical score of -0.20
for the towed array, it is possible within the
virtual environment to define completely fixed arrays (like volume arrays) relative to
the coordinate system of the vehicle. Two of these volumetric arrays were created and
tested against the one-sided vertical noise profile. These had the same dimensions as
the normal towed array, but were held at fixed angles of 45' and 75' relative to the
horizontal plane, extending in an upward and backward direction from the AUV. The
verticalness of these volumetric arrays was measured just like the towed arrays with
vertical scores of 0.48 and 0.81 respectively. Experiments with these arrays, as well
97
One SIded - VgdtIcal Ary
80
50
80
60
45
60
40
40
20
20
-20
35
)
-40
1
>40
30
-
0
0
-20
-40O
-60
-s0
-80
-150
-100
100
50
Azimuthal Bearina. dearees
-50
0
150
20
40
60
Noise Level (dB/deg)
Figure 5-7: A full one sided ambient noise profile was developed to re-test the ability
of the towed array to match the ambient noise profile.
as with a towed array run with a yoyo period of 300 m (for maximum verticalness),
were conducted and the results can be seen in Figure 5-8. The comparison of the
average vertical profiles for each vertical score can be seen in Figure 5-9.
The results show that the towed array data (top picture in Figure 5-8), even with
the full exaggerated one-sided noise profile, does not seem to be able to capture the
noise field. There is some evidence of a dip, and the average vertical field of the profile
is slightly lower on the side that is in fact lower. However, this data does little to
capture the magnitude of what is actually occurring in the noise field (see Figure 59). The fixed arrays on the other hand, do begin to capture the magnitude of what's
happening. For the 450 tilted array, there is significant evidence of the existence of
the one-sided profile. The only problem is that the drop is somewhat smeared across
the transition. In the base picture measured by the vertical array there is a distinct
drop in the vertical profile between above the horizontal and below the horizontal,
while the 45' array tends to start high and then gradually work its way down, even
to a point where it drops below the actual low side noise level.
In the experiment where we see a tilt of 75', the results are significantly better,
except that it tends to over-exaggerated.
On the high side, the results are higher
than those obtained by the vertical array, and on the low, the results are lower.
While we can now see the general shape of the ambient profile, we can still see some
discrepancies between the actual picture and the measured ones. We will discuss
98
4
so
s0
60
40
45
j2
20
.
40
0
35
.4
20
30
as
Azimuthal Barino. dearees
60
50
Noise Level
55
Tilt = 45*
Vert = 0.5
40
(Wi)
so
s0
-80
40
4C
45
2C
-20
40
3S
**~ZZD
-40
-41
=750
25
Tilt
60
0
_6C
Azimuthal Beana. dearues
100
50
Noise Level
0
(Em)
55
8I
Tilt = 75*
\ Vert = 0.8
i
so
6
4C
40
45
20C
21
40
-20
CS-21
3S
-4(
30
-60
4(
25
Azimuthal
Beadna. dearees
100
s0
0
Noise Level (Em)
Figure 5-8: The 3D pictures resulting from three experiments run in one-sided ambient
noise profile. (Top) A towed array at the limitations of its yoyo maneuver, (Middle)
a fixed array held at 45', and (Bottom) a fixed array held at 75
.
se,
15
Maneuvering vert
limit: -0.2
99
60
vs. Vertical Array
-Towed
50
vert - 0. 20
vert = I
-
----
-
$40
20
10
0
-80
-60
-40
-20
0
Vertical Angle
20
40
60
80
Figure 5-9: The different average vertical noise profiles as measured by the arrays
for an exaggerated one sided ambient noise profile for testing purposes. The four
experiments shown are (blue) a towed array with a period of 300 m, (red) a fixed
array held at an angle of 45', (yellow) a fixed array held at 750, and (purple) a
vertical array.
some of the possible reasons for these results in Section 5.6. But before that, let us
examine how the fixed arrays perform in measuring just the noise notch.
5.5
Revisiting the Notch Profile with Fixed Arrays
The section examines the experimental results when using the fixed tilted arrays
described in the previous section to again measure the noise notch. The results are
shown in Figure 5-10. We can see with the fixed arrays with the higher levels of
verticalness that the measured noise fields begin to be measured with vertical scores
of greater than 0.80, however, we can still see some significant discrepancies between
the measured fields. It appears from these results that very high levels of verticalness,
essentially vertical arrays, are required to resolve these sorts of noise fields.
5.6
Beam Responses for a Vertical Notch
In order to understand why the vertical responses do not match the actual noise
profiles, we can look back at and examine the different beam responses used to create
these images. Figure 5-11 shows those beam responses to different levels of vertical
100
55
----
4o-
ert
-
0.21
-Yr-04
80
-60
-40
0
-0
20
40
80
Vertical Angle
Figure 5-10: A comparison of the average vertical noise fields generated by a towed
array (blue) with a yoyo period of 300 nm, and three fixed diagonal arrays held at
vertical angles of 450 (red), 60~ (yellow), and 750 (purple), compared against the
vertical array measurement of the noise field (purple).
array tilt. To better illustrate the points, I've exchanged the noise "notch" for a noise
"bump" and normalized the responses (i.e.
the delay vector used to create these
pictures has an amplitude of 1). The top left picture shows the normalized responses
to a vertical noise field to an array tilt of 20 , the top right 450, the bottom left 750,
and the bottom right a fully vertical array. It is clear from observing these pictures
that there is no clear indication in the beam response of the bump for lower tilt
angles. Even with an array response of 750, the beam response is still only ~-'40% of
the what the full beam response should appear to be. The flatness of these beams
are the reasons for the poor noise patterns. The iterative method used to create the
3D pictures will not be able to find the notch if the beam responses do not present
evidence of the notch or bump themselves.
To further amplify the point, we can look at the maximum beam response for a
number of array tilts ranging from perfectly horizontal to perfectly vertical. These responses are shown in Figure 5-12. In this figure the blue dots represent the maximum
normalized beam responses observed for different levels of array tilt when attempting
to resolve the notch, while the red-line represents the best fit exponential curve. The
maximum beam responses are small and don't tend to increase until we see array tilts
of 80 +, which is why the ability of a towed array to positively identify the location
101
Array
Tilt
=
Aro Til a 45
20*
0.8
so
0.8
50
0.6
0.6
0
M0
0.4
0.4
0.2
-50
0
100
200
300
0.2
>-50
0
0
200
100
300
Azimuthal Bearing
Azimuthal Bearing
Array Ti1t = 7S*
1
Ar
0.8
so0
I
a0
0.8
2 50
0.6
0.6
0
0
0.4
-0.4
02
-50
0
100
200
0
0.2
-50
0
300
100
200
300
Azimuthal Bearing
Azimuthal Bearing
Figure 5-11: The beam responses for a horizontally isotropic vertical noise field with
a bump a -30', as measured by arrays with angles of tilt.
of the notch is poor.
These results are likely because of a mix between two facts. First is that the
circular pattern on the horizontal plane no longer help to break any of the vertical
ambiguity the way it would for a point source. For a point source the cones developed
from arrays pointing in different azimuthal direction can help resolve the vertical
directionality, which is not the case for horizontally isotropic fields by their very
nature. The second reason is that the conical beams that would be able to differentiate
the noise field, or the ones that don't intersect the noise field and can break the
ambiguity, are almost always near endfire, where the beam resolution is poor. This
point is illustrated in Figure 5-13.
Furthermore, we should discuss the "wavy" pattern we see in the measure of
the maximum beam pattern response in Figure 5-12. To begin, in the bottom left
picture of Figure 5-11, the "bump" does not present itself as a single bump, but
as two individual bumps around the actual location of the bump in the noise field.
Remember that the beam pattern is created by convolving the actual noise field with
102
-
1
0.9-
0.8
-
0
a 0.70.6
-
,
tu
CL 0.5-
E
CU 0.4E
:: 0.3-
M 0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
Array Tilt
Figure 5-12: A graph of the maximum normalized beam responses received from a
horizontally isotropic vertical noise field with a "bump" at -30' for different array
tilts. The blue dots are data points while the red line is the best fit exponential
curve. The "waviness" in the data points is a consequence of the side lobes of the
array passing over noise "bump" location at different degrees of array tilt.
103
Conical
Beams
Array Tilt = 30*
Conical
Axis
Noise
"Bump"
Figure 5-13: A horizontally isotropic vertical noise field represented on a sphere,
as measured by a tilted array. The red dashed line represents the conical array
axis, while the white circles represent the lines of conical ambiguity. The color of
the sphere is the representation of the noise field with the "bump" at 30' below the
horizontal plane. In order for the array to be able to resolve the noise field in the
beam response, the separate cones must be able to differentiate themselves from one
another by intersecting the noise field by different amounts. In this case, many of the
cones do intersect the noise bump approximately the same amount, and the only ones
that don't are close to endfire. This is why we see poor resolution for these types of
fields when we measure them with a towed array.
104
the array's beam pattern, which has it's own individual peaks and valleys in the form
of side lobes. If, for a particular array tilt, the actual noise notch exists between two
side lobes of the beam pattern for the relative array tilt, a response similar to that
bottom left picture will result, with the maximum response lower than if the side
lobes matched up perfectly with the noise bump. As such, small changes in the tilt of
the array will result in slightly higher or lower beam responses, which we see evidence
of in the form of the wavy graph shown in Figure 5-12.
