Reference-free impedance-based crack detection in plates

Contents lists available at ScienceDirect

Journal of Sound and Vibration

Journal of Sound and Vibration 330 (2011) 5949–5962

0022-46

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/jsvi

Reference-free impedance-based crack detection in plates

M.K. Kim a, E.J. Kim b, Y.K. An a, H.W. Park b, H. Sohn a,n

a Department of Civil and Environmental Engineering, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Koreab Department of Civil and Environmental Engineering, Dong-A University, 840 Hadan 2-dong, Saha-gu, Busan 604-714, Republic of Korea

a r t i c l e i n f o

Article history:

Received 22 November 2010

Received in revised form

29 May 2011

Accepted 19 July 2011

Handling Editor: I. Trendafilovadance signals with ‘‘baseline’’ ones obtained from the pristine condition of a structure.

Available online 11 August 2011

0X/$ - see front matter & 2011 Elsevier Ltd.

016/j.jsv.2011.07.025

esponding author. Tel.: þ82 42 350 3625; fa

ail address: [email protected] (H. Sohn).

a b s t r a c t

Impedance-based damage detection techniques gained popularity among structural

health monitoring (SHM) and nondestructive testing (NDT) communities due to their

sensitivity to local damage and applicability to complex structures. In general, conven-

tional impedance-based techniques identify damage by comparing ‘‘current’’ impe-

However, in-situ structures are often subject to changing temperature and loading

conditions that can adversely affect measured impedance signals and cause false-

alarms. In this paper, a ‘‘reference-free’’ impedance method, which does not require

direct comparison of the current impedance signals with the previously obtained

baseline impedance signals, is developed for crack detection in a plate-like structure.

The proposed technique utilizes a single pair of PZTs collocated on the opposite surfaces

of a structure to extract mode conversion produced by crack formation. Then, a

reference-free damage classifier is developed and performed on the extracted mode

conversion for instantaneous damage diagnosis. Numerical simulations and experi-

mental tests have been conducted explicitly considering varying temperature and

loading conditions to demonstrate the robustness of the proposed damage detection

technique under varying operational and environmental conditions.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

There has been an increasing demand in adopting structural health monitoring (SHM) and nondestructive testing (NDT)techniques for continuous monitoring of in-situ structures [1,2]. Among several candidate techniques for SHM/NDT,impedance-based methods have shown a promise in detecting local defects in complex structures [3–8]. For impedance-based damage detection, a wafer-type lead zirconate titanate (PZT) is surface-mounted to a host structure and its electricalimpedance is measured in a high-frequency band. A key aspect of the impedance method is to use a high-frequencyexcitation band (around 10–100 kHz range) to monitor the change of the PZT electrical impedance that is associated withthe structural parameters of the host structure. By employing the high-frequency excitations, this technique becomessensitive to local incipient damage [9].

Conventional impedance-based techniques identify damage by comparing ‘‘current’’ impedance signals with ‘‘baseline’’ones obtained from the pristine condition of a structure. However, it has been reported that changing temperature andloading conditions adversely affect the impedance signals and these variations can often mask structural changes causedby damage [10–12]. Although some compensation techniques have been developed to minimize false alarms, the existing

All rights reserved.

x: þ82 42 350 3610.

www.elsevier.com/locate/jsvi

dx.doi.org/10.1016/j.jsv.2011.07.025

mailto:[email protected]

dx.doi.org/10.1016/j.jsv.2011.07.025

M.K. Kim et al. / Journal of Sound and Vibration 330 (2011) 5949–59625950

techniques require collection of multiple ‘‘baseline’’ data from a wide range of environmental or operational conditions,and the compensation has been performed mainly for temperature [11,13].

To tackle these problems, a new paradigm for damage detection called ‘‘reference-free’’ has been proposed by theauthors’ group [14–16]. The previous reference-free techniques utilize Lamb waves to identify a crack in a plate-likestructure by extracting mode conversions created by the interaction of propagating Lamb waves with the crack. Becausethese reference-free techniques identify damage without direct comparison with the previously obtained Lamb wavesignals, these techniques become less vulnerable to false alarms caused by changes of the surrounding environment.

In this study, the concept of reference-free diagnosis is extended to impedance signals. The proposed technique utilizesa single pair of collocated PZTs attached on the opposite sides of the plate to isolate crack-induced mode conversion frommeasured impedance signals. To the authors’ best knowledge, this is the first study that applies the concept of thereference-free paradigm to impedance-based damage detection. This paper is organized as follows. First, the proposedreference-free impedance method is theoretically formulated including the definition of a damage index and instanta-neous damage classification. Then, numerical simulations and experimental tests are performed to demonstrate theeffectiveness of the proposed reference-free crack detection technique. The robustness of the proposed reference-freeimpedance method under changing temperature and external loading conditions is explicitly examined throughexperimental tests. Finally, this paper concludes with a brief summary and discussions for future work.

