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dissertation entitled

ULTRASONIC MATERIAL CHARACTERIZATION
AND IMAGING BY UNSUPERVISED LEARNING

presented by

Jeng Tzong Sheu

has been accepted towards fulfillment
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Ph. D. degree in ETectricaT Engineering

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2/17 208 BIue FORM S/DateDueForms_2017.mdd ‘ p95

ULTRASONIC MATERIAL CHARACTERIZATION AND
IMAGING BY UNSUPERVISED LEARNING

By
Jeng Tzong Sheu

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical Engineering

1994

ABSTRACT

ULTRASONIC MATERIAL CHARACTERIZATION AND
IMAGING BY UNSUPERVISED LEARNING

By

Jeng Tzong Sheu

Attenuation coefficient has been considered as a very important feature in
biological tissues characterization. It is also a well-known fact that attenuation coefficient
is strongly frequency dependent. However, estimation of attenuation coefficient of
dispersive material is a very difficult task. Unlike traditional estimation methods, the
proposed approach extracted material dependent features from echoes for qualitative
analysis by unsupervised learning technique. Two unsupervised learning (clustering)
algorithms and two cluster validity indices were evaluated by Monte Carlo study to obtain
the statistical information. Finally, an algorithm and an index, according to the result of
Monte Carlo study, were chosen to employ in the application of ultrasonic material
characterization. The algorithm was implemented by the competitive learning model of
artificial neural networks. The clustering results are represented in the form of images in
which different color shades represents different clusters. Different data sets including
data extracted from a phantom and a slice of brain sample were used in the experiments.
The proposed method achieved some results which are very difficult to fulfill by

traditional methods.

In loving memory of my mother

iii

ACKNOWLEDGEMENTS

I sincerely thank Dr. B. Ho, my advisor, for his support, constant guidance,
encouragement, and inspiring suggestions and discussions during the course of this study.

I would also give my thanks to the guidance committee members, Dr. R. Zapp,
Professor J. Hall, and Professor L. Ni for taking time to serve in the committee.

Finally, I would like to thank my wife Chia-Hui and my daughter Sunny for their

patience, love, and joy with me.

iv

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

Chapter 1 1.0
l . l

1.2
1.3

Chapter 2 2.0
2.1
2.2
2.3

Chapter 3 3.0
3.1

3.2

Chapter 4 4.0
4.1
4.2
4.3
4.4

Introduction

Overview
1.1.1 Nondestructive evaluation by ultrasound
1.1.2 Biomedical ultrasound
1.1.3 Artificial neural networks

Objective and research tasks

Thesis organization

Background
Linear acoustics
Transmission, reflection, and attenuation coefficients
Neural networks for unsupervised learning
2.3.1 Competitive learning networks
2.3.2 Kohonen’s feature map

Time-domain and Frequency-domain Techniques
Dual-interrogation technique

3.1.1 Theoretical background

3.1.2 Advantages and limitations
Frequency domain technique

Material Characterization Using Unsupervised Learning
Introduction
Theoretical background
Feature extraction
Competitive unsupervised learning using neural networks
4.4.1 Training algorithms
4.4.1.1 Cluster validity
4.4.2 Modified K-means algorithm using competitive
learning
4.4.2.1 Cluster validity

vii

viii

OOQONAUJ-

12
15
18
20

22
22
23
32
35

41
41
43
46
49
51
58

60
64 _

Chapter 5 5.0
5.1
5.2
5.3

Chapter 6 6.0
6. 1
6.2

BIBLIOGRAPHY

Simulation and Experimental Results
Experimental results of time domain method
Comparison of two algorithms and two indices
Ultrasonic material characterization

Conclusions
Summary
Future work

vi

66
56
78
85

94
94
95

97

Table 1.1
Table 1.2
Table 5.1
Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

LIST OF TABLES

A comparison between modern techniques

Characteristics of neural networks and conventional computers
Single layer of plexiglass (W-P-W), Thickness = 17.02i0.01mm
Single layer of aluminum (W—A-W), Thickness = 12.70i0.01mm

Three layers, plexiglass-water-plexiglass (W-P-W-P-W),
Thickness: 11.02, 9.25, 7.02:0.01mm

Errors in estimating number of clusters using S, 100 patterns,
spread-=00] , overlap=0.1, spherical window

Errors in estimating number of clusters using MH, 100 patterns,
spread=0.01, overlap=0. l , spherical window

Errors in estimating number of clusters using S, 100 patterns,
spread=0.1, overlap=0.3, spherical window

Errors in estimating number of clusters using MH, 100 patterns,
spread=0.1, overlap=0.3, spherical window

vii

72

73

77

81

82

83

84

Figure 1.1
Figure 2.1

Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

LIST OF FIGURES

Setup of basic ultrasound system

Acoustic wave at interface of different media with different
impedance

Neuron of McCulloch and Pitts’ model

Transfer functions of neurons

Architecture of competitive learning networks
Architecture of two-dimensional Kohonen’s feature map
Bidirectional interrogation for N layered model
Reverberation paths of bidirectional interrogation

The impulse response pairs of dual interrogation
Multiple reflections of layer i

Experimental setup for incident signal measurement
Structure of multi-layered model for frequency domain method
System diagram

Stages of unsupervised learning

The three features in spectrum of echo signal

Demonstration of dead units problem. (a). A two-feature four
clusters data set. (b). Result with a dead unit. (0). Result of
MFSCL algorithm

Comparison of clustering results when size of clusters are
different with same initial weight vectors, training sequence and
learning rate. (a). Results of MSFCL method. (b). Results of
FSCL method

(a). Convergence comparison between MFSCL, FSCL, and
KSFM methods using well clustered data set. (b). Convergence
comparison between MFSCL, FSCL, and KSFM methods using
weak clustered data set. (c). Display of well clustered data set.
((1). Display of weak clustered data set

(a). Configuration of competitive neural network with n clusters
and five features. (b). Function of single neuron

viii

12
l6
17
18
21
24
24
27
29
33
37
44
45
48

52

55

56

62

Figure 4.8
Figure 5.1

Figure 5.2
Figure 5.3

Figure 5.4

Cost value v.s. number of clusters
Experimental setup of bidirectional interrogation

Reflection signals of single layer plexiglass in water. (a). Left—sided
reflections. (b). Right-sided reflections

Transmission signals of single layer plexiglass in water. (a). left to
right transmission signal. (b). Right to left transmission signal

Reflection signals of single layer aluminum in water. (a). Left-sided
reflection signals. (b). right-sided reflection signals.

Figure 5.5 Transmission signals of single layer aluminum in water. (a) left to

Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
Figure 5.12

Figure 5.13

Figure 5.14
Figure 5.15

right transmission signal. (b). Right to left transmission signal

Multiple reflections elimination. (a). Left-sided reflections. (b).
Left-sided signals after multiple reflections elimination.

Reflection signals of multi-layered model. (a). Left-sided
reflections. (b). Right-sided reflections

Transmission signals of multi-layered model. (a). Left to right
transmission signal. (b). Right to left transmission signal

Modified Hubert’s Gamma index v.s. number of clusters plot for
different data sets.

(a). top view of phantom. (b). Phantom covered with plexiglass
plate

Linear projection of five features onto two-dimensional space

Images of phantom. (a). C-scan image. (b). Reconstructed image
when segmented data set into two clusters. (c). Three clusters. ((1).
Four clusters

Images of phantom covered with plexiglass plate. (a). C-scan
image. (b). Reconstructed image when segmented data set into two
clusters. (c). Three clusters. ((1). Four clusters

Picture of human brain sample with hemorrhaged tumor

Images of human brain sample with hemorrhaged tumor. (a). C-
scan image. (b). Reconstructed image when segmented data set into
two clusters. (c). Three clusters. ((1). Four clusters. (e) five clusters.
(f). Six clusters

65
67

68

69

70

71

74

75

76

87

88
89

9()

91
92

93

Chapter 1

1.0 Introduction

Ultrasonic techniques for nondestructive investigation have existed for a long period
of time. But some of their limitations are still troublesome for many applications. It is the
reason of this research to present an alternate approach in dealing with attenuation

estimation problems quantitatively by using artificial neural networks (ANNs).

This chapter begins with brief overview of ultrasonic techniques and the fizndamentals
of neural networks. The problem to be solved and research tasks are then stated. F inally,

the organization of chapters is outlined.

1.1 Overview

Ultrasonic techniques have wide variety of applications like in areas such as clinical
diagnostics [1], non-destructive evaluations [l4] (NDE), and many others [16]. The
attractive features of using ultrasound are that it can probe the target without resorting to
any destructive process, provides safety of operation, and acquire low examination cost as
compared with the cost of other radiological media. Although magnetic resonance
imaging (MRI), X-ray, and computer tomography (CT) outperformed ultrasound in image
clarity, these techniques use short duration and high intensity electromagnetic (EM)
energy emissions to penetrate the object to be examined. Cost of the equipment and the
expense of examination are extremely high. At the present time, short-term and long-term

exposure risks for both operator and living target are of great concerns. Instead of using

high energy EM source, ultrasound utilizes high frequency acoustic wave (stress wave) to
interrogate the internal structures.So far, no evident has been reported related the
operation risks for both the operators and targets. A comparisongbetween these techniques

is illustrated in Table 1-1.

A ultrasound system basically composed of following components: a pulser which
generates high voltage short duration trigger pulse for triggering the transducer;
transducers that can transform energy form between mechanical and electrical stimuli and
responses; a processing unit to store acoustic signal and signal preprocessing for future
use and display. Figure 1.1 shows the basic setup of a ultrasound system.

TABLE 1.1. A comparison between modern techniques.

 

 

 

 

 

 

 

 

 

 

Techniques Cost of system Image quality Operation safety ~
MRI Very High Excellent ?
X-ray Medium Good ?
CT High Good ?
Ultrasound Low Poor Yes

 

Acoustic impedance, speed, and attenuation are important parameters for material and
tissue characterization. In the past two decades, researchers put most of their efforts in
obtaining the quantitative relationship between acoustic parameters and material
properties and pathological changes in clinical environment. The applications in the
nondestructive evaluation of materials are rather successful. However, in clinical

evaluations a lot more are to be desired, as indicated in Table 1.1.

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

Target
.3323??? P u ls e r Display
Transducers T
' re rocessin
L—> samp""3—-> p p g
& A/D & storage

 

 

 

 

 

 

 

 

 

 

Figure 1.] Setup of a basic ultrasound system.

1.1.1 Nondestructive Evaluation by Ultrasound

Nondestructive evaluation of materials by ultrasound has shown rapid growth in
recent years, especially in the testing of composite materials which becomes a major
construction material in both automotive and aerospace industries [16, 17, 29]. A great
deal of information about the mechanical properties of material can be retrieved from the
ultrasonic echo returns. However, in order to assure the success and consistency of
nondestructive evaluation, the acoustical properties such as velocity, attenuation,

reflection coefficient, etc. should be obtained with high reliability and accuracy.

For composite material, a common defects is the delamination between layers. Time-
of-flight C-scan imaging technique can be used to display the amount of energy reflected
from certain distance in depth of a given layer. Successful C-scan imaging systems have
been implemented to display two dimensional images for defects and flaws inside

composite materials [14].

