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Microwave detection of cracks in buried pipes using the complex frequency technique

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MICROWAVE DETECTION OF CRACKS IN BURIED PIPES
USING THE COMPLEX FREQUENCY TECHNIQUE
MICROWAVE DETECTION OF CRACKS IN BURIED PIPES
USING THE COMPLEX FREQUENCY TECHNIQUE
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science in Electrical Engineering
By
Fadi G. Deek
American University of Science and Technology
Bachelor of Science in Computer and Communications, 2001
May 2010
University of Arkansas
UMI Number: 1484666
All rights reserved
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UMI
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UMI 1484666
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Abstract
Pipes are still used nowadays as a vital transporting means for gas, fuel and other goods.
It is very necessary to maintain pipes to avoid lethal leaks and financial losses. This work
provided a new noninvasive technique for evaluating the condition of buried pipes based on the
scattered fields received by the ground penetrating radar (GPR).
Several electromagnetic simulations were studied to understand this problem. The
commercial electromagnetic simulator FEKO was used in this thesis. The simulated model
constituted of a pipe buried in sand illuminated by a broadband antenna (Vivaldi) with bandwidth
3GHz - 10GHz. The involved method of moments requires meshing only the surfaces of the
different geometrical structures, which reduced the computational requirements.
The electrical signature of a 2 cm circular crack in a 50 cm long metallic pipe was
investigated. The pipe was buried at 30 cm below the interface of sand, clay, silt and loam. Also
humus concentrations up to 10% were considered. The results showed that the crack signature is
significant when fields were received right above the soil interfaces, depending on the attenuation
level in the soil.
The interesting phenomenon of the natural frequencies was explored to detect cracks in
buried pipes. It turned out that cracks exhibit additional resonances (to the pipe's main
resonance) when observed in the far scattered fields. An algorithm based on the Matrix Pencil
Method (MPM) was developed in order to extract these resonances to be expressed as poles.
The poles were dependent only on the size and shape of the pipe's cracks. Once a crack existed
in the pipe, additional poles were present. These poles indicate to the existence of a crack(s).
Unfortunately, this method does not provide information about the number of cracks, it does
provide information only about the presence of these cracks. An additional imaging technique can
be used in localized positions where these cracks are detected.
A motorized scanning system was built to collect data from a buried pipe in a controlled
environment. Measurements were first conducted in a 1 m 3 anechoic chamber to verify the
numerical results. The simulations showed that the algorithm was capable of extracting the
crack's poles with a signal to noise ratio SNR = 10 dB. The experimental data showed an SNR of
-5 dB. It is believed that the available anechoic chamber does not provide accurate far field
measurements due to its small size. Future research is necessary to improve the experiment set
up and the sensitivity of the proposed algorithm to the inevitable noise.
This thesis is approved for
recommendation to the
Graduate Council
Thesis Director:
Prof. Magda El-Shenawee
Thesis Committee:
Prof. Randy Brown
Prof. JingXian Wu
Thesis Duplication Release
I hereby authorize the University of Arkansas Libraries to duplicate this thesis when
needed for research and/or scholarship.
Agreed
Fadi Deek
Refused
Fadi Deek
Acknowledgements
I would like to thank God for his blessings during the past two years.
I dedicate this work which was the fruit of two years of perseverance to my advisor Professor
Magda El-Shenawee without whom none of this was possible. I would like to thank her for her
close guidance, patience and ever willingness to support and mentor. Her persistence and
experience have helped me develop the skills necessary for a researcher. I also thank my
committee members Professor Randy Brown and Professor Jingxian Wu for their invaluable input
and time.
I salute my friends and colleagues whom I have shared the most of my time with during
this work. I specifically mention Ahmad Hassan, Reza Hajihashemi, Douglas Woten and Jessica
Rutledge all of whom have shown a positive spirit.
Many thanks go to my family and friends from Lebanon whom have embraced me with all
the support and love needed to persevere in my spiritual and professional journey.
This work was funded by Entergy Incorporation. Also special thanks to Electromagnetic
Software and Systems Inc. (EMSS USA http://www.emssusa.com) for their technical support
and special pricing for FEKO Gold license.
VI
Table of Contents
Abstract
ii
Acknowledgements
vi
List of Figures
ix
List of Tables
xii
Chapter 1:
Introduction
1
1.1
Pipe Leakage and Industry Needs
1
1.2
Current Evaluation Techniques
2
1.3
Ground Penetrating Radars and Feature Extraction techniques
5
1.4
Field Simulators
7
1.5
Conclusions
8
Chapter 2:
2.1
Simulations In Three Dimensions and Measurements Setup
9
FEKO Configurations
9
2.1.1
Vivaldi Antenna
9
2.1.2
Effect of Dry Loamy Soil on Pipe with no Crack
11
2.1.3
Effect of Dry Loamy Soil on a Pipe with Crack
15
2.1.4
Crack Signature Comparison in Different Soils at Different Observation Points... 17
2.2
Measurement Setup
23
2.2.1
System Assembly
24
2.2.2
The Hardware
28
2.2.3
The Scanning System Labview Software
33
2.3
Conclusion
Chapter 3:
39
Natural Frequencies in Buried Pipes
40
3.1
Pole Extracting Methods
40
3.2
Matrix Pencil Method
41
3.2.1
Normal Matrix Pencil Method
42
3.2.2
Total Least Square Matrix Pencil Method
44
3.3
FEKO Simulations
45
3.3.1
Free Space Simulations
46
3.3.2
Target Detection at Different Burial Depths
59
3.4
Experiments in Anechoic Chamber
62
vii
3.4.1
Chamber Spatial Limitations
63
3.4.2
Measurements
63
3.5
Conclusion
Chapter 4:
76
Conclusion
78
References
81
VIM
List of Figures
Figure 1.1.1 Gas Pipe System [2]
1
Figure 1.2.1 Laser Controlled Camera [5]
3
Figure 1.2.2 a) X-Ray Tube on Tracks, b)X-Ray Image of Hidden Cylinders [8]
4
Figure 1.3.1 GPR System Scanning Pipe buried in Soil
6
Figure 1.3.2 Buried steel pipe without leak (left), buried steel pipe with leak (right) [4]
6
Figure 2.1.1 (a) Vivaldi Antenna, (b) Radiation pattern @ 5.6GHz
10
Figure 2.1.2 Vivaldi Measured S-parameters
10
Figure 2.1.3 (a) E-Plane Gain Plot, (b) H-Plane Gain plot
11
Figure 2.1.4 FEKO Configuration
12
Figure 2.1.5 Magnitude of Total Electric Field for Pipe in Loamy Sand: a) XZ Plane,
13
Figure 2.1.6 Magnitude of Total Electric field on Pipe in Loamy Sand
14
Figure 2.1.7 Phase of Total Electric Field for Pipe in Loamy Sand: a) XZ Plane, b) YZ Plane
14
Figure 2.1.8 Crack Dimensions
15
Figure 2.1.9 Magnitude of Total Electric field on Pipe w crack in Loamy Sand
15
Figure 2.1.10 Magnitude of Total Electric field on Pipe w crack in Loamy Sand
16
Figure 2.1.11 Phase of Total Electric Field for Pipe in Loamy Sand: a) XZ Plane, b) YZ Plane
16
Figure 2.1.12 X Plane Observation Points
17
Figure 2.1.13 X = 0 Plane Comparison of Magnitude of Crack electrical signature in 4 soil types at
4 observation points
17
Figure 2.1.14 Y Plane Observation points for Pipe w crack
18
Figure 2.1.15 Y = 0 Plane Comparison of Magnitude of Crack electrical signature in 4 soil types at
4 observation points
18
Figure 2.1.16 X = 0 Plane Comparison of Phase of Crack electrical signature in 4 soil types at 4
observation points
19
Figure 2.1.17 Y = 0 Plane Comparison of Phase of Crack electrical signature in 4 soil types at 4
observation points
19
Figure 2.1.18 Comparison of Magnitude of Ex Electrical Field for 4 soil types
20
Figure 2.1.19 Comparison of Magnitude of Crack Signature at three observations points for 3 soil
types
21
Figure 2.1.20 Magnitude of Electrical Signature in YZ plane at different Sand Humus
Concentrations
22
Figure 2.1.21 Magnitude of Electrical Signature in XZ plane at different Sand Humus
Concentrations
22
Figure 2.1.22 Magnitude of Electrical Field for sand of different humus concentrations and at 3
observation points
23
Figure 2.2.1 Experimental Configuration Setup
23
Figure 2.2.2 Main Bar
24
Figure 2.2.3 Antenna Pivot
25
Figure 2.2.4 Antenna Bracket
25
IX
Figure 2.2.5 Bracket Pivot
26
Figure 2.2.6 Clevis
26
Figure 2.2.7 Motor Pipe
26
Figure 2.2.8 Bracket Pivot
27
Figure 2.2.9 Platforms
27
Figure 2.2.10 Motor Assembly
28
Figure 2.2.11 Overall System Assembly
28
Figure 2.2.12 Antenna Actuating Motor
29
Figure 2.2.13 Linear Rails [44]
30
Figure 2.2.14 R256 [45]
30
Figure 2.2.15 PC - R256 connection
31
Figure 2.2.16 R256 Address Dial [44]
32
Figure 2.2.17 RS485 Circuit Board
32
Figure 2.2.18 Flowchart
33
Figure 2.2.19 Virtual Instrument
34
Figure 2.2.20 USB Port Control
35
Figure 2.2.21 VNA control & Error Monitor
35
Figure 2.2.22 Motor Setup Control
36
Figure 2.2.23 Cycle control
37
Figure 3.3.1 Electromagnetic Configuration
45
Figure 3.3.2 a) 10 cm Pipe w crack, b) Magnitude Scattered Electric Field Observed @ 60 cm
away from pipe
46
Figure 3.3.3 Gaussian Filter
47
Figure 3.3.4 a) Time Response, b) Late time Window
47
Figure 3.3.5 a) Magnitude of Scattered Electric Field Observed @ 60cm away from 10cm pipe, b)
Extracted Poles
48
Figure 3.3.6 Side View of Pipe w 4cm arced crack @ Bottom
48
Figure 3.3.7 a) Magnitude of Scattered field for 4cm crack on top and on bottom of 10cm pipe,
b) Extracted Poles
49
Figure 3.3.8 a) Magnitude of Scattered field for two cracks 4cm crack and 6cm on 10cm pipe, b)
Extracted Poles
49
Figure 3.3.9 Corrupted data a) 10cm Pipe w 6cm arced crack, b) 10cm Pipe w 4cm arced crack 50
Figure 3.3.10 Pipe Hidden Behind Plywood
51
Figure 3.3.11 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space and
behind Plywood, b) Extracted Poles for hidden pipe
51
Figure 3.3.12 Extracted Poles for Hidden Pipe w SNR =10dB
52
Figure 3.3.13 10cm Pipe Immersed in Sand
52
Figure 3.3.14 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space and
Immersed in Plywood, b) Extracted Poles for immersed pipe
52
Figure 3.3.15 10cm Pipe Buried in sand
53
Figure 3.3.16 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space and
buried in sand, b) Extracted Poles for buried pipe
x
53
Figure 3.3.17 Crack Detection Flowchart
54
Figure 3.3.18 a) Magnitude of Scattered Field for 50cm pipe w 6cm crack in Free space, b)
Extracted Poles for pipe
56
Figure 3.3.19 50cm Pipe corrupted with SNR =10dB
56
Figure 3.3.20 a) Magnitude of Scattered Field for 50cm pipe w 4cm crack on top and on bottom,
b) Extracted Poles for pipe
57
Figure 3.3.21 a) Magnitude of Scattered Field for 50cm pipe w 6cm crack in Free space and
hidden behind Plywood, b) Extracted Poles for hidden pipe
58
Figure 3.3.22 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space and
Immersed in Plywood, b) Extracted Poles for immersed pipe
58
Figure 3.3.23 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space and
buried in sand, b) Extracted Poles for buried pipe
59
Figure 3.3.24 3cm long and 4cm long pipes buried parallel to each other
60
Figure 3.3.25 a) Magnitude of Scattered Field 60cm away from sand interface for 4 cases buried
at 20cm, b) Extracted Poles
61
Figure 3.3.26 a) Magnitude of Scattered Field 60cm away from sand interface for 4 cases buried
at 20cm, b) Extracted Poles
61
Figure 3.4.1 Custom built Anechoic Chamber
62
Figure 3.4.2 HP8510C
62
Figure 3.4.3 Antennas on Same Side of Pipe
63
Figure 3.4.4 S2i Measured @ 30cm away from Pipe as in Figure 3.4.3
64
Figure 3.4.5 Scattered Field @ 30cm
65
Figure 3.4.6 Time domain for pipe @ 30cm
65
Figure 3.4.7 a) Scattered Field @ 30cm using PEC Sheet, b)Time Domain Response
66
Figure 3.4.8 a) Scattered Field, b) Time Response, c) Poles extracted
67
Figure 3.4.9 a) Total Field, b) Extracted Poles
67
Figure 3.4.10 Antenna Surrounding Pipe
68
Figure 3.4.11 Filtered Scattered Field @ 30cm: a) Span = 5, b) Span = 15
69
Figure 3.4.12 5pt Moving Filter - Total Back Scattered field 8cm away: a) 6cm Crack b) 4cm crack
72
Figure 3.4.13 Vivaldi Gain
73
Figure 3.4.14 Power Plots
74
Figure 3.4.15 Error Quantization @ 42cm
75
Figure 3.4.16 Error Quantization @ 8cm surrounding pipe
75
Figure 3.4.17 Comparison of SNR for 4 Setups
76
XI
List of Tables
Table 1.1.1 Example of Pipe Dimension Standards
2
Table 2.1.1 Soils Electrical Properties
9
Table 2.1.2 Humus Concentrations for Sand
21
Table 3.3.1 Summary of M vs Poles for several 10cm pipe cases
55
Table 3.4.1 Matlab Curve Filters
68
Table 3.4.2 Poles Extracted from Filtered Scattered Field @ 30cm away from pipe
69
Table 3.4.3 5 pt Moving Filter - Total Field Poles @ 42cm
70
Table 3.4.4 Poles Extracted From Filtered Total Field @ 30 cm away from Pipe
70
Table 3.4.5 5 pt Moving Filter-Total Field Poles @ 15cm
71
Table 3.4.6 5 pt Moving Filter-Total Field Poles @ 8cm
71
Table 3.4.7 5 pt Moving Filter - Total field for 50cm pipe @ 42cm away
71
Table 3.4.8 5 pt Moving Filter - Total field for 50cm pipe @ 30cm away
72
XII
Chapter 1:
1.1
Introduction
Pipe Leakage and Industry Needs
Pipes are used for transport of goods and other liquids or gases such as water, gas,
petroleum, sewage and many more. There are several locations through which pipelines can be
routed. Indoors, such as factories or houses, pipes can be routed behind walls made of wood or
cement. Outdoors, pipes typically run buried underground for thousands of miles covered by
layers of soil or concrete.
Thousands and thousands of miles of pipelines are put into use every year. Close to half
a million miles of gas pipelines are currently installed in North America alone and these numbers
are expected to increase at a yearly rate of two percent [1].
In general, as depicted in Figure 1.1.1, gas transporting pipe systems are made up of [2]:
The Natural Gas Production, Transmission and Distribution System
Oil and
Gas Well
Natural Gas
Company I
Gas Processing
Plant
.mM
M
,
mn
Consumers
m
-id
Gas Well
- Production-
-Transmission •
-Distribution
Figure 1.1.1 Gas Pipe System [2]
•
Flow lines: transport gas from wellhead to gathering lines
•
Gathering system/lines: transport gas from flow lines to transmission systems
•
Transmission systems: transport gas from gathering lines to distribution lines.
•
Distribution systems: transport gas from transmission lines to the customer meter.
Various pipe types are used in pipe line systems. Usually plastic composites are used for
low pressure transportation. Such composites include several reinforced fibers such as poly vinyl
chloride (PVC), poly ethylene and poly amides. On the other hand, steel pipes are used for high
pressure transmission that exceeds 5000 psi. Steel pipes can be seamless or electric resistance
weld. Concrete pipes are also commonly used for sewage transportation.
There exists different pipe size nomenclature in the industry [3] like the popular Iron Pipe
Size, IPS, sometimes called Nominal Pipe Size, NPS, and Copper Tubing Size, CTS. As their
names state, these standards compare any pipe of any material with industry tested and
tabulated dimensions. An example of such tables is shown in Table 1.1.1 below.
Table 1.1.1 Example of Pipe Dimension Standards
ASTM A53/A 53M - 02
Nominal
Size
Wall Thickness
Outside Dia.
Sch. No
Inch
Inch
mm
Inch
mm
1/2
0.840
21.3
0.109
2.77
40
0.147
3.73
80
Several installation methods are employed in the industry. Pipes can be laid in dug
trenches or inserted into drilled holes. Also grounding beds are commonly used as a shared
location for several pipelines.
The method by which the pipes should be installed is dominated by industry standards such as:
1.2
•
API: American Petroleum Institute.
•
ANSI: American National Standard Institute.
•
ASTM: American Society for Testing and Materials.
•
AGA: American Gas Association
Current Evaluation Techniques
All pipes whether made of coated steel or plastic composites will corrode and form some
kind of a defect in the form of a crack or small pit on the surface of the pipe. In power industries
any leakage due to these cracks might be hazardous to both man and nature. Also, such leaks
will eventually cause economical losses since the resources are wasted. Periodic inspection of
pipes is needed to satisfy regulatory requirements. The inspection characterizes the condition of
the pipes and directs strategic planning on whether and when to replace, repair or continue
operation of the pipe.
2
With the thousands of miles of pipes running underneath ground or hidden behind walls comes
the need for cost effective and fast detection techniques. These techniques will be used as
precautionary measures to constantly maintain the pipe lines. Since, frequent checks are needed
the idea of digging up pipes for check up can be very cumbersome. Some pipes lie meters below
the ground and may take several days to excavate. Thus, the industry turned to developing noninvasive techniques that need no digging.
