Review: Integration of EMI Technique with Global Vibration Technique
By
Suteng Ni
B.E., Civil Engineering
Nanyang Technological University, 2012
SUBMITTED TO THE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING IN CIVIL AND ENVIRONMENTAL ENGINEERING
AT THE
ARCHIVES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INS1'TUTE
OF TECH-NOLOGY
JUNE 2013
@2013 Suteng Ni. All rights reserved
L(BRARIES
The author hereby grants to MIT permission to reproduce and distribute publicly paper and
electronic copies of this thesis document in whole or in part in any medium now known or
hereafter created.
Signature of Author
Department of Civil & Environmental Engineering
May 10, 2013
Certified by
Jerome J. Connor
Professor of Civil & Environmental Engineering
Thesis Supervisor
Accepted by
II
'Heili M. Nepf
Chair, Departmental Committee for Graduate Students
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2
Review: Integration of EMI technique with Global Vibration Technique
By
Suteng Ni
Submitted to the
Department of Civil and Environmental Engineering on May 10, 2013
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Civil and Environmental Engineering
ABSTRACT
In the last decade, the development of Structural Health Monitoring (SHM) has been
skyrocketing because of the serious consequences that come with structural failure. Traditional
damage detection techniques, also known as local damage detections, such as visual inspection
and ultrasonic testing, have been implemented since the mid 20th century. However, these
techniques often require prior knowledge of potential damage locations and require bulky
testing equipment. Alternative techniques, the Global Vibration Techniques, were first
introduced to analyze the modal information of the structure to assess its overall health state.
The drawback of these methods is their insensitivity towards the incipient local damage. With
the development of sensor technology, a local damage detection technique, the Electro-
Mechanical Impedance (EMI) method, has emerged. EMI measures the electrical admittance by
the impedance analyzer, and evaluates the health status of the structure by comparing the
baseline signature with the damaged signature. It allows users to access the structure remotely,
but it loses its sensitivity when the damage is significant. Therefore, Bhalla, Shanker and Gupta
proposed integrating the Global Vibration Techniques with the EMI technique so as to tap on
the strengths of the respective techniques. This new method, the Integration of Global
Vibration Technique and EMI Technique, draws on EMI's high sensitivity towards early incipient
damage and Global Vibration Techniques' sensitivity at late damage stages. The author further
examines the integrated method in terms of practicality and scalability. With considerations of
some sensor related issues, the author would not suggest to apply the method to real
structures.
Thesis Supervisor: Jerome J. Connor
Title: Professor of Civil and Environmental Engineering
3
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4
ACKNOWLEDGEMENTS
First and foremost, I would like to express my deep and sincere gratitude to my thesis
Supervisor, Prof. Jerome J. Connor. The thesis could not have been accomplished without his
guidance and encouragements.
Secondly, I am very grateful to Pierre Ghisbain for his insightful comments and precious
suggestions.
Thirdly, I would like to extend my great gratitude to the Singapore University of Technology
Design (SUTD) for giving me the opportunity to study at such a prestigious university.
My special thanks go to Miao Shi, Heng Li, John Goo, Wanling Chong, Tim Lim, Siyuan Cao,
Andong Liu and Yaqing Zhang for their generous support.
Last but not least, I would like to thank my parents for their constant supports.
5
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6
Table of Contents
ABSTRACT
3
ACKNOWLEDGEMENTS
5
TABLE OF CONTENTS
7
LIST OF FIGURES
9
LIST OF TABLES
9
CHAPTER 1 INTRODUCTION
10
1.1
1.2
BACKGROUND
10
OBJECTIVES AND SCOPES
11
CHAPTER 2 LITERATURE REVIEW
12
2.1 NONDESTRUCTIVE EVALUATION (NDE)
2.2 STRUCTURAL HEALTH MONITORING (SHM)
2.2.1 GLOBAL INTERROGATION TECHNIQUE
2.2.2 LOCAL INTERROGATION TECHNIQUES
2.3 SMART MATERIAL
2.4 PIEZOELECTRIC TRANSDUCER
2.4.1 PIEZOELECTRIC EFFECT
2.4.2 PIEZOELECTRIC MATERIALS
2.5 ELECTRO-MECHANICAL IMPEDANCE (EMI) TECHNIQUE
12
12
14
16
17
18
18
20
22
CHAPTER 3 SUMMARY OF INTEGRATION OF EMI TECHNIQUE WITH GLOBAL VIBRATION TECHNIQUE 24
3.1 MODELING OF EMI TECHNIQUE
3.1.1 ONE DIMENSIONAL (1D) MEMBER MECHANICAL IMPEDANCE MODELING
3.1.2 Two DIMENSIONAL (2D) MEMBER MECHANICAL IMPEDANCE MODELING
3.2 GLOBAL VIBRATION TECHNIQUES
3.3 PRINCIPE OF INTEGRATION METHOD
24
24
26
28
32
CHAPTER 4 DISCUSSION
38
4.1 EXTERNAL FACTORS
4.1.1 TEMPERATURE
4.1.2 LOADS
4.2 SCALABILITY
4.3 SENSOR RELATED ISSUES
4.3.1 BONDING LAYER
4.3.2 SENSING REGION
4.3.3 SENSOR OPTIMIZATION
38
38
40
42
43
43
44
45
CHAPTER 5 CONCLUSIONS AND OUTLOOK
46
7
REFERENCE
48
APPENDIX
51
8
List of Figures
Figure 1 The four diagnostic levels in structural damage assessment. (Rytter, 1993).............14
Figure 2 Common Materials and Response (Chee-Kiong Soh, 2012) .......................................
18
Figure 3 Illustration of piezoelectric effect..............................................................................
Figure 4 Modelling of a piezoelectric plate under the action of stress and electric field (I D
19
interaction). (Ram a Shanker, 2011)................................................................................
20
Figure 5 Tetragonal perovskite structure transforms to cubic structure when temperature
increase beyond Curie tem perature................................................................................
21
Figure 6 Circuit for approximating PZT-Based EMI (Soh, 2009)..............................................