Revisiting the question left off in Section 5.4, this is the explanation for the mismatch in the pictures measured by the vertical array and the diagonal arrays, particularly the array held at an angle of 75'. In a towed array with changing verticality,
this is not a problem. However, when we hold the arrays fixed at certain angles, as
we did for some of these experiments, we will begin to see some of the effects of the
quirks of the beam pattern on the measured noise picture. This phenomenon will
affect not only the diagonal arrays, but the vertical ones as well, and we should bear
that in mind when evaluating the results.
105
106
Chapter 6
Future work and Conclusions
Real World Testing
6.1
All of the experiments conducted for the purposes of this thesis have been conducted
in a virtual environment. While the various models used have been tested in the past
as reliable, real world testing is the next clear step to moving this research forward.
In this section, I will propose a series of 4 real world experiments that will be done
to verify and test 6 different research objectives that have been demonstrated in this
research through simulation. The ICEX experiment planned for the Spring of 2016
would be an ideal setting to perform these experiments. As we have shown in Chapter
5, a towed array is a poor tool to measure horizontally isotropic noise fields, so some
of these objectives may only be accomplished through the use of a vertical line array
(VLA).
6.1.1
Objectives
The objectives for these real world experiments would be as follows:
1. Show that the increase in towed array verticalness through the use of a yoyo maneuver significantly improves the resolution and signal excess of the 3D acoustic
picture.
107
Objective
# Ojcie
InTime
Water Speed
Depth
Range
Range
fIe
Array
yp
Description
Demonstrate that
1
Verticalness
Resolutionvs.
1.5 hrs
1.5 m/s 20 - 100 m
5 km
Towed
increased levels of
verticalness increase the
resolution of the noise
field
Verify the predicted
5, 10, 15,
VLA
vertical beam pattern at
Ice Edge
5 min
per drop
0
~500 m
3
Convergence
30 min
1.5 m/s
20 - 100 m
5 km
Towed
4
Ranging
2 hrs
1.5 m/s
- 500 m
10 km
Towed
5
Bottom Response
5 hrs
1.5+ m/s 20 - 100 m
2-5 km
Towed source and observe the
2
Vertical Pattern to
6
Identify Notch
I
different distances away
from the ice edge
Demonstrate time to
convergence of the noise
field.
Verify that the distance
to Ice cracking noise can
be measured by the
vertical arrival structure
Find the response from a
reflected patterns
identify and measure the
0
10 min
I
20, 25 km
- 700 m
_I
N/A
I
VLA
location of the predicted
noise notch
Table 6.1: The various objectives that can be accomplished with the ICEX experiment
and the approximate time requirements for each.
2. Show that a vertical line array can detect the presence of ice cracking noise in
the Arctic.
3. Positively identify and quantify the presence of the noise notch.
4. Use the 3D acoustic picture to identify the range to an ice cracking event.
5. Observe the returns for bottom bounce at different frequencies in and around a
source to learn how bathymetry and bottom type affects the noise propagation.
6. Identify and measure the location of the predicted horizontally isotropic vertical
noise notch.
Demonstrate Adding Verticalness Increases the Resolution
The goal of this objective is to show the different pictures created in an actual Arctic
environment using the AUV with a towed array. This can be done simply with one
108
experiment by placing the AUV in the water in the Arctic environment, preferably
near an ice-cracking event if one can be identified. Then run the vehicle in the water
in a number of circular patterns (a radius of 100 m will do), with each circular pattern
having a different level of verticality. Finally, analyze the data in the same manner
done in Section 4.1.2.
Vertical Pattern to Ice Edge
The next goal is to measure the vertical arrival structure of the noise coming from the
ice edge. These noise patterns have been predicted in a new version of the OASES
code
[31].
Figure 6-1, gives the predicted noise patterns at 75 Hz for a number of
different distances away from a tensile crack source. The different vertical arrivals
correspond to noise arriving in the surface duct, noise incoming from the Reliable
Acoustic Path (RAP), and reflected noise from the surface and the seabed.
Note
that in the simulations in this thesis, the reflections from the seabed are removed by
placing the bottom below the path of the rays.
Identifying Convergence
In the same way we identified the time required for convergence in Section 4.3, we
should also seek to accomplish this in a real world experiment. The process for this
is simple - place the AUV in the water, preferably near some ice cracking noise,
and run the vehicle with a yoyo pattern. Then, at multiple points throughout the
maneuvering, measure the predicted noise field against the noise field obtained at the
end of the run.
Ranging
This objective is to find the range to a source using the measured vertical arrival
structure, using the method described in Section 4.4. Preferably, the location of the
source is already known and the goal here will be to verify it with the data. For this
test, the AUV should be run significantly deeper, preferably below the typical surface
duct, so that the only arrivals happen from the bottom bounced and RAP rays (see
109
OASE S BeamPattern 150 m array 1 m target 75 Hz 20 dB surface noise
80
100
60
90
40%
180
20
1 0
70
< -20
........
60
-40
50
-60
40
-80
5
10
15
30
25
20
Target Range (km)
35
40
Figure 6-1: The predicted vertical noise arrival structure for a noise source at 75
Hz [29]. The different vertical arrival structures correspond to reflected noise of the
sea bed, surface duct rays, and reliable acoustic path (RAP) rays, which can be
exploited in the 3D pictures for ranging.
110
BELLHOP- Arctic Environment. Sound Speed Profie
500-
1000
1500-
-
3500
4000-
0
05
1
1.5
2
2.5
3
Range (in)
3.5
4
4.5
1
101
Figure 6-2: The position of the AUV below the surface duct in order to predict
ranging from a source. Ranging can also be tested in the surface duct as well, the
analysis can be done from other experiments.
Figure 6-2. The circular yoyo pattern should be run to observe the noise field and
the resulting data evaluated.
Bottom Response
The objective here is to observe the bottom bounce for a number of different frequencies in order to observe the effects that the bathymetry, and possibly the sub-seabed
composition (for example natural gas or oil), will have on the acoustic picture. It
helps to have an already known bottom so that it can be compared against the picture, but it could also be run without knowing the bottom. After the locations of the
sound sources along the edge are known, the vehicle should be run with circular yoyo
patterns at different azimuthal angles away from the source. At each location, the
3D picture from the source can be evaluated to help understand the bottom bounce.
Comparing this against the actual known bathymetry in the area will give significant
data. With a vehicle speed of approximately 1.5 m/s and a total travel distance of
approximately 15 km, plus additional time built in for the vehicle to make the noise
run, this experiment could take upwards of 5 hrs.
111
Ice Eg
Hot Spot
5km
Figure 6-3: To measure the bottom response, the goal will be to run the vehicle in
a pattern in which it can develop a 3D noise picture at different azimuths from the
noise source. The response from the negative elevation angles at multiple frequencies
will be evaluated to see what information about the seabed can be extracted from
the picture.
6.1.2
Identifying the Notch
This objective is based on the discussion in Section 5.1, and is to find the notch in the
vertical arrival structure. The notch will be in the vicinity of the depth ranges from
approximately 500 m to 1000 m based on predictions from bellhop. As we learned in
Chapter 5, a towed array will not be sufficient for measuring a horizontally isotropic
vertical notch, so this will need to be done with a vertical line array, deployed at the
depth of the predicted notch.
6.1.3
Proposed Experiments
The following are the series of proposed experiments that could be conducted in order
to cover the objectives listed in Table 6.1.
Experiment 1
In the first experiment, the AUV with the towed array should be placed in the water
near
(5
km) from the location of where hot-spots are expected. From this location,
one could run the AUV in one location in a circular pattern at relatively shallow
112
depths, for example, between 20 and 100 m. This circular pattern will be run many
times, but after each consecutive completion of the pattern (or every other circle, if
time permits), the period of the yoyo maneuver will be changed to add more and
more verticalness into the array for each run.
From this data we will be able to test for the convergence (objective 3) of the
overall noise pattern for any period we wish, as well as check the verticalness vs. the
resolution (objective 1) of the noise picture for any identified noise sources in the
area. In addition, post processing of this data will allow us to identify the location of
any hotspots. If a hot spot is identified, then we could also attempt to see if there is
evidence that shows ranging (objective 4), although this may be difficult because the
vehicle is in the surface duct.
If, during the experiment the vehicle travels at 1.5 m/s, each circular pattern
will take approximately 7-8 minutes, depending on the additional yoyo maneuvers
involved. If we test each of the periods presented in Table 4.1 with a single circular
loiter pattern, that's 8 circles for approximately one hour of in water testing time, or
if each experiment is done with two circles, approximately two hours. When planning
also allow an additional hour or two to account for the time needed for transit, launch
and recovery, getting to depth, and possible troubleshooting. I total, one should allow
a total of 3-4 hours for the experiment.
Experiment 2
In the second experiment, it is helpful to have already identified the location of an ice
cracking "hotspot" from experiment 1. In this experiment, the AUV should be run in
a pattern similar to the path described in Figure 6-3. This path consists of circular
patterns with a yoyo maneuver (with as much yoyo as the vehicle limits allow) at
different locations but at the same range from an identified hotspot or noise source.