Due to the ringing of ultrasonic pulsed signal and the complexity of the acoustic beam
profile, the ultrasonic image quality is greatly deteriorated. A great deal of research efforts
have been spent in improving the range resolution and lateral resolution for better image
quality. Range resolution is the system ability to distinguish two different acoustic echoes
in time sequence. When the thickness of individual layers are thin, overlapping of echoes
from layer interfaces will occur. Theoretically, range resolution can be improved by using
narrow transmitting pulses which can be provided by a broad-bandwidth and low-Q
transducer. However, such transducers are not available due to the difficulties in
fabrication technology. Various techniques have been proposed to improve the range
resolution. Beretsky et.al., used frequency deconvolution to improve ultrasonic
imaging[32]. Steiner et. al., proposed a generalized cross-correlation to improve
resolution [33]. Yamada presented an on-line deconvolution for high resolution ultrasonic

pulse-echo measurements under the constraints of narrow-band transducer [34]. Papoulis

et. al., demonstrated a repetitive algorithm to distinguish two overlapping pulse echoes by

digital signal processing technique [37].

Lateral resolution is the ability to distinguish different nearby objects in the spatial
domain. Owing to the inherent drawbacks of dispersive nature and physical size of
acoustic beam, the lateral resolution of ultrasound system is highly hampered. Ho et. al.,
used correlation technique to improve the lateral resolution in C-scan imaging system
[35]. Hundt, et, al., reported that improvement can be achieved by using digital filtering
technique [36]. Yakota et. al., presented a method of firing transducer array repetitively to

obtain an adaptive focusing effect [53].

1.1.2 Biomedical Ultrasound

Acoustic impedance, attenuation, and speed of different tissues have been investigated
for more than two decades. Most of the work has been focused on getting quantitatively
relationship between acoustic parameters and different tissues. Under some controlled
environment and conditions, researchers did reach some significant results between
pathological changes and acoustic responses. Among all the acoustic parameters,
attenuation coefficient has been recognized as an important property in differentiating
tissues [38]. In general, one can either use transmission or reflection techniques for
biomedical applications. Transmission technique [3-6] for impedance and attenuation
estimation was proposed first due to its simplicity and straightforward manner.
Unfortunately, transmission technique suffers various drawbacks. Unlike X-ray, acoustic
beam has much wider beam cross-sections and divergency. It can easily be defocused after
it penetrates the biological structure. Greenleaf et. al., [7,39] used transmission technique
to estimate the attenuation of lesions of breast tissues. The results were not very
promising. R. Kuc et. al., [1, 43,45,471 proposed an approach to estimate the attenuation
from reflected echoes on the assumption that attenuation coefficient is a strong function of

frequency. Based on this assumption, two categories of approaches were presented to

estimated attenuation coefficient. The spectral-shift approach estimates attenuation
coefficient from the downshift of the echo spectra when comparing with that of the
incident pulse. This method assumes the pr0pagating pulse has a Gaussian-shaped
spectrum. The spectral-difference method estimate attenuation coefficient from the change
of slope between the near region and far region log spectra. This method does not require
a specific form of spectra but suffers from marginal estimation accuracy due to bias errors
from small scale size of data. Over the years, some researchers proposed time-domain
methods [46,54,551 for attenuation estimation. Although time-domain methods provide
straightforward and real-time processing ability, difficulties such as signal distortion from
highly dispersive media and echoes overlapping are remain to be resolved. In addition,
most of the time-domain methods require the use of narrow-band signal which is very
difficult, if not impossible, to generate by a practical transducer. Recently, P. He et. al.,
[11,18,27] proposed envelope peak method by preprocessing the wide-band signal using
the split spectrum technique [19-21] to obtain a bank of narrow-band signals. The
attenuation is estimate from these narrow-band signals by time domain methods. Based on
the methods described above both in vivo and in vitro measurements were conducted

[9,20,42].

K. .1. Parker et. al., [12,15,20,22] used statistical model to reduce the attenuation
estimation errors by separating absorption and scattering factors for B-scan imaging
system. P. S. Green [10,59] proposed a volumetric reflex transmission imaging system.
This method basically is an extension of the conventional C-scan imaging technique by
using annual array transducers to provide focal range for image display. It has the
disadvantages of requiring huge storage space for data and its long processing time.
Because of the difficulties in estimating acoustic parameters by traditional methods,
images processing and pattern recognition techniques [23,25,26,60] were adopted to

enhance the estimation results. But, almost all of these techniques were used in post-

processing stage. No fundamental improvement has been announced in biomedical

applications.

1.1.3 Artificial Neural Networks

An ANNs is a parallel distributed information processing system which consists of
neurons (processing elements) and synapses (connections). Each neuron, characterized by
its own specific working function, receives and generates signals to a number of neurons
via synapses. The function of an ANNs system depends on the structure of how neurons
and synapses are connected. Since the outputs of an ANNs system are the result of
c00perative work of all neurons, even though there may exist damages between
connections, and faults from neurons the system can still produce significant results as
long as the malfunction parts are not overwhelming. In other words, ANNs exhibits fault
tolerance property. The other important feature of ANNs is its massive parallel
computational ability which is essential for many applications requiring high computation
capacity such as pattern recognition, and combinatorial optimization problems. Table 1-2

demonstrates the characteristics differences between neural networks and conventional

 

 

 

 

 

 

 

 

 

 

 

 

digital computers [98].

TABLE 1.2. Characteristics of neural networks and conventional computers
Characteristics Neural Networks Conventional Computers

Memory Structure Distributed System-Dependent
Memory Access Associative Specific Input
Fault Tolerance Inherent . Not Inherent
Pattern Recognition Excellent Poor
Classification Excellent Poor
Learning Excellent Poor '
Arithmetic Capability Poor Excellent
Timing Scheme Asynchronous System-Dependent
Degree of Parallelism High System-Dependent
Degree of connectivity High Low
Processing Element Simple Complex

 

 

 

 

 

The ANNs architecture can basically be classified into two categories; recurrent
networks and layer-structure networks. In recurrent network, each neuron has synapses
connected to all others neurons including itself. Hopfield-Tank network [60] is the most
well-known one of this type. In layer-type network, synapses only exist between
consecutive layers or between peers. Multiple layer perceptron belongs to this type.
Artificial neural network has been applied to traveling salesman problem [61, 62], linear
programming [63], object recognition [64], and others [65, 66]. For ANNs, problems can
be solved by designing and training an appropriate network whose minimum energy states

correspond to the solutions of the given problem.

1.2 Objective and Research Tasks

Determination of materials (tissues) properties using ultrasound can be achieved by
extracting acoustic parameters from reflected echoes or from transmission signals.
Although there are numerous proposed methods for acoustical parameters estimations,
quantitative scheme for characterizating inhomogeneous material is still not well
developed. Echoes return from inhomogeneous material, especially biological tissues, are
basically resulted from a collective scatters which are random in nature to the ultrasound

beam. Estimation of the acoustical parameters of such targets is by no means an easy task.

Attenuation property has been recognized as an important feature for tissues
characterization. It is a well-known fact that the attenuation coefficient is highly frequency
dependent. In stead of solving the tissues characterization problem quantitatively,
qualitative scheme should first be devised. Features related to attenuation coefficient in
frequency domain are extracted from the echoes and constitute a pattern data set.
Unsupervised learning (clustering) will then be applied to classify the data set into
clusters. Different clusters represent different acoustical attenuation characteristics. To

accomplish this, following steps are to be followed.

(1) Time domain signals need to be sampled and stored in a cleamess manner.

(2) Range resolution and lateral resolution of the system have to be well calibrated

and documented.

(3) Develop an appropriate algorithm and forming an artificial neural networks for

clustering analysis.

Images will then be reconstructed from the clustering information such that different
color shades represent different clusters. In addition, image processing techniques can be

applied to the clustering results to provide further spatial information.

1.3 Thesis Organization

The organization of this dissertation is as followed. Chapter 2 contains a background
discussion of appropriate topics on ultrasound and artificial neural networks. In Chapter 3,
both time domain acoustic parameters estimation method and frequency domain method

are presented. Advantages and limitations are discussed.

Chapter 4 demonstrated the relationship between frequency response and attenuation.
Artificial neural networks for clustering will be presented. Algorithms are developed to

perform the unsupervised learning using neural network.

Chapter 5 shows the experimental setup and results for the time domain method. Then,
the Monte Carlo method is used to compare the algorithms. The images of clustering
results for different samples are included in this chapter. Finally, conclusions,

contributions, and suggested future research are stated in chapter 6.

Chapter 2
2.0 Background

This chapter begins with an introduction of the theory of linear plane acoustic wave.
Then, some important acoustic parameters which are widely utilized for material
characterization will be stated. Finally, models of artificial neural networks for

unsupervised learning will be introduced.

2.1 Linear acoustics

In order to present the fundamental phenomena of linear acoustics, its loss
mechanisms are ignored for simplicity. Furthermore, only on-dimensional plane wave is
demonstrated here. In reality, there may exist different types of acoustic wave in a given
system, such as longitudinal, shear, traverse etc. [68,69]. However, only the longitudinal
wave is considered here since it is almost exclusively used in the areas of nondestructive
evaluations of materials and clinical applications. Since acoustic wave is a mechanical
wave (stress wave), it propagates via media. Pressure and particle velocity are two

observable parameters of a propagating acoustic wave.

Assume that a homogeneous medium undergoes small departures from its rest state,

the particle velocity and pressure are related by

= —— (2.1)

10

and

a an
a—i = —p-a7 (2.2)
where k is the coefficient of elasticity and p is the density of the medium.

Equation 2.1 is the mass continuity equation and the equation 2.2 is the momentum

equation. From these two equations the acoustic plane wave equations can be obtained as

82 kaZ .
P P
at2 98x2
and
82 k8
u u
at2 98x2

The general solution for the pressure and the particle velocity in the forward x-

direction are

p = p (0) exp WWI—Kn) (2.5)

u = u(0)exp(i(wt—Kx)) - (2-6)

Where K is the wave number given by

K=wjg . (2.7)

In general, the wave number is a complex quantity. It consists of the phase constant [3

and the attenuation constant a ,

11

K = B—ja . (2.8)

The relationship between pressure and the particle velocity can be derived from
Equation 2.3, 2.5, and 2.6 as:

p = —u . (2.9)

The characteristic acoustic impedance is defined as the ratio of the pressure to particle

velocity,

N
III
: I‘D

_ ‘22
_ K , (2.10)

For a lossless homogeneous media, the phase velocity is

(2.11)

DIS

n
WIS

Therefore, the acoustic impedance for a lossless medium can be expressed as

Z = pvp. (2.12)

The evaluation of the velocity of propagating becomes rather complicated for a pulsed
acoustic signal since it contains many frequency components and the medium is general
dispersive in nature. A further complication comes from that the attenuation is also a
strong function of frequency. As a result, the frequency spectral distribution will be altered
when the wave is passing through a loosy medium. A more detail discussion of such

situation will be given in later chapter.

12

2.2 Transmission, reflection, and attenuation coefficients

Material characterization using acoustic wave is mainly based on the detection of echo
return from a material interface. It is therefore important to know how and where the wave
being reflected back. Consider a plane wave is propagating from medium 1 to medium 2,
as shown in Figure 2.1. By using the Snell’s law and the continuity of both pressure and

velocity at the boundary, we have

pi+pr = pt (2.13)
and
uicosfli—urcoser = ulcosel (2.14)

Medium 1 Medium 2

    

Pr

 

Pi

 

 

Figure 2.1 Acoustic wave at interface of different media with
different acoustic impedance.

