KSCE Journal of Civil Engineering

Vol. 10, No. 1 / Janualy 2006

pp. 33~39

Structural Engineering

Vol. 10, No. 1 / January 2006 − 33 −

Active Sensing-based Real-time Nondestructive Evaluations for

Steel Bridge Members

By Seunghee Park*, Chung-Bang Yun**, and Yongrae Roh*

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Abstract

This paper presents an experimental study on the applicability of piezoelectric lead-zirconate-titanate(PZT)-based active sensingtechniques for nondestructive evaluation (NDE) of steel bridge members. PZT patches offer special features suitable for real-time in-situ health monitoring systems for civil structures, because they are small, light, cheap, and useful as built-in sensor systems. In thisstudy, the impedance-based damage detection method and the Lamb wave-based damage detection method were applied to steelbridge members. Several damage sensitive features were selected: i.e., root mean square (RMS) changes in the impedance andwavelet coefficients, and the time of flights. Firstly, PZT patches were used in conjunction with the impedance and Lamb waves todetect the presence and growth of artificial cracks on a 1/8 scale model for a vertical truss member of Seongsu Bridge, Seoul, Korea,which caused the collapse in 1994. RMS changes in the impedances and wavelet coefficients are found to increase proportionally tothe crack length. Secondly, two PZT patches were used to detect damages on a bolted joint steel plate, which were simulated by loosebolts. The time of flight and wavelet coefficient obtained from the Lamb wave signals were used. The correlation of the Lamb wavetransmission data with the loose bolts was investigated. And, the support vector machine was used for damage classification. Resultsfrom the experiments showed the validity of the proposed methods.

Keywords: real-time nondestructive evaluation, active sensing, PZT, impedance, Lamb waves, steel bridge member, support vector

machines

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1. Introduction

In recent years, structural health monitoring (SHM) is

increasingly being evaluated by the industry as a possible

method to improve the safety and reliability of structures and

thereby reduce their operational cost. SHM technology is

perceived as a revolutionary method of determining the integrity

of structures involving the use of multidisciplinary fields

including sensors, materials, signal processing, system integration,

and signal interpretation. The core of the technology is the

development of self-sufficient systems for the continuous

monitoring, inspection and damage detection of structures with

minimal labor involvement. The aim of the technology is not

simply to detect structural failure, but also provide an early

indication of physical damage. The early warning provided by an

SHM system can then be used to define remedial strategies

before the structural damage leads to failure. A built-in SHM

system would consist of three major components: 1) Sensors/

sensor networking system, 2) Integrated hardware, and 3)

Software to monitor in-situ condition of on-service structures. In

this study, for the development of this SHM system, PZT-based

active sensing techniques for nondestructive evaluation (NDE)

of steel bridge members are proposed. For steel bridge members

such as steel truss member and bolted joint steel plate, especially,

detection and monitoring of fatigue cracks caused by external

loads is strongly required. Although conventional NDE techniques

such as ultrasonic testing and X-radiography can provide

significant details about the nature of damage, those techniques

usually require direct access to the structure and involve bulky

equipments. Moreover, the techniques usually require disruptions

of the operation of the structures/equipments, which is not

attractive for real-time in-situ SHM. To overcome those

limitations, PZT patches offer special opportunity, because they

are small, light, cheap, and useful as built-in sensor systems. In

this study, two kinds of PZT-based damage detection strategies

have been considered: (a) impedance-based method and (b)

Lamb wave-based method. For the impedance-based method,

successful applications to damage detection for various kinds of

structures have been reported (Ayres et al., 1998; Tseng et al.,

2000; Park et al., 2003; Park et al., 2005). The Lamb wave-based

approach using a pitch-catch method has been utilized by

identifying the changes in the transmission velocity and energy

of the elastic waves associated with damages (Cawley and

Alleyne, 1996; Wait et al., 2004). Firstly, in this paper, PZT

patches were used in conjunction with the impedance and Lamb

waves to detect the presence and growth of artificial cracks on a

1/8 scale model for a vertical truss member of Seongsu Bridge,

Seoul, Korea, which caused the collapse in 1994. Root mean

square (RMS) changes in the impedances and wavelet

coefficients of Lamb waves were found to be good damage

indicators based on the fact they show the rapid and exact

damage estimation results. Secondly, two PZT patches were used

*Ph.D. Candidate, Deprt. of Civil and Environmental Engineering, Korea Adv. Institute of Sci. and Tech., Korea (Corresponding Author, E-mail:

shparkpc@kaist.ac.kr)

