doi: 10.1177/1045389x18818775 estimation using lamb … jimss...detection in a large isotropic plate...

Original Article

Journal of Intelligent Material Systemsand Structures1–18� The Author(s) 2018Article reuse guidelines:sagepub.com/journals-permissionsDOI: 10.1177/1045389X18818775journals.sagepub.com/home/jim

Numerical and experimentalinvestigation of damage severityestimation using Lamb wave–basedimaging methods

Asaad Migot1,2 , Yeasin Bhuiyan1 and Victor Giurgiutiu1

AbstractIn this article, estimation of crack size, shape, and orientation was investigated numerically and experimentally usingLamb waves. A hybrid global–local approach was used in conjunction with the imaging methods for the numerical simula-tion. The hybrid global–local approach allowed fast and efficient prediction of scattering wave signals for Lamb waveinteraction with crack from various incident directions. The simulation results showed the directionality effect of thescattering wave signals and suggested an optimum transmitter–sensor configuration. Two imaging methods were used:one involves the synthetic time reversal concept and the other involves Gaussian distribution function. Both imagingmethods show very good agreement during simulations. Experiments were designed and conducted based on the simu-lated results. A network of eight piezoelectric wafer active sensors was used to capture the scattering waves from thecrack. Both the pitch-catch and pulse-echo experimental modes were used. The directionality effect of incident Lambwaves on the imaging results was studied. The effect of summation, multiplication, and combined algorithms for eachimaging method was studied. It was found that both methods can successfully predict the crack size and orientation. Anattempt was made to use these imaging methods for detecting and sizing smaller sized damage (1- to 3-mm-diameterhole). It was found that these methods can successfully localize the hole, but size estimation was a bit challengingbecause of the smaller dimensions. The scattering waves for various hole sizes were studied.

KeywordsStructural health monitoring, wave propagation, synthetic time reversal, crack sizing, scattering waves

Introduction

State of the art

In recent years, the damage quantification using Lambwaves has become one of the topical research areas.Lamb waves are suitable for fast damage detection,because they propagate at very high speeds and maycomplete the inspection in a very short period of time.They can propagate a long distance with very littleenergy loss, so they enable the inspection of large areasof structures. The analyses of Lamb wave interactioncould potentially detect, localize, and estimate the sizeof various kinds of damage in structures (Chang et al.,2007; Masserey and Fromme, 2015; Saravanan et al.,2015). An experimental study was performed to obtainan appropriate Lamb wave mode to detect structuraldefects (Ghosh et al., 1998).

Attempts have been made for quantifying structuraldefects using Lamb wave scattering field (Baghalianet al., 2017; He et al., 2016). A network of sensors was

used for defect visualization in the pitch-catch experi-mental mode (Ihn and Chang, 2008). Damage indexwas calculated for each sensing path to characterize thedefect. Crack orientation was quantitatively determinedusing scattered Lamb wave and by evaluating the dif-ferent amplitudes of energy peaks in the Hilbert spectra(Lu et al., 2007). A system of an electromagnetic acous-tic transducer (EMAT) array was designed for detect-ing artificial defects in large metallic structures usingsymmetric Lamb wave mode (Wilcox et al., 2005). Thephased array filter approach was developed for damage

1Department of Mechanical Engineering, University of South Carolina,

Columbia, SC, USA2Department of Mechanical Engineering, College of Engineering, Thi-Qar

University, Nasiriyah, Iraq

Corresponding author:

Asaad Migot, Department of Mechanical Engineering, University of South

Carolina, 300 Main St., Columbia, SC 29208, USA.

Email: [email protected]

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detection in a large isotropic plate using Lamb wave(Kwon and Kim, 2016; Purekar et al., 2004). A syn-thetic time reversal method was developed for imagingthe structural damage using a network of sensors(Wang et al., 2004). Defects with larger dimensionswere used for imaging and a threshold value was set fordefect imaging.