13

From Equation 2.9 and 2.14, we can obtain

 

pichose‘. prklcoser pthcose,
P. or ’ pz '

(2.15)

By rearranging Eq. 2.15 using the terms in Eq. 2.13, the pressure reflection and

transmission coefficients are

Kl K

 

 

p —cosOi——Zcos0,
rE—r = p] [)2 (2.16)
pi K1 K2
—cosei+—cosfll
pl 92
and
K2
p 2p—cosOi
rs: = 2 . (2.17)
pi K1 K2
—cosei + —cosfll
r 92

O

0 , the reflection and transmission coefficients

For normal incidence, i.e. 0,. = 0

7

become

 

K1 K2
P, p] 92

r = — = (2.18)
”i ’2 +52

14

K
p 252
t 2
I: — = —— (2.19)
, £1.52
P] 92

Using the acoustic impedance definition as given by Eq. 2.10, the reflection and
transmission coefficients can be put in terms of the acoustic impedance of the two media

as

 

Z——2_Z] 220
r_Zl+Zz (' )
2 2 l 221

: : + . .
t Z1+Z2 r ( )

These coefficients are defined as the ratio of the pressures at the interface location.
When considering pressure changes from one place to another, the effect of attenuation
has to be taken into account. The attenuation phenomena of a travelling acoustic wave is a
complicated one. Scattering and absorption all contribute to the attenuation of acoustic
energy. The scattering effect causes some acoustic energy off the acoustic pathway, while
the absorption results in heat generation. This is due to the fact that the density

fluctuations in the medium is out of phase with the acoustic pressure fluctuations [67].

Attenuation measurement can be accomplished by either using time domain or
frequency domain approach. Time domain technique requires a precise location of the
pulse and its amplitude, while frequency domain requiring a broadband transducer. The
accuracy of both techniques are highly limited by the measurement and the transducer

fabrication technology available todate.

When a plane acoustic pressure wave propagating through a lossy medium, the

amplitude of the acoustic pressure can be represented as

15

12(1) = roam—am!) (2.22)

where p0 is the initial pressure magnitude at a reference point, I is the distance travelled in
the medium. Once p, p0, and l are known, or (f) can be determined. Unfortunately, the
thickness of the layer is usually unknown, as a result, one can only obtain the a (f) - 1

product. In chapter 3, time domain and frequency domain methods for attenuation

estimation will be described in detail.

2.3 Neural networks for unsupervised learning

Neural networks incorporate a combination of features of information processing
systems together with some special features. These features include the use of simple
processing elements and learning abilities to adjust parameters and connection weights to
give desired responses as well as to compensate for inaccuracies and faults in the
hardware, and parallel processing ability. The use of simple processing elements can
facilitate the fabrication of such parallel systems. The learning features provides a very

important advantage in dealing with the detail knowledge necessary to build the system.

Neuron is the basic building block of a neural network. The simplest artificial neuron
model was first introduced by McCulloch and Pitts [70]. The neuron output of the model
is a function of the sums of weighted inputs. The model is shown in Figure 2.2. where X ,-’s
is the inputs from other neurons, Wij is the weight of the connection from the output of
neuron i to the neuron j, f(.) is the neuron transfer function, 0]. is the threshold value, and

Yj is the output of neuron j.

The transfer function of a neuron is commonly one of the three types: hardlimit, linear,
and sigmoid functions. Their input/output relationship are shown in Figure 2.3. Different

artificial neural networks can be achieved by interconnecting neurons in different ways

16

such that the networks have different training rules. In the following section, the basic

function of neural networks which are applied in the realm of unsupervised are introduced.

 

 

Figure 2.2 Neuron of McCulloch and Pitts’ model.

l7

 

 

 

f(x) f(x)
r A
p x
(a). Hardlimit (b). Linear
f(x)

 

(c). Sigmoid function

Figure 2.3 Transfer functions of neuron.

18

2.3.1 Competitive learning networks

In the competitive learning networks there is a single layer of output units Yi, each

fully connected to a set of inputs X 1- via connections WU" Figure 2.4 shows the architecture

of competitive learning networks. Only one of the output units, called the winner, can fire

at a time. The winner is normally the unit with the largest net input

for the current input vector X. This is equivalent to

IWI‘XISIWI‘XI

forall j¢i.

Y1 Y2 ‘Yn

0 9" 0 Output Nodes

(competitive layer)
)2? are m
Wk
6 Input Nodes

Figure 2.4 Architecture of competitive learning networks.

 

(2.23)

(2.24)

19

For each input pattern, we find the winner among the outputs and then update the
weight Wi‘i for the winning unit only to make the Wilt: vector closer to the current input

pattern. The updating rule is represented as

Wi(n+ 1) = W‘.(n) +n(x—wi(n))ri (2.25)

where n is the learning rate, and is typically decreased monotonically to zero as the

learning progresses.

According to the weight updating rule as described in Eq. 2.25, the cost (Lyapunov)

function [71] can be written as

2

 

1 u u 2 1 u
E{WU} = 5ZM‘IXI. —w‘.j) = iXIX —w,. (2.26)
it

w

M? is the cluster membership matrix which specifies whether or not input pattern Xp

activates unit i as winner:

Mt‘ = {I if TN“) (2 27)
‘ 0 ,otherwise .

Gradient descent on the cost function yields
- .. - "I . )
(AWU) _ 4817‘; _ nzle‘. x}. —w‘.j (2.28)

which is just the sum of the updating rule over all patterns p. for which i is the winner.
Thus, on average the updating rule will decreases until local minimum is reached if n is

properly chosen.

20

The competitive learning network has two fundamental drawbacks; First, there is no
guarantee of finding the global minimum. Many approaChes were proposed to kick the
system out of higher minimum and towards progressively lower ones. However, the
problem remains. Second, in a competitive learning network, some neurons may never
win during the whole learning training process. This is called the dead units problem. We

will discuss this problem and deal with it in Chapter 4.

2.3.2 Kohonen’s feature map

The KSFM networks [73] and the competitive learning networks are similar in weight
updating rule. However, in the KSFM structure each neural unit has its topological
neighborhood. During the training process, the weight vectors of the winning neuron as
well as the weight vectors of its topological neighbors are all updated. The size of the
neighborhood is decreased as the training progresses until the neighbor size equal to one.
As a result, KSFM will become competitive learning after a certain epochs of training. The

weight updating rule for neuron i and its neighborhood is

AWU = nMi. 1°) (X1... WU.) (2.29)

for all i and j. The neighborhood function A (i, i°) is l for i = i° and falls off with
distance lr‘. — ’1°| between units i and i ° in the output array. According to the updating rule

as described in Eq. 2.29, the cost function will be

 

2
X“ — wi,

 

1 . 2 1
E{W‘.j} = 52M?A(t,k)(X;l—WU) = 52M“ ) (2.30)
111

ijku

21

Again, M? is the cluster membership matrix. The gradient descent on this cost

function yields

(AWU) = 41% = “ZMiA (i, “(xii—WU) (2.31)
i} p

= 2M1. 1°)(xf—wq.) . (2.32)
it

This is just the sum of the Kohonen’s rule over all patterns. Thus, on average (if n
properly chosen) the Kohonen rule decreases the cost until we reach a local minimum. A
detail comparison in computation time and convergence of networks based on competitive
learning and Kohonen’s models will be given in detail in Chapter 4. The architecture of 2-

D Kohonen’s feature map is shown in Figure 2.5.

 

  

Output layer

Input layer

Figure 2.5 Architecture of two-dimensional Kohonen’s Feature map.

Chapter 3

3.0 Time-domain and Frequency-
domain Techniques

In this chapter time domain and frequency domain techniques for multi-layered model

will be reviewed. The limitations and advantages of these approaches will also discussed.

3.1 Dual-interrogation technique

Noninvasive evaluation of material characteristics is now a well accepted tool for both
clinical and industrial applications. To date, most of the systems are of reflection type. The
reflected acoustic signal from an interface received and processed by the conventional
pulse-echo technique, such as the B scan, is determined by the reflection coefficient at the
interface as well as the attenuation of substance along the acoustic beam path. It is
therefore impossible to retrieve these two type of information (attenuation and reflection)
by the knowledge of a signal trace of echo return. Additional information is needed to
evaluate the reflection coefficient and attenuation separately. A method proposed by Ho
[74] and modified by the author is accomplished by using a second pulse-echo process

from the opposite side of the object to furnish the necessary information.

Extensive work has been done on nondestructive evaluation of material properties by
ultrasonics over the years. However, the conventional pulse-echo technique suffers from
various drawbacks, such as the inability of evaluating material attenuation properties as

those from X-ray tomography and the inherent limitation in resolution [74]. An ultrasound

22

23

signal reflected from the internal discontinuities of an object contains not only information
about the reflection coefficient at the interface, but also the attenuation of the medium
between the boundaries. It is practically impossible to separate the backseatter and
attenuation from a single pulse echo return. Sophisticated techniques have been devised to
estimate the attenuation property by assuming that the reflection coefficient at the
discontinuity is either independent of frequency [75] or a simple linear function 'of
frequency [1]. Other authors have relied upon a model with known relationship between
successive interfaces [3]. A technique which is discussed in the following section allows
the computation of a quantity relates the attenuation-velocity product of the medium and
the reflection efficient at each interface in the medium from the experimental data is

developed.

3.1.1 Theoretical Background

Consider the object under tested consists of homogeneous layers, the impulse response

of the medium can be represented as

h(t) = 25,804,.) (3.1)

where t,- correspond to the locations of each reflecting surfaces. The quantity Er in the
equation includes the reflection and attenuation efforts. With this representation, the

amplitude of each echo can be obtained directly from the A-mode echo return.

A simple one-dimensional model for bidirectional (dual) interrogation is shown in
Figure 3.1. There are N layers of distinct materials comprising the model. On both sides,
transducers are used for transmitting and receiving echoes during the measurements. The
reverberation path of this multi-layered model is shown in Figure 3.2.' When considering

the reflection (or transmission) and attenuation effects in this model, the return echoes

24

 

 

 

 

 

 

 

 

 

 

 

 

1r/R

 

 

 

 

 

 

 

 

 

r1 r3 r4 rN-s rN-2 rN-r
17R 0‘0 a, 0‘2 a3 (14 aN—3 aN-ZaN—
V0 V1 V2 V3 V4 VN-3 VN-2 VN-l
Figure 3.1. Bidirectional interrogation for N layered model.
Layer 0 1 2 N -2 N-l
l1.0
1+r1 l'rN_2
1' 1+I'2
r .....
p/ 1' -1'N,3

 

1+I'N-1

Figure 3.2. Reverberation paths of bidirectional interrogation.

 

25

from individual layers and the transmission signals through the object can be expressed in

the following forms.

Echo received by the left transducer is

i-l

2 2 2
Eu(k, r) = ILOkOr,H(1—rj)kj . (3.2)
j=l

Echo received by the right transducer is

N—l
Emu, r) = 'roki(-’.~) [I (l-rjzjka . (3.3)

j = 1+1
Transmission signal from left to right is
N- 1

TLR(k, r) = ILOkOH (1 +rj)kj . (3.4)
j=l

Transmission signal from right to left is
N - l

TRL(k,r)) = [RD/<01] (1 —rj)kl. (3.5)
j=l

where r,- is the reflection coefficient of layer i, [RD and [Lo are the transmitting pulse
amplitudes from the right and left transducers respectively, and ’9 is the loss factor of layer

i which can be expressed as

k. = exp [—a.v.t.l (3.6)

1 ill

26

where a‘. is the attenuation coefficient, Vt is the propagation velocity, and It is the
propagation time delay of layer i. The impulse responses of dual interrogation is shown in

Figure 3.3.

In this generalized model, the unknown quantities include N -1 values of ri, N values of
k), and the initial intensities [b0 and 1R0, a total of 2N+l unknowns. Typically, the object is
emerged in water, such that the loss factors k0 and kN become known quantities. The total
number of unknowns are then reduced to 2N-1. From experimental data, we have N-l
echoes from the left receiver, and N-l echoes from the right receiver. Adding the
transmitted signals (T LR, T RL), we have altogether 2N equations. The system is therefore
solvable analytically. Two cases are considered here to obtain the attenuation-velocity

product (av) and the reflection coefficient (r) of all layers.