**Member, Prof., Deprt. of Civil and Environmental Engineering, Korea Adv. Institute of Sci. and Tech., Korea (E-mail: ycb@kaist.ac.kr)

***Prof., School of Mechanical Engineering, Kyungpook National University, Korea (E-mail: yryong@knu.ac.kr)

Seunghee Park, Chung-Bang Yun, and Yongrae Roh

− 34 − KSCE Journal of Civil Engineering

to detect damages on a bolted joint steel plate, which were

simulated by loose bolts. The time of flight (TOF) and wavelet

coefficients (WC) obtained from continuous wavelet transform

of the Lamb wave signals were used. The correlation of the

Lamb wave transmission data with the loose bolts was

investigated. And, the support vector machine was used for

damage classification. A flow chart of these research items are

summarized in Fig. 1.

2. Impedance-based Damage Detection Method

The coupling effect of the electro-mechanical impedance of a

system with PZT and a host structure can be conceptually

investigated as shown in Fig. 2. (Giurgiutiu and Rogers, 1997)

The mechanical aspect of the PZT is described by its short-

circuited mechanical impedance. The host structure is represented

by its driving point mechanical impedance, which includes the

effect of mass stiffness, damping, and boundary conditions. The

PZT is powered by voltage or current. The integrated electro-

mechanical system may be electrically represented by an

electrical impedance which is affected by the dynamics of the

PZT and the host structure. The mechanical impedance, Zs of the

host structure idealized as a SDOF system as in Fig. 2, is defined

as the ratio of a harmonic excitation force F0(ω) at an angular

frequency ω to the velocity response (ω) in frequency domain.

And, similarly, the electrical impedance, ZA of the PZT patch is

defined as the ratio of a harmonic input voltage V(ω) at an

angular frequency ω to the current response I(ω) in frequency

domain. Therefore, the apparent electro-mechanical impedance

of the PZT as coupled to the host structure is given by

(1)

where C is the zero-load capacitance of the PZT and κ31 is the

electromechanical coupling coefficient of the PZT.

The electromechanical impedance technique permits health

monitoring, damage detection, and embedded NDE because it

can measure directly the high frequency local impedance which

is very sensitive to local damage. This method utilizes the

changes that take place in the high-frequency drive-point

structural impedance to identify incipient damage in the

structure. Hence, changes of the mechanical properties of the

host structure may be detected by monitoring the variations of

the electro-mechanical impedance functions shown in Equation

(1). Experimental setup for the impedance-based NDE consists

of an impedance analyzer (HP4294A), a personal computer

which can control matlab programs for data acquisition, signal

processing and damage diagnosis, and PZT patch built-in

structural system as shown in Fig. 3.

3. Lamb Wave-based Damage Detection Method

Lamb waves refer to elastic perturbations propagating in a

solid plate with doubly free boundaries, for which displacements

occur both in parallel and perpendicular to the direction of wave

propagation (Viktorov, 1967). This type of wave phenomenon

was first described in theory by Horace Lamb in 1917. There are

two groups of waves, symmetric and anti-symmetric, that satisfy

the wave equation and boundary conditions and propagate

independently of each other. A graphical representation of those

two groups of waves can be seen in Fig. 4. The waves may

propagate over distances of several meters along a plate-like

structure depending on the material and geometry of the

structure. If a set of transmitting and receiving transducers are

placed on a structure, the received signal contains information

about the integrity along the wave path between two transducers.

Therefore, the present method may be used to monitor a path

rather than a point, and considerable savings in testing time may

be obtained. Since Lamb waves induce stresses throughout the

plate thickness, the entire thickness of the plate can be

interrogated. Unfortunately, however, Lamb wave testing gets

complicated by the dispersive nature of the Lamb waves. Fig. 4

shows the dispersion curves obtained theoretically for the Lamb

waves propagating in a steel plate. The diagram shows that many

wave components with different group velocities exist at the high

frequency range. Therefore, if a structure is excited by a

broadband pulse, many wave components with different

frequencies will travel at different speeds and the pulse shape

x·

Ztotal ω( ) iωC 1 κ312

Zs ω( )ZA ω( ) Zs ω( )+---------------------------------–⎝ ⎠

⎛ ⎞1–

=

Fig. 1. Research Outline of PZT-based Nondestructive Evaluations

Fig. 2. Electro-mechanical System between PZT and Host Struc-

ture (Giurgiutiu and Rogers, 1997)

