Evaluation of pipeline defect's characteristic axial length via model-based parameter

estimation in ultrasonic guided wave-based inspection

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Meas. Sci. Technol. 22 (2011) 025701 (13pp) doi:10.1088/0957-0233/22/2/025701

Evaluation of pipeline defect’scharacteristic axial length viamodel-based parameter estimation inultrasonic guided wave-based inspectionXiaojuan Wang, Peter W Tse and Alexandar Dordjevich

Department of Manufacturing Engineering & Engineering Management, Smart Engineering AssetManagement Laboratory (SEAM), City University of Hong Kong, Hong Kong,People’s Republic of China

E-mail: mepwtse@cityu.edu.hk

Received 10 August 2010, in final form 14 October 2010Published 23 December 2010Online at stacks.iop.org/MST/22/025701

AbstractThe reflection signal from a defect in the process of guided wave-based pipeline inspectionusually includes sufficient information to detect and define the defect. In previous research, ithas been found that the reflection of guided waves from even a complex defect primarilyresults from the interference between reflection components generated at the front and theback edges of the defect. The respective contribution of different parameters of a defect to theoverall reflection can be affected by the features of the two primary reflection components.The identification of these components embedded in the reflection signal is therefore useful incharacterizing the concerned defect. In this research, we propose a method of model-basedparameter estimation with the aid of the Hilbert–Huang transform technique for the purpose ofdecomposition of a reflection signal to enable characterization of the pipeline defect. Oncetwo primary edge reflection components are decomposed and identified, the distance betweenthe reflection positions, which closely relates to the axial length of the defect, could be easilyand accurately determined. Considering the irregular profiles of complex pipeline defects attheir two edges, which is often the case in real situations, the average of varied axial lengths ofsuch a defect along the circumference of the pipeline is used in this paper as the characteristicvalue of actual axial length for comparison purpose. The experimental results of artificialdefects and real corrosion in sample pipes were considered in this paper to demonstrate theeffectiveness of the proposed method.

Keywords: pipeline inspection, guided waves, defect characterization, parameter estimation,Hilbert–Huang transform

(Some figures in this article are in colour only in the electronic version)

1. Introduction

The use of ultrasonic guided waves [1] is a new and advancedtechnique in the nondestructive testing (NDT) field. Thanks toits continuous development in both theory and applications, theguided wave technique has become increasingly attractive forinspection of defects in pipelines. For example, even defects(gouge, dent and material loss) that exist in underground

pipelines can be successfully detected by the guided wavetechnique as reported by Ahmad et al in their experimentalwork [2]. The location of a pipeline defect can be determinedby the arrival time of the reflection signal that results fromthe interaction of propagating guided waves with a defect.However, after a defect has been found, evaluation of itsdimension or size is always a challenging task in NDT [3].That is, although the reflection signal in principle includes

0957-0233/11/025701+13$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA

Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

substantial defect information related to size and other featuresof the defect, it is usually rather difficult to interpret this signalfor defect characterization or sizing because of complexitiesof the interaction process. The utility of guided waves is thuslimited by the lack of detailed information on the detecteddefect. For further assessment of the defect’s features, forexample its severity, additional testing with the help of othermethods or direct measurement is then required. To accuratelyand efficiently carry out planned maintenance operation andreplacement of defective pipelines, the ability of defectcharacterization during pipeline inspection is very important inpractical application of the guided wave technique, particularlyfor defects that exist in parts of a pipeline that are difficult toaccess.

Most of the methods currently available for inspectionof pipelines are only capable of providing a qualitativeassessment of defects. Few research works have beenconducted on the possibility of using guided waves forevaluating the size of pipeline defects. Reported methodsfor this problem can loosely be classified into two groups: oneis to optimize the specific parameters of excited guided wavesor construct a sophisticated configuration of the transductionsystem so as to achieve well-defined or -controlled waveformof reflection. The methods in this group can maximizethe energy of the concerned wave signals and at the sametime simplify them for facilitating possible sizing of thedefect. Mu et al [4] determined the circumferential lengthof a pipeline defect by comparing theoretical reflectionprofiles with experimental ones obtained through performinga circumferential focusing scan at the known defect location.Li [5] developed an algorithm based on two-dimensionalblind deconvolution to estimate circumferential sizes ofdefects using the multiple reflection waveforms acquiredby a multiplexed circumferential transducer array. Thesemethods require a great deal of care in transduction;considerable time may have to be spent increasing precisionand reliability of instrumentation and checking repeatabilityof measurements. Methods in the other group make useof generally simpler and less specific instrumentation butneed greater analysis of the obtained reflection wave signalfor defect characterization. Such methods can decreasethe complexity of required instrumentation so that practicalapplications become convenient. However, the processing ofwaves implies more difficulties due to the more complicatedprocess of interaction of guided waves with different types ofdefects. Advanced signal processing techniques are needed toincrease the probability of success in defect characterizationand to ensure ease of practical application. For this motivation,Demma [6] investigated the effect of defect parameters onthe reflection so as to enable a more precise interpretationof a reflection signal for evaluating the defect size. Recentadvances include utilization of imaging and tomographytechniques for defect characterization. For example, Hayashi[7] developed a defect image technique by reconstructingspatial waveforms that have been separated into several single-mode signals. A review of available methods for defect sizingor characterization can be found in [3] as well. Although thesetechniques have proved to be successful in various degrees,

they are generally time/cost consuming and the results maybe insufficiently accurate. Moreover, they still have not solvedthe problem of directly evaluating the axial length of pipelinedefects.

