Research ArticleA Signal Decomposition Method for Ultrasonic GuidedWave Generated from Debonding Combining SmoothedPseudo Wigner-Ville Distribution and VoldndashKalman FilterOrder Tracking

JunhuaWu Xinglin Chen and ZheshuMa

School of Automotive and Traffic Engineering Nanjing Forestry University Nanjing Jiangsu 210037 China

Correspondence should be addressed to Junhua Wu bjtime13126com

Received 15 May 2017 Accepted 3 August 2017 Published 14 September 2017

Academic Editor Michele Palermo

Copyright copy 2017 Junhua Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Carbon fibre composites have a promising application future of the vehicle due to its excellent physical properties Debondingis a major defect of the material Analyses of wave packets are critical for identification of the defect on ultrasonic nondestructiveevaluation and testing In order to isolate different components of ultrasonic guidedwaves (GWs) a signal decomposition algorithmcombining Smoothed Pseudo Wigner-Ville distribution and VoldndashKalman filter order tracking is presented In the algorithm thetime-frequency distribution of GW is first obtained by using Smoothed Pseudo Wigner-Ville distribution The frequencies ofdifferent modes are computed based on summation of the time-frequency coefficients in the frequency direction On the basisof these frequencies isolation of different modes is done by VoldndashKalman filter order tracking The results of the simulationsignal and the experimental signal reveal that the presented algorithm succeeds in decomposing the multicomponent signalinto monocomponents Even though components overlap in corresponding Fourier spectrum they can be isolated by using thepresented algorithm So the frequency resolution of the presented method is promising Based on this we can do research aboutdefect identification calculation of the defect size and locating the position of the defect

1 Introduction

Carbon fibre composite is widely used in modern industrysuch as aerospace domain and military products because ofits high strength and light weight At present such a mate-rial has been generalized to automotive industry obviouslyreducing the weight of automobile Debonding defect is amajor defect of the carbon fibre composites A great numberof investigations of the nondestructive evaluation and testing(NDENDT) have done research for this type of defect [1ndash5]

Currently ultrasonic guided wave (GW) testing hasemerged as a popular NDENDT techniqueThemethod canestimate the location severity and type of defects Successfulapplications of defect identification of carbon fibre compos-ites have been done [3 6 7] However dispersion effects andnoise make ultrasonic testing waves as multicomponent sig-nals which results in that it is difficult to do NDENDT with

raw testing waves Therefore isolating different componentsof GW and obtaining the corresponding time-frequencydistributions (TFD) are vital for the inspection of the defect

A number of scholars have done investigations aboutsignal processing methods of GWs Kercel et al [8] usedBayesian parameter estimates to isolate multiple modes inGW signals collected from laser ultrasonic testing on amanufacturing assembly line Cai et al [9] provided a time-distance domain transform (TDDT) method to interpretthe dispersion of Lamb waves which can result in highspatial resolution images of damage areas Rizzo and diScalea utilized DiscreteWavelet Transform (DWT) to extractwavelet domain features for enhanced defect characterizationin multiwire strand structures [10] Gangadharan et al pre-sented a time reversal technique using GWs to detect damagein an aluminum plate and good results were achieved [11]The wavelet analysis is widely used [12ndash17] in domains many

HindawiShock and VibrationVolume 2017 Article ID 7283450 13 pageshttpsdoiorg10115520177283450

2 Shock and Vibration

successful applications of wavelet transform (WT) for GWsignals have been done Li et al [14] proposed a combinedmethod employing empirical mode decomposition (EMD)and wavelet analysis to attain good time resolution of theresponse signals Paget et al [15] proposed a new damage-detection technique based on WT with a new basis Yuet al [16] used the techniques of statistical averaging toreduce global noise and discrete wavelet denoising usinga Daubechies wavelet to remove local high-frequency dis-turbances Y Y Kim and E-H Kim [17] evaluated theeffectiveness ofWT analysis for studying thewave dispersion

EMD which can isolate adaptively different componentswas proposed by Huang in 1998 [18] At present manyinvestigations of theory and application have been done [19ndash24] Li et al [14] Osegueda et al [20] and Salvino et al[22] used EMD to process GW signals in plate structuresHowever the frequency resolution of EMD is a limitationReference [25] reveals that when the ratio between a relativelylow frequency and a relatively high frequency is greater than075 two components of a signal cannot be separated

In 1993 Vold and Leuridan [26] proposed VoldndashKalmanfilter order tracking (VKF OT) for the estimation of a singleorder component In 1997 they [27] derived a scheme tosimultaneously estimatemultiple components Instantaneousfrequency of the isolated component is a necessary priorknowledge for VKF OT Therefore we introduce SmoothedPseudo Wigner-Ville distribution (SPWVD) which canremove the cross-term in frequency direction and time direc-tion of the time-frequency panel to get instantaneous fre-quencies of isolated componentsWe present a signal decom-position method for ultrasonic GWs combining VKF OTand SPWVD in this paper

The rest of this paper is organized as follows Section 2presents the theories of Smoothed pseudo Wigner-Villedistribution and VoldndashKalman filter order tracking Theprinciple of algorithm is illustrated in Section 3 Section 4provides an illustration of the presented method The detailsof the experiment are described in Section 5 Section 6shows the application of the presented algorithm to theexperimental signals Finally Section 7 concludes

2 Smoothed Pseudo Wigner-Ville Distributionand VoldndashKalman Filter Order Tracking

21 Smoothed PseudoWigner-Ville Distribution Wigner-Villedistribution has a fine time-frequency resolution and canreach the low boundary of Heisenberg uncertainty principleIt is defined as [28]

WVD119904 (119905 119891) = intinfinminusinfin

119904 (119905 + 1205912) 119904 (119905 minus 1205912) 119890minus1198952120587119891120591119889120591 (1)

However for multicomponent signals it suffers frominevitable interference of cross-terms SPWVD can remove

it in frequency direction and time direction of the time-frequency panel And the formula of SPWVD is as follows[28]

SPW119904 (119899 Θ) = 119871minus1sum119896=minus119871+1

|ℎ (119896)|

sdot 119872minus1sum119897=119872+1

119892 (119897) 119904 (119899 + 119897 + 119896) 119904lowast (119899 + 119897 minus 119896) 119890minus1198952119896Θ(2)

where 119892(119897) and ℎ(119896) are smoothing window functions intime direction and frequency direction respectively 119904 isan analyzed signal and 119899 and Θ are time variable andfrequency variables respectively The time resolution andfrequency resolution of SPWVDare promisingMoreover nointerference is in the representation

22 VoldndashKalman Filter Order Tracking Isolation of differentmodes is important for defect identification by ultrasonicguided waves On this basic we can locate the defect andevaluate the defect size Therefore VKF OT is employed toseparate wave packages

In this paper the angular-displacement VKF OT tech-niques are adapted The method is used to obtain the trackedcomponents by minimizing the energy of errors for both thestructural and data equations by mean of one of the leastsquares approaches [29]

The 119896th order component can be defined as

119891119896 (119905) = 119886119896 (119905) 120579119896 (119905) + 119886minus119896 (119905) 120579minus119896 (119905) (3)

where 119886119896(119905) is the complex envelope and 119886minus119896(119905) is the complexconjugate of 119886119896(119905) to make 119891119896(119905) a real waveform It is notedthat 120579119896(119905) is a carrier wave and defined as

120579119896 (119905) = exp(119896119894 int1199050120596 (119906) 119889119906) (4)

where 119889119906 is the speed of the reference axle and int1199050120596(119906)119889119906 is

the elapsed angular displacementThediscrete formof (4) canthen be written as

120579119896 (119899) = exp(119896119894 119899sum119898=0

120596 (119898)Δ119879) (5)

221 The Structural Equation As the tracked component119891119896(119905) can be written as (3) where the envelope 119886119896(119905) needsto be computed Generally 119886119896(119905) fulfills [29]

119889119878119886119896 (119905)119889119905119904 = 120595119896 (119905) (6)

where120595119896(119905) is a higher-degree term in 119886119896(119905)The correspond-ing discrete forms can be expressed

nabla119878119886119896 (119899) = 120595119896 (119899) (7)

where nabla is the difference operator the index 119904 is the differen-tiation order and 120595119896(119899) physically is a combination of otherspectral components and additional measurement noise

Shock and Vibration 3

222 The Data Equation A measured signal 119910(119899) can betaken as a combination of several components 119891119896(119905) andmeasurement noise

119910 (119899) = sum119896isin119895

119886119896 (119899) 120579119896 (119899) + 120585 (119899) (8)

where the integral number 119895(= plusmn1 plusmn2 plusmn3 andor plusmn 119870)is the order of spectral components to be tracked and 120585(119899)is unwanted spectral components and measurement errorsEach component 119886119896(119899) of interest modulates with a carrierwave 120579119896(119899)223 Calculation of the Tracked Component 119891 Let 119904 = 2 andlet data length be119873 then the calculation matrix form can beexpressed as [29]

[[[[[[[[[[

minus2 1 0 0 0 sdot sdot sdot 0 01 minus2 1 0 0 sdot sdot sdot 0 00 1 minus2 1 0 sdot sdot sdot 0 0 0 0 0 0 0 sdot sdot sdot minus2 1

]]]]]]]]]]

[[[[[[[[[[

119886119896 (1)119886119896 (2)119886119896 (3)119886119896 (119873)

]]]]]]]]]]

=[[[[[[[[[[

120595119896 (1)120595119896 (2)120595119896 (3)120595119896 (119873)

]]]]]]]]]]

(9)

