wavelet transform analysis of guided waves testing

7/17/2019 Wavelet Transform Analysis of Guided Waves Testing

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N O V E M B E R 2 0 1 0 M A T E R I A L S E V A L U A T I O N 1273

A B S T R A C T

The torsional mode of guided wave, T(0,1), has

been applied to detect discontinuities in pipelines,

especially in the cases of coated, elevated and

buried pipes. The signals of minor corrosions

would be covered by the noise, unfortunately,

because the coated material and buried medium

always induce a strong attenuation of the guided

wave. The main objective of this study was to

discuss the effect of bitumen coating on guided

wave tests by the experimental and signal

processing techniques, based on the use of contin-

uous wavelet transform. The experiments were first

performed to collect the reflected signal of the

discontinuities on two 152.4 mm steel pipes. The

results showed that the bitumen coating seriously

attenuated the signals of every discontinuity onthe test pipes. The continuous wavelet transform

was then used to perform a distance-frequency

analysis in order to achieve the success of the

minor discontinuity detection. In conclusion, the

discussion of the effect of the bitumen coating on

guided wave propagation and useful signal

processing techniques will help to increase the

sensitivity of discontinuity detection on coated

pipe.

KEYWORDS: guided wave, torsional mode,

bitumen, wavelet transform.

Introduction

Pipelines are widely used in the gas, refinery, chemical andpetrochemical industries as a means of transporting gases andliquids over long distances to users. Discontinuities, likecracks and corrosions, are often found on the outer or innersurface of pipelines. Without discontinuity control and regular

inspection, discontinuities can cause failure of pipelinesystems. Pipeline coating systems have always used disconti-nuity control to protect the pipe surfaces under the corrosiveenvironment. The discontinuities occur on pipes, however, inthe wake of coating degradation and failure, and can some-times lead to serious thinning of wall thickness. In addition,injuries, fatalities and environmental damage can follow. Todeal with the crisis, there is a quick and reliable technique forthe detection of corrosion under insulation the guided wavetechnique of ultrasonic testing (UT).

The guided wave technique uses an ultrasound travelingalong a pipe, and is commonly used to provide the full exami-nation of long sections of pipe. The changes in the response

signal of the ultrasound indicate the presence of an imped-ance change in the pipe. The shape and axial location ofdiscontinuities and features in the pipe are also determined byreflected signals and their arrival times. Since the guided

waves are cylindrical Lamb waves along the pipe, no lateralspreading can occur and the propagation is essentially one-dimensional. There has been a considerable amount of workon the use of guided waves for pipe inspection (Rose et al.,1996; Alleyne et al., 2001; Mudge, 2001; Cawley et al., 2003).The guided wave application has been extended to buriedand/or coated pipes, which are materials that are necessary tothe manufacturing processes in the refinery, chemical andpetrochemical industries. Previous research has shown that

the typical loss rates at a test frequency were from 3 to10 dB/m (Cawley et al., 2001). The technique of reducingthe test frequency was able to diminish the effect of attenua-tion when testing partially buried pipes. The effects of the

buried material on the pipe have been previously studied(Cheng et al., 2006). Loosely bonded soil caused lower atten-uation than tightly bonded concrete on the T(0,1) modepropagation. The buried pipes were always coated with a

bitumen coating, located between the pipe and the soil. It haspreviously been shown that the bitumen coating was respon-sible for a reduction of the range of propagation of the signal

* Department of Mechanical and Electro-mechanical Engineering, NationalSun Yat-sen University, No. 70, Lienhai Rd., Kaohsiung, Taiwan 80424,R.O.C.; 886 7 5252000, EXT 4270; [email protected].

Taiwan Metal Quality Control Corporation, 7F, No. 702, Hanmin Rd.,Xiaogang Dist., Kaohsiung, Taiwan 80424, R.O.C.

Cepstrum Technology Corporation, 6F-3, No. 151, Ren Ti St., Ling YaDist., Kaohsiung, Taiwan 80424, R.O.C.

