F.2. Lerakódás jelének szimuláiója impulzus üzem¶ ECT mérésnél
F.2.2. Numerikus példa
A bemutatandó példábana vizsgáltmunkadarab, avizsgálófejésalerakódásanyagának a
paramé-tereimegegyezneka4.2.3.pontbananalizáltpéldákéval.Háromazonosalakúéskülönböz®
vastagsá-gúlerakódástvizsgálunk.A lerakódások alakjaegyentrálisanelhelyezked®
20
mm oldalhosszúságú négyzet, vastagságuk (d l) pedig rendre: 0,03
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Az F.2(a). ábránláthatók akit¶zött feladat megoldásaként kapottid®függvények. Ezekb®l
lát-hatjuk, hogy a lerakódás vastagságától függ®en jellemz®en a válaszjel nagysága változik. Látható
mégaz is,hogyaválaszagerjesztéshezképestegyrövidkésleltetéstszenved.Ezazikai
szemlélet-b®ladódóan úgymagyarázható,hogyaválaszjel valójában alerakódásról visszaverthullám, amely
terjedéséhez bizonyosid®revanszükség.Az F.2(b).ábrána
d l = 0,03
mmvastagságúlerakódásese-tében számított átviteli karakterisztika látható. Ez úgyértelmezhet®, hogy alasonyfrekveniákon
a kisindukáltgerjeszt® térmiatta válasz kisi,illetve nagyfrekveniákona kisbehatolási mélység
miatt nemlátható alemez túlsó oldalántalálható lerakódás.
[1℄ http://www-entre-salay.ea.fr/
[2℄ http://www-iva.ea.fr/
[3℄ http://www.ndesr.eng.iwate-u.a.jp/end e06/
[4℄ http://www.ende2008.org/
[5℄ http://www.usasymposium.om/ende/
[6℄ http://wwwso.nii.a.jp/jsaem/index-e.html
[7℄ http://www.lgep.supele.fr/
[8℄ http://www.lss.supele.fr/
[9℄ http://www.mfa.kfki.hu/
[10℄ http://www.snema.om/
[11℄ http://www.supele.fr/
[12℄ P.MIntire,Ed.,Nondenstrutivetestinghandbook,2nded. Colombus,Ohio,USA:Amerian
Soietyfor Nondestrutive Testing, 1986,vol. 4,Eletromagneti Testing.
[13℄ J.Blitz,Eletrial andmagneti methods of nondestrutive testing. Bristol: Hilger, 1991.
[14℄ KajdiGy.: Anyagvizsgálatörvényáramokkal. Budapest: SZTÁV, 1990.
[15℄ A. J. Moses and D. J. Jiles, Origin, measurement and appliation of the Barkhausen eet
inmagneti steel, inEletromagnetiNondestrutive Evaluation (X),ser. Studies inApplied
EletromagnetisandMehanis,S.TakahashiandH.Kikuhi,Eds. Amsterdam: IOSPress,
2007,vol.28,pp.48.
[16℄ D.O'Sullivan,M.Cotterell,D.A.Tanner, andI.Mészáros, Charaterisationofferriti
stain-lesssteelbybarkhausentehniques, NDT&E International, vol. 37,pp.265269, 2004.
[17℄ G. Vértesy, I. Tomás, S. Takahashi, S. Kobayashi, Y. Kamada, and H. Kikuhi, Inspetion
ofsteeldegradation bymagneti adaptive testing, NDT&E International,vol. 41,no.4,pp.
252257, 2008.
[18℄ G. Vértesy, I. Tomás, and I. Mészaros, Nondestrutive indiation of plasti deformation of
old-rolledstainless steelbymagnetiadaptive testing, Journalof Magnetism andMagneti
Materials,pp. 7682,2007.
[19℄ S.Takahashi,S.Kobayashi, Y.Kamada, H.Kikuhi,and K.Ara, NDEmethodusingminor
hysteresis loops in ferromagneti materials, in Eletromagneti Nondestrutive Evaluation
(X), ser. Studies inApplied Eletromagnetis and Mehanis, S. Takahashi and H.Kikuhi,
Eds. Amsterdam: IOSPress,2007, vol.28, pp.209216.