To simultaneously track multiple orders and spectral com-ponents such as resonance it can be extended to all ordercomponents of interest as well Let

larrrarr119872 =[[[[[[[[[

minus2 1 0 0 0 sdot sdot sdot 0 01 minus2 1 0 0 sdot sdot sdot 0 00 1 minus2 1 0 sdot sdot sdot 0 0 0 0 0 0 0 sdot sdot sdot minus2 1

]]]]]]]]]

larrrarr119860 =[[[[[[[[[[

119886119896 (1)119886119896 (2)119886119896 (3)119886119896 (119873)

]]]]]]]]]]

larrrarr119885 =[[[[[[[[[[

119896 (1)119896 (2)119896 (3)119896 (119873)

]]]]]]]]]]

(10)

and then (9) becomes

[[[[[[[[[[[[[

larrrarr119872 0 0 0 sdot sdot sdot 0 00 larrrarr119872 0 0 sdot sdot sdot 0 00 0 larrrarr119872 0 sdot sdot sdot 0 0 0 0 0 0 sdot sdot sdot 0 larrrarr119872

]]]]]]]]]]]]]

larrrarr119860 = larrrarr119885 (11)

where elements 119886119896 in the matrixlarrrarr119860 are column vectors witha length 119873 which is the 119896th order component 119896 are errorvectors with a dimension 119873 times 1 and 119872 is a matrix with adimension119873 times119873

The terms with negative indexes in (8) assure 119891119896(119905) to bea real waveform 119910 is the measured signal with a length of119873120585 an error vector with dimension 119873 times 1 andlarrrarr119861 119896 consists ofcarrier signals as

larrrarr119861 119896 =[[[[[[[[[[

120579119896 (1) 0 0 sdot sdot sdot 00 120579119896 (2) 0 sdot sdot sdot 00 0 120579119896 (3) sdot sdot sdot 0 0 0 0 sdot sdot sdot 120579119896 (119873)

]]]]]]]]]]

larrrarr119860 = larrrarr119885 (12)

Thus (8) can be rewritten as

119910 minus [1198611 1198612 1198613 sdot sdot sdot 119861119896][[[[[[[[[[

119886111988621198863119886119870

]]]]]]]]]]

= 120585 (13)

As the angular-velocity VKF OT scheme we introduce aweighting factor and combine (9) and (13) and then

[[[[[[[[[[[[[

0000119910

]]]]]]]]]]]]]

minus

[[[[[[[[[[[[[[[[

119903larrrarr119872 0 0 sdot sdot sdot 0 00 119903larrrarr119872 0 sdot sdot sdot 0 00 0 119903larrrarr119872 sdot sdot sdot 0 0 0 0 0 sdot sdot sdot 0 119903larrrarr1198721198611 1198612 1198613 sdot sdot sdot 119861119896minus1 119861119896

]]]]]]]]]]]]]]]]

[[[[[[[[[[[[[

119886111988621198863119886119870minus1119886119870

]]]]]]]]]]]]]

= [119903larrrarr119885120585 ]

(14)

4 Shock and Vibration

Equation (14) can be symbolized as

larrrarr119884 minuslarrrarr119875 larrrarr119860 = larrrarr119864 (15)

The evaluation of tracked order components is exactly to finda vectorlarrrarr119860 fulfilling

minlarrrarr119860

(100381710038171003817100381710038171003817larrrarr119864 1003817100381710038171003817100381710038172) = min

larrrarr119860

(larrrarr119864 119867larrrarr119864 ) = minlarrrarr119860

(119869) (16)

that is 120597119869120597larrrarr119860 = 0 The vectorlarrrarr119860 can be written as

larrrarr119875 119867larrrarr119875larrrarr119860 = larrrarr119875 119867larrrarr119884 (17)

The matrixlarrrarr119875 119867larrrarr119875 is written as

larrrarr119875 119867larrrarr119875 =[[[[[[[[[[[[[

larrrarr119878 larrrarr119861 12 larrrarr119861 13 sdot sdot sdot larrrarr119861 1119870larrrarr119861 21 larrrarr119878 larrrarr119861 23 sdot sdot sdot larrrarr119861 2119870larrrarr119861 31 larrrarr119861 12 larrrarr119878 sdot sdot sdot larrrarr119861 3119870 dlarrrarr119861 1198701 larrrarr119861 1198702 larrrarr119861 1198703 sdot sdot sdot larrrarr119878

]]]]]]]]]]]]]

(18)

wherelarrrarr119878 = 1199032larrrarr119872119879larrrarr119872+larrrarr119868 andlarrrarr119861 119906V = 119861119867119906 119861V Moreoverlarrrarr119875 119867is written as

larrrarr119875 119867 = [larrrarr119861 1 larrrarr119861 2 larrrarr119861 3 sdot sdot sdot larrrarr119861 119870]119879 (19)

wherelarrrarr119861 119870 is the complex conjugate oflarrrarr119861 1198703 Principle of the Presented Algorithm

As mentioned above SPWVD has a promising time-frequency resolution Therefore we obtain frequencies anddurations of modes from SPWVD distributions of testingguided waves Furthermore VKF OT is adapted to realizeisolation of different wave packages with obtained modefrequencies Finally the final mode waveforms are cut outfrom the wave packages of modes by durations of modesThe processing steps of the extension algorithm are shown inFigure 1 and are as follows

(1) Smoothed Pseudo Wigner-Ville Distribution SPWVD isused for processing testing signal to get corresponding time-frequency distribution And the promising time-frequencyresolution of the method can lead to a high calculationaccuracy of frequencies and durations of modes

(2) Extracting and Separating Valuable Areas of the Time-Frequency Panel To extract and separate different modes

we do the following (1) sum coefficients of each frequency-indexed group and the calculation formula is

119864 (Θ) = 119873sum119899=1

SPW119904 (119899 Θ) (20)

where119873denotes the number of the time variables of the time-frequency panel (2) Calculate minimal values andmaximumvalues of summations Lines of the minimal values in thetime-frequency panel can separate the valuable areas And themaximum value evaluates whether the energy of a mode isstrong enough to be kept (3) Conduct threshold processingfor the maximum values And the equation is defined as

119864 (Θ)max = keep 119864 (Θ)max gt 1198790discard 119864 (Θ)max le 1198790 (21)

where 119864(Θ)max means the maximum of 119864(Θ) 1198790 denotesthe threshold for sift valuable modes A mode with a strongenergy is more valuable for detecting the debonding defectso a threshold process is introduced to improve calcula-tion efficiency Moreover the noise can also be removedby this operation After this step the areas of the time-frequency panel corresponding to the significant modescan be extracted and separated Moreover correspondingfrequencies at the maximum values are taken as the modefrequencies

(3) VoldndashKalman Filter Order TrackingThemode frequencieshave been calculated in Step (2) So we employ VKF OT tofilter the specific mode waveform with these frequenciesThedifferent modes 1198910119894 (119894 = 1 2 119872) can be preliminarilyisolated and119872 is number of the maximum values obtainedin Step (2)

(4) Peak-Track Algorithm Conduct the peak-track algorithmfor the significant areas of SPWVD to obtain the primary IAof different modesThe principle of the peak-track algorithmcan be found in [30] And then the IAs of significant modescan be obtained

(5) Constructing Filters in Time Domain To remove calcula-tion error of the mode waveform from result obtained in Step(3) we construct a corresponding filter in time domain basedon the primary IAs of different modes obtained in Step (4)And the equation is as follows

119860 119894 = 1 1198600119894 gt 1198791198600 1198600119894 le 119879119860 (22)

where 119860 119894 is the value of the 119894th filter in time domain and 1198600119894denote the primary IAs of the 119894th modes 119879119860 is a threshold toremove calculation error of the mode waveform

Shock and Vibration 5

Testing signals

Smoothed Pseudo Wigner-Ville distribution

Time-frequencycoefficients

Summing coefficients of eachfrequency-indexed group

Calculation of minimal valuesand maximum values ofsummations

Threshold processingExtracting and separatingvaluable areas of the time-frequency panel

Valuable areas fordifferent modes

Peak-track algorithm

Instantaneousamplitudes ofmodes

Threshold process

Filters in time domain

Frequencies ofmodes

VoldndashKalman filter ordertracking

Waveforms ofdifferent modes

Filtering in time domain forcalculation result of VoldndashKalman filter order tracking

Final waveforms ofdifferent modes

Figure 1 The different steps of the algorithm presented in the paper

(6) Filtering in Time Domain for Calculation Result ofVoldndashKalman Filter Order Tracking Calculate the inner prod-uct between the mode waveforms obtained in Step (3) andthe filter in time domain from Step (5) And then the finalcalculation result is obtained The equation is

119891119894 = 119860 119894 lowast 1198910119894 (23)

In Section 4 the details of the present algorithm will beillustrated with a sample signal

4 Illustration of the Presented Algorithm

We construct a sample signal to illustrate the presentedalgorithm

6 Shock and Vibration

119904 (119905) = 1199041 (119905) + 1199042 (119905) + 1199043 (119905)

1199041 (119905) =

0 0 le 119905 le 0000054000 (119905 minus 000005) sin (300000 times 2120587119905) 000005 lt 119905 le 00003minus4000 (119905 minus 000055) sin (300000 times 2120587119905) 00003 lt 119905 le 0000550 000055 lt 119905 le 0001

1199042 (119905) =

0 0 le 119905 le 0000254000 (119905 minus 000025) sin (55000 times 2120587119905) 000025 lt 119905 le 00005minus4000 (119905 minus 000075) sin (55000 times 2120587119905) 00005 lt 119905 le 0000750 000075 lt 119905 le 0001