23
Figure 7 Interaction model of PZT patch and host structure (Chee-Kiong Soh, 2012).............25
Figure 8 A square PZT patch under 2D interaction with host structure (Chee-Kiong Soh, 2012).26
Figure 9 Conductance and susceptance plots of PZT patch bonded to the host structure (CheeKio n g So h , 2 0 1 2 )...................................................................................................................2
7
Figure 10 Experiment setup for mode strain shape (Chee-Kiong Soh, 2012)...........................29
Figure 11 Typical FFT of response from PZT patch (Chee-Kiong Soh, 2012).............................29
Figure 12 Curvature mode shapes including mode 1,2,3 (Rama Shanker, 2011).....................31
Figure 13 Bhalla, Shanker and Gupta's experiment study for the integration method (CheeKio ng So h , 2 0 12 )...................................................................................................................3
2
Figure 14 Different stage of damage severity (Chee-Kiong Soh, 2012)...................................33
Figure 15 Conductance signature of sensor 6 (Chee-Kiong Soh, 2012)...................................34
Figure 16 Changes in stiffness identified by sensors ...............................................................
35
Figure 17 Curvature mode shapes of steel beam at different stages including mode 1 and 2
(Chee-Kio ng So h, 20 12)........................................................................................................36
Figure 18 Plot of D.1 for the Beam (Chee-Kiong Soh, 2012).....................................................37
Figure 19 Conductance signature for PZT patch bonded beam specimen (a) and plate (b)
specimen with ambient temperature changing from 30 to 80 degree (Yaowen Yang, 2008)
..............................................................................................................................................
39
Figure 20 Probability of detection (Pd), considering damage element located far from source of
excitation: (a)mode shape curvature, (b) change in flexibility; (c) change in flexibility
curvature methods, (d) strain energy method (C.Cremona, 2005).................................41
Figure 21 Effect of delamination on the fundamental mode curvature (Y.Zou, 1999) ............ 43
Figure 22 Conductance signatures for PZT patches bonded on a plate specimen with different
bonding thicknesses. (a) 10-20 kHz. (b) 240-260 kHz. (Yaowen Yang, 2008) .................. 44
List of Tables
Table 1 Sensitivities of common local techniques (Chee-Kiong Soh, 2012) .............................
16
Table 2 Various types of piezoelectric material (Miao, 2010)..................................................20
9
Chapter 1 Introduction
1.1 Background
In the past hundred years, many catastrophic structural failures including aircraft, bridges,
dams and radio towers. As a result, there has been not only a great loss of revenue, but also
devastating loss of life. A recent incident, the sudden collapse of a building in Savar, Bangladesh,
caused more than 350 deaths and 2500 casualties. (List of structural failures and collapses) The
devastating consequences of structural failure demonstrate the need for periodic structural
monitoring, to ascertain the structure's strength and performance, with the added ability to
detect damage at the earliest possible stage.
In general, most of the damage-detection methods are based on Non-Destructive Evaluation
(NDE) methods, using visual or localized experimental methods such as acoustic or ultrasonic
methods, magnetic field methods, radiography, eddy-current methods and thermal field
methods. (Worden, 2013) The methods mentioned above are considered local inspection
methods and need to be conducted near the damage location. With additional testing, the
exact location of the damage can be identified. However, in inaccessible or hard to access
locations, the usage of local damage detections is limited.
With the development of sensors, a piezoelectric material called Lead Zirconate Titanate (PZT)
has been widely used as both actuator and sensor, and has made the Electromechanical
Impedance (EM I) technique possible. This method has the advantage of detecting the damage
remotely. Besides the sensors, the LCR (Inductance L,Capacitance C,and Resistance R)meter is
the other key component, which measures the electro-mechanical (EM) admittance of the
bonded PZT patch. The difference between the baseline signature and damaged signature give
us the health status of the structure.
Global interrogation techniques evaluate the overall performance of the structure by examining
the changes in the vibration characteristics of the structure. In other words, the global methods
can be achieved with fewer sensors to monitor the severity of the damage. (Fritzen, 2005) The
drawback of this method isthat the ambient noise sometimes can be overwhelming.
10
In the last few years, much research has been dedicated to studying how to combine various
sizes of sensors to tackle incipient damage. (Gtuhae Park, 2003) Recently, Bhalla proposed a
new approach to Structural Health Monitoring (SHM), when integrate the EMI technique with
the Global Vibration Technique and use the same set of sensors. (Rama Shanker, 2011)
1.2 Objectives and Scopes
The main objective of this thesis is to further study the new approach proposed by Bhalla, the
integration of the EMI Technique with the Global Vibration Technique, with respect to
practicality and scalability. For practicality, external factors such as temperature, load, etc. will
be examined. In addition, the possibility of implementing the technique in complex structures
will be discussed. Last but not least, other sensor related issues will be presented.
11
Chapter 2 Literature Review
2.1 Nondestructive Evaluation (NDE)
Ingeneral, there are two kinds of structural defect detection. One isthe destructive evaluation
and the other one is non-destructive evaluation (NDE). NDE has very wide range of application
because of its high efficiency and low cost. In traditional NDE, the testing device is external to
the structure. Moreover, the data isobtained under careful examination. Furthermore, the
measured data will be further processed to assess the structure. There are many nondestructive evaluation (NDE) inspection techniques including Ultrasonic Testing (UT),
Radiographic Testing (RT), Liquid penetrant Testing, Magnetic Particle Testing, and
Electromagnetic Testing (ET). Among all of these techniques, UT has been most used for several
decades. (Krautkramer, 1990)
Generally, certain measurements are taken when Ultrasonic NDE is performed. For instance,
Wave Amplitude, angle of wave deflection, time of flight (TOF). Because all these parameters
help explain wave behavior. Once wave behavior can be explained, the detection can be
achieved accordingly.
Conventional ultrasonic methods encompass the pulse-echo, the pitch-catch and the pulseresonance techniques. (Blitz, 1996) Detailed explanation of the three techniques can be found
in Shi Miao's FYP report. (Miao, 2010)
2.2 Structural Health Monitoring (SHM)
SHM can be considered as a novel and improved way to perform the Non Destructive
evaluation (NDE) when only the diagnosis function istaking into account.
Various research groups have different definitions for SHM. For example, SHM is a system with
the ability to detect and interpret the adverse "changes" in a structure for the sake of
enhancing reliability and reducing life cycle costs. (Hall, 1999) (Kessler, September 2001) SHM
was also defined as "continuous, autonomous in-service monitoring of the physical condition of
a structure by means of embedded or attached sensors with minimum manual intervention, to
monitor the structural integrity of the structure." (Speckmann, September 2006) With both
12
definitions, SHM is a holistic monitoring system with integration of sensors, smart material,
data transmission, processing ability inside the structure, which can assess the structure's
health statue independently through interpreting the collected the data.