[20℄ I. Mészáros, Complex magneti investigation of ferriti stainless steel, Materials Siene
Forum,pp.231236, 2005.
[21℄ I.Mészáros,Miromagnetimeasurementsandtheirappliations, MaterialsSiene Forum,
pp.275280, 2003.
[22℄ D. O'Sullivan, M. Cotterell, and I. Mészáros, The haraterization of work-hardened
austenitistainlesssteelbyNDTmiro-magnetitehniques, NDT&EInternational, vol.37,
pp.265269, 2004.
[23℄ A.Kloster, M.Kroning, J. Smorodinski, andV. Ustinov,A linearmagnetistrayux array
basedonGMRgradiometers, inEletromagnetiNondestrutive Evaluation(VII),ser.
Stud-iesin Applied Eletromagnetis and Mehanis, G. Dobmann,Ed. Amsterdam: IOSPress,
2006,vol. 26,pp.173179.
[24℄ Z. Zeng, P. Ramuhalli, L. Udpa, and S. Udpa, Optimization of pipeline inspetion tool
using Taguhi method, in Eletromagneti Nondestrutive Evaluation (VI), ser. Studies in
Applied Eletromagnetis and Mehanis, F. Kojima, T. Takagi, S. S. Udpa, and J. Pávó,
Eds. Amsterdam: IOSPress,2002, vol.23,pp.203210.
[25℄ G. Vértesy,T. Uhimoto, T. Takagi, and I. Tomás, Magneti adaptive testing: inuene of
experimental onditions, in Eletromagneti Nondestrutive Evaluation (X), ser. Studies in
Applied Eletromagnetis and Mehanis, S. Takahashi and H. Kikuhi, Eds. Amsterdam:
IOSPress,2007,vol.28, pp.186192.
[26℄ G.Vértesy,T.Uhimoto,T.Takagi, I.Tomás,O.Stupakov,I.Mészáros, andJ.Pávó,Minor
hysteresisloopsmeasurementsforharaterizationofastiron, PhysiaB:CondensedMatter,
vol. 1-2,no.372, pp.156159,February2006.
[27℄ M.UesakaandK.Miya,Miro-ECTtehnique, inNondestrutive Testingof Materials,ser.
StudiesinApplied Eletromagnetisand Mehanis, R.Collins, W.D.Dover, J.Bowler,and
K.Miya,Eds. Amsterdam: IOSPress,1995, vol. 8,pp.265270.
[28℄ M.Kurokawa,R.Miyauhi,K.Enami,andM.Matsumoto, NeweddyurrentprobeforNDE
ofsteamgeneratortubes, inEletromagneti Nondestrutive Evaluation(III),ser. Studiesin
AppliedEletromagnetisand Mehanis,D.LesselierandA.Razek,Eds. Amsterdam: IOS
Press,1999, vol.15, pp.5764.
[29℄ T.Sollier,M.Talvard,andM.Aid,UseofECsensorarraysonthinlms, inEletromagneti
NondestrutiveEvaluation(IV),ser.StudiesinAppliedEletromagnetisandMehanis,S.S.
Udpa,T. Takagi,J. Pávó,and R.Albanese, Eds. Amsterdam: IOSPress, 2000,vol. 17,pp.
6570.
[30℄ T. Sollier, O. Loreki, and O. Goupillon, CODECI, a new system for the inspetion of
surfaebreaking awsbased oneddy urrent array probeand highresolution CCD amera,
inEletromagnetiNondestrutiveEvaluation(VIII),ser.StudiesinAppliedEletromagnetis
and Mehanis, T. Sollier,D. Prémel, and D. Lesselier, Eds. Amsterdam: IOSPress, 2004,
vol. 24,pp.215222.
[31℄ C. Abbate, M. Morozov, G. Rubinai, A. Tamburrino, and S. Ventre, A probe array for
fast quantitative eddy urrent imaging, in Eletromagneti Nondestrutive Evaluation (X),
ser. Studies inApplied Eletromagnetis and Mehanis, S.Takahashi and H. Kikuhi, Eds.
Amsterdam: IOSPress, 2007,vol. 28,pp.7582.