Local wavenumber analysis approach was used fordamage quantification in isotropic or composite plates(Mesnil et al., 2014; Tian et al., 2013). A transversecrack in a metallic beam was quantified by a signal pro-cessing algorithm in the time–frequency domain basedon the wavelet transform technique (Su et al., 2003).This technique suppresses the diverse broadbandinterferences and effectively extracts useful damageinformation. However, damage quantification in a one-dimensional structure was considered. Numerical meth-ods are used for impact damage localization using sev-eral networks of sensors. The results showed that theerrors of impact damage localization decreased withincreasing the number of sensors (Migot andGiurgiutiu, 2017). Manufacturing defect in a compositewas identified using wavefield imaging (Juarez andLeckey, 2016). It had been shown that the time of flight(TOF) of a Lamb wave pulse can be used for damagedetection in a composite (Kessler et al., 2002). An ima-ging method based on correlation analysis called‘‘RAPID’’ (reconstruction algorithm for probabilisticinspection of defects) was used to inspect corrosion in awing skin (Hettler et al., 2015). A network of lead zir-conium titanate (PZT) sensors and the integration ofthe RAPID algorithm were used to detect and localizedamages in thermoplastic matrix composite plates(Azuara et al., 2018). An integrated methodology hasbeen developed to detect an impact event on a compo-site plate using a coarse network of sensors. Impactlocalization and impactor feature estimation were per-formed based on the dynamic response signals(Theodosiou et al., 2018).

The Lamb wave scattering from a simulated damagein a thick steel beam was considered using both thepitch-catch and pulse-echo experimental modes (Sunet al., 2009). The interaction of Lamb waves with a rivethole crack was studied both theoretically and experi-mentally (Bhuiyan et al., 2017; Fromme and Sayir,2002). The studies showed that the crack in the hole sig-nificantly changes the scattered wavefield. Fatiguecrack and defects in adhesive bonding were identifiedby analyzing the scattering Lamb wave (He et al., 2017;Tashakori et al., 2018). Crack length estimation in rivetholes was attempted using training datasets (He et al.,2013). However, only a few number of features such ascorrelation coefficient, signal’s amplitude, and phasewere considered. A network of PZT sensors and wave-number analysis were used for crack identification andcrack imaging (Lu et al., 2006; Yu et al., 2015).Ultrasonic imaging approach was used for predicting

the envelope of scattering waves (Ebrahimkhanlouet al., 2016). The damage was simulated by placingmagnets. The tomographic imaging technique was usedfor quantifying the corrosion damage in a hole (Wanget al., 2016). The iterative algebraic reconstruction tech-nique was utilized for generating the imaging results.

The scope of this study

This article presents the numerical and experimentalinvestigations to estimate the crack size using Lambwave–based imaging methods. A hybrid global–localapproach was used for fast and efficient numericalsimulations. Two imaging methods were used: (1) asynthetic time reversal concept and (2) a Gaussian dis-tribution function. Each imaging method was investi-gated with the scattering waves from the pitch-catchand pulse-echo experimental modes. The effect of sum-mation, multiplication, and combined algorithms wasstudied. These imaging methods were also attempted toperform localization and size estimation for varioussmall size holes (1 to 3 mm diameter).

Principles of the imaging methods

Two imaging methods were implemented using the scat-tered wave signals. The first method involved synthetictime reversal to determine the field values of each pixelusing the scattering signal’s amplitude. This method ishereafter referred to as ‘‘method A.’’ The flowchart ofmethod A is illustrated in Figure 1. The concept of thesynthetic time reversal method was first presented byWang et al. (2004). In this study, summation, multipli-cation, and combined algorithms were used to visulizethe damage in conjunction with the synthetic timereversal concept.

The second method involved the Gaussian distribu-tion function and scattering signals. This method ishereafter referred to as ‘‘method B.’’ The flowchart ofmethod B is illustrated in Figure 2. In this method, atfirst, the scattering wave signals were determined usingthe pitch-catch and/or pulse-echo experimental mode/s.The interested area was divided into pixels. The TOFof every pixel was determined using the equation ofellipse/circle. The pitch-catch experimental modeinvolved elliptical orbit and the TOF can be determinedusing equation (1)

tij=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(xT � xi)2 +(yT � yj)2

q

vg+

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(xi � xR)2 +(yj � yR)2

q

vg

ð1Þ

where tij is the TOF of the scattered signal;xT , yT , xR, yR, and xi, yj are the coordinates of thetransmitter sensor, receiver sensor, and pixel, respec-tively; and vg is the group velocities of Lamb wave

2 Journal of Intelligent Material Systems and Structures 00(0)

mode. When the pixels lay on the damage orbit of aparticular sensing path, then tij = td (td is the TOF fordamage; Figure 3).

