ResearchonPipelineDamageImagingTechnologyBasedon …downloads.hindawi.com/journals/sv/2019/1470761.pdf · 2019-07-30 · 3.5.2. Relationship between the Guided Wave Propagation Characteristics

Research ArticleResearch on Pipeline Damage Imaging Technology Based onUltrasonic Guided Waves

Jian He Chen Zhou Liang Yang and Xiaodan Sun

College of Aerospace and Civil Engineering Harbin Engineering University Harbin 15001 China

Correspondence should be addressed to Xiaodan Sun sunxiaodanhrbeueducn

Received 22 February 2019 Revised 26 May 2019 Accepted 19 June 2019 Published 24 July 2019

Academic Editor Francesco Pellicano

Copyright copy 2019 Jian He et alis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Pipeline structures are important structural components that cannot be replaced in actual engineering applications Damage to apipeline structure will create substantial safety hazards and economic losses in a project erefore it is extremely important tostudy damaged pipeline structures In this paper L(02) mode guided waves are used to identify locate and image single anddouble defects in straight pipe structures For the case where there is a single defect in the straight pipe section the influence ofdifferent excitation frequencies on the reflection coefficient of L(02) modal guided wave is studied and the optimal excitationfrequency of L(02) guided wave is 70 kHz when single damage is determined For the case of double defects in the straight pipesection the double-defect size the distance between the defects and the relative defect positions are studied and the influence ofthe defect recognition effect is analyzed e propagation path of the ultrasonic guided wave in the double-defect pipe section isanalyzed Finally the effectiveness of the three-point axial positioning method and damage imaging method is verified by thesingle-defect tube segment ultrasonic guided wave flaw detection experiment

1 Introduction

As one of the important forms of modern industrial trans-portation pipeline transportation has substantial advantagesin the transportation of gases liquids and slurries and iswidely used in several fields such as natural gas and petro-leum transportation However pipelines work in harshconditions such as underground or in water Cracking andleaking are likely to occur in response to external damagebacterial corrosion damage to the anticorrosion layer andother factors which in turn cause major problems such asproperty damage environmental damage and casualties[1 2] Regular monitoring and testing of pipelines in denselypopulated areas and environmentally protected areas is aneffective means to provide safe protection for pipelines Inultrasonic inspections of pipelines an ultrasonic guided wavepropagates rapidly along the tube wall and experiences a smallattenuation of its own energy over a long distance ultrasonicguided waves can comprehensively detect the structure of apipeline erefore the use of ultrasonic guided waves is anideal technical method to detect damage in a pipeline [3]

As early as the end of the 19th century guided waveswere used to study hollow cylinders on the basis of cy-lindrical guided wave theory Love [4] analyzed and studiedthe propagation law of ultrasonic guided waves in hollowcylindrical shells based on the theory of plates and shells Inthe middle of the 20th century Davies [5] performed adetailed analysis of longitudinal mode guided waves in afree rod Gazis [6] solved the steady-state harmonic so-lution of a wireless long hollow cylinder and presented thedispersion curves of the axial mode and the torsional modeIn the late 1980s Silk and Bainton [7] began to use pie-zoelectric ceramic probes as excitation sources to excitelongitudinal mode beams According to Snellrsquos law thelongitudinal L(01) and longitudinal L(02) modes weregenerated for defects e state is distinguished and crackdetection at different depths is studied Rose et al [8]proposed the general principles of ultrasonic guided wavedetection in pipeline structure applications and providedtheoretical guidance for researchers in the direction ofmodal excitation of guided waves At the end of the 20thcentury based on the gradual maturity of ultrasonic guided

HindawiShock and VibrationVolume 2019 Article ID 1470761 18 pageshttpsdoiorg10115520191470761

wave excitation and signal receiving technology Zhenget al [9] used the FE method to establish a 3D pipe modelwhich simulates the applied force for generating the desiredguided waves e phenomenon shows that L(02) guidedwave mode conversion provides valuable theoreticalguidance for the pipeline on-site testing and laboratorytests Carandente et al [10] proposed a study of the re-flection of the fundamental torsional mode T(01) from anaxisymmetric defect with varying depth profile via finiteelement modeling and experimental validation Nishinoet al [11ndash13] studied the guided mode transition of guidedwaves under different elbow angles ey find that theinfluence of the curved member also complicates the ex-planation of the reflected signal due to the presence of localdamage

In recent years foreign experts and scholars have beenworking to improve the ability of ultrasonic guided wavesto detect and locate defects in pipeline structures Mu andRose [14] solved the problem of guided wave propagationin free hollow cylinders with viscoelastic coatings by asemianalytical finite element (SAFE) method and theo-retical proof of the orthogonality between guided wavemodes in a viscoelastic coated hollow cylinder is providedby them Deng et al [15] used the temporal-spatial focusingeffects of the time-reversal method on the guided waveinspection in pipes and improve ultrasonic guided wavedetection capabilities e phenomena of energy focusingcan magnify the small defect and the location of the defectis given simultaneously Da et al [16] proposed theQuantitative Detection of Fourier Transform (QDFT) anovel approach capable of providing a high level of ac-curacy and efficiency for nondestructive detection of de-fects e proposed approach contributes to thecharacterization of surface defects and would also broadenthe scope of nondestructive defect inspection using ul-trasonic guided waves El Mountassir et al [17] proposed anew method for damage detection and localization ofpipeline structures which is based on the sparse estimationof the measured signals by the reference signals esparsity helps to enhance damage detectability because adamaged signal will have a high estimation error comparedto that of a healthy signal

In this paper based on the ultrasonic guided wavetheory the dispersion curve of the pipeline structure isdrawn and the dispersion characteristics of the guidedwave are analyzed Second ABAQUS software is used toestablish a finite element model of a pipe structure tosimulate the propagation behaviours of ultrasonic guidedwaves in straight pipe sections and the damage identifi-cation location and imaging of single cracks and doublecracks Based on the ellipse localization method we pro-posed a new method for damage localization of straightpipe structures which combines the data of multiple signalreceiving points and axially locates the defect boundary bya three-point positioning method Finally an ultrasonicguided wave detection experiment of a straight pipe sectionwith a single defect is performed and the results arecompared with the simulation results to verify the feasi-bility of the simulation

2 Basic Theory

21 Concept ofUltrasonicGuidedWaves e propagation ofmechanical vibration in an elastic medium is called an elasticwave (sound wave) the elastic medium is defined as awaveguide and the ultrasonic wave propagating in thewaveguide is called an ultrasonic guided wave e ultra-sonic guided wave is essentially a mechanical vibrationgenerated by the disturbance source that propagates throughthe waveguide which contains the information of the dis-turbance source (excitation) and the mechanical charac-teristics of the waveguide material

e frequency of the ultrasonic guided wave is higherthan 20 kHz When an ultrasonic guided wave propagates inan elastic medium it has the advantages of good di-rectionality high energy strong penetrating power and noharm to the human body An ultrasonic guided wave cangenerate reflection refraction and waveform conversion atthe interface of the elastic medium e ultrasonic guidedwave can also be combined with the change in the intensityof the acoustic wave to determine the physical character-istics such as the size and position of the internal defects of acomponent

22 Drawing of the Dispersion Curve

221 Group Velocity and Phase Velocity of Guided WavesGroup velocity (cg) and phase velocity (cp) are the two mostbasic concepts in guided wave theory e group velocitycharacterizes the propagation velocity of the overall waveenergy of a pulse wave whereas the phase velocity is thevelocity that directs a fixed phase point of the wave in thepropagation direction For waves with only a single fre-quency and wavelength the phase velocity is equivalent tothe group velocity e conventional guided wave propa-gation velocity is the group velocity of the guided wave andthe phase velocity does not reflect the propagation velocity ofthe guided wave as a whole in the waveguide medium erelationship between the group velocity and phase velocity isas follows

cg d(ω)

d(k)

d kcp1113872 1113873

dk cp + k

d cp1113872 1113873

dk (1)