1199043 (119905) =

0 0 le 119905 le 0000454000 (119905 minus 000025) sin (50000 times 2120587119905) 000045 lt 119905 le 00007minus4000 (119905 minus 000075) sin (50000 times 2120587119905) 00007 lt 119905 le 0000950 000095 lt 119905 le 0001

(24)

The sampling frequency is 2MHzThe sample signal consistsof three modes at frequencies of 50 55 and 300 kHz Thecurve of the sample signal in time domain is shown inFigure 2

Firstly we employ SPWVD for the sample signal to obtainthe corresponding time-frequency panel which is shown inFigure 3 As can be seen in Figure 3 the time resolution andfrequency resolution of the time-frequency are promisingBesides no interference is in the representation Howeverthe difference between the component at 50 kHz and thecomponent at 55 kHz is so little that the two componentscannot be separated in the SPWVDdistribution of the samplesignal so is in Fourier spectrum as shown in Figure 4

After that (20) is used on the SPWVD distribution Asshown in Figure 5 three maximum values at 50 55 and300 kHz are kept So VKF OT is employed on the samplesignal with 50 55 and 300 kHz to get the correspondingfiltering results

And then the primary IAs of differentmodes are obtainedby the peak-track algorithm The filters in time domainof different modes are obtained by employing (22) on theprimary IAs as shown in Figure 6 We can adjust thethreshold in (22) to get filters in time domain of differentmodes with a high accuracy in time resolution

Finally we conduct time-domain filter for the result ofVKF OT and the results are shown in Figure 7 As presentedin Figure 7 the decomposition results almost overlap withthe corresponding original modes To further validate theeffectiveness of the presented algorithm we calculate theerror of the decomposition result as shown in Figure 8 Theabsolute error is less than 01 for the modes at 50 and 55 kHzand is less than 002 for the mode at 300 kHz which reveals

that the calculation accuracy of the presented algorithm ispromising

To compare with EEMD the sample signal is alsoprocessed by this decomposition method Figure 9 showsthe coefficients of correlation between different IMFs andthe sample signal We can learn that IMFs 1ndash4 are vitalcomponents of the signal as the coefficients of correlationare relatively greater So these IMFs are shown in Figure 10It is visible that the mode mixing occurs in EEMD for modesat 50 and 55 kHz as shown in Figure 10(b) Because theratio between modes at 50 and 55 kHz is greater than 075they cannot be separated as revealed in [25] Therefore thepoor frequency resolution is a limitation of EEMD for itsapplication

5 Details of the Experimental

Thematerial of the specimen is a specific composite materialThe size is 400mm times 300mm times 3mm and contains 15 layersThe corresponding size diagram is presented in Figure 11 Twodebonding defects are in the specimenThe side length of thedefects is respectively 20mm and 30mm

Figure 12 is the diagram of the testing principle Intesting process the exciting probe sends an exciting waveand then the receiving probe will receive excited lamb wavesThe excitation wave is a sine wave with a frequency of100 kHz The sampling frequency is 20MHz Three sets ofsignal are collected in the experiment responding to threesituations that is no defect 20mm defect and 30mmdefect respectively The corresponding GWs collected in theexperiment are presented in Figure 13

Shock and Vibration 7

minus15minus1

minus050

051

15

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

Figure 2 The curve of the sample signal in time domain

50 kHz

300 kHz

55 kHz

02 04 06 08 10Time (ms)

0

100

200

300

400

500

Freq

uenc

y (k

Hz)

(a)

55 kHz

50 kHz

300 kHz 55 kHz

500400

300200

1000

0

02

04

06

08

1

0

20

40

60

Am

plitu

de

Frequency (kHz)Time (m

s)

(b)

Figure 3 The representation of the sample signal by using SPWVD

40 50 60 70 80 90 1000

005

01 55 kHz50 kHz300 kHz

0

005

01

015

Am

plitu

de

100 200 300 400 500 600 700 800 900 10000Frequency (kHz)

Figure 4 The Fourier spectrum of the sample signal

times104

10050 150 200 250 300 3500Frequency (kHz)

0

1

2

3

Sum

mat

ion

Figure 5 The different frequency-group summations of the time-frequency panel of the sample signal

6 Result and Discussion

Figure 15 presents the decomposition result of experimentalsignals by using the presented algorithmAs shown in Figures14 and 15 two modes exist in the experimental signal of no

defect and are at 503 kHz and 345 kHzThe signal of 20mmdefect consists of modes at 492 kHz 412 kHz and 341 kHzAnd the signal of 30mmdefect consists ofmodes at 498 kHz448 kHz and 339 kHz Figure 16 shows these modes aredecomposed by the presented algorithm This indicates the

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

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RotatingMachinery

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Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Shock and Vibration 3

222 The Data Equation A measured signal 119910(119899) can betaken as a combination of several components 119891119896(119905) andmeasurement noise

119910 (119899) = sum119896isin119895

119886119896 (119899) 120579119896 (119899) + 120585 (119899) (8)

where the integral number 119895(= plusmn1 plusmn2 plusmn3 andor plusmn 119870)is the order of spectral components to be tracked and 120585(119899)is unwanted spectral components and measurement errorsEach component 119886119896(119899) of interest modulates with a carrierwave 120579119896(119899)223 Calculation of the Tracked Component 119891 Let 119904 = 2 andlet data length be119873 then the calculation matrix form can beexpressed as [29]

[[[[[[[[[[

minus2 1 0 0 0 sdot sdot sdot 0 01 minus2 1 0 0 sdot sdot sdot 0 00 1 minus2 1 0 sdot sdot sdot 0 0 0 0 0 0 0 sdot sdot sdot minus2 1

]]]]]]]]]]

[[[[[[[[[[

119886119896 (1)119886119896 (2)119886119896 (3)119886119896 (119873)

]]]]]]]]]]

=[[[[[[[[[[

120595119896 (1)120595119896 (2)120595119896 (3)120595119896 (119873)

]]]]]]]]]]

(9)

To simultaneously track multiple orders and spectral com-ponents such as resonance it can be extended to all ordercomponents of interest as well Let

larrrarr119872 =[[[[[[[[[

minus2 1 0 0 0 sdot sdot sdot 0 01 minus2 1 0 0 sdot sdot sdot 0 00 1 minus2 1 0 sdot sdot sdot 0 0 0 0 0 0 0 sdot sdot sdot minus2 1

]]]]]]]]]

larrrarr119860 =[[[[[[[[[[

119886119896 (1)119886119896 (2)119886119896 (3)119886119896 (119873)

]]]]]]]]]]

larrrarr119885 =[[[[[[[[[[

119896 (1)119896 (2)119896 (3)119896 (119873)

]]]]]]]]]]

(10)

and then (9) becomes

[[[[[[[[[[[[[

larrrarr119872 0 0 0 sdot sdot sdot 0 00 larrrarr119872 0 0 sdot sdot sdot 0 00 0 larrrarr119872 0 sdot sdot sdot 0 0 0 0 0 0 sdot sdot sdot 0 larrrarr119872

]]]]]]]]]]]]]

larrrarr119860 = larrrarr119885 (11)

where elements 119886119896 in the matrixlarrrarr119860 are column vectors witha length 119873 which is the 119896th order component 119896 are errorvectors with a dimension 119873 times 1 and 119872 is a matrix with adimension119873 times119873

The terms with negative indexes in (8) assure 119891119896(119905) to bea real waveform 119910 is the measured signal with a length of119873120585 an error vector with dimension 119873 times 1 andlarrrarr119861 119896 consists ofcarrier signals as

larrrarr119861 119896 =[[[[[[[[[[

120579119896 (1) 0 0 sdot sdot sdot 00 120579119896 (2) 0 sdot sdot sdot 00 0 120579119896 (3) sdot sdot sdot 0 0 0 0 sdot sdot sdot 120579119896 (119873)

]]]]]]]]]]

larrrarr119860 = larrrarr119885 (12)

Thus (8) can be rewritten as

119910 minus [1198611 1198612 1198613 sdot sdot sdot 119861119896][[[[[[[[[[

119886111988621198863119886119870

]]]]]]]]]]

= 120585 (13)

As the angular-velocity VKF OT scheme we introduce aweighting factor and combine (9) and (13) and then

[[[[[[[[[[[[[

0000119910

]]]]]]]]]]]]]

minus

[[[[[[[[[[[[[[[[

119903larrrarr119872 0 0 sdot sdot sdot 0 00 119903larrrarr119872 0 sdot sdot sdot 0 00 0 119903larrrarr119872 sdot sdot sdot 0 0 0 0 0 sdot sdot sdot 0 119903larrrarr1198721198611 1198612 1198613 sdot sdot sdot 119861119896minus1 119861119896

]]]]]]]]]]]]]]]]

[[[[[[[[[[[[[

119886111988621198863119886119870minus1119886119870

]]]]]]]]]]]]]

= [119903larrrarr119885120585 ]

(14)

4 Shock and Vibration

Equation (14) can be symbolized as

larrrarr119884 minuslarrrarr119875 larrrarr119860 = larrrarr119864 (15)

The evaluation of tracked order components is exactly to finda vectorlarrrarr119860 fulfilling

minlarrrarr119860

(100381710038171003817100381710038171003817larrrarr119864 1003817100381710038171003817100381710038172) = min

larrrarr119860

(larrrarr119864 119867larrrarr119864 ) = minlarrrarr119860

(119869) (16)

that is 120597119869120597larrrarr119860 = 0 The vectorlarrrarr119860 can be written as

larrrarr119875 119867larrrarr119875larrrarr119860 = larrrarr119875 119867larrrarr119884 (17)

