A Modified Time Reversal Method for LambWave-based Diagnostics of Damage Severity

Ryan Watkins1 and Ratneshwar Jha2,∗

1,2Department of Mechanical and Aeronautical Engineering, Clarkson University

Potsdam, NY 13699, USA

ABSTRACT: Baseline-free diagnostics of damage severity using a Lambwave-based time reversal method are investigated. Due to the complex transducerarray necessary for time reversal diagnostics of a structure, a modified time rever-sal method is developed. Theoretical analysis of Lamb wave propagation, actuatedby piezoelectric transducers, and experimental comparison with the original timereversal method are used as a basis for validation of the modified time reversalmethod. Experimental applications of the modified time reversal method are thenused in analysis of damage severity classification. Increasing levels of damage aresimulated by incrementally impacting a composite plate with a steel ball. A trans-ducer array consisting of piezoelectric discs is used to send and receive A0 Lambwaves. The modified time reversal method is conducted for each actuator-sensorpair and a damage index is computed. Results show magnitude of the damageindex to be directly correlated to the severity of damage within the signal path.

Key Words: time reversal, damage severity, Lamb wave

INTRODUCTION

Due to the complex cyclic and discrete loading experienced while in service, regular inspectionand maintenance of aircraft is necessary to verify and maintain overall structural safety. Insome cases, parts must be replaced without regard to condition due to the high stress orhigh fatigue experienced during operation. Alternatively, damages may develop to a criticallevel between inspection cycles leading to catastrophic failure. It is estimated that 20% ofan aircraft’s lifetime costs go into inspection and maintenance (Kessler, 2002). The abilityto diagnose the structural integrity of an aircraft has the promise to change the currentinspection cycles into “condition based maintenance” and increase the use and safety ofaircraft structures.

In recent years, the use of composites has increased significantly in aerospace vehicles.The Airbus A380 is composed of approximately 25% composites and it is estimated thatBoeing’s 787 will contain 50% structural composites. Due to their high specific stiffness,composites result in lighter aircraft and are slowly replacing traditional aluminum parts.Along with weight reduction, composites are also corrosion resistant, have improved fatiguelife and can be fabricated into more form fitting designs than traditional materials. However,the laminated makeup of composites allows for possible delaminations and other internalflaws which severely decrease the material’s performance. “Barely visible impact damage” incomposites is a particular concern with respect to maintenance and reliability. The idea ofIntegrated Structural Health Monitoring (ISHM), wherein sensors/actuators are integratedwithin the structure itself, has therefore become of increasing interest. The goal of ISHM is todetermine presence, location, type, and severity of damages within a structure. ISHM woulddecrease the amount of time and effort necessary to inspect a structure and would allow forreal-time damage diagnosis on the ground and during flight.

The use of Lamb wave based structural health monitoring has shown promise in publishedresearch (Boller, 2000; Kessler, 2002; Kaczmarek, 2003; Toyama et al., 2003; Tua, 2004;

∗Author to whom correspondence should be addresses. E-mail: rjha@clarkson.edu

Lestari and Qiao, 2005; Banerjee et al., 2007; Kim et al., 2007; Raghavan and Cesnik, 2007).Lamb waves are of particular interest due to the similarity between their wavelength andthe thickness of composite structures generally used and their ability to travel far distances.These two features allow for detection of not only superficial but internal flaws and the abilityto examine large areas. Unfortunately, it is difficult to analyze measured responses due tothe multimodal and dispersive characteristics of Lamb waves propagation. Signal processingand dispersion curves have typically been used to help the damage detection process andunderstand the complex Lamb waves. The use of a time reversal method is a new approachdeveloped to mitigate Lamb wave dispersion effects and increase the applicability of Lambwaves for ISHM.