SHM has very wide range of applications, as all in-service structures require maintenance to
keep its integrity to prevent a situation of catastrophic failure. The SHM has been used for the
following sectors and detailed illustration is in the reference. (Giancarlo C. Righini, 2009)
Civil Sector
Space Sector
Geotechnical Application
Combustion - Pressure Sensors for Automotive Engines
Fuel Tanks for Natural Vehicles
Railways Transportation
Wind Energy
Oil Production and Pipeline Industry
The SHM consists of two parts, they are Diagnosis and Prognosis.
Diagnosis, is the real time monitoring of the health statue of a life structure, so the diagnosis
result will reveal the onset of damages for instance, the crack location and extent. Diagnosis is
further divided into two categories. The First one is the passive diagnosis which involves using
distributed passive sensor to obtain limited information, so the passive SHM only "listens" to be
structure but never interact with it. A passive SHM system consisting of acoustic emission
transducers, resistance strain gages, fiber optic strain gages, filament crack gages, and corrosive
environment sensors was demonstrated by Kudva et al. (Kudva, 1993) and Van Way et al. (Van
Way, 1995) Conversely, the active diagnosis that is based on actuator induced sensor
measurements to obtain unlimited information to interrogate the structure to detect the
presence of damage. Victor Giurgiutiu and Adrian Cuc presented some of the outstanding
achievement in its application to active diagnosis. (Cuc, March 2005) In short, the classification
of passive and active is depending on whether or not they involve the use of actuators
respectively.
13
Prognosis, is based on the computation of the severity of the crack to estimate the residual life
of the structure.
The continuous development of SHM brings lots of benefit as follow: (Srinivasan
Gopalakrishnan, 2011)
1. Optimize the use of the structure and minimize the chance of failure of the structure.
2. Help designers improve their products.
3. Change the maintenance services of the structure entirely.
At the same time, as Rytter proposed the five-level damage assessment scale, the highest level
requires the prognosis of the remaining lifetime of the structure. It sets a goal for SHM future
development.
Figure 1 The four diagnostic levels in structural damage assessment. (Rytter, 1993)
With the benefit SHM brought to the society and guidance of the five level damage
assessments, SHM achieved successful development. In fact, the development of sensor
technologies and modeling methods are paramount to the success of SHM. As the sensor
technology advanced, the number of sensors mounted on the structure reduced. At the same
time, the data are also more accurate with the high sensitivity of the improved sensors. The
development of modeling helps explain the measured data significantly.
2.2.1 Global Interrogation Technique
In general, the global interrogation techniques apply to the complex structures to examine the
change in the vibration characteristics. The assumptions behind the theory are that damage will
cause changes in stiffness, mass or energy dissipation of the system. Thus, the global dynamic
14
response will alter accordingly. By comparing the initial and final state of the system, damage
detection can be achieved. (Worden, 2013) Based on the nature of imposed disturbance, global
interrogation method can be classified into static and dynamic global interrogation technique.
2.2.1.1 Static Global Interrogation Technique
The most well known static global interrogation techniques measure the displacement and
strain correspondingly under the static force. In 1994, Banan et al first introduced the static
global technique, which involves applying a static force at certain nodal points of the structure
and measuring corresponding displacement response. With the information of displacement
response, other parameters that indicate the health state of the structure can be derived. The
major drawbacks of this method are that tedious computation, high difficulty to establish the
reference and contact measurement. While for the static strain measurement proposed by
Sanayei and Saletnik, its advantage over the displacement measurement technique is that the
surface strain can be measure without establishing the reference frame. The application of this
method is limited to certain structure size.(Chee-Kiong Soh, 2012)
2.2.1.2 Dynamic Global Interrogation Technique
For dynamic global interrogation technique, the entire structure will be excited by low
frequency actuation, which can be either harmonic or impulse. The corresponding response,
such as displacement, velocity or acceleration can be captured at specific location along the
structure. By reviewing the change in its first few modes of the structure, it helps understand
the damage location and severity. With the development of sensor technology, testing
hardware and data processing techniques, more researchers came up with smart algorithms
under the guideline of the fundamental principle, for instance change in stiffness method,
damage index method. However, the effectiveness of the method limited to structure up to
certain scale. When it comes to building and offshore structure, the their responses
demonstrate high level of complexity. In short, below are the summarized shortcomings of
dynamic global interrogation techniques. (Chee-Kiong Soh, 2012)
1.
Low sensitivity toward local incipient damage
2. High adaption cost
15
3. High sensitivity toward ambient noise.
4. Bulky test equipment
5. Applicable to structure with simple geometry and configuration
6. Have difficulty to handle multiple-damage case.
2.2.2 Local Interrogation Techniques
Local interrogation techniques are the other damage detection approaches, which are opposed
to the global interrogation techniques and most of them are NDE-based damage detection
methods. As mentioned before, visual inspection, acoustic or ultrasonic methods, Magnetic
field methods, radiography, eddy-current methods and thermal field methods are very effective
tool to identify the local damage location and severity. (Worden, 2013)
Minimum detectable
Technique
crack lengthlength
High probability
(>95%) detectable
5-6 mm
2 mm
Ultrasonic
Eddy currents
Remarks
Dependent upon structure
geometry and material
Suitable for thickness
(low-frequency)
2 mm
4.5-8 mm
Eddy currents
(high-frequency)
2 mm (surface)
0.5 mm (bore holes)
2.5 mn (surface)
1.0 mm (bore holes)
X-ray
4 mm
10 mm
Magnetic particle
2 mm
4 mm (surface)
Dye penetrant
2 mm
10 mm (surface)
<12 mm only
Dependent upon structure
configuration. Better for
thickness >12 mm
Table I Sensitivities of common local techniques (Chee-Kiong Soh, 2012)
In ultrasonic inspection, ultrasonic transducer will be placed on the testing objective and it will
generate a short ultrasonic wave (frequency ranging from 0.1-15MHz). As the wave propagates
along the object, it will reflect back once it encounters the flaw and be captured by the
transducer. By evaluating the arrival time and amplitude change of the reflected wave, the
16
damage can be identified. However, the testing equipment can be bulky and large data take
time to process. (Ultrasonic Testing)
Other method such as X-ray may have potential hazard to inspector and the eddy current limits
its test range to the surface of the structure. In addition, most of methods are operated
manually.
In general, the local interrogation techniques often require the inspector to know vicinity of the
damage location. However, the potential damage location may not be accessible. Therefore,
the local interrogation techniques are preferred when the potential damage location is
accessible in the structure with less complexity. Hence, there is a great need to develop realtime, autonomous, efficient monitoring techniques to replace the exiting ones.