Case I . Using both the reflected and transmitted signals
The product of Eqs. 3.2 and 3.3 can be put in terms of the product of equations 3.4 and

3.5 as follows.

 

2
-r.
Euuc, mama, r) = TLR(k,r)TRL(k,r)[ ‘2] (3.7)

l—ri

where i=1 to N-l.

The reflection coefficient of layer i can then be obtained as

(3.8)

 

_ —EL[(krr) ERA/(yr) “2
r ‘ T“, (k, r) TRL (k, r) — Eu (k, r) ER‘. (k, r)

After all reflection coefficients r,- are evaluated, the loss factor of each layer can be

obtained as follows.

27

Time

 

pairs

 

Time

 

gafion.

pairs of dual interro

Figure 3.3. The impulse response

28

Taking the ratio of two consecutive echoes received by the left transducer

 

 

52.41“") 2( 2) ri+1
____ = k. 1- . 3.9
Eu(k,r) 1 rl ri , ( )
the loss factor of layer i becomes
E‘. (k, r)r. ”2
k;=[ L” ’ ‘ 2‘] (3.10)
EL1("")’;+1(1"1) '

Similarly, this loss factor can also be obtained from the echo return received by the

right transducer,

ERi(k’r)ri+l

1/2
i“ 2 I;
[ERi+l (k’r)ri(1-ri+l)]

(3.11)

 

As a result, the loss factor of each layer can be expressed by the echo information from

either side. The attenuation-velocity product of the layer i ca be expressed, from Eq.3.6, as

(xiv‘. = 411(79):? . (3.12)

In reality, multiple reflections do exist in individual layer especially when the
reflection coefficient at the interfaces are large. Under such a situation, it is impossible to
solve the problem by using the equations given above. The multiple reflections of layer i is
demonstrated in Figure 3.4. The echoes of layer i with infinite multiple reflections can be

expressed as

(3.13)

29

LayerO l i N-l

Z
4
//

 

 

 

 

 

 

1'" \\\\ /
\

Figure 3.4. Multiple reflections of layer i.

 

30

ELMi(k’ r) = 51.1“”) [1 + 2 (-1)nr?_1r?k?] (3.13)

n=l

where n=l to 0°.

The multiple reflections of layer i is a train of echoes which are equally spaced in time.
In order to eliminate multiple reflections, we utilized the properties of the primary echo of

layeri:
a) Time(ELi (k, r) ) + Time(ERl. (k, r) )= Time(TLR (k, r) ) + Time(TRL (k, r) )
b) Sign(ELi (k, r) ) = - Sign(ERi (k, r) )

Assuming that there is no overlapping between the echoes and the multiple reflections,
the primary data set {EL (k, r) , ER (k, r) , TLR (k, r) ,TRL (k, r) [Ml-ma,y can be obtained
from experimental data set {EL (k, r), ER (k, r), TLR (k, r), TRL (k, r) } by

experiment

the following algorithm. The reflection coefficients and attenuation-velocity products of

all layers can then be evaluated.
Algorithm: {EL (’6, r) , ER (k, r) 9 TLR (k, f) a TRL (k, r) iexperimenl

Step 1. Echo acquisition. Obtain the experimental data set [ E L (k, r) , E R (k, r) .

TLR 0" r) ’ TRL 0" I“) lexperimenl'
Step 2. Fori = 1 to [maximum echo number between E L (k, r) and E R (k, r) }

If(T'1me(Eu (k, r) ) + Time(ERi (k, r) ) = Time(TLR (k, r) ) +
Time(TRL (k, r) )and

Sign(EL‘. (k, r) ) = - Sign(ERi (k, r) )),

31

then save Eu (k, r) and ER‘. (k, r) into {EL (k, r), ER (k, r), TLR (k, r),
TR), 0:. r) IPA-n.0,, and delete EU (k, r) and E,“ (k, r) from {EL (k, r) ,

ER (k! r) 9 TLR (k, r) 9 TRL (k, r) 1experimen1-
Step 3. If { EL (k, r), ER (k, r) } not empty, go to Step 2.

Step 4. Compute reflection coefficient r l. and attenuation-velocity product aiv‘. from

{EL(k, r) , ER(k, r) ,TLR(k, r) . TRL(k. r) Iprimary‘

Case 2. Using only the reflected signals

If the target is thick and/or extremely lossy, there may not be appreciable signal
transmitted. Under such situation, the attenuation-velocity product (raw) and reflection
coefficient (r) can be obtained by using the reflected signals alone, provided the initial
signal strengths [w and [RD are predetermined quantities. Taking the ratio of the

consecutive echo amplitudes from the left return, one has

 

E .(k, r) r.
_L‘__ : . ‘ 2; 2 (3,14)
ELIHMJ) flail—UNI
Similarly, for the right-side return, the ratio is
2 2
E .(k, r) ri(l —r. )k.
R1 1+1 1 (315)

 

Em+1 (k, r) = r.

1+1

Multiplying equations (3.14) and (3.15), it yields

32

2 2
ELi+1 (k’r) ERi+l (k’r) riz+1(l—r?)

(3.16)

 

 

The left-hand side of Eq. 3.16 can be obtained from the echo amplitudes received by
the transducers situated on both sides of the target. The right-hand side of Eq. 3.16,
however, contains two undetermined quantities, the successive reflection coefficients r,-
and n+1. In other words, if we know the reflection coefficient of the very first interface, we
can then evaluate all reflection coefficients by Eq. 3.16. We have assumed the target is

submerged in water, the first reflection coefficient is then

= M (3.17)

r
1 2
ILOkO

Since water is almost lossless, especially in a very shallow path, the value k0 is
approximately equal to unity. The incident signal strength 1L0 can be evaluated by
observing the echo reflected from a simple water—air interface setup as shown in Fig. 3.5.
Therefore, the reflection coefficient of the first interface can readily be determined. After
all reflection coefficients are evaluated, the loss factor k,- and thus the attenuation-velocity

product of all layers can be determined by Eqs. 3.1] and 3.12.

3.1.2 Advantages and limitations

The time domain technique described in the previous section provides a simple way to
determine both the reflection coefficient and attenuation-velocity product at the same
time. It also deal with the multiple reflections within layers which usually cause artifacts

in the ultrasonic image system [76]. On the other hand, this technique requires

33

 

water

 

Transducer

Figure 3.5. Experimental setup for incident signal measurement.

 

34

a good alignment of the transducer. A minor misalignment of the transducer with respect

to the'layer structure could cause a significant error at the end.

Assume that the incident acoustic signal has a Gaussian-shaped spectra:

2
x(t) = exp (intht) ~exp[-—-t-—2) (3.18)
' 20

where f0 is the central frequency, 0 is the standard deviation. The Fourier transform pair

of Eq. 3.18 will be

00

I x (t) - exp (—j27tft) dt

-00

X0)

.[27m - exp [42202 (f—fo) 2] . (3.19)

The transfer function of the medium, when the attenuation factor is taken its account,

has the following form
H U) = exp(—af"1) . exp (—jkl) (3.20)

where afn is the attenuation factor, I is the travel distance. k is the wave number, and n is

the frequency dependent factor (between 1 and 2). Then, the output spectrum will be

0m =X(f)-H(f) = mo-exp(—2nzoz(f—f0)2)-

exp( —0tlfn) - exp (—jkl) . (3.21)

Most of the materials have a linear frequency dependency, i.e. n=1, the inverse Fourier

transform becomes

35

 

orzl2 (t-l-ll)
o(t) = exp[-alfO+—-2——2]-exp - 2
81: o 20

 

exp{j21t(f0— 0:12)-(t—£)} . (3.22)

(12!2
0p(t) = exp[—af0+é—2——2] . (3.23)

It can be concluded that the output is strongly dependent on the spectra of the incident
signal as well as the exponential function of the attenuation coefficient. This method has

following drawbacks:

(1). Error accumulation. Since the incident signal of a given layer is the transmitted
signal from the previous layer, whatever error contains in the signal will

propagate on. The error is then accumulative.

(2). The acoustic pulse is in general not a narrowband signal in the spectral domain.

This will cause analytical error as described in Eq. 3.23.

(3). Normal incidence of the signal is assumed. Error will be introduced otherwise.

3.2 Frequency domain technique

If a broadband signal can be implemented in the ultrasonic system, the attenuation
property of the material can be estimated by observing the spectral distributions of the
incident and reflected waves. Two methods are commonly used; the spectral difference

[1,43,77] and the spectral shift methods [41,44,52,55]. The spectral difference method

36

estimates the attenuation factor from the difference of slopes between the low region and
far region of the log spectra. The advantage of this method is that no specific spectral form
of incident signal is required. The drawback is the frequency deference method didn’t
consider reflection and the attenuation as separate factors. On the contrary, the estimated
attenuation factor also contain the reflection information. Thus, the estimation results are

contaminated and the accuracy is not as good as the spectral shift method described next.

When an acoustic signal passes through a medium, there will be a down-shift effect of
the central frequency in the spectra of the echo signal. This is due to the fact that higher
frequency components of acoustic signal suffer higher attenuation than that of the lower
ones. The spectral shift method estimates the attenuation and reflection coefficients from
this down-shift information. Assume that the incident pulse has a Gaussian-shaped spectra

as described in Eq. 3.18 and the transfer function of the media is characterized as:

H(f) = exp(—ajnli) (3.24)

where a‘. is the attenuation coefficient of layer i, n is the exponent of frequency dependent,

l,- is the thickness of i-th layer.

The model of the multi-layered structure is shown in Figure 3.6. When there is a
normal incidence, the amplitude of the received echo signals from each boundary can be
expressed as:

i 2
'0”1 (1‘)] = [X(f)| - IR‘.+1 (r1, ’1+1)|' I1 lexp(—20tkl,f)| (3.25)

lt=l

where X (f) is defined as Eq. 3.19, and Rt.+1 (r1, r ) is the reflection function

i+l

and can be expressed as:

37

x(t) ’ o(t)

 

1: H10) = exp(—alllfn) + Layerl

,, , I

 

 

 

Layer i

 

 

ri+l

Figure 3.6. Structure of multi—layered model for frequency domain method.

38

i
2
Ri+](r1,...,ri+1) = rmnb—rk) (3.26)
k=I

for i=1 to N.

Let us consider the linear frequency dependency case, i.e. n=1. The echo pulse spectra

from the boundary (i+l)-th can be expressed as:

2 2 2
I0(f)l = Ki+1o|Ri+1|-exp(—27t 00(f—fiH) ) (3.27)

K 1+ , is a frequency-independent constant.

Assume that the first layer is water or couplant such that the attenuation is very small.

Then, the central frequency of layer i +1 will be

i
1
f1+1 =f0_ 2 22(1ka (3.28)
7‘ 00k=1

for i=1 to N.

From Eq. 3.25, the frequency difference of two successive layers will be:

I
Af‘. = f1+1 —fi = —2'§ailr (329)

2a 00

for i=1 to N.

So, the attenuation coefficient of i-th layer, or 1" can be obtained from Eq. 3.26 as

39

anogAf‘.
or, = "T—

l

(3.30)

Since I,- is usually unknown in a real situation, the product ail) is the quantity to be
used to estimated the attenuation property of materials. In order to obtain the reflection

coefficient of each layer, let us look at the amplitude ratio of two successive echoes.

i

2
IXUinll'lRIHl' NIH/10in”
pi+1_

 

 

k=1
Pt ' 1-1 2
IXWI-lR/l- IIIHNJI

k=1

2

|x<r...>|- mam-Hui
_ k=1

i—l

x(fi) ‘ HlHkU,)|2
k=l

- “NU—’1') (3.31)

 

 

r.
l

 

 

for i=1 to N.