Each loiter pattern should be run at a relatively shallow depth, for example, 20 m to
100 m, with the exception of two patterns, in which the vehicle should descend below
the surface duct at approximately 500 m to conduct a full circular pattern with a
yoyo maneuver there.
113
The purpose of gathering this data is two fold. First, we will be observing the bottom bounce of the acoustic waves (objective 5), and match it against the bathymetry
and known seabed type to see what can be learned from the bottom by observing
the pictures at different frequencies. This can be done at deep or shallow depths. In
addition, we can measure the vertical arrival structure from any noise sources to see
if we can use that information to infer the range, either from the bottom bounce and
the known bathymetry, or from the RAP (objective 4).
This experiment will take significantly longer than the previous one. A vehicle
traveling at 1.5 m/s in a semi-circular arc with a radius of 5 km while ascending
and descending in the water column to get information at lower depths, will take
approximately 3.5 hours. If we add an additional 7-8 minutes for each circular pattern
run at each location, and if 8 locations are chosen, that would be an additional
hour. Taking these into account, and the the time required for traversing, launch
and recovery, and troubleshooting, the expected experimental time would likely take
upwards of 6 hours.
Experiment 3
This experiment is to test the remaining objectives, 2 and 6.
Objective 2 is to
verify the vertical noise pattern (i.e. identify the noise notch), and 6 is to observe
the predicted noise notch. This experiment will require the stationary VLA. The
placement of the array is fairly simple, a simple drop at various distances away from
the ice edge. The array does not need to be deployed for long, a couple minutes of
data should be sufficient to build a reliable vertical noise profile. For identifying the
noise notch in objective 6, the array should be placed at a depth around 700 m in
any location, but if possible away from other noise sources.
6.2
Better Ranging Algorithms
As we have shown, it is possible using simple geometric methods to find the range
to a sound source by measuring the angle for the maximum reliable acoustic path.
114
BELLHOP- ArcUc
Environment, Incoherent
200
400
600
1000
12001400
1600
0
0.5
1
1.5
Range (m)
2
2.S
3
-10"
Figure 6-4: When ranging to a vehicle, the reliable acoustic path may not be the only
direction given the sensor and source locations, but in fact the sound can arrive from
multiple directions in the form of eigenrays. In this case, three eigenrays have been
found. The red line shows the reliable acoustic path, while the two black rays show
the arrival from two rays that have reflected from the surface.
However, this measurement makes a number of assumptions. It assumes a constant
gradient in the sound speed profile, and also that the ray path arrives only from the
reliable acoustic path (RAP). In reality, the sound speed profile is not linear and the
arrival structure of the sound may be the result of multiple rays called eigenrays,
which can be calculated [20]. Also, depending on the environment, the RAP may not
be a path at all, particularly if the bottom prevents it. Figure 6-4 shows an example
where these eigenrays have been calculated using an Arctic sound speed profile.
It is conceivable that a more robust algorithm could take all these factors into
account.
If bathymetry data, the sound speed profile, and the sensor and source
locations were input into the system, it may be possible to develop more robust
algorithms which would allow for more opportunities for ranging (for example, when
the RAP isn't present) and with greater accuracy.
115
Strike-Slip
Tensile
Dip-Slip
,
- 100.0 Hz
SO- 1.0mCONDR.IP
P 100.0 Hz
SO- 1.0 nCONDRFIP
10
F- 100.0
HS
SO- 1.0 CONDR.FIP
-55
-5
.0
.0
(0
.5
. 5. 0
-
0
0
Range (kin)
.5
10
I
.0
.
Range (kin)
.0
1010
0
Range (km)
Figure 6-5: This figure shows a model of three different ice cracking types and their
radiation patterns, as modeled by the work of Kim [21]. By measuring the 3D acoustic
picture at different locations relative to an ice cracking event, these models could be
verified and studied further outside of a modeled environment.
6.3
Ice Cracking Research
As mentioned in Section 2.3, the noise sources are the result of multiple ice cracking
"hotspots" along the ice edge. These hotspots last approximately for a day in duration. There has been research conducted at MIT modeling the acoustic properties of
different types ice cracking noise [21]. Figure 6-5 shows 3 different types of ice cracking mechanisms, and their predicted acoustic radiation patterns. By maneuvering the
vehicle in such a way that it develops multiple 3D acoustic pictures at various angles
and locations relative to the noise source, we could achieve better understanding the
mechanisms that occur in ice cracking and their acoustic properties.
6.4
Autonomy Solutions
The ultimate goal for this and other research is to develop a capability for AUVs to
be deployed for long amounts of time to survey the ice edge, map the bottom, or track
targets. Because acoustic communication underwater is very limited, this ultimate
capability will require a sophisticated and reliable autonomy solution. As we learn
more about the environmental characteristics of the Arctic, we should endeavor to
116
40
20
-20
-40
-60
-40
-20
0
X Pos (km)
20
40
60
Figure 6-6: A potential utility solution for vehicle maneuvering given the location of
multiple ice cracking "hotspots". After the hotspots are identified, the vehicle could
attempt to maintain distances to multiple sources for optimum surveillance capability.
Using the IvP behavior structure already existing in the MOOS-IvP database, this
could be balanced with other objectives the vehicle is attempting to accomplish.
use these characteristics to develop better autonomy systems.
In the case of tracking an ice edge, an AUV could be programmed to seek and
maintain a certain distance and depth from the ice cracking events. This of course
would require the AUV to be capable of analyzing its own acoustic data to find these
events.
Figure 6-6 shows an example of a potential utility function that could be
developed for an AUV, given the location and amplitude of ice cracking events. If the
type of radiation pattern could also be identified identified (Section 6.3) this could
also be included into a more sophisticated algorithm. Other consideration could be
to include cooperation with other AUVs through acoustic networks, and minimum
energy solutions to facilitate long deployment times.
6.5
Conclusions
There are three main conclusions that can be taken from this research, relating to the
3 contributions originally stated in Chapter 1. The first is that adding verticalness
to the array does in fact improve the acoustic picture for sound sources when tested
117
in the virtual environment. For a single sound source, the relative 3D picture peak
response for experiments with yoyo patterns (vertical score 0.3 or higher) can be on
average 6.5 dB higher than than experiments without yoyo patterns (vertical score of
0). In addition, the 3-dB down bandwidth of the vertical arrival structure from the
noise source decreased to less than half the result obtained from a horizontal array,
from more than 20' to less than 100. In addition, over the vertical scores tested, the
horizontal 3-dB down bandwidth did not appear to suffer.
The second conclusion is that range estimation is possible given the vertical arrival
structure of the sound, and that the uncertainty in that measurement (also measured
by the 3-dB down bandwidth) somewhat decreases with range. Using a number of
assumptions and some simple geometric calculations, I was able to calculate the location of a source 40 km away to within about 15% accuracy. These measurements
however are sensitive to the parameters chosen in the assumptions, such as the assumed constant sound speed gradient. Also the uncertainties in these measurements
is fairly high, measured at 30% to 60% of the actual distance. Additional research and
experiments could be developed to make these calculations more accurate if actual
ray tracing models are used with a full sound speed profile, and multiple arrival paths
are considered using eigenray calculations.
Finally, I've shown that horizontally isotropic vertical noise fields cannot be measured by a towed array for any realistic levels of verticalness. Evidence of a vertical
"notch" in the 3D beam response generally doesn't exist until array sees tilt angles of
more than 75'. These types of fields are best measured and characterized by vertical
line arrays.
118
Appendix A
Modeling the Pressure Field
A.1
Ray Tracing
In Section 4.4.2, we developed a simple geometry based on ray tracing, however, the
acoustic model for developing the acoustic signals are significantly more sophisticated.
In this section, we will discuss the derivation of how rays are traced in the ocean based
on the derivations provided in Computational Ocean Acoustics [20]. Rays are vectors
normal to a wavefront. The premise for ray curvature begins with notion of Snell's
Law, which states that a relationship between the grazing angle of a wave 0 and the
sound speed of a medium will always be constant.
cl
C2
cos0 1
cos02
Constant
(A.1)
So, as the speed of sound in which the acoustic waves are traveling speeds up, so
does cosine of the grazing angle go down. To make some more intuitive sense of this,
use the definition for the wave number k:
k
2rf
C
(A.2)
With this information, we can rearrange Equation A. 1 to the following:
k, cos 01S -k2 COS02(A3
119
(A.3)
Figure A-1: The incident angle of a ray will change based on the sound speed of the
media in which it travels.
and since w = 27rf and the frequency of the wave does not change,
k, cos 01 = k 2 cos
(A.4)
02
As illustrated in Figure A-1 for a stratified media the incident angle of a ray will
change as the the sound speed of the media changes.
For a linear sound speed profile with a constant gradient in an ocean acoustic
environment we would expect the rays to be traced in a circle, similar to the way
they are traced in Section 4.4.2, with a center equal to the location where the sound
speed is equal to zero. However, for any general sound speed variation we can perform
ray tracing using a general set of coupled ordinary differential equations, derived from
the Helmholtz equation:
A 2 P +W
P = -6(x - xo)
c2(x)
where x is the set of cartesian coordinates x
=
(A.5)
[x, y, z]. We begin by defining the
pressure from a point source in what is called the ray series:
p(x) = eiWT(X)
(A.6)
j
j=0 (iW)j
If we take the second derivative of the pressure with respect to x, we can write:
+A
j=0
(iw)j
120
+
AA +
A 2A
(+2)w
j=0
j=0 (iw)j
(A7)
Plugging this result back into the Helmholtz Equation A.5, we can obtain a series
of equations based on the order of each of the w terms. The two equations that are
found on the order of O(w) and O(w'-j) are known as the transport equations, and
the remaining equation, found on the order of O(w 2 ) is known as the eikonal equation.
