NDT&E International 54 (2013) 171–182

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Characterization of pipeline defect in guided-waves based inspectionthrough matching pursuit with the optimized dictionary

Peter W. Tse n, Xiaojuan Wang

The Smart Engineering Asset Management Laboratory (SEAM) and The Croucher Optical Non-destructive Testing and Quality Inspection Laboratory (CNDT), Department of Systems

Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China

a r t i c l e i n f o

Article history:

Received 12 July 2012

Accepted 22 October 2012Available online 7 November 2012

Keywords:

Guided waves

Defect characterization

Matching pursuit

Interfering reflection components

(IRC)-dictionary

95/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.ndteint.2012.10.003

esponding author. Tel.: þ852 27888431; fax:

ail address: meptse@cityu.edu.hk (P.W. Tse).

a b s t r a c t

An optimized dictionary of matching pursuit (MP) is designed and combined with the ultrasonic guided

wave for characterizing pipeline defect, which consequently achieves good performance in estimating

the axial length of a defect. In the research field of guided wave based pipeline defect inspection,

quantitative characterization on the detected defect remains as an unsolved research task and is

seldom reported in the related publications. This paper reports a new method of MP equipped with an

optimized dictionary through analyzing the interference between the reflection components embedded

in a defect reflection signal in order to enable efficient extraction of defect information. The proposed

method not only enhances signal-to-noise ratio of reflection signal, but also characterizes the axial

length of pipeline defect directly and accurately. The method has been verified by simulated data,

artificial defects in real pipes as well as real corrosion in a servicing pipe.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The advanced technique of ultrasonic guided waves [1] is nowin routine use of nondestructive testing (NDT) fields. Manyprogresses and advancements have been made for the applicationof guided waves in inspecting pipeline. However, the quantitativeevaluation of defect sizes or severity is always a challenging taskin NDT after a pipe defect has been found because of the complex-ities included in the reflection signal [2]. The scale of difficultymagnifies in real practices as the reflected waves are subjected tothe contamination from a diversity of noise sources. Such sourcescould be randomly generated environmental noise, unexpectedmodes from mode conversion and coherent noises introduced bythe irregularity of defect as well as the reverberation of waves. Theinsufficient defect information prevents an accurate indication ofdamage severity without applying additional testing or directmeasurement. To carry out maintenance remedy on defectivepipelines properly and efficiently, the ability of characterizingpipeline defect is very important, particularly for the cases inwhich the locations of defect are difficult to be accessed, such asburied pipelines or pipelines inside walls.

Most of the methods currently available for long-range inspectionof pipeline defect are only capable of providing a qualitative orsemi-quantitative assessment of defects. Few research works have

ll rights reserved.

þ852 27888423.

been conducted on the possibility of using guided waves forcharacterizing pipeline defects in a quantitative manner. Mu et al.[3] determined the defect’s circumferential extent by comparing thetheoretical reflection profiles to the experimental results obtainedthrough performing circumferential focusing scan. Li [4] developedan algorithm based on two-dimensional blind deconvolution toevaluate the circumferential size of the defects using multiplereflection waveforms acquired by a multiplexed circumferentialtransducer array. Satyarnarayan et al. [5] investigated circumferentialhigher order guided wave modes to estimate the size of defect inpipe support region. These methods are supposed to optimize thespecific parameters of excited guided waves or construct sophisti-cated configuration of transduction system so as to achieve well-defined or -controlled waveform of reflection for defect characteriza-tion. They usually require a great deal of experimental care andtremendous time to increase the precision and reliability of instru-mentation and the repeatability of measurements. Other methods fordefect characterization tried to use simpler and less specific trans-ducers, thus decreasing the complexity of instrumentation andinstallation for practical applications. A good example is presentedby Demma et al. [6] works. They investigated the effect of defectparameters on reflection for possible interpretation of defect sizeinformation. Recent advancements include the utilization of imagingand tomography techniques for defect characterization. For example,Hayashi and Murase [7] developed a defect image technique throughreconstructing the spatial waveforms that had been separated intoseveral single-mode signals. However, the post processing ofreflected waves for defect characterization contains more difficulties

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182172

due to the complicated interaction process of guided waves withdifferent defects. Advanced signal processing techniques are alwaysneeded to purify the reflection signal so that higher chance of successin defect characterization can be realized. Although the abovetechniques have proven to be successful in various degrees, theyare in generally time and cost consumption but the results containsuncertainty in the accuracy of characterizing defects. Moreover, theystill cannot provide the ability of directly characterizing pipelinedefects by only analyzing the defect reflection signal.