METECHNICAL PAPER wx

Wavelet Transform Analysis of Guided Wave Testingon Coated Pipesby Shiuh-Kuang Yang*, Ping-Hung Lee*, Chi-Jen Huang and Jyin-Wen Cheng


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METECHNICAL PAPER wx wavelet transform analysis

(Demma et al., 2005). Guided waves have also been proven toscreen the full length of the gas pipeline that was unable to beinspected by the intelligent pig inspection system, which is asystem that is used to measure pipe thickness along the

pipeline (Ledesma et al., 2009). A portion of the pipeline wasabove ground, while another portion of it was immersedunder water and an additional portion was buried in soil. Thisprevious study showed that the use of guided waves ensuredcomplete coverage of the line and achieved uniform full atten-tion at all locations, including the immersed and buriedsections. The choice of guided wave modes was anothermanner to diminish the effect of attenuation. The use oftorsional waves allowed a greater length of pipe to beinspected for each transducer ring setup position; in partic-ular, when the pipe was coated with the most attenuating bitu-minous-type coating (Alleyne et al., 2009).

As for the studies of plates and cylinders coated with a

viscoelastic layer, guided wave propagation theories have beenstudied for practical nondestructive testing (NDT). Theeffects on the propagation of Lamb waves and shear hori-zontal waves in metallic plates coated with viscoelastic layershave previously been studied (Simonetti et al., 2004). Inaddition to the investigation of phase velocity and attenuationdispersion curves of the bilayered plate model, the relation-ship between the mechanical energy, guided wave attenuationand acoustic properties of the viscoelastic layer were alsoinvestigated when considering two different material attenua-tion regimes. For a metallic plate coated with low-loss layers, amode-jumping phenomenon occurred. The coupling mecha-nism led to the jumping of the trajectories of the bilayerdispersion curves among several asymptotic modes in the plot

of the phase velocity dispersion curve. For a metallic platecoated with highly attenuative layers, such as a steel platecoated with a bitumen layer, the phase velocity dispersioncurve of the fundamental shear horizontal mode (SH0 mode)in the bilayered plate oscillated around that of the SH0 modein the steel plate as the frequency increased. The guided waveattenuation also exhibited periodic peaks that occured aroundthe through-thickness resonance frequencies of theunclamped viscoelastic layer when it was considered to beelastic.

In addition, the phase velocity dispersion curves of ahollow tube filled with viscoelastic bitumen have previously

been reported (Cawley et al., 2003). The guided wave attenu-ation maxima occured at the cut-off frequencies of the equiva-

lent elastic filled tube. Using the global matrix technique, amultilayer, hollow cylinder model that includes viscoelasticlayers was developed to describe the propagation of the longi-tudinal modes on the pipe (Barshinger et al., 2004).Moreover, a semi-analytical finite element technique was usedfor tracing the phase velocity and attenuation dispersioncurves for both axisymmetric and flexural modes for a hollowcylinder with viscoelastic coating (Mu et al., 2008). Thisprevious study addressed some interesting observations on

the attenuation of torsional modes, such as the attenuation ofthe T(n,1) mode increases monotonically with an increase infrequency. By understanding the dispersion characteristics ofthe multilayer cylinder model, it helps inspectors to establish

an optimal strategy for detecting discontinuities on a pipecoated with viscoelastic material using the guided wave testingtechnique.

Meanwhile, the same semianalytical finite element tech-nique was used to study three multilayer cylinder cases,including a copper tube filled with bitumen, a steel pipecoated with a thin layer of bitumen and a steel strandembedded in concrete structures (Marzani et al., 2008). Inthe cases of the elastic steel pipe coated with a thin layer of

bitumen, the study declared that the phase and energyvelocity dispersion curves of the bitumen coated pipe weresimilar to the dispersion curves of an elastic steel pipe withoutany coating on it. In the case of the copper tube filled with

bitumen, the dispersion curves of the fundamental torsionalmode for the undamped system (tube filled with elasticbitumen) were compared with those of the damped system(tube filled with viscoelastic bitumen). In the low frequencyregion of the phase velocity dispersion curve, the fundamentaltorsional modes for the two systems matched. The attenua-tion for the fundamental torsional T(0,1) mode increased

with the frequency exponentially from zero frequency to thecut-off frequency of the second torsional T(0,2) mode.

To understand the interaction between the guided wavesand the discontinuities, authors have previously discussed thequantitative study of the reflection of the T(0,1) mode from acrack-like discontinuity, a notch-like discontinuity and astepped notch-like discontinuity in pipes in a wide frequency

range (Demma et al., 2003; Demma et al., 2004). By testingunder more than one frequency, it would be possible to avoidmissing the response of discontinuities due to destructiveinterference. However, when guided waves propagate on thepipe coated with bitumen, the strength of the signals reflectedfrom a minor discontinuity would be attenuated and thesignal-to-noise ratio would be reduced at the same time.Therefore, more advanced signal processing techniques arerequired in order to enhance the weak signal of the disconti-nuity, and then the signals of the discontinuities are extractedfrom the noise signals.