The pulse-echo experimental mode involved the cir-cular orbit and the TOF can be determined using equa-tion (2). This orbit has one sensor in its center which

works as both a transmitter and a receiver at the sametime

tij =2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(xi � xT ,R)2 +(yj � yT ,R)2

q

vgð2Þ

Figure 1. Flowchart of the imaging method based on synthetictime reversal (method A).

Figure 3. Damage orbits: (a) elliptical orbit (pitch-catch) and (b) circular orbit (pulse-echo).

Figure 2. Flowchart of the imaging method based on Gaussiandistribution function (method B).

Migot et al. 3

The field value of each pixel was determined usingthe Gaussian distribution function (Su et al., 2009). Theequation of the Gaussian distribution function is shownbelow

f kij (x, y)=1

sffiffiffiffiffiffi2pp e�

(x�m)22s2 ð3Þ

where f kij (x, y) is the field value of every pixel P(x, y) ofthe image of a particular sensing path Tm � Rn (trans-mitter Tm and receiver Rn), x represents the TOF ateach pixel point tij(x, y) for the sensing path Tm � Rn,and m represents the TOF of the scattering wave packetfor the sensing path Tm � Rn which can be determinedexperimentally. The standard deviation, s, describesthe variability or dispersion of a data set, which wastaken as half the time range of the wave packet.m and n represent the indexes of the transmitters andreceivers, respectively, which vary from 1 to the totalnumbers of transmitters (NT ) and receivers (NR), suchas m= 1, 2, 3, . . . ,NT and n= 1, 2, 3, . . . ,NR.

To fuse all the images of different sensing paths,summation and/or multiplication algorithms were used(Michaels and Michaels, 2007; Wang et al., 2004) fol-lowing the equations below

Psum(x, y)=XNk = 1

f kij (x, y)

Pmult(x, y)=YN

k = 1

f kij (x, y)

ð4Þ

where Psum(x, y) and Pmult(x, y) are the total field valuesof each pixel point using the summation or multiplica-tion algorithm and N represents the total number ofsensing paths, that is

N =NT !

2! NT � 2ð Þ!ð5Þ

Numerical investigation of crack sizeestimation

In the past, many efforts have been made to developanalytical or numerical models of wave propagationand interaction with damages (Moreau et al., 2012;Wang and Chang, 2005). Numerical and experimentalstudies were adopted to analyze a crack at the interfaceof a structure subjected to pure shear loading and ultra-sonic loading. The results show the scattered wavesgenerated by the interaction of elastic waves with thecrack (Hafezi and Kundu, 2017). The local interactionsimulation approach (LISA) was developed to studythe nonlinear interaction of guided waves with fatiguecracks. The results show the nonlinear higher harmo-nics and mode conversion phenomena during the waveinteraction with crack (Shen and Cesnik, 2017; Shen

et al., 2018). In this article, a hybrid global–local(HGL) simulation approach (Shen and Giurgiutiu,2016) has been used for the numerical study. A sche-matic illustration of the HGL simulation is shown inFigure 4. A set of eight piezoelectric wafer active sensor(PWAS) transducers were used numbered from 1 to 8.Each of them was located at an equal distance of150 mm from the center of the crack. The crack lengthwas 18 mm. The Lamb waves were generated from thetransmitter PWAS. The transmitter PWASs (T1, T2,T3) were located at 0�, 45�, and 90� to the crack. Foreach transmitter, the rest of the PWAS transducersacted as receivers. The directionality of incident Lambwave and scattered wave was studied.

The HGL approach involved local finite elementmethod (FEM) simulation of the damage site accompa-nied with an exact analytical solution outside the dam-age region. The dimensions of the local FEM modelswere 100mm3 100mm3 1:6mm. A nonreflectiveboundary (NRB) was modeled using spring–damperelements surrounding the plate edges as in Shen andGiurgiutiu (2015) to minimize the edge-reflected waves.The overview of the entire HGL process is illustrated inFigure 5(a) following Shen and Giurgiutiu (2016). Thewave damage interaction coefficients (WDICs) wereobtained from the local FEM analysis and then insertedinto the global analytical framework. The WDICs wereobtained for three separate FEM models (0�, 45�, and90� crack orientation) as shown in Figure 5(b) to (d).The FEM model parameters were chosen based on ourprevious work as in Bhuiyan et al. (2017).