Applications of the time reversal method in damage evaluation are relatively new. Initialapplications for the time reversal method were aimed at increasing Lamb wave resolution byusing time reversal mirrors. In this process, a Lamb wave pulse is emitted at a target andthe reflected signal is recorded by an array of transducers, or time reversal mirrors. Thereflected section of the received signal is reversed in time and reemitted toward the target.By repeating this procedure, dispersion and unknown material deformation is compensatedfor by focusing the signal. Applications using this pulse-echo technique were also able todetect flaws in inspected areas (Ing and Fink, 1998). Later work further enhanced the timereversal method by using a pitch-catch method (Sohn et al., 2004). In this process, a toneburst signal is actuated from one transducer and received by another. The received signalis then reversed in time and re-emitted to the original transducer where the signal is againreceived and reversed in time. Based on the assumption of linear reciprocity within a healthystructure, the signal due to the time reversal process and the original signal compare exactly.However, for nonlinearities introduced into the system (damage), the linear reciprocity of thesystem breaks down and the irregularities between the two signals indicate the presence ofdamage. Unlike most other health monitoring techniques, this time reversal process introducesa baseline free method for damage detection. Validation of this technique was conducted byRose and Wang (2004), Butenas and Kazys (2006), and Giurgiutiu (2008) in which analytical(classical and Mindlin plate theory), numerical (FEM) and experimental testing were applied.The majority of recent work has been conducted by Sohn and Park applying the time reversalmethod to determine presence and location of damage. Improvement to the damage detectionalgorithm was made by first incorporating extreme value analysis (Sohn et al., 2004), and laterenhanced by adding consecutive outlier analysis to decrease the possibility of false positivedamage alerts . An enhanced time reversal method, using wavelet analysis, was developed tomake the time reversal process autonomous and increase the resolution of the process (Park etal., 2007). Effects of temperature on the time reversal process have also be briefly examined(Sohn et al., 2004).

This paper presents a modified time reversal method (MTRM) and evaluation of damageseverity within a structure. Development of the MTRM is used as a means to decreasethe hardware requirements of structural diagnostics. Theoretical analysis of Lamb wavepropagation, actuated by piezoelectric transducers, and experimental comparison with theoriginal time reversal method are used as a basis for validation of the modified time reversalmethod. Experimental applications of the modified time reversal method are then used inanalysis of damage severity classification. A composite plate containing impact damage isexperimentally investigated by integrating a piezoelectric transducer array onto the platesuch that each transducer can be used as both an actuator and a sensor. Increasing levelsof damage are simulated by incrementally impacting a composite plate with a steel ball. In

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diagnosing the health state of the plate, a damage index was used to quantitatively classifythe differences between the originally actuated signal and the final signal due to the modifiedtime reversal process. Magnitude of the damage index was used as basis for damage severityevaluation.

LAMB WAVES

Discovered by Horace Lamb in 1917 and first implemented as a means for damage detectionby Worlton in 1960, Lamb waves result from the superposition of guided longitudinal andtransverse (shear) waves. Lamb waves travel in thin plates with unconstrained boundariesand have the capability of traveling long distances with little attenuation. Due to their in-plane motion, Lamb waves can be used as a means to detect both superficial and internal flawsof a structure. Local stiffness changes, cracks and delamination (for composite structures)cause reflection, dispersion, attenuation and mode shape change. These changes in wavecharacteristics can be used to diagnose the corresponding structural defects.

2h

Symmetric

2h

Antisymmetric

Figure 1: Lamb wave mode shapes

As shown in Figure 1, Lamb waves exist in two mode shapes: symmetric and antisym-metric. Obtained from the three dimensional elasticity equations, the Lamb wave equationfor a plate is defined by (Xu and Giurgiutiu, 2007)

tan(βh)tan(αh)

= −[

4ξ2αβ(ξ2 − β2)2

]±1

(1)

where the positive exponential relates to symmetric waves, the negative exponential relatesto antisymmetric waves,

α2 =ω2

c2l− ξ2, β2 =

ω2

c2t− ξ2, ξ =

ω

cp

and ω, cl, ct, cp and h are the wave angular frequency, longitudinal velocity, transverse velocity,phase velocity, and plate half thickness, respectively. For isotropic materials,

c2l =λ+ 2µρ

and c2t =µ

ρ

where ρ is the material density and λ and µ are Lame constants.

Dispersion Curves

The Eigenvalue solutions to Equation (1) (ξS0 , ξS1 , ξS2 ... and ξA0 , ξA1 , ξA2 ...) exhibit themultimodal nature of Lamb waves. Further more, it can be shown that phase velocity, andcorresponding group velocity as defined by

cg =dω

dξ, (2)

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are dependent on frequency, making Lamb waves highly dispersive. Development of disper-sion curves, which map modal phase/group velocities with respect to propagation frequency,provide an important tool in examining the propagation characteristics of Lamb waves. Thequantitative dispersive characteristics of symmetric and antisymmetric Lamb waves are de-termined by solving Equation (1) for cp(ω) and evaluating Equation (2) for cg(ω). Due tothe dependency of longitudinal and transverse wave velocity on the properties of the medium,dispersive characteristics vary with material properties and geometry. The dispersive char-acteristics of the quasi-isotropic composite plates used in our experiments (carbon-epoxy,AS4/3501-6, [0/90]2s) are shown in Figure 2.