The wavelet transform technique has become popular inmany different types of signal processing techniques and has

been applied to recent NDT applications. Previously, several

adopted wavelet transforms to analyze the transient wavespropagating in a dispersive medium and the results provide aclear exposition of the signal during the dispersion process(Onsay et al., 1994). Other authors also conducted a studythat used a time-frequency analysis with wavelet transforms inthe case of wave propagation in 3D composites and obtaineda better interpretation of the signal (Leymarie et al., 2000). Asfor the pipe inspection, another previous study used a singletransducer to excite the L(0,1) and F(1,1) modes on the pipe

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with a lot of coherent noise (Siqueira et al., 2004). After usingthe wavelet transforms, they improved signal-to-noise ratiosuccessfully and gave the indications clearly. Furthermore,researchers have performed an automatic classification frame-

work for guided wave inspection on pipes by the wavelet-based multi-feature analysis (Rizzo et al., 2005). According tothe results of literature reviews, wavelet transforms have to beadopted in this study to extract the small signal reflected fromthe minor discontinuity under the attenuative coated material

when torsional mode T(0,1) was used as propagating mode.

Dispersion Curve of the Bitumen Coated PipeAs for the inspection of the coated pipe, a trial-and-error tech-nique was the only way to get the optimal parameters,including wave mode and operating frequency, without theinformation about the dispersion curves of coated pipes.Knowledge of the dispersion curves and wave structures of

the modes on the pipe is relevant in guided wave pipe inspec-tion for optimal performance, including precise location of thediscontinuities and low attenuation of the propagating modes.Because the frequency under examination was 21 to 32 kHz,the group velocity dispersion curves were traced for a152.4 mm steel pipe for bare case and coated case with a2 mm elastic bitumen coating. The results of the dispersioncurves were used to describe the propagating behavior of thefundamental torsional mode T(0,1) in the viscoelastic

bitumen coated pipe.To trace the group velocity dispersion curve and the wave

structure of the wave modes on coated pipes, modelingsoftware was used, based on the global matrix technique(Pavlakovic et al., 1997). The results are shown in Figure 1. It

should be noted that the blue dashed line T(0,1)b representsthe torsional mode for bare pipe and the other higher ordertorsional modes are not shown because their cut-off frequen-cies are higher than 120 kHz. The black solid lines T(0,1)cand T(0,2)c represent the torsional modes for the bitumencoated pipe. In addition, the wave structures of T(0,1)cweredominated by the profile of the tangential displacement Uthrough the wall thickness and the axial displacement Uz andthe radial displacement Ur are zero in this mode. U77 andU86 are the tangential displacement of the particle on theinner wall and the outer wall of the pipe, respectively.Figure 1a shows the group velocity dispersion curves below120 kHz; the T(0,1)b mode is non-dispersive across the

whole frequency range and its group velocity always keeps at

3260 m/s. Similarly, the T(0,1)c mode propagates at averagegroup velocity around 3145 m/s within the blue window boxat the frequency range from 21 to 32 kHz. The window box isthe frequency range of interest in this paper and the dashedcircle is the cut-off frequency of T(0,2)c, which is 93.5 kHz.The wave structures of the T(0,1)c mode are shown inFigures 1b and 1c at frequencies of 21 and 32 kHz. The top of

vertical axis is the 77 mm inner radius of the pipe and thebottom of the vertical axis is the 86 mm outer radius of the

coated layer. The wave structures normalized with respectedto their maximum value of displacement U86 show thedisplacement fields through the wall thickness at differentradial positions. Meanwhile, the displacement U77 of the

Figure 1. Group velocity and displacement data: (a) dispersioncurves of T(0,1) mode for a bare 152.4 mm pipe (blue dashedline) and a 2 mm elastic bitumen coated pipe (black solidline); (b) the wave structure of T(0,1)c mode at 21 kHz and (c)at 32 kHz.