2. Theoretical development

In this section, the proposed reference-free technique is theoretically formulated. First, the extraction of crack-inducedmode conversion from Lamb wave signals is described. Then, the concept is extended to impedance signals using therelationship between the impedance and Lamb wave signals. Finally, a damage classifier that operates on the extractedmode conversion is developed.

2.1. Decomposition and isolation of mode conversion

Since the proposed study extends the previously developed Lamb wave-based technique [16] to impedance signals, theconcept is first developed using Lamb waves and extended to impedance signals based on the relationship between theLamb wave and impedance signals. The proposed reference-free technique assumes that two identical PZT transducers,labeled PZTs ‘‘X’’ and ‘‘Y’’ in Fig. 1, are located exactly at the same position but on the opposite sides of the plate. Thearrows indicate positive poling directions of PZT transducers. Piezoelectric materials such as PZT transducers arecommonly used to excite and sense Lamb waves and impedance signals. Piezoelectric materials produce an electricalcharge when stressed mechanically, and mechanical strain is conversely produced when an electrical field is applied. Usingthis unique nature of piezoelectric materials, the piezoelectric materials mounted on the surface of a host structure can beused to generate and sense Lamb waves and impedance signals. In Fig. 1, Lamb waves are generated by activating one ofPZTs X and Y or by simultaneous excitation of both PZTs. The generated waves are then reflected from the boundaries ofthe structure and sensed by the same PZTs in a pulse-echo mode.

Mode conversion of Lamb waves takes place when waves propagating along the plate encounter a discontinuity such asa sudden thickness variation due to damage [17]. That is, the propagating fundamental symmetric (S0) mode istransformed to the fundamental anti-symmetric (A0) mode, and vice versa. Note that the S0 and A0 modes arrive at thesensing PZT with different arrival times due to their different group velocities. However, the two fundamental modeconversion components (one converted from the S0 mode to the A0 mode, and the other from the A0 mode to the S0 mode)concurrently reach at the sensing PZT in the pulse-echo mode, and they are grouped together and denoted as MC inthis paper.

If a particular input voltage on PZT X produced a particular set of S0 and A0 modes, the same input to PZT Y wouldgenerate an identical S0 mode but an A0 mode with the opposite sign. Similar argument used for Lamb wave generation canbe used for Lamb wave sensing as well. Both PZTs X and Y measure the same voltage for an S0 mode but would measureequal but opposite voltages for an A0 mode. Selective generation of either S0 or A0 mode can be done by simultaneousexcitation of PZTs X and Y with appropriate input voltages [18]. Fig. 2(a) schematically shows all six signals measured froma damaged case.

Fig. 1. The configuration of the proposed reference-free impedance technique with a single pair of collocated PZTs: PZTs X and Y are attached at the same

location but on the opposite sides of the specimen (the arrows indicate positive poling direction of the PZTs).

s

M

A

0

0

0

0

AY

AX

SY

SX

YY

XX

Decompositionusing Eq. (1)

Fig. 2. Decomposition of individual mode signals from measured Lamb wave signals obtained from a pair of collocated PZTs X and Y: (a) six measured

signals (VXX to VAY) and (b) three decomposed Lamb wave signals (ZS(t), ZA(t) and ZM(t)) (the dashed line indicates that the specific mode has the opposite

sign compared to the same mode in VXX).

Fig. 3. Selective excitation of either S0 or A0 mode: (a) only the S0 mode is generated by simultaneous ‘‘in-phase’’ excitation of PZTs X and Y and (b) the

A0 mode is selectively produced by simultaneous ‘‘out-of-phase’’ excitation of PZTs X and Y.

M.K. Kim et al. / Journal of Sound and Vibration 330 (2011) 5949–5962 5951

Fig. 2(a) shows six different time signals that can be obtained from the collocated PZTs X and Y. VXX(t) denotes thepulse-echo time signal excited by PZT X and sensed by PZT X, and VYY(t) represents the response signal excited by PZT Y

and sensed by PZT Y. It can be seen that the A0 and S0 modes in VXX(t) and VYY(t) are identical while the MCs in VXX(t) andVYY(t) have the opposite signs (The dashed line in Fig. 2(a) indicates that the specific mode has the opposite sign comparedto the same mode in VXX). VSX(t) and VSY(t) are the responses of PZTs X and Y when only the symmetric mode is generatedby simultaneous in-phase excitation of PZTs X and Y as shown in Fig. 3(a). Similarly, VAX(t) and VAY(t) are the responses ofPZTs X and Y when the anti-symmetric mode is generated by exciting PZTs X and Y out-of-phase as shown in Fig. 3(b).The S0 modes in VXX(t) and VYY(t) are identical while the MCs have the opposite signs. Furthermore, the amplitudes of theS0 mode in VSX(t) and VSY(t) are two times larger than those of the S0 modes in either VXX(t) or VYY(t) because PZTs X and Y

are excited simultaneously. Similar finding can be observed from the pair of VAX(t) and VAY(t).By defining the individual time signals containing only the S0, MC and A0 modes in Fig. 2(b) as ZS(t), ZM(t) and ZA(t),

respectively, these individual mode signals can be related to the measured signals using the following equation:

