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Magnetostriction-Based Omni-Di
Magnetostriction-Based Omni-Di

Magnetostriction-Based Omni-Directional Guided Wave Transducer for High-Accuracy Tomography

of Steel Plate Defects

Zheng Wei,Songling Huang,Shen Wang,and Wei Zhao

Abstract—An omni-directional(OD)magnetostriction-based electromagnetic acoustic transducer(EMAT)is suitable for use in the guided wave(GW)tomography of steel plate defects.Because the GW is characterized by multiple modes and frequency dispersion,the waveforms detected by the traditional magnetostriction-based OD GW EMATs are complex, which substantially reduces the accuracy of projection data extraction and then decreases the quality of GW tomography and the accuracy of defect quanti?cation.This paper proposes a new magnetostriction-based OD EMAT to generate shear-horizontal(SH)GWs of a special mode to reduce the interference of multiple modes and the frequency dispersion of GWs.The new EMAT consists of a contra-?exure coil and a pre-magnetized thin circular nickel foil.The theoretical background and working principle of this EMAT are presented. The results of pitch–catch experiments on a healthy steel plate demonstrate that the new EMATs can transmit and receive purer single SH1-mode GWs and have improved the accuracy of projection data extraction,compared with the traditional EMATs.The performance of SH1wave tomography of the traditional and new EMAT arrays are compared via experiments implemented on a3-mm-thick steel plate with an arti?cial corrosion defect.The experimental results indicate that higher tomographic reconstruction quality,clearer normalized slowness curves with less noise and higher accuracy of tomographic defect quanti?cation can be achieved by the new EMAT array, which has improved the projection data extraction accuracy, compared with the traditional EMAT array.

Index Terms—Omni-directional EMAT,shear-horizontal guided wave,magnetostriction,tomography,steel plate defect.

I.I NTRODUCTION

T HE technique of tomography of steel plate defects based on ultrasonic guided wave(GW)inherits the merits of GW inspection technology,such as speed and ef?ciency during long-range inspection[1].It can utilize a set of Manuscript received May31,2015;revised July3,2015and July28,2015; accepted July28,2015.Date of publication July30,2015;date of current version September14,2015.This work was supported in part by the National High Technology Research and Development Program of China (863Program)under Grant2011AA090301,in part by the Tsinghua University Initiative Scienti?c Research Program under Grant20111080983, and in part by the National Natural Science Foundation of China under Grant51107058.The associate editor coordinating the review of this paper and approving it for publication was Prof.Istvan Barsony.(Corresponding author:Songling Huang.)

The authors are with the State Key Laboratory of Power Systems, Department of Electrical Engineering,Tsinghua University,Beijing100084, China(e-mail:weizhengbj@https://www.sodocs.net/doc/1f9797588.html,;huangsling@https://www.sodocs.net/doc/1f9797588.html,; wangshen@https://www.sodocs.net/doc/1f9797588.html,;zhaowei@https://www.sodocs.net/doc/1f9797588.html,).

Color versions of one or more of the?gures in this paper are available online at https://www.sodocs.net/doc/1f9797588.html,.

Digital Object Identi?er10.1109/JSEN.2015.2462834GW inspective data,which are referred to as projection data, from all directions to capture images of steel plate defects and obtain detailed information about defects via a certain algorithm.In existing studies,GW tomography is implemented with different types of projection data,imaging algorithms and transducer array geometries[2]–[4].

Omni-directional(OD)GW transducers offer a convenient and cost-effective method for transmitting and receiving GWs from all directions,to facilitate the collection of projection data in all https://www.sodocs.net/doc/1f9797588.html,pared with OD piezoelectric GW transducers[5],[6],electromagnetic acoustic transducers(EMATs)[7],[8]have several advantages such as the ability to control the modes of the generated GWs using different types of permanent magnets and coils.Thus, they are suitable for being used as OD GW transducers. In previously published papers,Lorentz force-based OD EMATs have been employed to omni-directionally transmit and receive GWs and to conduct GW tomog-raphy[9],[10].Compared with Lorentz force-based OD GW EMATs,magnetostriction-based OD GW EMATs have unique advantages,such as higher transducing ef?ciency on steel plates and superior performance at high temperatures[11].Kwun[12]and Light et al.[13] proposed a patch-type magnetostriction-based EMAT that employs a magnetostrictive patch and a traditional racetrack coil(referred to as a traditional EMAT).This traditional EMAT can omni-directionally transmit and receive GWs in steel plates.Because GW is characterized by multiple modes and frequency dispersion[14],the detected waveforms of traditional EMATs are always complex and contain GW signals of numerous different modes.The complexity of the waveforms of traditional EMATs substantially in?uences the accuracy of extracting the projection data,which comprises the input of GW tomography.Thus,the low accuracy of the projection data extraction deteriorates the quality of GW tomography and results in low accuracy for the defect quanti?cation.