(a) (b)

Figure 2: Analytical dispersion curves for AS4/3501-6 [0/90]2s: (a) phase velocity and (b)group velocity

Actuation

Due to the highly dispersive nature of Lamb waves, mode tuning has been used as a meansto analyze the influence of input excitation on the modal characteristics of the resultant wavepropagation. In particular, modeling of the interaction between surface mounted piezoelectric(PZT) transducers and isotropic plates has been used to analyze the propagation of straight-crested and circular-crested waves (Giurgiutiu, 2005 and Raghavan and Cesnik, 2004). Foran ideally bonded PZT disc transducer, the shear stress in the bonding layer is representedby the pin force model

τ(r) = τ0δ(r − a)eiωt, (3)

where a is the radius of the PZT transducer, τ0 is the pin force at the ends of the PZTtransducer, r is the position along the transducer and ω is the angular frequency of theactuator. The resultant surface displacement wave solution is found to be (Raghavan andCesnik, 2004)

ur(r, t) = −πiτ0aµeiωt

∑ξS

J1(ξSa)NS(ξS)D′S(ξS)

H(2)1 (ξSr) +

∑ξA

J1(ξAa)NA(ξA)D′A(ξA)

H(2)1 (ξAr)

(4)

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where

DS = (ξ2 − β2)2 cos(αh) sin(βh) + 4ξ2αβ sin(αh) cos(βh)

DA = (ξ2 − β2)2 sin(αh) cos(βh) + 4ξ2αβ cos(αh) sin(βh)

NS = ξβ(ξ2 + β2) cos(αh) cos(βh)

NA = ξβ(ξ2 + β2) sin(αh) sin(βh)

and τ0, a, r, J1(.) and H(2)1 (.) are the maximum shear stress at the end of the actuator, the

actuator diameter, radial distance from the actuator, the first order Bessel function of thefirst kind and the first order Hankel function of the second kind, respectively. Expandingupon the displacement results as found by Raghavan and Cesnik, the corresponding surfacestrain wave solution is obtained from

εr(r, t) =∂ur(r, t)∂r

= −πiτ0aµeiωt

∑ξS

J1(ξSa)NS(ξS)D′S(ξS)

∂H(2)1 (ξSr)∂r

+∑ξA

J1(ξAa)NA(ξA)D′A(ξA)

∂H(2)1 (ξAr)∂r

. (5)

Applying the derivative for a first order Hankel function of the second kind as defined by

∂H(2)1 (ξr)∂r

=12ξ[H

(2)0 (ξr)−H(2)

2 (ξr)], (6)

the closed form surface strain wave solution for disc actuators is

εr(r, t) = −πiτ0a2µ

eiωt

∑ξS

ξSJ1(ξSa)NS(ξS)D′S(ξS)

(H

(2)0 (ξSr)−H(2)

2 (ξSr))

+∑ξA

ξAJ1(ξAa)NA(ξA)D′A(ξA)

(H

(2)0 (ξAr)−H(2)

2 (ξAr)) . (7)

Based on the displacement and strain relations defined by Equations (4) and (7), re-spectively, the modal effects of actuation frequency are investigated. Normalizing the dis-placement and strain with respect to their peak values, the mode tuning for the compositeplate/transducers used in the following experiments (carbon-epoxy, AS4/3501-6, [0/90]2s and10mm actuators) with respect to A0 and S0 Lamb waves are shown in Figure 3. Such thatthe actuation frequency is tuned properly, a single mode excitation can be simulated (as isfurther discussed later in the paper).