Non destructive evaluation, NDE, techniques have received the attention of many
researchers. Such techniques rely on remote detection of cracks. Various people categorized
such methods differently. The authors of [4] differentiated between two groups. The first group
relies on biological means for crack detection. For example trained individuals used trained dogs
to smell or hear the hissing sound resulting from a leak. The second group of techniques is
hardware based. By the use of special hardware, the pipe and the environment are characterized
and a conclusion is drawn to whether a crack exists or
not.
When considering the hardware techniques
there can be further classifications. Techniques which
require direct contact or probing of the pipe are fairly
common. These techniques are still non-destructive
since the pipes can be accessed at exposed points.
The use of the material depends on the dimensions of
the pipe and the installation methods. If the pipe
dimensions are large enough, a robot based approach
can
be used to evaluate
the
Figure 1.2.1 Laser Controlled
Camera [5]
pipe conditions.
References [5-7] discuss the use of laser controlled camera placed inside a sewage pipe as
shown in Figure 1.2.1. This technique is also known as the Closed-Circuit television, CCTV. A
fuzzy logic neural network is then used to process the raw images collected from the camera.
Features of the pipe are extracted to characterize the condition of the pipe walls. It is a humanoriented approach based on offline analysis of the raw images. Evidently, size is a limitation for
3
the use of this technique.
Today the most common types of examination techniques in power environments are
ultrasonic and radiographic [8].The use of high-frequency ultrasonic waves, in pipes helps in
determining the material thickness and any existing flaws. Waves propagating along length of the
pipe provide an estimate of the crack size [9-10]. This technique can be used in free space or
when the pipe is partly inaccessible. Yet, ultrasonic detection has not been able to successfully
detect corrosion and fatigue cracking from the inside of a pipe.
Radiography was used as a weld examination technique and has been accepted as a for
crack detection since many years. This technique illuminates a pipe and records the exiting
backside radiation by either photographic or electronic means. The radiation may be produced by
an x-ray machine. One of the advantages of radiography is that it provides a permanent record of
each investigation that can be post processed for later review. However, it has many
disadvantages such as safety and speed. Human exposure to x-rays is lethal thus leaving the
system remotely accessible and hard to manipulate. Taken from Electric Power Research
Institute's website Figure 1.2.2a shows a setup for an x-ray tube installed on a set of rails facing
boiler pipes hidden behind walls. It is obvious from the figure how bulky the system and how
tedious setting up and utilizing such a system is. Figure 1.2.2b shows an example of an x-ray
image of a pipe hidden behind a wall. The cracks appear as thin lines.
Figure 1.2.2 a) X-Ray Tube on Tracks, b) X-Ray Image of Hidden Cylinders [8]
An example of probing techniques is found in references [11-14], where probes are
placed on a pipe in several locations. Then cylindrically guided waves excite the pipe at one axial
location. These waves propagate along the length of the pipe wall. If the waves encounter any
4
feature such as cracks or weld points they will partially reflect. The reflections flag that a change
in the pipe geometry has occurred.
1.3
Ground Penetrating Radars and Feature Extraction techniques
In modern days the most popular methods for subsurface detection and characterization are
known as geophysical tools. Such tools are trenchless and operate remotely. They use
electromagnetic waves to scan the surface and what lies beneath it in order to remotely
characterize the physical properties of the media and localize certain buried targets. Ground
penetrating radars, GPR systems, illuminate the ground surface with microwave frequencies. Part
of the wave will reflect from the surface of the ground and carry back information to the scanner.
The other part of the waves will traverse through the surface and interact with the subsurface.
Again the scattered waves will reflect back through the surface and carry more information to the
receiver. Such systems use cost effective antennas that usually operate in the bandwidth of 0.3300GHz. GPR systems have found many different applications, the most common of which is to
characterize the soil composition and texture. In this remote sensing application, scattered fields
are collected by satellites. Lots of information can be derived from the fields such as the humidity
of the soil, the type of the soil and the percentage composition. In order to accomplish this, the
electrical properties of the soil should be readily available.
Over the years, the relative dielectric constant e and the conductivity a of the different types
of soils with different humus concentrations was measured and tabulated. A valuable reference of
such tables can be found in [15], were the electrical properties are collected versus several
frequencies.
Another application where microwave scanners are used, which is of growing attention, is the
attempt of breast cancer detection [16]. The idea is dependent on the difference of texture
between healthy cells and tumor cells. Having the proper dielectric properties an image can be
reconstructed of the internal breast tissue in order to locate any potential infected cells.
A third application, which is the focus of this research, is the detection of cracks in buried
pipes using GPR systems. Many methods and research papers have been developed to improve
both the hardware and software of the radar system due to the versatility of such a tool.
5
The basic idea is to use a transmitter
Rx
to illuminate the entire medium containing the
buried pipe as shown in Figure 1.3.1. The
receiver antennas in turn collect the scattered
ill
Tx
Rx
:JBs\
field. Any physical change in the environment is
carried back by the reflected waves. The waves
Pipe
/ Anterm§\
/ Beam
\
Soil
\
travel at velocities that depend on the dielectric
Figure 1.3.1 GPR System Scanning
Pipe buried in Soil
constant of each medium they encounter.
Reflections are produced at each boundary and due to any change in the medium conditions. The
travel time of the transmitted waves and the reflected waves is a function of the depth of the
reflection point and the electric properties of the media. Proper processing of the propagating
energy can describe the underlying geometry and any variation in the media. For example, any
leak from the pipe will result in a change in the moisture content of the surrounding soil [17-28].
HAIM.faMJIIll.HJiHIHJjmjII
Figure 1.3.2 Buried steel pipe without leak (left), buried steel pipe with leak (right) [4]
The authors of [4] present the GPR profile for a pipe buried in a wooden sandbox as shown in
Figure 1.3.2. They conducted experiments show how a water leak alters the GPR profile; thus,
detecting a change in the medium.
In order to automate the crack detection method from GPR profiles, researchers use
neural networks and image processing techniques [29-32]. By extracting certain features from the
data a check can be done on the condition of the pipe and the medium. The authors of [33] use
back propagating neural networks to identify hyperbolic signatures that are a result of a pipe.
6
A feature extraction technique introduced in this work is the matrix pencil method [34]. By
solving for the Eigen values for the matrix of collected data, complex natural poles can be
extracted. This concept has been used by others for reading RFIDs [35]. The idea is that these
natural poles are unique to these cracks, whether the pipe is immersed in air or buried at several
feet below the surface. These cracks can be identified as separate poles the same way the RFID
is read. This is a new contribution of this work.
1.4
Field Simulators
In general, field simulators are divided into time domain solvers and frequency domain
solvers. Time domain solvers include methods such as Finite Difference Time Domain (FDTD)
which calculates the difference in the electric and magnetic fields at several time steps. The
frequency domain counterparts include Method of Moments (MOM) and Finite Element Methods
(FEM). Both methods start by dividing the domain into a mesh of electrically small geometrical
shapes where Maxwell's equations are solved. Usually the edge size of such shapes is one
tenths of the highest frequency of interest.
In the FEM solvers the geometrical shapes are three dimensional tetrahedrons. The final
solution is just a combination of all the different elements. This is due to the fact that in FEM the
entire domain is meshed.
In the MoM, surface triangles are used to divide the boundaries of the different structures in
the domain. The overall solution is then solved at each triangle relative to all other triangles
creating a large matrix to be computed. Yet, there are a lot of hybridizations of the MoM method
that can save lots of time and memory. However, the use of the Fast Multipole Method, FMM,
speeds up the MoM and reduces its memory requirements. In this approximation, the mesh is
further divided into boxes. Inside each box the individual elements are solved using the MoM.
Afterwards, the bigger boxes are solved using the multipole interactions.
At the beginning of this work, a commercial FEM solver, Ansoft's High Frequency Structure
Simulator, was used. Due to the nature of our problem, which is electrically large, the computer
resources prohibited the use of our resources. The machine used was an AMD Opteron
Processor 246, having two 2GHz processors with a total memory of 4GB. For example, a 1x1x0.4
7
meter sand box with a pipe buried inside was taking over a week to finish and the accuracy was
not convincing. With the many simulations that need to be run this was not an option. For this
reason, several three dimensional Method of Moments solvers were evaluated and the
commercial FEKO solver was used. FEKO is a hybrid tool that is based on the MoM method with
the option of using the Fast Multipole Method.
1.5
Conclusions
Geophysical techniques are generally more efficient than excavation. GPRs have the
advantage of being safer in hazardous environments. In Chapter 2 simulations were modeled for
an environment consisting of soil, an antenna and a buried pipe. The effects of soil types such as
silty, clay, loamy and sandy with humus concentrations up to 10% per weight on the electric fields
are investigated. A description of a physical system that was built in parallel to the problem
analysis is also described.
The focus of this work is to prove that a natural frequency technique can be applied in
detecting cracks in buried pipes. An algorithm in Chapter3 employs the natural frequency method
on scattered fields of pipes with cracks buried underneath sand and hidden behind walls. FEKO
simulations for pipes in free space, buried underneath sand and hidden behind plywood are
presented. In addition, measurements inside an anechoic chamber are documented.
Chapter 4 provides conclusions of this work. As well many suggestions for future work are
listed in order to provide the algorithm with improvements when operating under noise.
8
Chapter 2:
2.1
Simulations In Three Dimensions and Measurements Setup
FEKO Configurations
The purpose of the simulations is to prove conceptually that a pipe at a given burial depth will
have a detectable electrical signature. The configurations consisted of a Vivaldi antenna and a
pipe buried in a finite size sand box. The dimensions of the sand box were chosen in conjunction
with the dimensions of an existing glass tank found at the lab. The glass tank will be used as an
experimental setup as will be discussed later in this chapter. The pipe diameter and thickness are
chosen according to standard ASTMA53-ERW. Thus according to schedule 80, a galvanized
steel gas transporting pipe buried at around 29cm should be at least 5cm in diameter and 0.55cm
thick. The length of the pipe was the same as that of the depth of the sand box.
Four different types of soils are
Table 2.1.1 Soils Electrical Properties
are
Dry Soil
type
£r @ 5GHz
tabulated in Table 2.1.1. These soil types are
Loamy
2.44
0.0011
Silty
2.4
0.0041
references in the literature list their electrical
Sandy
2.54
0.0062
parameters at several frequencies [41]. ]. The
Clay
2.27
0.015
considered
most
in
abundant
the
in
simulations
nature
and
and
many
tan5(5
5GHz
soil types have been ordered in the table by
ascending order of their loss tangent. It will be shown that this parameter has the most influence
on the electrical signature of the crack. Also considered are three different humus concentrations
of sandy soil. The conductivity of the soil when it is humid is expected to increase and this will
further affect the signature. The electrical properties of any material are frequency dependent.
Thus using the values at the frequency of operation is crucial for an accurate solution. An
approximation was done here were the values of the properties at 5GHz instead of 5.6 GHz were
used, which is the frequency of the solution.
2.1.1
Vivaldi Antenna
The antenna used in this design is a Vivaldi antenna [40]. The dimensions of the
antenna are shown in Figure 2.1.1a. It is composed of two metallic patches each side of an Arlon
9
dielectric.
Arlon has a dielectric constant er = 2.5 and a loss tangent of tan5 = 0.0022. The Vivaldi
antenna is chosen due to linear polarization of the electric field along. The direction of the electric
field is parallel to the radiating edge
of the antenna as shown in Figure
2.1.1a. The antenna is designed for
an
input
impedance
of
50
Q.
Another important characteristic of
the antenna is the radiation pattern.
This
shows
the
direction
of
propagation of the radiated waves. It
also reveals a spatial It also reveals
a spatial representation of the power
distribution. In Figure 2.1.1b it is
Figure 2.1.1 (a) Vivaldi Antenna, (b) Radiation pattern
@ 5.6GHz
shown that the power concentration of the antenna's radiation is in the direction parallel to the
plane of the antenna. That is if the antenna is set along the z axis, the radiation direction is
normal to the XY- plane.
One of the most significant
characteristic of an antenna are
the
S-parameters
or
the
scattering matrix. If the antenna
is
considered
network,
the
as
a
1
port
parameter
Sn
relates the voltage incident on
the port to the voltage reflected
Figure 2.1.2 Vivaldi Measured S-parameters
back towards the source. In particular, the Sn is called the reflection coefficient. Typically, a
reflection coefficient below -10dB is desired in the required frequency range. In the lab, there are
10
two Vivaldi antennas. A HP8510C vector network analyzer is used to measure the S-,-,
parameters for both. The measured S-parameter plots are shown in Figure 2.1.2.
By investigating the radiation pattern for the Vivaldi antenna over its operating frequency, it
was shown that at 5.6GHz it was narrow and focused as shown in the three dimensional color
map of Figure 2.1.1b. This frequency was a good compromise between the higher frequencies
which had a better directivity but required a very fine mesh and the lower frequencies which had
worse directivity but with a coarser mesh. The polar plots of Figure 2.1.3 show the electric field
cuts and the magnetic fields cut. It is visible in Figure 2.1.3a that the beam is tilted to one
direction. This effect is also visible in the plots of the illuminated pipe in section 2.3.
Figure 2.1.3 (a) E-Plane Gain Plot, (b) H-Plane Gain plot
2.1.2
Effect of Dry Loamy Soil on Pipe with no Crack
The first configuration is for dry loamy sand and is shown in Figure 2.1.1. The picture was
created inside FEKO's CAD tool, CADFEKO. The configuration shows a Vivaldi antenna placed
A
at 20 cm above the surface of a sand box. The antenna is oriented such that the electric field Ex
is along the axis of the pipe. The pipe is highlighted in yellow, has no crack and is buried inside
the sand box. The burial depth considered is 30 cm which is a normal depth for such pipes. The
pipe is considered to be a perfect electric conductor. Inside the pipe free space medium is
11
considered. The sand box is also shown to have a height of 33cm, a width of 90 cm and a depth
50 cm.
The pipe has the same
Vivaldi
Operating
@ 5.6GHz
length of 50cm as the depth of the
box, has a wall 0.5cm thick and a
diameter of 5cm. The problem was
solved at a frequency of 5.6GHz
Dry Loamy Sand
Height = 20cm
and the finest mesh used was one
er=2.44
tan5= .0011
tenth of the wavelength in free
Burial depth
= 30 cm
space. Thus the triangle edge of
the
smallest
surface
I
Mesh size A/10
GO
CO
o
triangle
^£P„
element using equation (2.1) was:
90cm
X^Y
50cm
Figure 2.1.4 FEKO Configuration
h _ C
10"fx10
3x108
=
1 0 x 5 6 x 1 0
9
(21)
In order to understand how the waves are interacting with the different components of the
configuration several cut planes were used to display the fields from different angles. The color
map plot in Figure 2.1.5a shows a XZ-plane cut for the geometry that is taken at point y = 0; thus,
laterally bisecting the pipe. The magnitude of the total electric field is shown. The plot shows the
Vivaldi antenna radiating toward the box. The thick line marked interface signifies the end of free
space and the start of the sand medium. The pipe is marked in white dashed lines. The first thing
that needs is observed in this plot is how the radiation beam is directing the power towards the
pipe. There is a noticeable left shift of the radiation which was also noticed in the three
dimensional view in Figure 2.1.5b. It is also worth observing how the waves are further apart in
free space and come closer together inside the medium. This is due to the fact that the
wavelength inside a medium is dominated by formula (2.2). The formula simply states that there
is the wavelength is shortened by a factor of the relative permittivity of the medium. In case of
12
free space er = 1.
A=
(2.2)
fx-y/eT
The plot also shows how the waves get attenuated as they propagate through the
medium. The shades of green reveal this phenomenon. This attenuation is accounted for by the
loss factor of the soil. It is also visible how the PEC pipe walls reflect all the waves away and little
circulate around the pipe. The right plot, Figure 2.1.5 b is an YZ plane cut at x = 0. First, notice
that the radiation beam is much wider in this plane having more of an oval shape. Again, as the
wave crosses from one medium to the next, the wavelength is shortened and the shades of green
come closer together. The inside of the pipe is shown to have zero electric field as is expected.
One important thing to mention here is the excitation effect of the edges of both the pipe and the
sand box. In practice, pipes that are being investigated are usually longer than the width of the
[V/m]
Antenna
1QQ.Q
90.Q
60.1
70.1
60.1
Z
50.2
40.2
30.2
20.3
10.3
0.3
u
a)
Interface
Interface
X
u
^S^S^-jf'
XZ Plane
b)
0
Pipe
YZ Plane
Figure 2.1.5 Magnitude of Total Electric Field for Pipe in Loamy Sand: a) XZ Plane,
b) YZ Plane
beam. Thus no field is expected to penetrate into the pipe unless there is a crack. In order to
mimic this effect, the edges of the pipe are closed with a perfect electric conductor.
Consequently, all waves will reflect away from the edges. On the other hand, to minimize
the edge effect of the sand box, it is important that the antenna used has a narrow beam width.
The magnitude of the wave on the edges of the sand box in both plots is shown to be less
infinitesimal compared with the strength of the field in the middle. Specifically, the edges witness
13
a magnitude of 0.3, while the middle has a magnitude of 100 V/m as is shown in the legend of the
color maps.
Two plots of the total electric field residing on the pipes are shown in Figure 2.1.6. The
top view of the pipe shows how the electric
[V/m]
field illuminates the surface. It is clear from
the top view how the left side of the pipe has
View of Pipe Top
higher red shades than the other half of the
* ;
pipe. This is due to the effect of the tilt in the
radiation pattern. The bottom view simply
View of Pipe Bottom
I
shows weak shades of the electric field since
37.fi
33.9
3Q.2
2G.fi
22.9
19.2
15.fi
11.9
6.2
4.6
Q.9
Figure 2.1.6 Magnitude of Total Electric field on
Pipe in Loamy Sand
the surface is hidden from the direct antenna
radiation.