For the purposes of ray tracing, it is this eikonal equation that we are concerned with,
and is written as such:
AT 12 =
1
c2
(A.8)
(x)
From here, we need to define some further terms. In ray coordinates, we can define
the ray trajectory x(s) as by the differential equation:
dx = CAr
ds
(A.9)
where s is the arc length along the ray. From the eikonal equation, the right hand
side of Equation A.9 can be shown to be unity. If we consider only one direction x,
and differentiate Equation A.9 with respect to s, we find:
d
ds
-
-
cds)
d /dx
OT)
-
ds
o)x
92 TT&X 02T(Y
-
2
-9x
-
&s
+
(A. 10)
Oxoyas
Substituting this back in Equation A.9, this can be re-written again as:
d (
ds
dx
c ds
_
&2 TOT
=+c
OX2 OX
2
& T&o
+
19x1y
-
y)
cT
C
--
[T OT
-
2
2 Ox -Ox)
+(0
r
21
(A. 11)
OY
and since the term in the square brackets is equal to the left hand side of the eikonal
Equation A.8, we find that:
d (1dx)
ds cds
c 0
1
2Ox
c2
1 ic
c 2 Ox
If we apply the same method we used for the x-direction for all direction x = [x, y, z],
the vector equation for the for ray trajectories can be obtained:
121
d (1 dx
ds c ds
1
(A.13)
c2
This equation is the basis for the ray equations. If we transform the cartesian coordinates to cylindrical coordinates about the ray source, we arrive at the general
ray-tracing equations:
dr
-= c ((S),
ds
d
ldc
ds
c2 dr
dz
d(
1 dc
ds
ds
c2 dz
(A.14)
(A.15)
In these equations, r(s), z(s) is the trajectory of the ray in the range-depth plane
(
in cylindrical coordinates, where s is the arc length along the ray. The variables
and
have been introduced so that the equations are expressed in first-order form
only. These equations, along with a set of initial conditions for the source position
(r, zO) and take-off angle
A.2
00, are the basis upon which ray paths can be calculated.
Finding the Phase Difference
The phase difference is found by solving the eikonal equation in the cylindrical coordinate system of the rays [20]. From the eikonal equation, Equation A.8:
AT - AT =
12
AT -
2
c
ldx
c ds
1
=d
- I
C2
(A.16)
or
dT
1
ds
c
(A.17)
If we then take the integral:
T(S) = T(0) +
1 ds'
122
To c(s')
(A.18)
we can find the travel time along the ray - and thus the phase difference of the ray is
just delayed by the time it takes for the pressure wave to travel along the ray.
A.3
Calculating Ray Pressures
Recall that from equation A.7 we obtained three equations, one the eikonal equation,
and the other two were the transport equations. Again, the method presented here
is from Computation Ocean Acoustics [20]. To find the pressure, we are concerned
with the equation resulting from the terms with w on the order of O(w):
2AT - AAO + (
2
T)Ao = 0
(A.19)
or
A - (A0 AT) = 0
(A.20)
Now, if we consider Gauss's theorem (or the divergence theorem) for an arbitrary
field F in any volume V, we know that the integral of the divergence of F (A - F)
is equal to the flux of the field running the volume V. Using this, we can rewrite
Equation A.20 in the following form:
A0 AT - ndS
(A.21)
where V is any volume with a surface S with the normal vector n. This is useful when
we look at rays, because we want to define what we call a ray tube as the volume with
which we're concerned, which contains a family of rays. On the ends of the ray tube,
dx
we define the normal vector n =
-,
ds'
and since the rays follow the inside of the ray
tube by definition, the termAr -n = 0 on all the sides of the ray tube. These are all
illustrated in Figure A-2. Lastly, if we take the eikonal equation written in terms of
the ray coordinate s, we see that AT - n = 1/c and we can obtain the following using
the energy conservation law:
123
Vron=0
ayV
family
of rays
8V
-------
n= dx /ds
Figure A-2: An illustration of a ray tube. The flux of the rays through the sides is
zero, and the normal vectors to the ends are defined as n = dx/ds.
j
A0dS
=
VOC
av
= const
A2dS
a V, A2C
(A.22)
where &V and &V1 represent each of the end caps of the ray tube. If we let the ray
tube become infinitesimally small and set an arbitrary value for the amplitude of the
pressure at s = 0, we can conclude that:
Ao(s) = Ao(0)
(A.23)
c(S) J(0)
c(0) J(s)
where J(s) is a quantity proportional to the cross sectional area of the ray tube. J(s)
can be calculated by the hypotenuse of dr and dz for a given section of the array:
-
)2-
2
(00
00
1/2(A.24)
_
where r is the distance in cylindrical coordinates, assuming symmetry about the zaxis (depth in the water column). We can also see that the value J can also be found
by taking the Jacobian with respect to (s, o, #0), where 0 and
#o are the
declination
and azimuthal ray take-off angles, respectively [20].
With these relationships to the cross sectional areas to the tubes, we can now
set some initial conditions to find the resulting pressures. We set the initial pressure
conditions at the beginning of the ray to be as follows:
po(s) = Ao(s) eiwTo(s)
where
124
(A.25)
Ao(s) =
1
and
,
To(s) =
2
(A.26)
and co is the sound speed at s = 0. This poses a problem because for Equation A.23
the amplitude appears to go to infinity when s = 0. We can solve this problem,
however, because the limit of A(s) J(s) 1/2 as s -s oc does in fact converge to a finite
value:
lim A(s) J(s)|1 / 2
s-+oo
1
47r
cos 00
1 2
/
(A.27)
and we can therefore rewrite Equation A.23:
Ao (s) =II c(s) cos 0o
47r
(A.28)
1/2
c(0)
Putting this amplitude equation together with the phase difference (Equation A. 18)
and plugging it back into the original pressure Equation A.25, we can now solve for
the pressure at the end of the ray:
p(s) =
A.4
c(s COS0 1/2 ei fo 1/c(s')ds'
(A.29)
Finding the Total Pressure
Now that we have solved for the pressures of a generalized ray tube, we now want
to find the pressure resulting from a source and receiver. We do this by finding the
eigenrays between the two points using the ray tracing calculations and the definition
of the bathymetry in the environment (because rays will bounce off the surface and
the bottom). By this method, we identify all the rays that originate from the source
and end at the receiver at their corresponding incident angles and pressure losses.
Each ray makes a contribution to the complex pressure field and therefore we sum
the contributions from each of the eigenrays, such that:
125
N(r,z)
Ptot (r, z) = E
Pj (r, z)
(A.30)
j=1
where N(r, z) represents the total number of eigenrays for that particular range and
depth, and p1 represents the the pressure from the jth eigenray. This gives us the
pressures we use in the acoustic model.
126
Appendix B
Bellhop Inputs
The following is the information that was used as inputs into the Bellhop Program:
frequency = 800
Fitting type:
SVF (Analytic or C-linear Interpolation)
bottom = 3750 m
Run Type = I (R = Ray, C = Coherent, I = Incoherent, S - Semi-coherent)
Number Beams = 0 (Allows matlab to choose optimal number of beams)
Number of Sources = 1
Source Depth = 5 m
Number of Receiver Depth Steps = 201 (every 2 m)
Receiver Depth Range = 0 400.0 (0 to 400 m)
Number of Distance Steps = 501 (every 10 m)
Receiver Distance Range = 0.0 5.0 (0 to 5 km)
Step Size = 0 (automatic), ZBOX = 500, RBOX = 5
127
128
Appendix C
Modeling of a Towed Array
C.1
Modeling of an Array
One of the major areas that needs to be understood is the modeling of an array. This
is done in the virtual environment by the program uSimTowedArray, which models the
x,y, and z coordinates. uSimTowedArray is based off a Matlab program pArraySim,
which has been shown to match fairly consistently with real world experiments [7].
To begin describing the model, we first make a series of assumptions:
Small Perturbations are Negligible Local perturbations of the cable from its
overall shape (due do small local eddies and other environmental factors) are
negligible.
Torsion and Rotational Intertia are Negligible The rotation and torsion of the
array about the axis normal to a cross section of the array cable are both
negligible.
Bending Stiffness is Negligible Bending the array cable does not produce a bending moment. Instead, the cable acts as a "loose string" being towed behind the
AUV.
No Effect From Waves Waves from the surface do not affect the motion of the
array.
This is a particularly good assumption given that the AUV will be
129
operating at depths of more than 20 m below the surface, where most surface
waves have little effect.
Based on these assumptions, a set of governing equations is developed [16]. While
the actual equations work in three dimensions for the array, only two dimensions will
be discussed here in order to keep the equations succinct.