TIME REVERSAL METHOD

Current structural health monitoring techniques are often based on the comparison of currentstructural responses with a baseline “healthy” response case. Variations from the baseline casealerts the presence of damage. Unfortunately, operational and environmental conditions causevariations in the “healthy” response and, therefore, it is generally necessary to have baseline

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(a) (b)

Figure 3: Theoretical mode tuning for 1mm thick AS4/3501-6 [0/90]2s: (a) normalized dis-placement and (b) normalized strain

data for all possible operational and environmental conditions. For most structures, thereexists a complex array of possible functional conditions, making it necessary to perform front-end data mining for all of the structural response characteristics. Furthermore, the necessarydata storage increases the cost/decreases the efficiency of these diagnostic techniques. Theconcept of using a Time Reversal Methods (TRM) has recently been proposed as a baseline-free diagnostics technique in attempts to address these problems. Currently, the TRM hasbeen successfully implemented to detect the presence and location of damage and has thepotential to determine extent and type of damage.

To implement the TRM method for damage diagnosis, a transducer array is setup andused in a pitch-catch arrangement (that is, a signal is actuated from one transducer andrecorded at another). Each transducer must work both as a sensor and actuator, so typicallypiezoelectric (PZT) transducers are used. The time reversal process is as follows (and shownin Figure 4):

1. A Lamb wave tone burst is sent from transducer A and recorded at transducer B

2. The received signal at B is reversed in time [i.e., VB(t)→ VB(−t)]

3. The time reversed signal is sent from B back to A where it is recorded

4. The received signal at A is time reversed and compared to the original signal actuated

Since the TRM is based on the linear reciprocity of the system, for a linear elastic structure,reemission of the time reversed signal from B focuses the waves such that the signal received atA is qualitatively identical to the original signal emitted. When nonlinearities are introducedinto the signal path, the linear reciprocity of the system breaks down and the time reversalfails. In application to damage diagnostics, differences between the original signal and thefinal signal signify the existence of damage within the signal path.

Theoretically, the TRM for plate diagnostics was first validated by Wang (2003) andPark (2007) for low frequency A0 Lamb waves (actuated by disc transducers) and based onMindlin plate theory. Although, Mindlin plate theory improves upon classical plate theoryby incorporating shear deformation, it is still a simplified version of the three dimensionalelasticity equations for a plate and only approximates the propagation of low frequency A0

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Lamb waves. An enhanced investigation of the TRM was conducted by Xu and Giurgiutiu(2007) using the exact solutions to the three dimensional elastic equations, resulting in anexact validation of A0 and S0 Lamb waves (actuated by rectangular transducers) in TRMapplications.

B

A

1) Actuate signal

2) Read signal

3) Time reverse

5) Read signal

4) Actuate signal

6) Compare signals

Figure 4: Time reversal processes

Modified Time Reversal

In application, the time reversal method needs a complex actuator/sensor array. AlthoughPZT transducers alleviate some of the problems associated with actuation and sensing at thesame position, other complexities still exist. In particular, the hardware (power amplifier,data acquisition) necessary to support both actuation and sensing at all sensor locations isquite high. Therefore, a Modified Time Reversal Method (MTRM) is developed.

The MTRM is as shown in Figure 5. Step by step, the procedure is as follows (where themodified steps are denoted in bold font):

1. A Lamb wave tone burst is sent from transducer A and recorded at transducer B

2. The received signal at B is reversed in time [i.e., VB(t)→ VB(−t)]

3. The time reversed signal is sent from A to B where it is recorded

4. The received signal at B is time reversed and compared to the original signalactuated

Although the MTRM is similar to the original TRM, only one actuator is necessary for theprocess. Over a large structure, instead of actuating and sensing between every transducer,only a few actuators are necessary within a grid of sensors.

The MTRM can be validated by analyzing the process in Fourier space. For the trans-ducer arrangement in Figure 5, the signal received at B due to an input signal at A can berepresented by

V1(ω) = I(ω)G(ω), (8)

7

B

A

2) Read signal

3) Time reverse

1) Actuate signal

4) Actuate signal

5) Read signal

6) Compare signals

Figure 5: Modified time reversal process

where ˆ denotes the Fourier transform of the function, I is the input signal at A, and G isthe structural transfer function (and is defined in a later section). In Fourier space, the timereversal of the signal at B is defined by

V (ω) TR−−→ V ∗(ω), (9)

where ∗ denotes the complex conjugate of the function. Therefore, the time reversed signalat B (step 2) can be represented by

Vtr1(ω) = I∗(ω)G∗(ω). (10)

In the modified time reversal method proposed here, the time reversed signal is actuated fromA to B (step 3), resulting in

V2(ω) = Vtr1(ω)G(ω) = I∗(ω)G∗(ω)G(ω). (11)

Time reversing the final signal V2 (step 4),

Vtr2(ω) = I(ω)G∗(ω)G(ω) = I |G(ω)|2 (12)

and transforming the signal back into the time domain,

Vtr2(t) =1

2π

∫ ∞−∞

I(ω) |G(ω)|2 eiωtdω. (13)

Such that |G(ω)|2 is independent of ω (as discussed later), the signal at the end of the timereversal process is directly related to the originally actuated signal as found by

Vtr2(t) = CI(t), (14)

where C = |G(ω)|2 /2π. This is the same result as found for the original TRM (Park et. al.,2004 and Xu and Giurgiutiu, 2007).