Fig. 3. Experimental Setup for Impedance-based NDE

Active Sensing-based Real-time Nondestructive Evaluations for Steel Bridge Members

Vol. 10, No. 1 / January 2006 − 35 −

will change as it propagates along the plate. So, attempts have

been made to limit the bandwidth of the excitation to a low

frequency range over which there exist only two fundamental

modes (A0 or S0). An investigation on the dominance of the

fundamental Lamb modes over the proper frequency range for

the steel members was reported (Ghosh et al., 1998). In the

present study, the only A0 mode is intentionally utilized and

investigated. A propagating wave is reflected and/or partially

transmitted, when it encounters a defect or boundary. Then,

damage detection can be carried out based on both the

attenuation and the time delay of the wave component.

Experimental setup for the Lamb wave-based NDE consists of a

Pulser/Reciever (5077PR), a digital oscilloscope (TD2022), a

personal computer which can control matlab programs for data

acquisition, signal processing and damage diagnosis, and PZT

patch built-in structural system as shown in Fig. 5.

3.1 Wavelet Transform for Feature Extraction

The Fourier transform decomposes a signal into its various

frequency components. As it uses the sinusoidal basis functions

that are localized in frequency only, it loses the transient feature

of signals. Therefore, it is necessary to implement the time-

frequency analysis for diagnostics of transient signals induced by

the impulse loading. In time-frequency analysis, the short-time

Fourier transform calculates the local spectral density using

windowing techniques to analyze a small section of the signal at

a time. However, it has a higher resolution in the frequency

domain but a lower resolution in the time domain. Moreover, it is

impossible to simultaneously achieve high resolution in time and

frequency. In order to overcome the limitations of harmonic

analysis, it has been considered to use alternative families of

orthogonal basis functions called wavelets. The continuous

wavelet transform (CWT) decomposes a signal into time and

frequency domain by the dilatation of a wavelet ψ(t) given in the

following equation, where continuous variables a and b are the

scale and translation parameters, respectively (Jeong and Jang,

2000).

(2)

where the asterisk (*) denotes the complex conjugate. In the

present study, a robust wavelet decomposition using “Morlet

wavelet” is employed for the efficient extraction of some

damage sensitive features.

3.2. Support Vector Machines

The Support Vector Machine (SVM) is a mechanical learning

system that uses a hypothesis space of linear functions in a high

dimensional feature space (Vapnik, 1995). The simplest model is

called Linear SVM (LSVM), and it works for data that are

linearly separable in the original feature space only. In the early

1990s, nonlinear classification in the same procedure as LSVM

became possible by introducing nonlinear functions called

Kernel functions without being conscious of actual mapping

space. This extended technique of nonlinear feature spaces is

called Nonlinear SVM (NSVM) shown in Fig. 6. Assume the

training sample S consisting of vectors with i = 1, ..., N,

and each vector xi belongs to either of two classes thus is given a

label . The pair of (w, b) defines a separating hyper-

plane of equation as follows:

(3)

(4)

where w and b are arbitrary constants.

However, Equation (4) can possibly separate any part of the

feature space, therefore one needs to establish an optimal

separating hyper-plane (OSH) that divides S leaving all the

points of the same class on the same side, while maximizing the

margin which is the distance of the closest point of S. The closest

vector xi is called support vector and the OSH (w', b') can be

determined by solving an optimization problem. The resulting

SVM is called Hard Margin SVM. In order to relax the situation,

Hard Margin SVM is generalized by introducing non-negative

slack variables ξ = (ξ1, ξ2, K, ξN) as follows:

Minimize (5)

Subject to

The purpose of the extra term of the CΣξi, where the sum of

i=1, ..., N is to keep under control the number of misclassified

vectors. The parameter C can be regarded as a regularization

parameter. The OSH tends to maximize the minimum distance of

1/w with small C, and minimize the number of misclassified

vectors with large C. To solve the case of nonlinear decision

surfaces, the OSH is carried out by nonlinearly transforming a

set of original feature vectors xi into a high-dimensional feature

space by mapping Φ: xi α zi and then performing the linear

separation. However, it requires an enormous computation of

inner products (Φ(x) · Φ(xi)) in the high-dimensional feature

space. A Kernel function that satisfies the Mercer’s theorem

given in Equation (6) significantly reduces this process. In this

study, a radial basis function machine with convolution function

given in Equation (7) was used as the kernel function (Duda et

al., 2000; Mita and Taniguchi, 2004).