The WDIC is the measure of Lamb wave interactionwith the crack and is a complex-valued parameter. TheWDIC polar plots for all three incident directions ofLamb waves are shown in Figure 6. Both amplitudeand phase of WDIC show that the scattered waves fromthe crack have the directionality effect. For example,

Figure 4. Schematic illustration of the hybrid global–local(HGL) simulation.


when Lamb waves were incident at 45� to the crack, themaximum scattering amplitude occurred at 135� to thecrack. This means that a receiver sensor would pick upstronger scattering signals when it would be installed inthis direction. It can also be noticed that the maximumWDIC occurs when the Lamb waves were incident per-pendicular (90�) to the crack. For the 0� Lamb waveincident, weak WDIC occurred. This study of direction-ality effect suggested using the optimum transmitterand receiver combination for the imaging method asdiscussed later.

The scattering waveforms for the 0�, 45�, and 90�incident Lamb wave (transmitters T1, T2, T3) are illu-strated in Figure 7(a) to (c). The strongest scatteringsignal was observed for path 2-4 (transmitter, T2, recei-ver, R4), which corresponds to the 45� incident Lambwave and scattering wave received at 135�, which isexpected based on the WDIC profile (Figure 6(b)). Thescattering waveform for path 3-3 (transmitter, T3,

receiver, R3) also shows the stronger scattering signals,which corresponds to the 90� incident Lamb wave andscattering wave received at 90�. Note that WDICs ofthe scattered S0 Lamb wave mode for the incident S0Lamb wave (S0_S0) are plotted in Figure 7. The scat-tered shear horizontal (SH0) mode does exist for theincident S0 Lamb wave, but is not shown here.

For the imaging methods, the sensing signals atreceivers for two incident directions (45� and 90�) wereused. The imaging results of the simulated signals areillustrated in Figure 8. The combined summation andmultiplication algorithm was adopted to produce betterimages of the crack. It can be observed that both ima-ging methods predict the crack size to be 16 mm,whereas the simulated crack size was 18 mm. The simu-lated results also show the horizontal orientation of thecrack. It should be noted that during the simulation thescattering signals were not affected by any confoundingfactors (sensor bonding, environmental noise, electrical

Figure 5. (a) Overview of the combined global analytical and local FEM analyses and (b) three local FEM models for 0�, 45�, and90� crack orientation with the incident Lamb wave.

Migot et al. 5

connections, temperature–humidity, etc.) commonlyencountered in practice. Hence, an experimental inves-tigation was also performed as discussed later.

Experimental investigation of crackdetection and size estimation

Experimental setup

A large aluminum plate-like specimen with the dimen-sions of 1220 mm 3 1220 mm 3 1.6 mm was used.A sub-inspection area of 610 mm 3 610 mm wasinstrumented with an active network of eight PWAStransducers as shown in Figure 9. This sub-inspectionarea contained a very narrow slit which was manufac-tured using a 0.25-mm thin dental cutting disk. This isa simulated crack; for convenience, we will call it here-after as ‘‘crack.’’ The crack length was about 10 mmand oriented horizontally. The zoomed-in view of thecrack is shown in the inset of Figure 9. The center ofthe horizontal crack was located at (303 mm, 300 mm)with the left bottom corner of the sub-area as the

origin. The sensor network circumscribed the crack atthe center. The PWAS transducers of the network weredistributed with equal radial and angular distances.The diameter of the circular network was 300 mm. Thediameter of each PWAS transducer was 7 mm and thethickness was 0.2 mm.

A function generator was used to generate the three-count tone burst excitation signal at a center frequencyof 450 kHz. This frequency was chosen based on thetuning curve of PWAS. At this frequency–thicknessproduct, the symmetric Lamb wave (S0) was dominantin this plate specimen. The same PWAS transducer canbe used as a transmitter and a receiver of Lamb wavesignals. An oscilloscope recorded the received Lambwave signals. The specimen edges of the sub-area werecovered with damping clay to minimize the edge-reflected wave signals. Two experimental modes wereused: (1) pitch-catch and (2) pulse-echo modes. Inpitch-cath modes, each PWAS transducer acted as atransmitter, whereas the rest of them in the networkacted as receivers. In the pulse-echo mode, each PWAStransducer served as a transmitter and the same PWAS

Figure 6. WDIC directivity plot (amplitude and phase) at 450 kHz for the three different directions (0�, 45�, 90�) of the incidentLamb wave (LW) (‘‘S0_S0’’ means scattered S0 Lamb waves for the incident S0 Lamb wave): (a) 0� LW incidence, (b) 45� LWincidence, and (c) 90� LW incidence.


acted as a receiver. In both experimental modes, theimaging methods were performed for crack detectionand quantification as discussed next.