[32℄ J.R.Bowlerand V.Katyal,Magneti sensorarrayfor eddyurrent eldmeasurement with
araetrakoil exitation, inEletromagneti Nondestrutive Evaluation(VIII),ser.Studies
in Applied Eletromagnetis and Mehanis, T. Sollier, D. Prémel, and D. Lesselier, Eds.
Amsterdam: IOSPress, 2004,vol. 24,pp.3643.
[33℄ Y.Le Bihan,P.Y.Joubert,andD.Plako,Wallthiknessevaluationofsingle-rystalhollow
bladesbyeddyurrentsensor, NDT&E International,vol.34,no.5,pp.363368,July 2001.
[34℄ A. Yashan, R. Beker, and G. Dobmann, Use of GMR-sensors for eddy-urrent testing, in
Eletromagneti NondestrutiveEvaluation(V),ser.StudiesinApplied Eletromagnetisand
Mehanis, J. Pávó, G. Vértesy, T. Takagi, and S. S. Udpa, Eds. Amsterdam: IOS Press,
2001,vol.21,pp.187193.
[35℄ M. Valentino, A. Ruosi, G. P. Pepe, and G. Peluso, Superondutive and traditional
ele-tromagneti probes in eddy urrent NDE for detetion of deep defets, in Eletromagneti
Nondestrutive Evaluation (III), ser. Studies in Applied Eletromagnetis and Mehanis,
D.Lesselier andA. Razek,Eds. Amsterdam: IOSPress, 1999,vol.15,pp.159170.
[36℄ G. Vértesy, A. Gasparis, and J. Szöll®sy, High sensitivity magneti eld sensor, Sensors
andAtuators A:Physial,vol. 85,pp.202208, 2000.
[37℄ G. Vértesy and A.Gasparis, Nondestrutive material evaluation by novel eletromagneti
methods, MaterialsSiene Forum,pp.343353, 2003.
[38℄ M.Morozov, G.Rubinai,A.Tamburrino,S.Ventre, andF.Villone,Aeronatialstrutures
examination using Fluxset type ECT proba, in Eletromagneti Nondestrutive Evaluation
(VII), ser. Studies in Applied Eletromagnetis and Mehanis,G. Dobmann, Ed.
Amster-dam: IOSPress, 2006,vol. 26,pp.136143.
[39℄ G.VértesyandB.Idzikowski,AmorphousandnanorystallineFe-Ni-Zr-Bribbonsassensing
elements inmagnetield sensors, Journal of Magnetism and MagnetiMaterials, pp.112
119,2006.
[40℄ I. Sebestyén and J. Pávó, Flaw detetion using DC magneti eld measurement,
Inter-national Journal of Applied Eletromagnetis and Mehanis, vol. 15, no. 1-4, pp. 5360,
2001/2002.
[41℄ J. R. Bowler, N. Bowler, and W. Podney, Evaluation of rak signal for superondutive
pulsed eddy-urrent probe, inEletromagneti Nondestrutive Evaluation (VI), ser. Studies
inApplied Eletromagnetis and Mehanis,F. Kojima,T. Takagi, S.S.Udpa, andJ. Pávó,
Eds. Amsterdam: IOSPress,2002, vol.23, pp.108115.
[42℄ M. Isobe, R. Iwata, and M. Nishikawa, High sensitivity remote eld eddy urrent testing
by using dual exiting oil, in Nondestrutive Testing of Materials, ser. Studies in Applied
Eletromagnetis and Mehanis, R. Collins, W. D. Dover, J. Bowler, and K. Miya, Eds.
Amsterdam: IOSPress, 1995,vol.8,pp.145152.
[43℄ R.Levy,E-NDEinthenulearindustry: viewpointofauser, inEletromagneti
Nondestru-tive Evaluation (VIII), ser. Studies in Applied Eletromagnetis and Mehanis, T. Sollier,
D.Prémel, and D.Lesselier, Eds. Amsterdam: IOSPress, 2004,vol. 24,pp.37.
[44℄ G.Anger, Inverse problems in dierential equations. New Yorkand London: PlenumPress,
1990.