2.3 Smart Material
The techniques presented in the previous sections are considered as conventional SHM
methods, which involve bulky test equipment and are passive techniques to measure the
physical response of testing object such as displacement and strain. As the development of the
sensor technology, the "smart material" came to the people's eye as new invention. (CheeKiong Soh, 2012) One of its definition is that Smart materials are designed materials that have
one or more properties that can be significantly changed in a controlled fashion by external
stimuli, such as stress, temperature, moisture, pH, electric or Magnetic field. (Smart material)
Most of smart materials are considered as solid-state transducer with following properties
including piezoelectric, pyroelectric, electrostrictive, magnetostrictive, piezoresistive,
electroactive or others. (Inpil Kang, 2006) The diagram shown below illustrates the common
smart materials and its associated stimulus-response.
17
1) Stress
(2) Electric field
Heat
Electric field
Temnperature, pressure,
mechanical strain
M agnetic field
Piezoelectric
material
(1) Electric charge
(2) Me chanical strain
Shape memory
Original memoriz
ed shape
Electro-rheological
fluid
Change in viscosit
(Internal damping )
. Optical fiberChneiop-
Change in opto-
Magneto-strictive
material
Mechanical strain
signals
Oelectronic
Figure 2 Common Materials and Response (Chee-Kiong Soh, 2012)
2.4 Piezoelectric Transducer
2.4.1 Piezoelectric Effect
The piezoelectric effect was first discovered by Jacques and Pierre Curies Brothers and it
describes the relationship between the mechanical stress and electrical voltage in solids. Inthe
other words, it is understood as the conversion of electrical pulses to mechanical vibrations and
the conversion of returned mechanical vibrations back into electrical energy. The piezoelectric
effect is a reversible process for instance, an applied mechanical stress will generate a voltage
and an applied voltage will change the shape of the solid by a small amount. (Piezoelectric
material)
18
cebi.
.
9pp qa
positiv charge
to
ntor~i
a al
Iakd
4
c"nsr o
n~g*av chrg
1.The plazeelectric effect casm crystal materIals lie quartz to generate s electric chags wheO
the crysta imate.
rat Iscompressed, tWisted, or pulhed. The reverse Also Istrue, n the crystal rateril cMpresses or apands when
an electric elstage Isapped.
Figure 3 Illustration of piezoelectric effect
The constitutive relationship for piezoelectric materials, under small field conditions are (CheeKiong Soh, 2012):
(2.1)
D, ={TE +d,,T,,
jk j +SE
Si =d E, + s.T,,,
S k =d
c
km
T
(2.2)
The first equation demonstrates the direct effect, while the second equation shows the
converse effect. In general, the above can be rewritten into the following tensor form (CheeKiong Soh, 2012):
I
D
S
dd
dc
SE
J[TJ
E
(2.3)
where D is the electric displacement vector, S is the second order strain tensor, E is the applied
external electric field vector and T is stress tensor. E is the second order dielectric permittivity
tensor under constant stress, dd is the third order piezoelectric strain coefficient tensors,
S
the fourth order elastic compliance tensor under constant electric field. The superscripts "d"
and "c" indicate the direct and converse effect of piezoelectric materials.
19
is
1
w
Figure 4 Modelling of a piezoelectric plate under the action of stress and electric field (I D interaction).
(Rama Shanker, 2011)
2.4.2 Piezoelectric Materials
Various types of piezoelectric materials are available. (See Table 2)
* Quartz SiO2
Barium titanate BaTiO3
" Zinc oxide ZnO
* Berlinite AIPO4
Lead zirconate titanate PZT
" Aluminum nitride AIN
* Gallium orthophosphate
" Polyvinylidene fluoride
GaPO4
PVDF
" Tourmaline
" More piezo materials
Table 2 Various types of piezoelectric material (Miao, 2010)
20
These materials are commonly ceramics with a perovskite structure (See Figure 5) perovskite
structure exists in two crystallographic forms. They are tetragonal structure and cubic structure.
When the temperature is above the Curie temperature, it appears in cubic structure. While
when the temperature is below the Curie temperature, it transforms to tetragonal structure
and each cell has an electric dipole in the tetragonal state. A mechanical deformation can
decrease the separation between the cations and anions, which produces an internal field or
voltage. (Azom.com)
a)
*
Ba2+
(b)
020
T4
T
Figure 5 Tetragonal perovskite structure transforms to cubic structure when temperature increase beyond
Curie temperature
One of the commercially available piezoelectric materials is piezoceramics and one of most
commonly available piezoceramics is Lead Zirconate Titanate (PZT). PZT is made of solid
solution of PbZrO 3 (53%) and PbTiO 3 (46%). High strength, chemically inert and relatively low
cost to manufacture are the three major attributors for its popularity. Moreover, PZT can be
easily produced in various shapes such as tubes, rings, discs, plates and hemispheres with
extremely high precision. Other typical PZT characteristics include:
1. Wide range of frequencies in transit and receive
2. High output, low drive material
3. Ability to use with low voltage or high voltage
21
4. Good mechanical and acoustic coupling.
However, its fragility, brittleness and low tensile strength limit application. Specifically, PZT may
be unable to endure bending because of its poor conformity and its electrical properties may
fluctuate under unstable temperature. (what is "PZT"?)
2.5 Electro-Mechanical Impedance (EMI) Technique
EMI technique was considered as a promising tool for real-time structural damage assessment.
(Gyuhae Park, 2000 ) Professor Craig A. Rogers and his students made huge contributions to the
development of EMI Technique. The direct and converse electro-mechanical properties make
PZT a good sensor candidate for the EMI techniques. The general principle of the method is to
monitor the variation in the structural property caused by the presence of damage, which is
similar to global dynamic interrogation method. The key difference is that EMI techniques
employ high frequency excitation with range of 30-400khz, while the other one uses low
frequency. Comparing with structural mechanical impedance, the impedance of piezoelectric
material is easier to measure by making full use of the PZT's material property. When the PZT is
bonded to the testing object, the structural mechanical impedance is directly related to the
electrical impedance of the transducer. Therefore, the presence of damage will affect its
structural mechanical impedance initially, which will affect the transducer's electrical
impedance eventually. As the EMI technique requires high frequency excitation, the
wavelength of the excitation will be shorter, which has higher sensitivity toward the damage.