From the measured data, i.e., pm and pi, and the estimated attenuation coefficient of
each layer obtained from Eq. 3. 30, the reflection coefficient of each layer can be obtained
as

1-1
2
H p. X02) . HIHkU‘”
Iri+l| = ‘ 2' 1+]. kzgl (3.32)
IXU1+1)|'H|HI¢UI+1)|2

k=1

 

 

40

for i= 1 to N.

Ho et. a1. [78] has developed extended work on nonlinear frequency-dependent case

(1<n<2) in attenuation estimation.

Although the spectral shift method can provided both the reflection coefficient and

attenuation-thickness product of each layer, it suffers from the following drawbacks:

(1).

(2).

(3).

(4)-

(5).

The incident signal must assume to have the Gaussian-shaped spectra. This may

not be the case in the real system.

The error is accumulative from layer to layer. That is, the error in the previous .

layer will propagate to the next layer and so on.

In the analysis given, the frequency dependent exponent, n, of each layer is

assumed to be the same.

The incident signal is to be normal to the boundaries of the structures which is
difficult to accomplish in experimental setup. This is also not true for real

situation.

The multiple reflections within layer are ignored. This is may not be true for

medium with low attenuation and large reflection coefficients.

Experimental setup and results of time domain technique on multi-layered model will

be described and demonstrated on Chapter 5.

Chapter 4

4.0 Material Characteriza-
tion Using Unsupervised
Competitive Learning

In this chapter, a new methodology is proposed to resolve the material characterization
problem quantitatively. F irst, the overall concept and background will be introduced.
Then, details of each stage in the unsupervised learning will be given. Neural network for
unsupervised learning is also included. Two clustering algorithms and two cluster validity

indices are developed.

4.1 Introduction

The estimation and measurement of attenuation properties of biological tissues has
received much attention in the field of ultrasonic tissue characterization. During the past
two decades, many clinical studies and measurements on liver, breast, and myocardial
tissues demonstrated correlations between pathological status and tissue attenuation values
[9,41,42,79,80]. In spite of the encouraging results showing that attenuation measurement
of biological tissues may provide a useful noninvasive tools for diagnosis, tissue

attenuation measurement or estimation in vivo applications is still a very difficult and

41

42

tedious task [81,82]. Difficulties arise from the facts that the acoustic wave is scattered by
the biological structures and that the media are dispersive in nature. Although some
improvement can be made in data acquisition techniques, nevertheless, tissue
characterization based on the information from scattered ultrasonic signal is by no mean

trivial since itself is a random process [2,181.

Methods for attenuation estimation can generally be divided into two categories. The
time-domain method [46,55,821 has the advantage of being easily implemented and thus is
suitable for real-time processing. However, it can only provide limit amount of
information. On the other hand, the frequencyfdomain methods [1,83,84] give more feature
parameters and better accuracy. The trade-off is that it requires more extensive processing
procedures such as windowing and FFI‘, those will introduce new variance into the

estimation values.

Material characterization utilizes its estimated attenuation property is not reliable at the
present time. In order to improve the accuracy of identification, we proposed a method of
applying the clustering technique based on the features extracted from the echo return
signals. The competitive unsupervised learning technique using layered artificial neural
network structure is used to classify the multi-dimensional data set into clusters after
features are extracted from the returns. Image processing technique will be used for adding
spatial information to the clustering result. This method can be applied to both the
conventional B-scan and C-scan imaging reconstructions. The advantages of the proposed

method are outlined below.

( l ). Since many features are to be used for material characterization, both time-domain

and frequency-domain information will be utilized.

(2). Features can easily be added or deleted from the feature space for the improvement

of classification capability.

43

(3). Does not require the knowledge of the frequency spectrum of the incident acoustic
pulse which is very difficult to obtain experimentally or the relationship between

attenuation coefficient and frequency.

The presentation is organized as follows. The feature extraction section describes how
the features are extracted from the pulsed-echo signals, and the procedure of selecting the
independent features from the feature space. Next, competitive unsupervised learning
technique which is implemented by artificial neural network is described. Clustering
validity and local minimum problem will also be addressed. Finally, experimental setup
and the segmented C-scan images using clustering information will be presented for
various test objects. The system diagram is shown in Figure 4.1 and the unsupervised

learning is composed of stages as shown in Figure 4.2.

4.2 Theoretical Background

From chapter 2, we know that the stress wave propagating in the x direction can be

expressed as
p = p (0) cos (21tft— kx) (4.1)

where p is the pressure, p(0) is the maximum pressure, f is the frequency, and k is the wave
number or reciprocal wavelength. As the pressure wave travels through a medium, it will

’0‘!"

experience a exponential decay in the amplitude with a factor e , where af is the .

attenuation coefficient at frequency f and x is the distance the wave has traveled. Including

the attenuation factor, the pressure variation becomes
““r‘
= p (0) e cos (2an — kx) (4.2)

In a real system, a transducer which is excited by a trigger pulse will produce a band of

frequency components. Therefore, the total stress wave propagates through medium

 

 

'stip'er'viseci':

Learning

44

   

  
 

Data
Acquisition

  
    
    

Acoustic Echoes

 

     

Esti ation

I
Extracted :
Data Patterrts

Learning

b------------------------.

 

 

  
 

  

. Material

 

  
    
 

   

: Traditional 5
: Approach 1 .
J

.------

  
 
   

Segmentation
Image

  

 

 

Characterization

  

Figure 4.1. System diagram.

45

X-Y SCANNING

Reflection Signals

FEATURE EXTRACTION
& DEPENDEN CY CHECK

M ulti-dimensional
Data set ’

   
 

 

 

 

UNSUPERVISED
LEARNING CORE

Cost value

OPTIMIZE
THE CLUSTERING

RESULTS

 

Clustering information

IMAGE SEGMENTATION
& PROCESSING

Figure 4.2. Stages of unsupervised learning.

46

becomes an additive effect of all frequency components and can be expressed as

"an

x —(lnx
P = P(f])e cos (27tf1 —k1x) +P(fz)e cos(27tf2—k2x) +

"1n
= 2p ()3) e cos (21:);- kix) (4.3)

where p(f) is the amplitude of excitation at the given frequency. If the material is dispersive,
each component of Eq. 4.3 will travel with its own phase velocity cn=fnlkn. Since the higher
frequency components will be attenuated more than the lower ones, there will be a

downshift of spectrum shape in the frequency domain.

Based on this principle, the attenuation coefficient of materials have been evaluated by
several researchers, Dines and Kak [2], .l. Ophir et al. [51 1, and Shaffer et al. [68]. However,

either a known spectral shape of incident wave or n value has to be assumed

4.3 Feature Extraction

Five different features are extracted from each reflected signal at the initial phase of the
process. That is, at each scanning position, five frequency-dependent features are extracted
from each echo return. These features are: total energy, central frequency, peak frequency,
3-dB bandwidth of echo spectrum, and correlation coefficient between incident and

reflected signals.

Total energy

The total energy of the reflected signal is related to the reflection coefficient, which
contains the information of acoustic impedance of the medium. Let the sampled echo be

s(N), then the t0tal energy can be expressed as

47

N 2
Et = 2 Is(i)| (4.4)
i=1

where N is the number of sampling points of each echo signal.

Central frequency, peak frequency, and bandwidth

Attenuation coefficient has been shown to be highly related to spectral-shift and
spectral-difference of the echo spectrum [43]. These phenomena will cause central
frequency and peak frequency shifted downward and in the meantime the 3-dB bandwidth
of the echo spectrum will also be widened. For a Gaussian-shaped spectrum, the center

frequency can be estimated by the mean frequency [85, 861, Fm, and is given by

i=1
Fm: N (45)
211131.) '
i=1

 

where HP 1') is the i-th element of the N-point FFT, which is ranging from the lower 3-dB
to the upper 3-dB level. The peak frequency PK (F) is the frequency having a maximum
magnitude within the 3-dB bandwidth. Figure 4.3. shows these features on spectrum of

echo signal.

Correlation between incident and reflected signals

Correlation between the reflected and incident signals at a given interface can provide
useful information about the medium under interrogation. The properties such as elasticity,

stiffness, velocity, and attenuation are all embedded in this feature.

Relative magnitude

0.8

0.6

0.4

0.2

48

 

 

 

 

 

 

 

central frequency peak frequency
< D
3dB
. 4
0.5 l 1 .5 2 2.5 3 3.5 4
Frequency (MHz)

Figure 4. The three features in spectrum of echo signal.

49

In order to avoid redundant selection of the features, linear dependent test is performed
to measure the degree of feature dependence between features. The linear dependency

between two features, i and j, is measured by [871

n

(g) 2 (xri-mi) (xrj_mj)

dour) = (=1

 

 

 

s is j (46)

where sj and mj are the sample variance and sample mean, respectively, for feature j
respectively.The absolute value is used since the correlation could have either a positive or
negative value. The magnitude is being used as an index for dependency. If d(iJ) = 0, the
features i and j are linearly independent. Whenever d(iJ) approaches unity, one of the

features can then be discarded.

4.4 Competitive unsupervised learning using neural networks

In this section, two unsupervised learning algorithms will be introduced and
implemented with competitive neural network. The basic problem of competitive learning
neural network will stated first. Followed by the comparison of convergence between

different neural network models for unsupervised learning.

As described in chapter 2, the competitive learning network is the simplest way and the
fastest way to perform the unsupervised learning. Yet, it suffers the dead units problem
which make it less competitive when compared with other methods. The dead units

problem can be prevented by the following ways:

(1). Update the weights of all the losers as well as the winner, but with a much smaller

learning rate for the losers. This will make the units that never win gradually move

towards the average of input patterns and eventually win the competition. The is

 

50
called leaky learning.

(2). Update not only the weights of winner but also weights of its neighbors. This is

basically the essence of Kohonen feature map and is discussed later.

(3). Suppress the frequent winner by adding a frequency counter in the decision of
winner. The frequent winner will become less competitive as it win more and give
units that never win a increasing chance to win. This mechanism is sometimes

called conscience method.

(4). The input pattern vectors are smeared with additional noise, using a distribution

with a long tail so that there is some positive probability for any input pattern [961.

Although the methods described above can avoid the dead units problem, they all pay
the price on the computation load. A modified algorithm MFSCL will show improvement

in computation load but also prevent the dead units problem in the later section.

Among the features of neural networks, Ieamin g ability is the most attractive one which
makes it suitable for problems requiring large amount of computation and combinatorics.
Pattern recognition belongs to this category of problems. Pattern recognition covers two
types of Ieaming: supervised and unsupervised learning [90]. In supervised learning, the
learning is improved by the available class information of data patterns. On the other hand,
unsupervised Ieaming does not involve class information.

Among the models of neural networks for unsupervised learning, competitive Ieaming
[91] and Kohonen self-organizing feature maps [73] are the most widely used models in
many applications. The self-organizing map basically involves competitive Ieaming.
During the training, connection weights of the winning neuron and its neighbors are
updated. As training progresses, the size of neighborhood is minimized. As soon as the
neighborhood size is reduced to one. the competitive learning is assumed to converge.

we begins with the basic competitive learning in this section. We then compare various

51

training algorithms for unsupervised learning, including the proposed training algorithm.
Then, test data sets are used to justify our method. Finally, acoustic imaging segmentation

results will also be presented.

4.4.1 Training Algorithms

A. Competitive Learning Neural Networks (CL): Let X = {x§1), ...,x§n} be

the training pattern vectors set, where the dimension of vectors is d. The class information
of each pattern vector is unknown. The objective is to estimate the number of classes
(clusters) for the given data set X. The output of each neuron in competitive learning is
determined by

{1 if dist(x,W‘.(n) ) Sdist(x,Wj(n) ) forall j
~ (4.7)

O , Otherwise

The dist(x,W(n)) is the Euclidean distance between vector x and the weight vector

W(n). The weight updating rule of the neuron i is

Wi("+1) = W;(")+11(x—W;("))01 (4.8)

where parameter 11 is the learnin g rate, and is typically decreased monotonically to zero as

learning progresses.