222 Dispersion Curve is paper selects a 20 type steelpipe with an outer diameter of 219mm and a wall thickness of8mm e elastic modulus of the material is 206 times 105Poissonrsquos ratio is 0305 and the material density is 7850 kgm3According to the dispersion equation the dispersion curve isdrawn in conjunction with MATLAB software as shown inFigure 1

e dispersion curve shows that the L(02) mode wave isin the 20sim100 kHz region and the velocity of the guidedwave group hardly changes with respect to the frequency Inthis frequency band the guided wave does not have dis-persion therefore this excitation frequency of the probe issuitable for ultrasonic guided wavese L(02) mode guidedwave has the largest group velocity and the excitation

2 Shock and Vibration

waveform can be effectively distinguished from other modalwaveforms

3 Numerical Simulation of Ultrasonic GuidedWave in Straight Pipe Section

31 Geometric Models and Material Parameters A finiteelement model is established by considering the size of thepipeline and the simulation calculation time in the actualproject is paper selects a 20 steel pipe with an outerdiameter of 219mm a wall thickness of 8mm and a lengthof 3m e material parameters of the pipeline are shown inTable 1

Using ABAQUS the pipeline finite element model isbuilt as shown in Figure 2

32 Unit Type and Meshing Using ABAQUS to simulateguided wave propagation the pipe must be defined as adeformable body using a C3D8R unit (eight-node linearbody) To ensure the calculation accuracy and reduce thecalculation time the pipe unit size should be selected so thatthe unit length is less than 110 of the excitation guide wavewavelength this size selection criterion will control thepropagation error of the guided wave

dlt110

CL

f (2)

In the formula the guided wave excitation frequency isthe cell size e mesh structure of the pipe structure unit isshown in Figure 3

33 Guided Wave Excitation and Boundary ConditionsIn this paper L(02) mode guided waves are mainly used asexcitation guided waves for ultrasonic guided wave de-tectione excitation guided wave signal usually needs to bemodulated by the Hanning window to solve the high-fre-quency interference and energy spectrum leakage in thesignal the specific formula is shown in equation (3) eHanning windowing process of the guided wave signal in-troduces a cosine window that reduces the values of the leftand right edges of the waveform to approximately zerowhich highlights the waveform near the centre improves the

vertical resolution and makes the guided wave signal morecharacteristic

x(t) 05 times 1minus cos2πft

n1113888 11138891113888 1113889 times sin(2πft) (3)

In this formula n represents the number of signal cyclesand t represents the time interval

e waveform data corresponding to the guided wavesignal are imported into ABAQUS and edited into amplitudedata e local coordinate system of the pipe end face istransformed into a cylindrical coordinate system and theunit concentrated force is symmetrically loaded on thecentreline node of the end face to excite the L(0 2) guidedwave and the signal receiving point set is set at the node30 cm away from the excitation end for guiding wave signaldata extraction When performing the finite element sim-ulation according to the needs of calculation the boundaryconditions can be simplified wherein the environment suchas water and soil and the supporting structure can beignored

34 Guided Wave Propagation in Defective Straight TubesA permeation defect with a circumferential angle of 15deg(circumferential length of 2867mm) and a width of 2mm isprovided at a distance of 1m from the excitation end of thepipe section Material damping is minimal in practice andwas ignored in the model e finite element model of thestraight pipe with a single defect is shown in Figures 4 and 5

Ultrasonic guided waves of different frequencies from30 kHz to 100 kHz are excited at the end of the finite elementmodel of a single-defect straight tube and the guided wavesignal is received at a distance of 30 cm from the excitationend to extract numerical simulation results e time do-main diagram of the guided wave signal is shown in Figure 6

e numerical simulation results of the defective finiteelement model are extracted e data are processed by the

0 50 100 150 200Frequency (kHz)

0

2000

4000

6000G

roup

spee

d (m

s)

L(02)

L(01)

T(01)F(12) F(11)

F(13)

Figure 1 Group velocity dispersion curve

Table 1 Pipe material parameters

Mechanicalproperties

Modulus of elasticity(MPa)

Poissonrsquosratio

Density(kgm3)

Numericalvalue 206 times 105 0305 7850

x

y

z

x

y

z

Figure 2 Finite element model of a straight pipe section

Shock and Vibration 3

Hilbert transform e displacement amplitudes of thedamage signals are comparede amplitudes of the damagesignals are similar at different excitation frequencies and theamplitudes of the damage signals are slightly higher between60 kHz and 80 kHz than those at the other tested frequenciese ratio curve of the amplitude of the damage signal and theamplitude of the initial received signal is then drawn Asshown in Figure 7 the ratio is the largest at 70 kHz whichmeans that the damage signal is the most substantial at thisfrequency these results are consistent with those of theguided wave time domain Combined with the time domaindiagram the damage signal is the most apparent at a fre-quency of 70 kHz and thus 70 kHz can be used as theoptimal excitation frequency for ultrasonic guided wavedetection

35 L(02) Mode Guided Wave Characteristics and DoubleDefects

351 Relationship between the Guided Wave PropagationCharacteristics and Double-Defect Distance A finite ele-ment model of a pipeline with defects was established Anannular penetration defect (distal defect 2) was set at adistance of 1m from the excitation end and a signalreceiving end was set at a distance of 03 m from theexcitation end of the defect A schematic diagram of thespecific model is shown in Figure 8 To consider the in-fluence of the relative distance of the same type of defecton the detection effect another annular permeabilitydefect (proximal defect 1) was set between the excitationend and defect 2 and the distance between the proximaldefect and the distal defect was set to 05m 04 m 03 m02 m or 01 m e two defects have the same axial di-rection shape and size and the cross-sectional area ratio(A) is 833

Numerical simulations were performed by ABAQUS toplot the time domain of the guided waves with differentrelative distances as shown in Figure 9 According to theguided wave time domain diagram the existence of doubledefects greatly increases the complexity of the guided wavesignal compared to the guided wave signal in the pipelinemodel with a single defect and there are multiple obviouswaveform signals in the time domain diagram At this timethe damage echo signal can only be identified based on theshape of the waveform signal

e time domain diagram clearly shows that the echosignal of the near-end defect decreases with increases inthe relative distance and the reflected echo signal shiftsbackward in the time domain diagram and graduallyechoes with the far-end defect e far-end defect and thereflected echo signals partially overlap e Hilberttransformation was then performed on the time domainmap signal the displacement amplitudes of each signal inthe time domain diagram were highlighted and the rel-ative distances of the double defects were converted intodistances between the near-end defect and the excitationend then the displacement amplitude information wasextracted and the signal amplitude was plotted is curveis shown in Figure 10

As the distance between the near-end defect and theexcitation end increases the amplitude of the damage echosignal of the proximal defect decreases is result is in-versely proportional to the theory that the attenuation of

Figure 3 Grid diagram of the finite element model of the straight pipe section

Defect location

x yz

Received signal

Figure 4 Defective straight pipe finite element model

Defect

Figure 5 Mesh distribution at the defect


the cylindrical guided wave propagation is inverselyproportional to the square of the distance As the relativedistance decreases the amplitude of the reflected echo

signal of the far-end defect gradually decreases andgradually approaches the amplitude of the reflected echosignal of the near-end defect

15times10ndash9

times10ndash3

Damage signal

1

05

0

Disp

lace

men

t (m

)

ndash05

ndash10 02 04 06

Time (s)08 1 12

(a)

times10ndash10

Damage signal

8

Disp

lace

men

t (m

)

ndash8

ndash6

ndash4

ndash2

0

2

4

6

times10ndash30 02 04 06

Time (s)08 1 12

(b)

Damage signal

8times10ndash10

Disp

lace

men

t (m

)

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(c)

Damage signal

times10ndash10

6

4

2

0

ndash2

ndash4D

ispla

cem

ent (

m)

ndash6


Time (s)08 1 12

(d)