(On
fU=m
at
F,=m
at
Da
N
v
at
T
1
-wcosa--pdCtulu|
2
as
u +m,
at )
at =T as -2sina-
2 pdCHvv
(C.1)
(C.2)
In the above equations, Fu represents the forces in the tangential direction toward
the cable and F, represents the force in the normal direction to the cable. These terms
are expanded on the left hand side of the equations and represent the acceleration of
motion of an element of the array. The right hand side is a sum of the forces on the
OT
array. In Equation C.1, the u-direction
is the change in tension in the tangential
Os
1
direction, the -pdCulul term is the drag on the array element due to the element
2
moving through the water, and w cos a is the effect of gravity on the array element
transformed from the x-y coordinate system to the local u-v. In Equation C.2 for
the v-direction, the terms are similar with the exception that there is an added mass
Ov
term, ma OV, that occurs due the need to account for the moving fluid around the
at
outside of the cable. The balanced forces on the element are shown in Figure C-1.
The compatibility relations in terms of the velocities are expressed as follows:
O- Oa =O
Os
as
Ot
Ov
Os
a
Oa
as
at
(C.3)
(C.4)
In order to separate the static and dynamic parts of the problem we expand the
the tension T ~ T
+
T and the angle a ~ d + d. Using these decomposed forces we
can account for the forces of the current in the water in Morison form:
130
U
7
Aa
u-drag
a
S
v t
Yu
v-drag
Figure C-1: The individual forces that act on an element of the towed array. On the
left side is a picture of an element on the array, and on the right are the forces (not
including current) of the forces that act on the element.
1
Fe-rrentu-2pdCU sin ajUsina| 1+
2
(C.5)
TE
2EA
(C.6)
2
1+
)
(
1 ,IYT
IT
Fcurrent,v =-pdCtUcosaU cosa|
T)
2 EA
where U is the is the current in the x-direction. Next through a series of steps, we
remove the static terms, and use the small angle assumption on d. We also remove
nonlinear terms higher than the first order, allowing us to substitute OP for u and
at
dq for v. With these terms and the expanded forms of T and
oz, we can derive the
at
resulting dynamic equations:
a2p
at
m2
+wocoscoa
Jatap
-
Ucosd
1+2EA
(
pdCaP
+ 2Pt
at - Ucos-
1
+ 1pdCtU cos dIcos a
2
(1 2EA)
+
as
131
(C.-7)
Parameter
Nsub
Length (in)
Sector 1
20
Sector 2
30
Sector 3
20
20.0
36.0
20.0
0
0.0095
0.2
0
0.035
0.0024
0.5
0
0.0095
0.001
0.2
1.0e8
1.0e8
1.0e8
Weight (N/m)
Diameter (in)
0.001
td
nd
E (N/m )
2
Table C.1: A table of the variables used in modeling the DURIP array.
-
T
ad
~ ad
= - T
02
(m
1
ma) Ot 2
+ IPdC O
+
-wsin a a
g
O +U
~)
1 pdCdUTsinTsin.
2
Pd
snasn
I+
kj
~
(i\
k '1
__
2EA)
(C.8)
T
2EA}
T
The 1 + 2EA above comes from the definition of strain that c = T/EA and the
compatibility relation:
1+ - =1+
2
2EA
(C.9)
These are the governing equations which are used to solve the shape of the towed
array. For modeling the DURIP array, the array is divided into three sections, the
20 m tow cable (sector 1), the 36 m acoustic body with the center 30 in as the towed
array section (sector 2) , and the 20 m drogue (sector 3). The parameters used for
each of these sectors in the cable model are shown in Table C.1.
132
Appendix D
Spherical to Conical
Transformation
For an assumed straight array, a conical coordinate system can be used to compare
the 2D beam pattern to the 3D one. In addition, one can find the conical angle 3
through this transformation [36]. The geometry for the transformation can be derived
from Figure D-1. The array axis is represented by the line OP and
# is the
angle of
the conical beam. To keep the calculations simple the sphere is presented as a unit
sphere.
To begin the derivation we geometrically define some relationships:
Oa = cos$
sin
$
-c=
(D.1)
(D.2)
Ob = Oa cos 0 = cos $ cos 9
(D.3)
ab = Oa sin 0 = cos $ sin 9
(D.4)
133
P
Y
conica\
ray
I
Pherical
Noise Equator
Figure D-1: The measurements needed for the geometric transformation between the
spherical and tilted conical coordinates. The sphere represents the noise sphere, OP
represents the axis of the array with tilt a, and 3 is the angle of the conical beam.
134
a-J
cos-'(Ob) = cos 1 (cos # cosO)
S=tan-1
= tan-
(
(D.5)
0_
sin
(D.6)
Cos # sin 0
In the above equations the bar represents the distance of the line segment between
the two points. Now, using the law of cosines for the spherical triangle, defined by
-
the points c, P, and X < PXc on the unit sphere with an interior angle of (90
at the angle < PXc, we can come up with the following equation:
-
cos Pc = cos Xc cos XP + sin Xc sin XP cos(90
(D.7)
where the rocker (-) denotes the are length on the surface of the unit sphere. Now
we define some additional relationships among the arcs:
XP = a,
cos(90 -
)
PC =,3,
=
sin
= sin
and
tan-1
Xc
cos- 1 (cos # cos 0)
= sin tan- 1
6
(
sin q5
cos # sin 0
(D.8)
(D.9)
Next we take these relationships and definitions, and substitute them back into Equation D.7. Taking the inverse cosine of that result yields the following:
= cos-
1
cos
#
cos O cos a + sin[cos--1 (cos# cos 0)]
x sin a sin Itani
sin#
cos# sin9)_
}
(D.10)
This completes the transformation between the tilted conical coordinates and the
array coordinates.
135
136
Appendix E
3D Acoustic Pictures for a Simple
Source
137
3D Noise Field - Period 300
80
80
75
60
40
70
L
20
O'
0
0
65
60
-20 >
55
-40
-60
50
-80
45
0
-50
Azimuthal Bearing, degrees
L- ------ -Vert Score
150
0--
100
-20--------------
50
0
-50
-100
-150
0
100
50
Ambient Noise Level (dB)
0.3-
0.20003
=
- - - ------
-60-
600.1
-80-100--- -- -- -- - --- - -0
-100
0
x (m)
100
0
100
200
7-
I
300
0
400
100
200
300
400
Time (s)
Time (s)
Figure E-1: Simple Source Results for Period 300
3D Noise Field - Period 500
80
80
1
80
75
60
;
60
a)
0) 40
4
40
70
20
20
65
C
0
0
60
-20>
-20
S-40
-60
55
-40
50
-60
-80
-80
45
100
0--20 -
50
A-4
.50
0.3
---------------
-- - - - - - - - - - - - - --
>
-80
-100-----100
0
x (m)
100
J
-U
-50
-100
-150
0
----
100
300
200
Time (s)
400
Vert Score= 0.19349
0.2
0.1
0
0
100
200
300
Time (s)
400
Figure E-2: Simple Source Results for Period 500
138
0
Ambient Noise Level (dB)
Azimuthal Bearing, degrees
150
100
50
3D Noise Field - Period 600
80
80
75
40
60
40
70
20
20
65
0
0
60
--
-20>
20
-40
55
-40
-60
so
-60
-80
-80
45
-150
-100
0 ------ ---- - -----
50
0
-5 0
60
40
Ambient Noise Level (dB)
80
re
CL -0-6.