[45℄ J.Hadamard,LeturesonChauhy'sproblemsinlinearpartialdierentialequations. Mineola,
New York: DoverPubliation In.,1952.
[46℄ J.R.Bowler,Eddy-urrentinteration withanidealrak.I.Theforwardproblem, Journal
of Applied Physis,vol. 75,no.12, pp.81288137, June 1994.
[47℄ N.Ida,Numerial modellingfor eletromagnetinon-destrutive evaluation. London:
Chap-man&Hall, 1995.
[48℄ D.Lesselier andA. Razek,Eddy-urrent sattering: Green's integral and variational
formu-lations, inSattering, sattering and inverse sattering in pure and applied siene, R. Pike
andP.Sabatier, Eds. New York: AademiPress, 2002,h.1.6.6,pp.486507.
[49℄ D. Lesselier and J. Bowler, Eds., Inverse Problems, Speial Setion on Eletromagnei and
Ultrasoni Nondestrutive Evaluation, Deember2002,vol. 18,no.6,pp.17331958.
[50℄ J. R. Bowler, S. A. Jenkins, L. D. Sabbagh, and H. A. Sabbagh, Eddy-urrent probe
impedaneduetoavolumetriaw, JournalofAppliedPhysis,vol.70,no.3,pp.11071114,
August1991.
[51℄ V.Monebhurrun,D.Lesselier,andB.Duhene,Evaluationofa3-Dboundeddefetinthewall
ofa metaltubeat eddy urrent frequenies: thediretproblem, Journal of Eletromagneti
Wavesand Appliations, vol. 12,pp.315347, 1998.
[52℄ C.T. Tai, Dyadi Green's funtionsin eletromagneti theory. Sranton: Intext,1971.
[53℄ W.C. Chew, Wavesand eldsin inhomogeneous media. New York: IEEE Press,1995.
[54℄ J.R.Bowler,Eddyurrentalulationusinghalf-spaeGreen'sfuntions, JournalofApplied
Physis, vol.61,no. 2,pp.833839, February1987.
[55℄ D.DosReis,M.Lambert,andD.Lesselier,ExtendedBorndomainintegralmodelsofdiusive
elds, IEEE Transations on Magnetis,vol.38, no.2,pp.577580, Marh 2002.
[56℄ T.Theodoulidis andJ.Bowler,Eddy-urrent interationoflongoilwithaslotina
ondu-tiveplate, IEEE Transations on Magnetis,vol.41,no. 4,pp.12381247, April2005.
[57℄ V. Bertrand, D. Lesselier, and S. Mastorhio, Numerial modelling of eddy-urrent
non-destrutiveevaluationwithFEM-BEMTRIFUsoftwareinontrolledongurations, in
Ele-tromagneti Nondestrutive Evaluation (IV), ser. Studies in Applied Eletromagnetis and
Mehanis,S.S. Udpa,T. Takagi, J.Pávó, and R.Albanese, Eds. Amsterdam: IOS Press,
2000,vol. 17,pp.3241.
[58℄ Z. Badis, Y.Matsumoto, K.Aoki,F. Nakayasu, M. Uesaka,and K. Miya,An eetive 3-D
nite element sheme for omputing the eletromagneti eld distortions due to defets in
eddy-urrent nondestrutive evaluation, IEEETransationson Magnetis,vol.33,no.2,pp.
10121020, Marh1997.
[59℄ M. Morozov, G. Rubinai, A.Tamburrino, and S.Ventre, Numerial models of volumetri
insulating raks in eddy-urrent testing with experimental validation, IEEE Transations
on Magnetis,vol. 42,no.5,pp.15681576, May2006.
[60℄ Z.Badis,H.Komatsu,Y.Matsumoto, andK.Aoki,Inversionshemebasedonoptimization
for 3-D eddy urrent aw reonstrution problems, Journal of Nondestrutive Evaluation,
vol.17, no.2,pp.6778,1998.
[61℄ Z. Badis, J. Pávó, H. Komatsu, S. Kojima, Y. Matsumoto, and K. Aoki, Fast aw
reon-strution from 3D eddy urrent data, IEEE Transation on Magnetis, vol. 34, no. 5, pp.
28232828, September1998.
