This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 143.248.122.79

This content was downloaded on 14/07/2017 at 02:24

Please note that terms and conditions apply.

Baseline-free fatigue crack detection based on spectral correlation and nonlinear wave

modulation

View the table of contents for this issue, or go to the journal homepage for more

2016 Smart Mater. Struct. 25 125034

(http://iopscience.iop.org/0964-1726/25/12/125034)

Home Search Collections Journals About Contact us My IOPscience

You may also be interested in:

Development and field application of a nonlinear ultrasonic modulation technique for fatigue crack

detection without reference data from an intact condition

Hyung Jin Lim, Yongtak Kim, Gunhee Koo et al.

Baseline-free damage visualization using noncontact laser nonlinear ultrasonics and state space

geometrical changes

Peipei Liu, Hoon Sohn and Byeongjin Park

Wireless ultrasonic wavefield imaging via laser for hidden damage detection inside a steel box

girder bridge

Yun-Kyu An, Homin Song and Hoon Sohn

Health monitoring of cuplok scaffold joint connection using piezoceramic transducers and time

reversal method

Liuyu Zhang, Chenyu Wang, Linsheng Huo et al.

Complete noncontact laser ultrasonic imaging for automated crack visualization in a plate

Yun-Kyu An, Byeongjin Park and Hoon Sohn

Guided wave based structural health monitoring: A review

Mira Mitra and S Gopalakrishnan

A structural damage detection indicator based on principal component analysis and statistical

hypothesis testing

L E Mujica, M Ruiz, F Pozo et al.

Residual fatigue life estimation using a nonlinear ultrasound modulation method

Gian Piero Malfense Fierro and Michele Meo

Baseline-free fatigue crack detection basedon spectral correlation and nonlinear wavemodulation

Peipei Liu, Hoon Sohn, Suyoung Yang and Hyung Jin Lim

Department of Civil and Environmental Engineering, Korea Advanced Institute of Science andTechnology, Daejeon, 34141, Korea

E-mail: hoonsohn@kaist.ac.kr

Received 3 June 2016, revised 11 August 2016Accepted for publication 6 September 2016Published 15 November 2016

AbstractBy generating ultrasonic waves at two different frequencies onto a cracked structure,modulations due to crack-induced nonlinearity can be observed in the corresponding ultrasonicresponse. This nonlinear wave modulation phenomenon has been widely studied and provencapable of detecting a fatigue crack at a very early stage. However, under field conditions, otherexogenous vibrations exist and the modulation components can be buried under ambient noises,making it difficult to extract the modulation components simply by using a spectral densityfunction. In this study, the nonlinear modulation components in the ultrasonic response wereextracted using a spectral correlation function (the double Fourier transform) with respect to timeand time lag of a signal’s autocorrelation. Using spectral correlation, noise or interference, whichis spectrally overlapped with the nonlinear modulation components in the ultrasonic response,can be effectively removed or reduced. Only the nonlinear modulation components areaccentuated at specific coordinates of the spectral correlation plot. A damage feature is definedby comparing the spectral correlation value between nonlinear modulation components withother spectral correlation values among randomly selected frequencies. Then, by analyzing thestatistical characteristics of the multiple damage feature values obtained from different inputfrequency combinations, fatigue cracks can be detected without relying on baseline data obtainedfrom the pristine condition of the target structure. In the end, an experimental test was conductedon aluminum plates with a real fatigue crack and the test signals were contaminated by simulatednoises with varying signal-to-noise ratios. The results validated the proposed technique.

Keywords: nonlinear wave modulation, spectral correlation, noise reduction, fatigue crack,baseline-free damage diagnosis

(Some figures may appear in colour only in the online journal)

1. Introduction

Fatigue in metals is a subject of great practical importancebecause fatigue cracks are a major cause of the failure ofengineering components and structures made of metals [1].Therefore, non-destructive testing (NDT) and structural healthmonitoring (SHM) communities have a keen interest in earlydetection of fatigue cracks. Among various NDT and SHMtechniques, ultrasonic techniques have gained popularity forfatigue crack detection, because those techniques can benefit

from built-in transduction and moderately large inspectionranges. Conventional linear ultrasonic techniques detect acrack by measuring variations of the amplitude, phase, andmode conversion of ultrasonic waves which are either trans-mitted or reflected from the crack [2–5]. However, fatiguecrack typically grows rapidly and leads to sudden failure onceit becomes detectable by the conventional linear techniques.