Damage signal

times10ndash10543210

ndash1ndash2ndash3ndash4

Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damage signal

times10ndash104

Disp

lace

men

t (m

)

ndash4

3

2

1

0

ndash0

ndash2

ndash3


Time (s)08 1 12

(f )

Damage signal

times10ndash10

4

Disp

lace

men

t (m

)

ndash4

ndash3

ndash2

ndash1

0

1

2

3


Time (s)08 1 12

(g)

Damage signal

times10ndash103

Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2


Time (s)08 1 12

(h)

Figure 6 Time domain diagram of guided waves in single-defective sections at different excitation frequencies (a) 30 kHz guided wavesignal (b) 40 kHz guided wave signal (c) 50 kHz guided wave signal (d) 60 kHz guided wave signal (e) 70 kHz guided wave signal(f ) 80 kHz guided wave signal (g) 90 kHz guided wave signal (h) 100 kHz guided wave signal


352 Relationship between the Guided Wave PropagationCharacteristics and Dierent Dimensional Defects A niteelement model of a defective pipeline was established and acircular permeability defect (distal defect 2) was set at adistance of 1m from the excitation end e ratio of thecross-sectional area A was 417 and the circumferentialangle of the defect was 15deg A signal receiving end wasprovided at the centre axis of the defect and 03m from theexcitation ende proximal defect 1 was located 07m awayfrom the excitation end and defect 1 and defect 2 whichwere both transparent annular defects were located on thesame axis e circumferential angle of defect 1 is variedfrom 15deg to 90deg with an angular separation of 15deg edouble-defect pipeline model is shown in Figures 11 and 12

e numerical simulation in ABAQUS was used toextract the time and displacement amplitude results of thedata simulation e time domain diagram of the pipelineultrasonic guided wave signal for plotting the change in thesize of defect 1 is shown in Figure 13

e data of the time domain graph are subjected to theHilbert transform the displacement amplitude of each echosignal is extracted and the displacement amplitude variationcurves of the echo signals of dierent sizes are drawn inFigure 14

As the size of the near-end defect increases the am-plitude of the rst received signal is almost constant whereasthe amplitude of the damage echo signal of the near-enddefect increases linearly e damage echo signal of the far-end defect exhibits a decreasing trend as the near-end defectsize increases and as the size of the proximal defect in-creases the attenuation amplitude decreases

353 Relationship between the Guided Wave PropagationCharacteristics and Circumferential Relative Defect PositionsDistal defect 2 is xed at a distance of 1m from the excitationend and the circumferential angle of the proximal defect isvaried in relation to distal defect 1 e relative angle changeinterval of the proximal defect is set to be 0deg to 180deg with aninterval of 15deg

e double-defect pipeline model diagram is shown inFigures 15 and 16 e proximal defect is 07m away fromthe excitation end e defect size is the same as the distaldefect and both are 30deg Both defects are transparent holesand the circumferential position of the proximal defect isclockwise and variable

ABAQUS was used to simulate ultrasonic guided wavepropagation in a double-defect pipeline with circumferentialrelative positional changes e data from the numericalsimulation results are processed the time and displacementamplitudes in the guided time domain map are extractedand the amplitude variation curve is plotted as shown inFigure 17

According to the amplitude curve of the guided wave thedisplacement amplitude of the echo signal of the far-enddefect rst increases and then decreases with the change in thedeection angle and then tends to stabilizee reason for theanalysis is that the ultrasonic guided wave undergoes modaltransition in the near-end defect and generates a newwaveform e propagation path of the new waveformchanges with the change in the circumferential relative po-sition and increases with the increase in the deection anglee group velocity of the newly generated waveform will besubstantially smaller than that of the L(02) mode guidedwave e new waveform has a slow wave velocity and a shortpropagation path whereas the L(02) mode waveform has afast wave velocity and a long propagation path ereforedierent waveforms are observed at the receiving pointMoreover waveform superposition occurs which causes theamplitude curve to rise and fall

4 Defect Identification and Imaging in aStraight Pipe Segment

e method adopted in this paper is to use a piezoelectricsensor array to excite the ultrasonic guided wave signal andto analyse the dierence between the excitation signal andthe echo signal to realize the positioning of the structuraldefects in the pipeline Meanwhile based on the ellipselocalization imaging method of plate structure [18] themethod is proposed and applied for the axial localizationand damage imaging method which is suitable for bothsingle and double defects of pipe segment

41 Axial Positioning of a Single Defect in a Straight PipeSection e ultrasonic guided wave signal is excited at oneend of the pipe section and the receiving point is set at acertain distance from the pipe end e distance from thedamage to the exciting end is dened as x the time when thesignal receiving sensor receives the signal for the rst time isrecorded as t1 and the receiving time of the damaged echo

04035

03025

Refle

ctio

n co

effic

ient

02015

01005

030 40 50 60 70

Frequency (kHz)80 90 100

Figure 7 Ratio of the damage signal to rst received signalamplitude

Receivedsignal Defect 1

r

z

Defect 2

Figure 8 Schematic diagram of the double-defect pipeline model


signal is recorded as t2 e damage axial position x can becalculated by equation (4) e schematic diagram of thecalculation of the axial position of the damage is shown inFigure 18

Damagesignal 1 Damage

signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Figure 9 Time domain diagram of guided signals with dierent relative distances (a) Relative distance is 05m (b) Relative distance is04m (c) Relative distance is 03m (d) Relative distance is 02m (e) Relative distance is 01m

6

1

2

3

4

5

Disp

lace

men

t (m

)

05 055 06 065 07Proximal defect and ecitation end distance (m)

075 085 0908

times10ndash10

Received signal amplitude for the first timeNear-end defect signal amplitudeRemote defect signal amplitude

Figure 10 Signal amplitude curves with dierent relative distances

Receivedsignal

Defect 1

r

z

Defect 2

Figure 11 Double-defect pipe models of dierent sizes


x Cg middotΔt2 (4)

In equation (4) Δt t2 minus t1A defect was established in the straight pipe e ratio of

the cross-sectional area of the defect to the section of thetube section is 124 the circumferential length is 5733mmthe width is 2mm and the defect type is full permeabilitydamage e ultrasonic guided wave was excited at one endof the pipe and the receiving sensor was set at a distance of30 cm from the exciting end and the defect was located 1mfrom the exciting end Using the Hilbert transform theenvelope diagram of the time domain graph packet is drawnand the maximum value is considered to be the arrival timeof the wave packet e result is shown in Figure 19

e signal excitation occurs at time zero the rst re-ceiving signal time is t0 9520 μs the damage signal re-ceiving time is t2 36235 μs and the end echo receivingtime is t1 112785 μs

e damage distance is 99831mm from the calculatedend Considering the defect width of 2mm the actual defectdistance is 998mm e error between the calculation resultand the model is 017 and the simulation result is moreaccurate than the calculation

42 Single-Defect Imaging of the Axial Positions of KnownDefects e excitation end plane is taken as the cylindricalcoordinate system z 0 plane which makes the inside of thepipeline the z-axis forward direction e signal receivingpoints are numbered in a clockwise direction and the eightsignal receiving points are evenly arranged along the pe-riphery of the pipe segment and they are numbered S1 S2S3 S8 e cylindrical coordinate system is in the di-rection of the zero point of the polar coordinate θ of thesignal receiving point S1 direction e model cylindercoordinate system and receiving point number are shown inFigures 20 and 21 respectively e circumferential angle ofthe defect is 15deg and the width is 2mme receiving pointsare evenly arranged according to the symmetric axis of thedefect and the damage boundary is 998mm from the planewhere the receiving point is located