The problem of competitive Ieaming networks, according to its learning mechanism,
is that it sometimes leads to unused neuron units, or the so-called dead units
(underutilization) problem. That is, the network is trapped in a local minima for some initial
weight vectors. Consequently, only some of the neurons get updated. The results on a two-

feature data set with four clusters are used to demonstrated this problem. The initial weight

 

 

 

 

52

Inna Vader: P14) l Wedge Vim W:(o)

 

 

 

 

 

 

 

 

0.: o o r o 0.81-
03 - 0 ° go o o 0
° ‘ Q 0 o o
0.4- ° {goo $0 0° 0’ 0%
0.1+ .
1 °-
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O o o o
.o.4- 9 ° 0° 0 0 0° :1 .
O Q o a
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5.4 .11.. 4.4 -oa r «:1. 1 0.2 0.4 0.4 0.4 III 4.4 44 oz PMnew”) oz 04 of. of:
(a) (b).
Figure 4.4. Demonstration of dead
units problem. (a). A two-feature
four clusters data set. (b). Result
0'. mvm eroriwmvmnwro) with a dead unit. (c). Result of
MFSCL algorithm.
'05.: of. o 4 2 5 of: o 4 oi. of:
mm WM)

(C)

 

 

53

vectors of all the neurons were set close to the. mean value of data set (-0.0103, 00160).
As shown in Figs. 4.4(a) and 4.4(b), weight vector of one of the neurons was not updated
during the training process. This problem was first discussed by Grossberg [92]. Later,
Desieno [93] suggested conscience method to cope with this problem. However,
conscience method is suitable for dividing data vector space into e’quiprobable regions.
Unlike vector quantization, clustering needs different methods to yield the desirable result. '

This is because the clusters in a data set may contain different number of data patterns.

B. Kohonen Self-organizing Feature Maps (KSFM). The KSFM networks [731 and
the competitive learning networks are similar in weight updating rule. However, in the
KSFM structure each neural unit has its topological neighborhood. During the training
process, the weight vectors of winning neuron as well as the weight vectors of its
topological neighbors are all updated. The size of the neighborhood is decreased during the

training progresses until the neighborhood

size equals to one. As a result, KSFM will become competitive learning network after a
certain epochs of training. The weight updating rule of neuron i and its neighborhood will

be

WM") +n[x-—Wi(n)],i€ N(i*) (4.9)

Wi(n+ 1) = {
W; (n), Otherwise

where N(i*) is the topological neighbors of neuron 1'. Again, the Ieaming rate T] decreased

as training progresses.

Because of the weight vectors of both winning neuron and its neighbors are updated,
the KSFM structure indeed avoids the dead units problem. However, it pays a high price of

additional computation load as compared to the competitive learning. This computation

load is coming from the weight vectors calculation and updating for the neighbors and

 

54

winning neuron itself. We suggest an alternative network that reduces the additional

computation load and in the meantime resolve the dead unit problem.

C. Modified frequency-sensitive competitive learning (MFSCL). The motivation of
the modified frequency-sensitive competitive learning is to overcome the limitations of
simple competitive learning network while retaining its computational advantages. From
our experience, dead units occur either at the beginning of the training phase or when
weight vectors are trapped in pool mean of clusters during the training. In other words,
some neurons could never be activated from the beginning of training because of the
corresponding weight vectors are too far away from the input patterns in the pattern space.
The KSFM uses multiple activation of neurons to avoid this trap. The frequency-sensitive
competitive learning (FSCL)[95] introduces the winning frequency of each neuron to the
distance calculation for the next winner. This method ensures that all neurons have equal
opportunity and approximately equal number of times to be modified for avoiding dead

units problem.

In FSCL network, each neuron incorporates a count of the number of times it has been

the winner. Also, the distance measure to determine the winner is modified as
dist* (x, W1) = dist (x, W!) (pi (n) (4.10)

where dist(x,Wi) is the Euclidean distance between x. and W1 as described previously.
‘91 (n) is the count of winning frequency of neuron iduring the training. If a given neuron
wins the competition frequently, the count and the dist will increase as well. This reduces
the likelihood that this neuron will again be a winner, and give other neurons with lower
frequency count a higher chance to win the competition. Consequently, only the weight

vector of the winning neuron is updated by Eq. 4.8.

The FSCL networks do achieve the goals of avoiding dead units problem and reducing

computation load as compared to KSFM. However, it presents two drawbacks. First,

1mm V0601! P10) I W! V“ W10)

 

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55

 

m vm n1.) 0 was: Venn-0 mo)

 

 

 

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0.0
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Q
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O i. q.
o 4
'02 ¢ 9' 0.:
i 0 N
O
'°10.0 -0.4 01 0 01 0.4 0.0 0.0 1 11
Pan Wm)

Figure 4.5. Comparison of clustering results when size of clusters are different with
same initial weight vectors, training sequence and learning rate. (a). Results of

MFSCL method. (b). Results of F SCL methods.

56

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cormaiaon otaomm: WSCL FSCL KSFM Conparson 01¢»)ch ('0‘ me): WSCL. FSCL, KSFM
T v 1 I v v 1 v r v 1 '7 Y I v v f v I I
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1‘ KSFM. °~°’ 1 KSFM-
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Faun Fennel
(c) (d)

 

Figure 4.6. (a). Convergence comparison between MFSCL, F SCL, and KSFM methods
using well clustered data set. (b). Convergence comparison between MFSCL, FSCL, and

KSFM methods using weak clustered data set. (0). Display of well clustered data set. (d).
Display of weak clustered data set.

 

57

pattern data set tends to be partitioned into same size of clusters as training progresses.
Second, for data pattern set contains various size of clusters, the clustering results, i.e.
cluster centroids, will be less optimal compared to other methods. This phenomena is
demonstrated in Figure 4.5 by using same initial weight vectors and training sequence for

FSCL and MFSCL methods.

Unlike the FSCL algorithm which uses frequency information during the entire training
process, we introduce an algorithm that employes the frequency information only at the
beginning of the training process and at situation when average error (distance) reaches
minima. After sensing all neurons have been modified, the learning follows the CL
mechanism. Therefore, the MFSCL method not only avoid dead units but also provides
better clustering results than FSCL on data sets with various size of clusters. Using the same
data set as in Fig. 4.4(a) the dead units problem is resolved by MFSCL and the result is
shown in Fig. 4.4(c). Furthermore, it requires less computation time than FSCL and KSFM .
methods. A comparison of convergence of KSFM, FSCL, and MFSCL with same initial
weight vectors and same presentation sequence on weak clustered data set and well

clustered data set are shown in Fig. 4.6. The algorithm of MFSCL is described below.
Algorithm: Modified F requency-Sensitive Competitive Learning (MFSCL)
Step 1: Set C=1.

Step 2: Initialize weight vectors and set all frequency counters of output neurons to

zero.

Step 3: Choose the input pattern randomly and if all neurons have been updated set

C equal to zero.
Step 4: Present the pattern to the networks

Determine the winner by Eq. 4.10 if C equal to one, else by Eq.

58
4.7.

Update the weight vector of winning neuron, and its frequency

counter if C equal to one.

Step 5: If Al?2 5 8, then go to Step 6, else go to Step 3.

Step 6: Perturb the results by presenting all patterns once by Eq.4.10.
If new results better than that of Step 5, then go to Step 3.
Else stop and done.

2 . . . .
The A5 rs the average error (distance) between two consecutive epochs and e rs the

threshold value for stopping the learning.

4.4.1.1 Cluster Validity

After the clustering process is performed, the next task is to find the most suitable
number of clusters for the given data set. This problem continues to evade solution in
cluster analysis. To circumvent this problem, many indices are evaluated by Milligan and
Cooper [95]. Here, we adopted an internal index, the modified Hubert’s (MH) Gamma,
suggested by Jain and Dubes[87] because of its best performance. This statistic is the point
serial correlation coefficient between proximity matrix of data patterns and a model matrix.
In order to obtain the model matrix, distance between two patterns is set by the distance
between centers of two clusters to which the patterns belong. The MH index is defined as

following.

Let L denote the label function that maps the sets of patterns to the set of cluster

labels and expressed as:

59

L(i) = k ifie C,( (4.11)

Parameters that defined the average-distance between all patterns, average distance

between clusters, and two standard deviation are defined as:

1
r = (fi)225(xi.2{j)5(mw,.mLm) (4.12)
Mp = ([14)225(X1’Xj) (4.13)
1
Me = (fi)225(’-’-‘L(i)’mw>) (4'14)
2 1 2 2

0,, = (117)228 (Xv!) —MP (4.15)
o: =(fi14)2252(mm,mw))—Mf (4.16)

where M =n*( n-l )/2, 5 (x, y) is the Euclidean distance between x and y, X is the pattern
vector, 11L (0 is the mean vector of cluster i. Using the parameters defined above, the MH

index for the clustering {C,, . . . , CK) is expressed as:

M
MH(K) = ————L—‘ . (4.17)
oPoC

60

The number of clusters is estimated by seeking a significant knee in the MH versus
number of clusters plot. Although there is no theoretical proof, MH index will decrease if
true clusters were forced to merge or split. But if data set is grouped into more clusters than
that of the data set itself, the MH index will be increased because of good correlation

between data patterns. The MH statistic is bounded between 0 and 1.

4.4.2 Modified K-means (MK) algorithm using competitive learning

The second algorithm for the competitive learning is basically modified from the K-
means method [88] and implemented by ANN structure. The algorithm is described as

follows.
MK Algorithm: Data pattern set: {X}.

Step 1. Randomly select data patterns as the cluster centroids (C i) from data

pattern set {X}.

Step 2. Assign data pattern to the nearest cluster and modified the very cluster

centrOid until all data patterns are presented.
Step 3. Reassign each data pattern to the cluster with nearest distance.
Step 4. If classification of all data patterns remain unchanged,
perturb the clustering results.
If the results unchanged, then stop.
Else go to step 2.
Else go to step 2.

In step 4, the perturbation includes two procedures for escaping from the local minima.

61

First, different presentation order of data patterns are presented to the unsupervised
Ieaming mechanism. Second, shuffle boundary data patterns to different clusters. The
clustering result with K clusters is determined by the cost function S =Sw/Sb. The with-

class-scatter, SW, is defined as

K "a
SW = 2 2(xf—kaxf—mky (4.18)

. . . k .
where K rs the number of clusters, nk rs the number of patterns in the k-th cluster, x j rs the
pattern vector belong to the k-th cluster, and m" is the vector feature means of the k-th

cluster. The between-class-scatter, Sb, is defined as

Sb = i §(mk—m)(mk—m)r (4.19)

where the pooled mean, m, is the grand mean vector for all patterns.

The smaller the SW, the more compactness will be the cluster. A larger value of 5,,
implies the cluster is more isolated. Following the modified K-mcans clustering algorithm,
the clustering results are determined by the cost function S = SMSb. As a result, a small cost

value of the cost function

01 02 ‘s‘on

0 a ' ° ° 0 Output Nodes
§4§ / (competitive layer)
"w.

wnS

 

o o a o a lnputNodes

(a)

 

Figure 4.7 (a). Configuration of competitive neural network with n clusters
and five features. (b) Function of sigle neuron.

63
will give a better clustering result.