[62℄ H. Huang, T. Takagi, and T. Uhimoto, Crak shape reonstrution in ferromagneti
ma-terials using a novel fast numerial simulation method, IEEE Transations on Magnetis,
vol.40, no.2,pp.13741377, Marh 2004.
[63℄ A.H.Kahn,S.Spal,andA.Feldman,Eddy-urrentlossesduetoasurfaerakinonduting
material, Journal of Applied Physis, vol.48,no. 11,pp.44544459, November 1977.
[64℄ J. R. Bowler, Eddy urrent eld theory for a awed onduting half-spae, in Review of
Progressin Quantitative Nondestrutive Testing,D.O. Thompsonand D.E. Chimenty, Eds.
NewYork: Plenum, 1990, vol.5A, pp.149155.
[65℄ J.R. Bowler, Y.Yoshida, and N.Hareld, Vetor-potential boundary-integralevaluation of
eddy-urrent interation with rak, IEEE Transations on Magnetis, vol. 33, no. 5, pp.
42874294, September 1997.
[66℄ P.Beltrameand N.Burais,Generalization oftheidealrakmodelineddyurrent testing,
IEEE Transations on Magnetis,vol. 40,no.2,pp.13661369, Marh 2004.
[67℄ R.Albanese, G. Rubinai, and F. Villone, Anintegral omputational model for rak
sim-ulation and detetion via eddy urrents, Journal of Computational Physis, vol. 152, pp.
736755, 1999.
[68℄ J.R. Bowlerand N. Hareld,Evaluation of probe impedane due to thin-skineddy-urrent
interationwithsurfaeraks, IEEETransationsonMagnetis,vol.34,no.2,pp.515523,
Marh 1998.
[69℄ H. Huang, T. Takagi, and H. Fukutomi, Fast signal preditions of noised signals in eddy
urrent testing, IEEE Transations on Magnetis,vol. 36,no.4,pp.17191723, July 2000.
[70℄ Z. Badis, Y. Matsumoto, S. Kojima, Y. Usui, K. Aoki, and F. Nakayasu, Finite element
modelingofonduting shellsforeddyurrentNDEproblemsusingimpedane-typeinterfae
onditions, IEEE Transations on Magnetis,vol. 33,no.2,pp.13341337, Marh1997.
[71℄ L.KrähenbühlandD. Muller,Thinlayers ineletrialengineering. Exampleofshell models
inanalyzing eddy-urrents byboundary and nite element methods, IEEE Transations on
Magnetis,vol. 29,no.2,pp.14501455, 1992.
[72℄ I. D. Mayergoyz and G. Bedrosian, On alulation of 3-D eddy urrents in onduting and
magneti shells, IEEE Transations on Magnetis, vol.31,no. 3,pp.13191324, 1995.
[73℄ Z. Badis, Y. Matsumoto, K. Aoki, and F. Nakayasu, Eetive probe response alulation
usingimpedaneboundaryonditionsineddyurrentNDEproblemswithmassiveonduting
regionspresent, IEEE Transations on Magnetis,vol. 32,no.3,pp.737740, May1996.
[74℄ C. V. Dodd and W. E. Deeds, Analytial solution to eddy-urrent probe-oil problems,
Journal of Applied Physis, vol. 39,no.6,pp.28292838, May1968.
[75℄ T.P.Theodoulidis,Modelofferrite-oredprobesforeddyurrentnondestrutiveevaluation,
Journal of Applied Physis, vol. 93,no.5,pp.30713078, Marh2003.
[76℄ T.P.TheodoulidisandE. E.Kriezis,Impedaneevaluationofretangular oilsforeddy
ur-renttesting ofplanarmedia, NDT&E International,vol. 35,no.6,pp.4074014, September
2002.
[77℄ T.Theodoulidis,Analytialmodelfortiltedoilsineddy-urrentnondestrutive inspetion,
IEEE Transations on Magnetis,vol. 41,no.9,pp.24472454, September 2005.
[78℄ M.Bensetti,Y.LeBihan,C.Marhand,C.M.Tassetti,E.DufourGergam,andJ.P.Gilles,A
hybridnite-elmentmethodforthemodelingofmirooils,IEEETransationsonMagnetis,
vol. 41,no.5,pp.18681871, May2005.