Scattering waveforms for the pitch-catch mode

First, the waveform results of the pitch-catch experi-ment are presented. For demonstration, only one set ofsignals is shown in Figure 10. In this set, PWAS #3 wasthe transmitter and the rest of the seven PWAS trans-ducers were the receivers. Figure 10(a) shows a set ofbaseline signals which were recorded in the beginningwithout any crack in the circular network. Figure 10(b)shows a set of measured signals with a 10-mm crack inthe circular network. In these signals, the first wavepackets are S0 Lamb waves. These S0 wave packets arestronger than the A0 wave packet as expected at

450 kHz frequency. The path as indicated in Figure 10represents a pair of transmitter and receiver. For eachtransmitter, there are seven possible paths for whichthe wave signals can be received by the receivers.

There are some additional scattered wave packetsdue to the crack in the specimen. These scattered wavepackets are plotted in Figure 11. The scattered wave sig-nals (scattered S0) were determined by the subtractionof baseline signals from the signals with 10-mm crack.This entire process was repeated for all possible sets oftransmitter and receivers. The scattered signals from allsets of transmitter and receiver were used for imagingmethods to quantify the crack size.

Imaging results for the pitch-catch mode

The direction of incident Lamb waves with respect tothe crack significantly affects the imaging results. Thecrack localization imaging results of method A (withsummation algorithm) for one transmitter are illu-strated in Figure 12. The pixel with the highest fieldvalue (the brightest pixel) indicates the crack location.Three incident directions were considered. For 0� inci-dence of the S0 Lamb wave, the imaging result is verypoor since the brightest pixel appeared near the trans-mitter (Figure 12(a)). This is because the scattering sig-nals are very weak for 0� incidence. For 45� incidenceof the S0 Lamb wave, the imaging result (Figure 12(b))is fair since the scattering signals are relatively stronger.For 90� incidence of the S0 Lamb wave (the incidentwave was perpendicular to the crack orientation), theimaging result (Figure 12(c)) is good since the scatteredsignals are the strongest of these three cases. Similarresults were obtained for method B; they are notrepeated here for the sake of brevity. One transmittermay not be sufficient to estimate the crack size, but itmay predict the location of the crack when it is placedin the best location with respect to the crack.

For estimating the crack size, method A (with sum-mation algorithm) imaging was used with a set of twotransmitters (for each transmitter, the rest of the sevenPWAS transducers were the receivers). The imagingresults are illustrated in Figure 13. The crack tips canbe identified using the sensing paths of two transmit-ters. Two dots with maximum field value (index value)can be obtained which represent the two crack tips.Figure 13(a) shows the imaging result after setting athreshold value (about 80% of maximum field value).This image was obtained using the scattering wave sig-nals of all the sensing paths of the transmitter setPWAS #2 and #3. From the zoomed-in image, twostrong spots can be identified. The distance between thetwo spots is 9 mm which is close to the crack length.Also, it can be noted that the crack is oriented horizon-tally as seen from the imaging result.

The similar procedure was repeated for the transmit-ter set PWAS #2 and #6. In this case, both transmitters

Figure 7. Scattering waveforms at various receivers for (a) 0�incident Lamb wave (S0), (b) 45� incident Lamb wave (S0), and(c) 90� incident Lamb wave (S0).

Migot et al. 7

are oriented at 45� to the crack. Based on the imagingresults shown in Figure 13(b), the crack length can beestimated to be 8 mm. This predicted crack length devi-ates from the actual crack length since the scatteringwave signals were relatively weaker for the 45� incidentLamb wave. When PWAS #2 and #7 were used as thetransmitters, the predicted crack length was 12 mm asshown in Figure 13(c).