8

Structural transfer function

The structural transfer function for Lamb wave propagation in a plate, as defined in Equation(8), is rewritten as

G(ω) =V (ω)I(ω)

. (15)

Based on the coupling between a PZT sensor (with thickness ta and Young’s Modulus Ea)ideally bonded to a plate (with thickness tp and Young’s Modulus Ep), the electric potentialexperienced by the sensor is defined by

V (t) =(ζ + ψ)tad13ζ

ε(t) (16)

where ε is the plate surface strain at the center of the sensor, ζ is related to the platedisplacement, strain and stress field (for low frequencies ζ = 4), d13 is the piezoelectriccoupling coefficient relating electric potential across the transducer thickness to in-plane radialstrain, and ψ = Eptp/Eata. For K ≡ ta(ζ + ψ)/d13ζ,

G(ω) =F {Kε(t)}I(ω)

. (17)

For a unit input actuation I(t) = eiω0t, the resulting strain response at a distance r fromthe actuator is as found by Equation (5). Such that only the A0 + S0 modes are excited,substitution of Equation (5) into Equation (17) results in

G(ω) =

(S(ξ)

∂H(2)1 (ξSr)∂r

+A(ξ)∂H

(2)1 (ξAr)∂r

)F{eiω0t

}F {eiω0t}

(18)

and reduces to

G(ω) = S(ξS0 )∂H

(2)1 (ξS0 r)∂r

+A(ξA0 )∂H

(2)1 (ξA0 r)∂r

(19)

where

S(ξ) = −πiKξ τ0aµJ1(ξa)

NS(ξ)D′S(ξ)

A(ξ) = −πiKξ τ0aµJ1(ξa)

NA(ξ)D′A(ξ)

.

Such that ξr >> 3/4 (ADD FIGURE TO SHOW RELATION?), the first order Hankelfunction can be approximated to be

H(2)1 (ξr) ≈

√2ξrπ

e−i(rξ−3π4

), (20)

resulting in the approximate derivative

∂H(2)1 (ξr)∂r

≈ T (ξ)e−irξ (21)

9

where

T (ξ) = −√

2ξrπ

ei3π4

(12r

+ iξ

). (22)

The time reversal transfer function is therefore approximated to be

|G(ω)|2 ≈∣∣T (ξS)S(ξS)

∣∣2 +∣∣T (ξA)A(ξA)

∣∣2 + S(ξS)A∗(ξA)T (ξS)T ∗(ξA)eir(ξA−ξS)+

S∗(ξS)A(ξA)T ∗(ξS)T (ξA)eir(ξS−ξA). (23)

Examining the effects of the time reversal transfer function on Equation (13) it can benoted that, such that the original signal actuated is a single mode (A0 or S0) and a singlefrequency (i.e., G becomes independent of driving frequency), then the results of Equation(14) are valid. However, for a multiple mode excitation S0 +A0, the exponentials in the lasttwo terms in Equation (23) cause side-bands, symmetric about a central wave, to appear asdefined by the time shifting principle of the Fourier transform. Therefore, only single modeexcitations for use in the time reversal method are valid. A single mode excitation is typicallyaccomplished by tuning the excitation frequency such that one mode is dominate over theother. Referring to Figure 3(b), it can be seen that the A0 mode is dominant for frequenciesaround 20kHz, 190kHz etc and that S0 is dominant for frequencies around 130kHz, 310kHzetc. In the following experiments, a 20kHz signal was used to simulate an A0 single modeexcitation.