Recent studies have shown that fatigue cracks and theirprecursors often serve as a source for generating nonlinearwaves, and the sensitivity of the nonlinear ultrasonic

Smart Materials and Structures

Smart Mater. Struct. 25 (2016) 125034 (12pp) doi:10.1088/0964-1726/25/12/125034

0964-1726/16/125034+12$33.00 © 2016 IOP Publishing Ltd Printed in the UK1

techniques to fatigue crack is much higher than what can beachieved by conventional linear ultrasonic techniques [6–15].More specifically, nonlinearity due to crack evolution candistort ultrasonic waves, create accompanying harmonics andmodulations of different frequencies, and change resonancefrequencies as the amplitude of the driving input changes. Asthis nonlinearity comes from a very small breathing crack oreven from plastic deformation, it can effectively allowdetection of the crack at its early stage.

Among all the nonlinear ultrasonic techniques, nonlinearwave modulation is based on nonlinear mixing of two dis-tinctive input signals [6]. Normally, low-frequency and high-frequency inputs are used to create modulations for crackdetection [6–14]. Using a piezoelectric stack actuator forgeneration of a low-frequency signal and a surface-mountedpiezoelectric transducer for creation of a high-frequency sig-nal, a fatigue crack in an aluminum plate was detected [7].Nonlinear wave modulation has also been used for detectingfatigue cracks in welded pipe joints and concrete beams [8, 9].Moreover, fixed low-frequency, and swept high-frequency,inputs were used to find an optimal combination of the low-frequency and high-frequency inputs that could amplify themodulation level caused by cracks [10]. Fatigue cracks incomplex structures, such as aircraft fitting-lug mock-up spe-cimens, have been detected during investigation of variouslow-frequency and high-frequency combinations [11]. Inanother study, broadband laser input was used instead of two

individual input frequencies, and cracks were detected bycounting the spectral peaks produced by modulations amongthe broadband input frequencies [12].

In spite of the development of various nonlinear wavemodulation techniques, there are still technical hurdles thatneed to be overcome before these techniques can maketransitions to real NDT/SHM applications. First, because

Figure 1. Spectral correlation results (ignoring symmetric values at α<0) for (a) response signal from a linear system, (b) response signalfrom a nonlinear system.

Table 1. Summary of the peak coordinates in spectralcorrelation (a > 0).

Frequencycombination

Coordinate of spectral cor-relation peak ( )af ,

Linear f ,a fb f ,a fb +-

⎛⎝⎜

⎞⎠⎟

f ff f

2,a b

a b

Nonlinear f ,a f ,b

+f f ,a b

-f fa b

f ,a fb +-

⎛⎝⎜

⎞⎠⎟

f ff f

2,a b

a b

f ,a -f fa b -⎛⎝⎜

⎞⎠⎟f

ff

2,a

bb

f ,a +f fa b +⎛⎝⎜

⎞⎠⎟f

ff

2,a

bb

f ,b -f fa b ∣ ∣-⎛⎝⎜

⎞⎠⎟

ff f

2, 2a

a b

f ,b +f fa b +⎛⎝⎜

⎞⎠⎟f

ff

2,b

aa

+f f ,a b -f fa b ( )f f, 2a b

2

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

the amplitude of the modulation components is at least oneor two orders of magnitude smaller than that of the linearcomponents, it becomes difficult to extract the modulationcomponents simply by using the spectral density function,especially under noisy field conditions. Second, with only a

few exceptions [16, 17], the existing nonlinear wave mod-ulation techniques detect fatigue cracks by comparing theamplitudes of the modulation components obtained from thecurrent and pristine conditions. However, these existingtechniques can be susceptible to false alarms due to signal

Figure 2. Illustration of spectral correlation properties: (a) stationary noise signal exhibits no spectral correlation; (b) and (c) two statisticallyweak-linked components exhibit weak spectral correlation.

Figure 3. Different components contributing to the response of the spectral density function at f fa b.

3

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

variations under changing temperature or loading condi-tions [18].

In this paper, a baseline-free technique based on spectralcorrelation and nonlinear wave modulation is developed forfatigue crack detection. The proposed technique offers thefollowing advantages: (1) nonlinear modulations are morereliably extracted using spectral correlation instead of

conventional spectral density function, (2) spectral correlationis used to detect nonlinear modulations other than thecyclostationarity of the response signal or the statistical linkbetween the original input frequencies, (3) stationary noiseand statistically weak-linked components in ultrasonicresponse signals are removed or reduced through spectralcorrelation, (4) a damage feature is defined by comparing thespectral correlation value between nonlinear modulationcomponents with other spectral correlation values amongrandomly selected frequencies, and (5) fatigue cracks can bedetected without relying on any baseline data obtained fromthe pristine condition of a target structure.