[79℄ S. K. Burke, A benhmark problem for alulation of
∆Z
in eddy-urrent nondestrutive evaluation (NDE), Journal of Nondestrutive Evaluation, vol. 7, no. 1-2, pp. 3542, June1988.
[80℄ T. Takagi, H. Fukutomi, M. Hashimoto, Y. Yoshida, K. Miya, H. Tsuboi, Y. Harada, and
J.Shimone,ECT researh ativitiesinJSAEM benhmarkmodels ofeddyurrent testing
for steamgenerator tube (Part 1), inNondestrutive Testing of Materials, ser. Studies in
AppliedEletromagnetisandMehanis,R.Collins,W.Dover,J.Bowler,andK.Miya,Eds.
Amsterdam: IOSPress, 1995,vol. 8,pp.253264.
[81℄ T. Takagi, M. Uesaka, and K. Miya, Eletromagneti NDE researh ativities in JSAEM,
inEletromagneti Nondestrutive Evaluation, ser. Studies inApplied Eletromagnetis and
Mehanis, T. Takagi, J. R. Bowler, and Y. Yoshida, Eds. Amsterdam: IOS Press, 1997,
vol. 12,pp.916.
[82℄ T. Takagiand H.Fukutomi, Benhmarking ativitiesof eddyurrent testing for steam
gen-erator tubes, in Eletromagneti Nondestrutive Evaluation (IV), ser. Studies in Applied
Eletromagnetis and Mehanis, S. S. Udpa, T. Takagi, J. Pávó, and R. Albanese, Eds.
Amsterdam: IOSPress, 2000,vol. 17,pp.235252.
[83℄ D. J. Harrison, L. D. Jones, and S. K. Burke, Benhmark problems for defet size and
shape determination in eddy-urrent nondestrutive evaluation, Journal of Nondestrutive
Evaluation,vol. 15,no.1,pp. 2134,1996.
[84℄ T. Chadi,M. Enokizono, T.Todoka,Y. Tsuhida, and R.Sikora, Evaluationof theJSAEM
roundrobintestsamplesusingmulty-frequenyexitationandspetrogrammethod, in
Ele-tromagneti Nondestrutive Evaluation (V), ser. Studies in Applied Eletromagnetis and
Mehanis, J. Pávó, G. Vértesy, T. Takagi, and S. S. Udpa, Eds. Amsterdam: IOS Press,
2001,vol. 21,pp.171178.
[85℄ G. Simone and F. C. Morabito, Plural defet separation using wavelet Hough transform,
inEletromagneti Nondestrutive Evaluation (IV),ser. Studies inApplied Eletromagnetis
and Mehanis, S. S. Udpa, T. Takagi, J. Pávó, and R. Albanese, Eds. Amsterdam: IOS
Press,2000, vol.17, pp.196203.
[86℄ T.Taniguhi,D.Kaprzak,S.Yamada,M.Iwahara,andT.Miyagoshi,Wavelet-basedimage
proessing for inspetion of printed iruit board using eddy-urrent testing tehnique, in
EletromagnetiNondestrutive Evaluation(V),ser.Studies inAppliedEletromagnetisand
Mehanis, J. Pávó, G. Vértesy, T. Takagi, and S. S. Udpa, Eds. Amsterdam: IOS Press,
2001,vol. 21,pp.226233.
[87℄ P. Ramuhalli, L. Udpa, and S. Udpa, Neural network algorithm for eletromagneti NDE
signal inversion, in Eletromagneti Nondestrutive Evaluation (V), ser. Studies in Applied
Eletromagnetisand Mehanis,J.Pávó, G.Vértesy,T.Takagi, andS.S.Udpa,Eds.
Am-sterdam: IOSPress, 2001,vol.21,pp.121128.
[88℄ M. Bensetti, Y. Le Bihan, C. Marhand, and J. Pávó, Deposit haraterization by eddy
urrent nondestrutive evaluation, International Journal of Applied Eletromagnetis and
Mehanis,vol. 19,no.1-4, pp.537540, 2004.