It is assumed that the excitation and reception processesof the ultrasonic guided waves are performed in accordancewith the shortest propagation path of the guided waves eaxial position of the defect is 998mm and the propagationpath distances between the eight signal receiving points andthe defect reection point are calculated as shown in Table 2

e coordinates of the receiving point are dened as(x0 y0 300) and the coordinates of the reection point aredened as (x1 y1 z1) e signal receiving point issubstituted with the defect boundary reection point anglecoordinates θ0 and θ1 via the following transformation

x 05d middot cos θy 05d middot sin θ

(5)

In equation (5) d is the outer diameter of the cylinderwhich is 219mm

en the distance between the receiving point and thereecting point can be expressed by the following equation

s 05d times θ1 minus θ0( )[ ]2 + z1 minus 300( )2

radic (6)

e angular coordinates of the signal receiving pointsS1 through S8 are [θ0] 0 025π 05π 075π π 125π[15π 175π ] By substituting the received point angle co-ordinate value and the corresponding distance into equation (5)a circular trajectory curve centred on the signal receivingpoint can be calculated Using MATLAB the pipe lengthdefect and the circular trajectory curve are drawn in the samecylindrical coordinate system and the circumferential lengthof the pipe segment defect and the tting eect of the defectimaging and the model defect can be obtained [19 20] theimaging results are shown in Figure 22

In the cylindrical coordinate system point A is expressedas (1095 742deg 99780) and point B is expressed as(1095 minus 745deg 99810) e intersection position repre-sents the left and right boundaries of the damage and theangular dierence between the two points is 1487deg theactual damage hoop size is 15deg and the error is 087 eabove algorithm can eectively reect the damage in-formation of the defect in the loop direction of the pipesegment and the circumferential dimension of the pipesegment defect can be determined by drawing the two endpositions on one side boundary and then the damage degreecan be ascertained

43 Single Damage Imaging of the Axial Positions ofUnknown Defects In the previous algorithm of damageimaging there were three basic assumptions (1) eactual axial positioning of the defect is known and thesubsequent calculation with reference to it (2) the signalpropagation path of the sensor exists along a straight lineand the axial position of the defect can be calculated byusing the data received by sensor S1 (3) the receivingsensor arrangement is symmetric about the defect andthus the guided wave signal has symmetry and regularityand the signal has an intrinsic reference

e rst hypothesis was removed and the numericalsimulation was substituted to calculate the axial position ofthe defect at 99831mm On this basis the propagation pathdistances between the eight dierent receiving points andthe defect reection point are calculated and the results areshown in Table 3

Defect 2Defect 1

r

Figure 12 Model section


In the cylindrical coordinate system a circular trajec-tory is drawn with the eight signal receiving points as thecentre and the signal propagation distance as the radiusUsing MATLAB the imaging results are shown inFigure 23

In the cylindrical coordinate system point A is expressedas (10950minus748deg 9980) and point B is expressed as(10950 748 9979) e pipe segment has a circumferentialorientation of 1496deg and an actual damage of 15deg withminimal error

44 Damage Imaging of a Single Defect in the Pipe SegmentExcluding the three hypotheses mentioned above only thedamage model of the segment to the general condition of thedefect is establishedemodel size and sensor arrangement

are the same as before and the defects in the previous modelare deflected to ensure that the defect does not form a linearreflection with any of the receiving sensors e defect doesnot form a symmetry with the receiving sensor and the axisof the damage is assumed in the calculation e orientationis unknown e cross-section of the numerical model isshown in Figure 24

In Figure 24 the circumferential angle of defect 1 is 15degand the difference between the left boundary and the signalreceiving point S1 is 10deg e type of defect is a through-holecrack with a width of 2mm It is now assumed that therelative position between the defect and the sensor and theaxial position of the defect are unknown Before calculatingthe axial position of the defect a basic judgement of thepositional relationship between the defect and the sensor isrequired

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )

Figure 13 Time domain diagram of guided waves with different defect sizes (a) Circumferential angle is 15deg (b) Circumferential angle is30deg (c) Circumferential angle is 45deg (d) Circumferential angle is 60deg (e) Circumferential angle is 75deg (f ) Circumferential angle is 90deg


On the defect side the height dierence between thereection point and the reception point is a xed value andthe distance between the sensors is equal Based on thiscondition the data of the three sensors on the defect side canbe used to locate and image the defect e receiving pointsignal data are processed and the total propagation distanceof the ultrasonic guided wave signal between the receivingpoint and the defect is calculated and the calculation resultsare shown in Table 4

e propagation distance between the signal receivingpoint and the defect includes the linear distance between thesignal passing through the receiving point plane and thereecting point and the curved distance between thereecting point and each signal receiving point e straightline distance is set to h and the distance between the signalreection point and the receiving point S1 is x1 en therelationship between the distances can be represented byFigure 25

e distance data corresponding to the three receivingpoints of S1 S8 and S7 in the gure are selected and thevalues of x1 and h are determined to be 17905 and 698609respectively through the triangular relationship e samemethod can be used to process the signal data on the otherside of the defect which results in x2 3619 andh 698569 e axis distance data on both sides are av-eraged to obtain the axial position of the defect as((698609 + 698569)2) + 300 998589mm e actualdefect boundary distance is 998mm from the excitation endand the error between the three-point axial positioningresult and the actual distance is extremely small

MATLAB is used to draw a circular trajectory with thereceiving point as the centre and the distance between thereceiving point and the reecting point as the radius and thedamage imaging is shown in Figure 26

In the cylindrical coordinate system point A isexpressed as (10950 2450deg 99830) point B is expressedas (10950 1050deg 99810) the circumferential angle is1400deg and the error is small and can reect the damagedegree information of the defect

45 Double-Defect Identication and Positioning Due to thedierence in size position and circumferential relativeposition of the two defects there are some dierences in thedamage location In this paper only one form of doubledefect is used for positioning calculation e nite element

6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)

30 40 50 60 70Cirumferential angle of proximal defect (deg)

80 90

times10ndash10


Figure 14 Deformation amplitude curves of dierent size defects

Received

Defect 1r

z

Defect 2

Figure 15 Double-defect model diagram for dierent circum-ferential positions

Defect 1

Corner

Defect 2

Figure 16 Schematic diagram of the model


0

6times10ndash10

5

4

3

2

1

020 40 60

Circumferential relative deflection angle (deg)

Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180

Figure 17 Guided amplitude curves of dierent relative cir-cumferential angles

Excitingend Receive

X

Defect

Figure 18 Schematic diagram of the calculation of the axial po-sition of the damage


model was established and the near-end defect 1 was set at adistance of 07m away from the excitation end and the distaldefect 2 was set at a distance of 10m away from the ex-citation end e two defect shapes were equal in size andlocated on the same axis of the pipe segment A schematicdiagram of the model is shown in Figure 8

451 Local Defect Location e guided signals of the eightsignal receiving points are extracted and after the Hilbert

transform the near-end defects and the far-end defect echodata are obtained and the data are sorted the results areshown in Table 5

According to the three-point axial positioning methodthe nearest three points are selected on both sides of defect 1e distance data corresponding to the three receivingpoints S1 S2 and S3 are selected to calculate the coordinatesof point A as (10950minus654deg 697768) e distance datacorresponding to the three receiving points S8 S7 and S6 areselected to calculate the coordinates of point B as (10950787deg 697959) After combining the results of the two sidesof the data the axial positioning is averaged the near-enddefect is 697864mm away from the excitation end in theaxial direction and the difference from the actual distance ofthe model is 698mm e circumferential angle of the near-end defect is calculated to be 1441deg which is smaller than themodel defect size of 15deg

452 Remote Defect Location As before the nearest threepoints are taken on both sides of the far-end defect pointsS1 S2 and S3 on one side and points S8 S7 and S6 on theother side e distance data corresponding to the threereceiving points S1 S2 and S3 are selected to calculate thecoordinates of point A as (10950 662deg 998051) edistance data corresponding to the three receiving pointsS8 S7 and S6 are selected to calculate the coordinates ofpoint B as (10950 minus 775deg 998147) e calculated cir-cumferential angle is 1437deg therefore compared with theactual model distal dimension of 15deg the error is smalle calculated axial positioning average shows that thefar-end defect is 998099mm from the excitation endcompared with the actual distance of 998mm the error issmall