The paper is organized as follows. The working principleof spectral correlation with nonlinear modulated waves isintroduced in section 2. A baseline-free fatigue crack detec-tion technique is presented in section 3. This is followed bysection 4, in which the results of an experimental test arereported to validate the proposed technique. Finally, theconclusions of the paper are presented in section 5.

2. Spectral correlation of nonlinear modulated waves

When two inputs with different frequencies fa and fb( )>f fa b are applied to a linear system, the system responsecontains the output frequency components correspondingonly to the input frequencies. However, if the system behavesnonlinearly (e.g., due to fatigue crack existence or evenplastic deformation), the system response will contain notonly the input frequencies but also their harmonics (multipliesof input frequencies, i.e., f2 a and )f2 b and modulations (linearcombinations of input frequencies, i.e., f f ,a b f f2 ,a b

f f2 ,a b etc) [19, 20]. This phenomenon is called nonlinearwave modulation or nonlinear ultrasonic modulation. Becausethis phenomenon occurs only if there are nonlinear sources, itcan be considered a signature of the presence of nonlinearity,and thus the existence of a crack. Typically, spectral densityfunction is used to extract the harmonics or modulations.Given a random signal ( )x t , its spectral density function

Figure 4. Spectral correlation value ( )S fxf

ar2 br obtained from a

randomly selected frequency combination of f fand .ar br

Figure 5. Calculation of the damage feature defined in equation (10)by comparing spectral correlation value ( )S fx

fa

2 b with the thresholdvalue T evaluated using multiple ( )S fx

far

2 br .

Figure 6. Aluminum plate with fatigue crack: (a) geometrical dimensions and PZT transducer arrangement; (b) a close-up of the fatiguecrack.

4

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

(power spectrum) is given by

( ) [ ( ) ( )] ( )*=P f E X f X f , 1x

where X( f ) is the Fourier transform of ( )x t and * denotes thecomplex conjugate. In this study, only the first-order mod-ulations at f fa b are considered for fatigue crack detection,and spectral correlation is adopted to extract these modulationcomponents from the response signals.

Spectral correlation has been exploited in various fields,such as diagnosis of gear faults in moving mechanical sys-tems [21–23], and channel sensing and spectrum allocation inwireless communication [24–26]. In general, spectral corre-lation is used to identify second-order (or wide-sense)cyclostationary stochastic processes whose autocorrelationfunctions vary periodically with time [27]. For ( )x t , itsautocorrelation is defined as

( ) [ ( ) ( )] ( )*t t t= + -R t E x t x t, 2 2 , 2x / /

where t is the time lag. If ( ) ( )t t= +R t R t T, , ,x x p signal( )x t is second-order cyclostationary for all t with a cyclic

period T .p Spectral correlation is then the double Fouriertransform of the autocorrelation function ( )tR t,x with respectto t and t [27]

∬( ) { ( )}

( )( )

t

t t

=

=

at

pa p t- -

S f FT R t

R t t

,

, e e d d ,3

x t x

xt f

,

i2 i2

/

where a is cyclic frequency and f is spectral frequency.Equation (3) can also be written as

( ) [ ( ) ( )] ( )*a a= + -aS f E X f X f2 2 . 4x / /

To interpret the results brought by spectral correlation, letus consider a signal [21]

( ) ( ) ( ) ( )= +p px t a t b te e , 5f t f ti2 i2a b

where ( )a t and ( )b t are two low-pass filtered random ampl-itude modulations. This signal ( )x t can also present theresponse of a linear system subjected to inputs at frequenciesfa and f .b The calculation of the autocorrelation of ( )x t will

furnish the following equation

( )

( )

( )

( )

*

*

*

*

tt t

t t

t t

t t

= + -

+ + -

+ + -

´

+ + -

´

p t

p t

p p t

p p t

-+

-+

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎡⎣⎢

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥

⎡⎣⎢

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥

⎡⎣⎢

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥

⎡⎣⎢

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎤⎦⎥

R t E a t a t

E b t b t

E a t b t

E b t a t

,2 2

e

2 2e

2 2

e e

2 2

e e .

6

xf

f

f f tf f

f f tf f

i2

i2

i2 i22

i2 i22

a

b

a ba b

b ab a

Next, by calculating the double Fourier transform ofequation (6) with respect to t and t, we obtain the followingspectral correlation equation

( ) ( ) ( ) ( ) ( )

( ( ))

( ( ))

( )

g d a g d a

g d a

g d a

= - + -

+ -+

- -

+ -+

- -

a

⎛⎝⎜

⎛⎝⎜

⎞⎠⎟

⎞⎠⎟

⎛⎝⎜

⎛⎝⎜

⎞⎠⎟

⎞⎠⎟

S f f f f f

ff f

f f

ff f

f f

2

2,

7

x a a b b

aba b

a b

bab a

b a

where d is the Dirac delta function, ga and gb are the spectradensities of ( )a t and ( )b t , gab and gba are the cross-spectraldensities between ( )a t and ( )b t , respectively. Here, g ,a γb,g ,ab and gba are functions with a zero-centered peak [21].