[89℄ R. C. Popa and K. Miya, A data proessing and neural network approah for the inverse
probleminECT, inEletromagneti Nondestrutive Evaluation (II),ser. Studies inApplied
EletromagnetisandMehanis,R.Albanese,G.Rubinai,T.Takagi,andS.S.Udpa,Eds.
Amsterdam: IOSPress, 1998,vol. 14,pp.297304.
[90℄ W.H.Press,B.P.Flannery,S.A.Teukolsky,andW.T.Vetterling, Numerial ReipiesinC.
Cambridge: Cambridge UniversityPress,1988.
[91℄ S.J.NortonandJ.R.Bowler,Theoryofeddyurrentinversion, Journalof AppliedPhysis,
vol. 73,no.2,pp.501512, January1993.
[92℄ J.R.Bowler, S.J.Norton,andD.J.Harrison,Eddy-urrent interationwithanidealrak.
II. The inverse problem, Journal of Applied Physis, vol. 75, no. 12, pp. 81388144, June
1994.
[93℄ V.Monebhurrun, B.Duhene,and D.Lesselier,Three-dimensional inversionofeddyurrent
datafornon-destrutiveevaluationofsteemgeneratortubes, InverseProblems,vol.14,no.3,
pp.707724, June 1998.
[94℄ Z.Badis,Y.Matsumoto,S.Kojima,Y.Usui,K.Aoki,F.Nakayasu,andA.Kurokawa,Rapid
aw reonstrution sheme for three-dimensional inverse problems in eddy-urrent NDE,
in Eletromagneti Nondestrutive Evaluation, ser. Studies in Applied Eletromagnetis and
Mehanis, T. Takagi, J. R. Bowler, and Y. Yoshida, Eds. Amsterdam: IOS Press, 1997,
vol. 12,pp.303309.
[95℄ H.Fukutomi,H.Huang,T.Takagi,andJ.Tani,Identiationofrakdepthsfromeddy
ur-renttestingsignal,IEEETransationsonMagnetis,vol.34,no.5,pp.28932896,September
1998.
[96℄ D. Prémel and A. Baussard, Eddy-urrent evaluation of tree-dimensional aws in at
on-dutive material using Bayesian approah, Inverse Problems, vol. 18, no. 6,pp. 18731889,
Deember 2002.
[97℄ Y. Nagaya, T. Takagi, T. Uhimoto, and H. Huang, Identiation of multiple raks from
eddy-urrent testing signals with noise soures by image proessing and inverse analysis,
IEEE Transations on Magnetis,vol. 40,no.2,pp.11121115, Marh 2004.
[98℄ F.Zaoui, C. Marhand,andJ. Pávó,Stohastirak inversionbyan integral approah, in
EletromagnetiNondestrutive Evaluation(V),ser.StudiesinApplied Eletromagnetisand
Mehanis, J. Pávó, G. Vértesy, T. Takagi, and S. S. Udpa, Eds. Amsterdam: IOS Press,
2001,vol.21,pp.129136.
[99℄ A. Tamburrino and G. Rubinai, Fast methods for quantitative eddy-urrent tomography
of ondutive materials, IEEE Transations on Magnetis, vol. 42, no. 8, pp. 20172028,
August2006.
[100℄ G. Rubinai, A. Tamburrino, and S. Ventre, Regularization and numerial optimization of
fast eddy urrent imaging method, IEEE Transations on Magnetis, vol. 42, no. 4, pp.
11791182, April2006.
[101℄ D. Bouden, I. Lemahieu, and J. Basart, Inversion of eddy urrent impedane hange data
forsingleraksand separateraks, inEletromagneti NondestrutiveEvaluation (V),ser.
StudiesinApplied EletromagnetisandMehanis,J.Pávó,G.Vértesy,T.Takagi,andS.S.
Udpa,Eds. Amsterdam: IOSPress,2001, vol. 21,pp.105112.
[102℄ N. Yusa, Z. Chen, K. Miya, T. Uhimoto, and T. Takagi, Large-sale parallel omputation
for the reonstrution of natural stress orrosion raks from eddy urrent testing signals,
NDT&E International, vol.36, no.7,pp.449456, Otober2003.