VðtÞ ¼DZðtÞ, where VðtÞ ¼

VXXðtÞ

VYY ðtÞ

VSXðtÞ

VSY ðtÞ

VAXðtÞ

VAY ðtÞ

26666666664

37777777775

, D¼

1 1 1

1 �1 1

2 1 0

2 �1 0

0 1 2

0 �1 2

2666666664

3777777775

and ZðtÞ ¼

ZSðtÞ

ZMðtÞ

ZAðtÞ

264

375 (1)


From Eq. (1) and Fig. 2, it can be easily shown that VXX(t) is a simple superposition of ZS(t), ZM(t) and ZA(t) and thisrelationship is described in the first row of the matrix D. Similarly, VYY(t) can be obtained by summing up ZS(t), ZM(t) andZA(t). The only difference is that the sign of ZM(t) should be flipped before the summation. This summation operation withthe sign change is expressed in the second row of the matrix D. The remaining rows of the matrix D can be obtained in asimilar manner.

Finally, the matrix Z is estimated by taking the Moore–Penrose (pseudo) inverse of the matrix D and multiplying it tothe matrix V [16]

~ZðtÞ ¼DyVðtÞ where ~ZðtÞ ¼

~ZSðtÞ~ZMðtÞ~ZAðtÞ

0B@

1CA (2)

where y denotes the pseudo-inverse operation of a matrix, and � represents an estimated value. Ideally, ~ZMðtÞ should bezero for an undamaged plate but non-zero for a damaged one. However, ~ZMðtÞ even for the undamaged case can have non-zero values due to PZT imperfection, misalignment and different bonding conditions between PZTs X and Y. Therefore, adecision boundary is necessary to determine whether the magnitude of ~ZMðtÞ is large enough to indicate damage. Thisissue is further discussed in Section 2.3.

Note that the theoretical formulation is described so far assuming that there are only three Lamb wave components,S0, A0 and MC for simplicity of discussion. In reality, multiple mode conversions occur as propagating waves are reflectedoff from structural boundaries and pass through the crack multiple times. Even in this case, the proposed technique can beused because all Lamb wave modes can be grouped into three categories: (1) modes start as the S0 mode and end as theS0 mode (the previous S0 mode), (2) modes start as the A0 mode and end as the A0 mode (the previous A0 mode), and(3) modes start as the S0 mode and end as the A0 mode or vice versa (the previous MC). Furthermore, the reflections fromthe structural boundaries do not produce mode conversion due to the symmetry geometry and boundary condition [19].Finally, the proposed technique is applicable even when multiple higher Lamb wave modes are present.

2.2. Relevance of impedance signals to Lamb waves

Lamb waves can be viewed as traveling waves produced by a tone-burst input excitation. When these traveling wavesreach the boundary of the structure, reflections occur. As we continue to excite the structure by shifting from a tone-burstexcitation to a harmonic excitation, the combination of forwarding and reflected waves develops standing waves if thedriving frequency is identical to one of the natural frequencies of the structure. These standing waves constitute preciselythe normal modes which are implicitly reflected on the impedance signals through the electro-mechanical interactionbetween the PZT and the structure [20,21]. Note that the relationship between the decomposed S0, A0 and MC modes andthe measured signals shown in Eq. (1) is preserved even when the transient input signal becomes a harmonic steady-statesignal and the corresponding response converges to the normal mode of the structure, that is, VðoÞ ¼DZðoÞ. Based on thisfinding, the matrix ~ZðoÞ can be obtained from the measured impedance signals, VðoÞ, using the same pseudo-inverseoperation as before, ~ZðoÞ ¼DþVðoÞ. According to this equation, the measured impedance signals can be separated intoindividual mode signals containing only S0, A0 and MC modes. Note that only ~ZMðoÞ contains additionally converted modescreated by damage. As mentioned earlier, because ~ZMðoÞ may not be zero even without damage due to initial errors, it ischallenging to determine whether this additional mode is due to mode conversion or PZT imperfections. To tackle thisissue, a new damage classifier is developed in the following subsection. For the sake of convenience, the parenthesis (o) isdropped from all signal notations in the remainder of the paper unless it is necessary for clarity.

2.3. Instantaneous damage diagnosis

The objective here is to determine the existence of a crack solely based on the impedance signals measured from thecurrent state of the structure. To achieve this, a damage classifier is developed by comparing the energy level of crack-induced mode conversion with a certain threshold value. The energy level of the mode converted signal, which is producedby a crack, is estimated by computing the rms (root mean square) value of ~ZM

MCrms ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

oe�os

Z oe

os

ð ~ZMÞ2 do

s(3)

where MCrms is the total energy of ~ZM over the entire sweeping frequency range. os and oe denote the starting and endingangular frequencies of the impedance measurement, respectively.