Methods for solving these problems include consideration of certain frequency components of GW signals using time-frequency analysis[15].Due to the serious frequency dispersion and time-domain tailing phenomenon of the GW signals of traditional EMATs,the GW signals of useful modes usually cannot be completely separated from other modes even if time-frequency analysis is used.Recently,some mode-controlled magnetostriction-based OD GW EMATs have

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See https://www.sodocs.net/doc/1f9797588.html,/publications_standards/publications/rights/index.html for more information.

Fig.1.Model of the free steel plate in the space.

been investigated.These EMATs are employed to generate Lamb wave or shear-horizontal(SH)GWs of special modes in steel plates[11],[16],which obtains a more distinct interpretation of the received signals and improved accuracy of the projection data extraction.Because the GW of different modes have different wavelengths at given frequency,each of these EMATs realizes the mode selections by adjusting the radii of the circular magnetostrictive patch or the coil in the EMAT to ensure that the resonant wavelengthλpatch of the EMAT is equivalent to the wavelength of the GW of the desired mode at a speci?c operation frequency.As a result,the generated GW of the desired mode at the selected frequency will have a larger amplitude than the generated GW of other modes.However,at the selected frequency,when GW of an unwanted mode has the wavelength that is not equivalent to theλpatch of the EMAT but falls within a certain range,which contains theλpatch,this GW of the unwanted mode can be effectively generated by the EMAT and so is the GW of the desired mode,despite the smaller amplitude of the former compared with the latter.Thus,the mode selections of these EMATs are fuzzy and sometimes fail.

To overcome these drawbacks,this paper proposes a new magnetostriction-based OD EMAT(referred to as the new EMAT)to transmit and receive the pure single1st-order SH mode GW(SH1wave)in steel plates.The new EMAT has a simple structure that only includes a contra-?exure coil(CFC)and a piece of pre-magnetized thin circular nickel foil.The EMAT with this new structure is utilized for OD GW generation and GW tomography of steel plate defects.The theoretical background and the working principle of the new EMAT are presented and https://www.sodocs.net/doc/1f9797588.html,ing the experimental results,which are based on the method of pseudo Wigner-Ville distribution(PWVD),the ability to transmit and receive the pure single SH1wave and the accuracy of projection data extraction of the traditional and new EMATs are compared. The performance of the traditional and new EMATs employed in the SH1wave tomography and defect quanti?cation are experimentally analyzed and compared.

II.S TRUCTURAL D ESIGN OF THE N EW

M AGNETOSTRICTION-B ASED OD GW EMAT

A.Theoretical Background of SH Mode GWs

To ensure that the new EMAT that is proposed in this paper achieves acceptable performance,the propagation characteris-tics of the SH mode GWs in steel plates and the ideal operation point of the new EMAT should be analyzed.The model of the free steel plate in the space is shown in Fig.1.

In Fig.1,the thickness d of the free steel plate is equivalent to2h.The planes in which x2=±h are the free surfaces

of Fig.2.SH wave frequency dispersion curves for the3-mm-thick steel plate: (a)Frequency dispersion curves of c p and(b)Frequency dispersion curves of c g.

the plate.In the plate,the linear vibration source of

the SH waves,which only has the displacements in the

x3direction,is located at x1=0,is uniform and is of in?nite extent in the x3direction.Thus,the SH waves generated

by this vibration source only have displacements in the x3direction,which are denoted by u3;these displacements are independent of x3.The wave equations of the generated SH waves in the free steel plate are

?2u3

?x21

+

?2u3

?x22

=1

c2T

?2u3

?t2(1) where c T is the velocity of the transverse wave in the free steel plate.The SH waves propagate along the x1direction and have speci?c distributions in the x2direction.By solving equation(1),the expressions of the u3are determined as[17] u s3(x1,x2,t)=B cos(qx2)×exp[i(kx1?ωt)](2)

u a3(x1,x2,t)=A sin(qx2)×exp[i(kx1?ωt)](3) where A and B are constants,q=(ω2/c2T?k2)1/2,k is the wave number,ω=2πf is the angular frequency and f is the frequency of the SH waves.Each of the solutions in equations(2)and(3)is independent of x3and consists of a traveling wave component along the x1direction and a standing wave component along the x2direction. Equations(2)and(3)express the symmetric mode SH waves and the antisymmetric mode SH waves,respectively.

The frequency dispersion equation of SH waves can be

achieved using equations(2)and(3)and the boundary con-

ditions of zero stress for the free steel plate in the space. According to the frequency dispersion equation and the de?n-ition of the phase and group velocities(c p=ω/k,c=d.ω/d k) of SH waves,the expression of c g of SH waves can be achieved as follows:

c g(f d)=c T

1?(nc T)2/(2f d)2(n∈{0,1,2,...})(4) The frequency dispersion curves of SH waves for the 3-mm-thick steel plate in this paper are calculated and shown in Fig.2.The operation frequency of the new EMAT should be selected in the range that contains the fewest SH wave modes to reduce the number of interferencing modes that need to be suppressed.As shown in equation(4),the(nc T)2/(2fd)2 should be less than or equal to1.Thus,the lower cut-off frequency f L of the n th-order SH wave can be achieved by solving(nc T)2=(2f L d)2[17].From solving this equation,