Since it is not possible to excite a single frequency, a narrow-band tone burst is typicallyused to simulate a single frequency excitation. A tone burst consists of a windowed sine waveof finite energy. There are various forms of windowing functions that are used to smooth thesignal such as, Gaussian, Hamming or Hanning windows. Typically, a Hanning window isused and is defined by

h(t) ={

0.5[1− cos(2πt/τ)] for t ∈ [0, τ ]0 otherwise

(24)

where τ is the period of the window. The resulting tone burst is represented by

x(t) = h(t) sin(2πft) (25)

where f is the frequency of the signal in Hz (Xu and Giurgiutiu, 2007). The respectivebandwidth of a Hanning windowed tone burst is as defined by

b =4fn

(26)

where n is the number of cycles in the tone burst (n = τ/f) (Raghavan and Cesnik, 2004).Since the frequency of the actuation signal is chosen such that one mode is dominant, thebandwidth of the signal is decreased by increasing the number of cycles in the tone burst.However, although an extremely large number of cycles results in a very narrow bandwidth,the corresponding signal can become exceedingly complex (especially for short signal paths).Therefore, a 9.5 count tone burst was used in experiments such that the bandwidth wasnarrow enough, but the resulting signals were not too complex.

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Damage Index

The detection of damage using the time reversal method is accomplished by comparing theinput actuation signal with the signal due to the time reversal process. Deviations from theactuated signal signify the existence of damage which is typically quantified using a DamageIndex (DI). However, different methods of determining and interpreting these DI values havebeen used by researchers.

Sohn and Park (2003, 2007) used a damage index defined by

DISP = 1−

√√√√√ [∫ t1t0I(t)V (t)dt

]2∫ t1t0I(t)2dt

∫ t1t0V (t)2dt

(27)

where I(t) is the original signal, V (t) is the signal due to the time reversal process, and t0and t1 define the time interval over which the signals are compared. Based on this definition,DISP = 0 represents identical signals whereas DISP = 1 represents very dissimilar signals.Furthermore, it can be shown that for I(t) = βV (t), DISP = 0 for all β. Note however thatβ is a generic constant which does not relate to C. Therefore, this damage index focuses onshifts in frequency and changes in the overall shape of the time reversed signal but does notcapture differences in signal amplitudes.

Contrary to Sohn and Park’s quantification of dissimilarity, Giurgiutiu (2008) uses sim-ilarity based on an L2 error norm. So as to have the same basis as DISP , we redefine theresulting damage index to be

DIG = ‖V − I‖2 =

√√√√√√√∑N

[V − I]2∑N

(I)2(28)

where V and I are discrete data sets of the time reversed signal and the actuated signal,respectively, and N is the number of data points. Since the amplitude of the two signals Vand I are typically of different orders of magnitude as defined by C in Equation (14), eachsignal is normalized with respect to itself before determining the similarity. This damageindex also only focuses on shifts in frequency and changes in the overall shape of the timereversed signal and not differences in signal amplitudes since the amplitude information ofeach signal is lost in the normalization process.

EXPERIMENTAL SETUP

An experimental set-up using a quasi isotropic carbon/epoxy plate with surface bonded piezo-electric disc sensors was used to implement the MTR method. An eight ply carbon/epoxyplate, in a symmetric [0/90]2s layup, was fabricated using AS4/3501–6 pre-preg and a vacuumbag/oven curing technique. A piezoelectric (PZT) actuator/sensor network was integratedonto the composite plate as shown in Figure 6(a) where each transducer was affixed usingepoxy. The transducers have dimensions of 10mm diameter and 0.5mm thickness and theplate was tested in a cantilever set-up. Two impact damages were introduced into the plateas denoted by A and B in Figure 6(a). Damage A was constant for all tests where as thedamage at B was incrementally increased. For a controlled increase damage at B, a 175 g

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steel ball was dropped down a tube, onto B, from a fixed height of 4 ft. Based on the modetuning curve in Figure 3, a single frequency excitation of an A0 Lamb wave was simulatedusing a 20kHz, 9.5 cycle tone burst with amplitude of 100V . Do to a faulty sensor at location4, only the signal paths relating to transducers 1, 2 and 3 were used in the analysis.

The experimental setup is as shown in Figure 6(b). A National Instruments PCI 6229data acquisition card and a BNC-2110 board were used to actuate and record Lamb waves.A QuickPack R© power amplifier, made by Active Control Experts, was used to amplify theactuation signal and 3 Dual Mode Charge Amplifiers, made by Kistler, were used to amplifythe signals read from the PZT sensors.