As shown in equation (7), for a = 0, the first two termson the right side of the equation represent spectral correlationvalues at =f fa and f ,b respectively, and ( )S fx

0 becomes( )P f ,x defined in equation (1). For a ¹ 0, we can find two

symmetric spectral correlation values at

( )( )a= = -+f f f, .

f fa b2

a b Figure 1(a) presents the

spectral correlation of the response signal ( )x t obtained froma linear system (ignoring symmetric values at α<0). Forsimplicity, we set ( ) ( )= =a t b t 1 in figure 1.

For a nonlinear system, there are two additional modu-lated frequency components +f fa b and -f fa b in the

Figure 7. Experimental setup: (a) test schematic; (b) hardware and specimen configurations.

5

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

response signal besides fa and f .b By expanding equation (7)with four input frequencies, a total of ten peak values appearin the spectral correlation, as shown in figure 1(b). For a = 0,we again encounter its spectral density function with fourpeak values at f ,a f ,b +f f ,a b and -f f .a b When a ¹ 0, sixpeaks are produced among the frequency components f ,a f ,b

+f fa b and -f fa b and their ( )af , coordinates in spectralcorrelation are listed in table 1.

Comparison of figures 1(a) and (b) shows that there arefive more peaks ( )a > 0 in spectral correlation when mod-ulation components exist in the response signal. That is, thespectral correlation values at those five coordinates willincrease when fatigue cracks exist in the target structure andcause nonlinear wave modulation. In this study, we considerthe spectral correlation value ( )S fx

fa

2 b between the two non-linear modulation components at +f fa b and -f f .a b The

Figure 8. Spectral correlation values obtained from the intact and damaged specimens for multiple frequency combinations.

6

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

major departure of this study from the aforementioned studies[21–27] is that spectral correlation is used to detect the non-linear modulations instead of the cyclostationarity of theresponse signal ( )x t , or the statistical link between the ori-ginal input frequencies fa and fb.

Two notable properties of spectral correlation [28] arethat, (1) stationary noise exhibits no spectral correlation (for

)a ¹ 0 , and (2) two statistically weak-linked componentsexhibit weak spectral correlation (for )a ¹ 0 . To understandthese two properties, simulation results are plotted in figure 2.Figure 2(a) shows the spectral correlation of stationary whitenoise; its spectral correlation values appear only at a = 0.Figures 2(b) and (c) show the spectral correlation of signal

( )x t defined in equation (5). In this case, ( )a t and ( )b t arestrongly correlated when ( ) ( )= =a t b t 1, as shown infigure 2(b). This also indicates a strong statistical linkbetween the two frequency components at fa and f .b On theother hand, when ( )a t and ( )b t are stastically independent(not statistically linked), the last two terms on the right side ofequations (6) and (7) become zero and the peak value at

( )-+f f,

f fa b2

a b vanishes, as shown in figure 2(c). That is,

signal ( )x t in figure 2(c) becomes stationary, and the spectralcorrelation of ( )x t contains only two peaks at a = 0. The

spectral correlation value ( )- +Sx

f f f f

2a b a b can be estimated as

[28]

( ) ( ) ( )+

~- ⎛⎝⎜

⎞⎠⎟S

f fc S f S f

2, 8x

f f a ba b x a x b,

0 0a b

where ( )S fx a0 and ( )S fx b

0 are spectral density values of ( )x t atfrequencies fa and f ,b respectively, and ca b, ( )1 is the cor-relation coefficient, reflecting the statistical link between thetwo frequency components at fa and fb.

As shown in figure 3, there are many components( )S f fx a b i

0 contributing to the spectral responses at f f .a b

Here, ( )S f fx a b i0 are the spectral density values of the ith

component at the modulation frequencies f f .a b First, thereare the real modulations ( )S f fx a b

01 caused by two inputs at

fa and f .b Second, modulations ( )S f fx a b0

2 among noise atother frequencies, can occur at f fa b (e.g.,

- = -f f f f ,a b a b1 1 )+ = +f f f f .a b a b2 2 Third, harmonics( )S f fx a b

03 caused by noise inputs at ( )-f f 2a b / and

( )+f f 2,a b / can appear at -f fa b and +f f ,a b respectively.Fourth, additional noise ( )S f fx a b