WEI et al.:MAGNETOSTRICTION-BASED OD-GUIDED WA VE TRANSDUCER FOR HIGH-ACCURACY TOMOGRAPHY6551

the2nd-order SH wave(SH2wave)has the lower cut-off frequency of f L=1MHz and the SH waves of higher order have the f L>1MHz.The results indicate that the range of0-1MHz contains the fewest SH wave modes;this range only contains the0th-order SH wave(SH0wave)and the 1st-order SH wave,which have lower cut-off frequencies of f L=0MHz and f L=0.53MHz,respectively.In order to avoid the interference of multi-modes characteristic,the operation frequency of the new EMATs should be chosen in the range of0-1MHz which contains only SH0wave and SH1wave.In addition,the c g of the SH0wave is a constant, whereas the c g of the SH1wave is sensitive to the plate thickness change induced by defects.Thus,the SH1wave is more suitable for defect detection and tomography. The frequency of665kHz is selected as the operation frequency,and the SH1wave is selected.The c p and c g of the 665kHz SH1wave in3-mm-thick steel plate are5357m/s and1911m/s,respectively,and the wavelength is8mm. The c p and c g of the665kHz SH0wave are both3200m/s.

B.The Structure and Working Principle of the New EMAT When ferromagnetic materials are placed in a magnetic ?eld,their dimensions change.This phenomenon is referred to as the magnetostrictive effect.In the inverse phenomenon, the change in dimension yields a magnetic induction,which is referred to as the inverse magnetostrictive effect.They can be expressed as

ε=s Hσ+d H(5)

B=d Tσ+μσH(6) whereε,σ,B and H represent the strain,stress,magnetic ?ux density and magnetic?eld strength,respectively;s H is the elastic compliance matrix,which is measured when H is constant;μσis the magnetic permeability matrix,which is measured whenσis constant;d is the piezomagnetic coef?cient matrix and d T is the transpose of d.For the new EMAT,the magnetostrictive effect is utilized to transmit SH waves and its inverse effect is employed to receive SH waves.

Similar to the traditional EMAT,the new EMAT is composed of a piece of thin circular nickel foil and a coil, as shown in Fig.3(a).The nickel foil and the coil are concentric.The couplant is located between the nickel foil and the steel plate.As shown in Fig.3(b),the racetrack coil is employed in the traditional EMAT.As shown in Fig.3(c),the CFC is employed in the new EMAT.Both types of coils are fabricated using printed circuit board(PCB) technology.For the convenience of discussion,a cylindrical coordinate system is established with its origin below the center of the CFC and in the middle plane of the plate, as shown in Fig.3(a)and(c).In the coordinate system,the r andθdirections represent the radial direction and circum-ferential direction of the CFC,whereas the direction of x2 comprises the thickness direction of the plate.The nickel foil, which is denoted by the shaded region enclosed with dashed lines in Fig.3(c),is pre-magnetized along theθdirection and has a circumferential static residual magnetic?eld H0θ

.Fig. 3.Structures and schematics of the magnetostriction-based OD GW EMATs:(a)Structure of the new EMAT,(b)Racetrack coil and (c)CFC.

When the pulse current I with the frequency f is activated, each annular wire in the CFC should induce a dynamic magnetic?eld H r in the r direction in the nickel foil.The superimposition of H0θand H r causes a periodically changed resultant magnetic?eld H c.Due to the impact of H c,when no external stress exists,a circumferentially uniform and periodically changing magnetostrictive force f Mθforms in the θdirection.The expression of the f Mθon the nickel foil under one annular wire can be derived from equation(5)and described as[18]

f Mθ=?2(1+ν)c66

εM

H0θ

?H r

?r(7) whereνis Poisson’s ratio,c66is the element of the elastic stiffness coef?cient matrix,andεM is the magnetostriction.

f Mθcauses a circumferentially uniform ultrasonic vibration in theθdirection in the nickel foil.The ultrasonic vibration propagates into the steel plate through a couplant and forms a circular vibration source of SH waves which has displacements only in theθdirection and is uniform in theθdirection. The linear vibration source of in?nite extent introduced in the previous part can be considered to be a circular vibration source with in?nite radius.In this situation,it has only circumferential displacements and is uniform in the circum-ferential direction;thus,it is approximately identical to the circular vibration source provided by the CFC annular wire. Thus,the conclusions in the previous part can be extended and employed to obtain the characteristics of the SH waves generated by the circular vibration source,which is provided by the CFC annular wire.The SH waves generated by any CFC annular wire propagate alon

g the r direction and have speci?c distributions in the x2direction.They only have displacements in theθdirection,whic

h are denoted by uθ;

6552IEEE SENSORS JOURNAL,VOL.15,NO.11,NOVEMBER2015 these displacements are independent ofθ.However,when

they propagate along the r direction,because their wave fronts

spread,their amplitudes reduce.These results indicate that the

circumferentially uniform OD SH waves can be generated in

the steel plate.When only the OD SH wave components that

propagate along the positive direction of r are considered,the

expressions of the u.θof the OD SH waves generated by any

CFC annular wire can be derived from equations(2)and(3)

and described as

u sθ(r,x2,t)=B o(r)cos(qx2)

×exp{i[k(r?r0)?ωt]}(r>r0)(8)

u aθ(r,x2,t)=A o(r)sin(qx2)

×exp{i[k(r?r0)?ωt]}(r>r0)(9)

where r0is the radius of the CFC annular wire.The

amplitudes A o(r)and B o(r)reduce as the r increases due

to the attenuation of the OD SH wave.