2. The interference phenomenon of two reflectioncomponents

It has been found by some researchers that reflection of guidedwaves from a defect primarily results from the interferencebetween the two reflection components generated at the frontedge and the back edge of the defect [6, 8, 9]. Further wehave reported in our earlier research [10] that the complexityof the reflection signal is essentially a result of differentfeatures represented by front-edge and back-edge reflectioncomponents. In previous studies, researchers mainly usedsimplified models, such as a notch or a circular hole, toapproximate a pipeline defect. Realistic defects like corrosionare far more complex and irregular in three-dimensionalprofiles. Demma indicated in [11] that maxima and minimaof reflectivity resulting from the interference of two reflectioncomponents could occur on real defects without a sharp andrectangular profile in practical inspection. Ma and Cawleyfurther employed a part-thickness taper elliptical defect modelto represent a closer match to real corrosion shapes in theirlatest research [12] for investigating the effect of differentdefect parameters on reflection. Their research showed that thereflection ratio spectrum from a complex defect still exhibitedperiodic patterns due to interference between reflections fromthe two edges of the defect. Thus, all of these findings suggestthat the reflection signal from even a complex defect mainlyconsists of reflection components from the two edges of thedefect, and the respective contributions of different parametersof the defect to the overall reflection can be represented by thefeatures of these two reflection components. Identificationof these components embedded in the reflection signal istherefore useful in characterizing the concerned defect.

The concept of applying the two primary edge reflectionsignals for defect characterization can be further explainedas follows. The occurrence of reflection is due to thechange of acoustic impedance in the structure. When theexcited guided waves propagate to the locations of eitherthe front edge or the back edge of defect, the acousticimpedance undergoes a fundamental change, which resultsin the occurrence of two strong reflection components. Thedefect area inside two edges can also generate reflectionsin the axial direction, but those reflections are generallynegligible due to the small change of impedance within thedefective area. Further, the small reflection is not observablebecause of energy attenuation after the waves propagate backto the transducer position. Irregularity of a defect in thecircumferential direction inevitably makes the reflection signalat each edge of the defect complex. This complexity ofthe signal can be reduced by use of specific transduction.For example, in our experiments, the length-expander typeof transducers were axially symmetrically distributed aroundthe circumference of the pipe being tested and the signalsreceived at all transducers were summed up, which can ensure

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the maximal receipt of energy of waves propagating in theaxial direction while other waves are ignored. When wavespropagating to the defect can form a normal incidence at someregion of the defect edge, especially a region with a large radialdepth, the strong energy of reflected waves will be primarilyconcentrated in the axial direction and maximally collectedby the length-expander transducers in axially symmetricdistribution. Comparatively, other reflection processes aresubject to attenuation of propagation or ignorance of atransducer, so the effects of these reflection components onthe overall reflection signal are not significant. Moreover,each collected edge reflection signal is the result of reflectionscaused at all points of the defect edge. The profile of a practicaldefect in three-dimensional directions is gradually developedinstead of a profile showing sharp or sudden variances, whichimplies high probability of two primary reflection componentsbeing generated in the process of interaction of guided waveswith the defect.

Because of the presence of the interference phenomenoncaused by two reflection components, the resulting reflectionsignal is seriously affected by the axial length of thedefect. Therefore, identification of edge reflection componentsembedded in the overall reflection signal is useful forsimplifying analysis of the interaction process and enablingdefect characterization. Considering that the distance betweentwo reflection positions at the defect edges closely relates to theaxial length of the defect, the identified reflection componentscan help determine the axial length. Therefore, in this paper,we propose a method based on parameter estimation with theaid of an advanced signal analysis technique as a preprocessorfor the purpose of reflection decomposition to enable defectcharacterization. This could efficiently decompose a noise-contaminated reflection signal into its primary componentsthat correspond to the two edge reflections in guided waves-based measurement. The identified edge reflection signals canthen be used for evaluating the axial length of the pipelinedefect. In practice, for an irregular defect, ‘front edge’ and‘back edge’ refer to the two boundaries between the defectiveand the non-defective areas of the pipeline body. Consideringthe irregular profiles of complex pipeline defects like corrosionat two edges, the average of varied axial lengths of suchdefects along the circumference of the pipeline is used as acharacteristic value for representing the actual axial length.It can to a certain degree reflect all factors that have effectson the edges and the corresponding axial lengths of defects.A comparison of results from the proposed method and theactual experimental measurement is presented to verify theeffectiveness of the findings of this work.