Combining the calculation results of the near-end defectand the far-end defect the circular trajectory is drawn inMATLAB and the defect boundary image is obtained asshown in Figure 27

5 Experiment Research

51 Straight Pipe Section Defect Detection Experimentis test mainly studies the identification of single damagein straight pipe sections e specifications of the ex-perimental pipe section used are length 3000mm pipeouter diameter 219mm pipe inner diameter 203mm andmodel 20 steel Eight piezoelectric ceramic sensors areevenly arranged at one end of the pipe for exciting theultrasonic guided wave and eight piezoelectric ceramicsensors are uniformly mounted along the circumference ata distance of 30 cm from the excitation end for receivingthe guided wave signal e excitation sensor is on thesame axis as the receiving sensor e defect position is1000mm from the end face e entire test process isshown in Figure 28

(1) e test pipeline is placed on a customized base thesurface of the pipeline is polished the sensor anddamage position are marked on the surface of the

5

First received signal

Damage signal

End-face echo signal

times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14

Figure 19 Guided time domain diagram of the Hilbert transform

Z

θ

r

Defect

Figure 20 Schematic diagram of the cylinder coordinate system ofthe model

S2

S3

S4

S5

S6

S7

S8

S1Defect

Figure 21 Receiving point number


pipeline and the piezoelectric ceramic sensor ispasted after wiping the installation position

(2) Connect the signal excitation piezoelectric sensorwith the signal amplifier and connect the signalreception piezoelectric sensor with the oscilloscopethrough the dividing connector

(3) Based on the numerical simulation results the ex-citation frequency suitable for the test pipeline is

selected and the guided wave propagation law in thelossless pipeline is studied according to the wave-form displayed by the oscilloscope

(4) At the damage location marker the crack is cutartificially the ultrasonic guided wave is activatedagain the data of each receiving sensor are collectedand the damage location is located by combining thenondestructive guided wave data

Table 2 Guide wave propagation distances between the signal receiving point and defect reflection point

Number First signaltime (μs)

End echo signaltime (μs)

Transmissionspeed (ms)

Damage signaltime (μs)

Timedelay (μs)

Propagationdistance (mm)

S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)

Figure 22 Single-defect imaging of pipe segment structure (a) overall display (b) partial display and (c) detail display


511 Nondamaged Straight Tube Experiment e test ofthe nondestructive pipe section structure is the basis forthe identification and location of the damaged pipe Afterthe outer surface of the test tube is polished the markactivates and accepts the sensor position Eight piezo-electric ceramic sensors are attached to the end and as thesignal exciter the sensors are evenly distributed on thesame circumference and each sensor is connected in

parallel with each other and corresponds to the sameguided excitation channel At a distance of 30 cm from theexcitation end 8 sensors were attached to the coaxial lineof the excitation end sensor as signal receiving means epiezoelectric ceramic sensor paste diagram is shown inFigure 29

e ArbExpress software is used to compile the sinu-soidal signals of different periods as the excitation signal ofthe active acoustic emission experiment and this signal caneffectively guarantee the signal-to-noise ratio of the guidedwave signal According to the numerical simulation resultsthe 5-cycle guided wave signal has the characteristics ofenergy concentration and high recognition erefore theguided wave signal with the number of cycles of 5 is selectedas the excitation guided wave signal

Referring to the excitation frequency of the numericalsimulation in the experiment 70KHz is preferred as theexcitation guide centre frequency and combined with thegroup velocity dispersion curve in the range of 20KHz to80KHz the centre frequency of the excitation guide wavesuitable for the test is found Finally based on the experi-mental results the most suitable guided wave frequency isdetermined to be 50 kHz According to the experimentalcomparison when the excitation frequency is 50KHz theguided wave signal has the best quality e time domainmap of the ultrasonic guided wave in the tube is shown inFigure 30

Table 3 Guide wave propagation distances between the signal receiving points and defect reflection point




Damagesignal time (μs)

Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)

Figure 23 Single-defect imaging of the tube segment structure with unknown axial positioning (a) partial display and (b) detail display

S2

S3

S4

S5

S6

S7

S8

S1 Defect

Figure 24 Schematic diagram of the defects and sensor layout


Table 4 Guided wave propagation distances between the receiving point and the defect boundary





Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1

140447 ndash h139701 ndash h

Figure 25 Guided wave propagation distances

1000

(a)

B A

(b)

Figure 26 Single-defect segment imaging (a) partial display and (b) detail display

Table 5 Double-defect guided signal data

NumberFirst signalreceptiontime (μs)

End echosignal

time (μs)

Wavespeed (ms)

Near-enddefect echotime (μs)

Proximal defectsignal propagationdistance (mm)

Remote defectecho time (μs)

Remote defectsignal propagationdistance (mm)

S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796


e nondestructive signal is subjected to Hilbert trans-form and the initial receiving signal time is 1091 μs the endecho signal receiving time is 11257 μs and the calculatedultrasonic guided wave propagation speed in the pipe segmentis 531182ms Combined with the dispersion curve thetheoretical value of the 50KHz guided wave group velocity inthe pipe segment is 533449ms and the error between thiswave velocity and the experimental value is 042

512 Single-Defect Pipe Section Experiment e position ofthe piezoelectric ceramic sensor that excites the guided waveand the received signal is the same as above and the re-ceiving sensors are numbered counterclockwise from S1 to

1000

500

(a)

1000

(b)

500

(c)

Figure 27 Double-defect guided wave imaging of the pipe section structure (a) partial display (b) distal detail and (c) proximal detail

Arbexpressapplication

Arbitary waveform generator

Power amplifier

Test pipe section

Oscilloscope

Figure 28 Acoustic emission test flowchart

Figure 29 Piezoelectric ceramic sensor paste

008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal


Figure 30 Time domain map of the ultrasonic guided wave in thenondestructive section


S8 A ring-shaped through-hole crack with a length of57mm and a width of 2mmwas cut at a distance of 1m fromthe excitation end and the defect axis coincided with the S1sensor axis e centre point of the defect boundary near theexcitation end was positioned at (1095 0deg 1000) e cracklocation is shown in Figure 31

In the experiment eight excitation piezoelectric ceramicsheets were used to simultaneously excite the guided wavethe excitation frequency was 50 kHz the excitation voltagewas 10V and eight signal receiving sensor data signals weresequentially measured and saved in numerical order eexperimental data of the eight signal receiving points wereextracted and after the Hilbert transform the first receivedsignal time of the defect the damage signal receiving timeand the end-face echo time were obtained the sorted dataare shown in Table 6

According to the three-point axial positioning methodthe two end points on the single-defect boundary are pointsA(10950 2295deg 996724) and B (10950 2295deg 996724)respectively

e axial position of the pipe can be determined by theaverage of the axial positions of the above two boundary endpoints which is 996589mm In the experiment the defectboundary near the excitation end of the pipe segment islocated 1m away from the excitation end face and the errorbetween the experimental measured value and the actualvalue is 034 therefore the error is small In the loopdirection the calculated angular dimension is 4339degwhereas the actual angular dimension is 30deg therefore theerror between the two values is large

52 Damage Imaging e axial positioning results calcu-lated above are substituted into Table 6 and the propagationdistance between the ultrasonic guided wave reflection pointand each signal receiving sensor is obtained the sorteddistance data are shown in Table 7

e defect boundary trajectory is drawn in MATLABand the obtained defect boundary image is shown inFigure 32

e MATLAB imaging results were combined andtransformed them into a cylindrical coordinate system toobtain the two end points A(1095 2050deg 99650) andB (1095 minus 1950deg 99670) of the defect boundarye axial

defect of the pipe segment is 9966mm which is very smallcompared with the previous calculation results In the cir-cumferential direction the angular dimension is 4000deg