04 at f fa b can be added

to the modulation components at f f .a b Under harsh testconditions, the effect of the true modulation can be smearedby the aforementioned noise components. In the presence ofthe noise components, similar to equation (8), ( )S fx

fa

2 b can berevised as follows

( ) ( ) ( ) ( )å~ + -+ -S f c S f f S f f , 9xf

ai

a b a b x a b i x a b i2

,0 0b

i

where + -ca b a b, iis the corresponding correlation coefficient

indicating the statistical link between the ith components atf f .a b For ( )S f f ,x a b

01 because they are produced by the

common input at fa and f ,b they are strongly correlated with ahigh + -ca b a b, 1

value. On the other hand, the modulationcomponents ( )S f fx a b

02 caused by frequencies f ,a1 fb1 and

f ,a2 fb2 ( )¹ ¹ ¹ ¹f f f f f f, ,a a a b b b1 2 1 2 and the harmonics( )S f fx a b

03 caused by frequencies ( )-f f 2a b / and

( )+f f 2a b / exhibit weak spectral correlations( )» »+ - + -c c 0a b a b a b a b, ,2 3

because their noise inputs are atdifferent frequencies and uncorrelated. Moreover, most of the

Table 2. Sensitivities of different spectral correlation values to afatigue crack shown in figure 8.

Spectral correlation value between s

-f f f,b a b (figure 8(a)) 12.65-f f f,a a b (figure 8(b)) 7.09+f f f,b a b (figure 8(c)) 40.96+f f f,a a b (figure 8(d)) 20.46

+ -f f f f,a b a b (figure 8(e)) 93.21f f,a b (figure 8(f)) 1.06

Figure 9. Spectral correlation values obtained at ( fa, )f2 b and a single random selected ( f ,ar )f2 br from: (a) intact specimen; (b) damagedspecimen.

7

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

experimental noises ( )S f fx a b0

4 are stationary, and a sta-tionary signal exhibits no spectral correlation ( )=+ -c 0 .a b a b, 4

Hence, the spectral correlation ( )S fxf

a2 b of a signal can be

properly measured, even when the signal is contaminated bynoise.

3. Development of a baseline-free fatigue crackdetection technique

The majority of the existing nonlinear wave modulationtechniques detect fatigue crack by comparing the modulation

Figure 10. Damage feature d values from the proposed baseline-free fatigue crack detection technique: (a) intact specimen; (b) damagedspecimen.

Figure 11. Spectral correlation values ( )S fxf

a2 b calculated from the noise contaminated test signals with different SNRs.

8

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

components obtained from the current state of the targetstructure with the baseline data from its pristine condition.However, the varying operational and environmental condi-tions of the structure can also change the collected data andcause false alarms.

To address this problem, a baseline-free fatigue crackdetection technique is proposed in this paper. The premise ofthe proposed baseline-free technique is as follows. When thetarget structure is intact, the spectral correlation value ( )S fx

fa

2 b

obtained from fa and fb combination will be small. Moreover,its magnitude will be comparable to the value ( )S fx

far

2 br

obtained from a randomly selected combination of far and fbr( far and fbr should not be equal to fa and f ,b harmonics of faand f ,b and modulations between fa and )fb as shown infigure 4. Once a fatigue crack appears, the spectral correlationvalue ( )S fx

fa

2 b will dramatically increase to over ( )S fxf

ar2 br .

Based on this premise, a normal distribution is fitted tospectral correlation values ( )S fx

far

2 br obtained from multiplecombinations of far and f .br Then, a threshold value, T ,corresponding to a 99.99% one-side confidence interval isobtained as depicted in figure 5. A damage feature is definedas

( )( )=

-d

S f T

T, 10x

fa

2 b

where d value is within ( )-1, 0 for an intact case, and itbecomes positive only when a fatigue crack exists in thetarget structure.

Figure 12. Spectral density values ( ) ( )+ -S f f S f fx a b x a b0 0 calculated from the noise contaminated test signals with different SNRs.

Figure. 13. DI values calculated from the noise contaminated testsignals with different SNRs.

9

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

Note that, for the generation of nonlinear ultrasonicmodulation, the following binding conditions should besatisfied in addition to the existence of a fatigue crack[13, 14]: (1) crack perturbation condition: the strain (dis-placement) at the crack location should be oscillated by bothof the two inputs; (2) mode matching condition: the crackmotion induced by one of the two inputs should modulate theother input at the crack location. That is, the generation ofmodulation can be affected by unknown topological config-urations (location and size) of the crack and varying envir-onmental and operational conditions (e.g., temperature andloading) of the target structure. There is no single optimalcombination of fa and f .b To address this problem, both faand fb frequencies are swept over certain frequency ranges,increasing the possibility of modulation generation by thepresence of a fatigue crack.