The rest of this paper is structured as follows. Insection 2, the experimental setup and data collection aredescribed. Section 3 presents formulation of the concernedproblem and describes the proposed method in detail. Insection 4, the proposed method is applied to the experimentaldata and the results are discussed. A conclusion is given at theend.

varying axial length

Figure 1. Illustration of varying axial lengths of the pipe defectunder examination.

3. Acquisition of guided wave reflection signals

As aforementioned, the axial length of a defect is a criticalfactor that causes the complexity of the reflection. In order toinvestigate and establish the relationship between the edgereflections and axial length of a pipeline defect, and tofurther validate the method proposed in this work, a seriesof experiments were performed to collect reflections of guidedwaves created by artificial defects with varying axial lengthsin pipeline samples. The focus of this paper is to present themethod of evaluating defect length through considering edgereflection components. Therefore, although the motivationof the paper was related to industrial inspection tasks, tosimplify mechanical processing of defects and clearly clarifythe principle of the proposed method, only circumferentialdefects are discussed in this paper.

The first group of experiments was conducted on a steelpipe that had an external diameter of 34 mm, a wall thicknessof 4 mm and a length of 2030 mm. We introduced artificialnotches in the sample to simulate defects, radial depth andcircumference of which were kept constant at 21.25% of thepipe’s wall thickness and 100% of circumference, respectively.Over the course of the experiments, the values of axial lengthwere gradually increased from 6 to 170 mm using a millingmachine to simulate defects of varying axial lengths, which isillustrated in figure 1.

We adopted the longitudinal L(0, 2) mode for excitedwaves as it is easy to excite and has a relatively simpleacoustic field [13]. The L(0, 2) mode has roughly uniformstress distribution over the cross-section of the pipe, whichmakes it sensitive to changes in the cross-section of the pipe.Therefore, it is favored for detecting circumferentially aligneddefects in hollow pipelines discussed in this paper. It is notedthat for defect characterization in real operating environmentswhere the pipeline may be covered by soil and filled withfluid, the wave mode needs to be carefully selected such thatstrong reflections are generated to maximize the effectivenessof post-processing for characterizing the defect. Frequenciesranging from 0.1 to 0.24 MHz were chosen in this paperfor the pipe under examination because the L(0, 2) modeexcited accordingly is non-dispersive in this frequency range.Figures 2(a) and (b) display phase and group velocitydispersion curves, respectively. Within the above-selectedfrequency range shown in figure 2, velocity values remainalmost constant with only small variations. These curveswere calculated using the DISPERSE program [14]. The useof the single L(0, 2) mode and the non-dispersive operatingfrequency range makes the reflection signals as simple aspossible, relieving the burden of subsequent analysis.

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0

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F(1,1)

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h (

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s)

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F(1,3)

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F(1,1)

group velocity dispersion curve phase velocity dispersion curve (a) (b)

(100k~200k)

(0.1M~0.24M)

(0.1M~0.24M)

Figure 2. (a) Phase velocity dispersion curves; and (b) group velocity dispersion curves derived based on the properties of the examinedpipe.

Signal Generator

Pulser/Receiver

PC

Transducersdefect

pipe

PC-based DAQ

0.0040.0030.0020.0010.0000.00

0.02

0.04

0.06

frequency(MHz) (b)(a)

Figure 3. (a) Schematic representation of the experimental setup; and (b) the excited tone burst signal and its FFT spectrum.

The experimental setup and instruments used are depictedschematically in figure 3(a). A Hamming windowed toneburstconsisting of five cycles at the chosen frequency was deliveredthrough an arbitrary signal generator. It is formulated asfollows:

s(t)excitation = sin(2πf t)(0.08 + 0.46(1 − cos(2πf t/5))).

(1)

The temporal waveform of such an excitation and its FFTspectrum are shown in figure 3(b). The measurement systemwas carefully designed to excite a single L(0, 2) mode intothe pipe under examination. A ring consisting of a certainnumber of piezoelectric transducers (PZTs) was bonded toone end of the pipe to generate and receive guided waves.The PZTs were made of length expander-type piezoelectricmaterial and distributed axisymmetrically, thus ensuring thatonly the longitudinal modes were excited while the undesiredflexural modes were suppressed.

Figure 4 shows the collection of signals reflected fromsome defects with varying axial lengths under excitation atcenter frequencies of 175 kHz. It is clearly observed thatwhen the axial length of each reflection signal is changed,its waveform is extended in time with an increased number ofwave cycles and distorted amplitude under irregular variations.

For example, some of the signals in this figure exhibit thesuperposition effect, whereas others represent the cancellationeffect. As indicated before, the complexity of these signalsis the result of the interference caused by reflections atdifferent edges of the defect. A certain amount of noisethat follows the main signal sequence in figure 4 is due tomultiple reverberations of reflections between two edges ofthe defect.