(a)

T(0,1)b

T(0,1)c T(0,2)

c

Excitation zone

fT(0,2)c

= 93.5 kHz

0 20 40 60 80 100 120

Frequency (kHz)

Groupvelocity,

Vgr

(m/s)

5000

4000

3000

2000

1000

0

(b)

Radialposition(mm)

T(0,1)c, f = 21 kHz

-1 0 1

78

80

82

84

86

Ur

Uz

Uq

Uq86

Uq77

(c)

Radialposition(mm)

T(0,1)c, f = 32 kHz

-1 0 1

78

80

82

84

86

Ur

Uz

Uq

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particle on the inner radius of the pipe shows the minimumvalue both in Figures 1b and 1c. At a high frequency of 32kHz, the normalized tangential displacement U86 throughthe bitumen coating is obviously dominant, in contrast to low

frequency of 21 kHz for which the normalized tangentialdisplacement U77 is almost the same as U86. That is to say,the T(0,1)c mode leaks more energy into the bitumen coatingand is attenuated more seriously at 32 kHz than at 21 kHz.

Continuous Wavelet TransformWavelet transforms break signals into components that varyin scaling and translation of the original mother waveletfunction. To scale a wavelet means to stretch the mother

wavelet function and to translate a wavelet means to move thewavelet function along the X axis, which usually indicates thetime aspect. The continuous wavelet transform is achievedthrough continued scaling and translation of the mother

wavelet function along the length of a signal and consequentlyproduces a time-scale view of the signal. For a given signalf(t)in the time domain, the continuous wavelet transform is theinner product of the signal with a series of wavelet functionsdepending on the scale parameter a and the translationparameter b, as defined by the following equation:

(1)

where(t) indicates a mother wavelet* indicates its complex conjugation.

Wf(a,b) is a wavelet coefficient for the wavelet (t).Wf(a,b) measures the variation of the signal when the time tis equal to b. The higher the correlation between thefrequency of the wavelet and the frequency of the partialsignal, the larger the coefficient. A large value of scale standsfor a big window with a widespread view of the signal withlower resolution; a small value of scale represents a small

window with a detailed view of the signal with more accurateresolution. The continuous wavelet transform features the full

provision of the signal information and describes the energydistribution of the signal over the time-scale domain.

ExperimentAn experiment was designed to investigate the guided wave-based inspection technique for detecting the discontinuities ofthe wall on a bitumen coated pipe.

Experimental Setup

The experimental instrument was a pipe screening systemthat consisted of an ultrasonic guided wave transducer ring, aninstrument for the generation and reception of the guided

wave signal, power supply, computer and cables, as shown inFigure 2a (Guided Ultrasonics Ltd., 2005). To perform

guided wave testing, the transducer ring was first mounted onthe pipe, as shown in Figure 2b. After connecting the ring, theinstrument and the computer, signals with different frequen-cies were used to generate the torsional mode T(0,1) propa-gating forward and backward on the pipe. The guided waves

were reflected by features such as bends, supports, welds anddiscontinuities, while the reflected signals were received bythe same transducer ring. All features in the scanning sectionof pipe were detected at the same measurement and the

Wf a ba

f t t b

adt( , ) ( )==

--

**

--

1

y


Figure 2. (a) The guided wave testing system that was used;(b) the schematic diagram of a typical guided wave testingconfiguration; (c) the coordinate system to describe the axialand circumferential location.

(a)

(c)

(b)

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results were presented by an A-scan and C-scan display. Thecoordinate system used in the A-scan and C-scan display isshown in Figure 2c. The circumferential location wasmeasured in a counter-clockwise direction, if facing theforward direction of wave propagation, and the axial location

was measured from the distance between the transducer ringand the feature.

Two samples, Pipe 1 and Pipe 2, of 152.4 mm Schedule40 steel pipes with partial bitumen coating on the pipe wallwere manufactured. Experiments were performed in thefollowing cases: (a) four artificial discontinuities on bare Pipe1; (b) three natural discontinuities on bare Pipe 2; (c) fourartificial discontinuities on bitumen coated Pipe 1; (d) threenatural discontinuities on bitumen coated Pipe 2. The Pipe 1sample had two pipe ends, three welds and four artificialdiscontinuities (notches) on it. The whole length of Pipe 1

was 6 m and Figure 3a shows the positions of various featureson it. Between Weld 2 and Weld 3, four artificial discontinu-ities, labeled AD1, AD2, AD3 and AD4, were machined onthe section. The geometrical parameters of the artificialdiscontinuity are described in Figure 3b. The four artificial

discontinuities had different dimensions in circumferentiallength and depth, but the same axial extent. Table 1 gives thedimension and location of the artificial discontinuities. Theartificial discontinuities AD1, with 20% of the circumferenceof the pipe and 50% of the wall thickness, was machined onthe axial location 2000 mm from the transducer ring.Compared with the entire cross-sectional area of the pipe,