Considering that the SH waves of different modes have

different wavelengthsλs at any operation frequency f,

the mode selection of the new EMAT can be realized

by implementing a wavelength selection.According to

equations(8)and(9),when two OD SH waves are generated

by any two adjacent annular wires W1and W2of the CFC of

the new EMAT,which have the radii of r1and r2(r1

the phases of the vibrations induced by the two generated

OD SH waves at any radial location r a(r a>r2)in the steel

plate are?1=[2π(r a?r1)/λ?ωt+?10]and?2=[2π(r a-r2)/

λ?ωt+?20],respectively.λ,which is equivalent to2π/k,

is the wavelength of the generated OD SH wave.The

?10and the?20represent the initial phases.In addition,

(?10??20)is equivalent to±πbecause the special structure

of the CFC determines that,at any time,±πrepresents the

phase difference between the two dynamic magnetic?elds H r

induced by W1and W2.Thus,the phase difference between

the?1and?2is ?=?1??2=[2πl/λ+(?10??20)]=

[2πl/λ±π],where l=r2?r1is the constant distance

between any two adjacent annular wires,as shown in Fig.3(c).

At the selected f,when the two OD SH waves generated by

W1and W2have the same wavelength ofλ=[2l/(2p+1)],

where p is arbitrary integer and p≥0, ?is equivalent

to2pπ.At any radial location r a(r a>r2)in the steel plate,

the vibrations induced by these two OD SH waves have the

same phase and constantly reinforce each other.As a result,

at the selected f,the resultant SH wave with a wavelength of

λ=[2l/(2p+1)]generated by the entire EMAT can have an

effectively enhanced amplitude.Conversely,at the selected f,

when the two OD SH waves generated by the W1and the

W2have the sameλ,which is not equivalent to[2l/(2p+1)],

the vibrations induced by these two OD SH waves at the

radial location r a have different phases and continuously

weaken each other.As a result,at the selected f,the resultant

SH wave with a wavelength ofλ=[2l/(2p+1)]generated by

the entire EMAT can have an effectively suppressed amplitude.

By setting the parameter l of the proposed EMAT to satisfy

the following relation

f o=c p_SH1

λSH1

=c p_SH1

2l

(10)

where f o is the selected operation frequency,that is,665kHz,

and c p_SH1and theλSH1represent the phase velocity and the

wavelength of the SH1mode GW at the f o,respectively,it can

be ensured that only the SH1wave has a wavelength equivalent

to[2l/(2p+1)].Thus,only the SH1wave can be effectively

generated at f o.

Only the OD SH wave components that propagate along the

positive direction of r are considered in the above analyses.

Similarly,when the OD SH wave components that propagate

along the positive and negative directions of r are concurrently

considered and the parameter l is set,the inner diameter D

of the CFC of the new EMAT should be set to satisfy the

following relation

D=0.5mλSH1(m is odd number,m>0)(11)

In this manner,the two SH1wave components that propagate

along the positive and negative directions of r generated by

any CFC annular wire always reinforce each other,whereas the

two components of another mode SH wave,which propagate

along the positive and negative directions of r generated

by any CFC annular wire,always weaken each other.

In conclusion,when the parameters l and D of the CFC of

the new EMAT are set to satisfy the equations(10)and(11),

only the SH1wave can be effectively generated by the new

EMAT.Thus,the mode selection of the new EMAT may

be more accurate than the mode selection of the previously

reported EMATs[11]–[13],[16],which do not have the

CFC with the special structure.The increase in the accu-

racy of the mode selection of the EMAT is conducive to

improving the accuracy of the SH1wave time-of-?ight(TOF)

extraction.

III.T OMOGRAPHIC M ETHOD

A.SH Wave Tomographic Method

In this paper,the crosshole method[3],which is ef?cient

and convenient,is employed.In this method,the rectangu-

lar area of the steel plate being imaged is subdivided into

M×N small and equal meshes.The transmitters and receivers

are arranged along the two opposite sides of the area.The

SH1wave rays of all possible transmitter-receiver pairs pass

through these meshes from different directions.When a

SH1wave ray meets a mesh which contains defects,its c g will

change with the thickness of the defects area.The change in c g

induces change in the TOF projection data,which represents

the time required by the SH1wave pulse to propagate from

the transmitter to the https://www.sodocs.net/doc/1f9797588.html,ing the simultaneous iterative

reconstruction technique(SIRT)[4],the distribution of the

slowness(the reciprocal of the c g of the SH1wave)and the

defects of all meshes are determined by solving

T i=

n

j=1

L ij S j(i=1,2,...,m)(12)

where L ij is the length of the i-th ray in the j-th mesh;T i is

the TOF of the i-th ray,which is extracted from the waveform

detected by the i-th transmitter-receiver pairs,and S j is the

slowness of the j-th mesh to be solved.