The crack size can also be determined using a com-bined summation and multiplication algorithm fordetermining the total field values of pixels. The advan-tage of this method is that no threshold setting isrequired. This combined algorithm was used with bothmethod A and method B. The imaging results of bothmethods are illustrated in Figure 14. A set of two trans-mitters (PWAS #2 and #6) were used for this purpose.All seven sensing paths were used for each transmitter.

First, the summation algorithm was applied to generatethe image for an individual transmitter. Then, the mul-tiplication algorithm was applied to these images toobtain the final image as shown in Figure 14. Hence,two images were fused providing a clean image by thiscombined algorithm.

Figure 14(a) shows the imaging results of method Awhich predicts the crack length of 8 mm. Figure 14(b)shows the imaging results of method B which predictsthe crack length of 12 mm. Both methods show that thecrack is oriented horizontally.

Scattered waveforms and imaging results for thepulse-echo mode

In the pulse-echo experimental mode, each PWAStransducer acted simultaneously as both a transmitter

Figure 8. Estimation of crack size based on imaging (a) method A and (b) method B with the combined summation andmultiplication algorithm (‘‘T’’ means transmitter, two transmitters at 45� and 90� were used, and all the receivers for eachtransmitter were used).


and a receiver. The S0 Lamb waves originated from aPWAS, hit the crack, and scattered back to the samePWAS. The pulse-echo signals were recorded by theoscilloscope for all the sensors (PWAS #1, ..., #8). Thewaveform signals are shown in Figure 15. It can beobserved that path 3-3 and path 7-7 have the strongestscattering waveforms since they are directly perpendi-cular to the crack. The path 2-2, path 4-4, path 6-6,and path 8-8 have relatively weaker signals since theyare at an oblique (45�) incidence. These signals appearto have a similar amplitude as expected. However, path1-1 and path 5-5 have very weak scattering signals sincethey are parallel to the crack.

To estimate the crack size, the pulse-echo waveform sig-nals were fed into the two imaging methods (methods Aand B). In both methods, the summation algorithm with-out any threshold setting was used to determine the totalfield value at a pixel. The imaging results using method Aand method B are illustrated in Figure 16(a) and (b),respectively. It shows that the sensing paths were circularin shape. The intersecting sensing paths resulted in a hori-zontal band of bright dots where the field values were con-centrated. This is because the scattering waves originatedfrom this region.

From the zoomed-in image, two intensive red spotscan be identified which represent the crack tips.According to method A, the crack length can be esti-mated as 9 mm. According to method B, the cracklength can be estimated as 12 mm. In both methods,the crack orientation appears to be horizontal.However, method A shows many pixels with a similarlevel of field values on both sides of the two highestfield values along the crack length (which appear as aband of red pixels along the entire crack length). Onthe other hand, method B shows concentrated brightpixels at the two crack tips.

In both experimental modes (pitch-catch and pulse-echo), it appears that method A slightly underestimatesthe actual crack length, whereas method B slightly over-estimates the actual crack length.

Through-thickness hole detection and sizeestimation

The Lamb wave–based imaging methods were used todetect through-thickness hole with various diameters.The pitch-catch experiments were conducted in a

Figure 9. The experimental setup of using the SHM technique for crack detection.

Migot et al. 9

plate-like specimen. The details of the experimentalsetup and imaging results are discussed next.

Experimental setup

An aluminum plate-like specimen with the dimensionsof 600 mm 3 600 mm 3 1.6 mm was used in thisexperiment (Figure 17). A 1-mm through-thicknesshole was manufactured at a location with the coordi-nates (315 mm, 249 mm), while the bottom left cornerwas the origin. The specimen was instrumented with sixPWAS transducers (PWAS #0, ..., #5) as shown inFigure 17. These transducers were bonded at arbitrarylocations around the hole. A function generator wasused to generate the three-count tone burst signals at acenter frequency of 450 kHz and an oscilloscope wasused to record the signals. At this frequency–thicknessproduct, the symmetric Lamb wave was dominant inthe aluminum plate. The baseline signals wererecorded for all possible sensing paths correspondingto the 1-mm hole. The hole size was enlarged gradually:starting from 1 mm to 1.5, 2, 2.5, and 3 mm. The wave-form signals were measured for each hole size at allpossible sensing paths.