The threshold is established by computing the difference between the measured V and the reconstructed ~V as follows:

E¼ V� ~V ¼ V�DDþV¼ ðI�DDþ ÞV (4)

where ~V is the reconstructed version of V, and E is the reconstruction error. Measurement errors, non-ideal PZT bondingconditions, and PZT misalignment all can contribute to E. Therefore, a reasonable damage threshold can be set based onthe energy level of the reconstruction errors E. The following Erms gives the averaged error committed in reconstructing the


six measured impedance signals from the least-square estimates

Erms ¼1

6

X6

i ¼ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

oe�os

Z oe

os

ðEiÞ2 do

s(5)

where Ei is the ith reconstruction error. For example, E1 is the error in reconstructing signal VXX, i.e. E1 ¼ VXX�~V XX , etc.

MCrms and Erms are thus the quantitative measures of the damage and the threshold both computed from the currentimpedance signals, respectively. Finally, damage diagnosis for classifying a given structure into an undamaged or damagedcondition is performed by comparing MCrms and Erms:

Nor

mal

ized

Impe

danc

eN

orm

aliz

edIm

peda

nce

Nor

mal

ized

Impe

danc

e

Fig. 5.VSX9VSY

Fig. 4.conduc

If MCrms4Erms , crack exists. Otherwise no observable damage beyond the error level exists.

This damage classifier identifies crack damage when the energy level of crack-induced mode conversion becomes largerthan that of the errors. In summary, this section formulates an impedance-based reference-free damage detectiontechnique. In the subsequent sections, the effectiveness of the proposed theory is investigated through numericalsimulations and experiments.

15 20 25-1

0

1

2

Frequency [kHz]

VXX VYY

15 20 25-1

0

1

2

Frequency [kHz]

VSX VSY

15 20 25-1

0

1

2

Frequency [kHz]

VAX VAY

15 20 25-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VXX VYY

15 20 25-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VSX VSY

15 20 25-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VAX VAY

Comparison of the impedance signals obtained from intact and damage cases in numerical simulation: (a), (c) and (e) indicate impedance signals VXX9VYY,

and VAX9VAY, respectively, without a notch and (b), (d) and (f) indicate impedance signals VXX9VYY, VSX9VSY and VAX9VAY , respectively, with a notch.

Dimensions (in mm) of an aluminum plate, PZTs and a notch used in numerical simulation (2D simulation with plain strain assumption was

ted).


3. Numerical simulation

3.1. Numerical setup

The proposed reference-free technique was first validated through 2D numerical simulation of a crack damage in aplate structure shown in Fig. 4. A plain strain was assumed in the simulation. The plate length was 200 mm, and itsthickness was 6 mm. Two identical 12 mm diameter and 0.508 mm thick PZTs, PZTs X and Y, were attached to the platemodel as shown in Fig. 4. A 3 mm deep and 1 mm wide notch was introduced 50 mm away from PZT X. A chirp signalranging from 15 to 25 kHz with an incremental value of 1 Hz was used as an input signal and the elastic modulus andPoisson ratio were set to 70 GPa and 0.33, respectively. The simulation was conducted through ‘Steady-State DynamicsAnalysis, Direct’ of ABAQUS 6.7-4/Standard [22]. In 2-D FE simulation, 24 8-node quadratic plane strain piezoelectricelements (1 mm�0.508 mm per each element) and 1200 8-node quadratic plane strain solid element (1 mm�1 mm pereach element) were employed for refining the PZT wafer and the aluminum plate, respectively.

3.2. Simulation results

In Fig. 5(a), (c) and (e), three pairs of impedance signals are obtained from the pristine condition of the plate by using sixdifferent combinations of exciting and sensing PZTs. The impedance pair of VXX and VYY was practically the same, and thisobservation matches well with theory. The other pairs, VSX9VSY and VAX9VAY, were also identical to each other. When the notchwas introduced, the differences between the paired signals, VXX9VYY, VSX9VSY and VAX9VAY become noticeable as a result of themode conversions induced by the notch as shown in Fig. 5(b), (d) and (f). The individual S0, A0 and MC components wereextracted from the six measured impedance signals using Eq. (2). Fig. 6 compares the decomposed impedance signals obtainedfrom the undamaged and damaged conditions. It shows that mode conversion is clearly observed in the damaged plate, asopposed to the absence of mode conversion in the undamaged one. Note that ~ZM is absent in the signals obtained from theundamaged plate because of the ideal conditions neglecting PZT imperfection and bonding variation in numerical modeling.

15 20 25-1

0

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

SZ

15 20 25-1

0

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e AZ

15 20 25-1

0

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

MZ

15 20 25-1

0

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

SZ

15 20 25-1

0

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

AZ

15 20 25-1

0

Modeconversion

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

MZ

~ ~

~ ~

~ ~

Fig. 6. Comparison of the decomposed individual impedance signals obtained from intact and damaged cases in numerical simulation: (a), (c) and (e)

indicate decomposed individual impedance signals ~Z S, ~Z A and ~Z M , respectively, without a notch and (b), (d) and (f) indicate decomposed individual

impedance signals ~Z S, ~Z A and ~Z M , respectively, with a notch.