2. Defect characterization with reflection components

It is important to understand reflection procedure for quanti-tative and accurate characterization of defect. It has been foundby some researchers such as Demma et al. [8,9] that the reflectionof guided waves from a defect is primarily resulted from theinterference between the two reflection components generated atthe edges of the defect. We further revealed in our earlierresearch work [10] that the complexity of the reflection signalwas essentially a result of the different features represented bythe front-edge and back-edge reflection components. Two edgereflection signals exhibit similar wave patterns in terms of thenumber of cycle, frequency, and modulation but have differentamplitude and duration of phase shift. The reflection coefficient oftotal resulting defect reflection signal thus exhibits a periodicvariation with the change of axial length of defect. That is, thetotal reflections are being constructive in some defect cases whilebeing destructive in some other defects cases, due to interferencebetween the reflections from two edges of defect. It is noted thatin all of the above studies, the researchers mainly used artificialdefects to develop simplified models, such as notch or circularhole, to approximate the case of real defects or corrosion inpipeline. The real pipeline defect is far more complex andirregular at its three dimensional profiles. Demma [11] indicatedthat maxima and minima of reflectivity resulted from the inter-ference of two reflection components could occur on real defectsthat would not have a sharp and rectangular profile in practicalinspection. Ma and Cawley [12] further employed a part-thickness taper elliptical defect model as a closer match to realcorrosion shape for investigating the effect of different defectparameters on the reflection. Their research showed that reflec-tion ratio spectrum from such a complex defect still exhibitedperiodic pattern due to the interference between reflections fromthe two edges of defect. That is, all of these researches suggestthat reflection signal captured even from a complex defect mainlyconsists of two reflection components from the front and backedges of defect, and the respective contribution of differentparameters of defect to overall defect reflection can be affectedby the features of these components. The identification of thesetwo primary components embedded in defect reflection signal istherefore greatly useful to characterize the concerned defect.

Considering the distance between two reflection positions,which are at the front and back defect edges, is closely relatedto the axial length of defect. Hence, the identified reflectioncomponents could thus help to determine the value of axiallength. Moreover, they can enable the evaluation of more defectparameters because each identified edge signal embeds geometricinformation such as circumferential extent and radial depth of thecorresponding edge of the defect. Therefore, the decomposition ofreflection signal together with the identification of axial length ofdefect is a very important step for comprehensive defectcharacterization. The axial length obtained through the use ofprimary reflection components refers to the characteristic valueof real axial length since the generation of these components isstrongly affected by the combined features of the defect edge’s

parameters. In this research, a method in the frame of matchingpursuit (MP) decomposition technique with an optimizeddictionary was developed to resolve the primary reflection com-ponents from defect reflection signal so that the quantitativecharacterization of defect length can be realized. MP is atime–frequency signal analysis technique for decomposing thewaveform into a linear combination of basis functions as definedin a dictionary. During the stage of developing our method, theprior knowledge about the relationship between the edge reflec-tion components and their respective features was adopted asprior information to establish the required dictionary for MPdecomposition procedure. This method not only provides anability of efficient noise immunity for the complex guided wavereflection signal, but also enables the characterization of defectlength directly from the defect’s reflection signal. The rest of thepaper starts with a detailed description of the rationale of theproposed method in Section 3, especially the construction of thedictionary optimized for the concerned application. In Section 4,the proposed method is applied to the simulated signals toillustrate its ability. The performance of our method is furtherinvestigated and presented in Section 5, in which the experimentsconducted on arbitrary defects and real corrosion in the testedpipe samples as well as the experimental results are stated indetails. Finally, the special observations, the conclusion and thepotential of research outcomes are summarized in Section 6.

3. Matching pursuit with optimized dictionary forcharacterizing axial length of defect

As explained in Section 2, both reflection components exhibitnearly the same patterns in terms of the frequency, cycle number,and modulation, but are different in phase, regardless of dispersioneffect as it can be controlled with proper arrangement of transduc-tion system. Once they have been decomposed and correctlyrecovered to their original temporal waveforms, then the charac-terized axial length of defect will be easily determined based onthe wave group velocity and the time shifts of two primaryreflection signals. It has been indicated in Section 2 that thesereflection components appear in the collected defect reflectionsignal with an interference form. The interference will not onlyresult in the complexity of waveform, but also cause the lost ofinterested information relevant to defect characteristics. Most ofthe conventional time–frequency signal processing methods areinadequate in identifying edge reflection components, especiallyunder the cases in which substantial environmental noises andcoherent noises are embedded in the reflection signal. Here, weproposed the method of optimized matching pursuit for decom-posing the reflection signal so that the original reflections causedby the front-edge and the back-edge of the defect can be recoveredfor estimating its axial length.