(6)

Wf b a,( ) x∞–

∞

∫ t( )1

a------ψ*

t b–

a---------⎝ ⎠⎛ ⎞dt=

xi Rn∈

yi 1– 1,{ }∈

S x1 y1,( ) … xN yN,( ), ,( )=

w x⋅( ) b+ 0=

d w'( )1

2--- w' w'⋅( ) C ξi∑+=

yi w' xi⋅( ) b'+( ) 1 ξi–≥

Φ x( ) Φ xi( )⋅( ) K x xi,( )=

Fig. 4. Lamb modes and Dispersion Curves

Fig. 5. Experimental Setup for Lamb Wave-based NDE

Seunghee Park, Chung-Bang Yun, and Yongrae Roh

− 36 − KSCE Journal of Civil Engineering

(7)

4. Verification of the Proposed Methods

4.1 Experimental Study I: Crack Monitoring on Steel

Truss Member

First experimental study was carried out to check the

feasibility of crack detection using PZT patches built in on the

structural member. PZT patches were used in conjunction with

the impedance and Lamb waves to detect the presence and

growth of artificial cracks on a 1/8 scale model for a vertical truss

member of Seongsu Bridge, Seoul, Korea, which caused the

collapse in 1994 (Fig. 7(a)). The original member consists of two

segments with wide flange sections of different flange thickness

welded together. Fatigue cracks developed at the welded zone of

two flanges, and caused eventual sever of the member.

In the impedance approach, five PZT patches of 25×15×0.5

mm were attached to the outside surface of a flange as shown in

Fig. 7(b). Damages were inflicted by cutting the flange at 2

locations sequentially, and 3 damage cases were constructed.

The impedance signatures obtained at the PZT patch #2 in each

damage case are shown in Fig. 7(b). The RMS (root mean

square) changes of the impedance signatures were considered as

the damage indicators (Equation (8)).

(8)

where Z(ωi) is the post-damage impedance signature at the i-th

measurement point and Z0(ωi) is the corresponding pre-damage

value. The results indicate that the RMS changes of the impedance

signatures according to the cracks give good information for

damage localization and severity.

In the Lamb wave propagation approach, a sensor networking

system composed of four PZT patches was embedded to the

surface as shown in Fig. 7(c). In order to detect and monitor two

cracks with different lengths inflicted artificially, four pair pitch-

catch signals of the Lamb wave propagations (#1 to #2, #1 to #4,

#3 to #2, and #3 to #4) were analyzed according to the initiation

and growth of crack. For damage scenario, two cracks were

artificially inflicted up to 4cm from both sides by the increment

of 1 cm. So, totally, 8cm crack was cut. In order to extract

damage sensitive features, the continuous wavelet transform was

applied as a robust signal processing technique, and wavelet

coefficients based on peak values were selected. Statistically,

RMS changes in the wavelet coefficients of four pair pitch-catch

signals were considered according to the damage states. Damage

indicator obtained by a least square curve fitting algorithm was

found to increase proportionally to the crack length as shown in

Fig. 7(c).

The above experimental results verified the efficacy and the

robustness of the proposed approaches, emphasizing the great

potential for developing an automated, real-time and in-situ health

monitoring system for application to large civil infrastructures.

Both approaches would be enhanced by the use of pattern

recognition algorithm that can estimate and classify damages

based on a learning process.