AD1 induced a 10% change of cross-sectional area and therest of the discontinuities induced an approximate 5% changeof cross-sectional area. The distance between the axiallocation of the three discontinuities AD1, AD2 and AD3 was500 mm and they were distributed distributed on the top ofpipe and ordered from AD1 to AD3. The AD4 was machinedon the same axial location with AD3, but with 270 of circum-

ferential location.To get the realistic result of the guided wave testing, the

Pipe 2 sample was formed by welding a new pipe and an oldpipe cut from one non-functional pipeline in the refineryfactory. Because the coated bitumen of the old pipe wasdegraded during the period of service, the corrosive environ-ment induced some wall loss on the pipe. As shown in Figure3c, Pipe 2 has two pipe ends, four welds and three naturaldiscontinuities distributed on the pipe. The section from

Figure 3. The profile of test Pipe 1 and Pipe 2: (a) the trans-ducer ring is mounted 1.5 m from End 1 on Pipe 1; (b) thegeometry parameters of the artificial discontinuity on Pipe 1;(c) the transducer ring is mounted 3.24 m from End 3 on Pipe2; (d) the geometry parameters of the natural discontinuityon Pipe 2.

(a)

(b)

(d)

(c)

TABLE 1

List of the artificial discontinuities on pipe 1.

Discontinuity Axial location Circumferential Circumferential Depth Axial extent Cross-section(mm) location () length (mm) (mm) (mm) change

AD1 3500 0 100 3.5 30 10%AD2 4000 0 50 3.5 30 5%

AD3 4500 0 100 2 30 5%

AD4 4500 270 30 6 30 5%

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End 3 to Weld 5 is a new pipe and the rest is the old one.When the old bitumen coating was removed between Welds5 and 6, three natural discontinuities (general corrosions),labeled ND1, ND2 and ND3, with different dimensions were

revealed on the section. The depth parameter D of the naturaldiscontinuity is described in Figure 3d. The three naturaldiscontinuities on Pipe 2 were marked and photographed, asshown in Figure 4. A profilometer was also used to measurethe depth on the chalked area for the discontinuity map of thethree natural discontinuities. As shown in Figure 4, thediscontinuity maps were plotted as a contour image from thedata measured by the profilometer. The horizontal axis of themap indicates the axial location calculated from the middle of

the transducer ring position, and the vertical axis of the mapindicates the circumferential location around the pipe. Zerodegrees refers to the topmost point of the pipe. The color ateach point is associated with the measured depth, with the

lighter color corresponding to the greater depth, and the darkcolor corresponding to the lesser one. The discontinuity mapsshowed the variation of the wall thickness loss in the threeareas of ND1, ND2 and ND3. By comparing Figures 4a, 4band 4c, the ND1 with a maximum depth of 3.95 mm wasidentified as severe corrosion, the ND2 with a maximumdepth of 2.39 mm was classified as minor corrosion and theND3 with maximum depth of 3.34 mm was classified asmedium corrosion.



Figure 4. The discontinuity map measured by the profilometer. Results show the photo and map of (a) ND1; (b) ND2; (c) ND3.

(a)

(b)

(c)

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Figure 5. The reflected signals from various features on the 152.4 mm Pipe 1 and Pipe 2: (a) the complete signal of bare Pipe 1;(b) the zoomed view of 5a; (c) the zoomed signal of bare Pipe 2; (d) the zoomed signal of coated Pipe 1; (e) the zoomed signalof coated Pipe 2.

(a)

(b)

(d)

(c)

(e)

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the coating. From Figure 5d, there was still a chance toidentify the four artificial discontinuities on Pipe 1 after fittingthe correct DAC curves, because the amplitudes were largeenough and the shapes were isolated. Nevertheless, Figure 5e

reveals that after fitting the correct distance calibration ampli-tude curves, only the ND1 and ND3 on Pipe 2 were clearlyidentified, due to the large amplitude. The minor disconti-nuity ND2, with small amplitude caused by the effect ofexisting of the bitumen coating, might have been undetected.