The matrixlarrrarr119875 119867larrrarr119875 is written as

larrrarr119875 119867larrrarr119875 =[[[[[[[[[[[[[

larrrarr119878 larrrarr119861 12 larrrarr119861 13 sdot sdot sdot larrrarr119861 1119870larrrarr119861 21 larrrarr119878 larrrarr119861 23 sdot sdot sdot larrrarr119861 2119870larrrarr119861 31 larrrarr119861 12 larrrarr119878 sdot sdot sdot larrrarr119861 3119870 dlarrrarr119861 1198701 larrrarr119861 1198702 larrrarr119861 1198703 sdot sdot sdot larrrarr119878

]]]]]]]]]]]]]

(18)

wherelarrrarr119878 = 1199032larrrarr119872119879larrrarr119872+larrrarr119868 andlarrrarr119861 119906V = 119861119867119906 119861V Moreoverlarrrarr119875 119867is written as

larrrarr119875 119867 = [larrrarr119861 1 larrrarr119861 2 larrrarr119861 3 sdot sdot sdot larrrarr119861 119870]119879 (19)

wherelarrrarr119861 119870 is the complex conjugate oflarrrarr119861 1198703 Principle of the Presented Algorithm

As mentioned above SPWVD has a promising time-frequency resolution Therefore we obtain frequencies anddurations of modes from SPWVD distributions of testingguided waves Furthermore VKF OT is adapted to realizeisolation of different wave packages with obtained modefrequencies Finally the final mode waveforms are cut outfrom the wave packages of modes by durations of modesThe processing steps of the extension algorithm are shown inFigure 1 and are as follows

(1) Smoothed Pseudo Wigner-Ville Distribution SPWVD isused for processing testing signal to get corresponding time-frequency distribution And the promising time-frequencyresolution of the method can lead to a high calculationaccuracy of frequencies and durations of modes

(2) Extracting and Separating Valuable Areas of the Time-Frequency Panel To extract and separate different modes

we do the following (1) sum coefficients of each frequency-indexed group and the calculation formula is

119864 (Θ) = 119873sum119899=1

SPW119904 (119899 Θ) (20)

where119873denotes the number of the time variables of the time-frequency panel (2) Calculate minimal values andmaximumvalues of summations Lines of the minimal values in thetime-frequency panel can separate the valuable areas And themaximum value evaluates whether the energy of a mode isstrong enough to be kept (3) Conduct threshold processingfor the maximum values And the equation is defined as

119864 (Θ)max = keep 119864 (Θ)max gt 1198790discard 119864 (Θ)max le 1198790 (21)

where 119864(Θ)max means the maximum of 119864(Θ) 1198790 denotesthe threshold for sift valuable modes A mode with a strongenergy is more valuable for detecting the debonding defectso a threshold process is introduced to improve calcula-tion efficiency Moreover the noise can also be removedby this operation After this step the areas of the time-frequency panel corresponding to the significant modescan be extracted and separated Moreover correspondingfrequencies at the maximum values are taken as the modefrequencies

(3) VoldndashKalman Filter Order TrackingThemode frequencieshave been calculated in Step (2) So we employ VKF OT tofilter the specific mode waveform with these frequenciesThedifferent modes 1198910119894 (119894 = 1 2 119872) can be preliminarilyisolated and119872 is number of the maximum values obtainedin Step (2)

(4) Peak-Track Algorithm Conduct the peak-track algorithmfor the significant areas of SPWVD to obtain the primary IAof different modesThe principle of the peak-track algorithmcan be found in [30] And then the IAs of significant modescan be obtained

(5) Constructing Filters in Time Domain To remove calcula-tion error of the mode waveform from result obtained in Step(3) we construct a corresponding filter in time domain basedon the primary IAs of different modes obtained in Step (4)And the equation is as follows

119860 119894 = 1 1198600119894 gt 1198791198600 1198600119894 le 119879119860 (22)

where 119860 119894 is the value of the 119894th filter in time domain and 1198600119894denote the primary IAs of the 119894th modes 119879119860 is a threshold toremove calculation error of the mode waveform

Shock and Vibration 5

Testing signals

Smoothed Pseudo Wigner-Ville distribution

Time-frequencycoefficients

Summing coefficients of eachfrequency-indexed group

Calculation of minimal valuesand maximum values ofsummations

Threshold processingExtracting and separatingvaluable areas of the time-frequency panel

Valuable areas fordifferent modes

Peak-track algorithm

Instantaneousamplitudes ofmodes

Threshold process

Filters in time domain

Frequencies ofmodes

VoldndashKalman filter ordertracking

Waveforms ofdifferent modes

Filtering in time domain forcalculation result of VoldndashKalman filter order tracking

Final waveforms ofdifferent modes

Figure 1 The different steps of the algorithm presented in the paper

(6) Filtering in Time Domain for Calculation Result ofVoldndashKalman Filter Order Tracking Calculate the inner prod-uct between the mode waveforms obtained in Step (3) andthe filter in time domain from Step (5) And then the finalcalculation result is obtained The equation is

119891119894 = 119860 119894 lowast 1198910119894 (23)

In Section 4 the details of the present algorithm will beillustrated with a sample signal

4 Illustration of the Presented Algorithm

We construct a sample signal to illustrate the presentedalgorithm

6 Shock and Vibration

119904 (119905) = 1199041 (119905) + 1199042 (119905) + 1199043 (119905)

1199041 (119905) =

0 0 le 119905 le 0000054000 (119905 minus 000005) sin (300000 times 2120587119905) 000005 lt 119905 le 00003minus4000 (119905 minus 000055) sin (300000 times 2120587119905) 00003 lt 119905 le 0000550 000055 lt 119905 le 0001

1199042 (119905) =

0 0 le 119905 le 0000254000 (119905 minus 000025) sin (55000 times 2120587119905) 000025 lt 119905 le 00005minus4000 (119905 minus 000075) sin (55000 times 2120587119905) 00005 lt 119905 le 0000750 000075 lt 119905 le 0001

1199043 (119905) =

0 0 le 119905 le 0000454000 (119905 minus 000025) sin (50000 times 2120587119905) 000045 lt 119905 le 00007minus4000 (119905 minus 000075) sin (50000 times 2120587119905) 00007 lt 119905 le 0000950 000095 lt 119905 le 0001

(24)

The sampling frequency is 2MHzThe sample signal consistsof three modes at frequencies of 50 55 and 300 kHz Thecurve of the sample signal in time domain is shown inFigure 2

Firstly we employ SPWVD for the sample signal to obtainthe corresponding time-frequency panel which is shown inFigure 3 As can be seen in Figure 3 the time resolution andfrequency resolution of the time-frequency are promisingBesides no interference is in the representation Howeverthe difference between the component at 50 kHz and thecomponent at 55 kHz is so little that the two componentscannot be separated in the SPWVDdistribution of the samplesignal so is in Fourier spectrum as shown in Figure 4

After that (20) is used on the SPWVD distribution Asshown in Figure 5 three maximum values at 50 55 and300 kHz are kept So VKF OT is employed on the samplesignal with 50 55 and 300 kHz to get the correspondingfiltering results

And then the primary IAs of differentmodes are obtainedby the peak-track algorithm The filters in time domainof different modes are obtained by employing (22) on theprimary IAs as shown in Figure 6 We can adjust thethreshold in (22) to get filters in time domain of differentmodes with a high accuracy in time resolution

Finally we conduct time-domain filter for the result ofVKF OT and the results are shown in Figure 7 As presentedin Figure 7 the decomposition results almost overlap withthe corresponding original modes To further validate theeffectiveness of the presented algorithm we calculate theerror of the decomposition result as shown in Figure 8 Theabsolute error is less than 01 for the modes at 50 and 55 kHzand is less than 002 for the mode at 300 kHz which reveals

that the calculation accuracy of the presented algorithm ispromising

To compare with EEMD the sample signal is alsoprocessed by this decomposition method Figure 9 showsthe coefficients of correlation between different IMFs andthe sample signal We can learn that IMFs 1ndash4 are vitalcomponents of the signal as the coefficients of correlationare relatively greater So these IMFs are shown in Figure 10It is visible that the mode mixing occurs in EEMD for modesat 50 and 55 kHz as shown in Figure 10(b) Because theratio between modes at 50 and 55 kHz is greater than 075they cannot be separated as revealed in [25] Therefore thepoor frequency resolution is a limitation of EEMD for itsapplication

5 Details of the Experimental

Thematerial of the specimen is a specific composite materialThe size is 400mm times 300mm times 3mm and contains 15 layersThe corresponding size diagram is presented in Figure 11 Twodebonding defects are in the specimenThe side length of thedefects is respectively 20mm and 30mm

Figure 12 is the diagram of the testing principle Intesting process the exciting probe sends an exciting waveand then the receiving probe will receive excited lamb wavesThe excitation wave is a sine wave with a frequency of100 kHz The sampling frequency is 20MHz Three sets ofsignal are collected in the experiment responding to threesituations that is no defect 20mm defect and 30mmdefect respectively The corresponding GWs collected in theexperiment are presented in Figure 13

Shock and Vibration 7

minus15minus1

minus050

051

15

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

Figure 2 The curve of the sample signal in time domain

50 kHz

300 kHz

55 kHz

02 04 06 08 10Time (ms)

0

100

200

300

400

500

Freq

uenc

y (k

Hz)

(a)