In order to further verify the effectiveness of the proposedmethod on complex pipeline defects, the test using the sametransduction set-up as shown in figure 3 was conducted on areal gas pipe. The pipe was provided by a natural gas supplierin Hong Kong and it had a naturally developed corrosion, acommonly occurring defect type in the field. The picturesof pipe and corrosion are shown in figure 5. The pipe wasoriginally located underground in operation and was coveredcompletely by soil. Appropriate stresses exerted on pipes dueto the result of soil movement, thermal contraction or thirdparty interference can cause circumferential damage to coatingor pipe body [15], especially in small diameter pipes. Due toadverse soil environment of high humidity and salinity in HongKong, pipes suffer further surface corrosion after the protectivecoating is damaged. Corrosion starts at the outmost surface

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

Figure 4. Examples of reflection signals from defects with different axial lengths.

Corrosion

Figure 5. The real gas pipe with natually developed corrosion.

of the pipe and gradually extends to other parts. The largestcorroded area is thus at the outer surface of the pipe.

The tested gas pipe had an external diameter of 88.6 mmand a wall thickness of 5 mm. The corrosion distributed alongthe circumference of the pipe had a nonuniform axial length of59 ± 5 mm. Detailed information on this corrosion is given intable 1 and the profile of the axial length of the corrosion alongthe circumference is also plotted in figure 6. Figure 7 showsthe raw reflection signals collected from the tested pipe. Thetoneburst signal at center frequencies of 110 kHz was chosenas the excitation for this testing based on the dispersion curvesof the tested pipe. The group velocity of propagating guidedwaves in the pipe was 5.4 m ms−1. It is to be noted here that theuse of higher frequency may reduce or avoid the interference ofreflection components, but the energy of reflection signals willthus be greatly attenuated, resulting in difficulty in accuratedefect characterization.

Table 1. Description of the real corrosion tested in the case study.

Defect Circumferential Radial depth Axial lengthtype length (deg) (mm) (mm)

Real 360 Nonuniform Nonuniformcorrosion (0.01–1.3) (59 ± 5)

4. Proposed method for evaluating the axial lengthof defect

4.1. Problem formulation

As noted earlier, the reflection signal from a defect includestwo primary components, i.e. the ‘front-edge signal’ and the‘back-edge signal’ as illustrated in figure 8(a). Reflectionsfrom front edge and back edge of defect are reflections fromhard boundary and soft boundary, respectively, so the phase

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

0 50 100 150 200 250 300 350

0

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50

60

axia

l le

ng

th o

f th

e te

ste

d c

orr

osio

n (

mm

)

circumferential position ( )°

Figure 6. Profile of the axial length of corrosion along thecircumference.

of the front-edge signal is the reverse of that of the back-edge signal. Both signals exhibit nearly the same patternsin terms of frequency, cycle number and modulation, but aredifferent in phase. If they could be decomposed and correctlyrecovered to their original temporal waveforms, then the axiallength of the defect will be easily evaluated. This is becausethe axial length is related to the distance between reflectionpositions of two edge reflection signals. The axial lengthcan be derived based on wave group velocity and time shiftsof the two reflection signals. Traditional methods like linearfilters are ineffective for such decomposition because the tworeflection signals present the same spectrum in the frequencydomain but their amplitudes and phases are unobservable inthe time domain.

It is apparent in figure 8(b) that there exist two non-overlapping regions and one overlapping region in thesimulated reflection signal. The non-overlapping regions (1)and (2) correspond to partial observation of front-edge andback-edge signals, respectively. Therefore, the basic ideaof signal decomposition proposed in this paper is based onestimation of an edge reflection signal from the data in the non-overlapping region. The front-edge signal is relatively simplerto determine compared to its back-edge counterpart becausethe former depends primarily on the front edge of the defectonly, and it reaches the transducer position the earliest among

back-edge signal front-edge signal un-overlapping region (1)

overlapping region

un-overlapping region (2)

(a) (b)

Figure 8. (a) Simulated front- and back-edge reflection signals; and (b) the resulting signal after the two edge signals are superimposed oneach other.

0.0000 0.0001 0.0002 0.0003

-0.5

0.0

0.5

am

plit

ud

e(v

)

time (ms)

Figure 7. Collected reflection signals from the tested gas pipe withreal corrosion.

all reflection components caused by a defect. In contrast, theback-edge signal is related to a larger number of factors andits rear is subjected to distortion due to reverberations betweenthe two defect edges. Hence, we exploit the partial data ofthe front-edge signal in the maximum likelihood estimation(MLE) framework to resolve two overlapping signals. Inpulse-echo ultrasonic guided wave-based measurement, thesignal reflected from the defect edge can be modeled in theform of excitation integrated with the effect of dispersion andattenuation of involved guided waves. The mode consideredin our study works within its non-dispersion frequency range(0.1–0.24 MHz), which allows the effect of dispersion to beneglected in the proposed reflection model.