The signal of W2 on Pipe 1 and the signal of W5 on Pipe 2are considered reference signals; the reflection ratio of thediscontinuities with different frequency regimes can beobtained by calculating the ratio of amplitude of the disconti-nuity and the weld. As shown in Figure 6a, the reflection ratioof all the artificial discontinuities was reduced by increasingthe frequency regime. It can be seen that the three curves

varying with frequency regime marked as triangle, diamond

and square in Figure 6a display similar shapes, with the

maximum value occurring in the lower frequency regime of0.0. In the high frequency regime of 3.0 and 4.0, the reflectionratio of the triangle is lower than that of the diamond. It might

be the reason that the constructive interference happened

between the reflected signal of AD3 and AD4 when the wave-length was small enough to distinguish the two discontinu-ities. In Figure 6b, the frequency-dependent behavior of theND1 (curve marked as diamond) is similar to the artificialdiscontinuity shown in Figure 6a, but the reflection ratio ofND3 (curve marked as triangle) got a bigger response in thehigh frequency regime than in the low frequency regime. Inaddition, the reflection ratio of ND2 (curve marked assquare) was smallest and changed slightly with frequencyregime.

As for Pipe 1 and Pipe 2 coated with bitumen, the reflec-tion ratio of all discontinuities under the coating was smallerthan those without the coating. Figure 6c shows the decrease

in the reflection ratio of the discontinuity with increasing

Figure 6. Variation of reflection ratio with the operating frequency regime: (a) each artificial discontinuity on bare Pipe 1;(b) each natural discontinuity on bare Pipe 2; (c) each artificial discontinuity on coated Pipe 1; (d) each natural discontinuity oncoated Pipe 2.

(a)

(c)

(b)

(d)

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frequency regime when the artificial discontinuities wereunder bitumen coating. Figure 6d shows the reflection ratio ofnatural discontinuities under bitumen coating. A minimum

value of the reflection ratio for the three natural discontinu-

ities occured when the frequency regime equaled zero. Thisindicates that without sweeping the frequency regime fromlow to high, the indication of minor corrosion, such as ND2,

would be missed when only using low frequency guidedwaves on bitumen coated pipe inspection. To avoid missingany information of the reflected signal, the wavelet transformtechnique was adopted to process the received signals comingfrom the features on the coated pipes.

Detection of Minor Discontinuities by Wavelet Transform

As for the detection of minor discontinuity ND2, there arefour results shown in Figure 7ad with respect to thefrequency regime: 1.0, 2.0, 3.0 and 4.0, presented in A-scan

display. The natural discontinuity ND2 was characterized by adiscriminating black signal in the range of high frequencyregime 3.0 to 4.0. However, the signal of ND2 was covered bythe noise signals in the lower frequency regime. To extract the

small signal of ND2 from the experimental results of coatedpipe 2, the wavelet transform analysis was applied to processthe data. The wavelet transform analysis aims at character-izing the reflection in the time-frequency domain. However,

the time-amplitude signals had been automatically convertedto the distance-amplitude signals in the A-scan display by themodeling software. Therefore, the data processed by contin-uous wavelet transform was presented in the distance-scaledomain to analyze the frequency response of the naturaldiscontinuities in the whole frequency range of interest.

Regarding the reflection of W5 as the reference signal, thefour signals in Figures 7ad were normalized and combined.The combined data was extracted and processed for theproposed continuous wavelet transform technique. To applythe continuous wavelet transform, it was important to selectthe most appropriate mother-wavelet function. The mostappropriate mother-wavelet function was selected by trial and

error. The analysis was carried out using the Daubechieswavelet (db3) on a window of 307 data points of the entiresignals used in this study. Continuous wavelet transform withselective mother-wavelet function was performed on the


Figure 7. The reflected signals from various features on the 152.4 mm coated pipe 2: (a) frequency regime = 1.0; (b) frequencyregime = 2.0; (c) frequency regime = 3.0; (d ) frequency regime = 4.0.