(Gyuhae Park, 2000 ) The impedance can be measured FFT analyzer with the following circuit.
22
VO
Figure 6 Circuit for approximating PZT-Based EMI (Soh, 2009)
Here the R, represent the sensing resistor. As you can see from the schematic diagram, the Rs is
in series with the PZT transducer, so output voltage is proportional to the current passing
through the sensing resistor. Here, we usually use the amplitude of the current called electrical
admittance to record the state of the structure.
23
Chapter 3 Summary of Integration of EMI Technique with Global
Vibration Techniques
With the brief literature review, we understand that the global vibration techniques are capable
of detecting the overall health state of the structure by identifying the changes in the first few
natural frequency. However, the tedious computation limits the application of the method. On
the other hand, the EMI technique, which is introduced in the previous chapter, is good
approach for local damage detection. Bhalla, Shanker and Gupta believed that the combination
of the EMI technique and Global Vibration Technique works the best for damage detection. In
this chapter, firstly, the modeling of EMI technique will be presented in details and then the
Global Vibration Techniques. Lastly, the application of the integration method will be
elaborated.
3.1 Modeling of EMI Technique
3.1.1 One Dimensional (1D) Member Mechanical Impedance Modeling
Even though there are many ways to model the interaction between the host structure and the
PZT transducer, Liang's approach was first proposed in 1993 considering as one of the best
approaches. (Chee-Kiong Soh, 2012) Basically he made the following assumptions,
1.
The PZT patch behaves as a thin bar with only axial vibration.
2.
Electric field in direction 3 is uniform.
3.
Zero displacement at center of the patch.
4. The dynamic stiffness of the host structure remains the same through the bonded area.
The following schematic drawing shows the modeling of PZT patch - structure interaction.
24
I (XI
Alternating electric
PVT Patch
field source
o
structure
tc
PZT patch
Of .l
mechanical
fixityStructural
mpedance
Figure 7 Interaction model of PZT patch and host structure (Chee-Kiong Soh, 2012)
As stated in the previous assumptions, one-dimensional member is considered. Therefore, the
vibration in the direction 2 can be ignored. In addition, the size of PZT patch makes it unlikely to
reach the resonant frequency of the host structure. Hence, the vibration in direction 3 can be
ignored as well.
With the above assumptions, equation (2.1) and (2.2) can be simplified as follows. (Chee-Kiong
Soh, 2012)
D= E 3E 3 +d
S1 =
T
T,+d
3
T,
31 E 3
(3.1)
(3.2)
YE
D3 is the electric displacement. S1 is the strain and T1 is stress. Both of them are in the X
direction. YE and ET are the Young's modulus of elasticity and electric permittivity respectively.
At the same time, the following dynamic force equation can be obtained.
Y
-
ax2
= P.
at2
(3.3)
With the boundary condition: u=0 at x=0, the u can be solved.
Together with the simplified PZT constitutive equation (3.1) and (3.2), the one-dimensional (1D)
EM admittance (the inverse of impedance) can be derived as follows,
25
Y=
wLE33-
+
h
Z
(3.4)
j
Z+Z,
W1
where o is the excitation frequency; w,l,h are the dimension of the PZT patch (width, length,
thickness);
K
isthe wave number, which is equal to w
. Z and Za are the mechanical
impedance of the host structure and PZT transducer respectively. Therefore, the measurement
of the mechanical impedance can be achieved by measuring the Y (electric admittance) (Soh,
2009)
3.1.2 Two Dimensional (2D) Member Mechanical Impedance Modeling
Roundar% S
P/
I patch
inte~ratwn frce at boundarN)
Nodal line
"Unknown" host stucture
Figure 8 A square PZT patch under 2D interaction with host structure (Chee-Kiong Soh, 2012)
The traditional definition of Mechanical Impedance of the structure isthe driving force over the
resulting velocity at the end of PZT patch (drive point). In fact, the force transmission between
the PZT patch and host structure happens along the entire boundary of the patch. Moreover,
the earlier assumptions, for example, the patch is small compared with host structure are still
valid. As the planar force causes the planar deformations in the PZT patch, Bhalla and Soh
redefined the mechanical impedance as "effective mechanical impedance". (Chee-Kiong Soh,
2012)
Z,4
a,,eff =
(3.5)
1f
26
deff can be obtained by differentiating the uff (effective displacement) with respect to the time.
u is the change of surface area of the patch over its perimeter in the undeformed condition.
Together wit the PZT constitutive relation and the dynamic force equation, the expression of
the electrical admittance for the 2D member is shown below.
12 -Y = 4coj- i T-
2d yE
-
h
33(1
-v
)
+
2d32Y E
(I -v
Znff1
Z,
i
(
"I
) (Zs,,ff+
,f
where 1 is half-length of the patch, v is the Poisson's ratio and K is (o
Zs,,
(3.6)
Icl
yE V)
e (.,,
Z. e] and
are the effective impedance of the PZT patch and the host structure respectively.
Compared the electric admittance expression for 1D and 2D member, the interaction between
the patch and 2D member is effectively represented by a single complex Zs,,ff , which is a big
advantage. (Chee-Kiong Soh, 2012)
The EM admittance Y is consisted of a real parts (conductance, G) and imaginary parts
(susceptance B). The commercial impedance analyzers can record the conductance and
susceptance signature in the frequency domain. The typical plots of conductance and
susceptance are shown below.
0.0008.
0.008
0.00070.0006-0.006S0.00046.0
140
142
144
146
148
150
140
l'requency (kinz)
142
144
146
148
150
Frequency (kilz)
Figure 9 Conductance and susceptance plots of PZT patch bonded to the host structure (Chee-Kiong Soh,
2012)
The baseline signature has to obtain at the initial state of the host structure. Any changes in the
conducetance or susceptance of the PZT patch give relevant information about the health state
of the structure.
27
3.2 Global Vibration Techniques
For dynamic system, the general equation isas follows,
Mi+Ca+Ku=F(t)
(3.7)
where M is the mass of the system, Cisdamping and Kisthe stiffness. iii,u are the
acceleration, velocity and displacement vector. F(t) isthe force function. For free vibration, the
F(t) = 0.