4.2. Description of the proposed method

As described above, partial data of the front-edge signal,which corresponds to the non-overlapping region (1) shownin figure 8(b), is used to estimate the front-edge signal.Therefore, the first crucial problem is to determine theoverlapping points of front-edge and back-edge signals sothat the non-overlapping region (1) could be identified. Asmentioned in the previous section, front- and back-edgesignals have a certain phase difference but the same frequencyspectrum. Hence, instantaneous frequency discontinuity will

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

appear at the overlapping points of the two signals. Such adiscontinuity can be indicated by the abrupt change of thefrequency value in the form of a higher order derivative intime–frequency representation of the reflection signal. Theconcerned discontinuity points, i.e. overlapping points ofthe two edge signals, can be accordingly determined. Thecollected reflection signal is inherently susceptible to noisescaused during propagation and interaction of guided wavesin the pipeline. Moreover, traditional signal processingmethods may be inadequate for analysis of complicatednonlinear and non-stationary guided waves. In order to revealhidden reflection signals in the collection and to provide aprecise definition of partial data of a front-edge signal forthe proposed estimation context, the Hilbert–Huang transform(HHT) method is used as a preprocessor to reconstruct therequired data from the collected raw reflection signals.

HHT is an empirically based data-analysis methodproposed by Huang et al [16] to efficiently obtain informationin both time and frequency domains directly from the data.It is adaptive, automatic, efficient and without any priorassumptions. The HHT consists of two parts: empiricalmode decomposition (EMD) and Hilbert spectral analysis(HSA). EMD can be treated as a time–frequency filteringmethod for decomposing the signal into a collection of intrinsicmode function (IMF) components. The detailed theory andprocedures to derive and compute IMFs can be found in[16, 17]. The collected raw reflection signal s(t) is thenexpressed as the sum of IMFs (IMFi) and a residue (rn+1),as defined in the following:

s(t) =n∑

i=1

IMFi + rn+1 (i = 1, . . . , n). (2)

Each IMF is a unique band-limited function and different IMFsexhibit different frequencies at the same time. Some extractedIMFs belong to noise-related components identified with theaid of frequency spectrum analysis and correlation analysisof all IMFs. In our application, proper IMFs constitutingedge reflection signals should contain frequency components(fc) close to the center frequency (175 kHz) of an excitationtoneburst signal. Moreover, the decomposition procedure ofEMD may introduce aliasing in IMFs. Hence, the correlationcoefficient (cc) between the proper IMF and the excitationsignal should have a large value. Based on these two criteria (fcand cc) for evaluating IMFs, proper IMFs can be discriminatedfrom the original data to reconstruct the actual reflection signals′(t) for subsequent analysis:

s ′(t) = IMFa + IMFb + · · · IMFz (a, b . . . z ∈ i). (3)

After obtaining the reconstructed signal, the easiest way tocompute its instantaneous frequency is by performing thecorresponding HSA, through which the relevant complexconjugate u′(t) of any real-valued function s′(t) can bedetermined by

u′(t) = s ′(t) = H(s ′) = 1

π

∫ +

−

s ′(τ )

t − τdτ. (4)

The signal for the concerned time–frequency analysis canthen be constructed from the input signal s′(t) and its Hilbert

transform u′(t) as

A(t) = s ′(t) + iu′(t) = a(t) ejθ(t), and ω = dθ/dt

(5)

where a(t) is the instantaneous amplitude, θ (t) is the phasefunction and ω is the instantaneous frequency. The abruptchange of instantaneous frequency in the form of kneepoints will be displayed clearly in the result of time–frequency analysis of the reflection signal s′(t). That is, thefirst overlapping point of the two edge signals and partialobservation data su1

′(t) in the non-overlapping region (1) canbe efficiently identified.

Resolution of the two edge signals is achieved fromthe model-based parameter estimation perspective. Inexperiments conducted for this research, the signal reflectedfrom an edge of the defect can be described by using aparametric signal model, which is the time-delayed andamplitude-scaled replica of the excitation toneburst signal asgiven by equation (1):

s(p; t) = α1 sin(2πf1t + β1)

×(0.08 + 0.46α2(1 − cos(2πf1t/5 + β2))

p = [α1 f1 β1 α2 β1]. (6)

The parameter vector p of the edge signal includes theamplitude α1, the center frequency f 1, the phase β1, thewindow function amplitude coefficient α2 and the windowfunction phase β2. The vector p is estimated from the identifiedpartial observation data s ′

u1(t) so that the whole front-edgesignal can be determined. This parameter estimation problemis achieved by using the maximum likelihood estimation(MLE), a common statistical method for fitting a statisticalmodel to data, and providing estimation for parameters ofthe model. The MLE for the vector parameter p is definedas the value that maximizes the likelihood function L(p),now a function of components of p for estimation. Thelikelihood function is usually defined as the joint probabilitydensity function (PDF) of the observed data with respect to theparameter vector p, which obeys normal distribution assumingthat the data are independent and identically distributed (iid):

PDF(s(x);p) = 1

2πn/2∣∣∑(p)

∣∣1/2

× exp

{−1

2(x − m(p))T

∑(p)−1(x − m(p))

}(7)

where m(p) is the mean vector, �(p) is the covariance matrixand n is the dimension of the considered signal su1

′(x). For thecase of s ′

u1(x) with constant parameter vector, the problem ofmaximizing the PDF can usually be simplified to minimizingthe least-square function (LSF) defined as

p = arg max(PDF(p)) = minn∑

i=1

(s ′u1(xi;p) − s(p))2

= min∥∥s ′

u1(xi;p) − s(p)∥∥

2 . (8)

The minimum values of the above objective function willprovide the optimal solution for parameters being estimated.That is, the optimal MLE of the parameter vector p can bedetermined by considering only the partial observation data

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

Table 2. Correlation coefficients for all signal components decomposed from the reflection signal.