The phase of the total electric field is also plotted in the y=0 and x = 0 near field cut
planes in Figure 2.1.7a and Figure 2.1.7b respectively. The medium effect is more visible on the
wavelength in the plots. It is clearly seen how the distance between the propagating waves
contracts inside the loamy medium relative to the propagation in air. Note here that there seems
to be a phase change inside the pipe itself. This is theoretically not expected since no wave is
supposed to pass through a PEC wall. The inaccuracies should not appear if a mesh of smaller
ieo r
144
109 y
* -177r j ^ - - —
* j a !-v~:x:*-
a
o
.:;;=
)
XZ plane
b)
YZ plane
Figure 2.1.7 Phase of Total Electric Field for Pipe in Loamy Sand: a) XZ Plane, b) YZ Plane
14
^
size were used. However, due to memory limitations a finer mesh could not be achieved.
2.1.3
Effect of Dry Loamy Soil on a Pipe with Crack
The same configuration was repeated again but with a crack added to the pipe. The
crack, shown in Figure 2.1.8 is a cylinder 2cm in diameter that cuts the pipe from the top side and
passes through the entire wall thickness. Cracks in reality have been reported in different sizes
and shapes. They could be a hair like defects, pits on the
wall surface or noticeable holes. For the purpose of this
work a significant hole was used just to make sure that
the electrical signature of the crack would appear within
the frequency bandwidth of the Vivaldi antenna. Hair-like
cracks appear at very high frequencies (e.g. Ku band 1218 GHz); whereas, electrically large holes appear at
Figure 2.1.8 Crack Dimensions
lower frequencies (e.g. L band 1-2GHz).
The same solutions discussed for the previous configuration were requested for the
configuration of the pipe with a crack. The magnitude plots of the total electric field are shown in
Figure 2.1.9. The Y = 0 plane in Figure 2.1.9a shows the lateral cut of the pipe which is marked in
black dashed lines. The electric field has a higher magnitude at the crack location. This is due to
the definition of the total electric field that is the sum of the incident field from the wave minus the
scattered field from any object. The scattered field normally has an opposite sense of that of the
Antenna
Antenna
YZ Plane
a)
XZ Plane
Figure 2.1.9 Magnitude of Total Electric field on Pipe w crack in Loamy Sand
15
incident field. Since there is a hole in the pipe, the waves will propagate through the pipe and thus
less reflection will appear at the surface of the pipe at the crack location. This explains why there
is a higher total field signaled by darker red shades. Also, the inside of the pipe shows lighter blue
shades of the electric field which means that the electric field is truly propagating inside the pipe.
The X = 0 plot in Figure 2.1.9b also shows the crack effect as a red shade in the midst of a yellow
shade. There is also light green shade in the inside of the pipe near the top surface which verifies
the penetration of the electric field into the pipe.
For even a better view of the crack
38.1
34.3
effect Figure 2.1.10 shows a top view and a
View of Pipe Top
bottom view of the surface of the pipe. The
top view has a red shade sitting right at the
middle of the pipe were the crack resides.
View of Pipe Bottom
The phase plots of the total electric
23.1
19.3
15.6
11.6
6.1
4.3
Q.G
field for the pipe with a crack configuration
are shown in Figure 2.1.11. It is surely
30.G
26.6
Figure 2.1.10 Magnitude of Total Electric field
on Pipe w crack in Loamy Sand
expected in these plots to see a phase difference inside the pipe since waves will be propagating
through the hole.
Antenna
a
)
XZ plane
Figure 2.1.11 Phase of Total Electric Field for Pipe in Loamy Sand: a) XZ Plane, b)
YZ Plane
16
2.1.4
Crack Signature Comparison in Different Soils at Different Observation Points
It is of great interest to look at the crack electrical signature at different points away from
the pipe. The cross-sectional view in Figure 2.1.12 shows the location of three observation
points at 3 cm, 15 cm and 30 cm above the surface of the pipe. The interface line between the
sand interface and free space is shown as a dashed line at 25 cm above the pipe's surface. The
light brown shade is there to resemble the soil medium. The definition of the electrical signature
is the subtraction of the electric field for the configuration for a pipe with no crack and the
configuration of a pipe with a crack. The resulting field is the isolated effect of the crack itself.
The electric field of the Vivaldi is linearly polarized and oriented along the X-axis in all of the
configurations. Thus, the x-component of the electric field is used since the energy is
concentrated along that direction.
: Observation points
30cm
25cm
2.1.4.1 Magnitude of Crack Signature
There are three plots in Figure 2.1.13 that
Interface
15cm
compare the electrical signature for the four different
3cm
U
electrical parameters are considered for the dry
Pipe Center (45,0)
Radius 2.5 cm
mediums only. The plots are taken in the X = 0 cut
LoamyEx-Mag- Z = 3cm - YZ plane
- -Silty
>y v
r^
soil types at the three different locations. The soils'
Figure 2.1.12 X Plane Observation
Points
• Sandy
Clay
Ex-Mag- Z = 15cm - YZ plane
Ex-Mag- Z = 30cm - YZ plane
• y
''
1
1
i
I
i
i
'
1 f .••'••J.
fc-
.••-•-%
45
Y[cm]
'
50
Figure 2.1.13 X = 0 Plane Comparison of Magnitude of Crack electrical signature in 4 soil types
at 4 observation points
plane and a close up to the neighborhood of the pipe is taken. The grey shades in the plots
17
resemble the edges of the crack. The dashed lines in the plots resemble the edges of the pipe.
The red curves resemble the magnitude of the electrical signature of the crack buried under dry
loamy sand. The magenta is the magnitude of the dry silt, the blue plot is for the dry sandy and
the green is for dry clay. The plots show that at 3 cm the magnitude of the crack signature is
significant. It also shows that the magnitude of the signature is lower for the soil types with
higher loss tangent because of the attenuation of the signal. This is clear at the 3 cm observation
point. At points further away from the pipe, parts of the blue plot, the dry sandy soil, behave
inaccurately and rise above the silty sand which has a lower loss tangent. The red plot, the dry
loamy soil, also falls below the silty sand plot even though it has a lower loss tangent. These
inaccuracies are related to the fact that the mesh is not fine enough.
Another view to look at is the lateral cut in the Y = 0 near field plane. The diagram in
z Observation points
Figure 2.1.14 shows the Y = 0 cut of a buried pipe
30cm
25cm
with a crack relative to the observation points.
The crack is located at point x = 22 cm and a close
15cm
up to the neighborhood of the crack up is shown in
3cm
Interface
n
the plots of Figure 2.1.15. The magnitudes of the x
Crack @ x =22 Pipe Radius 1 cm
component of the electrical signatures of the crack in
Figure 2.1.14 Y Plane Observation
points for Pipe w crack
the four dry soil types are plotted for the Y = 0 plane
for each plot in Figure 2.1.15. The grey shades there show the edges of the crack which is 2 cm
Loamy
Ex-Mag- Z = 3cm - XZ plane
Silty
• Sandy
Ex-Mag- Z = 15cm - XZ plane
Clay
Ex-Mag- Z = 30cm - XZ plane
»-•'
20
25
30 Ss
20
25
30 15
25
X[cm)
X[cm]
X[cm]
Figure 2.1.15 Y = 0 Plane Comparison of Magnitude of Crack electrical signature in
4 soil types at 4 observation points
20
30
in diameter. The results in these plots agree to a high extent with the results in Figure 2.1.13. The
18
soils with higher loss tangent have the lowest electrical crack signatures. The soils with lower loss
tangent have the highest crack signature. The plots tend to violate the rule here at the points
further away from the crack. This is because the attenuation renders the crack electrical
signatures so close in value to each other. A finer mesh is needed to precisely calculate their
proper values.
2.1.4.2 Phase of Crack Signature
The phase of the x-component of the crack's electrical signature is plotted in Figure
2.1.16. There are three plots showing the phase at the three observation points in the Y = 0 plane
for the four different dry soils. The grey shades resemble the edge of the crack and the dotted
lines resemble the pipe sides.
Loamy
Silty
Ex-Phase- Z = 3cm - YZ plane
6000-
•Sandy
Clay
Ex-Phase- Z = 15cm - YZ plane
:*-*
2500
2000'
2000
w 4000
1500-
1500
12000.
0i
sWVS:-:
s
1000
1000
J& \\ *Sk>
500
V\V-*
/ / '
0
20
40
60
80
100
500
°1
-500
-500
-2000,
'0
Ex-Phase- Z = 30cm - YZ plane
20
40
60
80
40
60
Y[cm]
Yjcm]
Y[cm]
Figure 2.1.16 X = 0 Plane Comparison of Phase of Crack electrical signature in 4 soil types at 4
observation points
The phase plots are also shown in Figure 2.1.17 for the X = 0 plane. It is important to
note here that not much information was extracted from the phase plots. Their inclusion was done
for the sake of completeness only.
Loamy — • -Silty
Ex-Phase- Z = 3cm - XZ plane
• Sandy
Ex-Phase- Z = 15cm - XZ plane
Clay
Ex-Phase- Z = 30cm - XZ plane
800
600
400
.....••' r*^;^"\
V)
0)
f \ ••»
£ 200
$
3
o
-200
i
-4001
10
20
X[cm]
30
40
Figure 2.1.17 Y = 0 Plane Comparison of Phase of Crack electrical signature in 4 soil types
at 4 observation points
19
2.1.4.3 Crack Signature Relative to Soil Loss Tangent
It is of most importance to evaluate the effect of the crack on the total electric field and to
confirm that the changes are due to the existence of the crack. For this purpose Figure 2.1.18
shows the X = 0 plots of the magnitude of the x-component of the total electric field for the four
soil types. The plots compare the electric fields' magnitude of the configuration of a pipe with no
crack with that of a pipe with a crack at an observation point of 3cm. It is clear that at the location
of the crack, between Y = 42 cm and Y = 44 cm, the magnitude of the total electric field
increases. This is justified by the statement that less reflection results due to the crack. Thus, the
subtraction of the total field is less.
Pipew Crack
Dry Loamy
80
Pipe w/o Crack
z = 3cm - yz plane
Dry Sandy Z = 3cm - yz plane
60
•
40
20 l u 1 If
1 1
f
I f \ mm
MB
IH
•J •
HB
n
T)
50
Y[cm]
Dry Silt Z = 3cm - yz plane
VI
100
80 r
"0
50
Y[cm]
Dry Clay Z = 3cm - yz plane
100
60
50
Y[cm]
100
100
Figure 2.1.18 Comparison of Magnitude of Ex Electrical Field for 4 soil types
Another important element of comparison is to explore the effect of the soil electrical
parameters on the electrical signature. The plots in Figure 2.1.19 compare the electrical signature
of three types of soils at the three observation points. The soils shown here are chosen according
20
to that of lowest loss tangent, which is loamy soil with tan5 = 0.0011, with clay that has highest
loss tangent of tan5 = 0.015. Also sandy soil that has the highest relative dielectric constant of Er
= 2.54 is compared with clay that has the lowest dielectric constant of er = 2.27. What is clear
from the three plots is that the electrical signature of a crack buried in clay has the least
magnitude. This is noticed at all the observation points and is mainly due to the high loss tangent.
3cm
Ex-Mag -Dry loamy- yz plane
— — — 15cm
30cm
Ex-Mag -Dry Sandy- yz plane
40
Ex-Mag -Dry loamy- yz plane
30.
tan5=.0011>
er =2.54
£r = 2.27
tan5=.015.
45
Y[cm]
Figure 2.1.19 Comparison of Magnitude of Crack Signature at three observations
points for 3 soil types
2.1.4.4 Crack Signature in Humid Sand
What has been shown so far is that the signature of the crack gets attenuated more with
as the loss factor increases. In a real life situation the soil has
Table 2.1.2 Humus
Concentrations for Sand
certain water content. This water content could significantly
tr @
5GHz
tanS (
5GHz
change the electrical characteristics of the soil. Therefore, it is
of high importance to consider cases were the soil is not dry.
Loamy
2.44
0.0011
For this reason, sandy soil type is considered since it is one of
Silty
2.4
0.0041
the common soil types one would find in a field. Two different
Sandy
2.54
0.0062
humus concentrations of sand are listed in Table 2.1.2 which
—
2
27
0.015
are 5% and at 10% per weight. Notice that the relative
permittivity of the soil is also affected by the water content.
Plots in Figure 2.1.20 and Figure 2.1.21 compare the effect of the humidity on the crack
signature. The three plots in Figure 2.1.20 for the X = 0 plane compare the signature for dry sand,
5% and 10 % per weight humid sand at the three observation points. At 3 cm it can be seen that
21
in the 10% humid sand the crack signature is detectable. As well, moving to an observation point
of 30cm the pipe shows high attenuation and but is still detectable above the interface.
5%
Dry
—
10%
Ex-Mag- Z = 15cm - yz plane
Ex-Mag- Z • 3cm - yz plane
Ex-Mag- Z = 30cm - yz plane
To
45
50 $0
45
50
45
Y[cm]
Y[cm]
Y[cm]
Figure 2.1.20 Magnitude of Electrical Signature in YZ plane at different Sand
Humus Concentrations
50
The Y = 0 plane cuts in Figure 2.1.21 for the same simulations agree with the results of
the previous figure. Since this is a lateral cut of the pipe, there are only grey shades showing the
edge of the cracks. The attenuation of the signal highly affects the accuracy by which the used
mesh can calculate precise values of the fields. This is obvious in the signals' comparison plots
signals at the observation point of 30 cm.
Dry
Ex-Mag- Z = 3cm - XZ plane
10%
• 5%
Ex-Mag- Z = 15cm - XZ plane
Ex-Mag- Z = 30cm - XZ plane
| 20'
20
25
X[cm)
20
25
X[cm]
20
25
X|cm]
Figure 2.1.21 Magnitude of Electrical Signature in XZ plane at different Sand
Humus Concentrations
To properly summarize the results a bar graph in Figure 2.1.22 shows a comparison of all
the soil types. The bars in red show the maximum magnitude of the crack signature at an
observation point of 3cm. The magnitude of the field on top of the center of the crack at
coordinate x = 23 and y = 43 cm is considered. There is a big difference between the types of the
soils which is due to the difference in their loss tangent. The results describe exactly the real life
expectations and set a good reference for any experimental setup that needs to be done.
22
Figure 2.1.22 Magnitude of Electrical Field for sand of different humus concentrations
and at 3 observation points
2.2
Measurement Setup
The experiment setup is composed of
Glass Tank
a scanning system mounted on top of a
glass tank as shown in Figure 2.2.1
below. The glass tank
has a glass
thickness of % of an inch. Two linear rails
shall be mounted along the length of the
tank. Each rail will be responsible of
moving an antenna in the longitudinal
direction. The antennas will be mounted
on the middle of the bar hanging along the
Figure 2.2.1 Experimental Configuration Setup
width of the tank. The image shows two identical bars. One bar holds the transmitter and another
holds the receiver. A pipe will be placed at the center of the tank along the width. The rails will
23
move the receiver from its initial position to its final destination in linear increments, gathering
scattered parameters along the way. Each antenna will have a motor actuating it in angular
increments. The scanning process is detailed in the section about the software. The
specifications about the motors and the rails are detailed in the chapter about the hardware.
The purpose of this experiment is to collect data from a buried pipe at multiple view points
above the ground surface. The results shall be compared to the results from the simulations.
2.2.1
System Assembly
In order to properly mount the rails on the tank and provide the necessary parts for the
mechanism of the scanning system lots of machining was required. A machine shop course that
lasted 8 weeks was attended in order to learn the necessary skills. The machine shop included
learning
how to
operate
a
— 3.96" —
milling
2.46" 2.2IT •
machine, a lathe and a press drill. The
tolerances of the machines were down
*
to one thousandth of an inch.
a
C
a2
t
M
«
i
Different types of plastic were
si—r
used in manufacturing each part. Half
extends from one rail to the other. As
-.
I
machine the bar, Figure 2.2.2, which
Eft
h
c
e
can be noticed eight holes on one edge
T
B
I
s as
3
55
n
i
c
II
1
of the bar indicate the side where the
-11.88*
inch thick Polypropylene was used to
)C-
«t
0.25" 1.75"
bar sits on two carriages. The slot in the
-2.45"
- 3.70"
-3.95"
-4.20"
middle of the bar is where the antenna
and its support will fit.
1
1
S.33" —
5.58"
7.20"
The axis in Figure 2.2.3 below
7.95*
-9.20
is used to pivot the antenna in the
Figure 2.2.2 Main Bar
angular direction.
24
t
i
<i3
y
"I
a
I
0.50"
0.88"
3.13" —
4.00" — -
r-41—L-l-
Figure 2.2.3 above using one
-
face.
The
bottom
of
the
bracket has two screw holes
to
which
the
antenna
is
screwed.
CNJ
i
pair of holes on the bracket's
- r-
i /
i
i
r-q
oi
oi
i
i
1.50" - -!
!
i
i
l_
-1—
1.50" -
2.2.4 is screwed to the axis in
0.25'
The bracket in Figure
<_>
The clevis in Figure
2.2.5 is strapped to the two
|— 2.50"
i
Figure 2.2.3 Antenna Pivot
arms of the axis in Figure
2.2.6. The axis is screwed to the other pair of holes on the face of the bracket in Figure 2.2.4. It is
essential that the pivot axis is screwed to the pair of holes that are 2.75 inches from the edge of
the rotary bracket. The clevis has a "#2-56" hole on its bottom face to provide a screw hole for the
shaft of the antennas' motors.
The motor is fitted
into the pipe in the Figure
2.2.7 below. The holes on
the sides of the pipe, third
view to the right, are used
for two rotary pins. The pins
are inserted into the pipe
from
one
side
and
go
through the faces of the
brackets
-ru
The
in Figure 2.2.8.
u i *
brackets
u
have
*•
two
Figure 2.2.4 Antenna Bracket
a
screw holes on their bottom to mount them on the main bar of Figure 2.2.1.