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6553

Fig.4.The schematic diagram of experimental system.

B.Relation Between the TOF Extraction Accuracy

and the Tomographic Performances

The TOFs of the SH1waves are the inputs of the SIRT-based SH1wave tomography.The accuracy of the SH1wave TOF extraction directly determines the performance of the SH1wave tomography.If a group of SH1wave TOFs achieved by the EMAT array during the detection contain errors ofδT i(i=1,2,...,m),equation(12)will become

T i+δT i=

n

j=1

L ij(S j+δS j)

=

n

j=1

L ij S j+

n

j=1

L ijδS j(i=1,2,...,m)(13)

whereδS j denotes the error of the slowness.By subtracting equation(12)from equation(13),the relation between the errorsδT i and the errorsδS j can be obtained and described as follows:

δT i=

n

j=1

L ijδS j(i=1,2,...,m)(14)

According to equation(14),the errorsδS j are always very

sensitive to the errorsδT i because the majority of the achieved matrixes(L ij)in the SIRT-based SH1wave tomography are substantially ill-conditioned.If the SH1wave TOF extraction

has relative low accuracy,the large TOF errorsδT i will produce large slowness errorsδS j in tomography.The large errorsδS j will cause the tomographic result of the S j distribution in the imaged area to have numerous artifacts and noise.The artifacts and noise in the results will reduce the tomographic reconstruction quality and in?uence the accuracy of the defect quanti?cation based on the tomography.Thus, the accuracy of the SH1wave TOF extraction is important to improve the tomographic reconstruction quality and the accuracy of the defect quanti?cation.

IV.E XPERIMENTS AND R ESULTS

A.The Experimental System

To verify the ability to transmit and receive a pure single SH1wave,the accuracy of the SH1wave TOF extraction and the performance of the SH1wave tomography of the new EMAT,several experiments have been conducted on steel plates.A schematic of the experimental system is shown in Fig.4.There are two groups of EMATs:transmitters and receivers.The transmitters are excited by a RF power ampli?er (AG1024)that is controlled by a personal computer(PC). The peak-to-peak amplitude of the tone-burst pulse excitation signal is approximately500V,and the periodicity is

12.Fig.5.Detected waveforms for different values of L,when the new and traditional EMATs are employed for pitch-catch experiments:(a)L=20cm, using the new EMATs,(b)L=37cm,using the new EMATs,(c)L=20cm, using the traditional EMATs and(d)L=37cm,using the traditional EMAT. The transmitted SH wave passing pulse signals are detected by the receivers.The detected signals are?ltered and ampli?ed

by a signal conditioning circuit and subsequently collected by a high-speed DAQ card.The collected detection data are

sent to the PC to be calculated,analyzed and utilized for the

tomography.

The thickness of each new EMAT employed in experiments

is0.8mm,which equals to the summation of the

CFC thickness and the nickel foil thickness.The diameter of each new EMAT is32mm.The inner diameter D of the

CFC of each new EMAT is set to be1.5λSH1=12mm according to equation(11).The thickness of each tradi-

tional EMAT employed in experiments is0.8mm,which

equals to the summation of the racetrack coil thickness and the nickel foil thickness.The diameter of each traditional EMAT is32mm.

B.Transmitting and Receiving a Pure Single SH1Wave

To verify the ability to transmit and receive a pure single SH1wave of the new EMATs,the pitch-catch experiments are conducted on a3-mm-thick healthy steel plate.First,the new EMATs are employed as the transmitter and the receiver. When the distance L between the transmitter and the receiver are20and37cm,the originally detected waveforms are as shown in Fig.5(a)and5(b),respectively.Second,traditional EMATs are employed.When the distance L are20and37cm, the detected waveforms are as shown in Fig.5(c)and5(d), respectively.In each waveform of Fig.5(a)–(d),the signal on the left is the initial pulse induced by the receiver coil in the space of the pulse excitation current and the remaining signals are the passing pulses of GWs.

To identify the modes of GW signals in Fig.5,the original waveforms in Fig.5(a)–(d)are expanded in time-frequency domain by the PWVD method[15].The PWVD method has a relatively high time-frequency resolution when processing non-stationary signals and can be implemented using only one test,without the need for two-dimensional sampling.

6554IEEE SENSORS JOURNAL,VOL.15,NO.11,NOVEMBER

2015

Fig.6.Results of the time-frequency analysis using the PWVD method:(a)Analysis results for the waveform in Fig.5(a),(b)Analysis results for the waveform in Fig.5(b),(c)Analysis results for the waveform in Fig.5(c)and (d)Analysis results for the waveform in Fig.5(d).