4.2 Experimental Study II: Loose Bolt Monitoring on

Jointed Steel Plates

Second experimental study has 2 objectives: (1) to extract the

efficient feature vectors from wavelet transform of Lamb wave

signals, and (2) to improve the damage detection performance by

using the SVMs trained by a set of the feature vectors. An

experimental setup and its overall configuration are shown in

Fig. 8. The specimen (700×100×2mm) was made of 2 steel

plates (400×100×2mm) jointed. Eight steel bolts with 10mm in

diameter with washers and nuts were used. Two PZTs were

placed at locations 100mm apart from the ends. The distance

between two PZTs is 475mm. The dimension of each PZT patch

is 35×25×0.2mm. An impulse waveform was applied to PZT 1

serving as a transmitter, and the propagating wave signal was

measured at PZT 2 serving as a sensor. The exciting frequency

by the PZT patch was found as 23.4 kHz. It is noted that the most

Lamb waves tend to propagate along with the path (area between

two red dotted lines) which depends on the width of the PZT

patch as in Fig. 6. Therefore, it can be expected that damages out

of the Lamb wave path (damages out of path, DOP) do not cause

significant changes in the Lamb wave signal compared with the

case of damages in the Lamb wave path (damages in path, DIP).

Damages were introduced by removing several bolts from the

joints. At first, the test was carried out on the intact state of the

bolted joints, and then experiments were performed on 8

different damage cases. The continuous wavelet transform

technique also was explored for detecting the changes in the

dispersive Lamb waves due to damages as in example study I.

The TOF (time of flight) and WC (wavelet coefficient) were

obtained based on peak values. The results were obvious that

damages in the Lamb wave path (as in Bolts 2, 3, 6 and 7) caused

significant changes in TOF and WC, while damages out of the

Lamb wave path (as in Bolts 1, 4, 5 and 8) did not. That is, for

K x xi,( ) expx xi– 2

σ2

-----------------–⎝ ⎠⎛ ⎞=

RMSD %( )Σi 1=

i N= Z ωi( ) Z0 ωi( )–( )2

Σi 1=i N= Z0 ω i( )( )2

-------------------------------------------------- 100×=

Fig. 6. Non-linear Support Vector Machine

Active Sensing-based Real-time Nondestructive Evaluations for Steel Bridge Members

Vol. 10, No. 1 / January 2006 − 37 −

the former cases, TOF and WC gave good representation for

identifying of localized damages. For the latter cases, however,

their variations did not give consistent trend correlating with

damages.

To improve the damage detection performance for the latter

cases, the proposed pattern recognition technique, SVM was

investigated. Firstly, three damage classes were introduced

considering damage locations, as described in Table 2. Totally,

Fig. 7. Experimental Study I: Crack Detection on Welded Zone

Fig. 8. Experimental Configuration

Table 1. Damage Scenario

Damage Cases Locations of Loosened Bolts

Case 1 #1

Case 2 #2

Case 3 #1 & 4

Case 4 #2 & 3

Case 5 #1,2,3 & 4

Case 6 #1,2,3,4,5 & 8

Case 7 #1,2,3,4,5 & 6

Case 8 #1,2,3,4,5,6 & 7

Seunghee Park, Chung-Bang Yun, and Yongrae Roh

− 38 − KSCE Journal of Civil Engineering

120 patterns to train SVMs were prepared by forty samples with

1 bolt removed from each class. They composed a 2D feature

space as shown in Fig. 9. From Fig. 9, it can be noted that the

distinctions of each class’s regions are very ambiguous.

Therefore, probabilistic decision-making (the establishment of

optimal decision boundaries) between three classes were

strongly required. Fig. 10 shows three kinds of classifying cases

with different combinations of classes, and the optimal decision

boundaries for each case were constructed on high dimensional

feature space. To verify the effectiveness of the SVM-based

classifier, 20 test patterns prepared by ten arbitrary samples with

1 loose (not removed) bolt from Classes 2 (DOP) and 3 (DIP)

were also used, and the results are showed in Fig. 11. It can be

founded that the SVM gave very good detection performance for

not only DIP (detection rate: 100%) but also DOP (detection

rate: 90%).

5. Conclusions

The applicability of piezoelectric lead-zirconate-titanate(PZT)-

based nondestructive evaluation (NDE) techniques for steel

bridge members has been presented from experimental studies.