Finally, the existence of fatigue cracks is diagnosed bycomputing the following damage index value using the dvalues obtained from n different combinations of fa and fb

( ( ))( )å

=- -

>= ⎧⎨⎩n

DId 1 1 intact

1 damage.11i

ni1

2

For the intact condition, the DI value will be <1. Once the DIvalue increases to >1, the existence of a fatigue crack isindicated. Note that the evaluation criterion in equation (11) isbased on the assumption that initial nonlinearity of the targetstructure, such as material nonlinearity, is negligible.

The proposed baseline-free fatigue crack detection tech-nique can be summarized as follows

Step 1: For each fa and fb combination, the spectralcorrelation value ( )S fx

fa

2 b is calculated.Step 2: Evaluate spectral correlation values ( )S fx

far

2 br frommultiple combinations of far and fbr .Step 3: Fit a normal distribution to ( )S fx

far

2 br and establish athreshold T corresponding to a 99.99% one-side confidenceinterval.Step 4: The damage feature d is obtained fromequation (10).Step 5: Repeat steps 1–4 for n number of fa and fbcombinations.Step 6: Compute DI using equation (11), and fatigue crackis detected when DI>1.

4. Experimental validation

4.1. Experimental setup

The effectiveness of the proposed technique was examinedusing the test data obtained from two identical aluminumplate (6061 T6) specimens. The geometrical dimensions ofthe specimens are presented in figure 6(a). Packaged PZTs,named PZT1, PZT2, and PZT3, are attached to each speci-men. PZT1 and PZT2 were used for generating high-fre-quency fa and low-frequency fb input signals, respectively;while PZT3 was used for sensing. A 15 mm fatigue crackpropagated from the center hole, as shown in figure 6(b). This

was induced in one specimen after 37 000 cycles of a cyclicloading test, and its width was less than 20 μm. A universaltesting machine (INSTRON 8801) with a 10 Hz cycle rate, amaximum load of 25 kN, and a stress ratio of 0.1 was used forthis cyclic loading test.

The packaged PZTs were connected to a data acquisitionsystem (figure 7) [16], which consists of two NationalInstruments (NI) NI-PXI-5421 arbitrary waveform generators(AWGs) and a NI-PXI-5122 high-speed digitizer (DIG). OneAWG is used to generate the high-frequency input signal onPZT1 and the other to generate the low-frequency input signalon PZT2. The response from PZT3 is measured by DIG. TheAWGs and DIG are synchronized and controlled by Lab-VIEW software.

The amplitudes of the high-frequency and low-frequencyinput signals are set to a peak-to-peak voltage of 20 V. Theresponses are measured with 1MHz sampling rate for 0.25 s.Each response is measured 10 times and averaged in the timedomain to improve the signal-to-noise ratio. For the sweepingof high-frequency and low-frequency inputs, fa is swept from183 to 185 kHz, and fb from 30 to 40 kHz both in 1 kHzincrements, resulting in a total of 33 input-frequency com-binations. These fa and fb combinations were selectedbecause the responses had relatively large amplitudes at thecorresponding input and modulation frequencies.

4.2. Fatigue crack detection results

Figure 8 displays the spectral correlation values obtained forsix different frequency combinations listed under ‘nonlinear’case in table 1. The spectral correlation values fromfigures 8(a) to (d) show the correlation between one of twolinear components ( fa or fb), and one of the modulationcomponents ( +f fa b or fa−fb). As a fatigue crack is formed,these four spectral correlation values increase overall for mostof the input frequency combinations investigated. Figure 8(e)shows the spectral correlation value between two modulationcomponents at f f .a b Comparison of figure 8(e) withfigures 8(a) to (d) indicates that the spectral correlation valuebetween two modulation components is more sensitive to thefatigue crack than the spectral correlation values between thelinear and modulation components. On the other hand, thespectral correlation value between the two linear componentsat fa and fb is insensitive to the fatigue crack, as displayed infigure 8(f). The sensitivities of different spectral correlationvalues in figure 8 to the fatigue crack are quantitativelycompared using the following index

( )å==

⎛⎝⎜

⎞⎠⎟s

N

S

S

1, 12

n

Nd n

i n1

,

,

2

where Sd n, and Si n, represent the spectral correlation valuesobtained from the damaged and intact specimens, respec-tively, and N is the total number of fa and fb combinations( )=N 33 . Table 2 demonstrates that the spectral correlationvalue ( )S fx

fa

2 b between two modulation components at f fa bshown in figure 8(e) has the highest sensitivity to the fatiguecrack among all investigated spectral correlations.