1

23

4

A B 9.5”

5”

(a)

Sensor Steel ballCantilevered plate

(b)

Figure 6: Experimental setup: (a) transducer arrangement and (b) experimental test equip-ment

RESULTS AND DISCUSSIONS

Modified time reversal

To experimentally validate the use of the modified time reversal, a comparison between theresults generated by the TRM and MTRM was made. For each signal path, both the TRMand MTRM were conducted and the results were compared. Figure 7 shows the results forsignal path 1-2. Qualitatively, it can be noted that the two signals are close to identical.Quantitatively, the similarity between the two signals was determined as defined by

Similarity = 1− ‖Vtrm −Vmtrm‖2 (29)

where Vtrm and Vmtrm are the time reversal responses of the TRM and MTRM, respectively.Results are as shown in Table 1. For all three signal paths, the results from the MTRM methodare very similar to the results as found by the TR method. For those areas that are dissimilar,it is mostly due to the noise in the signal and could be mitigated using basic denoisingtechniques. Finally, it can be shown that the TRM/MTRM results are not dependent oninitial actuator (i.e., the results are the same for initial actuation at 1 for path 1-2 as the resultsfor initial actuation at 2 for path 1-2). This realization cuts down on the plate diagnosticprocedure from (N − 1)(N − 2) TR/MTR evaluations down to N(N − 1)/2 TRM/MTRMprocedures, where N is the number of transducers.

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Figure 7: TR/MTR comparison

Table 1: Comparison between TR and MTRPath Similarity(%)1-2 89.181-3 92.182-3 98.42

Damage severity

A set of test cases, with incremental damage levels, were examined to determine the applica-bility of the MTR for evaluation of damage severity. For each test case, the MTRM processfor all signal path permutations was performed. The test cases analyzed consisted of a base-line case and three damage levels (DL) referenced to as DLbase, DL1, DL2 and DL3 andcorresponding to 0, 4, 8 and 12 impacts at B, respectively . In evaluation of the results, bothdamage indexes (Eqns. 27 and 28) were used.

Figure 8: Baseline DI calculations

With respect to the baseline results, as shown in Figure 8, path 1-3 exhibits the highest

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(a) (b)

(c)

Figure 9: Damage index evaluation and comparison for increasing damage at B: (a) path1-2, (b) path 1-3 and (c) path 2-3

DI values for both damage indexing systems. Due to the initial damage at A and healthyconditions for paths 1-2 and 2-3, this is as expected. In analyzing the effects of increaseddamage on the DI values, the DI results at each damage level were compared to the baselineresults (by DIi/DIbase where i references the damage level case) and are as shown in Figure 9.For both damage indexing systems, it is shown that the damage index for path 1-2 increasesincrementally as the damage level is increased at B whereas the damage indices for paths 1-3and 2-3 remain close to the baseline values. It is important to note that baseline data is notnecessary to determine the presence of damage but it rather used as reference to show theeffects of damage on the indexing methods.

CONCLUSIONS

This paper has presented a time reversal method to detect the presence of damage within athin composite plate. A cross-ply carbon-epoxy composite plate with 8 layers was fabricatedand four PZT actuator/sensor were bonded to the plate surface. A modified time reversalmethod was developed to enhance the applicability of the process by decreasing the necessaryhardware to monitor the health of the structure. Two damage indexing systems, as developedby Park et al (2003 and 2007) and Giurgiutiu (2008), were used to evaluate the effects ofseverity of damage. It was found that both damage indexing evaluations increased as severityof damage increased, verifying the ability of the modified time reversal method to determine

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not only the presence of damage, but also the severity.This evaluation of damage severity is still in the preliminary stages of research and needs

further validation. Firstly, a larger array of damage types is necessary to investigate theapplicability of using the time reversal method for all damage cases. In particular, compositedelaminations are of interest in that they can not be seen by the naked eye. Furthermore,a more in depth correlation between the actual severity of damage within the plate and theindicated damage severity as indicated by the time reversal method is necessary. In thisstudy, there was little know about the actual extent of damage within the plate althoughit was assumed that each impact “increased” the damage at the impact location. Use ofcurrently accepted non destructive testing methods, such as use of a C-scan or x-ray imaging,to determine that actual state of damage within the structure would allow for a better com-parison of the accuracy of the the time reversal’s ability to detect damage severity. Finally, italso found that each indexing system exhibited different characteristics as the damage levelwas increased. Further study of the damage indexing systems and their ability to identifyincreases in damage severity is necessary to determine which method is best to be used in thetime reversal method.