3.1. Matching pursuit decomposition

Matching pursuit (MP) decomposition is a highly adaptivetime–frequency signal processing technique introduced by Mallatand Zhang [13]. A similar algorithm was developed independentlyby Qian and Chen [14]. It can decompose any given signal into alinear expansion of components that belong to a redundantdictionary of waveforms. The dictionary is a collection of para-meterized waveform atom, which is presented by amplitude,phase, frequency, or other vital parameters. The components areselected from the dictionary to approximate the signal structuresso that any interested information embedded in the signal can bereconstructed. That is, MP can provide a representation or inter-pretation of signal structure through decomposition process.

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182 173

To explain MP decomposition, assuming {y1,y2,yyl} is the noisyobservation of a target function f at points {x1,x2,yxl}. Given anover-complete dictionary D¼{g1,g2,ygm}, which is a redundantcollection of unit vectors in a Hilbert space H, the function f can bedecomposed into a linear expansion of N atoms selected from D

and a residual term RN(t), as follows:

f ðtÞ ¼XN

n ¼ 1

angnþRNðtÞ,:gn:¼ 1 ð1Þ

f N ¼XN

n ¼ 1

angn ð2Þ

where {g1,g2,ygN}CD is the basis of this expansion, and{a1,a2,y,aN}CRN is the set of corresponding coefficients of theexpansion. fN presents an approximation of f through selecting N

proper basis atoms from the dictionary. The algorithm is to selectthe basis {g} and the corresponding coefficient {a} so that theycan iteratively minimize the second-order norm of the residualcomponent for optimal approximation:

:RN:2¼ :f�f N:

2¼Xl

i ¼ 1

ðyi�f N xið ÞÞ2¼min ð3Þ

In the first step of matching pursuit, the waveform atom g0

that best matches the given signal f is chosen through evaluatingthe similarity by inner product. The attractive theoretical proper-ties of MP algorithm guarantee the rigorous proofs of exactreconstruction in many applications [15]. Assuming the signalhas been decomposed to M�1Z0atoms, the further anM-atom decomposition in the consecutive steps is performed asfollows [16]:

(1)

Compute 9/RM�1,gS9 for all gAD; (2) Select an atom that best matches the residual RM�1from the

dictionary;

/RM�1,gMS�� ��Zrsup /RM�1,gS

�� ��,gAD

where 0orr1 is some number independent of M.

(3) Compute the new residual as

RMðtÞ ¼ RM�1ðtÞ�/RM�1,gMSgMðtÞ:

Fig. 1. Examples of the atoms in IRC-dictionary.

The signal based on M-atoms after M�1 decomposition inter-actions can be then represented with a finite expansion as

f ðtÞ ¼XMn ¼ 1

/Rn,gnSgnðtÞþRMðtÞ ð4Þ

Matching pursuit can maintain energy conservation duringdecomposition, which guarantees its convergence [14]. For acomplete dictionary, matching pursuit procedure converges to f

f ðtÞ ¼X1n ¼ 1

/Rn,gnSgnðtÞ ð5Þ

3.2. The optimized dictionary based on two interfering reflection

components (IRC-dictionary)

As indicated by Mallet and Zhang [13], MP decompositionprovides extremely flexible signal representation since the choiceof dictionaries is not limited. The time–frequency atoms in adictionary are dilations, translations, and modulation of anelementary function. The convergence :RðtÞ:2

of residual isindependent of the type of elementary function used for matchingpursuit in principle. That is, we could use any function to matchthe given signal so that optimal approximation for a specificapplication could be achieved.

The classic MP dictionary usually uses Gabor functions andconsists of waveforms described by different parameters, forexample, frequency, time span, amplitude, and phase [17,18].Such dictionary works adequately for enhancing the resolution inconventional ultrasonic inspections but is inappropriate in theapplication of characterizing complex defect reflection signals.Our research aim is to establish a new MP dictionary optimizedthrough correlating the underlying physical mechanisms of theconcerned application to incorporate the features of reflectionsignal. As discussed in Section 2, the reflection signal from apipeline defect primarily includes the reflection componentsgenerated at the two edges of defect. The waveform of eachsignal reflected from any edge of the defect can be described as atime-delayed and amplitude-scaled replica of the toneburst signalused in excitation. The excitation signal S(t) used in our researchwas a Hamming windowed toneburst consisting of five cycles, asshown below