(a)

(c)

(b)

(d)

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combined data and Figure 8a shows the distribution of thewavelet coefficients in the distance-scale domain. In Figure 8a,the horizontal axis of the contour plot indicates the distancedivision. Each distance division corresponds to 0.018 m and

the beginning point of the horizontal axis is 1.21 m. Thevertical axis indicates the wavelet scaling parameter a,which isinversely proportional to frequency. The wavelet transformshows the frequency range of the experimental data between 5and 39 on the scaling parameter, which is related to thefrequency range from 48 to 5 kHz. The color at each point isassociated with the magnitude of the wavelet coefficients, withthe lighter color corresponding to a larger coefficient, and thedark color corresponding to a smaller one. The distribution of

wavelet coefficients in the distance-scale domain showed theobvious indication of three natural discontinuities ND1, ND2and ND3.

In the higher range scale (lower frequency), only Welds

W5 and W6, and Discontinuity ND1, show the dominant

wavelet coefficients distribution. In the lower range scale(higher frequency), more than three reflected signals ofdiscontinuities are exhibited clearly. Furthermore, the waveletcoefficients presented in Figure 8b for a constant scale unveil

minor corrosion ND2 with a larger reflection ratio andidentify the location of ND2 along the pipe. Due to thepresence of the discontinuities, the larger wavelet coefficients

were obtained from the results of continuous wavelet trans-form. There were still some dominant spots, which can beseen clearly in Figure 8a. These spots might be minor discon-tinuities located on the pipe wall because this section of Pipe2 was cut from the refinery factory and had a high level ofgeneralized external corrosion on pipe surface. Thus, theattenuation effect of the bitumen coating on torsional guided

wave based inspection was overcome by processing the atten-uated reflection signal with continuous wavelet transform.

ConclusionWavelet transform analysis has been adopted to process thesignal of guided wave propagation on a bitumen-coatedpipe. The signals reflected from various discontinuities on a152.4 mm steel pipe were measured to illustrate the effectsof the bitumen coating. The results showed that the effectsof the coating on the reflection comprise signal attenuationincreased in difficulty for minor discontinuity detection. Acomparison was also made between the signals of T(0,1)mode reflected from the artificial discontinuity and thenatural discontinuity. The results show the multiplicity ofthe natural discontinuity, especially in frequency-dependent

behavior. In the experimental results of coated pipe cases,the signals of every discontinuity on Pipe 1 and Pipe 2 were

attenuated by the bitumen coating. Other than the signal ofND2, however, the responses of the other discontinuitieswere sti ll large enough to give an obvious indication,despite whether or not the coating was wrapped. To extractthe small signal of ND2, the continuous wavelet transformtechnique was used to perform a distance-frequencyanalysis. The results shown as a contour plot give a clearindication of ND2 in the distance-scale domain. Therefore,it is possible to find a minor discontinuity under the

bitumen coating on the pipe by continuous wavelet trans-form. With an understanding of the signal processing tech-nique applied to a reflected signal, this technique can helpinspectors improve the ability of guided wave inspection of

bitumen-coated pipe.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of this work by theNational Science Council of Taiwan under Grant No. NSC 97-2221-E-110-029.

REFERENCES

Alleyne, D. N., B. Pavlakovic, M. J. S. Lowe and P. Cawley, Rapid LongRange Inspection of Chemical Plant Pipework Using Guided Waves,

Insight, Vol. 43, No. 2, February 2001, pp. 9396.

Figure 8. (a) The result of continuous wavelet transform forthe combined signal of the natural discontinuities on coatedPipe 2; (b) the wavelet coefficient extracted from the Figure8a for a constant scale.

(a)

(b)

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Alleyne, D. N., T. Vogt and P. Cawley, The Choice of Torsional or Longi-tudinal Excitation in Guided Wave Pipe Inspection,Insight, Vol. 51, No. 7,July 2009, pp. 373377.

Barshinger, J. N. and J. L. Rose, Guided Wave Propagation in an ElasticHollow Cylinder Coated with a Viscoelastic Material, IEEE Transactions

on UFFC, Vol. 51, No. 11, November 2004, pp. 15471556.Cawley, P., M. J. S. Lowe, D. N. Alleyne, B. Pavlakovic and P. Wilcox,Practical Long Range Guided Wave Testing: Applications to Pipes andRail,Materials Evaluation, Vol. 61, No. 1, January 2003, pp. 6674.

Cheng, J. W., S. K. Yang and B. H. Li, Torsional Guided Wave Attenua-tion in Buried Pipe,Materials Evaluation, Vol. 64, No. 4, April 2006,pp. 412416.

Demma, A., D. N. Alleyne and B. Pavlakovic, Testing of Buried PipelinesUsing Guided Waves, Third Middle East Non-Destructive Testing Confer-ence and Exhibition, Manama, Bahrain, 2730 November 2005.