4. Experimental verifications

4.1. Description of experimental setup

To further examine the proposed reference-free impedance technique, experimental tests were conducted onaluminum plates. The overall test configuration and the test specimen are shown in Fig. 7. The data acquisition system

vi

voCr

i

Self-sensing circuitbased on voltage dividerKapton tape for

insulation

Fig. 8. A self-sensing circuit for impedance measurement [23].

PZT Y

PZT X

30mm long,3mm deep,

1mm wide notch

80

PZT Y

PZT X

30mm long,3mm deep,

1mm wide notch

80 80

610

305

400

6

PZT Y

PZT X

PZT Y

PZT X

60mm long,3mm deep,

1mm wide notch

25

Fig. 9. Investigated intact and three damage cases: (a) intact case; (b) damage case I; (c) damage case II; and (d) damage case III (two cracks of the same

size as damage case II). All dimensions are in mm.

Insulated PZT X(PZT Y on opposite side)

305 mm

610 mm

200

mm

SMAConnector

PZT

Fig. 7. Overall experimental set-up and test specimen: (a) data acquisition system and (b) an aluminum plate with a single pair of collocated PZTs

(the PZT transducer is packed by a Kapton tape to insulate it from the specimen).


was composed of a 12-bit arbitrary waveform generator (AWG), a 16-bit high-speed signal digitizer (DIG), threemultiplexers and a self-sensing circuit. More detail on the self-sensing circuit is described later. The dimension of theplate was 610 mm�400 mm�6 mm, and two PSI-5A4E type circular PZT transducers with a diameter of 12 mm and athickness of 0.508 mm were mounted in the middle of the plate. The two identical PZTs, PZTs X and Y, were collocated onthe opposite sides of the plate. Note that the PZTs were insulated from the aluminum specimen using Kapton packing asshown in Fig. 7(b). Using the AWG, a chirp input signal ranging from 15 to 25 kHz with a 710 peak-to-peak voltage wasgenerated to excite the PZT transducers. The frequency range was identical to that of the previous numerical simulation. Inorder to improve the signal-to-noise ratio, 10-time averaging was performed in the frequency domain.

Conventionally, a commercial impedance analyzer such as Agilent 4294A is used for impedance measurement. In thisstudy, AWG, DIG and multiplexers are integrated to allow measurements of both Lamb wave and impedance signals. Theultimate goal of our ongoing research is to integrate impedance and Lamb wave-based damage detection techniques forimproved damage diagnosis. Impedance measurement is achieved using a simple self-sensing circuit [23] as shown inFig. 8. Here, a self-sensing circuit is used to allow the measurement of the output current from the PZT as well as theexcitation of the same PZT. When a known input voltage (Vi) is applied to the PZT, the output current (Io) can be obtainedby measuring the voltage (Vo) across the reference capacitor (Cr). In Fig. 8, the value of the reference capacitor was selectedto be close to the capacitance value of the PZT (10 nF). Then, the electrical impedance of the PZT can be computed as theratio of the voltage across the PZT (Vi–Vo) to the output current (Io¼VojoCr) at any given driving frequency

Z ¼1

joCr

Vi�Vo

Vo

� �(7)

In Eq. (7), the electrical impedance of the PZT contains both real and imaginary components. In the conventional impedancetechniques, the real part of an impedance signal is mainly used for damage diagnosis since it is more sensitive to the changeof structural parameters than the imaginary part is [9]. Therefore, the real impedance of the PZTs is used in this study as well.

Three different damage cases in addition to an intact condition were investigated as shown in Fig. 9. In damage cases Iand II, a notch was introduced along the horizontal (60 mm long, 3 mm deep and 1 mm wide) and vertical (30 mm long,

20 21 22 23

0

2

4

Frequency [kHz]

Nom

aliz

edIm

peda

nce

VXX VYY

20 21 22 23

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VSX VSX

20 21 22 23

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VAX VAY

20 21 22 23

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VXX VYY

20 21 22 23

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VSX VSY

20 21 22 23

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

VAX VAY

Fig. 10. comparison of the impedance signals obtained from intact and damage case III: (a), (c) and (e) indicate impedance signals VXX9VYY, VSX9VSY and

VAX9VAY, respectively, without a notch and (b), (d) and (f) indicate impedance signals VXX9VYY, VSX9VSY and VAX9VAY, respectively, with a notch.


3 mm deep and 1 mm wide) directions of the specimen, respectively. In damage case III, two vertical cracks (30 mm long,3 mm deep and 1 mm wide) were introduced.