SðtÞ ¼ sinð2pf tÞð0:08þ0:46ð1�cosð2pf t=5ÞÞÞ ð6Þ

Considering the interference structure of primary edge reflec-tion components in reflection signal, the dictionary with theatoms representing the two interfering reflection components isdesigned and termed as the IRC-dictionary here. That is, the priorknowledge about the relationship between the two edge reflec-tion components and their respective features is adopted toconstruct the atom of dictionary for MP decomposition procedure.The two edge reflection waveforms appears in the each definedatom g with an interfere structure.

gðtÞ ¼X2

i ¼ 1

sgn Uð ÞAiSi tþyið Þ, :g:2¼

ZgðtÞ�� ��2dt¼ 1, ð7Þ

where A and y are amplitude and phase index respectively. As thecurrent authors indicated in their previous work [9], the firstcomponent that corresponds to front edge reflection always keepsconstant while the second component that corresponds to backedge reflection changes at amplitude and phase with the changeof axial length of defect. Some examples of the atoms in IRC-dictionary are presented in Fig. 1. The atoms in a row illustratethat the time shift between two components embedded in eachatom varies gradually, and the atoms in a column illustrate thevariation at amplitude of the components in atoms.

Such function provides a relationship to correlate the atom toany defect reflection signal, which can also be applied to theresults of signal decomposition procedure for characterizationpurposes. Hence, the matching pursuit decomposition with IRC-dictionary not only provides improved signal-to-noise ratio (SNR),but also localizes and characterizes the two edge reflection

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182174

components directly from the decomposition parameters. Themain question is how to select the dictionary atom with theappropriate parameters (A1, y1, A2, y2) to match the collecteddefect reflection signal.

3.3. IRC-dictionary based MP for defect characterization

In the process of characterizing axial length of pipeline defect, itfirstly constructs defect reflection signal and then determines thecorresponding physical edge reflection components. Since reflec-tions occur at both the front edge and the back edge of the defect,the resultant reflection components embed in the overall defectreflection signal are in pairs. By using the IRC-dictionary to matchthe overall reflection signal, primary edge reflection components canbe efficiently reconstructed, thereby providing a significant advan-tage in increasing signal-to-noise ratio. The reconstructed resultmainly includes the information that can be used for accurate defectcharacterization. Reconstruction procedure of primary reflectioncomponents further enables the determination of parameters ofcomponents involved in reconstruction. Because the use of IRC-dictionary inherently provides the correlation of reconstructedsignal with the physical process of reflections at the two edges ofdefect, the concerned primary reflection components can be finallyidentified through a limited interactive process. The illustration ofproposed method is presented in Fig. 2.

The procedure of evaluating axial length of defect is summar-ized as follows:

Step 1: generate an optimized IRC-dictionary based on priorinformation of the excitation signal, S(t), used in a specificinspection;Step 2: carry out matching pursuit (MP) algorithm by using theIRC-dictionary on the collected defect reflection signal, y(t),until defined stopping criterion has been met;Step 3: reconstruct the defect reflection signal, f(t), using thedecomposed atoms obtained in Step 2;Step 4: enable the determination of the parameter features(time shift, amplitude) of the embedded components in theconstructed defect reflection signal, that correspond to thefront-edge reflection signal S1(t)and the back-edge reflection

Collected defect reflection signal

MPIRC dictionary

Recon struction of defectreflection signal

Enable

Decomposed atoms Determination of edgereflection component features

Identification of two primaryedge reflection components

Fig. 2. The schematic diagram of interference matching pursuit for decomposition

of edge reflections.

signal S2(t), with the information of atoms in the IRC-dictionary;Step 5: obtain the front-edge and back-edge reflection signalsaccordingly; andStep 6: evaluate the axial length of defect by using the knowl-edge of the obtained edge reflection signals.

4. Numerical investigation

In this section, the performance of the proposed MP basedmethod is investigated through applying it to a simulated reflec-tion data. As mentioned in previous sections, environmental noiseand coherent noise must be considered for accurate defectcharacterization in practical cases. To examine the tolerance ofthe proposed method in adverse environment, artificial noiseswere added into the simulated reflection signals. In the first twocases, a simulated reflection signal f(t), which has comprised thetwo time-shifted signal components assumed to have originatedfrom two edges of the pipe defect, is used and defined as in thefollowing equation:

f ðtÞ ¼ S1 t; a¼ 1,y¼ 5:07E�4ð ÞþS2 t; a¼ 0:8,y¼ 5:148E�4ð Þ ð8Þ

where S1 and S2 refer to the simulated front-edge reflection signaland back-edge reflection signal, respectively. a is the amplitude(volt) and y is the phase (second) of the reflection component. Theresulting time shift of two components is thus 7.8E-6s, whichensures that their temporal waveforms are overlapped formethod validation. Accurate determination of this parametercan lead to an efficient evaluation of the distance between thepositions where simulated reflections happen, as indicated inSection 3. Assuming f(t) has been corrupted by a random whitenoise e(t), the noisy signal f̂ ðtÞ can be written as