-80
-100
0
x (m)
100
=
0.15525
0.2
-4
1
- - --100 - - - - - - 0
100
200
300
Time (s)
-L
0
400
100
300
200
Time s)
400
(
0
150
0.3
15 0
10
-10 0
-15 i
100
50
-50
0
Azimuthal Bearing, degrees
Figure E-3: Simple Source Results for Period 600
3D Noise Field - Period 700
so
80
75
40
c
70
60
40
M
7
20
65
20
00
0
60
-20
-40
-
20
55
-40
50
-60
-80
45
Azimuthal Bearing, degrees
0.3
150
100
-20 - - - -
50
E
0
400
0
0.2
t0.1
-50
-so-
-100
-150,
013631
- - - - - - - - - - -
-100
0
x (m)
100
-100- - - --100
0
-- - -- 300
200
Time (s)
--400
0
0
100
300
200
Time (s)
Figure E-4: Simple Source Results for Period 700
139
400
40
80
60
Ambient Noise Level (dB)
>
3D Noise Field - Period 1000
80
80
80
75
60
40
60
40
70
20
/
65
20
CP
0
0
60
-20
-20
t-40
55
-60
50
->
-40
-60
-80
-80
-100
15 0
10 0
E
50
-S0
-10 0
-15 01
-50
0
50
Azimuthal Bearing, degrees
L
-100
0
100
- - - - - - - - -6c
--
-60-80
-100-0
45
150
40
60
Ambient Noise Level (dB)
80
0.3
-
-20 - - - - -40-
x (m)
100
Vert Scar e
0.12258
0.2
t
0.1
0
-
0
--- -- - --100
200
300
400
Time (s)
0
100
200
Time
(
-150
300
400
s)
Figure E-5: Simple Source Results for Period 1000
3D Noise Field - Period 1500
80
80
80
75
60
70
40
4
S20
65
0
40
20
C
0
o
60
-20>
-20
-40
-60
55
-40
50
-60
-80
-80
45
Azimuthal Bearing, degrees
150
100
0 ------------------ - - - - - -0
-20 - - - - - - - -
-
50
0.3
Vert Score
=
0.080045
0.2
-40-----
40t
-50
-100
-150
V)
-80
-100----------------------100
0
x (m)
100
0
100
0.1
-
8j
60
300
200
Time (s)
400
0
0
100
300
200
Time (s)
400
Figure E-6: Simple Source Results for Period 1500
140
80
60
40
Ambient Noise Level (dB)
3D Noise Field - Period 2000
80
80
75
60
40
70
01
20
65
:2
00
P
60
-20 c
55
-40
50
-60
-80
45
.LUU
I.:)U
Azimuthal Bearing, degrees
15
10
5
-5
-10
0
00
3
0.-0
-15
-100
0.3
0 -------------- - - - - - - ---
S20
Vert Score
>
0
100
0
100
x (m)
=
0.057055
0.2
-40
80-
--
80
60
40
Ambient Noise Level (dB)
200
300
Time (s)
400
0,1
0,0
100
300
200
Time (s)
400
Figure E-7: Simple Source Results for Period 2000
3D Noise Field - Const depth
80
80
80
75
60
e 40
60
40
70
20
51
20
65
0
0
60
-20
-20
N
U
-40
55
-40
-60
50
-60
-80
-80
45
10
0
Azimuthal Bearing, degrees
150
100
0 ------------------------20 - - - - - - - - - - - - - - - - w'
-40
50
0
Vert Score = 0.018588
0.2
-60t
-50
-80>
-100
-150'
0.3
----------------------
-100
-100
0
x (m)
100
0
100
200
300
400
Time (s)
0
100
200
300
400
Time (s)
Figure E-8: Simple Source Results for Constant Depth
141
80
60
40
Ambient Noise Level (dB)
142
Appendix F
3D Acoustic Pictures for Noise
Notch
143
3D Noise Field - Vert array
55
80
80
50
Ln
y
60
40
40
01
45
20
02
40
0
0
-20
-20
6C
35
-0,
-40
30
A8C
-60
-80
25
-50
0
50
Azimuthal Bearing, degrees
150
100
Score =
0.98833
200
300
Time (s)
400
Vert
-
-60
-80
-100----
0.2
-
-50
-100
-150'
0.3
0-----------------------20 - - - - - - - - - - - - - - -40
so
60
40
20
Ambient Noise Level (dB)
-100
0
x (m)
100
0
0.1
-------- -100
200
300
Time (s)
-- --400
0
0
100
Figure F-1: Vertical ambient noise field results for a vertical array.
3D Noise Field - Period 300
55
80
80
60
0
50
60
40
40
45
GO
(U
20
20
40
0
Go
-20
-20
35
-40
-40
-60
30
-60
-80
-80
-:)u
U
25
)U
Azimuthal Bearing, degrees
50
E
0
-60
-80
-50
-100
-150,
- ---
- ---
- - --
/
-
'
-20--0
-40.-
-
0 ------------------ 0.3
150
100
Vert Score
=
50
48
46
Ambient Noise Level (dB)
0.20641
0.2~^
0.1/
0.
-- --
-
-100------------------------
-100
0
x (m)
100
0
100
200
300
Time (s)
400
0
100
200
300
400
Time (s)
Figure F-2: Vertical ambient noise field results for period 300.
144
3D Noise Field - Period 500
55
80
80
50
60
c
60
40
40
45
CU
20
20
40
0
C
0
-20 >
-20
35
-40
w -40
30
-60
-60
-80
-80
vUU
25
L)u
Azimuthal Bearing, degrees
10
5
-5
-10
-15
0
E
0
0t
00
0
x (m)
100
Vert Score= 0.1903
40.2
-60 -1
-80
>
-------
---------
100
-100
0.3
0 ----------------------.
- - - - - - - - - - ---20 - - --
0
100
300
200
Time (s)
-
15
46
48
50
Ambient Noise Level (dB)
400
0
100
0
200
300
Time (s)
400
Figure F-3: Vertical ambient noise field results for period 500.
3D Noise Field - Period 600
55
80
50
60
40
40
45
20 0
20
40
0
0
0
-20 >
-20
35
-40
-40
30
-60
-60
-80
-80
25
-50
0
50
Azimuthal Bearing, degrees
0-----------------------20 - - ------- - --
50
0
-50
-100
-1501
-400
-40,0.
-100----------------100
0
x (m)
100
0
100
46
48
50
Ambient Noise Level (dB)
0.3- - - - - - -
150
100
-
CU
60
Vert Score = 0.15467
0.2
C0.1
200
300
Time (s)
------
400
0
100
200
300
Time (s)
400
Figure F-4: Vertical ambient noise field results for period 600.
145
3D Noise Field - Period 700
55
80
so
60
Si
Si
40
45
Si
V
20
40
0
VS
@1
0
-20 >
35
-40
0)
30
-60
-80
25
-50
0
50
Azimuthal Bearing, degrees
50
o
-50
0 ---------------------4---)-----20 --40
60t
.-80.
-----100
I
-
-100
-150'
0
-100
100
0
100
x (m)
0.3
Vert Score= 0.1388
0.2
0.1
-
150
100
45
50
55
Ambient Noise Level (dB)
200
300
Time (s)
0-
0
400
100
300
200
Time (s)
400
Figure F-5: Vertical ambient noise field results for period 700.
3D Noise Field - Period 1000
55
80
50
60
40
40
45
20
20
40
0
0
U
-20
-20
35
-40
40
30
-60
-60
-80
-80
25
Azimuthal Bearing, degrees
150
100
50
0
-50
-100
-150
- -- - - - -
--
Vert Score - 0.12349
o"
0.2
-j
0.1
-
-60
-
-20 - - - - -
45
50
55
Ambient Noise Level (dB)
0.3-
0 ------------------------
(U
li
-80->
-100- ------------------100
0
x (m)
100
0
100
200
Time
300
(s)
400
0
100
300
200
Time (s)
400
Figure F-6: Vertical ambient noise field results for period 1000.
146
3D Noise Field - Period 1500
55
80
80
i
60
50
60
40
40
45
CM
20
20
40
0
-20 >
-20
35
-40
C -4C
30
-6C
-60
-80
25
Azimuthal Bearing, degrees
150
-20
- -
-40
-
- - - -
,
-
- - - - -
-
02
-
-60
-80
0
x (m)
wi
>
-----------
-100 -----
-
-100
100
0
100
0.082 134
Vert Score
V.
0.1-
-----
300
200
Time (s)
-
50
0
-50
-100
-1501
0.3-
0 -------------------.
100
45
50
55
Ambient Noise Level (dB)
0
400
100
300
200
Time (s)
400
Figure F-7: Vertical ambient noise field results for period 1500.
3D Noise Field - Period 2000
55
80
60
50
40
CU 40
45
20
20
01
40
0
0
-20
-20
35
-40
-i40
30
-60
-60
-80
25
-50
0
50
Azimuthal Bearing, degrees
150
100
-100
-150
0.3
0
---------------------20 - - - - - - - - - ---------40
50
0
-50
-80
-100- -100
0
x (m)
100
40
50
60
Ambient Noise Level (dB)
0
Vert Score
=
0.058683
-0
0-60
.1
---------------------
100
200
0
300
Time (s)
400
0
100
200
300
Time (s)
400
Figure F-8: Vertical ambient noise field results for period 2000.
147
D
3D Noise Field - Diag 45
55
80
580
60
50
60
40
40
(
45
20
20
0
40
0
-20
20
35
-40
-40
0
-60
30
-80
I25
-80
50
-50
0
Azimuthal Bearing, degrees
-100
-150
150
100
E
50
0
50
f
c
>
Ul
- -- -- -- -- -0----------20 - - - - - - - - - - - - - - - -
~-404
_
_
_
_
40
50
45
Ambient Noise Level (dB)
150
100
0.3
Vert Score= 04848
e
0.2
U__
t
-60-
-V0
>.
-100-80
200
300
Time (s)
-
-150
-100
0
x (m)
100
0
100
400
0
100
400
200
300
Time (s)
Figure F-9: Vertical ambient noise field results for 450 tilted array.
3D Noise Field - Diag 60
55
80
80
50
60
60
40
40
45
20
20
40
0
0
0
-20 >
-20
W
35
m-40
A40
-60
30
.80
-80
-100
-150
-50
0
50
Azimuthal Bearing, degrees
150
0 -------
100
50
45
40
Ambient Noise Level (dB)
0.3
-----------------
Vert
50
Score=
0.65381
0E0.2
at-60
t
-8U
0.1
0
--
-100
-100
0
x (m)
100
1
0
100
300
200
Time (s)
400
-
0
-
-
0
-50
-150
25
150
100
100
300
200
Time (s)
400
Figure F-10: Vertical ambient noise field results for 60' tilted array.
148
3D Noise Field - Diag 75
-
80
55
80
50
60
60
40
40
45
C
20
20
20
0
--
0
40
20
-20
-40
-40
-60
30
-80
7.
-60
-80
-
25
-150
-100
-50
0
50
100
150
60
Azimuthal Bearing, degrees
150
100
50
E
c.
