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(,430070)(,430074):,,,,:;;;:TG115.28:A:100026656(2003)0520225204MATHEMATICMODELFORTHETRUEPENETRATINGDEPTHOFEDDYCURRENTFEED2THROUGHPROBEYOUFeng2he(Dep.ofMeasurementandControl,WuhanUniversityofTechnology,Wuhan430070,China)GUOWen2ting(SchoolofInformationEngineering,HuazhongUniversityofScienceandTechnology,Wuhan430074,China)Abstract:Thefactorsaffectingthetruepenetratingdepth(TPD)ofeddycurrentprobewerestudiedbydirectlymeasuringthedistributionofthemagneticfieldinsideasolidconductor.ResultsindicatedthatTPDwasrelevanttotheshapeofcoilandstimulatingmagneticfieldinadditiontotheelectricalconductivityandmagneticpermeabilityofaconductoraswellasthetestingfrequency.ThemodelestablishedbygeneticalgorithmwasexpectedtoprovideareliablecriterionfortheTPDofeddycurrentin2sideasolidconductor.Keywords:Eddycurrenttesting;Depthofpenetration;Mathematicmodel;Sensor,,,1/e,,,[1],,:2003202217,,,;,[24],[5,6],,11.152225520035NDTVol.25No.5May2003©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(1),,,,,,,1,,,,1.2,,,(=0),fH0L/D1.3L/D=3,;L/D=1,,2,,22.1,,,,(L/D=3),(a)L/D=3,,(b)L/D=3,,(c)L/D=1,,(d)L/D=1,,2(3),,;,,,2.2,622:©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3,[6]H=H0e-2x(1)J=J0e-2x(2)H,H0J,J0,x=11f(3),,,H=K1e-K2x(4)K1,K2x,,H=K1(f,H0)e-K2(f,H0)x(5)K1(f,H0),K2(f,H0)K1K2f,H0K1K2f,H0,[7],,K1K2,,K1,K2H=(1H0+2lnf+3)e(4H0-5f12)x(6)1533.1,GA=(P0,M,,,,t)P0Mt(1),(),(2)(RouletteWheelMethod)Pc()Mxi=(xi1,xi2,xi3,,xin),i=1,2,,M(+1)M()V=x|XSx=Mi=1aixi,aiMi=1ai=1,-0.5ai1.5(3),Pm()Gauss,xi=xi+N(0,1)N(0,1)[0,1]12Ri,i=1,2,,12();Q,Q=12i=1Ri-63.2,X=(H0,f,x)C=(1,2,3,4,5)H(X,C)=(1H0+2lnf+3)e(4H0-5f12)x(7)3.2.1722:©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(1)4%,W300.000000(2)2,30000,1003.2.2L/D=3H=(1.43H0+2.15lnf-15.80)e(0.0009H0-0.0043f)x(8)L/D=1H=(3.63H0+4.64lnf-41.80)e(0.0034H0-0.0031f)x(9),3.82%4(8)(9),,t=1C1H0+C2f(10)tC1,C255.1(8)(9),,(8),(9)(1),,,,,,,,,[810](1),(8),(9)2ac,,5.2(3),(10),2bd,,,(8)(9),0H0C1C2f(11)(11),:[1]LiuZ,TsukadaK,HanasakiK.One2dimensionaleddycur2rentmulti2frequencydatafusion:amulti2resolutionanalysisapproach[J].INSIGHT,1998,40(4):286-289.[2]IdaN,PalanisamgR,LorW.Eddycurrentprobedesignfi2niteelementanalysis[J].MaterialsEvaluation,1983,41(12):1389-1394.[3]KolyshkinAA.Methodofsolutionofforwardproblemsined2dycurrenttesting[J].JApplPhys,1998,77(10):4903-4913.[4]AlbertzD,HennebergerG.Calculationof3Deddycurrentfieldsusingbothelectricandmagneticvectorpotentialinconductingregions[J].IEEETransactionsonMagnetics,1998,34(5):2644-2647.[5]MottlZ.Thequantitativerelationsbetweentrueandstandarddepthofpenetrationforair2coredprobecoilsineddycurrenttesting[J].NDTInternational,1990,23(2):11-18.[6]SullivanS,AthertonDL,SchmidtTR.Comparingaone2di2mensionalskineffectequationwiththroughtransmissioneddycurrentphenomena[J].BritishJournalofNDT,1990,32(2):71-75.[7],,.[J].,2001,47(1):57-60.[8],.2[J].,1999,48(6):1044-1051.[9],.[J].,2000,45(7):689-693.[10].[M].:,1992.357.822:©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.