f̂ ðtÞ ¼ f ðtÞþeðtÞ ð9Þ

where the signal-to-noise ratio (SNR) is defined as

SNR¼ 10 log10

Pi f tið Þ�� ��2

Pi e tið Þ�� ��2 dBð Þ ð10Þ

Relevant parameters of the signal under analysis in cases 1 and2 are tabulated in Table 1.

The temporal signals of the first and second reflection compo-nents generated by the front edge and back edge respectively areshown in Fig. 3(a). The overlapped waveform after the aggrega-tion of the two reflection components is shown in Fig. 3(b). Fig. 4presents the noisy signals under various SNRs: 15 dB for case 1 inFig. 4(a) and 5 dB for case 2 in Fig. 4(b). The results of reconstruc-tion using MP equipped with IRC-dictionary for the two cases areexhibited in Fig. 5(a) and (b). The two estimated reflectioncomponents of the front and back edges after the decomposedprocess for cases 1 and 2 are shown in Fig. 6(a) and (b),respectively. Fig. 7(a) and (b) presents the reconstructed defectreflection signals as well as the residual signals from the givensignals as shown in Fig. 4 for case 1 with the SNR at 15 dB andcase 2 with the SNR at 5 dB, respectively. The residual signal canhelp to understand the noise level and the presence of other

Table 1Parameters of simulated signals in case 1 and case 2.

Pulse number Amplitudes

of pulses (v)

Time shift

of components (s)

SNR (dB)

Case 1 2 1, 0.8 7.8E-6 15

Case 2 2 1, 0.8 7.8E-6 5

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0 first component

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0

Time (s) Time (s)

Am

plitu

de (v

)

Am

plitu

de (v

)second component

Fig. 3. (a) Two individual components of the simulated signal; and (b) the overlapped signal after the aggregation of the two components.

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

Time (s)

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

Time (s)

Am

plitu

de (v

)

Am

plitu

de (v

)

Fig. 4. The simulated signals with the SNRs of (a) 15 dB; and (b) 5 dB.

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0reconstructed reflection

simulated signal

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0 reconstructed reflection

simulated signal

Am

plitu

de (v

)

Am

plitu

de (v

)

Time (s) Time (s)

Fig. 5. The reconstruction of reflection signals from given signals with the SNRs of (a) 15 dB; and (b) 5 dB.

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182 175

possible modes. The prescribed time shift between two compo-nents and the estimation counterpart are identified and tabulatedin Table 2. The relative errors indicate that the proposed methodcan provide excellent estimations of the two reflection componentstogether with their time shifts, even under small SNR. The resultsalso exhibit that the proposed method can provide good immunityto noise embedded in the reflected guided wave signals.

Another three cases were simulated to examine the perfor-mance of the proposed method when reverberation effect wasconsidered. Different situations that may occur in pipelineinspection practice were considered in these three cases, whichinvolved the normal reverberation, the reverberation withsmall time-shift and the reverberation with small reflectionamplitude. Two additional components (S3, S4) were added into

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0 decomposed front-edge reflection

decomposed back-edge reflection -1.0

-0.5

0.0

0.5

1.0 decomposed front-edge reflection

decomposed back-edge reflection

Time (s)

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

Time (s)

Am

plitu

de (v

)

Am

plitu

de (v

)

Fig. 6. The decomposed edge reflection signals under the SNRs of (a) 15 dB; and (b) 5 dB.

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0 decomposed reflection signal decomposed reflection signal

residual signalresidual signal

-1.0

-0.5

0.0

0.5

1.0

Time (s)

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

Time (s)

Am

plitu

de (v

)

Am

plitu

de (v

)

Fig. 7. The reconstructed defect reflection signals and residual signals under the SNRs of (a) 15 dB; and (b) 5 dB.

Table 2Evaluation results of time shift in case 1 and case 2.

Prescribed

time shift (s)

Evaluated

time shift (s)

Relative

error (%)

Case 1 7.8E-6 7.8E-6 0

Case 2 7.8E-6 7.8E-6 0

Table 3Parameters of simulated signals in case 3, case 4 and case 5.