25
The glass tank sides are
0.38" r-J
]
0.13"
@::p:
0.50"
0.25"
purpose 6 platforms, as shown in
0.38"
TT"^!--^
of the aluminum rails. For this
0.50"
i
too thin and fragile to support any
p! ,?
? U
r>-!o.25"| ||
fi—\ 0.75'j ! |
Figure 2.2.8, are used to fix the
rails on the sides of the glass
tank. As can be seen in the
1 75
# i o - 3 2 _ _ / \~
I
|—
figure, the rails will be firmly
screwed into the platform. This
- ":
|!
2.25" --j !
2.50" — |
Figure 2.2.5 Bracket Pivot
resists any motion that might occur whenever scanning is in process.
2.50"
2.25"
1
2.50"
s
CM
1.25"
M 0.25"
r
U
IT)
CM
d
t
eg
d
in
o
ID
CM
#2-56UNC-2A THREAD.
Figure 2.2.6 Clevis
0.70"
0.146"
0.35"
press fit for 0.125 pin
(=0.120mils,#31 drill)
0.13"
CO
d
d
CO
1.10"
d
1.38"
IT)
T
O
1.75"
2.00"
Figure 2.2.7 Motor Pipe
26
0.38"
i;:^
i
i
L
b
in
oo
.J
P?
d °
£
co
T-
d
c
£
o
,
i 0.25" i
K. •1' 0.75'iJ
i
l•
#10-32__.
/
S
^
d 2°
•
1.75
•>
i
i
2.25"
--i
2.50"
— !
Figure 2.2.8 Bracket Pivot
#6-32
POLYPROPYLENE.
o
o
c\i
o
o
4.00"
0.25"
M
Figure 2.2.9 Platforms
To clearly depict how the different machined parts are connected photographed pictures
of the real system are included. The antenna actuating mechanism, Figure 2.2.10, shows how the
motor is fitted inside the motor pipe. The pipe pivots about two pins that pass through the pipe
sides and into the motor brackets. The brackets are screwed on the bars that extend across from
one rail to the other. The clevis is connected to the motor from one side and to the clevis' axis
from the other side. The clevis axis is screwed onto the rotary bracket. The rotary bracket pivots
about the pivot axis. The antenna is screwed to the bottom face of the rotary axis.
27
The overall system is depicted in Figure 2.2.11. It is clear how each bar is fixed on two
carriages, one passive and one active, from one side and one passive carriage on the opposite
side. The reason for this was to distribute the load of the bar-motor weight on two different
carriages. This minimized the lagging effect that would result when pushing the bar from one end
only.
Figure 2.2.10 Motor Assembly
Figure 2.2.11 Overall System Assembly
2.2.2
The Hardware
The hardware system constitutes of four stepper motors, two 24 inch rails and four motor
28
drivers. Several companies were contacted for price quotes. These included:
http://www.baldormotion.com. This company dealt with high power motors and the
system they offered cost 6000$.
http://www.autotrol.com
http://www.applied-motion.com
http://www.portescap.com
http://www.linengineering.com/LinE
http://www.haydonkerk.com
Comparison between the above was based on manufacturing lead time, size and price. The
motors were purchased from Haydonkerk and the drivers were purchased from linengineering.
2.2.2.1 Antenna Actuating Motors
The actuating motors for each of the two
antennas were HaydonKerk's Z26343-05 bipolar noncaptive linear actuator. These are shown in Figure 2.2.12
below which was taken from the datasheet of the motor.
They cost 71.3$ each. The motors were rated at
*%
340mA/phase at 5V. The rotational step angle is 7.5°.
The motors had a 3 inch screw that would extend or
Figure 2.2.12 Antenna Actuating
Motor
retract according to the rotational direction of the motor. The linear travel/step of the motor is
0.0005 inches. This meant for each 7.5° the screw will extend from the motor or retract into the
motor by 0.0005 inches.
2.2.2.2 Linear Rails
The two linear rails used were also a HaydonKerk's product, part number RGS06KRM43-0100-17-A01 and cost $594 each. It is worth noting that this part number referred to a new
product that was being sold by the company at the time when the purchase was made. This part
included both a linear rail and a size 17 captive hybrid linear motor. Specifically, the motors are
43F4 series. The linear rails were RGS6010 that had a pitch of 0.1 inches. A picture of the rails
29
taken from the ".pdf document is shown in Figure 2.2.13. The size 17 motors were rated at
700mA for 5V with a step
size of 1.8°. Each rail
came
with
three
carriages with only one
active carriage installed
between
two
passive
ones. The maximum load
that can be supported on
the rail and not affect the
Fi
9ure 2-213
Linear Rails
I44!
performance of the motor is 16Kg.
2.2.2.3 Motor Drivers
The bipolar motor drivers are Linengineering's
R256 shown in Figure 2.2.14. The common name in the
industry is the pulse and direction drivers. Four drivers
were purchased at 200$ each. The peak current rating for
the drivers is 2A at 40V. The rule of thumb in the industry
is to operate the drivers at eight times the voltage rating
Figure 2.2.14 R256 [45]
of the motor. Since both motors will be operated at 5V,
the driver's voltage calculates to 40V. The drivers have a micro stepping resolution of 256 micro
steps. This means, for example, to move the z26000 motors 7.5°, 256 pulses need to be
generated from the driver. This provides a combined resolution of 7.5/256 = 0.03o. For this
project, the resolution of 2x, meaning two pulses for each 7.5°, was used. The 2x micro stepping
was enough to provide seamless motion which is crucial when moving the antenna to avoid any
vibration that might cause inaccuracies.
The drivers are rated at 2A peak, where as the motors are rated in A/phase. The drivers'
supply current needs to be set according to the motor it is driving. If more current is being
supplied from the driver, the motor will burn. To change from A/phase to peak current, the
30
A/phase value should be multiplied by a factor of 1.4. This means for the z26000 the current in
the R256 should be set to 1.4*300mA = 420mA. So the drivers for those motors need to be set at
20% of the 2A. The rail motors need to be set at 1.4*700mA = 980mA. So the driver needs to be
set at 40% of the 2A peak current. This current is called the run current of the motor, or the
current that the motor is allowed to draw from the driver while in motion. Sometimes a hold
current is required to keep the motor from moving under the effect of any weights imposed on the
motor shaft. This hold current is by default 10% of the run current. More information can be found
in the datasheet of the R256 part on the company website.
The velocity or the pulses per second, pps, and the acceleration of the driver need to be
set as well. The acceleration value is actually the time required to reach top speed. This is done
by multiplying the acceleration number by a factor of 6103.5. This only means that for a velocity
of 1000 and an acceleration of 100, the driver will require 1000/(100*6103.5) = 0.0016 seconds to
reach top velocity.At a resolution of 2x a velocity of 1000 pps and an acceleration of 100 were
adequate.
The drivers communicate with their external via an RS485 port. In order to control
multiple drivers, the RS485 control lines are paralleled. Since most computers come with a built in
USB serial port, a USB to RS485 converter was used. A diagram of the connections is shown in
Figure 2.2.15.
1 st Unit
2nd Unit
nth Unit
Power
Supply
,
USB
Converter
Card
R.q4Rfi+
RS4A5-
Figure 2.2.15 PC - R256 connection
31
Since multiple RS256 units are connected in parallel, the
address of each should be set to allow independent control.
This is done by screwing a dial on top of the unit itself as
shown Figure 2.2.16. A maximum of 16 units can be
connected in parallel. In order to connect the four drivers in
parallel, a small circuit board was soldered as shown in the
Figure 2.2.16 R256 Address
Dial [44]
following Figure 2.2.17.
Figure 2.2.17 RS485 Circuit Board
The following are examples of the commands used to set the current, velocity and
acceleration of any driver. For a complete list of the commands please check the command
manual:
/1m20hOR: sets unit whose address is 1 to 20% run current and 0% hold current. R is
carriage return
/CV1000L100R: uses the multiple unit command, C, to set units 3 and 4 to a velocity of
1000 and an acceleration of 100.
32
One of the issues faced when programming the R256 was moving in the negative direction.
The R256 has an internal counter that keeps track of any step taken in the positive direction.
Thus once the motors settle in their initial position, the z home command should be sent to the
units to set the current position as the home or point zero. No negative movement is allowed
behind the home. This means that if the motor takes 100 steps in the positive direction, it is
allowed no more than 100 steps in the backward direction. Since the rails are installed on the
tank with their motors on the same side, this means that one antenna needs to move toward the
motor of the rail, and one needs to move away. The positive direction is by default the sense
away from the motor. The negative is towards the motor. To overcome this, the direction of the
unit which is attached to the rail with the negative sense was reversed using the 1F1R command.
This means that whenever a positive command is given to that rail, the motion is towards the
motor of the rail.
2.2.3
The Scanning System Labview Software
The general operation of the software can be explained through the flowchart in Figure
Figure 2.2.18 Flowchart
33
2.2.18.0nce the motors are set in their initial position, a sequence of data acquisitions and motor
stepping persist till the entire area beneath the system is scanned. The receiver starts by entering
a loop of acquiring data from the VNA and then moving one step forward. Once the total number
of steps has been travelled, the receiver backs to its initial position ending one receiver cycle. At
this stage, the transmitter moves one step forward and the receiver repeats another cycle. This
will end once the transmitter has moved to its final position, completing a full scanning process.
Labview 7.1 from National Instruments, www.ni.com, was the programming platform
used. The developed application, referred to as a Virtual Instrument in Nl's terminology, is
basically composed of buttons and text boxes that define the various elements required for the
proper operation of the scanning process.
The control panel of the VI is composed of four groups of controls as shown in Figure 2.2.19.
OB*
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to«c««y«inctort*>*i»t
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Figure 2.2.19 Virtual Instrument
2.2.3.1 Main Interface
Moving into details, the bottom left control, Figure 2.2.20, is the control for opening and
closing the proper serial port for the Motor USB-RS485 driver. The Resource Name list box is
used to specify the appropriate COM port that is assigned to the USB-RS485 converter.
34
Whenever plugged into a USB port, the converter is detected at COM3, but this doesn't always
have to be the case. An easy way to recognize which COM port is assigned to the driver is to
simply check what the newly added COM port is when the
Resource Name
cable is plugged in. The baud rate is set to 9600 bits and
hcova
Baud Rate (9600)
the rest of the serial port properties are left as default.
r-9600
2.2.3.2 USB Control
Open
£
The middle Open switch in Figure 2.2.20 is to
ensure that the connection session to the COM port is
Note: Default parameters are used for the
serial port setup. This includes 8 data bits,
1 stop bit, no parity, and no flow control.
dose
opened. This should be ON before the program is run.
OFF
Otherwise, the connection to the USB-RS485 will not be
established. The bottom close switch is used at the end of
J
IF the VISA Session is not closed
when communications are finished,
non VISA communications with the
port may not be possible.
Figure 2.2.20 USB Port Control
the scanning process. This should be switched ON once done with all the measurements to
ensure that the connection is closed properly and to free the port for other applications.
VISA resource n a m e
2.2.3.3 Network Analyzer Controller
%|GPIB::16
The bottom right group, shown in
JZI
i
Error I n p u t (no error)
Error Opening VISA
status
status
code
m 3-F
Figure 2.2.21, represents the controls for the
bytes to read
S {200000
code
H "W
Vector Network Analyzer. The "VISA resource
name" drop down list represents the name or
Write error code out
Read error code out
VISA WRITE ERROR
VISA READ ERROR
j.
___
the address of the port to which the VNA is
connected. The bytes to read represent the
status
number of bytes to be read from the network
source
code
jr
status
1
code
SI "F
source
analyzer. There are also four error output
8510C Data
boxes which report any error that may exist
6.226074000000000E+00, 9.071289000000000E+00
6.62u36100u000u0rjE+00, -3.S53223000000000E+00
-1.0967290000rjOuOOE+01, -S.8«4766ut)uTJ00u0uE+0u
-8.9794920OO0OUU0OE-KIO, -l.SW8iaJOuuOOOuuE+01
-7.26S62500u00rjrj00E-ul, -1.419727000000000E+01
before the connection to the port is being
opened.
Such
errors
may
result
A
T
—
^
from
Figure 2.2.21 VNA control & Error
Monitor
establishing a connection, errors writing to the
port and errors reading from the port. These are provided for debugging purposes only. The last
frame in this control group gives a sample of the information being retrieved from the VNA.
35
2.2.3.4 Driver Controller
The top control group, shown in Figure 2.2.22 below, contains four buttons and eleven
text boxes for setting the basic parameters of the motors. The textboxes are grouped into four
columns under each button they are related to.The first button, Set Current, takes the desired
motor address, the Run Current and the required Hold current. This provides either single unit
control, using the numerical address, or multiple units, control using alphabetical commands. The
second column with the Set Velocity button takes the address of the motor and sets the velocity
of the motor and the acceleration. The third column is for setting the micro stepping. Here the
user is confined to selecting one of the entries of the drop down menu. The last column is for
setting the origin of the motors.
O
Tojpedryamotor(s)Typa:
Tternotorrurr»wtospee»Yas»ioJemotor(l,2,3,4)
A to specify motors 1& 2
CtospBrfymotors3&.4
,
O
O
To spadry a motor's) Type;
T!iemd«numbsrtaspedfyailndemotor(lJ213,4)
Atospetjryaacorsl&Z
Ctospefjfymotors3&4
,
C3>
Tosp8dryamotor(s)Type:
TrBm(tanuiitatospBofyasfiotemotor(l,2,3,4)
AtospBofymotorsl &2
c to spedfy motors 3 M
I
-
__^_, l T
I?i?^a'™i~w5'pBj
. .
™»motor nintatospeoTy a suiote motor (1,2,3,4)
Atospecffy motors 1 & 2
CtospBofymotors3».4
(shodd be between 1400 -1650)
Figure 2.2.22 Motor Setup Control
2.2.3.5 Cycle Controller
Although the order by which the parameters above need to be set is not crucial it is
recommended that the user starts by setting them from left to right as they are laid on the panel.
The last group is the motion control shown in Figure 2.2.23. This is used for moving each motor
to its initial position independently as well as starting the scanning cycle.
In order to select which motor to move the address of the motor should be specified in
the text box reserved for the antennas, which is the top most text box in the list. This will be later
used to specify the address of the motors controlling the antennas once the cycle starts. At this
stage, the motors are just being moved to initial position. For initialization, the receiver needs to
be moved towards the motor, negative sense, till it reaches the start of the track. The transmitter
needs to be moved away from the motor, positive sense, to the end of the track. There are three
buttons provided for moving any motor. The LEFT button moves the motor indefinitely in the
36
negative direction. The right button moves the motor indefinitely in the positive direction and the
TERMINATE button brings the motor to a stop. The "command sent" text box, is just an indicator
of what command is currently being sent through the serial port to the motor drivers.
LEFT
1 OFF 1
RIGHT
S OFF!
TERMINATE
WrbedatatoMe
i~OFn
o
Command Sent
mtfeecondstowait
OUTER MOST LOOP
ti|3
0
AntennaActuatelterator
0
'
Ral Transmitter Iterator
0
To specify a motor(s) for receiver Type:
The motor number to specify a single motor (1,2,3,4)
A to specify motors 1 & 2
C to specify motors 3 & 4
Antenna Angular PosWons
^0
RaJ Receiver Iterator
o
To specify motor (s) for antennas Type:
The motor number to speafy a single motor (1,2,3,4)
A to specify motors 1 & 2
Ctospecify motors 3 & 4
To specify a motor(s) for transmitter Type:
The motor number to specify a single motor (1,2,3,4)
A to specfy motors 1 & 2
Ctospecify motors 3 & 4
Ral Receiver
lis"
Rail Transmitter
::;o
Figure 2.2.23 Cycle control
Once initialized, the user must specify the number of step increments for the different
motors. This is done in the second column in the bottom left of the group. The white text boxes
are used to specify the number of angular positions required and the number of receiver and
transmitter positions. The scanning cycle will depend on those values to know how many times to
iterate. The grey text boxes to the left of those are just status indicators. They declare the current
loop iteration the system is in.
The "milliseconds to wait" text box is used to set the time that is required to wait for each
motor to move to its next location before the measurements are acquired from the VNA. This
value should be set dynamically and is relative to the speed of the motor. Thus, the delay should
be set according to the slowest running motor, to ensure all motors settle in their new location
before taking any measurements.
The outer most loop indicator is just an indicator that runs indefinitely. If the indicator is
counting this means the program is running but the scanning process hasn't been started yet.
37
Once the process starts, this indicator will pause for the entire duration of the process. Once the
process is finished the indicator will resume counting again.
When the user is ready to start the data acquisition cycle, the motor addresses should be
assigned. This is done in the textboxes in the right column of the group. After setting the
addresses for the actuators, the receiver and the transmitter in their respective textboxes, the
user can press the "Write Data to File" button to start the scanning cycle.
Once finished the program will generate a comma separated file that contains the real
and imaginary parts of the s-parameters gathered at the different positions. The file can then be
post processed to derive different parameters like the magnitude, the phase plus others.
2.2.3.6 Labview Algorithm Structure
Moving into the programming details of the software, the application consists of four
nested loops. The outer most loop provides continuous execution of the program. Software that
implement parallel processing, like Labview, will run all commands on the same level at the same
time and only once. So to keep the program from exiting, a loop containing the rest of the
program was used. This loop is an endless while loop with an iteration indicator named OUTER
MOST LOOP. Before Labview enters into this loop it acquires the COM PORT of the USB-RS485
converter card and the VNA GPIB port number. This information is set by the user in the
respective text boxes before the program is even run. Once the play button is pressed, the user
will be prompted for the name and location of the file to which all the gathered S-parameters from
the VNA would be written. It is only after the proper VISA connections are established with the
different ports, does Labview enter inside the outer most loop. VISA is a built in VI that can
manage the port connections masking most of the low level details from the programmer.
Three nested FOR loops are used to control the automated motion of the scanning cycle.