-50
-100
-150
0 ----20 -- ------
- ---
------------ ---
---
-60 -
t 0.1
w
-100---------------------0
x (m)
100
Vert Score= 0.82141
o0.2
>
-80
-100
0
100
300
200
Time (s)
400
0
0
100
200
300
Time (s)
400
Figure F-11: Vertical ambient noise field results for 75' tilted array.
149
40
Ambient Noise Level (dB)
0-3
_
_
-40
-
50
0
150
Appendix G
Noise Code
function
%%
get-3D-noise
Load in the settings
= '-/thesis-data/simple-src/';
directory
period_300';
period_500';
period_600';
'period-700';
'period-1000';
'period-1500';
'period_2000';
experiment{1} =
experiment{2} =
experiment{3} =
experiment{4} =
experiment{5} =
experiment{6} =
experiment{7} =
experiment{8} =
% experiment{l}
% experiment{2}
const-depth';
=
'vert-array';
% experiment{3}
=
=
'diag_45';
'diag_60';
% experiment{4}
=
'diag_75';
% Get the start and end files you want to test to and from
file-start
=
file-end
= 22C
1;
% Picture Resoltion theta-resolution
= 3;
phi-resolution
= 3;
for
expt-num
=
greatly affects calculation times
1:length(experiment)
% Location of files
=
input-filepath
% Location
output-filepath
for
[directory,experiment{expt-num},
deposit
=
of ACOUSFIELD.mat
file
[directory,experiment{expt-num},
151
'/acous/'];
'/'];
%Processing Information
fs = 12000;
% Inpute the sampling frequency
% Frequencies to process
= 900;
freqs-to-proc
%%
Calculate/Initiate
% Array Resolution
some important
in Hz
numbers
Information
thetas= 0:theta-resolution:359;
phis= -90:phi-resolution:90;
% Environmental Information
c = 1495;
% Speed of sound in water
% Get the f-axis and closest frequencies along it to processing
% frequencies, as well as those indicies on f-axis
faxis=linspace(0,fs,fs/10);
(size
freq-index=zeros
for
(freqs-to-proc));
i=1:length(freqs-to-proc),
freq-index(i)=find(faxis>=freqs-to-proc(i),l,
'first');
end
fc=faxis(freq-index); % Corrected frequencies to calculate
k=2*pi*fc/c;
% Wave number for fc's
% Initiate the data file
data.
angles=thetas;
data.phis=phis;
data. freq=freqs-to-proc;
data.info='angles,field,freq,position,info,phis,time';
%%
Pull the data from NAS and ACO files,
lrmsg
=
logs
0;
fprintf(['***********
for i =
add it to
',experiment{expt-num},'
************\n']);
file-start:file-end
% Get
the acoustic and non-acoustic file data names
= sprintf('%09d',i);
files
strcat(input-filepath,'ACO',filenum-str,'.DAT');
files
strcat(input-filepath,'NAS',filenum-str,'.DAT');
filenum-str
% acoustic
acofile
=
% non-acoustic
nasfile
=
% Get the non-acoustic data
fidnas = fopen(nasfile);
% Get the timestamp
= textscan(fidnas,
line-nine
8);
'headerlines',
'%s',
1,
timestamp = str2double(line-nine{1});
% Get the array positions
152
'delimiter',
'\n',
next-line = textscan(fidnas, '%s',
'headerlines', 0);
element-pos = 0;
array-positions
= zeros(1,3);
== 0
while isempty(next-line{l})
element-pos = element-pos + 1;
line-cell-array
1,
'delimiter',
= strsplit(next-line{l}{l},
'\n',
'\s* \s*',
'DelimiterType', 'RegularExpression');
= str2double(line-cell-array{l});
array-y = str2double(line-cell-array{2});
array-x
array-z
= str2double(line-cell-array{3});
(element-pos, :)
array-positions
next-line = textscan(fidnas,
'headerlines', 0);
=
[array-x,array-y,array-z];
'%s',
1,
'delimiter',
'\n',
end
fclose(fidnas);
if
i
== file-start
num-proc-files = file-end
- file-start
+
timestamps-log = zeros(num-proc-files,1);
pos-log = zeros (num-proc-files,element-pos,3);
length(freqs-to-proc),
fx-log
= zeros(element-pos,
1;
% picket
fence!
num-proc-files);
end
% Get the Acoustic Data
fidaco = fopen(acofile);
temp = fread(fidaco, [2*fs,element-pos], 'float32');
tempdata = zeros (element-pos,length(faxis));
for id=l:(2*fs/length(faxis))
todo= (id-1) *length (faxis);
tempdata=temp(todo+(1:length(faxis)),:).';
end
tempdata=tempdata./id;
fclose(fidaco);
freqx=fft(tempdata, [],2); clear tempdata;
fx = freqx(:,freqcindex);
% Double check if there is NaN in data.
if sum(temp)>0
fprintf('found nan in data, skipping %3.0f\n',i);
% Reduce the size of the vectors by 1 now.
timestamps-log = timestamps-log(l:end-1);
pos-log = pos-log(:end-l,:,:);
fx-log = fx-log(:,:,l:end-1);
continue;
end
%% Add the data to the logs
% Record the
fx,
positions and the
153
times in a
log for processing.
% Log will be held back as far as the time
%
1st
-
frame specified
Shift the old data back
timestamps-log(2:end) = timestamps-log(1:end-1);
pos-log(2:end,:,:) = pos-log(1:end-1,:,:);
fx-log(:,:,2:end) = fx-log(:,:,1:end-1);
% 2nd - Record the new data
timestamps-log(1) = timestamp;
pos-log(l,:,:)
fx-log(:,:,1)
fprintf
msg =
fprintf
limsg
=
=
array-positions;
fx;
(repmat ('\b' ,1, 1msg));
sprintf('loaded file number %3.0f/%3.Of',i,file-end);
(msg);
= numel(msg);
end
%% Do the field calculation
tic
calculation
fprintf(['\nStarting
experiment{expt-num}, '\n'])
% Now Calculate the
for
ACOUSFIELD
field for the current time,
for
save the
fieldN = calculate-noisefield3d(fx-log(:,:,:),freqs-to-proc,
pos-log(:,:,:),thetas,phis,c);
for ACOUSFIELD
calculation
Finished
fprintf(['
experiment{expt-num}, '\n'1)
t = toc;
fprintf('Time elapsed = %f seconds\n\n',t)
data.field =
for
',
fieldN;
size (data.field)
data.time =
timestamp;
data.positions
= squeeze (array-positions);
save( [output-filepath,
'ACOUS-FIELD'], 'data');
end
fprintf('FINISHED CALCULATIONS\n')
end
function [fieldN]=calculate-noisefield3d(fx, freqs,
positions, angles, vert-angles, c)
fprintf('building
3D acoustic pictures...
threshold=.005;%.005;
k=permute(2*pi*freqs(:)/c, [2,3,4,1);
lf=length(freqs);
lels=size(positions,2);
154
...
data
lt=length(angles);
lp=length (vert-angles);
nsamples=size(positions,1);
dd=permute (fx, [3, 4, 5,2, 1]);
thetas=permute(angles(:), [2,1]);
phis=permute (vert-angles (:), [2,3,1]);
arraypos=permute(positions, [1,4,5,3,2]);
% Center arrays on first element
for i =
1:nsamples
arraypos(i,:,:,l,:) = arraypos(i,:,:,l,:)
arraypos(i,:,:,2,:) = arraypos(i,:,:,2,:)
arraypos(i,:,:,3,:) = arraypos(i,:,:,3,:)
- arraypos(i,:,:,1,1);
- arraypos(i,:,:,2,1);
- arraypos(i,:,:,3,1);
end
% Calculate the added dists for each phi/theta to the elements
dists= (- repmat (arraypos (:,1,1,1, :), [1, lt, lp, 1, 1]) ...
.*sind(repmat(thetas, [nsamples,1,lp,1,lels]))...
- repmat(arraypos(:,1,1,2,:),[l,lt,lp,1,1]) ...
.*cosd(repmat(thetas, [nsamples,1,lp,l,lels])))...
.*cosd(repmat(phis, [nsamples,lt,1,1,lels])) ...
+ repmat(arraypos(:,1,1,3,:),[1,lt,lp,1,1]) ...
.*sind(repmat(phis, [nsamples,lt,1,1,lels]));
% Calculate the complex beam pattern
m=1/lels.*sum(repmat(dd, [1,lt,lp,1,1])
.*exp(li.*repmat(k, [nsamples,lt,lp,1,lels])
[1, 1,1,1f, 1) ) , 5);
.*repmat (dists,
...
% Find the actual baem pattern in power
M=real(abs(m));clear m; %this is r-true;
% Find the beam pattern in dB
R-true=10*loglO (abs (M));
fprintf('done.\nextracting noise...
')
%% Iterate to find the Noise Field
Nguess=ones(1,lt,lp,lf);
deltalog=[];
endvals=1;
prevsig=O;
ii=O;
msg =
[1;
while max(endvals)>threshold & ii<60,
ii=ii+l;
ntemp=10.^(Nguess./10);
% Get the delay vector for each element (for each element)
...
x-hat=l./(sum(cosd(phis),3)*lt)
.*sum(sum(repmat(ntemp, [nsamples,1,1,1,lels]) ...