4.2. Experimental results

In Fig. 10, the impedance signals obtained from the intact case and damage case III are shown. Note that thenormalized impedance is obtained by subtracting the mean value from the measured impedance signal. The impedancesignals are zoomed in at the frequency range of 20–23 kHz for better comparison. As expected, signals VXX and VYY

in the intact condition were close to each other, and similar results were obtained for VSX9VSY and VAX9VAY pairs.However, small differences, especially in the amplitude of the signals, existed even in the absence of damage due to thevariations of PZT size, alignment and bonding conditions. Once notches were introduced in damage case III, shifting of theimpedance peaks resulted from mode conversion and the differences between VXX9VYY, VSX9VSY and VAX9VAY pairs becameeminent.

Fig. 11 shows the individual mode signals, ~ZS, ~ZA and ~ZM obtained from the intact and damage case III. Note that evenfor the undamaged case, small non-zero components in ~ZM exist due to measurement noise, size difference betweenPZTs X and Y, their non-identical bonding conditions, and misalignment. On the other hand, the presence of mode conversionin ~ZM becomes prominent for damage case III and can be attributed to notch formation as shown in Fig. 11(f). Similar resultsare obtained for damages I and II, but they are not reported here due to the limited space. Table 1 summarizes sixreconstruction errors obtained from intact and three damage cases as defined in Eq. (4). It can observed that thereconstruction error signals of the undamaged and damaged cases exhibit nonzero values, and the energy level of thereconstruction error varies for each case. The average value of the six reconstruction errors serve as the damage threshold asmentioned in Section 2.3.

15 20 25

0

1

2

3

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

ZS

15 20 25

0

1

2

3

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

ZA

15 20 25

0

1

Frequency [kHz]

Initial errors

Nor

mal

ized

Impe

danc

e

ZM

15 20 25

0

1

2

3

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

ZS

15 20 25

0

1

2

3

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

ZA

15 20 25

0

1

Frequency [kHz]

Modeconversion

Nor

mal

ized

Impe

danc

e

ZM

~ ~

~~

~ ~

Fig. 11. Comparison of the decomposed individual impedance signals obtained from intact and damage case III: (a), (c) and (e) indicate decomposed

individual impedance signals ~Z S, ~Z A and ~Z M , respectively, without a notch and (b), (d) and (f) indicate decomposed individual impedance signals ~Z S , ~Z A

and ~Z M , respectively, with a notch.


4.3. Reference-free damage diagnosis

Based on the decomposed mode conversion signals, reference-free damage diagnosis is performed as shown in Fig. 12.For the undamaged case, Erms, which indicates the energy level of the reconstruction errors, is larger than MCrms, which is

Am

plitu

de

Am

plitu

de

Am

plitu

de

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0

ERMS MCRMS ERMS MCRMS


Am

plitu

de

Fig. 12. Instantaneous damage diagnosis using the decomposed mode conversion signals: (a) intact case; (b) damage case I; (c) damage case II; and

(d) damage case III (a structure is classified as damaged only when ‘MCrms’ becomes larger than ‘Erms’).

Insulated PZT X(PZT Y on the opposite side)

Fig. 13. Experimental setup for temperature variation and external loading tests: (a) test specimen in the temperature chamber and (b) test specimen

with a shaker.

Table 1Errors in reconstructing six measured impedance signals for intact and three damage cases.

Case Reconstruction error in rms (�10–7)

Intact Damage I Damage II Damage III

VXX�~V XX

1.54 1.37 1.03 1.08

VYY�~V YY

1.47 1.28 1.02 1.01

VSX�~V SX

1.12 0.87 0.72 0.75

VSY�~V SY

1.14 1.00 0.81 0.87

VAX�~V AX

1.19 1.06 0.84 0.91

VAY�~V AY

1.12 0.87 0.73 0.75

Average (Erms) 1.27 1.07 0.86 0.89


the energy level of the decomposed mode conversion signals. Therefore, it can be instantaneously concluded that the platedid not have any significant crack beyond the error level. On the other hand, the energy levels of the mode conversionsignal for all damage cases were much higher than those of the errors.

4.4. The effect of environmental variations

In-service structures are often subjected to changing environmental and operational conditions that affectmeasured signals, and these ambient variations can adversely affect the performance of SHM techniques, especiallythe ones which depend on previously obtained baseline data [24]. To tackle this issue, the effects of temperaturevariation and external dynamic loading on the proposed reference-free damage detection technique are investigatedin this subsection. Fig. 13 shows the overall experimental setup for temperature variation and external loadingtests. The same damage cases as shown in Fig. 9 are investigated again under varying temperature and loadingconditions.

For the temperature variation test, a thermocouple was used for precise temperature measurement of the specimen andthe temperature inside the temperature chamber was varied from –30 1C to 70 1C. To improve the signal-to-noise ratio,10-time averaging was performed in the frequency domain. Fig. 14 shows the decomposed individual modes obtainedfrom the intact case and damage case III at different temperatures. Each individual mode changes dramatically accordingto temperature variation. However, the energy level of the decomposed mode conversion signal obtained from thedamaged specimen was higher than that of the error at all investigated temperature values. Table 2 summarizesinstantaneous damage classification results for all investigated cases. Correct damage diagnosis was provided for all thecases investigated.