Pulse

number

Start of

1st pulse (s)

Amplitudes

of pulses (v)

Time shift

of pulses (s)

SNR

(dB)

Case 3 4 5.07E-4 1, 0.6, 0.2, 0.05 6.4E-6 5

Case 4 4 5.07E-4 1, 0.6, 0.2, 0.05 2.3E-6 5

Case 5 4 5.07E-4 1, 0.3, 0.1, 0.01 1.0E-5 5

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182176

the simulated reflection signal consisting of two edge reflectioncomponents (S1, S2) as the reverberation signal, which had loweramplitudes than the simulated main reflection components. Onlythe first two primary components were to be reconstructed as thesimulated reflection signal for the purpose of axial characteriza-tion. Actually, in practice, the small rear reflection components inreverberation are prone to attenuation during propagation, thusbeing neglected in the collected data. Reflection signals in the fourcases are expressed as below and the relevant parameters aretabulated in Table 3.

f ðtÞ ¼ S1 t; a¼ 1,y¼ 5:07E�4ð ÞþS2 t; a¼ 0:6,y¼ 5:134E�4ð Þ

þS3 t; a¼ 0:2,y¼ 5:198E�4ð ÞþS4 t; a¼ 0:05,y¼ 5:262E�4ð Þ

ð11Þ

f ðtÞ ¼ S1 t; a¼ 1,y¼ 5:07E�4ð ÞþS2 t; a¼ 0:6,y¼ 5:093E�4ð Þ

þS3 t; a¼ 0:2,y¼ 5:116E�4ð ÞþS4 t; a¼ 0:05,y¼ 5:139E�4ð Þ

ð12Þ

f ðtÞ ¼ S1 t; a¼ 1,y¼ 5:07E�4ð ÞþS2 t; a¼ 0:3,y¼ 5:17E�4ð Þ

þS3 t; a¼ 0:1,y¼ 5:27E�4ð ÞþS4 t; a¼ 0:01,y¼ 5:37E�4ð Þ

ð13Þ

The temporal signals of four simulated components, whichinclude the reflection signals from the front edge (the firstcomponent), the back edge (the second component) and thetwo signals from the reverberation (the third and fourth compo-nents) are shown in Fig. 8(a), (b), (c) for cases 3, 4 and 5 respec-tively. Correspondingly, the finally overlapped waveforms in theabove three cases are presented in Fig. 9(a)–(c). The noise of 5 dBwas introduced into the signals, as shown in Fig. 10(a)–(c) for thethree cases. By using the proposed methods, signal componentsthat correspond to simulated front-edge and back-edge reflectionsignals were obtained, which are presented in Fig. 11(a)–(c).Fig. 12(a)–(c) presents the reconstructed defect reflection signalsas well as the residual signals from the given signals in Fig. 10 inthree cases. The results are summarized in Table 4. The relative

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0

third component

fouth component

second component

first component

-1.0

-0.5

0.0

0.5

1.0

third componentfouth component

second componentfirst component

-1.0

-0.5

0.0

0.5

1.0 first component

second componentthird component

fourth component

Time (s)

0.00

048

0.00

050

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052

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054

0.00

056

0.00

058

0.00

060

Time (s)

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

Time (s)

Am

plitu

de (v

)

Fig. 8. The four components of simulated signals with different amplitudes and time shifts in (a) case 3; (b) case 4; and (c) case 5.

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

0.00

058

0.00

060

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

Time (s)

0.00

048

0.00

050

0.00

052

0.00

054

0.00

056

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058

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060

Time (s)

0.00

048

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050

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052

0.00

054

0.00

056

0.00

058

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060

Time (s)

Am

plitu

de (v

)

Fig. 9. The overlapped signals after the aggregation of the four components in (a) case 3; (b) case 4; and (c) case 5.

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052

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056

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058

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060

Time (s)

Am

plitu

de (v

)

Fig. 10. The simulated signals with 5 dB-SNR noise introduced in (a) case 3; (b) case 4; and (c) case 5.

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182 177

0.00

048

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050

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-1.0

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decomposed -1.0

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decomposed -1.0

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decomposed

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052

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058

0.00

060

Time (s)

Am

plitu

de (v

) front-edge reflection

back-edge reflection

front-edge reflection

back-edge reflection

front-edge reflection

back-edge reflection

Fig. 11. The decomposed edge reflection signals in (a) case 3; (b) case 4; and (c) case 5.

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-0.5

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1.0decomposed reflection signal

residual signal

Time (s) Time (s)

Am

plitu

de (v

)

Time (s)

Fig. 12. The reconstructed defect reflection signals and the residual signals in (a) case 3; (b) case 4; and (c) case 5.

Table 4The evaluation results of time shift in case 3, case 4 and case 5.