Signal component IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 RES

Correlation coefficient 0.0223 0.0228 0.0145 0.0103 0.7914 0.3409 0.0559 0.0027 0.0040

s ′u1(x) and the model s(p). Different optimization methods can

be considered to realize minimization of the objective functionin equation (8). We exploited the Levenberg–Marquardtalgorithm (LMA) [18] in this research. The LMA interpolatesbetween the Gauss–Newton algorithm and the method ofgradient descent. It has the advantages of being quick andstable in converging to the optimal solution, especially whena good initial guess is used for p.

The front-edge signal x(t) can be identified by applyingestimation of the parameter vector p to the reflection modeldefined by equation (6). The back-edge signal y(t) embeddedin the collected reflection signal will then be extractedsimply by subtracting the front-edge signal x(t) from thereconstructed overall reflection signal s′(t). Since front- andback-edge signals present similar patterns in the time domain,the time shift D between these two signals can be computed byusing the cross-correlation function (CCF). With this method,the time shift D between the two signals corresponds to themaximum value of their CCF, as shown below:

D = max

(1

T

∫ T

0−x(t)y(t + τ) dt

), (9)

where T is the observation time, x and y are identified front-and back-edge signals. D corresponds to the time the guidedwaves take to propagate between front and back edges of thedefect, namely twice the evaluated axial length of the defect.Therefore, the axial length of the defect can be calculated as

L = (D × vgr)/2, (10)

where L is the evaluated length of the defect in the axialdirection and vgr is the group velocity of the propagatingguided waves.

In summary, the proposed method for evaluation of theaxial length of pipeline defects comprises the following sixsteps.

• S0: use EMD to decompose the collected raw signal s(t)into a collection of IMFs;

• S1: select the proper IMFs to reconstruct the reflectionsignal s′(t) based on two criteria (fc and cc);

• S2: perform HSA to determine the overlapping pointsand the data s ′

u1(t) in the un-overlapping region of thefront-edge signal;

• S3: take s ′u1(t) as observation to estimate the signal

parameters p and then identify the front-edge signal x(t);

• S4: obtain the back-edge signal y(t) by subtracting thefront-edge signal x(t) from the constructed reflectionsignal s′(t), i.e. y(t) = s′(t) − x(t);

• S5: evaluate the axial length L of the defect fromknowledge of the obtained front-edge signal x(t) andback-edge signal y(t).

0.00050 0.00051 0.00052 0.00053 0.00054 0.00055 0.00056

-0.3

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0.0

0.1

0.2

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Am

plit

ud

e

Time

Figure 9. The reflection signal collected from the pipe with18.5 mm axial length defect.

5. Application results and discussion

Firstly, performance of the proposed method is illustrated byevaluating an artificial notch-type defect with the axial lengthof 18.5 mm in guided wave-based inspection. Reflectiondata of this defect were already collected in the first groupof experiments described in section 3. Figure 9 shows theraw reflection signal collected from the pipe with this defect.Compared to the excitation toneburst signal, it exhibits anincreased cycle and distorted amplitude due to the interactionprocess and kinds of noise. This case is used to demonstratethe validity of our method for evaluating the axial length ofthe pipeline defect.

The EMD is first applied to decompose the collectedreflection data into a series of IMFs. The results are shownin the first column of figure 10. The frequency spectrumof each IMF and its correlation coefficient with the originalexcitation signal are presented in the second column offigure 10 and table 2, respectively. The eight IMFs yieldedby the EMD procedure show the variation (from high to low)in their frequencies. It is apparent that only IMF5 and IMF6have frequency components close to the center frequency of175 kHz of the excitation signal. Other IMFs have eitherhigher or lower frequencies. They are assumed to be causedby different sources of noise. Analysis of the correlationcoefficient of each IMF further demonstrates that IMF5 andIMF6 have high cc values (0.7914 and 0.3409) comparedto other IMF components. Therefore, the defect reflectionsignal is reconstructed to be IMF5+IMF6, which is shown infigure 11.

The frequency–time representation of the reconstructedsignal based on the HSA is presented in figure 12. Itshows that two obvious frequency discontinuities exist. One

8

Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

IMF Decomposed component Frequency spectrum

IMF1

0.00050 0.00051 0.00052 0.00053 0.00054 0.00055 0.00056

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-0.004

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0 10000000 20000000 30000000 40000000 50000000

0.00000

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0 10000000 20000000 30000000 40000000 50000000

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0 5000000 10000000 15000000 20000000

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IMF4

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000000510000000100000050

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IMF7

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0 50000 100000 150000 200000 250000 300000 350000 400000

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Frequency (Hz)

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Figure 10. Decomposed components of the raw reflection signal and their FFT spectra after applying EMD to this signal.