Demma, A., P. Cawley, M. J. S. Lowe and A. G. Roosenbrand, The Reflec-tion of the Fundamental Torsional Mode from Cracks and Notches inPipes,Journal of the Acoustical Society of America, Vol. 114, No. 2, August2003, pp. 611625.

Demma, A., P. Cawley, M. J. S. Lowe, A. G. Roosenbrand and B.Pavlakovic, The Reflection of Guided Waves from Notches in Pipes: a

Guide for Interpreting Corrosion Measurements,NDT & E International,Vol. 37, No. 2, April 2004, pp. 167180.

Rose, J. L., D. Jiao and J. Spanner, Ultrasonic Guided Wave NDE forPiping,Materials Evaluation, Vol. 54, No. 11, November 1996,pp. 13101313.

Guided Ultrasonics, Ltd., Wavemark G3 Procedure Based Inspector TrainingManual, Version 1.0, Guided Ultrasonics, Ltd., Nottingham, England,2005.

Leymarie, N. and S. Baste, Guided Waves and Ultrasonic Characterizationof Three-dimensional Composites, Review of Progress in Quantitative

Nondestructive Evaluation, Vol. 19, New York, Plenum, May 2000,pp. 11751182.

Marzani, A., E. Viola, I. Bartoli, F. Lanza di Scalea and P. Rizzo, A Semi-analytical Finite Element Formulation for Modeling Stress Wave Propaga-tion in Axisymmetric Damped Waveguides,Journal of Sound andVibration, Vol. 318, No. 3, 2008, pp. 488505.

Mu, J. and J. L. Rose, Guided Wave Propagation and Mode Differentia-tion in Hollow Cylinders with Viscoelastic Coatings,Journal of the

Acoustical Society of America, Vol. 124, No. 2, 2008, pp. 866874.

Mudge, P. J., Field Application of the Teletest Long Range UltrasonicTesting Technique,Insight, Vol. 43, No. 2, February 2001, pp. 7477.

Nunez Ledesma, V. M., E. Perez Baruch, A. Demma, and M. J. S. Lowe,Guided Wave Testing of an Immersed Gas Pipeline,Materials Evaluation,Vol. 67, No. 2, February 2009, pp. 102115.

Onsay, T. and A. G. Haddow, Wavelet Transform Analysis of TransientWave Propagation in a Dispersive Medium,Journal of the Acoustical Societyof America, Vol. 95, No. 3, 1994, pp. 14411449.

Pavlakovic, B., M. J. S. Lowe, D. N. Alleyne and P. Cawley, Disperse: AGeneral Purpose Program for Creating Dispersion Curves,Review of

Progress in Quantitative Nondestructive Evaluation, Vol. 16, New York,Plenum, 1997, pp. 185192.

Rizzo, P., I. Bartoli, A. Marzani, and F. Lanza di Scalea, Defect Classifica-tion in Pipes by Neural Networks Using Multiple Guided Ultrasonic WaveFeatures Extracted After Wavelet Processing,Journal of Pressure VesselTechnology, Vol. 127, No. 3, 2005, pp. 294303.

Simonetti, F., Lamb Wave Propagation in Elastic Plates Coated withViscoelastic Materials,Journal of the Acoustical Society of America, Vol. 115,

No. 52, 2004, pp. 20412053.Simonetti, F. and P. Cawley, A Guided Wave Technique for the Charac-terization of Highly Attenuative Viscoelastic Materials,Journal of the

Acoustical Society of America, Vol. 114, No. 1, July 2003, pp. 158165.

Simonetti, F. and P. Cawley, On the Nature of Shear Horizontal WavePropagation in Elastic Plates Coated with Viscoelastic Materials,Proceed-ings of the Royal Society of London A, Vol. 460, No. 2048, 8 August 2004,pp. 21972221.

Siqueira, M. H. S., C. E. N. Gatts, R. R. da Silva and J. M. A. Rebello, TheUse of Guided Waves and Wavelets Analysis in Pipe Inspection, Ultra-sonics, Vol. 41, No. 10, May 2004, pp. 785797.

Yang, W. X., A Natural Way for Improving the Accuracy of the Contin-uous Wavelet Transforms,Journal of Sound and Vibration, Vol. 306,September 2007, pp. 928939.


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