REFERENCES

[1] Banerjee, S., Ricci, F., Monaco, E., Lecce, L. and Mal, A. 2007. “Autonomous Impact Damage Monitoringin a Stiffened Composite Panel,” Journal of Intelligent Material Systems and Structures, 18.

[2] Boller, C. 2000. “Next Generation Structural Health Monitoring and its Integration into Aircraft Design,”International Journal of Systems Science, 31(11):1333–1349.

[3] Butenas, G. and Kazys, R. 2006. “Investigation of Time-reversal Approach for Detection and Character-ization of Ultrasonic Defects in Dispersive Plates,” Ultragarsas, 61(4).

[4] Giurgiutiu, V. 2005. “Tuned Lamb Wave Excitation and Detection with Piezoelectric Wafer Active Sensorsfor Structural Health Monitoring,” Journal of Intelligent Material Systems and Structures, 16:291–305.

[5] Giurgiutiu, V. 2008. “Structural Health Monitoring with Piezoelectic Wafer Active Sensors,” Elsevier.

[6] Ing, R. and Fink, M. 1998. “Time-reversed Lamb Waves,” IEEE transactions on Ultrasonics, Ferro-electrics, and Frequency Control, 45(4):1032–1043.

[7] Kaczmarek, H. 2003. “Lamb Wave Interaction with Impact-induced Damage in Aircraft Composite: Useof the A0 Mode Excited by Air-coupled Transducer,” Journal of Composite Materials, 37(3).

[8] Kessler, S. S. 2002. “Piezoelectric-Based In-Situ Damage Detection of Composite Materials for StructuralHealth Monitoring Systems,” PhD thesis at Massachusetts Institute of Technology.

[9] Kim, Y.-H., Kim, D.-H., Han, J.-H. and Kim, C.-G. 2007. “Damage Assessment in Layered Compositesusing Spectral Analysis and Lamb Wave,” ScienceDirect:Composites Part B: Engineering, 38:800–809.

[10] Lestari, W. and Qiao, P. 2005. “Damage Identification for Carbon/Epoxy Laminated Composite Struc-tures Based on Wave Propagation Analysis,” 46th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics & Materials Conference, .

[11] Park, H. W., Sohn, H., Law, K. H. and Farrar, C. R. 2007. “Time Reversal Active Sensing for HealthMonitoring of a Composite Plate,” Journal of Sound and Vibration, 302:50–66.

[12] Raghavan, A. and Cesnik, C. E. S. 2004. “Modeling of piezoelectric-based Lamb wave generation andsensing for structural health monitoring” Society of Photo-Optical Instrumentation Engineers (SPIE)Conference Series, Bellingham, WA.

[13] Raghavan, A. and Cesnik, C. E. S. 2007. “Review of Guided-wave Structural Health Monitoring,” TheShock and Vibration Digest, 39(2):91–114.

[14] Sohn, H., Park, G., Wait, J. R., Limback, N. P. and Farrar, C. R. 2004. “Wavelet-based Active Sensingfor Delamination Detection in Composite Structures,” Smart Materials and Structures, 13:153–160.

[15] Sohn, H., Park, H. W., Law, K. H. and Farrar, C. R. 2007a. “Combination of a Time Reversal Processand a Consecutive Outlier Analysis for Baseline-free Damage Diagnosis,” Journal of Intelligent MaterialSystems and Structures, 18.

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[16] Toyama, N., Okabe, T. and Takeda, N. 2003. “Lamb Wave Evaluation and Localization of TransverseCracks in Cross-ply Laminates,” Journal of Material Science, 38:1765–1771.

[17] Tua, P. S., Quek, S. T. and Wang, Q. 2004. “Detection of Cracks in Plates using Piezo-actuated LambWaves,” Smart Materials and Structures, 13:643–660.

[18] Wang, C. H., Rose, J. T. and Chang, F.-K. 2003. “A Computerized Time-reversal Method for Struc-tural Health Monitoring,” Nondestuctive Evaluation and Health Monitoring of Aerospace Materials andComposites II, San Diego, California.

[19] Xu, B. and Giurgiutiu, V. 2007. “Single Mode Tuning Effects on Lamb Wave Time Reversal with Piezo-electric Wafer Active Sensors for Structural Health Monitoring,” Journal of Nondestructive Evaluation,26:123–134.

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