Prescribed time shift (s) Evaluated time shift (s) Relative error (%)

Case 3 6.4E-6 6.45E-6 0.78

Case 4 2.3E-6 2.50E-6 8.69

Case 5 1.0E-5 9.82E-6 �1.80

Signal Generator

Pulser/Receiver

PC

Transducers defect

pipe

PC-based DAQ

Fig. 13. The schematic representation of experimental setup for pipeline

inspection.

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182178

errors are arranged from 0.78% to 8.69%, which indicate that goodestimations of time shift between two components have beenachieved.

5. Experimental results

In order to validate the performance of proposed methodin evaluating the axial length of practical defect, experimentswere conducted on a number of pipe samples with artificiallyintroduced notches. To simplify the mechanical processing ofdefects and clarify the principle of proposed method, onlycircumferential pipe defects were considered herein. The experi-mental setup and instruments used are depicted schematicallyin Fig. 13. All of the examined steel pipe samples have anexternal diameter of 34 mm, a wall thickness of 4 mm and alength of 2030 mm. The artificial notches, which were simulatedas defects, have radial depths that keep constant at 21.25%of the pipe wall thickness and the circumferential extents

covering 100% (3601) of the pipe circumference. Over the courseof experiments, the values of axial length were graduallyincreased using a milling machine to manufacture the notchesat varying axial lengths. The transduction system of experimentswas properly designed and the mode of excitation signal wasoptimally selected so that only the expected non-dispersivelongitudinal mode L(0,2) was excited whilst the undesired flex-ural modes were suppressed.

The reflection signals from defects with axial length of 6 mmand 16 mm are used in the following discussion to illustrate theperformance of proposed method. These two reflection signalsare shown in Fig. 14(a) and (b). Clearly, by observing the over-lapped reflection signals in Fig. 14, the reflection signal generatedby the 6 mm-length defect represents the superposition effect in

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Am

plitu

de (v

)

Fig. 14. The temporal waveform of the reflection signals generated by defects with axial lengths of (a) 6 mm and (b) 16 mm.

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Am

plitu

de (v

)

Am

plitu

de (v

)front-edge reflection

decomposed front-edge reflection

back-edge reflectiondecomposed

back-edge reflection

Fig. 15. The decomposed edge reflection signals of defects with axial lengths of (a) 6 mm and (b) 16 mm.

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decomposed reflection signal

residual signalAm

plitu

de (v

)

Am

plitu

de (v

)

Fig. 16. The reconstructed reflection signals and the residual signals of defects with axial lengths of (a) 6 mm and (b) 16 mm.

Table 5Evaluation results of defect sizes in cases of 6 mm- and 16 mm-defect.

Actual defect

size (mm)

Evaluated

defect size (mm)

Relative

error (%)

Case 6 6 5.89 �1.83

Case 7 16 16.43 2.69

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182 179

amplitude whereas the other reflection signal from the larger16 mm-length defect represents the cancellation effect.

Results of the analysis conducted by using the proposedmethod are presented in Fig. 15(a) and (b) for the defects withaxial lengths of 6 mm and 16 mm, respectively. They show thetwo identified front-edge and back-edge reflection componentsdecomposed from the original reflection for two defect cases.

Corrosion59 ± 5mm

Fig. 17. The real gas pipe with a naturally developed corrosion.

Table 6The description of the real corrosion tested in the case study.

Defect type Circumferential

length (1)

Radial depth

(mm)

Axial length

(mm)

Real corrosion 360 Nonuniform

(0.01–1.3)

Nonuniform

(5975)

0 50 100 150 200 250 300 3500

10

20

30

40

50

60

circumferential position (°)

°

axia

l len

gth

of th

e te

sted

cor

rosi

on (m

m)

Fig. 18. The profile of axial length of corrosion along the circumference.

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182180

Fig. 16(a) and (b) shows the reconstructed signals and theresidual components after decomposing the original reflectionsignals for two defect cases respectively. It can be seen fromFig. 15 that the first reflection components (the decomposedfront-edge reflections) are almost the same since these compo-nents primarily depends on the geometric profile of the start ofthe defect, including its depth and circumference which are thesame for both defect cases. The amplitude of second reflectioncomponent (the decomposed back-edge reflection) generated bythe 6 mm-defect is smaller than that of the back-edge signalgenerated by the 16 mm-defect. Hence, the real amplitude infor-mation related with the axial length of defects can be clearlypresented from the decomposed back-edge reflection signals afterthe success of the decomposition process.