Measured waveforms for various hole sizes

The scattering waveforms are the key elements for theimaging methods. The scattering waveforms wereobtained by subtracting the baseline signals from themeasured signals for various hole sizes. The measuredsignals for the 1- and 1.5-mm holes are shown in Figure18(a) and (b), respectively. The signals received by allthe five sensors (e.g. path 0-1, 0-2, 0-3, etc.) are shownin Figure 18 for PWAS #0 as a transmitter. The signalscorresponding to the 1-mm hole were taken as the base-line signals. The waveforms in Figure 18 show that allof them have a strong S0 Lamb wave packet and aweak A0 Lamb wave packet as expected at 450 kHzcenter frequency.

The scattering waveforms for the 1.5-mm hole areshown in Figure 19. It can be observed that there isstrong scattered S0 in all the waveforms. Some pathshave a relatively stronger signal than the others. Forexample, in this case, the scattered signal of path 0-1 isstronger than that of path 0-4.

The hole size significantly affects the scattering sig-nal as illustrated in Figure 20. Two particular sensingpaths, namely, path 0-2 (transmitter PWAS #0 andreceiver PWAS #2) and path 2-4 (transmitter PWAS#2 and receiver PWAS #4), were considered for illus-tration. Stronger scattered signals can be observed asthe hole size increases. Both paths show similar results.

Imaging results for various hole sizes

Method A was used for hole localization and size esti-mation. Both summation and multiplication algorithmswere used. The imaging results for the three hole sizes(2, 2.5, and 3 mm diameter) are presented in Figure 21.The imaging results of the summation algorithm areshown on the left side and those of the multiplication

Figure 10. The waveform signals of pitch-catch experimentalmodes: (a) baseline signals without any crack and (b) signals with10-mm crack (PWAS #3 as a transmitter and the rest of theseven PWAS transducers as receivers).

Figure 11. Scattering wave signals for various sensing paths.These signals were obtained by the subtraction of baselinesignals from the signals with 10-mm crack (PWAS #3 as atransmitter and the rest of the seven PWAS transducers asreceivers).


algorithm are shown on the right side of Figure 21. Theresults of the multiplication algorithm are shown as a

zoomed-in view for clarity. The sensing paths of fourtransmitters (PWAS #0, #2, #3, #4) were used to

Figure 12. Directionality effect on the imaging results of method A: (a) 0� incident (transmitter PWAS #1), (b) 45� incident(transmitter PWAS #2), and (c) 90� incident (transmitter PWAS #3).

Migot et al. 11

Figure 13. Estimation of crack size based on method A imaging results using the sensing paths of two transmitters: (a) PWAS #2and #3, (b) PWAS #2 and #6, and (c) PWAS #2 and #7. ‘‘T’’ indicates the transmitter. A threshold value (80% of maximum fieldvalue) was set to obtain these images.


produce these images. These transmitters were chosensince they produced relatively stronger scatteringwaves.

From Figure 21, it can be observed that as the holesize increases the imaging result gets better. Because thelarger hole size (3mm diameter) produced stronger scat-tering waves, it has better imaging result. The hole canbe localized based on the highest field value of pixels.For a larger hole, the brighter pixels become more con-centrated and provide accurate localization. For exam-ple, the imaging localization result predicts the hole tobe located at (315 mm, 248 mm), whereas the actuallocation of the hole is at (315 mm, 249 mm). The multi-plication algorithm provided similar results as the sum-mation algorithm. The only difference is that themultiplication algorithm provides a cleaner image thanthe summation algorithm.

The multiplication algorithm results in Figure 21show brighter pixels with a circular shape. These

circular brighter pixels suggest that the damage is apoint source or circular in shape. However, in this case,the size of the hole is difficult to predict since the holesize is very small. It may need further investigation todetermine the smaller size holes. However, the imaging

Figure 14. Estimation of crack size based on imaging (a) method A and (b) method B with the combined summation andmultiplication algorithm.

Figure 15. Waveform signals of the pulse-echo experiment.

Migot et al. 13

Figure 16. Crack size estimation for the pulse-echo experimental mode using (a) method A and (b) method B (both methods usedthe summation algorithm; no thresholding applied).

Figure 17. An instrumented aluminum plate with a through-thickness hole. The hole size was enlarged gradually: starting from1 mm to 1.5, 2, 2.5, and 3 mm.


methods could successfully localize the smaller hole.Method B also predicted similar results as method Aand is not repeated for the sake of brevity.