9

Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

IMF8

0.00050 0.00051 0.00052 0.00053 0.00054 0.00055 0.00056

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Frequency (Hz)

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Figure 10. (Continued.)

5.1 5.15 5.2 5.25 5.3 5.35 5.4 5.45 5.5 5.55 5.6

x 10-4

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Figure 11. Reflection signal reconstructed with EMD.

5.1 5.15 5.2 5.25 5.3 5.35 5.4 5.45 5.5 5.55 5.6

x 10-4

1.2

1.4

1.6

1.8

2

2.2

x 105

Time

Fre

quency

(0.0005185, ya)

(0.0005478, yb)

Figure 12. HSA representation of the reconstructed signal with twoknee points identified.

is at (0.000 5185, ya) and the other at (0.000 5478, yb).They correspond to the overlapping points of front-edgesignals and back-edge signals. From figure 11, the starttime for the reconstructed signal is directly known to be0.000 5085. Hence, the non-overlapping region of thefront-edge signal can be easily determined as [0.000 5085,0.000 5185]. Reconstruction of the reflection signal anddetermination of valid observation data through HHT aregreatly helpful in accurately estimating the concerned signalparameters for defect characterization.

The signal segment in the range of [0.000 5085,0.000 5185] is then extracted from the reconstructed reflection

5.08 5.1 5.12 5.14 5.16 5.18

x 10-4

-0.06

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Time

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[0.0005085, 0.0005185]

Figure 13. The signal segment extracted from the reconstructedreflection signal.

signal to form the partial observation vector of the front-edge signal for estimation of its parameters, shown infigure 13. Based on the information of the excitation toneburstsignal in the conducted experiment, the initial guess [−0.5,175 000, 0, −0.5, 0] is provided for the parameter vector ofthe front-edge signal in the estimation algorithm. The value−0.5 is used for the amplitude considering the attenuationeffect of guided waves in propagation and phase reversalof propagating waves at the front edge of the defect. Thevalue 175 000 is used because the center frequency of theexcitation toneburst signal is 175 kHz. The minimizationof equation (8) with a termination tolerance of 1 × 10−8

used toward the proposed edge reflection model provides theoptimal solution of estimated parameters. The finally obtainedsignal parameters are [−0.031 983, 161 190, 13.173, −4.9659,−9.2036]. That is, the amplitude is estimated to be −0.032,center frequency 161.12 kHz, phase 13.173, window functionamplitude −4.9659, and window function phase 9.2036. Theestimated signal is plotted with a dotted line together with theobserved signal as a solid line for comparison in figure 14. Itshows that excellent agreement is achieved between the twosignals.

With successful estimation of the concerned parameters,the front-edge signal can be produced based on the reflectionmodel as represented in equation (6). The result is shown

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

5.08 5.1 5.12 5.14 5.16 5.18x 10

-4

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0

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Time

Am

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Estimated dataobserved data

Figure 14. Partial data of the observed front-edge reflection signaland its estimation.

in figure 15(a). The back-edge counterpart can further beextracted from the reconstructed reflection signal as shown infigure 15(b). The evaluated axial length of the defect can thenbe calculated by using the CCF method. Alternatively, sincethe front-edge signal and back-edge signal have phase reversal,the time shift between these two signals can be determinedwith the distance between the lowest peak of the front-edgesignal and the highest peak of its back-edge counterpart. Thatis, the axial length L of the defect can be calculated as

L = (PH − PL) × vgr/2 = (5.3245 × 10−4

− 5.2519 × 10−4) × 5.35/2 = 19.4 mm, (11)

where PL and PH are the lowest peak of the front-edge signaland the highest peak of the back-edge signal, respectively. Thisindicates that the axial length of the defect evaluated by usingthe proposed method is very close to its actual measurement.The results of additional tests on defects with other axiallengths are listed in table 3. They also demonstrate that theproposed method can provide good performance in evaluationof the defect’s axial length, especially for the defects underserious conditions. The method can be optimized throughintroducing new techniques of parameter estimation whenthe defect is very small so that the limited partial data usedfor parameter estimation can guarantee sufficient estimationperformance.

0.00050 0.00051 0.00052 0.00053 0.00054 0.00055 0.00056

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front-edge signal back-edge signal

(a) (b)

Figure 15. The obtained (a) front-edge signal; and (b) back-edge signal.

0.00027 0.00028 0.00029 0.00030 0.00031 0.00032 0.00033

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Figure 16. The reflection signal generated by real corrosion thatexists in the real gas pipe.

0.00027 0.00028 0.00029 0.00030 0.00031 0.00032 0.00033

-0.15

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0.00

0.05

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Figure 17. The reflection signal reconstructed through theprocedure of EMD.