55 kHz

50 kHz

300 kHz 55 kHz

500400

300200

1000

0

02

04

06

08

1

0

20

40

60

Am

plitu

de

Frequency (kHz)Time (m

s)

(b)

Figure 3 The representation of the sample signal by using SPWVD

40 50 60 70 80 90 1000

005

01 55 kHz50 kHz300 kHz

0

005

01

015

Am

plitu

de

100 200 300 400 500 600 700 800 900 10000Frequency (kHz)

Figure 4 The Fourier spectrum of the sample signal

times104

10050 150 200 250 300 3500Frequency (kHz)

0

1

2

3

Sum

mat

ion

Figure 5 The different frequency-group summations of the time-frequency panel of the sample signal

6 Result and Discussion

Figure 15 presents the decomposition result of experimentalsignals by using the presented algorithmAs shown in Figures14 and 15 two modes exist in the experimental signal of no

defect and are at 503 kHz and 345 kHzThe signal of 20mmdefect consists of modes at 492 kHz 412 kHz and 341 kHzAnd the signal of 30mmdefect consists ofmodes at 498 kHz448 kHz and 339 kHz Figure 16 shows these modes aredecomposed by the presented algorithm This indicates the

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Shock and Vibration

Equation (14) can be symbolized as

larrrarr119884 minuslarrrarr119875 larrrarr119860 = larrrarr119864 (15)

The evaluation of tracked order components is exactly to finda vectorlarrrarr119860 fulfilling

minlarrrarr119860

(100381710038171003817100381710038171003817larrrarr119864 1003817100381710038171003817100381710038172) = min

larrrarr119860

(larrrarr119864 119867larrrarr119864 ) = minlarrrarr119860

(119869) (16)

that is 120597119869120597larrrarr119860 = 0 The vectorlarrrarr119860 can be written as

larrrarr119875 119867larrrarr119875larrrarr119860 = larrrarr119875 119867larrrarr119884 (17)

The matrixlarrrarr119875 119867larrrarr119875 is written as

larrrarr119875 119867larrrarr119875 =[[[[[[[[[[[[[

larrrarr119878 larrrarr119861 12 larrrarr119861 13 sdot sdot sdot larrrarr119861 1119870larrrarr119861 21 larrrarr119878 larrrarr119861 23 sdot sdot sdot larrrarr119861 2119870larrrarr119861 31 larrrarr119861 12 larrrarr119878 sdot sdot sdot larrrarr119861 3119870 dlarrrarr119861 1198701 larrrarr119861 1198702 larrrarr119861 1198703 sdot sdot sdot larrrarr119878

]]]]]]]]]]]]]

(18)

wherelarrrarr119878 = 1199032larrrarr119872119879larrrarr119872+larrrarr119868 andlarrrarr119861 119906V = 119861119867119906 119861V Moreoverlarrrarr119875 119867is written as

larrrarr119875 119867 = [larrrarr119861 1 larrrarr119861 2 larrrarr119861 3 sdot sdot sdot larrrarr119861 119870]119879 (19)

wherelarrrarr119861 119870 is the complex conjugate oflarrrarr119861 1198703 Principle of the Presented Algorithm

As mentioned above SPWVD has a promising time-frequency resolution Therefore we obtain frequencies anddurations of modes from SPWVD distributions of testingguided waves Furthermore VKF OT is adapted to realizeisolation of different wave packages with obtained modefrequencies Finally the final mode waveforms are cut outfrom the wave packages of modes by durations of modesThe processing steps of the extension algorithm are shown inFigure 1 and are as follows

(1) Smoothed Pseudo Wigner-Ville Distribution SPWVD isused for processing testing signal to get corresponding time-frequency distribution And the promising time-frequencyresolution of the method can lead to a high calculationaccuracy of frequencies and durations of modes

(2) Extracting and Separating Valuable Areas of the Time-Frequency Panel To extract and separate different modes

we do the following (1) sum coefficients of each frequency-indexed group and the calculation formula is

119864 (Θ) = 119873sum119899=1

SPW119904 (119899 Θ) (20)

where119873denotes the number of the time variables of the time-frequency panel (2) Calculate minimal values andmaximumvalues of summations Lines of the minimal values in thetime-frequency panel can separate the valuable areas And themaximum value evaluates whether the energy of a mode isstrong enough to be kept (3) Conduct threshold processingfor the maximum values And the equation is defined as

119864 (Θ)max = keep 119864 (Θ)max gt 1198790discard 119864 (Θ)max le 1198790 (21)

where 119864(Θ)max means the maximum of 119864(Θ) 1198790 denotesthe threshold for sift valuable modes A mode with a strongenergy is more valuable for detecting the debonding defectso a threshold process is introduced to improve calcula-tion efficiency Moreover the noise can also be removedby this operation After this step the areas of the time-frequency panel corresponding to the significant modescan be extracted and separated Moreover correspondingfrequencies at the maximum values are taken as the modefrequencies

(3) VoldndashKalman Filter Order TrackingThemode frequencieshave been calculated in Step (2) So we employ VKF OT tofilter the specific mode waveform with these frequenciesThedifferent modes 1198910119894 (119894 = 1 2 119872) can be preliminarilyisolated and119872 is number of the maximum values obtainedin Step (2)

(4) Peak-Track Algorithm Conduct the peak-track algorithmfor the significant areas of SPWVD to obtain the primary IAof different modesThe principle of the peak-track algorithmcan be found in [30] And then the IAs of significant modescan be obtained

(5) Constructing Filters in Time Domain To remove calcula-tion error of the mode waveform from result obtained in Step(3) we construct a corresponding filter in time domain basedon the primary IAs of different modes obtained in Step (4)And the equation is as follows

119860 119894 = 1 1198600119894 gt 1198791198600 1198600119894 le 119879119860 (22)

where 119860 119894 is the value of the 119894th filter in time domain and 1198600119894denote the primary IAs of the 119894th modes 119879119860 is a threshold toremove calculation error of the mode waveform

Shock and Vibration 5

Testing signals

Smoothed Pseudo Wigner-Ville distribution

Time-frequencycoefficients

Summing coefficients of eachfrequency-indexed group

Calculation of minimal valuesand maximum values ofsummations

Threshold processingExtracting and separatingvaluable areas of the time-frequency panel

Valuable areas fordifferent modes

Peak-track algorithm

Instantaneousamplitudes ofmodes

Threshold process

Filters in time domain

Frequencies ofmodes

VoldndashKalman filter ordertracking

Waveforms ofdifferent modes

Filtering in time domain forcalculation result of VoldndashKalman filter order tracking

Final waveforms ofdifferent modes

Figure 1 The different steps of the algorithm presented in the paper

(6) Filtering in Time Domain for Calculation Result ofVoldndashKalman Filter Order Tracking Calculate the inner prod-uct between the mode waveforms obtained in Step (3) andthe filter in time domain from Step (5) And then the finalcalculation result is obtained The equation is

119891119894 = 119860 119894 lowast 1198910119894 (23)

In Section 4 the details of the present algorithm will beillustrated with a sample signal

4 Illustration of the Presented Algorithm

We construct a sample signal to illustrate the presentedalgorithm

6 Shock and Vibration

119904 (119905) = 1199041 (119905) + 1199042 (119905) + 1199043 (119905)

1199041 (119905) =

0 0 le 119905 le 0000054000 (119905 minus 000005) sin (300000 times 2120587119905) 000005 lt 119905 le 00003minus4000 (119905 minus 000055) sin (300000 times 2120587119905) 00003 lt 119905 le 0000550 000055 lt 119905 le 0001

1199042 (119905) =

0 0 le 119905 le 0000254000 (119905 minus 000025) sin (55000 times 2120587119905) 000025 lt 119905 le 00005minus4000 (119905 minus 000075) sin (55000 times 2120587119905) 00005 lt 119905 le 0000750 000075 lt 119905 le 0001

1199043 (119905) =

0 0 le 119905 le 0000454000 (119905 minus 000025) sin (50000 times 2120587119905) 000045 lt 119905 le 00007minus4000 (119905 minus 000075) sin (50000 times 2120587119905) 00007 lt 119905 le 0000950 000095 lt 119905 le 0001

(24)

The sampling frequency is 2MHzThe sample signal consistsof three modes at frequencies of 50 55 and 300 kHz Thecurve of the sample signal in time domain is shown inFigure 2

Firstly we employ SPWVD for the sample signal to obtainthe corresponding time-frequency panel which is shown inFigure 3 As can be seen in Figure 3 the time resolution andfrequency resolution of the time-frequency are promisingBesides no interference is in the representation Howeverthe difference between the component at 50 kHz and thecomponent at 55 kHz is so little that the two componentscannot be separated in the SPWVDdistribution of the samplesignal so is in Fourier spectrum as shown in Figure 4

After that (20) is used on the SPWVD distribution Asshown in Figure 5 three maximum values at 50 55 and300 kHz are kept So VKF OT is employed on the samplesignal with 50 55 and 300 kHz to get the correspondingfiltering results

And then the primary IAs of differentmodes are obtainedby the peak-track algorithm The filters in time domainof different modes are obtained by employing (22) on theprimary IAs as shown in Figure 6 We can adjust thethreshold in (22) to get filters in time domain of differentmodes with a high accuracy in time resolution