In addition,it can eliminate the interference of cross-distribution by introducing a window function h (τ).When one of the original waveforms in Fig.5is denoted by s (t ),the W (t ,f s ),which is the time-frequency distribution of the energy of the signals in the s (t ),can be calculated by the PWVD method using the following equation:

W (t ,f s )=

h (τ)s ?(t ?τ

2)s (t +τ2)e ?j 2πf s τd τ.(15)

Thus,the time-frequency distributions of the signal energy

in the original waveforms in Fig.5(a)–(d)are calculated by equation (15)and shown in Fig.6(a)–(d).The GW modes can be identi?ed by comparing the achieved time-frequency distributions with the theoretical time-frequency curves of SH wave,which are calculated using equation (4).The results show that Fig.6(a)and (b)only contain the energy distribution of the SH1wave,whereas Fig.6(c)and (d)contain the overlapping energy distributions of the SH0and SH1waves.These results indicate that a purer single SH1wave can be transmitted and received by the new EMATs,compared with the traditional EMATs.The transmitting and receiving of the purer SH1wave is bene?cial for improving the accuracy of TOF extraction.

C.SH1Wave TOF Extraction

As previously mentioned,the accuracy of the SH1wave TOF extraction directly determines the tomographic perfor-mance of EMATs.Thus,the extracting accuracy of the SH1wave TOFs of the new and traditional EMATs are analyzed and compared.The results in Fig.6(a)and (c),which are achieved using the new EMAT and traditional EMAT

with

Fig.7.Energy-time curves at the frequency of f =665kHz for Fig.6(a)and (c):(a)Energy-time curves extracted from Fig.6(a)and (b)Energy-time curves extracted from Fig.6(c).

the same L ,are provided as examples for the SH1wave TOF extraction.

The exact TOF of the SH1wave should be the peak time of the SH1wave signal of the operation frequency in the detected waveform.However,the time-frequency distributions shown in Fig.6indicate that the SH1wave signal in each of the original detected waveforms consists of a group of SH1wave signals with different frequencies due to the frequency dispersion phenomenon.Thus,the peak time of the SH1wave signal in each of the original waveforms is not the exact SH1wave TOF.To eliminate the interference of frequency dispersion on TOF extraction,the energy-time curves at the operation frequency of f =665kHz for Fig.6(a)and (c)are extracted and shown in Fig.7(a)and (b).The extracted energy-time curves show the exact energy-time distributions of the SH1wave signals of the operation frequency,without the interference of the signal components of other frequencies.Thus,the peak time of the SH1wave signals in the extracted curves can be employed to estimate the exact SH1wave TOFs.This method of TOF extraction is referred to as the PWVD-based method.

According to the principle of the PWVD method,the signals a and b in Fig.7(a)and (b)represent the passing pulses of SH1waves.The signal a in the new EMAT waveform (FIG.7(a))has only one peak with steep edges.Thus,the peak time of the signal a is the SH1wave TOF,which can be accurately extracted using the new EMAT waveform.Because the signal b in the traditional EMAT waveform (FIG.7(b))is actually the SH1wave signal,which is partly superimposed on a SH0wave signal,its peak time is not the exact SH1wave TOF.Owing to aliasing of the SH1and SH0waves,the edges of signal b are gentle.Thus,accurate extraction of the SH1wave TOF by the traditional EMAT waveform is dif?cult.The SH1wave TOFs extracted using Fig.7(a)and (b)are 104.9μs and 99.6μs,respectively.As mentioned above,the theoretical group velocity c g_the of the 665kHz SH1wave in 3-mm-thick steel plate is 1911m/s.Thus,when L =20cm,the theoretical SH1wave TOF is t the =L /c g_the =104.7μs.The results indicate that the SH1wave TOF extracted using Fig.7(a)achieved by the new EMATs is more accurate than that extracted using Fig.7(b)achieved by the traditional EMATs.

To quantitatively compare the TOF extracting accuracy of the two types of EMATs,more pitch-catch experiments are conducted on the 3-mm-thick healthy steel plate.First,the new EMATs are employed as the transmitter and the receiver.

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Fig.8.Errors of TOFs achieved using the new and traditional EMATs as L changes.

When the distance L between the transmitter and the receiver changes from 0.2to 0.8m with a step of 1.5cm,the detected waveforms are achieved and the SH1wave TOFs are extracted using the PWVD-based method and recorded as T new (L ).Second,the traditional EMATs are employed.When L changes in the same manner,the detected waveforms are achieved and the SH1wave TOFs are extracted using the PWVD-based method and recorded as T tra (L ).For comparison,the errors of T new (L )and T tra (L )relative to the theoretical values are de?ned as

E ne w (L )=|T ne w (L )?T the (L )|(16)E tra (L )=|T tra (L )?T the (L )|

(17)

where T the (L )=L /c g_th is the theoretical SH1wave TOFs for the L ,and c g_th =1911m/s is the theoretical group velocity of the SH1wave at the operating frequency.The calculated E new (L )and E tra (L )are shown in Fig.8.The results indicate that the error E tra (L )is generally larger than the error E new (L ).As L increases,E tra (L )signi?cantly ?uctuates while the small E new (L )is always maintained.It testi?es that the accuracy of the SH1wave TOF extraction of the new EMATs is always higher than that of the traditional EMATs as L increases.