From the equation (3.7), it isclear that the basic structural parameter are the mass, stiffness
and damping, As discussed earlier, the Global Vibration Techniques are taking the structure as a
dynamic system, so the damage will cause the change in the above parameters. In general,
there are two approaches to monitor those parameters, one is called Traditional-Type Damage
Detection (TTDD) and other one isthe Modern-Type Damage Detection (MTDD). The TTDD is
taking advantages of the mechanics of the structure by measuring modal damping, modal
shapes etc., while the MTDD measures the real time response signal of the structure such as
Wavelet analysis, Genetic algorithm (GA) etc.. (Y.J. Yan, 2006) Since the Bhalla, Shanker and
Gupta used the TTDD to measure the strain mode shape to monitor the heath state of the
structure, the focus will be the TTDD in the following section.
For TTDD, experimental modal analysis isa common approach. According to Betti's theorem,
"for a linear elastic structure subject to two sets of forces {Pi} i=1,...,m and {Qj}, j=1,2,...,n,
the work done by the set Pthrough the displacements produced by the set Q is equal to the
work done by the set Q through the displacements produced by the set P." (Betti's theorem)
Therefore, the mode shape of the structure can be obtained by collecting the response signal
while varying the point of application of that force. The raw signals obtained from sensor have
to be processed by FFT. And then a plot of all the measurement points can be obtained as
follows,
28
Figure 10 Experiment setup for mode strain shape (Chee-Kiong Soh, 2012)
200
45 1l / IM ILd e lI
I
15 11/d Mde I
410 li IMode il
550
10(A
150
250
200
300
35
400
Rrequenc% OiW/
Figure II Typical FFT of response from PZT patch (Chee-Kiong Soh, 2012)
29
450
50
Referring to the PZT constitutive relations, the equation (3.1) can be simplified as follows,
(Rama Shanker, 2011)
D 3 =d 31T =d
(3.8)
ES
3
Because PZT transducer is designed as sensor, so there is no external electric field across its
terminal. Therefore, the term
YESI.
33E3
can be dropped out. In addition, T can be replaced with the
Moreover, we have the charge density has the following expression. (Rama Shanker,
2011)
E3
D3 =
(3.9)
h
where V is the potential difference across the terminal of PZT patch and h is the thickness of the
patch. With the above equations, the following expression can be obtained by rearranging.
(Rama Shanker, 2011)
V=
-
S,
= K,S
(3.10)
E33
The above equation demonstrates the relationship between the voltage output from the PZT
patch and the strain at measuring point.
On Top of that, we also know the relationship between the curvature and the strain as follows,
(Rama Shanker, 2011)
v =
(3.11)
d
where d is the distance of PZT from the neutral axis.
With all the information, we can obtain the curvature mode shapes of the testing object as
follows,
30
.NIi
Its
41
44M)
NI
1Q1
e
bisl anzc 0 c in
<0>
'l
211
I"
-
Ii
II,
- I fA
(I
110
2041
300
4M)
(ib
lit(
5.
-
10
11
40W
I ti
DoA nce icm)
(Fs,
Figure 12 Curvature mode shapes including mode 1,2,3 (Rama Shanker, 2011)
31
3.3 Principe of Integration Method
In the previous section, the EMI technique and the Global Vibration Technique have been
introduced separately. In the following section, the integration of the two methods will be
presented. In order to verify the integration method, Bhalla, Shanker and Gupta conducted
some experimental study.
3.3.1 Experiment Setup
Basically there are 11 equally spaced sensors placed on the top face of the steel I beam and the
damage location 800mm away from the left end.
Danage lOCUion
1
2
3
II PZT sensors (333 mmin)
4
5
6
7
8
\
9
10
Iti
-4.000mmn
Figure 13 Bhalla, Shanker and Gupta's experiment study for the integration method (Chee-Kiong Soh, 2012)
The introduced artificial damage at various stages is shown below. As you can observe from the
diagram, the steel beam experiences minor damage over the first three stages. However, when
it comes to the last stage, half of the beam is damaged.
32
1 .6 cm
.1.5 cm
1.6cm
. cmf
1.5
it c
S17e I
Stane 4
Stac c5
Siaac 6
Stae 7
Figure 14 Different stage of damage severity (Chee-Kiong Soh, 2012)
3.3.2 Incipient Damage Detection
As mentioned earlier, the Global Vibration Technique has difficulties to detect the incipient
damage. On the other hand, the EMI technique demonstrates high-level sensitivity towards
incipient damage. Therefore, the Bhalla, Shanker and Gupta proposed to utilize the EMI
technique to detect the incipient damage. The conductance signature of all sensors can be
obtained by impedance analyzer. Below is the conductance signature from sensor 6. As
discussed earlier, the damage will cause the change in the stiffness of the host structure.
Therefore, the natural frequency of the host structure will change as well. Hence the shift of the
conductance indicates the damage severity.
33
0.0003
0.00025/
No daage
.1jA
0.0002
15 Damage stage-3
100
105
110
115
120
Frequency (kilz)
Figure 15 Conductance signature of sensor 6 (Chee-Kiong Sob, 2012)
3.3.3 Damage Location Detection
As early as 1988, C.M. Harris presented the table to provide the mechanical impedance of
various combinations of spring, mass and damper. (Chee-Kiong Soh, 2012) The table can be
found in the Appendix. Therefore, the change of stiffness of the structure can be calculated at
different stages. According to Bhalla, Shanker and Gupta, the damage location coincides with
the point where the maximum changes in stiffness occur. Interpolation can be used if a
maximum change occurs between sensors.
34
PZT No.
PZT 1
PZT 2
PZT 3
PZT 4
PZT 5
PZT 6
PZT 7
PZT 8
PZT 9
PZT 10
PZT 11
k
k (1
0
Nhn)
656
8.67
7.65
5.97
8.45
6.78
8.56
653
8.56
6.63
7.89
Danage Stage 3
Damage Stage 2
Damage Stage I
k
Change
k
Change
k
Change
(10 Nhn)
(%)
(10N/m)
(%)
(10"N/m)
(%s)
6.86
9.47
8.51
6.41
8.92
7.04
9.44
6.73
8.65
6.68
7.92
4.7
92
11.2
7A
5.6
3.9
3.3
2.9
1.1
0.8
0.4
6.97
9.73
8.83
6.67
9.26
7.28
9.09
6.83
8.66
6.69
7.92
6.3
12.3
155
11.6
9.7
7A
6.2
5.4
1.2
0.9
0.4
7.44
10.54
9.53
7.20
10.03
7.70
9.37
6.83
8.66
6.69
7.92
13.5
21.6
24.6
20.7
17.5
13.6
9.5
7.2
1.2
0.9
0.4
Figure 16 Changes in stiffness identified by sensors
Besides the EMI techniques, the Global Vibration Technique is also able to identify the damage
location. As I discussed earlier, the curvature mode shape can be plotted at different damage
stages through the global vibration technique. After close inspection of the below figure, the
point that deviates the most from the undamaged baseline gives the damage location.