The outer most loop defines how many positions the transmitter needs to move. The middle FOR
loop controls the number of iterations of the receiver. The inner most loop controls the angular
positions of the antenna actuation. The latter loop performs N+4 iterations, were N is the
antenna's angular positions. After the antenna moves through all the angular positions, an extra
iteration is run to back the antenna to its home. A second iteration follows to move the receiver
38
one step forward. However, in case the receiver was at its last position the receiver does not
move in this iteration. Instead a third iteration is responsible to back the receiver to its home
position. The last extra iteration forwards the transmitter to a new position. This goes on until the
entire scanning cycle finishes. At the end the transmitter will remain it its final position to signal
the completion of the process.
2.3
Conclusion
Using the FEKO MoM solver a pipe buried at 30 cm inside a glass tank was simulated.
The model was illuminated with a Vivaldi antenna having the electric field parallel to the axis of
the pipe. The simulations were done for a pipe with a 5cm crack at its center. The crack signature
was shown to be visible above the sand interface for four different soil types with humus
concentrations up to 10% weight.
The mechanical system has been designed to mount PCB antennas, basically a Vivaldi
and a Bowtie. If other types of antennas were to be used, a complementary part can be machined
to overcome any compatibility issues. Also, the rails could be mounted on higher platforms if the
distance between the antenna and the target is below the far field region of the antenna.
39
Chapter 3:
3.1
Natural Frequencies in Buried Pipes
Pole Extracting Methods
Extracting the naturally occurring frequencies of exponentially decaying signal models, ESM,
has received a great deal of attention in the literature. Several methods have been developed for
such ESM signals. The singular value decomposition, SVD, technique has been put in use since
the 1980's [46]. One technique that uses the SVD concept is the linear prediction method that
employs eigen solutions [47-48]. The authors in those papers used a total least square
approximation to a correlation matrix. Another algorithm used is the Estimation of Signal
Parameters via Rotational Invariance Technique, ESPRIT [49-50]. The algorithm uses auto and
cross covariance matrices to determine signal parameters with high resolution. However, the
algorithm models non decaying sinusoid signals. Other methods include Prony, Pisarenko and
Pencil of function methods [51-54]. Prony's method, for example, can be very sensitive to noise
and requires an a priori selection of the model order. A survey of some available techniques can
be found in [55-56].
The main focus of this research is using what is known as the Matrix Pencil Method, MPM
[57-58]. The method has proven its low sensitivity to noise and computational efficiency [59]. In
[60] the parameters of an exponential decaying or growing sinusoidal model (ESM) are extracted
using the MPM. The method uses only a snapshot of the data to estimate the poles, or the
frequencies, and residues of a signal. At Syracuse University, work was done to apply the MPM
to ESM signals for the purpose of directional finding [61 -62].
It is well established in the literature that starting from a point in time where the incident field
has crossed a structure, the time domain can be modeled as a sum of complex exponentials as
stated by the singularity expansion method, SEM [63]. The extracted poles are independent of
the angle at which the structure is illuminated or the view. However, depending on the angle of
excitation or observation, the residues of the poles might differ.
In order to perform target identification, naturally occurring frequencies or poles of the
structure are desired. The transient response contains information of damping factors and
40
resonant frequencies that are only determined by the target's structure and material [64]. The
object needs to be excited with a wide band of frequencies in order to be properly identified. The
wavelengths must contain components proportional to the dimensions of the object [65]. Due to
the lack of a priori knowledge of the object a broadband waveform is required. Once the object is
hit by the waves, they reflect back any incident energy. Once the time domain responses have
been collected, an object can be distinguished by its resonant frequencies. Baum in [66]
expresses the scattered field in terms of an expansion of complex resonances. It is further shown
in [67] that there is a minimal set of poles with dominant residues that can reconstruct, to a
certain precision, the physical properties of the original signal. It should be stressed here that in
early time intervals that include the excitation signal, SEM representation will encounter
difficulties for extracting the structure's resonances. This is due to the fact that the targeted
structure might not be entirely illuminated by the signal. Also, evidently early time responses are
strongly dependent on the source, the location of the source, and the location of the observation
point. This difficulty is a limitation for the Matrix pencil method since the location of the object
needs to be known a priori.
3.2
Matrix Pencil Method
The Matrix Pencil method has been used in different disciplines as an identification
technique. For example, in [46] the author uses the MPM for speech processing and recognition.
In [68-72] the MPM is used for identification of different scattering objects. Particularly [73]
discusses using MPM for detecting unexploded buried ordinances. Of interest to this research is
the discussion in [74]. The authors there discuss free oscillations of a thin dipole buried in a
dispersive lossy half space.
The time domain transient response of a scattering object can be represented as a sum of
exponentially damped signals as in equation (3.1) by the SEM
M
x(kT s ) = S Rizf
fork = 0,1,
N-1
(3.1)
i=i
where x(t) is a vector of size N containing the discrete time points, R = Aje"J<Pi are the residues
41
composed
Z; = e s '
s
of the
= e^ a ' + J W ''
amplitudes
s
Aj's
and
the
phase
delays
d>j's. The
system
poles
are composed of damping factors a, and radial frequencies ov M is the
number of poles to be extracted.
Two approaches to formulate the Matrix pencil method will be discussed in the following two
sections. The first approach or the normal MPM extracts the poles from the data using one single
step. The extracted poles are not ordered in any manner. The second approach, known as the
Total Least Square MPM, TLSMPM, uses the SVD concept on the data vector. The poles are
then extracted from the resulting eigen vectors. The significance of this method is that the poles
are automatically ordered according to their respective singular values. As well, the latter method
has shown good performance under noise.
3.2.1
Normal Matrix Pencil Method
The problem at hand is to solve for the number of poles to be extracted, the value of M,
the poles zfy and their R, residuesRi. To start the formulation, consider the data vector X = {x^ x2,
x3,...,xN} containing the time domain transient discrete points. Define two matrices:
X,=
l
*1
x2
x2
X3
N-L
A
N-L+1
^L+1
^N-1 (N-L)xL
(3.2)
*L+1
(
X, =
l
N-L
A
L+2
N-L+2
(N-L)xL
The matrices can then be written in terms of their poles as
IX1J=[Z1IR]IZ01Z2J
(3.3)
IX2J=[ZJR][Z2J
(3.4)
where
42
1
1
Zl
Z2
..N-L-1
1
z
1
Z1
1
Z,
Z
..N-L-1
2
z
(3.5)
,N-L-1
Z
M
(N-L)xM
'
,L-1
(3.6)
,L-1
-M MxL
z.,
0
•••
0
0
z9
•••
0
0
0
-
Zn =
M
*"1
1 ZM
R =
1
zM
R,
0
0
0
R2
0
0
0
R
(3.7)
MxM
(3.8)
M MxM
and L is known as the pencil parameter. As well consider the maxtrix pencil:
[X1J-A[X2J= |zjR]{|ZoJ-A[l]}|z2J
(3.9)
If L satisfies the condition M < L < N - M the matrix [X., J- A[X2 J has a rank of M. Also, if A = z, for
i = {1,2
M} the rank is reduced to M-1. Thus, the Zj's can be found by solving the general eigen
value solution of the matrix pair {[XiJ.py}. The equation to be solved the following:
zl = [x|Ix 2 ]
(3.10)
where + denotes the moore-penrose pseudo inverse X+ = [XHX]"1XH and H denotes the conjugate
transpose. Once the poles are calculated the residues can be found by solving the least square
problem of
X1
X2
«R2
.N-1
_N-1
*M
43
,N-1|
-M
(3.11)
3.2.2
Total Least Square Matrix Pencil Method
In the presence of noise the data are perturbed and the eigen values are corrupted. The
method discussed in this section has shown better performance under real life noisy backgrounds
[67].The first step in this approach is to build the Hankel matrix as in equation (3.12)
XH =
| X N-L
X
N-L+1
'"
X
•"
x
L+1
L+2
'"
(3.12)
(N-L)x(L+1)
The singular value decomposition is performed on the matrix as in equation (3.13) in order to
obtain the eigenvectors and eigen values.
UIV H = SVD(XH)
(3.13)
The matrices U and V are the left and right unitary matrices respectively. Matrix U is composed of
the eigen-vectors of X H X H ; whereas, V is composed of the eigen-vectors ofX[l|X H . The diagonal
matrix X contains the singular values of X H as equation 3.14 shows
1=
a,
0
0
a2
•
0
0
0
0
(3.14)
; o
0
0
•••
aN.L0
(N-L)xL
The next step is to truncate the first M eigenvectors of either U or V. Considering U, as an
example, equation 3.15 shows the truncated matrix.
A
A
A
U = [ U 1 , U 2 . ••.U M ] T
(315)
The rest of this method is identical the normal MPM method. Thus, the poles are simply the
general eigen values of equation (3.16)
where
U,
zi^kkL,
< 3 - i6 >
=[UI.U2."-.UM-I]T
(3.17)
A
U2
A
A
=[U2.U3,--.UM]T
44
(3.18)
As stated earlier the resulting poles are ordered with respect to the singular value matrix
in equation 3.14. Thus, a., is the maximum entry and CTN_I, is the minimal entry of matrix 2- This
also means that z., corresponds to a-, and so on.
There are rules of thumb in the literature to what the best values of the pencil parameter
L and the numbers of poles M are [75-81]. It is recommended that the pencil parameter L have
values between N/3 < L < 3N/2 where N is the number of data points. As for M the ceiling value
depends on equation (3.19)
-^-«10"p
(3.19)
^max
where a , ^
is the maximum singularity value found in matrix 1, ocac is another singular value
entry down the matrix and p is the number of significant figures of the collected data. The
equation states that the singular value that is p orders lower than the maximum singular value is
the last pole that needs to be considered. The rest of the poles having lower singular values are
considered as noise. On the other hand, for PEC structures a minimal value of M is sufficient to
reconstruct the signal within a high accuracy [69].
3.3
FEKO Simulations
In order to retrieve the scattered fields of the different objects, the Method of Moments
solver FEKO was used. The configurations were solved in the frequency domain and a wide
frequency range from 50MHz up to 10.05GHz was collected. The frequency step used was
25MHz; thus, a total of
401 frequency points were
acquired.
depiction
A
general
of
the
Plane wave
Excitation
0.5cm thick
wall
o
10cm
Sand
Ex
"1
Observation @ 60
cm above ground
7.5 cm
2.5cm
electromagnetic
configuration is shown in
Figure 3.3.1.
/©->:
Figure 3.3.1 Electromagnetic Configuration
For a proof of concept a pipe that is 10cm in length and 2.5cm in diameter is
considered. The pipe is hollow with a wall thickness of 0.5cm. A plane wave excitation is used to
45
illuminate the entire domain. The electric field is parallel to the axis of the pipe in the x-direction.
The pipe is buried at 7.5 cm below the sand interface.
3.3.1
Free Space Simulations
3.3.1.1 Reference Pipe
As a start a pipe with the mentioned dimensions is simulated in free space. The same
simulation is then repeated for the same pipe but having at its center a 6cm arced length crack
that is half a millimeter wide Figure 3.3.2a. The scattered field is acquired at 60 cm away from the
surface of the pipe and is shown in Figure 3.3.2b. The red solid curve is the magnitude of the
scattered field of a pipe without a crack. It shows that the resonance of the pipe appears at
around 1GHz. The blue dashed curve shows the resonance of the pipe at 1GHz and also shows
two resonances associated with the crack itself the first at 3 GHz and the second at 9.1GHz. The
scattered field is then multiplied by a Gaussian filter in order to limit the bandwidth and smooth
the response at high frequencies. The frequency profile of the filter is shown in Figure 3.3.3.
2.5cm
0.12
LL
Electrii
t
10cm
*Ex
a)
1\
ield [V/m]
i
'
6cm arc;ed crack
5mnn wide
Pipe w/o crack
Pipe w 6dm arced crack
0.1
0.08
0.06
0.04
0.02
6cni crack
resonance
0
4
6
Frequency [GHz]
10
Figure 3.3.2 a) 10 cm Pipe w crack, b) Magnitude Scattered Electric Field Observed @ 60 cm
away from pipe
Once filtered, the scattered is Fourier transformed into the time domain. The symmetry
option for the inverse transform in Matlab was used to generate real valued data. This required
appending the conjugate of the frequency response to the original 401 points before transforming
them. Consequently, a total of 801 points were used to generate the time domain response. The
46
time step is then calculated by 3.20 as
1
T=
s
—
(3.20)
2*801*FC
where Ta is the time step and Fs is the frequency step and is
equal to 25 MHz. The normalized time response is shown in
Figure 3.3.4 a. It can be seen that at time t = 0.6m /
(3*108m/s) = 2ns the peak of the curve occurs. This is the
4 6 8 10 12
FreqGHz
Figure 3.3.3 Gaussian Filter
time required for the signal to traverse from the pipe to the observation point. A late time window
of 150 points is then extracted from the data starting at 2.5ns. The late time window, Figure 3.3.4
b, is essential to extract the poles since it is required that the entire structure is illuminated. As
well, the late time window is clear from any source excitation effects.
0.1
0.08
0.06
0.04
0.02
0
2ns
-0.02
-0.04
a)
0.5
1
1.5
-0.06
Time l O ^ s
4
5
Time10- 9 s
6
7
Figure 3.3.4 a) Time Response, b) Late time Window
The MPM, is then performed on the late time window to extract the poles and the
residues. The pencil parameter is fixed at 150/3 = 50. Only poles that appear in pairs and are in
the top left quadrant are real poles and are considered. Moreover, poles with the most dominant
residues are considered as the poles representing the original signal. The 1GHz resonant poles
that represent the pipe structure with no cracks are extracted at a value M = 6 as shown in Figure
3.3.5 b. It is this pole pair that will be used as a reference when later evaluating the condition of
other pipes. The dominant poles extracted for the pipe with a 6cm arced crack are shown in
Figure 3.3.5 b. At a value of M = 8 the reference pole of the pipe was extracted and two additional
poles were also extracted at 3 GHz and 9.1GHz. When a value of M = 6 was used to extract the
47
poles, a single dominant pole pair of 3GHz appeared. This led to incrementing M till the reference
1GHz poles appeared at M = 8. Since two extra poles appeared along with the reference, these
poles are associated with the crack.
1
Pipe w/o crack
' Pipe w 6cm arced crack
• Pipe w/o crack (reference) M = 6
" Pipe w 6cm arced crack M = 8
,x10
0.12
D 9GHz
N
0.5
3GHzQ
I
>.
+1GHzD 1GHz
O
§
+
0
CT
CD
D
D
-0.5
6cm arced crack
resonance poles
10
Frequency [GHz]
b)
D
-1
-1.5
-0.5
Damping Factor - a
x10
Figure 3.3.5 a) Magnitude of Scattered Electric Field Observed @ 60cm away from 10cm
pipe, b) Extracted Poles
3.3.1.2 Pipe with 4cm Arced Crack
The second simulation case considered was for a pipe with a 4 cm arced crack. A first
case is simulated for a 4cm arced crack sitting at the top of the pipe. The second case has the
4cm crack at the bottom of the crack as shown in Figure 3.3.6. A
comparison of the magnitude of the scattered field for three different
cases is shown in the plot of Figure 3.3.7a. The red solid curve is for
r
Ex
crack
the scattered field of the reference pipe with no cracks. The blue
long-dashed curve represents the field for the case of a 4cm crack at
the top of the pipe. The green short-dashed curve shows the
Figure 3.3.6 Side View
of Pipe w 4cm arced
crack @ Bottom
scattered field for the case of a 4cm crack at the bottom of the pipe. It is clear from the longdashed curve that the resonance of the 4cm crack is at 6.5GHz. The short-dashed curve on the
other hand shows only a slight perturbation at 6.5 GHz. Applying the MPM, the reference poles at
1 GHz are extracted for both cases and are shown in blue squares and green circles Figure
3.3.7b. In addition, a 6.5GHz dominant pole appears for both cases thus showing that a crack
exists. This case shows the strength of the method since by simply observing the scattered field
of the 4cm bottom crack it is not evident that a resonance exists. However, the MPM successfully
48
shows that a significant pole other than the reference is found. Thus, confirming the detection of
the crack.
• Pipe w/o crack
• Pipe w 4cm arced crack @ Top
Pipe w 4cm arced crack @ Bottom
+ Pipe w/o crack (reference) M = 6
B Pipe w 4cm arced crack @ Top M = 6
O Pipe w 4cm arced crack @ Bottom M = 8
X101'
6.5GHz
6.5GHz i
1GHz+
1GHZ
+
D
Q1GHZ
DO
b)
-2
-1.5
4
6
8
Damping Factor - a
x10
Frequency [GHz]
Figure 3.3.7 a) Magnitude of Scattered field for 4cm crack on top and on bottom of
10cm oioe, b) Extracted Poles
3.3.1.3 Pipe with both 4cm and 6cm Arced Cracks
A case with both 4cm and 6cm arced cracks set in the pipe is discussed next. The
magnitude of the scattered field is plotted in blue line in Figure 3.3.8a. The plots show that the
individual resonances of each pipe are still visible and distinguishable. The extracted poles are
plotted in Figure 3.3.8b. The dominant poles confirm the existence of a crack. Yet, not enough
information can be deduced about the number of cracks in the pipe, assuming that the pipe
shape is unknown.
•Pipe w/o crack
'Pipe w 4cm & 6cm arced cracks
• Pipe w/o crack (reference) M = 6
D Pipe w 4cm & 6cm arced cracks M = 10
,X1010
9.1GHz
S in g I e 4cm a reed
crack
D
° 6.5GHz
0.5r
3GHzD
+
oi
1GHz D 1GHz
+
D
-0.5>
b)
0
1 2
Single 6cm arced crack
3 4 5 6 7 8 9 10 11
Freq GHz
is
-2
-1.5
-1
-0.5
Damping Factor - a
x
0
^Q9
Figure 3.3.8 a) Magnitude of Scattered field for two cracks 4cm crack and 6cm on 10cm
pipe, b) Extracted Poles
49
3.3.1.4 Corrupted Data of Pipes in Free Space
The data from the simulated cases mentioned above were corrupted with a random noise
having a SNR = 10dB. The poles plot in Figure 3.3.9a shows the extracted poles for the cases of
a pipe with and without a 6cm arced crack. The reference 1 GHz was successfully detectable for
both noisy cases. As for the poles associated with the 6cm crack, only the low frequency pole
was detected. This was still enough to deduce that a crack does exist in the pipe. Another case
corrupted with noise is shown in Figure 3.3.9 b. The cases included are for the reference pipe, for
the pipe with a 4 cm arced crack at the top and a 4cm arced crack at the bottom. The reference 1
GHz poles were detected in addition to the 6.5GHz poles associated with the crack. The 4cm
crack pole for the case where the crack was on top appears to be shifted up to 7.6GHz. This is
due to the noise effect and does not negate the ability to detect the crack since it was extracted
as a significant pole.