Combined with the results of the above three-point axialpositioning and circular trajectory imaging it is not difficult

Figure 31 Pipeline defects

Table 6 Experimental data of the guided wave signals in singledamage section


End echosignal time

(μs)

Damagesignal time

(μs)

Calculateddistance (mm)

S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636

Table 7 Propagation distances between the reflection point and thesignal receiving point


End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)

Figure 32 Single segment damage imaging (a) partial display and(b) detail display


to find that the three-point axial positioning method caneffectively ascertain the axial position of the defect and thecircular trajectory imaging can also reflect the circumfer-ential direction and length of the defect However bothmethods rely on the accuracy of the ultrasonic guided wavesignal data

When using the experimental data for defect guidedwave imaging there is a case where there is a large error inthe calculated hoop size and the actual size e reasons forthis error can be attributed to the following three points (1)Uneven distribution of piezoelectric ceramic sensor arraysfor guided wave excitation and reception in the circum-ferential direction of the pipe segments in the experimentthere was a manual error in the positioning and installationof the sensors (2) e effect of sensor size the piezoelectricceramic sensor used in this experiment has a specification of25mm times 4mm and the sensor size also affects the result ofthe guided wave signal reception (3) e influence of theultrasonic guided wave signal acquisition frequency in theexperiment the accuracy of the guided wave signal acqui-sition is 05 and the ultrasonic guided wave propagationspeed is 5311824ms

6 Conclusion

is work studies the influence of single defect and doubledefect on the propagation characteristics of L(02) modalguided waves analyzed for the straight pipe section structuree three-point axial positioning method and circular tra-jectory imaging method suitable for single-defect anddouble-defect positioning and imaging of pipe segments areproposed and applied and we established an experimentalplatform for tube segment structure defect identificationlocalization and imaging research

Numerical results indicate that the guidedwavewith the bestdamage recognition is excited at 70kHz the number of exci-tation signal cycles is 5 and the propagation path of the ul-trasonic guided wave between the defect boundary emissionpoint and the signal receiving point is not a straight line butspreads along the two simple shortest paths e relationshipbetween the depth and circumferential length of the single defectand the reflection coefficient of the guided wave is discussed Asthe circumferential length of the single-defect increases thereflection coefficient of the guided wave increases linearly Withthe increase in the depth of the defect the reflection coefficient ofthe guided wave is linearly increased During the investigation ofthe double-defect size the distance between the double defectsand the relative positions of the double defects the existence ofnear-end defects affects the damage guided wave recognitioneffect of the distal defect and the new waveform formed by theboundary reflection of the near-end defect may be far awayeend defect reflection waveform forms a superposition whichreduces the signal recognition accuracy

e three-point circumferential positioning method andthe circular trajectory imaging method can be applied indouble-defect axial positioning and damage imaging of thepipe segment and can effectively reflect the axial positioningcharacteristics of the double defect and the axial dimensioninformation of the double defect For the results of ultrasonic

guided wave detection of single-defect tube segments thethree-point axial positioning method and the circular tra-jectory imaging method can also be effectively appliedHowever comparing the numerical simulation data imagingresults it can be seen that the above two methods have astrong dependence on the accuracy of the guided wave signaldata In other words if the guided wave signal quality ispoor the above two methods cannot accurately reflect theaxial positioning of the defect or the circumferential lengthinformation

Data Availability

e numerical data used to support the findings of this studyare included within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the Natural Science Foundationof Heilongjiang Province of China (QC2016057)

References

[1] R N Tuttle ldquoCorrosion in oil and gas productionrdquo Journal ofPetroleum Technology vol 39 no 7 pp 756ndash762 1987

[2] K G Boving ldquoNDE methods used in optimum maintenanceprograms for oil and gas-pipelinesrdquo Insight vol 37 no 6pp 444ndash446 1995

[3] J L Rose Ultrasonic Waves in Solid Media CambridgeUniversity Press Cambridge UK 1999

[4] A Love A Treatise on the Mathematical gteory of ElasticityDover Publications Mineola NY USA 1994

[5] R M Davies ldquoA critical study of the Hopkinson pressurebarrdquo Philosophical Transactions of the Royal Society AMathematical Physical and Engineering Sciences vol 240no 821 pp 375ndash457 1948

[6] D C Gazis ldquoree-dimensional investigation of the propa-gation of waves in hollow circular cylinders I Analyticalfoundationrdquo Journal of the Acoustical Society of Americavol 31 no 5 pp 568ndash573 1959

[7] M G Silk and K F Bainton ldquoe propagation inmetal tubingof ultrasonic wave modes equivalent to Lamb wavesrdquo Ul-trasonics vol 17 no 1 pp 11ndash19 1979

[8] J L Rose J J Ditri A Pilarski K Rajana and F Carr ldquoAguided wave inspection technique for nuclear steam generatortubingrdquo NDT amp E International vol 27 no 6 pp 307ndash3101994

[9] M F Zhang C Lu G Z Chen and P Men ldquoModeling three-dimensional ultrasonic guided wave propagation and scat-tering in circular cylindrical structures using finite elementapproachrdquo Physics Procedia vol 22 pp 112ndash118 2011

[10] R Carandente J Ma and P Cawley ldquoe scattering of thefundamental torsional mode from axi-symmetric defects withvarying depth profile in pipesrdquo Journal of the AcousticalSociety of America vol 127 no 6 pp 3440ndash3448 2010

[11] H Nishino K Yoshida H Cho and M Takemoto ldquoProp-agation phenomena of wideband guided waves in a bendedpiperdquo Ultrasonics vol 44 pp e1139ndashe1143 2006


[12] B Verma T K Mishra K Balasubramaniam et al ldquoIn-teraction of low-frequency axisymmetric ultrasonic guidedwaves with bends in pipes of arbitrary bend angle and generalbend radiusrdquo Ultrasonics vol 54 no 3 pp 801ndash808 2014

[13] W Zhou and M Ichchou ldquoWave propagation in mechanicalwaveguide with curved members using wave finite elementsolutionrdquo Computer Method in Applied Mechanic and En-gineering vol 199 no 33ndash36 pp 2099ndash2109 2010

[14] J Mu and J L Rose ldquoGuided wave propagation and modedifferentiation in hollow cylinders with viscoelastic coatingsrdquoJournal of the Acoustical Society of America vol 124 no 2pp 866ndash874 2008

[15] F Deng B Wu and C F He ldquoA time-reversal defectidentifying method for guided wave inspection in pipesrdquoJournal of Pressure Vessel Technology vol 130 no 2 article021503 2008

[16] Y Da G Dong B Wang D Liu and Z Qian ldquoA novelapproach to surface defect detectionrdquo International Journal ofEngineering Science vol 133 pp 181ndash195 2018

[17] M El Mountassir G Mourot S Yaacoubi and D MaquinldquoDamage detection and localization in pipeline using sparseestimation of ultrasonic guided waves signalsrdquo IFAC-Paper-sOnLine vol 51 no 24 pp 941ndash948 2018

[18] J He L Yang X D Sun and M P Hu ldquoDamage identifi-cation in welded structures using symmetric excitation ofLamb wavesrdquo Advances in Mechanical Engineering vol 10no 9 2018

[19] P Belanger P Cawley and F Simonetti ldquoGuided wavediffraction tomography within the born approximationrdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 57 no 6 pp 1405ndash1418 2010

[20] K R Leonard and M K Hinders ldquoGuided wave helical ul-trasonic tomography of pipesrdquo Journal of the Acoustical So-ciety of America vol 114 no 2 pp 767ndash774 2003