Considering the difference between the c g of the SH1wave and the c g of the SH0wave,the in?uence of aliasing of the SH1and SH0waves on the SH1wave TOF extraction may gradually reduce as L increases for traditional EMATs.Thus,the accuracy of the SH1wave TOF extraction of traditional EMATs may be improved as L increases.However,increase in L also induces increase in the size of the tomography devices composed of traditional EMATs,which may impair the ability of the tomography devices to image the steel plates in small or complex structures.

D.SH1Wave Tomography and Defect Quanti?cation To explore the performance of the new EMATs for use in SH1wave tomography and defect quanti?cation,the tomographic experiments are implemented on a 3-mm-thick steel plate that contains a defect using the new EMAT array and the traditional EMAT array,respectively.The experimental parameter settings are shown in Fig.9.All experiments are conducted in a 50×50cm imaged area of the steel plate,which is equally subdivided into 150×150small meshes.A 0.5-mm-deep arti?cial corrosion defect exists in this

area.

Fig.9.Parameter settings of the tomographic experiments.

The diameter d 0and the central location (x 0,y 0)of the defect are shown in Fig.9.The transmitter and receiver positions are equally established on two opposite sides of the area.In each tomographic experiment,the SH1wave TOFs of all possible transmitter-receiver pairs are obtained via pitch-catch experiments and the PWVD-based extracting method and are employed as the input data T i of the SIRT arithmetic.The tomographic result,which is the distribution of the normalized SH1wave S j ,is achieved after 100iterations.The relaxation parameter of the SIRT arithmetic is 0.1.

When the new EMATs are employed as the transmitters and receivers and the number of the transmitter-receiver pairs N are 14,12and 10,the experimental results of the SH1wave tomography are as shown in Fig.10(a)-(c).When the traditional EMATs are employed and N are 14,12and 10,the experimental results of the SH1wave tomography are as shown in Fig.10(d)-(f).For any two tomographic results that are achieved using the same N ,the tomographic results achieved by the new EMAT array contains fewer reconstructed artifacts in its background compared with the tomographic results achieved by a traditional EMAT array,which implies that the former has fewer slowness errors δS j than the latter.This ?nding can be explained as follows.The new EMATs have higher accuracy of the SH1wave TOF extraction than the traditional EMATs.According to equation 14,when the new EMATs are employed for tomography,the errors δS j can be reduced,compared with the traditional EMATs.Thus in the tomographic results which are the distributions of the S j ,the reconstructed artifacts are effectively suppressed and signi?cantly higher reconstruction quality are achieved by the new EMATs.These results correspond with the theoretical analysis.

Regardless of the use of new or traditional EMATs,the distortions of the reconstructed defects can be increased because the number of the transmitter-receiver pairs N is reduced,as demonstrated by the results in Fig.10.The reason for this phenomenon is as follows.For the SIRT-based SH1wave tomography,the tomographic result,which is the distribution of the SH1wave S j is determined by solving equation (12).In equation (12),the number of the unknowns S j is m ,whereas the number of the equations is n .To accurately solve S j ,a suf?cient number of equations are required,which implies that an adequate number of SH1wave

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Fig.10.Experimental results of the SH1wave tomography using the new and traditional EMAT arrays with different N :(a)N =14,using the new EMAT array,(b)N =12,using the new EMAT array,(c)N =10,using the new EMAT array,(d)N =14,using the traditional EMAT array,(e)N =12,using the traditional EMAT array and (f)N =10,using the traditional EMAT array.

rays and transmitter-receiver pairs are also required.Thus,an inherent characteristic of SIRT-based SH1wave tomography is that decreasing N may increase the distortion in the reconstructed images,which is independent of the type of EMAT employed.However,the experimental results reveal that for any two tomographic results that are achieved with the same N ,the tomographic results achieved by the new EMAT array contains fewer reconstructed artifacts than the tomographic results achieved by the traditional EMAT array,even for the smallest N of 10.This advantage of the new EMATs over the traditional EMATs is independent of N and causes the tomographic results of the new EMATs to have improved signal-to-noise ratios (SNRs),which is conducive to improving the accuracy of defect quanti?cation.