+ Pipe w/o crack (reference)
Q Pipe w 4cm arced crack @ Top
O Pipe w 4cm arced crack @ Bottom
+ Pipe w/o crack (reference)
Q Pipe w 6cm arced crack
1
;
X
SNR=10dB
10'°
X 10
10
SNR=10dB
7.6GHz H
N °-5>
X
>>
o
1GHz
•
•
Q)
a
1GHz
•
K1
|
a
*
1 G H Z
0
-0.5
9
,
6.5GHz
,GHZB
•
0
• 4 - 3 - 2 - 1
Damping Factor -a
x 10
B
-0.5-
J*
a)
-2
-1.5
-1
Dampiiig Factor-a
0.5
1 °0
a
"--0.5:
-1
-2.5
•o
3GHz
"^
0
1
^
Figure 3.3.9 Corrupted data a) 10cm Pipe w 6cm arced crack, b) 10cm Pipe w 4cm arced
crack
3.3.1.5 Hidden Pipe
Another situation considered was to hide the pipe under behind a 10 cm thick plywood
wall. The wall is infinite in the XY plane. Plywood has a dielectric constant of er = 1.9 and a loss
tangent tan5 = 0.027. The pipe is spaced at 5cm away from the wall on the opposite side of the
excitation as shown in Figure 3.3.10. The observation point is 60cm from the plywood interface.
50
The scattered field in Figure
3.3.11a shows four different
Ex
FREE SPACE
Observation
point: 60 cm
cases. The scattered fields for
the pipe without and with a
-»y
6cm arced crack are plotted in
a solid red line and dashed
PLYWOOD:
E = 1.9 tan6= 0.027
10cm
blue lines respectively. The
case for
the
hidden
pipe
i Pipe wall
(Q) Separation 5 cm
FREE SPACE
without a crack is shown in
Figure 3.3.10 Pipe Hidden Behind Plywood
light green short-dashed lines and the hidden pipe with a crack is plotted in dotted purple points.
It can be seen from the scattered fields that the resonances appear at the same frequencies as
those cases in free space. However, due to the conductivity of the wall attenuation occurs. The
hidden pole plots in Figure 3.3.11 b shows that the reference poles for the pipe itself were
extracted at 1GHz as expected. As well, the poles associated with the crack appear at 3GHz and
9.1GHz. This states that even if the pipe is running behind the walls of a building, for example,
cracks can still be detected successfully.
The scattered fields for the cases of the hidden pipe were corrupted with random white
• Pipe w/o crack
• Pipe w 6cm arced crack
Hidden pipe w/o crack
Hidden pipe w 6cm arced crack
<£> Pipe w/o crack (reference) M =
O Pipe w 6cm arced crack M = 8
x 10 10
i.1GHz
3GHz
1GHz
&
"JGHs
£
-0.5
0
-2
-1.5
-1
4
6
8
9
Damping Factor-a
x
10
Frequency [GHz]
Figure 3.3.11 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space
and behind Plywood, b) Extracted Poles for hidden pipe
noise. The pole plots of Figure 3.3.12 show that the 1GHz resonant pole was extracted. Also, an
additional 3GHz pole was extracted for the case with a crack. This shows that the crack can still
51
be detected in the presence of noise.
Q Pipe w/o crack (reference) M = 6
O Pipe w 6cm arced crack M = 8
3.3.1.6 Pipe Immersed in Plywood
,x10
An alteration of the above case is to
0.5!
immerse the pipe in the plywood wall. The pipe
3GHz
1GHz 0 ^ ( 0
is now buried at 7.5 cm below the surface of the
plywood interface as shown in Figure 3.3.13.
-0.5
The plots for the magnitude of the scattered
fields
are
shown
in
Figure
3.3.13a.
The
•-i
-3.5
reference cases in free space are plotted in a
-3
-2.5
-2
-1.5
-1
Damping Factor - a
-0.5
0
x10
Figure 3.3.12 Extracted Poles for Hidden
PipewSNR=10dB
solid red line and dashed blue lines for the case
of a pipe without and with a 6cm arced crack
FREE SPACE
Observation point @ 60
cm away from pipe
respectively. The scattered fields for the
z
A
immersed pipe cases are plotted in Figure
<>
3.3.13a in green for a pipe with no crack and in
PLYWOOD:
er= 1.9 tan9= 0.027
dotted purple for the case with a 6cm crack. It
Pipe burial depth
^
7 5cm
is seen from the latter two curves that due to
FREE SPACE
the medium contrast between the pipe in
Figure 3.3.13 10cm Pipe Immersed in Sand
•
' Pipe w/o crack
Pipe w 6cm arced crack
= = Immersed pipe w 6cm arced crack
—~~ Immersed pipe w 6cm arced crack
x 1010
0.12
:.7GHz
D
N
0.5
3s
U
c
a)
0
2.2GH1
a 0.7GHz
a
o
o-0.5
b)
-4
-3
-2
-1
0
4
6
8
Damping Factor -a
x 109
Frequency [GHz]
Figure 3.3.14 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space and
Immersed in Plywood, b) Extracted Poles for immersed pipe
2
52
plywood and air a shift occurs in the crests and troughs of the curves. This shift is also reflected
in the pole plot of Figure 3.3.13b. The resonant pole for the pipe was extracted at 0.7GHz and the
crack resonances showed up at 2.2GHz and 6.7GHz as poles of significant residues. Thus, a
pipe totally immersed in plywood can still be evaluated for cracks using the MPM.
3.3.1.7 Pipe Buried in Sand
Ex
I
The case of most interest
was
to
bury
the
pipe
7.5cm
FREE SPACE
Observation point: 60
cm away from surface
underneath a half space of sand as
shown in Figure 3.3.15. The sand
->y
has a relative permittivity of er =2.54
and a loss tangent of tan5 = 0.005.
The
plots
represent
in
the
Figure
case
Half space of Sand:
E =2.54 tan5= 0.005
Pipe burial depth 7.5cm
3.3.16a
were
the
Figure 3.3.15 10cm Pipe Buried in sand
scattered field was observed at
60cm away from the sand interface. The magnitude plots for the scattered fields are shown in
Figure 3.3.16a. As always, the red solid line and the blue dashed lines are for the reference pipes
in free space. The green short-dashed lines and the purple dots represent the buried pipes
Pipe w/o crack
Pipe w 6cm arced crack
Buried pipe w/o crack
Buried pipe w 6cm arced crack
+ Buried Pipe w/o crack M = 6
O Buried Pipe w 6cm arced crack M = 12
x 10 1 0
1
5.6GHz
a
1.8GHz
0.7GHz
0.7GHz •
a
O
b)
-2.5 -2 -1.5 -1
Damping Factor-a
4
6
8
Frequency GHz
-0.5
0
Figure 3.3.16 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space
and buried in sand, b) Extracted Poles for buried pipe
53
without a crack and with a 6cm arced crack respectively. The shift in the resonant frequencies
appears here again due to the contrast between the permittivity of free space and of sand. The
resonance attributed with the pipe structure appears at 0.7GHz for both cases. The buried pipe
with a crack has two extra poles appearing at 1.8GHz and 5.6GHz as shown in Figure 3.3.16b.
The MPM method was applied to data corrupted with white noise for both cases where
the pipe was buried in sand and immersed in plywood. However, at SNR = 10dB the resonances
were not extracted. This requires further improvements to the matrix pencil method in order to
perform better under noisy environments.
3.3.1.8 Crack Detection Algorithm
To illustrate the algorithm used in detecting the cracks the following flow chart in Figure 3.3.17
highlights the basic steps. A pipe of known diameter is simulated in FEKO in free space. The
scattered field is collected at far distances from the pipe; 60cm was used in this work. A Gaussian
filter is applied to limit the bandwidth. The filtered field is then Fourier transformed into the time
domain. The matrix pencil method is performed on a late time window of the overall time
Simulated scattered
field from pipe of
known diameter in free
Extract dominant pole and proper Pole
parameter "M"
Acquire scattered field of pipe with cracks
Apply Gaussian filter to Far
Field to limit bandwidth
Start with "M" of free space pipe and
increment till pole of free space crack free
pipe appears
Fourier transform into
Time domain
T
No
Apply MP method on
late time pipe
response
New
dominant
poles exist?
No crack
Yes
Crack
exists
Figure 3.3.17 Crack Detection Flowchart
response. The first value of M for which the resonance of the pipe appears with a significant
residue is saved. This value will be used as a reference starting point to evaluate pipes of
54
unknown condition. Then the same steps are performed on the data acquired from a pipe with a
crack starting from the reference value of M. A condition is set then as to whether the most
significant pole is the reference pipe pole or a different resonance. If it were different than a crack
is detected. Note that the value of M is incremented from 6 till the reference resonance of the pipe
appears. This serves as a confirmation that the pipe exists underground.
To summarize how the value of M served in detecting the cracks Table 3.3.1 shows a list
of values for several simulations. The table shows, for example, that for a pipe with no crack the
pipe resonance was detected at M = 6. Applying M = 6 for a pipe with a crack, the 3GHz
resonance appeared. Thus, M was incremented till the reference pole of 1GHz appeared at M =
8. Along with the reference pole two extra poles appeared at 3GHz and 9.1GHz showing that a
crack exists. This was the same for all of the cases.
Table 3.3.1 Summary of M vs Poles for several 10cm pipe cases
Poles
1 GHz
Pipe w/o Crack
(reference)
Pipew 6cm
crack
3 GHz
6.5 GHz
9.1GHz
M=6
|
Pipe w/o Crack
+ lOdB noise
M=8
M=6
Pipe w 6cm
crack+lOdB
noise
M=6
Pipe w 4cm
crack
M=6
Buried Pipe w/o
crack
M=6
Buried Pipe w 6
cm crack
M=7
M=6
M=8
M=8
M=6
M=6
M=7
M=7
3.3.1.9 A 50cm Long Pipe
A pipe with longer dimensions was used to further test the algorithm. The pipe used was
50cm long having a diameter of 2.5cm and a wall thickness of 0.5cm. The same configurations
used for the 10cm long pipe were also conducted on the new pipe.
55
3.3.1.9.1
Pipe in Free Space with a 6cm Arced Crack
The plots in Figure 3.3.18a show the magnitude of the scattered field observed at 60cm
away in free space from a 50cm pipe with no crack and a pipe with a 6cm arced crack on top and
a 6cm crack on bottom. The crack is 0.5mm thick. Having a larger dimension relative to the 10cm
pipe, the first resonance of the pipe appeared at 260MHz which is lower than the 1GHz 10cm
long pipe resonance. The pole of the 6cm crack appeared at 3GHz for both the cases on top and
at bottom, which was the exact place of the crack pole in the 10cm pipe. This is due to the fact
—
+ Pipe w/o crack (reference) M = 4
D Pipe w 6cm arced crack @ Top M = 8
O Pipe w 6cm arced crack @ Bottom M = 8
— Pipe w/o crack
— -
Pipe w 6cm arced crack @ Top
Pipe w 6cm arced crack @ Bottom
0.35
„
ox109
0.3
10.25
1
-.
3i—-—0~
2.9GHz
2.9GHz
I 1
02
0.23GHz
:s
0.26GHz
a)
a-
So.15
0.23GHz
-3> 0.1
0.05
0
A-- V -
lal
2
3
Freq GHz
^'
-2
"?4
bl
-3
-2
-1
Damping Factor - a
x10
Figure 3.3.18 a) Magnitude of Scattered Field for 50cm pipe w 6cm crack in Free space, b)
Extracted Poles for pipe
that the resonances depend solely on the geometry of the structure. The poles plot in Figure
3.3.18b shows that the reference resonances were
detected as well as an extra pole associated with
+ Pipe w/o crack (reference) M = 4
Q Pipe w 4cm & 6cm arced cracks M = 8
„x10 9
D 3.24GHz
the crack.
The data for the pipe was corrupted with a
+0.28GHz
SNR = 10dB. The pole plot in Figure 3.3.19 shows
4
0.22GHz
a
that the reference resonances of the pipe were
detected. Also, for the case of a pipe with a crack,
the 3GHz pole existed with a significant residue. It
was noticed that due to the noise, the resonances
-8
-6
-4
-2
Damping Factor - a
0
8
x irj
Figure 3.3.19 50cm Pipe corrupted with
SNR=10dB
56
shifted their position.
3.3.1.9.2
Pipe with a 4cm Arced Crack
The case for the 4cm crack was also repeated for the 50cm pipe. The magnitude of three
scattered fields is shown in Figure 3.3.20a. The curves are entirely overlapping except near the
resonance of the 4cm crack at 6.5GHz. The solid blue curve represents the case for which the
4cm crack was on top of the pipe. The case where the crack is on the bottom is shown in dashed
green lines. The algorithm was only able to detect the crack on top of the pipe as shown in Figure
3.3.20b. This is different to what was observed in Figure 3.3.7. The reason for the difference can
be associated with the standing waves that reflect off the edges of the pipe. For the case where
the pipe is 10cm long, the standing waves appear to magnify the effect of the crack. However, for
the 50cm long the reflections of the edges attenuate significantly before back propagating
towards the crack. Therefore, the crack effect does not get magnified in that case. This situation
can be faced in real life if a long part of pipe with no corners or bends is being illuminated.
Corners, bends and connection edges help reflect waves and magnify effects. The solution for
the problem could be by illuminating the pipe with more power.
+ Pipe w/o crack (reference) M = 6
O Pipe w 4cm arced crack @ Top M = 6
O Pipe w 4cm arced crack @ Bottom M = 8
• Pipe w/o crack
• Pipe w 4cm arced crack @ Top
Pipe w 4cm arced crack @ Bottom
x10
6.53GHz
0.5
N
I
0.26GHz
0.26GHz
I
-0.5
0
1
2
3
4 5 6 7
Freq GHz
8
9
10
:V
M.
-9
-8
-7
-6
Damping Factor - a
x
-5
^Q8
Figure 3.3.20 a) Magnitude of Scattered Field for 50cm pipe w 4cm crack on top
and on bottom, b) Extracted Poles for pipe
3.3.1.9.3
Pipe Hidden Behind Plywood
The 50cm pipe was hidden behind plywood 10cm thick. The magnitude of the scattered
57
field for four cases is shown in Figure 3.3.21a. The red and blue upper curves represent the field
scattered from the pipes in free space. The dashed green line and the purple solid line represent
the same pipe with no crack and with a 6cm crack hidden behind the wall. A close up is inset into
the graph to zoom onto the pipe effect. The reference poles were successfully extracted and the
crack was detected as shown in Figure 3.3.21 b.
Pipe w/o crack
Pipe w 6cm arced crack
Hidden pipe w/o crack
JHJdden pipe w 6cm arced crack
• Hidden Pipe w/o crack M = 4
O Hidden Pipe w 6cm arced crack M = 10
,x10 9
3.1GHz
0.2GHz
>>
o
0.21GHz
B *
S o
0)
b±
2
3
4
Freq GHz
5
-1.5
-1
-0.5
Damping Factor - a
x10
Figure 3.3.21 a) Magnitude of Scattered Field for 50cm pipe w 6cm crack in Free space and
hidden behind Plywood, b) Extracted Poles for hidden pipe
3.3.1.9.4
Pipe Immersed in P l y w o o d
The 50cm pipe was then immersed in the plywood wall. The magnitude of the scattered
Pipe w/o crack
Pipew 6cm arced crack
Immersed pipe w/o crack
Immersed pipe w 6cm arced crack
• i m m e r s e d Pipe w/o crack M = 6
Qlmmersed Pipe w 6cm arced crack M = 12
3
x109
2.21GHz
2
N
Q
A
I>> 1 0.23GHz
u
5 0
t3y
<U
D
+
0.23GHz
A
'—1'
u.
-2
•
b)
•
;•
-5
0
Damping Factor - a
-10
3
4
5
x10°
Freq GHz
Figure 3.3.22 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free
space and Immersed in Plywood, b) Extracted Poles for immersed pipe
0
1
58
-
field is shown in Figure 3.3.22a in comparison to the free space cases. The dips and peaks of
the field shift from the case in free space due to the medium contrast. Again, the algorithm was
successful in detecting the cracks as Figure 3.3.22b shows.
3.3.1.9.5
Pipe Buried in Sand
The last case done was to bury the pipe inside a half space of sand. A comparison of the
magnitude of the scattered field for the cases in free space and in sand are plotted in Figure
3.3.23a. The extracted poles in Figure 3.3.23b show that the detection of the cracks was
successful.
Pipe w/o crack
Pipew 6cm arced crack
Buried pipe w/o crack
Buried pipe w 6cm arced crack
+ Buried Pipe w/o crack M = 6
D Buried Pipe w 6cm arced crack M = 12
x10
1.84GHz
1.22GHz
1.32GHz
B
b)
-8
-6
-4
3
4
5
6
Damping Factor - a
x10°
Freq GHz
Figure 3.3.23 a) Magnitude of Scattered Field for 10cm pipe w 6cm crack in Free space
and buried in sand, b) Extracted Poles for buried pipe
1 2
3.3.2
Target Detection at Different Burial Depths
To further evaluate the capacity of the MPM method for buried target detection two
additional structures were investigated. The structures are 3cm long and 4cm long PEC pipes
having the same diameter of 2.5cm.