Because the waveforms of the front- and back-edge reflectionsignals present similar patterns in time domain, the time shift Ts

between these two determined edge signals can be computed byusing the cross-correlation function as defined in the followingequation:

Ts ¼max1

T

Z T

0S1ðtÞS2 tþtð Þdt

� �ð14Þ

where T is the observation time, and S1 and S2 are the front- andback-edge signals, respectively. Table 5 shows the results oftesting of two defects with different axial lengths. The relative

errors are ranged from 1.83% to 2.69%. It has proven that theproposed method can provide good evaluation performance evenwhen the axial length of the defect is very small.

Since the proposed method has performed well in de-noising,it can be applied in a very noisy environment. In order to furtherverify the effectiveness of the proposed method, particularlywhen complex pipeline corrosion exists, a test was continuedby using the same transduction system as shown in Fig. 13. Thistest was conducted on a real corroded gas pipe. The pipe wasprovided by a natural gas supplier in Hong Kong. It has a naturallydeveloped corrosion, which is a commonly occurring defect inHong Kong due to its humid and saline environment. The picturesof the tested pipe and its corrosion are shown in Fig. 17. Thetested gas pipe has an external diameter of 88.6 mm and a wallthickness of 5 mm. The corrosion is distributed along the entirecircumference of the pipe and has a non-uniform axial length of5975 mm. Detailed information of this corrosion is given inTable 6 and the profile of axial length of the corrosion along thecircumference is also plotted in Fig. 18. Two cases with theircentral frequencies of excitation set at 160 kHz and 110 kHz wereconsidered. The edge reflection components in the 110 kHz casewere more overlapped than that in the 160 kHz case. The originalwaveforms of the reflection signals generated from the realcorrosion with excitation signal set at 160 kHz and 110 kHz areshown in Fig. 19(a) and (b) respectively. The decomposed front-and back-edge signals are shown in Fig. 20(a) and (b) for thecentral frequencies of excitation set at 160 kHz and 110 kHzrespectively. The reconstructed reflection signals and the residualsignals decomposed from the original signals are presented inFig. 21(a) and (b) respectively. The results are summarized inTable 7. They indicate that good evaluation of the axial length ofthe corrosion has been achieved with the maximum relative errorof 6.34%.

6. Conclusions

This paper reports a method in the frame of matching pursuitdecomposition with the optimized IRC-dictionary to evaluate theaxial length of pipeline defect. The proposed method is based onthe fact that the overall reflection signal generated at a pipelinedefect is the interference between two edge-related reflectioncomponents in a complicated manner. The method allows for notonly an efficient reconstruction of defect reflection signal but alsoan accurate identification of the defect axial length through theclear identification of the primary front-edge reflection signal andthe back-edge reflection signal. That is, the method can effectivelyresolve the closely spaced overlapping and noise-contaminatedreflection components. Such task is difficult to achieve by usingother conventional algorithms. Simulation tests and real experi-ments were used to verify the effectiveness of the method. Thereal experiments involve the use of in-servicing pipes that haveartificial defects with different axial lengths as well as a corrodedgas pipeline. The results show that the maximum errors inevaluating the axial extent are 2.69% and 6.34% for the in-servicing pipes and corroded gas pipeline respectively. Although

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Time (s) Time (s)

Am

plitu

de (v

)

Am

plitu

de (v

)

Fig. 19. The reflection signals from real corrosion with excitation signal of (a) 160 kHz and (b) 110 kHz.

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front-edgereflection

Time (s) Time (s)

Am

plitu

de (v

)

Am

plitu

de (v

)front-edge reflection

decomposedback-edgereflection

Fig. 20. The decomposed edge signals under excitation with different central frequencies of (a) 160 kHz and (b) 110 kHz.

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signal

residualsignal

Am

plitu

de (v

)

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plitu

de (v

)

Time (s) Time (s)

Fig. 21. The reconstructed defect signals and the residual signals under excitation with different central frequencies at (a) 160 kHz and (b) 110 kHz.

Table 7The evaluation results of corrosion sizes when excitation with different frequen-

cies was used.

Actual

size (mm)

Excitation

frequency

(kHz)

Evaluated

size (mm)

Relative

error (%)

Case 8 5975 160 60.17 1.98

Case 9 5975 110 55.26 6.34

P.W. Tse, X. Wang / NDT&E International 54 (2013) 171–182 181

this paper focuses on the discussion on axisymmetric defect, forfurther research, we will focus on testing the method on morereal pipelines that have complex defects.

Acknowledgments

The work described in this paper was fully supportedby a grant from the Research Grants Council of the Hong KongSpecial Administrative Region, China (Project no. CityU 122011)and a grant from City University of Hong Kong (Projectno. 7008187).

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