10

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

Figure 9 compares ( )S fxf

a2 b and a randomly selected

( )S fxf

ar2 br for both the intact and damaged specimens. When

the specimen is intact, these two spectral correlation valuesshare similar amplitude levels, as shown in figure 9(a).However, for the case of damage, the spectral correlationvalue ( )S fx

fa

2 b becomes one or two orders of magnitude largerthan the ( )S fx

far

2 br value, as shown in figure 9(b).All the damage feature d values obtained from

equation (10) are plotted for different fa and fb combinationsin figure 10. It can be seen that the majority of the d values isbelow zero for the intact case, and they increase hugely forthe damage case. The DI value calculated using equation (11)becomes 0.57 for the intact case and 13.61 for thedamage case.

To investigate the effect of noise on the spectral corre-lation value ( )S f ,x

fa

2 b simulated stationary white noises withdifferent signal-to-noise ratios (SNRs) were added to theacquired test signals. The SNR is defined as

( ) ( )=E

ESNR 10log dBW , 1310

signal

noise

where Esignal and Enoise are the energy of the acquired testsignal and the added white noise, respectively. SNR wasvaried from 60 to 30 dBW, with 2 dBW decrement, and thespectral correlation value ( )S fx

fa

2 b was calculated using thesenoise contaminated test signals. For comparison, the mod-ulation components ( ) ( )+ -P f f P f fx a b x a b in the conven-tional spectral density function, which is equal to

( ) ( )+ -S f f S f fx a b x a b0 0 in equation (9), was also calcu-

lated. Figures 11 and 12 present ( )S fxf

a2 b and

( ) ( )+ -S f f S f fx a b x a b0 0 values calculated from the noise

contaminated test signals with SNR=60, 50, 40 and30 dBW, respectively. It can be seen that ( )S fx

fa

2 b was muchmore insensitive to the white noise level, while it becamedifficult to differentiate the damaged sample from the intact

one as SNR decreased for ( ) ( )+ -S f f S f fx a b x a b0 0 .

Figure 13 is a plot of the DI values obtained from thenoise contaminated test signals with different SNRs. The DIvalue for the damage case decreased as the SNR deteriorated.This change could be alleviated if the sampling length of thetest signals were increased [27]. However, the DI value waskept at <1 for the intact case and >1 for the damage case, asshown in figure 13, for all the SNRs investigated.

5. Conclusions

In this study, instead of using the conventional spectral den-sity function, spectral correlation is proposed to reliablyextract fatigue crack induced nonlinear modulation compo-nents from ultrasonic response signals. The major advantageof the spectral correlation over spectral density function is thatthe modulation components of interest can be reliablyextracted even when measured ultrasonic signals are heavilycontaminated by noise. Then, a baseline-free fatigue crackdetection technique was developed and applied to the detec-tion of a real fatigue crack on an aluminum plate. The

proposed technique was able to successfully detect a 15 mmlong fatigue crack with 20 μm width. Moreover, the damagediagnosis was repeated using the noise contaminated testsignals with different SNRs. For the given test cases, theproposed technique was able to detect fatigue crack evenwhen the SNR deteriorated from 60 to 30 dBW. On the otherhand, the conventional spectral density function failed todistinguish the intact and damage cases when SNR decreasedbelow 40 dBW. Note that the proposed baseline-free fatiguecrack detection technique was developed based on theassumption that the intact structure can be treated as a linearsystem. Modifications of this technique are needed when theintact structure exhibits nonlinear behavior such as materialnonlinearity.

Acknowledgments

This work was supported by the Korea Minister of Ministryof Land, Infrastructure and Transport (MOLIT) as U-CityMaster and Doctor Course Grant Program, and a grant fromSmart Civil Infrastructure Research Program (13SCIPA01)funded by Ministry of Land, Infrastructure and Transport(MOLIT) of Korea government.

References

[1] Forrest P G 1962 Fatigue of Metals (Oxford: Pergamon)[2] Qiu L, Yuan S, Bao Q, Mei H and Ren Y 2016 Crack

propagation monitoring in a full-scale aircraft fatigue testbased on guided wave-Gaussian mixture model SmartMater. Struct. 25 055048

[3] Cook D A and Berthelot Y H 2001 Detection of small surface-breaking fatigue cracks in steel using scattering of Rayleighwaves NDT & E Int. 34 483–92

[4] Tua P S, Quek S T and Wang Q 2004 Detection of cracks inplates using piezo-actuated Lamb waves Smart Mater.Struct. 13 644–61

[5] Ihn J B and Chang F K 2004 Detection and monitoring ofhidden fatigue crack growth using a built-in piezoelectricsensor/actuator network: I. Diagnostics Smart Mater. Struct.13 609–20