Because of correspondence of the procedure, the unsupervised competitive neural
network, as shown in Figure 4.7(a), was chosen to implement the algorithm. The number
of input nodes represents the dimensionality of the input patterns, while the number of
output nodes represents the
number of clusters. The function of each neuron is shown in Figure 4.7(b). Each time when
a pattern is presented, only one of the neurons will be activated and gives an output of unity.
This is accomplished by the following steps [89]: When the pattern vector X ,- is presented

to the network, the weight values of every neurons are computed by

s. = 2 szt-d for all i. (4.20)

The output of neuron j, 01-, will be forced to ‘one’ when S j is larger than S k, for all k. D is

the dimensionality of input pattern. Only the weighting vector (centroid) of neuron j

(cluster j) is updated by
Xi
Aw.. :1 ——w.. (4.21)
11 m 11
new old (4.22)
w.. = w.. + Aw..
ll 11 Jl

where l is the learning rate and m is a normalization factor.

64

4.4.2.1 Cluster Validity

After the clustering is performed, the next task is to find the optimal number of clusters
for the given data set. This remains an unsolved problem in cluster analysis, However, a
heuristic method can be adopted to give the best estimation. If the clusters are meaningful,
the cost value will decrease dramatically as the number of clusters increases. Therefore, the
last knee point in the cost value versus the number of clusters plot is used to determine the
number of clusters for a given data set. Figure 4.8 shows the knee point in the cost value

CUI'VC.

A detail comparison between the above two algorithms will be given in Chapter 5 using

Monte Carlo analysis on different data sets.

Cost value

 

65

knee point

>

 

2 3 4 5 No. of clusters

Figure 4. Cost value v.s. number of clusters.

Chapter 5

5.0 Simulation and
Experimental results

In this chapter, experimental results were given to demonstrate the theoretical
derivations of time domain technique. In the second section, a Monte Carlo method will be
used to study the algorithms and indices discussed in the previous chapter using synthetic
data sets. Finally, the results of material characterization using unsupervised learning

method will be given and discussed.

5.1 Experimental results of time domain technique

In order to justify the theory described in chapter 3, two cases of experiments were
conducted under the experimental setup as shown in Figure 5.1. The experimental setup
includes a PC—486, a PC-bascd A/D converter board with 40 MHz sampling rate and 8-bit
resolution (WAAG II), a Panametrics Inc. 5050 PR pulser, and two Panametrics V306
transducers. The central frequency of transducers is 2.25 MHz and their diameter is half

inch.

In the first case, two single layer materials, plexi glass and aluminum, were used in

the experiment separately to test the feasibility of experimental setup and observed errors

66

67

Layered Structure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5050 PR
Pulser

 

 

 

8-bit

 

A/D
Converter
(WAAG II)

 

 

 

 

PC-486

 

 

 

Figure 5.1. Experimental setup of bidirectional interrogation.

68

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200 I I I I I I
3150 _ _
<11
.3 * \W V V ” ’ "
4
E 100 - 4
50 l 1 l l l 1
O 100 200 300 400 500 600 700
(a) Time (25us)
300 I I I I F I
3200 - -
m
0
J M.
’3?
7!; 100 " r
O l 1 l 1 J J
0 100 200 300 400 500 600 700
(b)
Time (25us)

Figure 5.2. Reflection signals of single layer plexiglass in water. (a). Left-
sided reflections. (b). Right-sided reflections.

relaative amp.
_. _. m N
8 8 59 8 8

0

§ §

relaative amp.

Figure 5.3. Transmission signals of single layer plexiglass in water. (a). Left to
right transmission signal. (b). Right to left transmission signal.

69

 

 

 

 

 

 

50

150

200

Time (25us)

250

 

 

 

T

 

 

 

50

100

(b)

150

200

Time (25us)

250

relaative amp.
-b N m
8 8 8

§

70

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 1 L l l
o 100 200 300 400 500 600
(a) Time (25us)
250 I I I I I
. 200 - l -
E
w 150 » .
m
.2
g 100 - -
9
so ~ .
0 l 1 A 4 l
o 100 200 300 400 500 600
b
( ) Time (25us)

Figure 5.4. Reflection signals of single layer aluminum in water. (a). Left-

sided reflection signal. (b). Right-sided reflection signal.

250

200

relaative amp.
8 8

8

O

71

 

I

 

 

 

 

 

O

relaative amp.
=4 _. N m
8 8 8 8 8

O

20

40

120

140

160

180

Time (25us)

 

 

 

l

J

I

 

 

 

O

20

40

60

80

(b)

100

120

140

160

180

Time (25us)

Figure 5.5. Transmission signals of single layer aluminum in water. (a). Left to
right transmission signal. (b). Right to left transmission signal.

72

of the experimental results. The thickness of plexiglass and aluminum are 17.02 i001
mm and 12.70 :l:0.01 mm respectively. The received signals, two reflected signals and two
transmission signals, from both sides are shown in Fig. 5.2 to Fig. 5.5. The signals were
averaged 21 times to improve the signal-to-noise ratio. The impulse responses of the test
medium are determined by locating the peak amplitudes of each echo and their
corresponding traveling time. The algorithm of peak detection and traveling time
dcterminaion is implemented in c language and listed in Appendix A. According to the
Eq. 3.8 and Eq. 3.10. the estimated results of reflection coefficients and attenuation-
velocity product of each layer were calculated and are shown in Table 5.1 and Table 5.2

for plexiglass and aluminum respectively.

From the reflection signals of aluminum ( with high reflection coefficient) on both
sides, the multiple reflections can be easily distinguished from the primary echo signals.
As described in chapter 3, the multiple reflections of the same layer have properties of
equal traveling time and have same polar sign as the primary echo of same side (have
opposite polar sign to the primary echo of another side). The multiple reflections were

detected and eliminated by our algorithm and are shown in Figure 5.6.

TABLE 5.1 Single layer of plexiglass (W-P-W),
Thickness = 110210.01 mm.

Experimental

Parameters

results

Published Data“

 

r]

0.329

0.368

 

r2

0.323

0.368

 

av (nepers/sec)

138,575.26

138.850

 

v (m/sec)

2654.19

2680

 

 

52.21

 

51.81

 

 

73

TABLE 5.2 Single layer of aluminum (W-A-W),
Thickness = 117010.01 mm.

Experimental
Parameters results Published Data‘ Error(%)

r1 0.847 0.848 . 1.06%

 

 

r2 0.841 0.848 3.07%

 

av (nepers/sec) 3246.14 2984.32 8.77%
v (m/sec) 6369.97 6400 0.47%
a (nepers/m) 0.5096 0.4663 9.28%

 

 

 

 

 

 

 

For the multi-layered case, a model with two plexiglass layers separated by a layer
of water was examined. The thickness of each layer is: layer I (l = 11.02 mm), layer 11 (1 =
9.25 mm), and layer 111 (1 = 17.02 mm). The setup and the received signals from both sides
are shown in Fig 5.6 and Fig. 5.7. Again, all signals are averaged 21 times to increase the
signal-to-noise ratio. From the peaks of these echoes and the traveling time of each echo,

the results can be obtained and were shown in Table 5.3.

The experimental results compared well with the published data. We noticed that the
reflection coefficients in all cases are slightly smaller than the published data, while the
attenuation coefficients are slightly larger. This is possibly due to the fact that there exist
diffraction at each interface (deviated from normal incidence). The scattered energy will
not be captured by the receiving transducer. In theory, any energy loss is considered to be
attenuated (absorbed) by the medium. Unfortunately, the scattering effect is cumulative. It
will be very pronounced as the number of layers increases. The experimental results of the
multiple-layer structure demonstrates this effect. One of the drawbacks of this technique is
the error accumulation. That is, if acoustic parameters of the first layer on both sides are
not evaluated accurately, the errors will be propagating through the rest of process. To
minimize this effect, the alignment of the transducers becomes very critical. Other

drawbacks of this techniques were discussed in chapter 2.

250

relaative amp.
_s _L N
8 8 8 8

O

74

 

 

 

 

 

 

 

 

 

O

250

200

—A
0'1
0

a—A
o
O

relaative amp.

0'1
0

0
0

100 200 300 400 500 600
a
( ) Time (25us)

 

I

 

I I I I I

 

 

 

 

 

 

100 200 300 400 500 600
b
( ) Time (25us)

Figure 5.6. Multiple reflections elimination. (a). Left-sided reflections.

(b). Left-sided signals after multiple elimination.

§§§

E;

relaative amp.

8

8

relaative amp.
—5 —b N N
8 8 8 8

8

75

 

 

 

 

 

 

 

 

 

 

 

 

all) ‘
L l l l i l I ,
0 200 400 600 800 1000 1200 1400 1600
(a) Time (2505)
’ - ‘AW -
V
0 200 400 600 800 1000 1200 1400 1600
(b) Time (2511s) A

Figure 5.7. Reflection signals of multi—layered model. (a). Left-side reflections.

(b). Right-sided reflections.

relaative amp.
-~ _. 1x: m
8 8 8 8

8

relaative amp.
8 8 8 8 8

C)

76

 

I

 

 

 

 

 

O
O

40

100
(a)

120

140

160

180

200

Time (25us)

 

 

 

I

 

 

 

O

20

40

160
(b)

120

l
140

160

180

200

Time (25us)

Figure 5.8. Transmission signals of multi-layered model. (a). Left to right transmission

signal. (b). Right to left transmission signal.

77

TABLE 5.3 Three layers, plexiglass-water-plexiglass (W-P-W-P-
W), Thickness: 11.02, 9.25, 17.02i0.01 mm.

Parameters

Experimental
results

Published Data“

Error(%)

 

r1

0.319

0.368

12.8%

 

r2

0.336

0.368

8.7%

 

r3

0.323

0.368

12.2%

 

r4

0.367

0.368

0.3%

 

(111vl (nepers/sec)

143,799.12

138.850

3.56%

 

013113 (nepers/sec)

124,003.75

138.850

10.69%

 

v1 (m/sec)

2663.44

2680

0.62%

 

v3 (m/SCC)

2654.19

2680

0.96%

 

orl (nepers/m)

53.99

51.81

4.2%

 

a (nepers/m)

 

46.72

 

51.81

 

9.8%

 

78

5.2 Comparison of two algorithms and two indices

In this section, two algorithms and two indices described in the previous chapter
were compared using Monte Carlo study. Two experiments were conducted to get
statistical results of the algorithms and indices over different data sets. First, an
experiment for strongly clustered (well—clustered) data was performed. Then, an
experiment for loosely clustered (weak-clustered) data was conducted. These two
experiments are designed to test the clustering ability of the algorithms and cluster validity

ability of the two indices to the clustered data.

Data generation

Clustered data were generated by the modified algorithm [87] of the Neyman-Scott
[98] process in which spherically shaped Gaussian clusters are located randomly in the
sampling window. This algorithm ensures that the clusters do not overlap more than a
specified amount, provides for a minimum number of point per cluster, and permits the
exact number of clusters to be specified. The details of the algorithm is described in [87].
Two important parameters, the spread of cluster (0) and the overlap (I) between
clusters are used to defined the generated data. Strongly clustered data has 6 = 0.01 and
I = 0.1 ,while the loosely clustered data has 0 = 0.1 and I = 0.3. A spherical sampling
window is a hypersphere whose radius is adjusted in each dimension to provide a volume

of one.

Two experiments were performed to test two unsupervised learning (clustering)
methods, the modified frequency sensitive competitive learning (MFSCL)and modified k-

means (MK), and two indices, 8 and MH.
Experiment I

This experiment estimates the number of clusters in a well-clustered data set with a

hyperspherical sampling window. Since any reasonable estimator for the number of

79

clusters should work well for the well-clustered data, this experiment checks the
performance of two indices under almost ideal conditions. The experimental factors are

defined as following.