155
.*cosd(repmat(phis,[nsamples,lt,1,1,lels]))
.*exp(-li.*repmat(k, [nsamples,lt,lp,l,lelsl)
.*repmat(dists,[1,1,1,lf,l])),2),3);
...
% Calculate the complex beam array based on the guessed noise
...
M-guess=1/lels.*sum(repmat(x-hat, [1,lt,lp,1,1])
[nsamples,lt,lp,1,lels])
.*exp(li.*repmat(k,
.*repmat(dists,[1,1,1,lf,1])),5);
[sample#,
in dB
% Find the R-hat
...
phi]
theta,
R-hat=10*loglO (abs (M-guess));
% Get the average R-bar (average difference)
% each sample [sample#, 1]
R-bar=1/lt/lp*sum(sum(R-hat-R-true,3),2);
sig-j
% Get the
% [sample#, 1]
sig-j=sqrt(1/(lt*lp)
= 1/(lt*lp)
*
sig-p =
-
R-hat
-
R-bar)^2
.*(sum(sum((R-true-R-hat
-repmat (R-bar, [1,
% Get the
(R-true
value for
for
samples
lt,
1p, 1] )).^2,
sig-p
=
2),3)))
(1/nsamples)*sum(sig-j^2)
sig-p=sqrt(1/nsamples*sum(sig-j.*sig-j,1));
Delta= (R-true-R-hat) /2;
newN=Nguess+sum(Delta,1)./nsamples;
%sig=sum(squeeze (sig-p))/size (sig-p,2);
sig=max (sig-p);
endvals=abs(prevsig-sig);
prevsig=sig;
Nguess=newN;
deltalog=[deltalog;endvals];
fprintf(repmat('\b',1,numel(msg)))
sig-p
msg = sprintf('iteration: %g\n
= %5.3f\n
...
delta = %5.3f',ii,sig-p,endvals);
fprintf
(msg);
end
fprintf('\ndone.')
length(deltalog);
if max(endvals)>threshold,
%fieldN=zeros(lt,lp,lf);
disp('could
not resolve noisefield in time alotted')
else
end
freqs]
fieldN=squeeze(Nguess) ;%[angles,vert-angles,
end
156
[1
1]
Bibliography
[1]
University of Washington Applied Physics Laboratory. SeaGlider. 2015. URL:
http: //www. api. washington. edu/proj ects/seaglider/summary . html.
[2]
Michael R. Benjamin and Henrik Schmidt. Unmanned Marine Vehicle Autonomy, Sensing, and Communications. University Lecture. 2012.
[3]
Michael R. Benjamin et al. "An Overview of MOOS-IvP and a Users Guide to
the IvP Helm - Release 13.5". In: (2013).
[4]
Michael R. Benjamin et al. "Nested Autonomy for Unmanned Marine Vehicles
with MOOS-IvP". In: Journal of Field Robotics 27.6 (2010), pp. 834-875.
[5]
A Batelle Company Bluefin Robotics. Bluefin-21. 2015. URL: http: / / www.
bluefinrobotics.com/products/bluefin-21/.
[6]
A Battelle Company Bluefin Robotics. Bluefin Products. 2015. URL: http: //
www.bluefinrobotics.com/products/.
[7]
Roberto M. Borsotti. "Development of a System for Stable Towing of Hydrohpone Arrays for High Frequency Seabed Imaging". Master's Thesis. Massachusetts Institute of Technology, 2009.
[8]
Philip Budzik. Arctic oil and naturalgas potential. US Energy Information Administration, Office of Integrated Analysis, Forecasting, Oil, and Gas Division,
2009.
[9]
Autonomous Undersea Vehicle Applications Center. Scripps Spray Glider Configuration. 2015. URL: http: //auvac. org/configurations/view/70.
[10]
Navy Task Force Climate Change. U.S. Navy Arctic Roadmap 2014 - 2030. US
Navy, 2014.
[11]
0. I. Diachok and R. S. Winokur. "Spatial variability of underwater ambient
noise at the Arctic icewater boundary". In: The Journalof the Acoustical Society
of America 55.4 (1974), pp. 750-753.
[12]
R. Drucker, S. Martin, and R. Moritz. "Observations of ice thickness and frazil
ice in the St. Lawrence Island polynya from satellite imagery, upward looking
sonar, and salinity/temperature moorings". In: Journalof Geophysical Research
(Oceans) 108, 3149 (2003), p. 3149.
[13]
Teledyne Gavia ehf. AUVs. 2015. URL: http: //www. teledynegavia. com/
product-dashboard/auvs.
157
Inc. Falmouth Scientific. Solar A UV (SA UV 11). 2010. URL: http: / / www
.
[14]
falmouth.com/products/solarauv.html.
[15]
Open Source Robotics Foundation. ROS. 2015. URL: www. ros . org.
[16]
Frank S Hover, Mark A Grosenbaugh, and Michael S Triantafyllou. "Calculation
of dynamic motions and tensions in towed underwater cables". In: (1994).
[17]
Woods Hole Oceanographic Institution. Autonomous Underwater Vehicle ABE.
2014. URL: http://www.whoi.edu/main/ABE.
[18]
Woods Hole Oceanographic Institution. Ships and Technology: REMUS. 2014.
URL: http://www.whoi.edu/main/remus.
[19]
iXBlue. 4th Generation GAPS USBL. 2015. URL: http: //www. ixblue. com/
sites/def ault/f iles/downloads/ixblue-ps-gaps- 10-2014-web. pdf.
[20]
F.B. Jensen et al. Computational Ocean Acoustics. Modern Acoustics and Signal
Processing. Springer, 2011.
[21]
Jea Soo Kim. "Radiation from Directional Seismic Sources in Laterally Strat-
ified Media with Application to Arctic Ice Cracking Noise". PhD thesis. Massachusetts Institute of Technology, 1989.
[22]
Ocean Acoustic Library. Rays. 2015. URL: http: //oalib. hlsresearch. com/
Rays/index.html.
[23]
David Moore, Albert Huang, and Edwin Olson. LCM Reference Manual. 2008.
URL: http://lcm.googlecode.com/svn-history/r432/www/reference/
lcm/intro .html.
[24]
NASA. A VHRR-Pathfinder. 2015. URL: https : //podaac . jpl . nasa . gov/
AVHRR-Pathf inder.
[25]
US Navy. USNS Able (T-A GOS-20). 2015. URL: http: //www. navsource. org/
archives/09/66/6620.htm.
[26]
Maria Alejandra Parra-Orlandoni. "Target Tracking Onboard an Autonomous
Underwater Vehicle: Determining Optimal Towed Array Heading in an Anisotropic
Noise Field". Master's Thesis. Massachusetts Institute of Technology, 2007.
[27]
Bluefin Robotics. Bluefin Spray Glider. 2011. URL: http: //auvac .org/uploads/
platform-pdf/Bluefin-Spray-Glider-Product-Sheet.pdf.
[28]
Bluefin Robotics. HA UV. 2015. URL: http: / /www. bluef inrobotics . com/
product s/hauv/.
[29]
Henrik Schmidt. "The Information Content of Ocean Noise: Theory and Experiment". Arctic Muri Project Proposal. 2013.
[30]
Toby Schneider. Acoustic Communications Lecture. 2014. URL: http: //oceanai.
mit . edu/2.680S14/docs/2.680-13-acoustic-communications .pdf.
[31]
Henrik Scmidt. OASES: Version 2.1. User Guide and Reference Manual. Technical Report. Massachusetts Institute of Technology, 2015.
158
[32]
Henrik Scmidt and Nick Saflund. The Soundscape of the Changing Arctic Autonomous Underwater 'SoundScope'. Presentation. 2015.
[33]
Gobysoft.org Aquatic Software. Projects. 2015. URL: http: //gobysoft . org/
index.wt/projects/autonomy.
[34]
Barbara J. Sotirin and John A. Hildebrand. "Acoustic navigation of a large-
aperture array". In: The Journal of the Acoustical Society of America 87.1
(1990), pp. 154-167.
[35]
Inc. Teledyne Webb Research Teledyne Technologies. The Slocum Glider. 2010.
URL: http: //www.webbresearch. com/slocumglider.aspx.
[36]
R. A. Wagstaff. "Horizontal directionality estimation considering array tilt and
noise field vertical arrival structure". In: The Journal of the Acoustical Society
of America 67.4 (1980), pp. 1287-1294. URL: http: //scitation. aip. org/
content/asa/journal/jasa/67/4/10.1121/1.384181.
[37]
R. A. Wagstaff. "Iterative technique for ambient-noise horizontal-directionality
estimation from towed line-array data." In: Journal of the Acoustical Society of
America 63 (1978), pp. 863 -869.
[38]
R.A. Wagstaff and J. Newcomb. "Three-dimensional noise field directionality
estimation from single-line towed array data." In: Journal of the Acoustical
Society of America 102.2 (1997), pp. 1023 -1031.
[39]
TC Yang et al. "Acoustic properties of ice edge noise in the Greenland Sea".
In: The Journal of the Acoustical Society of America 82 (1987), p. 1034.
[40]
Y. Yu and R. W. Lindsay. "Comparison of thin ice thickness distributions derived from RADARSAT Geophysical Processor System and advanced very high
resolution radiometer data sets". In: Journal of Geophysical Research (Oceans)
108, 3387 (2003), p. 3387.
159