Finally we conduct time-domain filter for the result ofVKF OT and the results are shown in Figure 7 As presentedin Figure 7 the decomposition results almost overlap withthe corresponding original modes To further validate theeffectiveness of the presented algorithm we calculate theerror of the decomposition result as shown in Figure 8 Theabsolute error is less than 01 for the modes at 50 and 55 kHzand is less than 002 for the mode at 300 kHz which reveals

that the calculation accuracy of the presented algorithm ispromising

To compare with EEMD the sample signal is alsoprocessed by this decomposition method Figure 9 showsthe coefficients of correlation between different IMFs andthe sample signal We can learn that IMFs 1ndash4 are vitalcomponents of the signal as the coefficients of correlationare relatively greater So these IMFs are shown in Figure 10It is visible that the mode mixing occurs in EEMD for modesat 50 and 55 kHz as shown in Figure 10(b) Because theratio between modes at 50 and 55 kHz is greater than 075they cannot be separated as revealed in [25] Therefore thepoor frequency resolution is a limitation of EEMD for itsapplication

5 Details of the Experimental

Thematerial of the specimen is a specific composite materialThe size is 400mm times 300mm times 3mm and contains 15 layersThe corresponding size diagram is presented in Figure 11 Twodebonding defects are in the specimenThe side length of thedefects is respectively 20mm and 30mm

Figure 12 is the diagram of the testing principle Intesting process the exciting probe sends an exciting waveand then the receiving probe will receive excited lamb wavesThe excitation wave is a sine wave with a frequency of100 kHz The sampling frequency is 20MHz Three sets ofsignal are collected in the experiment responding to threesituations that is no defect 20mm defect and 30mmdefect respectively The corresponding GWs collected in theexperiment are presented in Figure 13

Shock and Vibration 7

minus15minus1

minus050

051

15

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

Figure 2 The curve of the sample signal in time domain

50 kHz

300 kHz

55 kHz

02 04 06 08 10Time (ms)

0

100

200

300

400

500

Freq

uenc

y (k

Hz)

(a)

55 kHz

50 kHz

300 kHz 55 kHz

500400

300200

1000

0

02

04

06

08

1

0

20

40

60

Am

plitu

de

Frequency (kHz)Time (m

s)

(b)

Figure 3 The representation of the sample signal by using SPWVD

40 50 60 70 80 90 1000

005

01 55 kHz50 kHz300 kHz

0

005

01

015

Am

plitu

de

100 200 300 400 500 600 700 800 900 10000Frequency (kHz)

Figure 4 The Fourier spectrum of the sample signal

times104

10050 150 200 250 300 3500Frequency (kHz)

0

1

2

3

Sum

mat

ion

Figure 5 The different frequency-group summations of the time-frequency panel of the sample signal

6 Result and Discussion

Figure 15 presents the decomposition result of experimentalsignals by using the presented algorithmAs shown in Figures14 and 15 two modes exist in the experimental signal of no

defect and are at 503 kHz and 345 kHzThe signal of 20mmdefect consists of modes at 492 kHz 412 kHz and 341 kHzAnd the signal of 30mmdefect consists ofmodes at 498 kHz448 kHz and 339 kHz Figure 16 shows these modes aredecomposed by the presented algorithm This indicates the

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 5

Testing signals

Smoothed Pseudo Wigner-Ville distribution

Time-frequencycoefficients

Summing coefficients of eachfrequency-indexed group

Calculation of minimal valuesand maximum values ofsummations

Threshold processingExtracting and separatingvaluable areas of the time-frequency panel

Valuable areas fordifferent modes

Peak-track algorithm

Instantaneousamplitudes ofmodes

Threshold process

Filters in time domain

Frequencies ofmodes

VoldndashKalman filter ordertracking

Waveforms ofdifferent modes

Filtering in time domain forcalculation result of VoldndashKalman filter order tracking

Final waveforms ofdifferent modes

Figure 1 The different steps of the algorithm presented in the paper

(6) Filtering in Time Domain for Calculation Result ofVoldndashKalman Filter Order Tracking Calculate the inner prod-uct between the mode waveforms obtained in Step (3) andthe filter in time domain from Step (5) And then the finalcalculation result is obtained The equation is

119891119894 = 119860 119894 lowast 1198910119894 (23)

In Section 4 the details of the present algorithm will beillustrated with a sample signal

4 Illustration of the Presented Algorithm

We construct a sample signal to illustrate the presentedalgorithm

6 Shock and Vibration

119904 (119905) = 1199041 (119905) + 1199042 (119905) + 1199043 (119905)

1199041 (119905) =

0 0 le 119905 le 0000054000 (119905 minus 000005) sin (300000 times 2120587119905) 000005 lt 119905 le 00003minus4000 (119905 minus 000055) sin (300000 times 2120587119905) 00003 lt 119905 le 0000550 000055 lt 119905 le 0001

1199042 (119905) =

0 0 le 119905 le 0000254000 (119905 minus 000025) sin (55000 times 2120587119905) 000025 lt 119905 le 00005minus4000 (119905 minus 000075) sin (55000 times 2120587119905) 00005 lt 119905 le 0000750 000075 lt 119905 le 0001

1199043 (119905) =

0 0 le 119905 le 0000454000 (119905 minus 000025) sin (50000 times 2120587119905) 000045 lt 119905 le 00007minus4000 (119905 minus 000075) sin (50000 times 2120587119905) 00007 lt 119905 le 0000950 000095 lt 119905 le 0001

(24)

The sampling frequency is 2MHzThe sample signal consistsof three modes at frequencies of 50 55 and 300 kHz Thecurve of the sample signal in time domain is shown inFigure 2

Firstly we employ SPWVD for the sample signal to obtainthe corresponding time-frequency panel which is shown inFigure 3 As can be seen in Figure 3 the time resolution andfrequency resolution of the time-frequency are promisingBesides no interference is in the representation Howeverthe difference between the component at 50 kHz and thecomponent at 55 kHz is so little that the two componentscannot be separated in the SPWVDdistribution of the samplesignal so is in Fourier spectrum as shown in Figure 4

After that (20) is used on the SPWVD distribution Asshown in Figure 5 three maximum values at 50 55 and300 kHz are kept So VKF OT is employed on the samplesignal with 50 55 and 300 kHz to get the correspondingfiltering results

And then the primary IAs of differentmodes are obtainedby the peak-track algorithm The filters in time domainof different modes are obtained by employing (22) on theprimary IAs as shown in Figure 6 We can adjust thethreshold in (22) to get filters in time domain of differentmodes with a high accuracy in time resolution

Finally we conduct time-domain filter for the result ofVKF OT and the results are shown in Figure 7 As presentedin Figure 7 the decomposition results almost overlap withthe corresponding original modes To further validate theeffectiveness of the presented algorithm we calculate theerror of the decomposition result as shown in Figure 8 Theabsolute error is less than 01 for the modes at 50 and 55 kHzand is less than 002 for the mode at 300 kHz which reveals

that the calculation accuracy of the presented algorithm ispromising

To compare with EEMD the sample signal is alsoprocessed by this decomposition method Figure 9 showsthe coefficients of correlation between different IMFs andthe sample signal We can learn that IMFs 1ndash4 are vitalcomponents of the signal as the coefficients of correlationare relatively greater So these IMFs are shown in Figure 10It is visible that the mode mixing occurs in EEMD for modesat 50 and 55 kHz as shown in Figure 10(b) Because theratio between modes at 50 and 55 kHz is greater than 075they cannot be separated as revealed in [25] Therefore thepoor frequency resolution is a limitation of EEMD for itsapplication

5 Details of the Experimental

Thematerial of the specimen is a specific composite materialThe size is 400mm times 300mm times 3mm and contains 15 layersThe corresponding size diagram is presented in Figure 11 Twodebonding defects are in the specimenThe side length of thedefects is respectively 20mm and 30mm

Figure 12 is the diagram of the testing principle Intesting process the exciting probe sends an exciting waveand then the receiving probe will receive excited lamb wavesThe excitation wave is a sine wave with a frequency of100 kHz The sampling frequency is 20MHz Three sets ofsignal are collected in the experiment responding to threesituations that is no defect 20mm defect and 30mmdefect respectively The corresponding GWs collected in theexperiment are presented in Figure 13

Shock and Vibration 7

minus15minus1

minus050

051

15

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

Figure 2 The curve of the sample signal in time domain

50 kHz

300 kHz

55 kHz

02 04 06 08 10Time (ms)

0

100

200

300

400

500

Freq

uenc

y (k

Hz)

(a)

55 kHz

50 kHz

300 kHz 55 kHz

500400

300200

1000

0

02

04

06

08

1

0

20

40

60

Am

plitu

de

Frequency (kHz)Time (m

s)

(b)

Figure 3 The representation of the sample signal by using SPWVD

40 50 60 70 80 90 1000

005

01 55 kHz50 kHz300 kHz

0

005

01

015

Am

plitu

de

100 200 300 400 500 600 700 800 900 10000Frequency (kHz)

Figure 4 The Fourier spectrum of the sample signal

times104

10050 150 200 250 300 3500Frequency (kHz)

0

1

2

3

Sum

mat

ion

Figure 5 The different frequency-group summations of the time-frequency panel of the sample signal

6 Result and Discussion

Figure 15 presents the decomposition result of experimentalsignals by using the presented algorithmAs shown in Figures14 and 15 two modes exist in the experimental signal of no

defect and are at 503 kHz and 345 kHzThe signal of 20mmdefect consists of modes at 492 kHz 412 kHz and 341 kHzAnd the signal of 30mmdefect consists ofmodes at 498 kHz448 kHz and 339 kHz Figure 16 shows these modes aredecomposed by the presented algorithm This indicates the

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

119904 (119905) = 1199041 (119905) + 1199042 (119905) + 1199043 (119905)