Performance of the proposed method is furtherdemonstrated by evaluating the axial length of real corrosionin the gas pipe shown previously in figure 5. Figure 16

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

2.8 2.9 3 3.1 3.2 3.3

x 10-4

1

1.05

1.1

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5

Time

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uenc

y

2.65 2.7 2.75 2.8 2.85 2.9 2.95 3

x 10-4

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Estimated data

Observed data

(0.000295, ya)

[0.00027, 0.000295]

(a) (b)

Figure 18. Results of HSA representation and parameter estimation.

0.00027 0.00028 0.00029 0.00030 0.00031 0.00032

-0.15

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0.00

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front-edge signal back-edge signal

2.9178E-4

3.1408E-4

(a) (b)

Figure 19. The obtained (a) front-edge signal and (b) back-edge signal.

Table 3. Comparison between the actual and evaluated results for the axial lengths of defects.

Actual axial length of defect (mm) 42 29.5 24 21 18.5 16 14 11 8 6Estimated axial length of defect (mm) 42.12 30.14 24.71 20.78 19.42 16.98 14.87 11.63 7.05 7.12Error (%) 0.28 2.13 2.95 −1.04 4.97 6.12 6.21 5.72 12.9 18.7

presents the collected signal reflected from the real corrosion.This reflection signal was reconstructed through the EMDprocedure, and the result is presented in figure 17. Thefrequency–time representation of the reconstructed defectreflection is shown in figure 18(a), in which the firstoverlapping point (0.000 295, ya) and the non-overlappingregion of the front-edge signal [0.000 27, 0.000 295] couldbe accordingly determined. Parameter estimation wasperformed on extracted partial observation data and thefinally obtained result was [−0.000 157 97, 113 500, −8.5537,575.99, −1.1354]. The front-edge signal and back-edge signalcan be further produced, as shown in figures 19(a) and (b),respectively. The evaluated axial length of corrosion can becalculated based on equation (11) as

L = (PH − PL) × vgr/2 = (3.1408 × 10−4

− 2.9178 × 10−4) × 5.4/2 = 60.21 mm. (12)

Compared to the notch type of defect considered in the firstgroup of experiments, the corrosion type of defect in thistesting has irregular profiles at its two edges. As mentionedin section 3, the length of corroded area is measured to be59 ± 5 mm along the axial direction of the pipe. The averageof varying axial lengths of corrosion along the circumferenceof the tested gas pipe is used as the characteristic value forrepresenting the actual axial length of this corrosion. Thevalue (60.21 mm) of the axial length evaluated by using ourmethod proved to be close to the characteristic value (59 mm)of the real axial length, which indicates that our method canalso efficiently provide useful information of complex pipelinedefects. It is noted that the effectiveness of the proposedmethod can be particularly well presented by the consideredcorrosion case, while other more complex defect cases needfurther investigation.

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Meas. Sci. Technol. 22 (2011) 025701 X Wang et al

6. Conclusion

This paper proposes a method to evaluate the characteristicaxial length of defects in pipelines. The evaluation makesuse of the fact that the overall reflection signal generated atthe defect is the interference between two primary reflectioncomponents, one from the reflected signal related to the frontedge of the defect and the other from the reflected signal relatedto the back edge of the defect. The evaluated axial length ofthe defect bears a direct relationship to the relative distancebetween reflection positions at the two edges of the defect,which is further closely related to the phase information ofthe two edges’ reflection signals. With the proposed method,the front-edge signal can be determined from a parametricmodel-based estimation procedure with the aid of HHT as asignal preprocessor, which further enables decomposition ofback-edge signals from the collected reflection data. Thatis, this method provides an effective tool to resolve theclosely spaced overlapping reflection components, which isdifficult to achieve by using other conventional algorithmsbecause the involved signals exhibit the same patterns exceptthe time phase. Once the two reflection signals have beendecomposed and identified, an axial length of the defectcan be easily evaluated. For complex defects with irregularshapes, since two primary reflection components are generatedin the interaction process of guided waves with defect asexplained in section 2, the axial length of such defects canstill be evaluated through two edge reflection componentsthat represent characteristic information related to the defect’sactual axial length. Verified against actual experiments withknown defects including real corrosion, the results provethat our proposed method is effective in evaluating thecharacteristic axial length of pipeline defects in the discussedcases.

Another benefit of the method proposed in this researchis that it can enable the evaluation of more defect parametersand further comprehensive defect characterization once twoprimary edge reflection components are identified. That is,each identified edge signal embeds geometric information ofthe corresponding edge of the defect, so the radial depth andcircumferential extent or other parameters of the defect couldbe assessed by using proper component analysis techniqueson the edge signals. This is another research work that will bereported in another forthcoming paper.

The current investigation is limited to circumferentialdefects in straight, empty pipelines. It is hoped that the methodproposed in this paper will be generalized to more complex realcases, which concern arbitrary-shaped and localized corrosiondefects in various operating environments. Further research isinevitably needed to improve the proposed method in future.

Acknowledgments

The work that is described in this paper is fully supported by theNational Natural Science Foundation of China and ResearchGrants Council of Hong Kong Special Administrative

Region (HKSAR) Joint Research Scheme (project no:N_CityU106/08) and the Research Grants Council of theHKSAR (project no: CityU 120605)

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