For the quantitative comparison,the normalized S j curves of the SH1wave on the cross sections at the positions of y =29cm for the tomographic results in Fig.10(a)-(f)are extracted and depicted by the solid lines in Fig.11(a)-(f).In addition,the actual defect distributions are calculated on the basis of the relation between the group velocity c g and the d in equation (4)and the fact that the slow-ness is the reciprocal of the group velocity.The calculated actual defect distributions are represented by dashed lines in Figures 11(a)-(f).For any two normalized SH1wave S j curves that are achieved with the same N ,the curve extracted from the tomographic results achieved by the new EMAT array contains less noise than the curve extracted from the tomographic results achieved by the traditional EMAT array.This ?nding may be explained by the notion that the tomographic results achieved by the new EMAT array has smaller.δS j than the tomographic results achieved by the traditional EMAT array.Because the normalized S j curve achieved by the new EMAT array is smoother in the defect zone and contains less noise,it matches the actual defect dis-tribution closer than the jagged normalized S j curve achieved by the traditional EMAT array for the same N .

By the normalized SH1wave S j curves in Fig.11(a)-(f),the defect diameter can be estimated.When the defect diameter is estimated by each of these curves,the horizontal positions of the two boundaries of the defect are determined by the horizontal coordinates of the points at which the rising and falling edges of the normalized S j curve in the defect zone intersect the line of the normalized slowness,which is equivalent to zero.The defect diameter is determined by the distance between the two achieved boundaries of the defect.The estimated results are shown in TABLE I,where the e d is the relative error of the estimated defect diameter relative to its actual value.

As shown in TABLE I,the defect diameters estimated using the S j curves achieved by the new EMAT array correspond with the actual values (e d within 16%).For each estimated result,the error e d is primarily induced by a slightly dis-torted shape for the reconstructed defect,which is caused by the low density of the SH1wave rays.To improve the accuracy of defect quanti?cation,additional new EMATs can be used to increase the density of the SH1wave rays.By contrast,the defect diameters estimated using the S j curves achieved by the traditional EMAT array have much larger

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Fig.11.Normalized SH1wave S j curves on the cross-sections at the positions of y =29cm for the tomographic results in Fig.10(a)-(f):(a)The normalized slowness curves extracted from Fig.10(a),(b)The normalized slowness curves extracted from Fig.10(b),(c)The normalized slowness curves extracted from Fig.10(c),(d)The normalized slowness curves extracted from Fig.10(d),(e)The normalized slowness curves extracted from Fig.10(e)and (f)The normalized slowness curves extracted from Fig.10(f).

TABLE I

R ESULTS OF D EFECT S IZE E STIMATES U SING THE E XPERIMENTALLY

A CHIEVED N ORMALIZED S LOWNESS C URVES

S HOWN IN F IG .11(a)-(c)

errors (e d more than 20%).The results indicate that in tomography,when the new EMATs,which have the improved accuracy of the SH1wave TOF extraction,are employed,the defect diameter can be estimated more accurately compared with the traditional EMATs.This ?nding corresponds with the theoretical analysis and may be explained as follows.Because the S j curves in Fig.11(d)-(f)are jagged and contain more noise compared with those in Fig.11(a)-(c),each of the curves in Fig.11(d)-(f)exhibits more rising and falling edges in the defect zone.Thus,determining the positions of the defect boundaries is substantially in?uenced by subjective factors and exhibits a higher degree of randomness and greater

uncertainty when the curves in Fig.11(d)-(f)are used to estimate the defect diameter.

V.C ONCLUSION

To overcome the drawbacks of the traditional magnetostriction-based OD GW EMATs,such as the low accuracy of GW TOF extraction,the poor quality in GW tomography and the low accuracy of defect quanti?cation,this paper proposed a new magnetostriction-based OD GW EMAT that consists of a CFC and a piece of pre-magnetized thin circular nickel foil.The theoretical analysis and the results of pitch-catch experiments on a healthy steel plate indicate that the new EMATs can transmit and receive purer single SH1-mode GWs and have higher accuracy of the SH1wave TOF extraction,compared with the traditional EMATs.The experimental results from imaging an arti?cial corrosion defect in a 3-mm-thick steel plate indicate that when the new EMAT array having the improved TOF extraction accuracy is employed,higher tomographic reconstruction quality,normalized S j curves with less noise and higher accuracy of tomographic defect quanti?cation can be achieved,compared with the traditional EMAT array.The new EMAT is suitable for application in high-accuracy SH wave tomography of steel plate defects.

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Zheng Wei was born in1986.He received the bachelor’s degree from Tsinghua University,in2009,where he is currently pursuing the Ph.D.degree with the Department of Electrical Engineering.His research interests focus on guided wave tomography and EMAT testing methods.

Songling Huang was born in1970.He received the Ph.D.degree from Tsinghua University,in2001.He is currently a Professor with the Department of Electrical Engineering,Tsinghua University.His current research interests are electromagnetic detection and nondestructive evaluation.

Shen Wang was born in1979.He received the Ph.D.degree from Tsinghua University,in2008.He is currently an Assistant Researcher with the Department of Electrical Engineering,Tsinghua University.His current research interests are EMAT guided waves and their signal processing.

Wei Zhao was born in1956.He received the Ph.D.degree from the Moscow Power Engineering Institute,in1991.He is currently a Professor with the Department of Electrical Engineering,Tsinghua University.His current research interests are electromagnetic measurement.

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