3.3.2.1 Multiple Scatterers Buried in Sand at 7.5cm depth
The pipes were individually buried 7.5cm underneath sand having the same electrical
parameters as mentioned earlier. Also one case considered was burying both pipes parallel to
59
each other at the same depth as shown in Figure 3.3.24. The excitation wave used was also a
plane wave.
Plane wave excitation
Sand Interface
v \4'
4cm
3 c m
Figure 3.3.24 3cm long and 4cm long pipes buried parallel to each other
Comparisons of the scattered fields for cases were the pipes were buried separately and
then together is shown in Figure 3.3.25a. The red solid curve shows the magnitude of the
scattered field of the 3cm long pipe, observed at 60cm away from the sand interface. The dashed
blue curve shows the scattered field for the 4cm pipe, the light green short-dashed curve is for the
10cm pipe and the cyan dotted curve is for the case were both the 3cm and 4 cm pipes were coexistent. The extracted poles in Figure 3.3.25b agrees with the resonance peaks in the scattered
field plots. The 3cm pipe has its first resonance at 1.8GHz and the 4cm pipe has a 1.5GHz
resonance. As expected when the overall dimension of the structure gets bigger the resonances
will appear at lower frequencies. This was clear by the resonances of the different pipes. When
the 3cm and 4cm long pipes were buried together the significant resonant pole appeared at
2.1GHz. This is a limitation of the algorithm since it is hard to distinguish between two co-existent
objects. Therefore, further investigation should be done in order to use techniques that can
distinguish between the different objects.
60
3 c i r i " - 10cm
— 4 c m " • • • • Both 3 cm & 4 cm
—
+ 3 cm O 1 0 c m
D
,x10"
46
II
II
1
1\
j=, 30
.2
o
•
^
/
1
1 ./<
20
i
i_
t3
3>
m
F = 2.1GHz
»
~ 40
E
'i
if
10
4 cm <0_ Both 3cm & 4 cm
A. /
V.
•
"
<r «»
•"- •« *•
o
/ ' » ..••' '•..•• ••.
.*
*•. .*
£ o*\#
^
F= 0.6GHz O
+ °
~""»
»/
2 3 4 5
6 7 8 9
Freq GHz
F = 1.5GHz
D
F = 1.8GHz
O
+
10 11
-a-8
bL
-6
-4
-2
Damping Factor - a
x10
Figure 3.3.25 a) Magnitude of Scattered Field 60cm away from sand interface for 4
cases buried at 20cm, b) Extracted Poles
3.3.2.2 Multiple Scatterers Buried in Sand at 20cm depth
The scattered field of the pipes was also acquired at a burial depth of 20 cm away from
the sand interface. The cases considered were for a 3 cm pipe, 4cm pipe, 10cm pipe and one
case for both the 3cm and 4cm pipes co-existing. The scattered field for all four cases is shown in
Figure 3.3.26 a. It is clearly observed that the magnitudes are attenuated compared to the cases
at a burial depth of 7.5cm. However, the poles plot in Figure 3.3.26 b shows that for the cases
were the pipes were individually buried, extraction of the resonant poles was successful.
~ - — _ — _ i n ,-r.r.
• • • • • • o cm™
10 c m
— — 4 c m — - — Both 3 c m & 4 c m
40
+
•
Q
3 c m O l 0 c m
^^
4 c m $ Both 3 c m & 4 c m
X100
F = 2.1GHz *
E 3°
D
O F = 0.6GHz
E,
s
20
F = 1 5 G H z
CD
O
jj 10 | '
F = 1.8GHz
D
-10
-5
Damping Factor - a
x10
LU
b)
Figure 3.3.26 a) Magnitude of Scattered Field 60cm away from sand interface for 4
cases buried at 20cm, b) Extracted Poles
61
3.4
Experiments in Anechoic Chamber
The results of the FEKO simulations
lead to the next step of experimental
validation. For this purpose the anechoic
chamber built by Dr.
El-Shenawee's
students at the Engineering Research
Center was used. The chamber was
custom
built
[83]
in
a
1mx1mx1m
wooden box. A picture of the inside of
Figure 3.4.1 Custom built Anechoic Chamber
the chamber is shown in Figure 3.4.2.
Also shown in the figure are two Vivaldi
antennas mounted on two levers. The
levers are connected to the shaft of a
motor
precise
that
provides
circular
automated
positioning
of
and
the
antennas around a pipe. Two coaxial
cables run off SMA connectors from the
antennas and to a HP8510C network
analyzer shown in Figure 3.4.1 to collect
the S-Parameters. The pipe under test is
typically hung down from the ceiling of
the chamber through a cut a hole.
Figure 3.4.2 HP8510C
The initial purpose is to validate the
free space results of the simulation inside the anechoic chamber. Four different aluminum pipes
were machined for this purpose. All pipes were from the same material. They were hollow and
had a wall thickness of 2mm. Three pipes were cut to be 10cm long and 2.5cm in diameter. A
6cm arced crack and a 4 cm arced crack were cut into the center of two different pipes. One
10cm long pipe was left without any cracks. As well, a 6cm arced crack was cut into the middle of
62
a 50 cm long pipe.
3.4.1
Chamber Spatial Limitations
The inner dimensions of the anechoic chamber allow for a maximum of 42 cm of separation
between the antenna and the pipe. This distance can be only achieved by placing the pipes and
the antennas at a diagonal very close to the corners. Usually the quiet zone inside the anechoic
chamber is at least a wavelength away from the walls. This zone is the volume in which the noise
level falls below a specified minimum [84]. Lack of space was the first limitation faced when
conducting the experimental results since the algorithm proposed was performed on fields
acquired 60 cm away from the pipe. Operating in the far fields is essential when detecting
resonances. The pipes were set up straight on absorbing material inside the chamber.
Another limitation faced was due to the antennas' operating range that is from 3GHz to
10GHz. The S-parameter plot in Figure 2.1.2 shows that the plot starts going beneath the -10dB
threshold at 3GHz. Oscillations occur where the plot rises above the -10dB line at some
frequencies after that but falls back below it for most of the frequencies. Data collected at
frequencies were the S-parameter plot is above the -10dB line are inaccurate data. For this
reason, the 1GHz resonance of the pipe was not expected to be detected. This affects the
application of the detection algorithm since the 1GHz poles are the reference for when to stop
incrementing the parameter M. However, those antennas were the only ones at the lab that
provide linear polarization. In addition, the poles are at 6.5GHz for the 4cm crack and at 3GHz
and 9.1GHz for the 6cm crack, which are within
the operating range. So the experiments were
conducted in the attempt of sensing the cracks.
3.4.2
Absorber Patch to
decrease cross talk
^_ /
Tx- Portl
Rx-Port2
\
Measurements
t k
10cm
Various experimental setups and data
30cm
processing techniques were done using the
i
different machined pipe samples. The first of
'
•
which is depicted in Figure 3.4.3 were the two
Pipe: L = 10cm, D = 2.5cm
Figure 3.4.3 Antennas on Same Side of
Pipe
63
antennas are 30cm away from the pipe. Absorbers were placed between the antennas to reduce
cross talk. The S2i-parameters were collected for 401 points from 1GHz up to 10GHz. Since the
FEKO simulations were generating only the scattered fields from the pipe, pairs of measurements
were done to attain that. One measurement was done for when the pipe was in the anechoic
chamber denoted by S 2 i Pe and it represents the total field. Another measurement was done were
the pipe was removed from the chamber denoted by S 2 1
By subtracting S 21 pe - S 2 1
pe
pe
and it represents the background.
the effect of the pipe is isolated and thus the scattered fields
were attained. Another factor that needs to be removed was the antenna effect. In order to deconvolve that effect two methods were tried. The first method used was through the following
equation,
cRpe
c NoPipe
(3.22)
c No Pipe
ij21
which was used in [85] to reconstruct an image of a target from its scattered field. Three different
collections of S 21 pe were taken with a delay of 45 min between each.
3.4.2.1 Raw Data Results
The results in Figure 3.4.4 are the average of the three measurements for both a case of
0
-10
•Pipe w/o Crack
- - P i p e w crack
-80
2
3
4
5
6
Freq GHz
8
Figure 3.4.4 S21 Measured @ 30cm away from Pipe as in Figure 3.4.3
64
10
a 10cm long pipe with no crack and one with a 6cm crack. The curves show the magnitude of the
total field in decibels.
3.4.2.1.1
Deconvolving Antenna Factor
The fields resulting from the division of equation (3.22) are shown in Figure 3.4.5. Clearly
the data has lots of noise in it and when the matrix method was performed the extracted poles
had no relevance to the simulated poles. This was repeated for a separation distance of 15cm
and 8cm between the antennas and the pipe but without success.
0.35
— P w/o Crack
Pipe w 6cm Crack
0.3
CD
Q.
0.25
KO
1ZCNJ
•
CD
Q.
O iZ CM
d)
O-T-
iE og
W
C/5
0.2
0.15
0.1
0.05h
Q
x10
Figure 3.4.5 Scattered Field @ 30cm
The time domain plot in Figure 3.4.6 shows that the peak pulse appears at 0.63 ns for a
pipe 30cm away from the antennas.
t = 0.63 ns
Ideally, the pipe should appear at
2ns.
The
time
difference
0.5-
is
attributed to the noise that was
added when dividing by the s
f
0
J^HH»*#WI* rttj^l^NFf
<
parameters of the background.
-0.5
Another
alteration
of
equation (3.22) was to de-convolve
the antenna factor by dividing the
'
0.5
'
1
1.5
nmes
Times
Figure 3.4.6 Time domain for pipe @ 30cm
65
2.5
x 10 8
scattered field by the response of a PEC sheet [86]. If a block of highly conductive metal is placed
at the same location of the pipe facing the antennas as in the setup of Figure 3.4.3, a direct link
between the antennas can be recorded. The recorded scattered field is then processed into the
time domain. All the values are set to zero except for the response of the PEC sheet. The time
domain points are Fourier transformed again to the frequency domain and used in the following
equation
c
Pipe
c
NoPipe
S Sheet
21
(3.23)
This equation was applied for the same setups mentioned above. For a separation distance of
30cm the scattered field is shown in Figure 3.4.7a. The time domain plot in Figure 3.4.7b shows
that the pipe appears at 2.27 ns which is only a 0.27ns difference from the actual time. Yet the
extracted poles were not significant. The same operation was repeated for distances of 15 cm
and 8cm with no true results.
x10
Figure 3.4.7 a) Scattered Field @ 30cm using PEC Sheet, b)Time Domain Response
3.4.2.1.2
Scattered Field
Next, the algorithm was performed on the scattered field without any division,
meaning S 2 p e - S 2 i
pe
• The acquired field at 30 away from the pipe is shown in Figure 3.4.8 a,
the time response in Figure 3.4.8 b and the extracted poles in Figure 3.4.8 c. As can be seen the
most dominant poles that appeared are very different from the real poles of the pipe and the 6cm
arced crack. This was also repeated at distances of 15cm and 8 cm with no resonances close to
66
those of the simulations.
1()s
„x 10
'•—P w/o Crack
.—Pipe w (Scrr^Cracki
O Pipe w/o crack
+ Pipe w 6cm arced crack
1
t = 1.66ns
0.5
f: 5.7GHz
Q
f: 3.5GHz
+
^ ^ | | | y ^ l L
0'
-0.5/
Freq Hz
x10
2
Times
n
-1-0
x10
Damping Factor - a
x1 g9
Figure 3.4.8 a) Scattered Field, b) Time Response, c) Poles extracted
3.4.2.1.3
Total Field
The total field S 2 i Pe was also considered and processed for poles. The scattered field is
shown in Figure 3.4.9a and the extracted poles are shown in Figure 3.4.9b. There are two poles
that closely resemble the 1GHz resonance of the pipe in both the case when there was no crack
and when there was a crack. However the pole appeared at 0.8GHz for the case with no crack,
which is outside the measured range from 1GHz - 10GHz. As well, the 8.6GHz was 0.5GHz far
from the 9.1GHz resonance of the crack. Thus, the results were still doubtful.
0.025
Q Pipe w/o crack (reference) M = 6
+
Pipe w 6cm arced crack M = 8
x10
:—P w/o Crack
• Pipe w 6cm Crack
f: 8.6GHz +
f: 0.8GHz
8
-10
-5
Damping Factor - a
Figure 3.4.9 a) Total Field, b) Extracted Poles
x10
9
x 10
Another setup conducted was putting the antennas on each side of the pipe as shown in
Figure 3.4.10. The algorithm was applied for both the case of the scattered field and for the case
with the total field. However, for both cases the extracted poles did not relate to the resonances
found in the simulations.
67
3.4.2.2 Filtering
In the attempt of reducing the
17cm
noise ripples in the curves smoothing was
considered. There were different curve
<
>
Tx- Portl
averaging filters that were considered and
Rx-Port2
Pipe: L = 10cm, D = 2.5cm
are shown in Table 3.4.1 as defined in the
Matlab
documents.
The
filters
were
applied on the scattered field before
Figure 3.4.10 Antenna Surrounding Pipe
Fourier transforming.
Table 3.4.1 Matlab Curve Filters
Method
Descirption
'moving'
Moving average (default). A lowpass filter with filter coefficients
equal to the reciprocal of the span.
'lowess'
Local regression using weighted linear least squares and a 1 st
degree polynomial model
'loess'
Local regression using weighted linear least squars and a 2nd
degree polynomial model
'sgolay'
Savitzky-Golay filter. A generalized moving average with filter
coefficients determined by an unweighted linear least-squares
regression and polynomial model of specified degree (default is
2). The method can accept nonuniform predictor data.
'rlowess'
A robust version of 'lowess' that assigns lower weight to outliers in
the regression. The method assigns zero weight to data outside
six mean absolute deviations.
A robust version of 'lowess' that assigns lower weight to outliers in
the regression. The method assigns zero weight to data outside
six mean absolute deviations.
'rloess'
The filters require as input the number of points, or the span, to average the curves. For
each span value the filters' performance varied. For example, the "rloess" and the "moving" filters
with a SPAN = 5 were applied to the scattered field acquired from a pipe at a distance of 30cm. It
is shown in Figure 3.4.11a that the moving filter was tracing the scattered field without
attenuation; whereas, the rloess filter had no effect on the signal. On the other hand, for a SPAN
= 15 the rloess filter was performing better; whereas, the moving filter was attenuating the signal.
68
Figure 3.4.11 Filtered Scattered Field @ 30cm: a) Span = 5, b) Span = 15
As a start each filter was applied individually to the scattered field at 30cm away from the
pipe. The SPAN used was 5, which is the best value for the moving filter. The extracted poles are
shown in Table 3.4.2 for M = 4 and M = 6. The table contains the case were the pipe had no
crack and a case were a 6cm crack existed. The poles at M = 4 for the pipe with no crack varied
for each case. For the case with a crack, the poles were always in the neighborhood of 4GHz.
When M was increased to 6, the poles started varying. Looking at the moving filter column for the
case of a pipe with a crack, the 4.07GHz pole was replaced by a 4.97GHz and a 2.49GHz poles.
The closest of which is 900MHz away from the original pole at M = 4. The resilient nature of the
poles was defied in this since it should be expected that the same pole should appear even when
incrementing M. Yet the poles that appeared had a big difference margin.
Table 3.4.2 Poles Extracted from Filtered Scattered Field @ 30cm away
M=4
None
movinq
lowess
loess
sqolay
rlowess
rloess
Pipe w/o crack
5.59
2.69
2.63
7.03
3.09
3.35
8.65
Pipe w 6cm crack
3.91
4.07
4.02
3.90
4.01
3.68
3.87
M=6
None
Movinq
lowess
loess
sqolay
rlowess
rloess
Pipe w/o crack
2.12
7.26
2.35
3.76
6.78
2.11
7.28
2.59
8.06
2.18
5.26
2.08
7.34
Pipe w 6cm crack
3.53
6.20
4.97
2.49
3.10
4.62
3.53
6.19
5.94
3.48
2.73
4.63
3.55
6.20
The same filters were applied on the scattered fields for the same setup but with a
separation distance of 15cm and 8 cm. The same observations were viewed and the resiliency of
the poles was not maintained.
69
Moreover, the filters were applied to the total field at three different separation distances.
The poles for two filters were tabulated in Table 3.4.3. For M = 4 a 1 GHz pole appeared in both
cases were a crack did and did not exist. At M = 6, the case for a pipe with no crack had no
dominant poles. The value of M was incremented till a value of 10 and no significant poles showed
up. For the case of a pipe with a crack, two poles appeared. For the moving filter, those poles
were close to the simulated poles of 1GHz and 3GHz. Never the less, this was not enough to
conclude that the method was successful and more experiments were needed to be done to prove
the repeatability.
Table 3.4.3 5 pt Moving Filter - Total Field Poles @ 42cm
M=4
None
Moving
rloess
Pipew/o crack
0.8
1.3
1.15
Pipe w6cm crack
0.7
1.13
1.06
M=6
None
Moving
Pipe w/o crack
6.9
0.5
Pipe w 6cm crack
8.64
1.37
rloess
No Siq Poles No Sig Poles
3.49
1.13
8.48
1.2
A series of other measurements were the total field was acquired at 42cm, 15cm and
8cm. A 5 point moving filter was used and the extracted fields for several values of M are tabulated
in Table 3.4.4, Table 3.4.5 and Table 3.4.6. At a distance of 42 cm, the first table shows that most
values of M extracted either erroneous poles outside the frequency response or no significant
poles at all. At M = 9 the pipe without a crack shows the assumed pipe resonant pole of 1GHz plus
an extraneous 2.58GHz pole. However, further incrementing M showed that both poles vanished.