1199041 (119905) =

0 0 le 119905 le 0000054000 (119905 minus 000005) sin (300000 times 2120587119905) 000005 lt 119905 le 00003minus4000 (119905 minus 000055) sin (300000 times 2120587119905) 00003 lt 119905 le 0000550 000055 lt 119905 le 0001

1199042 (119905) =

0 0 le 119905 le 0000254000 (119905 minus 000025) sin (55000 times 2120587119905) 000025 lt 119905 le 00005minus4000 (119905 minus 000075) sin (55000 times 2120587119905) 00005 lt 119905 le 0000750 000075 lt 119905 le 0001

1199043 (119905) =

0 0 le 119905 le 0000454000 (119905 minus 000025) sin (50000 times 2120587119905) 000045 lt 119905 le 00007minus4000 (119905 minus 000075) sin (50000 times 2120587119905) 00007 lt 119905 le 0000950 000095 lt 119905 le 0001

(24)

The sampling frequency is 2MHzThe sample signal consistsof three modes at frequencies of 50 55 and 300 kHz Thecurve of the sample signal in time domain is shown inFigure 2

Firstly we employ SPWVD for the sample signal to obtainthe corresponding time-frequency panel which is shown inFigure 3 As can be seen in Figure 3 the time resolution andfrequency resolution of the time-frequency are promisingBesides no interference is in the representation Howeverthe difference between the component at 50 kHz and thecomponent at 55 kHz is so little that the two componentscannot be separated in the SPWVDdistribution of the samplesignal so is in Fourier spectrum as shown in Figure 4

After that (20) is used on the SPWVD distribution Asshown in Figure 5 three maximum values at 50 55 and300 kHz are kept So VKF OT is employed on the samplesignal with 50 55 and 300 kHz to get the correspondingfiltering results

And then the primary IAs of differentmodes are obtainedby the peak-track algorithm The filters in time domainof different modes are obtained by employing (22) on theprimary IAs as shown in Figure 6 We can adjust thethreshold in (22) to get filters in time domain of differentmodes with a high accuracy in time resolution

Finally we conduct time-domain filter for the result ofVKF OT and the results are shown in Figure 7 As presentedin Figure 7 the decomposition results almost overlap withthe corresponding original modes To further validate theeffectiveness of the presented algorithm we calculate theerror of the decomposition result as shown in Figure 8 Theabsolute error is less than 01 for the modes at 50 and 55 kHzand is less than 002 for the mode at 300 kHz which reveals

that the calculation accuracy of the presented algorithm ispromising

To compare with EEMD the sample signal is alsoprocessed by this decomposition method Figure 9 showsthe coefficients of correlation between different IMFs andthe sample signal We can learn that IMFs 1ndash4 are vitalcomponents of the signal as the coefficients of correlationare relatively greater So these IMFs are shown in Figure 10It is visible that the mode mixing occurs in EEMD for modesat 50 and 55 kHz as shown in Figure 10(b) Because theratio between modes at 50 and 55 kHz is greater than 075they cannot be separated as revealed in [25] Therefore thepoor frequency resolution is a limitation of EEMD for itsapplication

5 Details of the Experimental

Thematerial of the specimen is a specific composite materialThe size is 400mm times 300mm times 3mm and contains 15 layersThe corresponding size diagram is presented in Figure 11 Twodebonding defects are in the specimenThe side length of thedefects is respectively 20mm and 30mm

Figure 12 is the diagram of the testing principle Intesting process the exciting probe sends an exciting waveand then the receiving probe will receive excited lamb wavesThe excitation wave is a sine wave with a frequency of100 kHz The sampling frequency is 20MHz Three sets ofsignal are collected in the experiment responding to threesituations that is no defect 20mm defect and 30mmdefect respectively The corresponding GWs collected in theexperiment are presented in Figure 13

Shock and Vibration 7

minus15minus1

minus050

051

15

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

Figure 2 The curve of the sample signal in time domain

50 kHz

300 kHz

55 kHz

02 04 06 08 10Time (ms)

0

100

200

300

400

500

Freq

uenc

y (k

Hz)

(a)

55 kHz

50 kHz

300 kHz 55 kHz

500400

300200

1000

0

02

04

06

08

1

0

20

40

60

Am

plitu

de

Frequency (kHz)Time (m

s)

(b)

Figure 3 The representation of the sample signal by using SPWVD

40 50 60 70 80 90 1000

005

01 55 kHz50 kHz300 kHz

0

005

01

015

Am

plitu

de

100 200 300 400 500 600 700 800 900 10000Frequency (kHz)

Figure 4 The Fourier spectrum of the sample signal

times104

10050 150 200 250 300 3500Frequency (kHz)

0

1

2

3

Sum

mat

ion

Figure 5 The different frequency-group summations of the time-frequency panel of the sample signal

6 Result and Discussion

Figure 15 presents the decomposition result of experimentalsignals by using the presented algorithmAs shown in Figures14 and 15 two modes exist in the experimental signal of no

defect and are at 503 kHz and 345 kHzThe signal of 20mmdefect consists of modes at 492 kHz 412 kHz and 341 kHzAnd the signal of 30mmdefect consists ofmodes at 498 kHz448 kHz and 339 kHz Figure 16 shows these modes aredecomposed by the presented algorithm This indicates the

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

minus15minus1

minus050

051

15

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

Figure 2 The curve of the sample signal in time domain

50 kHz

300 kHz

55 kHz

02 04 06 08 10Time (ms)

0

100

200

300

400

500

Freq

uenc

y (k

Hz)

(a)

55 kHz

50 kHz

300 kHz 55 kHz

500400

300200

1000

0

02

04

06

08

1

0

20

40

60

Am

plitu

de

Frequency (kHz)Time (m

s)

(b)

Figure 3 The representation of the sample signal by using SPWVD

40 50 60 70 80 90 1000

005

01 55 kHz50 kHz300 kHz

0

005

01

015

Am

plitu

de

100 200 300 400 500 600 700 800 900 10000Frequency (kHz)

Figure 4 The Fourier spectrum of the sample signal

times104

10050 150 200 250 300 3500Frequency (kHz)

0

1

2

3

Sum

mat

ion

Figure 5 The different frequency-group summations of the time-frequency panel of the sample signal

6 Result and Discussion

Figure 15 presents the decomposition result of experimentalsignals by using the presented algorithmAs shown in Figures14 and 15 two modes exist in the experimental signal of no

defect and are at 503 kHz and 345 kHzThe signal of 20mmdefect consists of modes at 492 kHz 412 kHz and 341 kHzAnd the signal of 30mmdefect consists ofmodes at 498 kHz448 kHz and 339 kHz Figure 16 shows these modes aredecomposed by the presented algorithm This indicates the

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

0049 05520

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(a)

0248 07510

05

1

15

Am

plitu

de

02 04 06 08 10Time (ms)

(b)

0448 0952 104 06 08020Time (ms)

0

05

1

15

Am

plitu

de

(c)

Figure 6The filters in time domain of different modes (a) mode at300 kHz (b) mode at 55 kHz and (c) mode at 50 kHz

method is effective in isolating different modes Besidesconsidering that 503 kHz 492 kHz and 498 kHz pose little

Original signalDecomposition signal

minus1minus05

005

1

Am

plitu

de

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

Original signalDecomposition signal

01 02 03 04 05 06 07 08 09 10Time (ms)

minus1minus05

005

1

Am

plitu

de(b)

Original signalDecomposition signal

minus1minus05

005

1A

mpl

itude

01 02 03 04 05 06 07 08 09 10Time (ms)

(c)

Figure 7 The decomposition result and the original modes of thesample signal 119909 by the presented algorithm (a)mode at 300 kHz (b)mode at 55 kHz and (c) mode at 50 kHz

differences and this phenomenon is similar to 345 kHz341 kHz and 339 kHz it seems that defects stimulate newmodes and 412 kHz for 20mm defect and 448 kHz for30mm defect On the basis of this phenomenon we cantry to detect the defect Moreover the frequency of the newmode becomes greater along with the defect size (412 kHzfor 20mm and 448 kHz for 30mm) Maybe we can try toevaluate the size of the defect according to this relationshipFinally as we have isolated different wave packets thelocation of defect can be obtained by the decompositionresults

7 Conclusion

This paper presents a decomposition algorithm aiming toanalyze the characteristics of ultrasonic GWs generated ina NDT for the debonding in a type of composite materialby combining SPWVD and VKF OT The presented methodsucceeds in isolating different GW modes On the basis of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

minus0050

005

Mod

e 1

01 02 03 04 05 06 07 08 09 10Time (ms)

(a)

01 02 03 04 05 06 07 08 09 10Time (ms)

minus010

01

Mod

e 2

(b)

minus010

01

Mod

e 301 02 03 04 05 06 07 08 09 10

Time (ms)

(c)

Figure 8 The errors of decomposition result of the sample signal 119909 by the presented algorithm (a) mode at 300 kHz (b) mode at 55 kHzand (c) mode at 50 kHz

1 2 3 4 5 6 7 8 9 100

02040608

Cor

relat

ion

coeffi

cien

ts

Numbers of IMFs

Figure 9 Correlation coefficients between IMFs and the original signal

minus1

0

1

IMF

1

minus1

0

1

IMF

2

minus2

0

2

IMF

3

minus02

0

02

IMF

4

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10

(a)

50 100 150 200 250 300 3500Frequency (kHz)

50 100 150 200 250 300 3500

50 100 150 200 250 300 3500

50 100 150 200 250 3000 350

0

0005

001

0

005

01

0

002

004

0

01

02

IMF

1IM

F 2

IMF

3IM

F 4

(b)