[6] Van Den Abeele K E A, Johnson P A and Sutin A 2000Nonlinear elastic wave spectroscopy (NEWS) techniques todiscern material damage: I. Nonlinear wave modulationspectroscopy (NWMS) Res. Nondestruct. Eval. 12 17–30

[7] Parsons Z and Staszewski W J 2006 Nonlinear acoustics withlow-profile piezoceramic excitation for crack detection inmetallic structures Smart Mater. Struct. 15 1110–8

[8] Sutin A M and Donskoy D M 1998 Vibro-acoustic modulationnondestructive evaluation technique Proc. SPIE 3397226–37

[9] Didenkulov I N, Sutin A M, Ekmov A E and Kazakov V V1999 Interaction of sound and vibrations in concrete withcracks Proc. 15th AIP Conf. pp 279–82

[10] Yoder N C and Adams D E 2010 Vibro-acoustic modulationusing a swept probing signal for robust crack detectionStruct. Health Monit. Int. J. 9 257–67

[11] Sohn H, Lim H J, DeSimio M P, Brown K and Derisso M 2013Nonlinear ultrasonic wave modulation for fatigue crackdetection J. Sound Vib. 333 1473–84

11

Smart Mater. Struct. 25 (2016) 125034 P Liu et al

[12] Liu P, Sohn H, Kundu T and Yang S 2014 Noncontactdetection of fatigue cracks by laser nonlinear wavemodulation spectroscopy (LNWMS) NDT & E Int. 66106–16

[13] Zaitsev V, Nazarov V, Gusev V and Castagnede B 2006 Novelnonlinear-modulation acoustic technique for crack detectionNDT & E Int. 39 184–94

[14] Zhou C, Hong M, Su Z, Wang Q and Cheng L 2013 Evaluationof fatigue cracks using nonlinearities of acousto-ultrasonicwaves acquired by an active sensor network Smart Mater.Struct. 22 015018

[15] Cantrell J H and Yost W T 1994 Acoustic harmonicsgeneration from fatigue-induced dislocation dipoles Phil.Mag. A 69 315–26

[16] Lim H J, Sohn H, DeSimio M P and Brown K 2014 Reference-free fatigue crack detection using nonlinear ultrasonicmodulation under changing temperature and loadingconditions Mech. Syst. Signal Process. 45 468–78

[17] Liu P, Sohn H and Park B 2015 Baseline-free damagevisualization using noncontact laser nonlinear ultrasonicsand state space geometrical changes Smart Mater. Struct. 24065036

[18] Sohn H 2007 Effects of environmental and operationalvariability on structural health monitoring Phil. Trans. R.Soc. A 365 539–60

[19] Lim H J, Sohn H and Liu P 2014 Binding conditions fornonlinear ultrasonic generation unifying wave propagationand vibration Appl. Phys. Lett. 104 214103

[20] Zaitsev V Y, Matveev L A and Matveyev A L 2009 On theultimate sensitivity of nonlinear-modulation method of crackdetection NDT & E Int. 42 622–9

[21] Bouillaut L and Sidahmed M 2001 Cyclostationary approachand bilinear approach: comparison, applications to earlydiagnosis for helicopter gearbox and classification methodbased on HOCS Mech. Syst. Signal Process. 15 923–43

[22] Dalpiaz G, Rivola A and Rubini R 2000 Effectiveness andsensitivity of vibration processing techniques for local faultdetection in gears Mech. Syst. Signal Process. 14 387–412

[23] Antoni J 2009 Cyclostationarity by examples Mech. Syst.Signal Process. 23 987–1036

[24] Han N, Shon S H, Chung J H and Kim J M 2006 Spectralcorrelation based signal detection method for spectrumsensing in IEEE 802.22 WRAN systems Proc. IEEE 8th Int.Conf. Advanced Communication Technology vol 3pp 1765–70

[25] Fehske A, Gaeddert J and Reed J 2005 A new approach tosignal classification using spectral correlation and neuralnetworks Proc. IEEE Int. Symp. on New Frontiers inDynamic Spectrum Access Networks pp 144–50

[26] Yoo D S, Lim J and kang M H 2014 ATSC digital televisionsignal detection with spectral correlation densityJ. Commun. Netw. 16 600–12

[27] Gardner W A 2006 Cyclostationarity: half a century of researchSignal Process. 86 639–97

[28] Gardner W A 1986 Measurement of spectral correlation IEEETrans. Acoust. Speech Signal Process. 34 1111–23

12

Smart Mater. Struct. 25 (2016) 125034 P Liu et al