20 21 22 23

-2

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

- 30°C 20°C 70°C

ZS

20 21 22 23

-2

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

- 30°C 20°C 70°C

ZS

20 21 22 23

-2

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

- 30°C 20°C 70°C

ZA

20 21 22 23

-2

0

2

4

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

- 30°C 20°C 70°C

ZA

20 21 22 23-1

0

1

Frequency [kHz]

Initial errorsNor

mal

ized

Impe

danc

e

- 30°C 20°C 70°C

ZM

20 21 22 23-1

0

1

Frequency [kHz]

ModeconversionN

orm

aliz

edIm

peda

nce

- 30°C 20°C 70°C

ZM

~ ~

~ ~

~ ~

Fig. 14. Comparison of the decomposed individual impedance signals obtained from varying temperature conditions: (a), (c) and (e) indicate

decomposed individual impedance signals ~Z S , ~Z A and ~Z M , respectively, without a notch and (b), (d) and (f) indicate decomposed individual impedance

signals ~Z S , ~Z A and ~Z M , respectively, with a notch.


Next, damage diagnosis under external dynamic loading was conducted. In order to simulate external dynamic loading,a random excitation with frequency contents up to 500 Hz and a force level of 112 N was exerted on the test specimenusing a shaker as shown in Fig. 13(b). Fig. 15 shows the changes of the decomposed individual modes due to external

ZS

15 20 25

-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e

No load Dynamic load

ZA

15 20 25

-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e


ZM

15 20 25-1

0

1

Frequency [kHz]

Nor

mal

ized

Impe

danc

e


ZS

15 20 25

-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e


ZA

15 20 25

-1

0

1

2

Frequency [kHz]

Nor

mal

ized

Impe

danc

e


15 20 25-1

0

1

Frequency [kHz]

Modeconversion

Nor

mal

ized

Impe

danc

e


ZM

~ ~

~~

~ ~

Fig. 15. Comparison of the decomposed individual impedance signals obtained from dynamic loading conditions: (a), (c) and (e) indicate decomposed

individual impedance signals ~Z S , ~Z A and ~Z M , respectively, without a notch and (b), (d) and (f) indicate decomposed individual impedance signals ~Z S , ~Z A

and ~Z M , respectively, with a notch.

Table 2Instantaneous damage diagnosis under varying temperature.

Case Temp. (1C) Damage Index (�10–7) Damage classification

MCrms Erms

Intact �30 0.38 0.57 Intact20 0.53 0.83 Intact70 1.11 1.68 Intact

Damage I �30 0.61 0.40 Damage20 1.25 0.54 Damage70 1.91 1.53 Damage

Damage II �30 0.54 0.38 Damage20 1.06 0.58 Damage70 1.42 0.74 Damage

Damage III �30 0.57 0.37 Damage20 1.85 0.62 Damage70 2.56 1.04 Damage

Am

plitu

de

Am

plitu

de

Am

plitu

de

3

2

1

0

3

2

1

0

3

2

1

0

3

2

1

0


ERMS MCRMS ERMS MCRMSA

mpl

itude

Fig. 16. Instantaneous damage diagnosis under external dynamic loading: (a) intact case; (b) damage case I; (c) damage case II; and (d) damage case III

(a structure is classified as damaged only when ‘MCrms’ becomes larger than ‘Erms’).


loading and damage. The corresponding damage diagnosis is reported in Fig. 16. As before, the energy level of the errorsignal fluctuated due to external loading, but the energy level of the mode conversion was always higher than the energylevel of the error signal for all damage cases. False positive alarms were not produced for the undamaged condition andcorrect damage decision was instantaneously made for all damage cases.

5. Conclusions

This paper describes a new impedance-based damage detection technique where crack formation in a plate structurecan be instantaneously detected without referencing to previously stored baseline data. This technique utilizes two wafer-type piezoelectric transducers, which are attached at the same position but on the opposite sides of the plate, to isolatedamage-induced mode conversion from measured impedance signals. Once the mode conversion is extracted from the rawimpedance signals, an instantaneous damage classifier, which operates on the energy level of decomposed modeconversion impedance signatures, is developed. Numerical and experimental tests are conducted to demonstrate theeffectiveness of the proposed technique for crack detection. Because this reference-free technique does not rely onpreviously obtained baseline data for crack detection, this approach is able to minimize false alarms of damage due tooperational and environmental variations. The robustness of the proposed technique under temperature and loadingvariations is confirmed through laboratory experiments. However, the applicability of the proposed reference-freetechnique is currently limited only to plate structures with uniform thickness. Further investigation is underway toextend the proposed technique to more complex structures so that this technique can be applied to continuous onlinemonitoring of in-service structures.

Acknowledgments

This work was supported by the Mid-Career Researcher (Takeoff) Program (2010-0017456) and the Nuclear Research &Development Program (2010-0020423) and the Basic Science Research Program (2010-0004625) of National ResearchFoundation (NRF) of Korea funded by Ministry of Education, Science & Technology (MEST).