35
lbi
12
x
8
4
I"italicx (c~II
201
15
101
(I
0I
0
100
200
3Ott
400
Distance (cm)
Figure 17 Curvature mode shapes of steel beam at different stages including mode I and 2 (Chee-Kiong Soh,
2012)
3.3.4 Damage Detection at High Severity Stage
At the early damage stage, the damage isvery sensitive towards the EMI technique, however,
as the damage grows, the EMI loses its sensitivity because the equivalent stiffness and damping
remain still as the damage grows. Therefore, Bhalla, Shanker and Gupta introduced the damage
index (D.1) as,
N
D .1.=
(da,wged
W
-
Cundamaged)
(3.12)
n=I
The index allows user to quantify the changes in curvature at different points of the testing
object, so the severity of the damage can be identified based on the damage index. Below is the
test result for the same beam structure.
36
10
* Damage I
* Damagc 2
8-
o
Damnagc3
0 Daimagc4
=
N Damage 5
6-
eJ~
* Dai age 7
4-
I)
4Ad I I
1
2
3
4
0 DanI
5
6
7
Ilement No.
8
9
to
ii
Figure 18 Plot of D.I for the Beam (Chee-Kiong Soh, 2012)
Although the experimental study presented is carried on the object that can be assumed as
one-dimensional member, they actually expanded their damage index in 2D member and had
experiment study.
37
Chapter 4 Discussion
In the last section, the integration method has been presented in great detail. In short, Bhalla,
Shanker and Gupta proposed that EMI techniques can be used to detect the early incipient
damage and effectively monitor the damage growth at early stages, while the global vibration
techniques can be used to monitor the severity of the damage at later stages.
In 1996, Doebling et al. first defined an ideal robust damage detection scheme as being "...able
to identify damage at a very early stage, locate the damage within the sensor resolution being
used, provide some estimate of the extent or severity of the damage and predict the remaining
useful life of the structural component in which damage has been identified. The method
should also be well suited to automation, and should be independent of human judgment and
ability." (D.Montalvao, 2006)
However, it is rare that approaches can meet the above definition, because of environmental
and operational conditions such as temperature, loads, etc. As such, the practical aspects of the
integration method will be discussed in this chapter. First, external factors such as temperature
and loads will be examined. Second, the scalability of the integration method will be
scrutinized. Third, sensor related issues will be discussed.
4.1 External Factors
4.1.1 Temperature
The global vibration technique as suggested by Bhalla, Shanker and Gupta uses the curvature
mode shape method. Essentially it measures the lower frequency global response of the
structure and requires comparing the damaged signal with the undamaged signal. However,
changes in temperature may add substantial noise to the damaged signals. Hence, the
conclusion drawn from the mode shape curvature is questionable. In the case of offshore
structures, increase in temperature may increase the growth rate of marine vegetation, which
adds weight to the original structure. Therefore, the effect of change in temperature has to be
considered when implementing the curvature mode shape method. (Peter C. Chang, 2003)
38
For the EMI technique, the PZT-structure interaction makes the major contribution to the
obtained conductance. Y.W. Yang, Y.Y. Lim and C.K. Soh conducted experiments to investigate
the effect of temperature.
0.002
b2
-
30C
j01001.-
0
C6OC
- 80fC
I
0
50
I
100
I
I
150
200
250
300
200
250
300
Frequency
ft,)
(a)
B4
0.002
0.0015
I
0.001
0.0005
04
0
50
100
150
Frequency (kft)
Figure 19 Conductance signature for PZT patch bonded beam specimen (a) and plate (b) specimen with
ambient temperature changing from 30 to 80 degree (Yaowen Yang, 2008)
39
As the above figures suggest, there is huge adverse effect of temperature on admittance
signatures. Meanwhile, Bhalla also conducted similar studies and found that temperature
changes cause vertical and horizontal shifts in conductance. In order to solve this problem, he
proposed to use unit temperature change to determine the corresponding changes in
conductance. Therefore, the baseline signature can be adjusted to avoid the confusion of
temperature effect. (Chee-Kiong Soh, 2012)
In short, the change in temperature seems to be more a problem to the global vibration
method than the EMI technique.
4.1.2 Loads
Similar to temperature, external loads such as wind loads and transient live loads are a source
of noise. The noise level affects the accuracy of the measurement. A. Alvandi and C. Cremona
conducted some experiments to assess vibration-based damage identification. Based on their
findings, the strain energy method presented the best stability with regard to noisy signals
amongst the curvature mode shape method, the change in flexibility method and the change in
flexibility curvature method. The following figure illustrated their research findings. Basically,
damage detection (Pd) decreases as noise level increases but increases with lost stiffness of the
structure. (C.Cremona, 2005) Peter C. Chang proposes using 25% of the damage signal as the
upper limit for noise level. As long as the noise level is within this limit, nearly all the vibration-
based methods can successfully detect damage. (Peter C. Chang, 2003) Therefore, the
curvature mode shape method performs best under controlled environments with minimal
noise levels. The integration of strain energy method is also another good option.
40
Damaged elemnt :11
120
0
Damaged eement: 11
-L
20
10
410
10
1
0.75
(
(a)
(
0.10
(b)V
Damaged0.5
100
80
/g
(dcns:11
2
4
-
0
03
Damaged ermuentr
100
10
32.-5
3
i
151
2.5
2~0.10.
of Zi
t .A .-
20f
02
0.5
(C)
0..
Ip
0-2
10
10 0 V
:0 0(d)
Figure 20 Probability of detection (Pd), considering damage element located far from source of excitation:
(a)mode shape curvature, (b) change in flexibility; (c) change in flexibility curvature methods, (d) strain
energy method (C.Cremona, 2005)
With regards to the EMI technique, the exiting load and damage in the structure poses
challenges in damage detection. In the absence of external loadings, Bhalla found that
susceptance signatures are sensitive towards the delamination in composite structures. In the
41
absence of damage, according to Annamdas et al., conductance and susceptance can be used to
identify the direction of the external loading (axial and transverse). Without external forces, the
integration method can perform very well. However, it is unlikely that external forces will be
absent, which limits the use of the EMI technique. Small external loads within some acceptable
range may minimize this adverse effect, allowing EMI technique to be used.