[103℄ H. Huang and T. Takagi, Inverse analyses for natural and multiraks using signals from
dierent transit-reeive ECT probe, IEEE Transations on Magnetis, vol. 38, no. 2, pp.
10091012, Marh 2002.
[104℄ N. Yusa, L. Janousek, M. Rebian, Z. Chen, K. Miya, N. Dohi, N. Chigusa, and Y.
Mat-sumoto,Cautionwhenapplyingeddyurrent inversionto stressorrosionraking, Nulear
Engineering andDesign, vol.236, no.2,pp.211221, January 2006.
[105℄ J.PávóandK.Miya,Reonstrutionofrakshapebyoptimization usingeddyurrenteld
measurement, IEEE Transationon Magnetis,vol.30, pp.34073410, September1994.
[106℄ J.PávóandD.Lesselier,Calulationofeddyurrentprobesignalwithglobalapproximation,
IEEE Transation on Magnetis,vol. 42,no.4,pp.14191422, April2006.
[107℄ J.Pávó,L.Maurie,D.Prémel,andD.Lesselier,Error estimationofalulatedECTsignals
duetothinraksinaplateusingaglobalapproximationofthedipoledensity, International
Journalof Applied Eletromagnetis and Mehanis,vol. 25,no.1-4,pp.347356, May2007.
[108℄ L. Maurie, D. Prémel, J. Pávó, D. Lesselier, and A. Niolas, Volumetri and surfae aw
modelsfortheomputationofECT/Rprobesignalduetothinopeningaw, inEle
tromag-netiNondestrutiveEvaluation(X),ser.StudiesinAppliedEletromagnetisandMehanis,
S.Takahashi andH.Kikuhi,Eds. Amsterdam: IOSPress, 2007,vol. 28,pp.4956.
[109℄ L. Maurie, D. Prémel, J. Pávó, D. Lesselier, and A. Niolas, Hybridization of volumetri
andsurfaemodels forthe omputationofthe T/RECproberesponsedueto athinopening
aw, COMPEL: The International Journal for Computation and Mathematis in Eletrial
andEletroni Engineering, vol.27, no.1,pp.298306, 2008.
[110℄ J.Pávó, Reonstrution ofgroup of raks inplate speimens using ECT impedane data,
inEletromagneti Nondestrutive Evaluation (IV),ser. Studies inApplied Eletromagnetis
and Mehanis, S. S. Udpa, T. Takagi, J. Pávó, and R. Albanese, Eds. Amsterdam: IOS
Press,2000, vol.17, pp.204211.
[111℄ J.Pávó,Forwardsolutionmethodforthereonstrutionoftheshapeofthinmetaldepositon
plate speimen, International Journal of Applied Eletromagnetis and Mehanis, vol. 14,
no.1-4,pp.483488, 2001/2002.
[112℄ J. Pávó, Numerial alulation method for pulsed eddy-urrent testing, IEEE Transation
on Magnetis,vol. 38,no.2,pp.11691172, Marh2002.
[113℄ J.Pávó,Approximate methods for thealulation of thesignalof a rakina plate oated
by onduting deposit, IEEE Transation on Magnetis, vol. 40, no.2, pp.659662, Marh
2004.
[114℄ J. Pávó, I. Sebestyén, G. Vértesy, and C. S. Darózi, Eletromagneti eld modelling of
the ferromagneti ore of Fluxset type sensors, in Applied Eletromagnetis and
Computa-tional Tehnologies, ser. Studies inApplied Eletromagnetis and Mehanis, H.Tsuboiand
I. Sebestyén,Eds. Amsterdam: IOSPress,1997, vol. 11,pp.172181.
[115℄ J.Pávó, Optimisation ofthe shape of theferromagneti ore ofFluxset type magneti eld
sensors, inProeedings ofthe 7thInternationalIGTESymposiumon Numerial Field
Calu-lation in Eletrial Engineering, Graz, Austria,September1996,pp.153158.
[116℄ J.Pávó andK. Miya,Optimal design of eddy urrent testing probe using Fluxset magneti
[116℄ J.Pávó andK. Miya,Optimal design of eddy urrent testing probe using Fluxset magneti