The work presented in this paper demonstrates that the

impedance-based damage detection method and Lamb wave-

based damage detection method applied with PZT patches are

both able to detect the damages such as cracks and loose bolts on

steel members. The sensor networking system composed of PZT

patches was built in to the host structure and used to record the

electromechanical impedance and the Lamb wave propagation

data. Hence, if there was any defect in the host structures, the

data obtained from the PZT patches would be modified by the

presence of the defects. The present approaches yield an

improved methodology for real-time damage detection and

monitoring in critical members of steel bridges. The real-time

smart NDE methods presented here can be applied to real steel

structures. One can envision in-situ networking systems

composed of PZT patches being placed on critical members to

detect the presence and growth of real damages. Through local-

area data collection, interpretation, and automatic system for

health monitoring and damage estimation can be devised and

installed. The use of the proposed damage index will allow rapid

estimation and automatic assessment of the structural health

condition in terms of a single scalar value. Important safety

enhancement and significant cost savings are predicted through

Table 2. Three Classes Considering Damage State

Classes Descriptions

1 Intact Case

2 Damages out of Lamb wave path (DOP)

3 Damages in Lamb wave path (DIP)

Fig. 9. Preliminary Test Results for Training Patterns

Fig. 10. Feature Space Divided by SVMs

Fig. 11. SVM-based Damage Estimation Results

Active Sensing-based Real-time Nondestructive Evaluations for Steel Bridge Members

Vol. 10, No. 1 / January 2006 − 39 −

the wide area implementation of this novel method for structural

health monitoring, damage detection, and failure prevention.

Acknowledgements

The study was jointly supported by the Smart Infra-Structure

Technology Center (SISTeC) at KAIST sponsored by the Korea

Science and Engineering Foundation (KOSEF), and the Infra-

Structure Assessment Research Center (ISARC) sponsored by

Ministry of Construction and Transportation (MOCT), Korea.

Their financial supports are greatly acknowledged.

References

Ayres, J. W., Lalande, F., Chaudhry, Z., and Rogers, C. A. (1998).

“Qualitative impedance -based health monitoring of civil

infrastructures,” Smart Materials and Structures, Vol. 7, pp. 599-

605.

Cawley, P. and Alleyne, D. (1996). “The use of Lamb waves for the long

range inspection of large structures,” Ultrasonics, Vol. 34, pp. 287-

290.

Duda, R.O., Hart, P.E., and Stork, D.G. (2000). Pattern Classification,

2nd Edition, Wiley-Interscience, New York, NY.

Ghosh, T., Kundu, T., and Karpur, P. (1998). “Efficient use of Lamb

modes for detecting defects in large plates,” Ultrasonics, Vol. 36, pp.

791-801.

Giurgiutiu, V. and Rogers, C.A. (1997). “Electro-mechanical (E/M)

impedance method for structural health monitoring and

nondestructive evaluation”, Proc., International Workshop on

Structural Health Monitoring, pp. 433-444, Stanford Univ., CA,

USA, Sep., pp., 18-20.

Jeong, H. and Jang, Y. (2000). “Wavelet analysis of plate wave

propagation in composite laminates,” Composite Structures, Vol. 49,

pp. 443-450.

Mita, A. and Taniguchi, R. (2004). “Active damage detection method

using support vector machine and amplitude modulation,”

Proceedings of 11th International Symposium on Smart Structures

and Materials, San Diego, CA, USA, SPIE Vol. 5391, pp. 21-29.

Park, G., Sohn, H., Farrar, C. R., and Inman, D.J. (2003). “Overview of

piezoelectric impedance-based health monitoring and path forward,”

Shock and Vibration Digest, Vol. 35, No. 6, pp. 451-463.

Park, S., Yun, C.-B., Roh, Y., and Lee, J.-J. (2005). “Health monitoring

of steel structures using impedance of thickness modes at PZT

patches,” Smart Structures and Systems, Vol. 1, No. 4, pp. 339-354.

Tseng, K. K.-H., Soh, C. K., Gupta, A., and Bhalla, S. (2000). “Health

monitoring of civil infrastructure using smart piezoceramic

transducers,” Proc., 2nd Int. Conf. on Composite Method for Smart

Structures and Materials, pp. 153-162.

Vapnik, V. N. (1995). The Nature of Statistical Learning Theory,

Springer, New York, NY.

Viktorov, I. A. (1967). Rayleigh and Lamb Waves-physical theory and

Applications. New York: Plenum Press.

Wait, J.R., Park, G., Sohn, H., and Farrar, C.R. (2004). “Active sensing

system development for damage prognosis,” Proceedings, 1st

international workshop on Advanced Smart Materials and Smart

Structures Technology, pp. 163-170, Honolulu, HI.

(Received on July 28, 2005/Accepted on November 23, 2005)