4.2 Scalability
In the past, since the beginning of the SHM, vast majority of the literature concentrated on
laboratory tests and numerical simulations. In addition, the used structure usually contained
few damages, which limited the number of independent damage events occurring between
successive assessments. (Fanning, 2004) Moreover, civil structures are usually built with
relatively low levels of precision as compared with aerospace or automotive structures. In fact,
on site construction may not exactly follow structural design because of unforeseen
circumstances. On top of all these, non-uniform material may be used and idealized behavior
such as fixed connections can never be achieved. According to a recent study of damage
detection for composite structures, the delamination will increase the damping of the structure
and decrease the stiffness. While the loss of mass due to delamination is negligible, the effect
of the delamination on mode shape curvature of composite beam is significant and is shown
below. The delamination configuration and location are the sources of irregularity of the curve.
Therefore, the existence of complex materials may cause some difficulty in data interpretation.
Last but not least, linear assumption of analytical model and material may not be accurate for
structure with high level of complexity. (Peter C. Chang, 2003) The above statements serve as
criteria for scalable methods. In experimental studies of the integration method, limited
damage was introduced to simple metal beams in a controlled environment. These three
experimental conditions differ significantly from actual conditions, and therefore, there is a lack
of evidences to support scalability.
42
15% thickness
reduction
I.j
Reduction thickness
region
5
0
10
15
Grid point number
20
25
Figure 21 Effect of delamination on the fundamental mode curvature (Y.Zou, 1999)
4.3 Sensor Related Issues
Besides external factors and scalability, there are other interesting issues worth mentioning
such as thickness of the bonding layer, the sensing region and sensor optimization
4.3.1 Bonding Layer
Astudy done by the Y.Yang et al showed the relationship between the thickness of the bonding
layer and changes in conductance. It suggested that as the thickness of bonding layer increases,
the upward shifts in conductance increase significantly with the increase in frequency.
Furthermore, it is recommended that the bonding layer should be less than 1/3 of PZT patch
thickness. Their experiment results are presented below.
43
0.00006
0.00006
S0.00004-
0.00003 o
0.00002 -II
0.00001
0
10
0.0040.0035 -
12
14
16
Frequency (kHz)
18
-- P1
P2
P3
20
(b)
0.003
0.0025
0.002
0.0015
I
0.001
0.0005 0 _1
240
245
250
Frequency (kH)
255
260
Figure 22 Conductance signatures for PZT patches bonded on a plate specimen with different bonding
thicknesses. (a) 10-20 kHz. (b) 240-260 kHz. (Yaowen Yang, 2008)
4.3.2 Sensing Region
With regards to sensing region, it largely dependent on many variables, for example, material
property of host structure, used frequency range and the material property of the sensor.
Therefore, the sensor region may vary from sensor to sensor. Among the three factors,
44
frequency range plays a very important role in determining the sensing region. As the vibrationbased technique uses low frequency global excitation, it is able to cover large sensing area. On
the other hand, the EMI technique uses high frequency excitation, and therefore has limited
sensing area. It is estimated that in composite materials, the sensor region can be as low as
0.4m, while in simple metal beams, the sensor region can be as high as 2m. (Soh, 2009)
Therefore, the sensor arrangements must be well planned, in order to cover the structure.
4.3.3 Sensor Optimization
As discussed earlier, the Global Vibration Methods require fewer sensors to cover the same
area compared with the EMI technique. In addition, over estimation of sensors lead to wastage
of money, while underestimation of sensors can be risky. Hence, sensor optimization is an
interesting issue in both methods. However, Soh believes that measured data cannot fully
detect damage location and quantity, and therefore, there can be no systematic way to
optimize sensors. Currently, the general practice is to focus on placing more sensors at
anticipated potential damage locations. (Soh, 2009)
45
Chapter 5 Conclusions and Outlook
The development of Structural Health Monitoring (SHM) has been rapid in the past few years.
The global interrogation techniques were designed to monitor structural health by analyzing
the modal information of the structure such as modal damping, modal shape, etc. However, it is
not sensitive towards local damage because the loss of individual members may not result in
any changes in the natural frequency, mode shapes, etc of the structure.
Local damage detection techniques such as ultrasonic detection, eddy-current testing are
manual and require access to the damage location.
With the development of smart materials which change properties in response to external
stimuli, mechanical deformation of materials can be measured in terms of electrical signals.
These materials were adopted to improve on existing SHM techniques.
The Electro-Mechanical Impedance (EMI) method was first introduced to measure the electrical
admittance by the impedance analyzer to evaluate the health status of the structure by
comparing the baseline signature with the damaged signature. However, EMI technique's
sensitivity reduces with increased damage. Therefore, Bhalla, Shanker and Gupta introduced a
new method "Integration of Global Vibration Technique and EMI Technique". This technique
takes advantage of EMI technique's high sensitivity towards the early incipient damage, while
simultaneously making full use of Global Vibration Technique at later damage stages.
The author further evaluated the integration method by examining the effects of the external
factors such as temperature and loads. Changes in temperature and loads are sources of noise
that can affect interpretation of the data. In addition, the author expressed some doubts about
the scalability of the method, due to differences in experimental and actual conditions.
Furthermore, the different frequency range for EMI technique and Global Vibration Technique
results in different sensing region for the PZT patch, which causes some difficulty in optimizing
the sensors. To conclude, it may not be feasible to implement this integrated method in real
structures.
Future work on damage detection can include
1.
Sensors optimization and development of advanced sensing systems
46
2.
Use of wireless sensors and their data transmission system.
3.
Advanced signal processing techniques to eliminate the effect of noise
4. To study feasibility of implementation of designed methods into complex structures
47
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50
Appendix
No. Combimtien
z
y
C
--
2
C
3
0
4.74
C
5
-.D
6
W.N -
J ILI-
vt
Feq. yvs. FReq.
mek
-W
FL
~
e- +(ony-
Ce +(&N. -
0
+--
7
e-V
-3/(.)f
e-4(/
-Wk -1/(.))
c -+(W/
-/(.k
C
13y
--
k-r
4.a -h(ea+Wa
c-
c +(Nty
H
£
-71
)
ate--'+(am)]
e-'
10
-'
-1
12
a[.('+ k-')-A
+(am/t)'
e -
e +(am-f-/
4
e.
e +(ik
4
I (a-1/I
- (9
-1
/
ag-
/(k -maw)f
]
.s
"
13
e- +(&a - k/o-
51