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wave excitation and signal receiving technology Zhenget al [9] used the FE method to establish a 3D pipe modelwhich simulates the applied force for generating the desiredguided waves e phenomenon shows that L(02) guidedwave mode conversion provides valuable theoreticalguidance for the pipeline on-site testing and laboratorytests Carandente et al [10] proposed a study of the re-flection of the fundamental torsional mode T(01) from anaxisymmetric defect with varying depth profile via finiteelement modeling and experimental validation Nishinoet al [11ndash13] studied the guided mode transition of guidedwaves under different elbow angles ey find that theinfluence of the curved member also complicates the ex-planation of the reflected signal due to the presence of localdamage

In recent years foreign experts and scholars have beenworking to improve the ability of ultrasonic guided wavesto detect and locate defects in pipeline structures Mu andRose [14] solved the problem of guided wave propagationin free hollow cylinders with viscoelastic coatings by asemianalytical finite element (SAFE) method and theo-retical proof of the orthogonality between guided wavemodes in a viscoelastic coated hollow cylinder is providedby them Deng et al [15] used the temporal-spatial focusingeffects of the time-reversal method on the guided waveinspection in pipes and improve ultrasonic guided wavedetection capabilities e phenomena of energy focusingcan magnify the small defect and the location of the defectis given simultaneously Da et al [16] proposed theQuantitative Detection of Fourier Transform (QDFT) anovel approach capable of providing a high level of ac-curacy and efficiency for nondestructive detection of de-fects e proposed approach contributes to thecharacterization of surface defects and would also broadenthe scope of nondestructive defect inspection using ul-trasonic guided waves El Mountassir et al [17] proposed anew method for damage detection and localization ofpipeline structures which is based on the sparse estimationof the measured signals by the reference signals esparsity helps to enhance damage detectability because adamaged signal will have a high estimation error comparedto that of a healthy signal

In this paper based on the ultrasonic guided wavetheory the dispersion curve of the pipeline structure isdrawn and the dispersion characteristics of the guidedwave are analyzed Second ABAQUS software is used toestablish a finite element model of a pipe structure tosimulate the propagation behaviours of ultrasonic guidedwaves in straight pipe sections and the damage identifi-cation location and imaging of single cracks and doublecracks Based on the ellipse localization method we pro-posed a new method for damage localization of straightpipe structures which combines the data of multiple signalreceiving points and axially locates the defect boundary bya three-point positioning method Finally an ultrasonicguided wave detection experiment of a straight pipe sectionwith a single defect is performed and the results arecompared with the simulation results to verify the feasi-bility of the simulation

2 Basic Theory

21 Concept ofUltrasonicGuidedWaves e propagation ofmechanical vibration in an elastic medium is called an elasticwave (sound wave) the elastic medium is defined as awaveguide and the ultrasonic wave propagating in thewaveguide is called an ultrasonic guided wave e ultra-sonic guided wave is essentially a mechanical vibrationgenerated by the disturbance source that propagates throughthe waveguide which contains the information of the dis-turbance source (excitation) and the mechanical charac-teristics of the waveguide material

e frequency of the ultrasonic guided wave is higherthan 20 kHz When an ultrasonic guided wave propagates inan elastic medium it has the advantages of good di-rectionality high energy strong penetrating power and noharm to the human body An ultrasonic guided wave cangenerate reflection refraction and waveform conversion atthe interface of the elastic medium e ultrasonic guidedwave can also be combined with the change in the intensityof the acoustic wave to determine the physical character-istics such as the size and position of the internal defects of acomponent

22 Drawing of the Dispersion Curve

221 Group Velocity and Phase Velocity of Guided WavesGroup velocity (cg) and phase velocity (cp) are the two mostbasic concepts in guided wave theory e group velocitycharacterizes the propagation velocity of the overall waveenergy of a pulse wave whereas the phase velocity is thevelocity that directs a fixed phase point of the wave in thepropagation direction For waves with only a single fre-quency and wavelength the phase velocity is equivalent tothe group velocity e conventional guided wave propa-gation velocity is the group velocity of the guided wave andthe phase velocity does not reflect the propagation velocity ofthe guided wave as a whole in the waveguide medium erelationship between the group velocity and phase velocity isas follows

cg d(ω)

d(k)

d kcp1113872 1113873

dk cp + k

d cp1113872 1113873

dk (1)

222 Dispersion Curve is paper selects a 20 type steelpipe with an outer diameter of 219mm and a wall thickness of8mm e elastic modulus of the material is 206 times 105Poissonrsquos ratio is 0305 and the material density is 7850 kgm3According to the dispersion equation the dispersion curve isdrawn in conjunction with MATLAB software as shown inFigure 1

e dispersion curve shows that the L(02) mode wave isin the 20sim100 kHz region and the velocity of the guidedwave group hardly changes with respect to the frequency Inthis frequency band the guided wave does not have dis-persion therefore this excitation frequency of the probe issuitable for ultrasonic guided wavese L(02) mode guidedwave has the largest group velocity and the excitation







dlt110

CL

f (2)





n1113888 11138891113888 1113889 times sin(2πft) (3)






0 50 100 150 200Frequency (kHz)

0

2000

4000

6000G

roup

spee

d (m

s)

L(02)

L(01)

T(01)F(12) F(11)

F(13)





Poissonrsquosratio

Density(kgm3)


x

y

z

x

y

z










Defect location

x yz

Received signal


Defect





15times10ndash9

times10ndash3

Damage signal

1

05

0

Disp

lace

men

t (m

)

ndash05

ndash10 02 04 06

Time (s)08 1 12

(a)

times10ndash10

Damage signal

8

Disp

lace

men

t (m

)

ndash8

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(b)

Damage signal

8times10ndash10

Disp

lace

men

t (m

)

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(c)

Damage signal

times10ndash10

6

4

2

0

ndash2

ndash4D

ispla

cem

ent (

m)

ndash6


Time (s)08 1 12

(d)

Damage signal



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damage signal

times10ndash104

Disp

lace

men

t (m

)

ndash4

3

2

1

0

ndash0

ndash2

ndash3


Time (s)08 1 12

(f )

Damage signal

times10ndash10

4

Disp

lace

men

t (m

)

ndash4

ndash3

ndash2

ndash1

0

1

2

3


Time (s)08 1 12

(g)

Damage signal

times10ndash103

Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2


Time (s)08 1 12

(h)














04035

03025

Refle

ctio

n co

effic

ient

02015

01005

030 40 50 60 70




r

z

Defect 2





signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)


6

1

2

3

4

5

Disp

lace

men

t (m

)


075 085 0908

times10ndash10



Receivedsignal

Defect 1

r

z

Defect 2



x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







dlt110

CL

f (2)





n1113888 11138891113888 1113889 times sin(2πft) (3)






0 50 100 150 200Frequency (kHz)

0

2000

4000

6000G

roup

spee

d (m

s)

L(02)

L(01)

T(01)F(12) F(11)

F(13)





Poissonrsquosratio

Density(kgm3)


x

y

z

x

y

z










Defect location

x yz

Received signal


Defect





15times10ndash9

times10ndash3

Damage signal

1

05

0

Disp

lace

men

t (m

)

ndash05

ndash10 02 04 06

Time (s)08 1 12

(a)

times10ndash10

Damage signal

8

Disp

lace

men

t (m

)

ndash8

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(b)

Damage signal

8times10ndash10

Disp

lace

men

t (m

)

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(c)

Damage signal

times10ndash10

6

4

2

0

ndash2

ndash4D

ispla

cem

ent (

m)

ndash6


Time (s)08 1 12

(d)

Damage signal



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damage signal

times10ndash104

Disp

lace

men

t (m

)

ndash4

3

2

1

0

ndash0

ndash2

ndash3


Time (s)08 1 12

(f )

Damage signal

times10ndash10

4

Disp

lace

men

t (m

)

ndash4

ndash3

ndash2

ndash1

0

1

2

3


Time (s)08 1 12

(g)

Damage signal

times10ndash103

Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2


Time (s)08 1 12

(h)














04035

03025

Refle

ctio

n co

effic

ient

02015

01005

030 40 50 60 70




r

z

Defect 2





signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)


6

1

2

3

4

5

Disp

lace

men

t (m

)