Sample size: { 100 }

Number of dimensions: { 2, 3, 4, 5 }
Number ofclusters: {2, 4, 6, 8}
Clustering method: { MFSCL, MK}
Sampling window: { Sphere }
Index: { S, MH}

These factors define 64 cells of experiment. Each cell was replicated 100 times.
Table 5.4. and Table 5.5 provides the raw results for the experiment I. From the Tables, the
MH index show better estimation results than that of S index under MFSCL method. The
S index is likely to underestimate the number of clusters. In all Tables, the cluster error is

defined by

cluster error = number of estimated clusters - true clusters.

Experiment 11

This experiment compares the performance of the algorithms and the indices with
o = 0.1 and I = 0.3 data sets. The clusters of generated data are basically loose and

overlap with each other. The factors of experiment is defined as following.

Sample size: { 100 }

Number of dimensions: { 2,3, 4,5 }
Number of clusters: { 2, 4, 6, 8}
Clustering method: { MFSCL, MK }

80

Sampling window: { Sphere }
Index: { 5, MH}

Again, the experiment has 64 cells. Each cell was replicated 100 times. The errors
increased dramatically from those of previous results. The number of errors increased as
the number of true clusters increased and as the dimensionality decreased and both indices
tend to underestimate the number of clusters. The results are shown in the Table 5.6 and

Table 5.7.

Both indices and algorithms performed well for the well-clustered data, the S
index has a 88% recognition rate and the MH index has a 96% recognition rate. Neither
index performed well with the weak-clustered data; S index has recognition rate of 28%
and MH index has 42% recognition rate. The MH index has higher reliability and provides
better results than those of the 8 index for both algorithms. Also, these results agree with
those of Milligan and Cooper [95] and those of Jain and Dubes [87]. Thus, the MH index

and the MFSCL were chosen in our application of ultrasonic material characterization.

81

TABLE 5.4 Errors in estimating number of clusters using S, 100

patterns, spread=0.01, overlap: 0.1, spherical window.

m
e
t
s
rm
c
2

4 clusters

6 clusters

8 clusters

 

82

TABLE 5.5 Errors in estimating number of clusters using MH, 100

patterns, spread=0.01, overlap: 0.1, spherical window.

5
R
m
c
2

4 clusters

6 clusters

8 clusters

 

83

TABLE 5.6 Errors in estimating number of clusters using S, 100
patterns, spread=0.l, overlap: 0.3, spherical window.
Methods
-1 O
2 clusters
29 30
31 27
29 34
37 35
19 51
13 82
14 84
17 83
4 clusters
14 11
17 19
21 15
13 20
36 21
26
41
49
6 clusters
11
12
8
12
3
19
20
31
8 clusters
6
8
13
5

r

U)
r

N

Error

=1
.5

UlfihINMbUN
OOOOOOOC
OOOCOOOO

.—
N

2
3
4
5
2
3
4
5

UlbUNUIbUN

UlbUNUI‘UN

 

84

TABLE 5.7 Errors in estimating number of clusters using MH, 100
patterns, spread=0.l, overlap: 0.3, spherical window.

Methods

1
N

0

Dim. 2 clusters
43

62

78

83

32

67

82

88

4 clusters
5

18

29

37

37

61

78

85

6 clusters
5

8

ll

20

30

45

59

67

8 clusters
11

10

17

20

11

16

25

29

Error -3

mauuuauu
OOOOOGOO
OOOOOOOO
—-t=~J-‘-\IAO\UJA
~4>woowNA~

2
3
4
5
2
3
4
5

OOOOOUJUIM

“814000108th

MthNUIbb-IN

 

85

5.3 Ultrasonic material characterization

In order to test the proposed method, several synthetic data sets and a well-known data
set ’iris’ were used. Then, a test phantom containing four different materials is scanned by
our acoustic imaging system and the data set is used for material characterization. Finally,

a slice of brain sample was examed.

To test the ability of pattern classification, a weakly clustered data set and a well
separated data set both containing two features, four clusters and 50 patterns per cluster are
presented to the neural network. These data sets are shown in Figs. 4.6(c) and 4.6(d). The
clustering results are verified by MH versus number of clusters plot as shown in Fig. 5.9.
The plot shows the significant knees of both cases occurred at an optimal number of
clusters, i.e., four clusters. Then, the well-known test data set ’iris’ was used. This four-
feature data set contains three categories of iris and each category has 50 data patterns. The
clustering result, shown in Fig. 5.9, suggests the desirable number of clusters for the given

data set.

A test phantom which contains four different materials (plexi glass, aluminum, lead, and
copper) with same thickness (6.24i0.01 mm) as shown in Fig. 5.10(a) is scanned by our
acoustic scanning system. A area of 60 mm by 40 mm of the sample is scanned with step
resolution of 1 mm. The structure arrangement of the phantom is shown in Fig. 5.10. Five
features are extracted from the echo return of the phantom.The dependency between
features is shown by eigenvector projection of the five features onto two-dimensional
space, as shown in Fig. 5.11. Two of the five features, peak frequency and total energy, are
discarded’due to their strong dependency to central frequency and correlation coefficient
respectively. The reduced 3-feature data set is then presented to the clustering network.
Fig.5.9 shows the clustering result. Fig 5.12 (a) shows the traditional acoustic C-scan
image. Figs. 5.12 (b)-(d) demonstrate the images reconstructed from clustering information

using different number of clusters. Notice that different color shades represent different

86

types of materials. With four clusters, the different types of materials (plexiglass,
aluminum, lead, and copper) are being differentiated (different color shades). To see the
ability of the system in retrieving information from multi-layered structure, a homogeneous
material was placed between the target and the transducer. A 3.25 mm plexiglass plate was
placed on top of the phantom. Fig. 5.13(a) shows the traditional acoustic C-scan image.
Figs. 5.13(b)-(d) show the images resulted from clustering information using different
number of clusters. The results are practically the same as those without the plexi glass plate
in place. This indicates that the technique proposed can be used to identify materials inside
a structure as well as being exposed. For the simulation data sets and the four-material
phantom, the proposed method performs well distinguishing various materials. The
computation time of the clustering process is in the order of tens of seconds to few minutes

on the SUN SPARC station IPX.

Finally, a slice of human brain sample with hemorrhaged tumor, as shown in Fig. 5.14,
was used. The clustering result suggests that separate the data set into four clusters is the
best and is shown in Fig. 5.9. The C-scan and reconstructed images from the clustering
information are shown in Fig. 5.15. Fig 5.15(a) shows the C-scan image. Fig. 5.15(b)-(f)
depict the images reconstructed from clustering information using different number of

clusters.

For the simulation data and the material phantom, the proposed method performs well
and materials were classified as expected. For the hemorrhaged tumor brain sample, the
clustering results do show the abnormal tissue portion. However, a detail identification of
the brain sample requires further investigation for conclusive results. On the other hand,
experts should joint and contribute their knowledge to the system while the system is
examining amount of samples. The computation time of the clustering process for the brain

sample is in the range of tens of minutes for our example.

87

 

0.95

 

0.9

MH index

0.75

0.7

 

 

l 1 J

I.
0.65 ‘

2.5 3 3.5 4 4.5
No. of clusters

 

 

Figure 5.9. Modified Hubert’s Gamma index v.s. number of clusters plots for
different data sets.

88

 

  

substrate CCh(

  

Copper

.Aluminum I

Plexiglass

 

 

 

(a)

  

scanning
transducer

       

0

  

4 \\\\\\\\\\\\\\\\\\\\\\\§}"A
Pl ex i glass

 
       
 
 

  

 

Figure 5.10 (a). Top view of phantom. (b). Phantom covered with plexiglass plate.

89

 

 

 

 

8 I l I I I I I
a. correlation
6 - .
" total energy
2 '- -(
i
._ o . .
It
.2 . .
4 ~ .
111 peak frequency
-6 1- ‘ ..
,4 central frequency
_8 l l l l l J_ l
6 -6 -4 - -2 O 4 6 8
Axis I

Figure 5.11. Linear (eigenvector) projection of five features onto two-dimensional space.

90

File = [az\triref.ingl

   

; Ia:\tr 11:1112. ingI

(a) (b)

File : [a:\triclu3.ing] File : [a:\triclu4.inq]

   

(C) (d)

Figure 5.12. Images of phantom. (a). C-scan image. (b). Reconstructed image when
segmented data- set into two clusters. (c). Three clusters. ((1). Four clusters.
Different colors represent different clusters.

91

 

File : [a:\ltriclu2.1nql

(b)

File : [a:\ltriref.ing]

File : fa:\ltriclu4.ingl

 

File : Ia:\llriclu3.ing]

(c) (d)

 

Figure 5.13. Images of phantom covered with plexiglass plate. (a). C-scan image. (b).
Reconstructed image when se mented data set into two clusters. (c). Three
clusters. (d). Four clusters. Di erent colors represent different clusters.

92

 

Figure 5.14. Picture of human brain sample with hemorrhaged tumor.

93

File : [clu2.inn]

(b)

File : [brain54a.inql

 

File = [clu4.inql

FIIP : [(‘lu5.rngl : lb:\(‘lufi.rngl

     

Figure 5.15. Images of human brain sample with hemorrhaged tumor. (a). C-scan image.
Reconstructed image when segmented data set into two clusters. (c).
Three clusters. ((1). Four clusters. (e) Five clusters. (1). Six clusters.

Chapter 6

6.0 Conclusions

Ultrasound is a very useful tool in a wide variety of applications, such as
nondestructive evaluation for composite materials and diagnosis in medical field. Due to
the complexity of acoustic beam profile and the random nature of its interaction with
scatters inside the investigated medium, conventional time domain and frequency domain
methods suffer from some inherent limitations in many applications. This thesis presents
an approach for ultrasonic material characterization.By utilizing many aspects of most of
the echo information and features of artificial neural networks, the proposed method do

achieve some results that conventional methods could not offer.

6.1 Summary
Some basic theory of linear acoustic waves have been reviewed. Time domain and
frequency domain methods for acoustic parameters estimation were described. Their

advantages and limitations were also discussed.

Unlike the traditional ultrasonic detection technique using A-mode signal directly
for material characterization, the proposed approach is to extract features from the echoes
and form the data pattern set. Then, artificial neural networks principle is employed to

perform the task of unsupervised Ieaming. The data pattern set is then fed to the

94

95

unsupervised learning mechanism to obtain the clustering information. Materials were
therefore classified by the clustering results in the form of color images. Different colors
represent different clusters (acoustic properties). To ensure the unsupervised learning
algorithm is efficient and the clustering results are trustful, a Monte Carlo study was
performed in order to have a statistic knowledge on different algorithms (MFSCL and
MK) and the cluster validity indices (S and MH). Finally, an unsupervised learning
algorithm (MFSCL) and a index (MH) were chosen to employ in the ultrasonic material
characterization system. The results demonstrate the superior performance of our

methodology over the traditional methods.

6.2 Future work
Some concerns about ultrasonic detection system in general are its clarity,
accuracy and real-time capability. Among the line of this research work, there are some

topics to be pursued in the future.

(1). Hardware implementation: Most of the processing time of our system is
consumed in carrying out tasks of signals processing and unsupervised
learning. These are mainly implemented by software. The system
performance can be speed up dramatically if hardware implementation is

achieved.

(2). transducer array: In stead of using the stepping motors to control the
movement of a single transducer, by the use of transducer array triggered by
the multiplex electronic circuitry will make the system more closer to real-

time operation.

(3). Clinical evaluation: To improve the accuracy in the clinical evaluation, two

aspects of works should be explored. First, build a knowledge base of

96

acoustic response of various biological tissues by the help of medical
experts. Second, perform a thorough study on the relationship between the
acoustic frequency response and the size of scatters in the biological tissue.
This will provide us wit better understanding of potential applications of our

system in noninvasive detection in general.

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