References

[1] D. Balageas, C.P. Fritzen, A. Guemes, Structural Health Monitoring, ISTE, Wiltshire, 2006.[2] H. Sohn, C.R. Farrar, M.H. Francois, J.C. Jerry, D.S. Devin, W.S. Daniel, R.N. Brett, A Review of Structural Health Monitoring Literature: 1996–2001,

Los Alamos National Laboratory Report, LA-13976-Ms, Los Alamos, NM, 2004.[3] J.W. Ayres, F. Lalande, Z. Chaudhry, C.A. Rogers, Qualitative impedance-based health monitoring of civil infrastructures, Smart Materials and

Structures 7 (1998) 599–605.[4] V. Giurgiutiu, A. Reynolds, C.A. Rogers, Experimental investigation of E/M impedance health monitoring of spot-welded structural joints, Journal of

Intelligent Materials Systems and Structures 10 (1999) 802–812.[5] G. Park, H. Cudney, D.J. Inman, Impedance-based health monitoring of civil structural components, ASCE Journal of Infrastructure Systems 6 (2000)

153–160.


[6] C.K. Soh, K. Tseng, S. Bhalla, A. Gupta, Performance of smart piezoceramic patches in health monitoring of a RC bridge, Smart Materials and Structures9 (2000) 533–542.

[7] A.N. Zagrai, V. Giurgiutiu, Electro-mechanical impedance method for crack detection in thin plates, Journal of Intelligent Material Systems andStructures 12 (2001) 709–718.

[8] S. Park, C.B. Yun, Y. Roh, J.J. Lee, PZT-based active damage detection technique for steel bridge components, Smart Materials and Structures 15 (2006)957–966.

[9] G. Park, H. Sohn, C.R. Farrar, D.J. Inman, Overview of piezoelectric impedance-based health monitoring and path forward, The Shock and VibrationDigest 35 (6) (2003) 451–463.

[10] K. Krishnamurthy, F. Lalande, C.A. Rogers, Effects of temperature on the electrical impedance of piezoelectric sensors, Proceedings of SPIE—TheInternational Society for Optical Engineering (San Diego) 2717 (1996) 302–310.

[11] G. Park, K. Kabeya, H. Cudney, D.J. Inman, Impedance-based health monitoring for temperature varying application, JSME International Journal:Mechanics and Material Engineering 42 (2) (1999) 249–258.

[12] V.G.M. Annamdas, Y. Yang, C.K. Soh, Influence of loading on the electromechanical admittance of piezoceramic transducers, Smart Materials andStructures 16 (2007) 1888–1897.

[13] K.Y. Koo, S. Park, J.J. Lee, C.-B. Yun, Impedance-based automated structural health monitoring incorporating effective frequency shift forcompensating temperature effects, Journal of Intelligent Material Systems and Structures 20 (2007) 367–377.

[14] S.B. Kim, H. Sohn, Instantaneous reference-free crack detection based on polarization characteristics of piezoelectric materials, Smart Materials andStructures 16 (2007) 2375–2387.

[15] Y.K. An, H. Sohn, Instantaneous crack detection under varying temperature and static loading conditions, Structural Control and Health Monitoring17 (2010) 730–741.

[16] H. Sohn, D. Dutta, Y.K. An, Temperature independent damage detection in plates using redundant signal measurements, Journal of NondestructiveEvaluation 30 (2011) 106–116.

[17] Y. Cho, Estimation of ultrasonic guided wave mode conversion in a plate with thickness variation, IEEE Transactions on Ultrasonics, Ferroelectrics, andFrequency Control 47 (2000) 591–603.

[18] Z. Su, L. Ye, Selective generation of Lamb wave modes and their propagation characteristics in defective composite laminates, The Institution ofMechanical Engineers, Part L: Journal of Materials: Design and Applications 218 (2004) 95–110.

[19] Y. Cho, J.L. Rose, A boundary element solution for a mode conversion study on the edge reflection of Lamb waves, Journal of Acoustical Society ofAmerica 99 (4) (1996) 2097–2109.

[20] A.P. French, Vibration and Waves, The MIT Introductory Physics Series, 1971.[21] E.J. Kim, M.K. Kim, H. Sohn, H.W. Park, Investigating electro-mechanical signals from collocated piezoelectric wafers for the reference-free damage

diagnosis of a plate, Smart Materials and Structures 20 (2011) 065001.[22] ABAQUS 6.7-4 User’s Manual, Dassault Systems, 2007.[23] S.J. Lee, H. Sohn, Active self-sensing scheme development for structural health monitoring, Smart Materials and Structures 15 (2006) 1734–1746.[24] H. Sohn, Effects of environmental and operational variability on structural health monitoring, Philosophical Transactions of the Royal Society A 365

(2007) 539–560.

Documents

Reference-free impedance-based crack detection in plates