Figure 10The IMFs 1ndash4 in the EEMDof the sample signal and the corresponding Fourier spectrums (a) the IMFs and (b) the correspondingFourier spectrums

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

30

400

300

20

3

Figure 11 The size diagram of the specimen

Receiving probeExciting probe

Guided waves

Exciting wave

Guided waves

Defect

Figure 12 The diagram of the testing principle

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(a)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(b)

02 04 06 08 10Time (ms)

minus1

minus05

0

05

1

Am

plitu

de

(c)Figure 13 The GWs collected in the experiment (a) no defect (b) 20mm and (c) 30mm

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

503 kHz345 kHz

0

20

40

60

80

100Fr

eque

ncy

(kH

z)

02 04 06 08 10Time (ms)

(a)

492 kHz412 kHz

341 kHz

0

20

40

60

80

100

Freq

uenc

y (H

z)

02 04 06 08 10Time (ms)

(b)

498 kHz448 kHz

339 kHz

02 04 06 08 10Time (ms)

0

20

40

60

80

100

Freq

uenc

y (k

Hz)

(c)

Figure 14 The SPWVD representations of the GWs in the experi-ment (a) no defect (b) 20mm and (c) 30mm

the presented algorithm the characteristics of the experi-mental signals were investigated Some conclusions whichare valuable for identification of defect calculation of defectsize and locating defect are obtainedThe technique also canbe applied in analogue NDTs and NDEs on the basic of theultrasonic GWs Further research will be done to validate thefeasibility for locating defects by the algorithm

503

345

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(a)

0 50 100 150 200 250Frequency (kHz)

492

412341

0

200

400

600

800

1000

1200

1400

Sum

mat

ion

(b)

498

448

339

0

500

1000

1500

2000

Sum

mat

ion

50 100 150 200 2500Frequency (kHz)

(c)

Figure 15 The different frequency-group summations of the time-frequency panel of the experimental signals (a) no defect (b)20mm and (c) 30mm

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

02 04 06 08 10

02 04 06 08 10Time (ms)

minus1

0

1

Mod

e 2

minus1

0

1

Mod

e 1

(a)

02 04 06 08 10

02 04 06 08 10

02 04 06 08 10Time (ms)

minus05

0

05

Mod

e 3

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 1

(b)

minus05

0

05

Mod

e 1

minus05

0

05

Mod

e 2

minus05

0

05

Mod

e 3

02 04 06 08 10Time (ms)

02 04 06 08 10

02 04 06 08 10

(c)Figure 16 The decomposition result of experimental signals byusing the presented algorithm (a) no defect (b) 20mm and (c)30mm

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] R Zhou Z Li and J Sun ldquoCrack deflection and interfacedebonding in composite materials elucidated by the configura-tion force theoryrdquo Composites Part B Engineering vol 42 no 7pp 1999ndash2003 2011

[2] T Liu W Zhang and S Yan ldquoA novel image enhancementalgorithm based on stationary wavelet transform for infraredthermography to the de-bonding defect in solid rocket motorsrdquoMechanical Systems and Signal Processing vol 62 no 10 pp366ndash380 2015

[3] J Li Y Lu R Guan and W Qu ldquoGuided waves for debondingidentification in CFRP-reinforced concrete beamsrdquo Construc-tion and Building Materials vol 131 pp 388ndash399 2017

[4] J Wu Z Ma and Y Zhang ldquoA Time-Frequency Research forUltrasonic GuidedWave Generated from the Debonding Basedon a Novel Time-Frequency Analysis Techniquerdquo Shock andVibration vol 2017 Article ID 5686984 2017

[5] L Longbiao ldquoModeling the Effect of Interface Wear on FatigueHysteresis Behavior of Carbon Fiber-Reinforced Ceramic-Matrix Compositesrdquo Applied Composite Materials vol 22 no6 pp 887ndash920 2015

[6] S Khare M Razdan P Munshi B V S Sekhar and K Balasub-ramaniam ldquoDefect detection in carbon-fiber composites usinglamb-wave tomographic methodsrdquo Research in NondestructiveEvaluation vol 18 no 2 pp 101ndash119 2007

[7] K S Tan N Guo B S Wong and C G Tui ldquoExperimentalevaluation of delaminations in composite plates by the use ofLamb wavesrdquo Composites Science and Technology vol 53 no 1pp 77ndash84 1995

[8] S W Kercel M B Klein and B Pouet ldquoBayesian separation ofLamb wave signatures in laser ultrasonicsrdquo in Proceedings of theApplications and Science of Computational Intelligence III vol4055 of Proceedings of SPIE pp 350ndash361 April 2000

[9] J Cai L Shi andX P Qing ldquoA time-distance domain transformmethod for Lamb wave dispersion compensation consideringsignal waveform correctionrdquo Smart Materials and Structuresvol 22 no 10 Article ID 105024 2013

[10] P Rizzo and F L di Scalea ldquoFeature extraction for defectdetection in strands by guided ultrasonic wavesrdquo StructuralHealth Monitoring vol 5 no 3 pp 297ndash308 2006

[11] R Gangadharan C R L Murthy S Gopalakrishnan and MR Bhat ldquoTime reversal technique for health monitoring ofmetallic structure using Lamb wavesrdquo Ultrasonics vol 49 no8 pp 696ndash705 2009

[12] T Liu S Yan and W Zhang ldquoTime-frequency analysis ofnonstationary vibration signals for deployable structures byusing the constant-Q nonstationary gabor transformrdquoMechan-ical Systems and Signal Processing vol 75 pp 228ndash244 2016

[13] W Wu G Jiang S Huang and C J Leo ldquoVertical dynamicresponse of pile embedded in layered transversely isotropicsoilrdquo Mathematical Problems in Engineering Article ID 12691612 pages 2014

[14] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[15] C A Paget S Grondel and K Levin ldquoDamage assessmentin composites by Lamb waves and wavelet coefficientsrdquo SmartMaterials and Structures vol 12 no 3 pp 393ndash412 2003

[16] L Yu J Bao and V Giurgiutiu ldquoSignal processing techniquesfor damage detection with piezoelectric wafer active sensors

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

and embedded ultrasonic structural radarrdquo in Proceedings ofthe Smart Structures and Materials 2004 - Sensors and SmartStructures Technologies for Civil Mechanical and AerospaceSystems pp 492ndash503 USA March 2004

[17] Y Y Kim and E-H Kim ldquoEffectiveness of the continuouswavelet transform in the analysis of some dispersive elasticwavesrdquoThe Journal of the Acoustical Society of America vol 110no 1 pp 86ndash94 2001

[18] D Yu J Cheng and Y Yang ldquoApplication of EMD methodand Hilbert spectrum to the fault diagnosis of roller bearingsrdquoMechanical Systems and Signal Processing vol 19 no 2 pp 259ndash270 2005

[19] L Yu S Wang and K K Lai ldquoForecasting crude oil price withan EMD-based neural network ensemble learning paradigmrdquoEnergy Economics vol 30 no 5 pp 2623ndash2635 2008

[20] R Osegueda V Kreinovich S Nazarian and E RoldanldquoDetection of cracks at rivet holes in thin plates using Lamb-wave scanningrdquo in Proceedings of the International Societyfor Optical Engineering Smart Nondestructive Evaluation andHealthMonitoring of Structural andBiological Systems II pp 55ndash66 USA March 2003

[21] Y Yu and C Junsheng ldquoA roller bearing fault diagnosis methodbased on EMD energy entropy and ANNrdquo Journal of Sound andVibration vol 294 no 1-2 pp 269ndash277 2006

[22] L Salvino A Purekar and D J Pines ldquoHealth monitoring of 2-D plates using EMD and hilbert phaserdquo in Proceedings of the4th International Workshop on Structural Health MonitoringStanford University Calif USA 2005

[23] Z H Guo W G Zhao H Y Lu and J Wang ldquoMulti-step forecasting for wind speed using a modified EMD-basedartificial neural network modelrdquo Renewable Energy vol 37 no1 pp 241ndash249 2012

[24] A Y Fu W Liu and X Deng ldquoDetecting phishing webpages with visual similarity assessment based on Earth MoverrsquosDistance (EMD)rdquo IEEE Transactions on Dependable and SecureComputing vol 3 no 4 pp 301ndash311 2006

[25] G Rilling and P Flandrin ldquoOne or two frequencies Theempirical mode decomposition answersrdquo IEEE Transactions onSignal Processing vol 56 no 1 pp 85ndash95 2008

[26] H Vold and J Leuridan ldquoHigh resolution order tracking atextreme slew rates using kalman tracking filtersrdquo SAETechnicalPapers 1993

[27] H Vold H Herlufsen M Mains and D Corwin-RennerldquoMulti axle order trackingwith theVold-Kalman tracking filterrdquoS V Sound and Vibration vol 31 no 5 pp 30ndash34 1997

[28] P Flandrin and B Escudie ldquoAn interpretation of the Pseudo-Wigner-Ville distributionrdquo Signal Processing vol 6 no 1 pp 27ndash36 1984

[29] M-C PanW-C Chu andD-D Le ldquoAdaptive angular-velocityVold-Kalman filter order tracking-Theoretical basis numericalimplementation and parameter investigationrdquo Mechanical Sys-tems and Signal Processing vol 81 pp 148ndash161 2016

[30] Z Chen and R C Maher ldquoSemi-automatic classification ofbird vocalizations using spectral peak tracksrdquo The Journal ofthe Acoustical Society of America vol 120 no 5 pp 2974ndash29842006

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of