Summary, conclusion, and suggestions forfuture work

Summary

This article briefly explained the principles of two ima-ging methods by presenting two flowcharts. Numericalsimulations were performed with the HGL approachand imaging methods (methods A and B). Method Ainvolves the synthetic time reversal concept and methodB involves Gaussian distribution function. Several localFEM simulations were performed for various Lambwave incidences (0�, 45�, and 90� to the crack). Thedirectionality effect and imaging results were studied.Two experimental investigations of two types of dam-age situations were considered: (1) crack and (2)through-thickness hole. The first experiment involved asparse array of eight PWAS transducers to quantify thecrack size using the imaging methods. The pitch-catch

and pulse-echo experimental modes were consideredfor each imaging method. The scattering waveform andimaging results were presented for both methods ineach experimental mode. The second experimentinvolved a network of sparse array of six PWAS

Figure 18. The waveform signals for (a) the 1-mm hole and (b)the 1.5-mm hole. The excitation signal was given from PWAS #0and received by the rest of the PWAS transducers.

Figure 19. Scattered signals at various receivers for the 1.5-mm hole, while the excitation was given by PWAS #0. Thesescattered signals were determined by subtraction of baselinesignals from the measured signals for the 1.5-mm hole.

Figure 20. The scattering signals for various hole sizes for twoparticular sensing paths: (a) path 0-2 (transmitter PWAS #0 andreceiver PWAS #2) and (b) path 2-4 (transmitter PWAS #2 andreceiver PWAS #4).

Migot et al. 15

Figure 21. Imaging results using the summation (left side) and multiplication (right side) algorithms for various hole sizes: (a) 2 mm,(b) 2.5 mm and (c) 3 mm diameter.


transducers to quantify the hole size using the sameimaging methods. The pitch-catch experimental modewas used to obtain the scattering signals. The relationbetween the hole size and the scattering signals wasstudied.

Conclusion

The HGL approach with imaging methods provided afast and efficient simulation of crack size estimation.The polar plot of the simulated WDICs revealed thedirectionality effect of the scattered wave signals ema-nated from the crack. Both the incident and sensingdirections of Lamb waves affect the scattering wave sig-nals which eventually affect the quality of imagingresults. The flowcharts of two imaging methods weredeveloped. The simulations and experiments show thatboth imaging methods successfully quantify the cracksize, shape, and orientation within an acceptable levelof accuracy. The experiment involved confounding fac-tors that affect the measurement of scattering wave sig-nals. These scattering signals play an important role incrack quantification. Stronger scattering waves result inbetter imaging results. The optimum sensor configura-tion results in better scattering signals which eventuallygive better damage quantification. For the pitch-catchmode, the sensing paths of two transmitters in optimumlocations may be enough to quantify the crack size. Thesynthetic time reversal–based imaging method (methodA) can be used with and without threshold setting. Theuse of the combined summation and multiplicationalgorithm may eliminate the need of thresholding forbetter crack imaging. Both the pitch-catch and pulse-echo modes show that the scattering waves are strongerwhen incident waves are perpendicular to the crack. Inboth experimental modes, the Gaussian distribution–based imaging method (method B) seems to overesti-mate the crack size. In an attempt to estimate a smaller(1–3 mm) through-thickness hole size, it was found thata smaller crack produces relatively weaker scatteringwaves. These scattering waves can be used for holedetection and localization but may not be sufficient toquantify the hole size.

Future work

These imaging methods may be used with passiveacoustic emission (AE) signals to quantify the AEsource. The experiment involving various hole dia-meters can be extended further. The diameter of thehole may be increased gradually to a size where onecan use these imaging methods to quantify the holesize. These methods may be used for sizing of actualfatigue crack. It would be interesting to study howsmall fatigue crack can be sized using these methods.

The study could be extended for estimating the butter-fly crack size in rivet holes.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication of thisarticle.

Funding

The author(s) disclosed receipt of the following financial sup-port for the research, authorship, and/or publication of thisarticle: This study was supported by Iraqi Ministry of HigherEducation and Laboratory for Active Materials and SmartStructures (LAMSS), which is thankfully acknowledged.

ORCID iDs

Asaad Migot https://orcid.org/0000-0002-6760-7718Yeasin Bhuiyan https://orcid.org/0000-0003-0365-5267

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doi: 10.1177/1045389x18818775 estimation using lamb … jimss...detection in a large isotropic plate...

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