For the pipe with a crack, 3 poles appear at M = 12 only one of which is close to the resonance of
the pipe. The other two poles have no relevance to simulations. At a distance of 15cm, Table
3.4.5, the poles in the neighborhood of the crack frequency appear at M = 7, 8 and 9. At a distance
Table 3.4.4 Poles Extracted From Filtered Total Field @ 30 cm away from Pipe
M=4
M=6
M=7
M=8
Pipe w/o crack
0.47
0.49
none
None
M=9
1.09
2.58
Pipe w 6cm crack
0.81
None
0.84
0.78
none
70
M = 12
None
1.19
2.12
3.96
of 8cm, Table 3.4.5 the poles listed are different than all the resonances of the simulations.
Table 3.4.5 5 pt Moving Filter - Total Field Poles @ 15cm
M=5
M=7
M=8
Pipe w/o crack
1.16
1.56
none
Pipe w 6cm crack
0.75
0.94
3.14
0.82
3.24
M=9
M = 10
1.17
2.78
6.39
6.99
2.64
1.33
3.52
7.92
7.72
3.66
Table 3.4.6 5 pt Moving Filter - Total Field Poles @ 8cm
M=5
M=6
M=8
Pipe w/o crack
0.64
6.03
5.58
3.43
5.90
Pipew 6cm crack
0.64
3.56
none
0.54
4.92
M = 10
none
1.68
0.16
6.70
4.22
It was suspected that the standing wave ratio resulting from the edges of the short pipe
were affecting the measurements. So the experiments were repeated with the longer 50cm pipe.
Since the pipe is longer, any effect resulting from the edges of pipe is reduced. In addition, the
resonance of the pipe is far below the collected frequency response at 150MHz. This would
validate whether the 1 GHz resonances that were appearing in the previous experiments were real
or not. The poles in Table 3.4.7 are for the total fields of the 50cm long pipe at a distance of 42cm.
Poles close to 1 GHz appear again here for both cases of a pipe with and without a crack. No poles
resembling the crack resonances appeared though. The poles for the 30cm separation distance
are shown in Table 3.4.8. Both the poles in the proximity of 1GHz and 3GHz appear for the cases
Table 3.4.7 5 pt Moving Filter - Total field for 50cm pipe @ 42cm away
M=4
M=5
M=6
M=7
M=8
3.13
1.89
0.34
0.85
6.80
Pipe w/o crack
0.83
1.86
2.54
none
Pipew 6cm crack
0.43
0.74
1.00
0.93
71
M=9
0.33
2.26
none
M = 11
None
2.66
7.37
of a pipe with and without a crack. This leads to the conclusion that those poles might be a result
of noise.
Table 3.4.8 5 pt Moving Filter - Total field for 50cm pipe @ 30cm away
M=4
M=6
M=7
M=8
Pipe w/o crack
0.85
1.27
3.85
1.54
3.64
none
Pipe w 6cm crack
none
3.42
0.95
1.05
3.25
3.78
1.86
M=9
1.68
3.80
8.99
3.56
1.73
Another technique for collecting scattered fields is by back scattering using a single
antenna. The method consists simply of putting a single antenna in chamber with the pipe. The
S22
pe
parameters were collected once for when the chamber is empty. Another set
of S 2 2 e parameters were collected when the pipe was at a distance away from the antenna. The
scattered field of the pipe would be the subtraction of S 2 2 e - S 2 2
pe
• The two graphs in Figure
3.4.12 show the magnitude of the backscattered field were the antennas are at a separation
distance of 8cm away from the pipe. The graph in Figure 3.4.12 a compares the case of a pipe
with no crack with a pipe with a 6cm arced crack. It is visible that there is an extra dip at 2.5GHz.
Also, Figure 3.4.12 b shows that there is a dip at 4.3GHz for the case of a 4cm arced crack.
However, the algorithm was never successful to extract those poles as dominant ones. Instead
irrelevant poles appeared. When the back scattered field was collected at separation distances
- ~ — Pipe w/o crack
- - - Pipe w 6cm arced crack
0.05
& fV A
/A*
y\
"J i */ i /\«
0.04
i
0.03
SRI
* IA
y»
II B
•
CO
0.02
CO
"0.01
a)
a
•
I I \tt
'•
1*:
a 1 '
\*J '
••
k / • »!
r
" • Pipe w/o crack
• - Pipe w 4cm arced crack
0.05
0.04
r
.
.\
0.03
v\
0.02
0.01
*" .
,
\ /
4
6
Freq Hz
0. bl_
x10
4
6
Freq Hz
x10
Figure 3.4.12 5pt Moving Filter - Total Back Scattered field 8cm away: a) 6cm Crack
b) 4cm crack
72
of 15cm and farther, those dips were no longer visible. This states that the sensitivity of the
antennas is not sufficient.
3.4.2.3 Noise Quantification
The problems that obstructed the proper detection of the poles need to be quantified.
Since the chamber was custom designed by fellow students in the lab, no full characterization
was provided. For this reason factors like the transmitted and received power and the Signal to
Noise ratios, SNR, were investigated.
The HP8510C vector network analyzer is set to a transmitted power of -17dBm or
0.02mW. To convert from dBm to dB one should subtract 30. This is the power incident at the
output port of the network analyzer. Neglecting the loss from the cables, the power transmitted
from the antenna itself is found through the reflection coefficients S ^
^
2
= 1-|S11
(3.24)
where Pt is the power transmitted and Pj is the power incident on the antenna's port. From Friis
formula the received power at a specific distance can be calculated from the transmitted power
and the antenna gain. The formula is as follows:
Pr=Pt
Gt*Gr*A2
(3.25)
(4*TT*R) 2
where Gr and Gt are the Vivaldi gain,
Gain in 6 = 90; <t> = 0
16
Pr is the received frequency at a
14
distance R from the transmitter and A
is the wavelength of the transmitting
3 10
Q.
frequency.
The maximum gain of the
E
<
8
6
4
Vivaldi was calculated using FEKO
2
from 1GHz to 10GHz and is shown in
0
0
Figure 3.4.13. Using the gain values
73
1
2
3
4 5 6 7 8
Frequency GHz
Figure 3.4.13 Vivaldi Gain
9
10
the power received at 8cm, 15cm, 30cm and 42cm is plotted in Figure 3.4.14.
Figure 3.4.14 Power Plots
The authors of [87] were trying to detect the resonances of notches in an elliptical
antenna situated at 1 m away from a probe. The notches were of the same width as the cracks
used. The required transmitted power they required to detect those resonances was -28dBm. The
threshold of their receiver was -110dBm. It can be seen from the plots that at 8cm we were only
able to transmit -60dBm. This value was decreasing even more as we go farther.
This meant that the power transmitted was not sufficient to scan the pipe efficiently and to excite
a significant reflection from the cracks.
To quantify the error coming from the background, the measurements were used to
calculate the signal to noise ratio. First consider the setup in Figure 3.4.3 where the two antennas
are at 42 cm away from the 10cm long pipe with a 6cm crack. The SNR is defined by the
magnitude of the scattered field divided by the background field as in equation (3.22) and is
plotted in blue in Figure 3.4.15. The curve was averaged with a 50 points rloess filter and plotted
in red. The value of SNR goes as low as -30dB and as high as OdB. This noise level is much
higher than the 10dB that was tried with the simulations. It was shown there that the algorithm
was not able to extract the poles. The green plot shows the deviation or the error at each
frequency point. On average the error is around 5dB which is also very high. The same
characterization was done for the setup in Figure 3.4.10 where the antennas were on either side
of the pipe 8cm away. The SNR level exhibits an improvement from the 42cm as Figure 3.4.16
shows. Still the level was below the OdB line which exceeds the 10dB level for the simulations.
74
Filtered
2
4
6
Frequency GHz
Error
10
8
Figure 3.4.15 Error Quantization @ 42cm
Measurements
Filtered
Error
CO
T3
<D
Q.
nO
T-
-iCM
CO
1
a)
O-T-
£ CM
CO
£
2 S -2
CO
-4
-6
-8
4
6
Frequency GHz
10
Figure 3.4.16 Error Quantization @ 8cm surrounding pipe
A comparison of the averaged signal to noise ratio for the different setups at distance of
8cm, 30cm and 42cm is shown in Figure 3.4.17. The curves show that the short dashed red line
show the lowest SNR values that go above the 10dB line for several frequency points. However,
the major parts of all the curves are below the OdB line which makes it very hard to detect those
resonances using the current setup.
75
00
T3
8cm surrounding pipe
30cm
42cm
15
.—.
'
Q.
0
£ -5
2 S -10
<D
CO
Q-TE CM
-15
CO
-20
-25
-30
-35
T-
,-•••, .-
CO
\ / \
f-
, - / " "
j^y
/
_
A
K.S
\
/
^z>
0
S\
£•• \
V>/
1
.—
/ x ^ N 0 ^ f >^ v ' ' y
(D
4.
O
8cm
10dB
4
i
i
6
8
Frequency GHz
i
i
10
12
Figure 3.4.17 Comparison of SNR for 4 Setups
3.5
Conclusion
This chapter introduced a method that uses the frequency response of a buried pipe to
confirm the existence of the pipe as well as checking it for cracks. Any structure excited by
magnetic waves will have a natural occurring frequency. Those frequencies or resonances
depend solely on the structure and not on the source or the observation angle. Consequently, a
pipe will have its own signature or resonances. In addition, a crack in a pipe will have its own
resonances that appear as dips in the scattered field response. It is essential that the scattered
field is obtained at a far distance from the structure for the resonances to be visible.
Of the many methods for resonance extraction, the Matrix Pencil method, MPM, was chosen for
its simplicity. The MPM can generate the poles by solving the general eigen value solution of the
data vector. The method is Matlab friendly and yields results in real time.
Simulations using the method of moments solver FEKO were conducted for cases of a
pipe in free space, hidden, or buried in sand and plywood. The frequency response was passed
to a developed algorithm that evaluates the condition of the pipe from the extracted poles.
Starting with a reference minimal value of the parameter M, which specifies the number of poles
to be extracted, the poles are extracted. If the pipe pole appears to be the dominant with no other
significant poles this means the pipe is flawless. If poles of significant residues appear before or
76
along with the reference pole, this means a crack is detected. Cracks as thin as 0.5mm and
having an arc length of 6cm and 4cm were successfully detected in 50cm and 10cm long pipes.
The algorithm also showed applicability to cases where the data was corrupted with random
noise of SNR = 10dB.
Experiments were conducted in an anechoic chamber that was custom built by fellow
university students. The chamber allowed a maximum of 42cm of separation between the
antenna and the pipes under test. Yet only a separation of 8cm can be achieved within the
chambers quiet zone. The simulations were successful at a distance of 60 cm though, and this
lead to unreliable outcomes from the measurements. The SNR inside the chamber was also well
below the 10dB line. This is a much higher noise level and not even the simulations were
successful in detecting cracks under such conditions.
77
Chapter 4:
Conclusion
The focus of this work was to introduce a new non destructive technique for detecting
cracks in buried pipes. Frequent maintenance on pipes is essential to know when to replace
them. Various methods and techniques have been developed that involved bulky equipment such
as cameras, x-ray and probing devices. Post processing such information is sometimes tedious
and time consuming due to the large amount of data that need to be processed which often
required some manual inspection. Among all, ground penetrating radars have shown to be the
most flexible and portable technique. The method of moments solver FEKO was used as the
basic simulator for the investigations for its relatively low memory requirements.
The first series of simulations were focused on observing the electrical signature of a
crack in a buried pipe buried in sand, silt, loam and clay. The models built included pipes buried
in a sand box that has the same dimensions as a glass tank used for the experimental setup. The
pipes used inside the simulations were perfect electric conductors that were 50cm long, 5cm in
diameter and contained free space. The cracks considered were 5cm cylindrical cuts in the wall
of the pipe. The pipe was buried at 30 cm below the sand interface. The sand box was illuminated
with a Vivaldi antenna 20cm above the sand at a frequency of 5.6GHz. The different simulations
showed that the crack electrical signature had a significant magnitude and thus detectable above
the ground interface. This was tested for sands of humus concentrations up to 10% per weight.
After validating that the electrical signature of the crack can be observed above the
ground interface, an algorithm was developed to detect whether a crack exists or not. The
algorithm used the Matrix Pencil Method which is a technique for extracting poles and residues
from a data vector. The pipes considered were 10cm long and 50cm long pipes having a
diameter of 2.5cm. The cracks considered were 6cm arced length crack and 4cm arced length
cracks with a width of 0.5mm. The algorithm showed that when a crack is present, additional
poles of significant residues associated to the cracks are extracted. The algorithm was tested
against a SNR = 10dB and was successful for detecting cracks in pipes in free space and hidden
behind a plywood wall. The algorithm also showed the ability to detect cracks when they are on
78
the bottom side of a pipe hidden from the direct illumination of the antenna. When the pipes were
buried in sand and in plywood the algorithm was also successful in detecting the cracks.
However, the algorithm was not very successful in detecting the poles under noise. It is proposed
as a future work that an alteration of the matrix pencil method should include the minimum mean
square error technique to calculate the poles rather than using the total least square technique.
Also acquiring the scattered field at different observation points and using them to average the
results could help in improving the SNR. Such a technique would collect multiple data sets from
different look directions [57, 60].
In parallel to the analytical work, an experimental setup was built using a glass tank that
is 50cm deep, 90cm wide and 33cm high. The scanning system used precision stepper motors
that provided linear positioning steps of 0.00127cm in the X-Y plane. The antennas would scan
the surface of the glass tank that would contain a pipe buried in soil. The motors were controlled
by a labview algorithm also controlled a HP8510C network analyzer. The purpose of the setup
was to provide a capability of taking multiple views for the buried pipe.
Before burying the pipe, free space measurements were conducted in a 1m cubed
anechoic chamber. Vivaldi antennas were used and connected to a HP8510C vector network
analyzer set at a transmission power of -17dBm. The chamber provided a maximum separation
distance of 42cm between the antenna and the pipe. At such distances the pipe is very close to
the walls of the chamber and thus outside the quiet zone. The SNR measured inside the chamber
was below -5dB. This is below the 10dB level at which the simulations were successful. The
Vivaldi antennas lacked the sensitivity required to detect the resonances in such noisy
environments.
Improvements for future work include working in a larger anechoic chamber supporting
far field measurements would be more compatible with the nature of the problem. The antennas
usually used in the literature are for such applications are horn antennas. They operate in the
wide frequency range that is from 1GHz to 10GHz. Multiple antennas with different operating
frequencies can also be used to break up the frequency range into smaller ranges. Also, existing
microwave amplifiers, Quinstar's QPJ06183520-AO, can be connected to the network analyzer to
79
increase the transmitted power. These amplifiers cost around 8000$ and require special
connection. Another improvement can be done by using special filtering to reduce the noise
ripples and generate a smoother curve.
The simplicity of the algorithm using the Matrix pencil method makes it ideal for detecting
pipes in real time. The algorithm processes a limited amount of data and only a limited number of
poles need to be saved. Using those poles the original data can be reconstructed with accuracy.
The algorithm is Matlab friendly and requires no sophisticated coding.
80
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APPENDIX A: MATLAB CODE FOR POLE EXTRACTION
%CODE USING NORMAL MATRIX PENCIL METHOD
fields = nf60;
% load scattered fields
total(1:401) = complex(nf60(:,1),nf60(:,2));
total(402:802) = conj(complex(nf60(:,1),nf60(:,2)));
tff = ifft(total,'symmetric')';
time = 0:1/(4*801*25e6):801*1/(2*801*25e6);
normtff= tff./max(abs(tff));
tff = normtff(100:400);
L = floor(length(ltff)/2);
for i = 1 : length(ltff)-L
%rows
for k = 1 :(L+1)
%columns
xh(i,k) = ltff(k+i-1);
end
end
sig = svd(xh);
for i = 1 :length(ltff)-L
%rows
for k = 1 :L
%columns
x1(i,k) = ltff(k+i-1);
x2(i,k) = ltff(k+i);
end
end
z = pinv(x1 '*x1 )*x1 '*x2;
e = eig(z);%e = pinv(e)';
M = 50;
e=e(1:M);
poles = imag(log(e))./(2*pi)*(2*801*25e6);
Z = ones(length(ltff),length(e));
% take late time snapshot window
% N/3 < L < 2N/3, let L = N/3 always,
% solve poles
for i = 1 :length(ltff)
for k = 1 :length(e)
Z(i,k) = e(kr(i-1);
end
end
R = pinv(Z'*Z)*Z'*ltff;
%solver residues
87
%CODE USING TOTAL LEAST SQUARE MATRIX PENCIL METHOD
% load scattered nearfields
fields = nf60;
total(1:277) =complex(fields(1:277,1 ),fields(1:277,2));
total(277+1:277*2)=conj(complex(fields(1:277,1),fields(1:277,2)));
SNR = sqrt(total.A2/exp(0.5*log(10)));
noise = randn(size(total)).*(SNR);
total = total + noise;
%add random noise
freq = (0.050e9:12.5e6:3.5e9);
%apply gaussian filter
T = 1/(2*277*12.5e6); to=2*10A-9;
total(1:277) = (total(1:277).*T*sqrt(pi)/2.*exp(-(T.*freq/2).A2-j.*freq*to));
total(273:277*2) = (total(273:277*2).*T*sqrt(pi)/2.*exp(-(T.*freq/2).A2-j.*freq*to));
tff = ifft(total,'symmetric');
time = 0:1/(4*277*12.5e6):277*2*1/(4*277*12.5e6);
normtff = tff./max(abs(tff));
Itff = normtff(35:235);
L = floor(length(ltff)/3)+1;
for i = 1 : (length(ltff)-L)
fork = 1:(L+1)
xh(i,k) = ltff(k+i-1);
end
end
[u.sig.v] = svd(xh);
M = 8;
v = v(:,1:M);
u1 =v(1:M-1,:);
u2 = v(2:M,:);
z = pinv(u1*u1')*u1*u2';
e = eig(z);
Z = ones(length(ltff),length(e));
for i = 1 :length(ltff)
for k = 1 :length(e)
Z(i,k) = e(k)A(i-1);
end
end
R = pinv(Z'*Z)*Z'*(ltff );
% N/3 < L < 2N/3,
%rows
%columns
%extract poles
%extract residues
88
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