075 085 0908

times10ndash10



Receivedsignal

Defect 1

r

z

Defect 2



x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Defect location

x yz

Received signal


Defect





15times10ndash9

times10ndash3

Damage signal

1

05

0

Disp

lace

men

t (m

)

ndash05

ndash10 02 04 06

Time (s)08 1 12

(a)

times10ndash10

Damage signal

8

Disp

lace

men

t (m

)

ndash8

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(b)

Damage signal

8times10ndash10

Disp

lace

men

t (m

)

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(c)

Damage signal

times10ndash10

6

4

2

0

ndash2

ndash4D

ispla

cem

ent (

m)

ndash6


Time (s)08 1 12

(d)

Damage signal



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damage signal

times10ndash104

Disp

lace

men

t (m

)

ndash4

3

2

1

0

ndash0

ndash2

ndash3


Time (s)08 1 12

(f )

Damage signal

times10ndash10

4

Disp

lace

men

t (m

)

ndash4

ndash3

ndash2

ndash1

0

1

2

3


Time (s)08 1 12

(g)

Damage signal

times10ndash103

Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2


Time (s)08 1 12

(h)














04035

03025

Refle

ctio

n co

effic

ient

02015

01005

030 40 50 60 70




r

z

Defect 2





signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)


6

1

2

3

4

5

Disp

lace

men

t (m

)


075 085 0908

times10ndash10



Receivedsignal

Defect 1

r

z

Defect 2



x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




15times10ndash9

times10ndash3

Damage signal

1

05

0

Disp

lace

men

t (m

)

ndash05

ndash10 02 04 06

Time (s)08 1 12

(a)

times10ndash10

Damage signal

8

Disp

lace

men

t (m

)

ndash8

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(b)

Damage signal

8times10ndash10

Disp

lace

men

t (m

)

ndash6

ndash4

ndash2

0

2

4

6


Time (s)08 1 12

(c)

Damage signal

times10ndash10

6

4

2

0

ndash2

ndash4D

ispla

cem

ent (

m)

ndash6


Time (s)08 1 12

(d)

Damage signal



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damage signal

times10ndash104

Disp

lace

men

t (m

)

ndash4

3

2

1

0

ndash0

ndash2

ndash3


Time (s)08 1 12

(f )

Damage signal

times10ndash10

4

Disp

lace

men

t (m

)

ndash4

ndash3

ndash2

ndash1

0

1

2

3


Time (s)08 1 12

(g)

Damage signal

times10ndash103

Disp

lace

men

t (m

)

ndash3

ndash2

ndash1

0

1

2


Time (s)08 1 12

(h)














04035

03025

Refle

ctio

n co

effic

ient

02015

01005

030 40 50 60 70




r

z

Defect 2





signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)


6

1

2

3

4

5

Disp

lace

men

t (m

)


075 085 0908

times10ndash10



Receivedsignal

Defect 1

r

z

Defect 2



x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













04035

03025

Refle

ctio

n co

effic

ient

02015

01005

030 40 50 60 70




r

z

Defect 2





signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)


6

1

2

3

4

5

Disp

lace

men

t (m

)


075 085 0908

times10ndash10



Receivedsignal

Defect 1

r

z

Defect 2



x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)


6

1

2

3

4

5

Disp

lace

men

t (m

)


075 085 0908

times10ndash10



Receivedsignal

Defect 1

r

z

Defect 2



x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


x Cg middotΔt2 (4)









(5)




radic (6)





Defect 2Defect 1

r








Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(a)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(b)


signal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(c)


signal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(d)

Damagesignal 1

Damagesignal 2



Disp

lace

men

t (m

)

ndash5


Time (s)08 1 12

(e)

Damagesignal 1

Damagesignal 2

times10ndash106

45

3210


Disp

lace

men

t (m

)

ndash6ndash5


Time (s)08 1 12

(f )









6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








6

1

2

3

4

5

Disp

lace

men

t am

plitu

de (m

)


80 90

times10ndash10



Received

Defect 1r

z

Defect 2


Defect 1

Corner

Defect 2



0

6times10ndash10

5

4

3

2

1

020 40 60


Disp

lace

men

t am

plitu

de (m

)

80 100 120 140 160 180


Excitingend Receive

X

Defect












5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











5


Damage signal


times10ndash10

times10ndash3

4

3

2

Disp

lace

men

t am

plitu

de (m

)

1

00 02 04 06

Time (s)08 1 12 14


Z

θ

r

Defect


S2

S3

S4

S5

S6

S7

S8

S1Defect













Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69861S2 9535 112780 523028 36300 26765 70188S3 9545 112785 523053 36580 27035 71607S4 9540 112770 523104 37030 27490 74001S5 9535 112786 522998 37645 28110 77215S6 9530 112770 523053 37025 27495 74013S7 9545 112785 523053 36575 27030 71581S8 9550 112780 523104 36310 26760 70183

3000 (unit mm)

2500

2000

1500

1000

500

N

00

ndash100100

100 0 ndash100

(a)

1000

(b)

B A

(c)












Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











Timedelay (μs)


S1 9530 112785 522977 36235 26705 69830S2 9535 112780 523028 36300 26765 70157S3 9545 112785 523053 36580 27035 71576S4 9540 112770 523104 37030 27490 73970S5 9535 112786 522998 37645 28110 77184S6 9530 112770 523053 37025 27495 73982S7 9545 112785 523053 36575 27030 71550S8 9550 112780 523104 36310 26760 70152

1000

(a)

B A

(b)


S2

S3

S4

S5

S6

S7

S8

S1 Defect








Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Timedelay (μs)


S1 9530 112775 523028 36240 26710 139701S2 9530 112760 523104 36255 26725 139799S3 9525 112775 523002 36440 26915 140766S4 9540 112755 523180 36825 27285 142750S5 9545 112765 523154 37385 27840 145646S6 9535 112760 523129 37245 27710 144959S7 9525 112775 523002 36715 27190 142257S8 9540 112775 523078 36380 26840 140447

142257 ndash h

Defect

h

S6πd8

S7πd8

S8πd8

S1x1



1000

(a)

B A

(b)




End echosignal

time (μs)

Wavespeed (ms)





S1 9540 112995 521966 24755 795737 36240 1396397S2 9540 112805 522926 24895 803059 36310 1400058S3 9540 112780 523053 25345 826594 36575 1413917S4 9540 112785 523028 25970 864511 37025 1437452S5 9535 112775 523053 27020 914457 37685 1472231S6 9540 112780 523053 25980 864249 37035 1437975S7 9540 112805 522926 25345 826332 36575 1413917S8 9535 112800 522926 24895 802797 36300 1399796




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




1000

500

(a)

1000

(b)

500

(c)




Power amplifier

Test pipe section

Oscilloscope



008

times10ndash3

006

0020

004

ndash002Vol

tage

(V)

ndash004ndash006

0 02 04 06Time (s)

08 1 12 14

End echo signal
















End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 1389308S2 10980 112580 37150 1390104S3 10920 112565 37290 1400728S4 10900 112565 37745 1425959S5 10925 112740 38485 1463939S6 10910 112570 37770 1426756S7 10920 112560 37310 1401790S8 10925 112580 37105 1390636



End echosignal time

(μs)

Damagesignal time

(μs)


S1 10910 112570 37065 692719S2 10980 112580 37150 693515S3 10920 112565 37290 704139S4 10900 112565 37745 729370S5 10925 112740 38485 767350S6 10910 112570 37770 730167S7 10920 112560 37310 705201S8 10925 112580 37105 694047

1000

500

(a)

1000 B A

(b)





6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




6 Conclusion





Data Availability




Acknowledgments


References

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

ResearchonPipelineDamageImagingTechnologyBasedon …downloads.hindawi.com/journals/sv/2019/1470761.pdf · 2019-07-30 · 3.5.2. Relationship between the Guided Wave Propagation Characteristics