TRANSFUSION OF TIME-DOMAIN AND FREQUENCY-DOMAIN EDDY

Transcription

1 4th Midde Est ND Conference nd Ehibition, Kingdom of Bhrin, Dec 007 For ppers of this pubiction cick: RANSFUSON OF ME-DOMAN AND FREQUENCY-DOMAN EDDY CURREN SGNAS brhim Eshfiey, Mjeed Aknh, nd Ayed Agrni Eectric Engineering Deprtment, King Sud University, P.O. Bo 800, Riydh 4, Sudi Arbi e-mi: ABSRAC Convention eddy current using singe-frequency ecittion hs imited mteri chrcteriztion cpbiities. Enrichment of the spectr informtion of the sign with techniques such s mutifrequency or swept frequency inspection coud be empoyed to improve the inspection process. Brodbnd ecittion is so impemented with time-domin inspection using pused eddy current PEC. he spectrum of PEC however hs decyed energy corresponding to higher frequencies. his pper ddresses the impementtion of technique, termed trnsfusion; to fuse prti eddy current informtion obtined from mesurements in the time domin with PEC with inspection resuts tht coud be vibe t fied points in the frequency domin, obtined with convention eddy current inspection. he technique is bsed on imge fusion methods, in ccordnce with incresed interest in c-scn representtion of eddy current signs. he deveoped gorithm depends on pcking muti-spectr nd muti-tempor dt into the vues of coor components of trnsfusion imge. Further enhncement coud be obtined by fusing this imge with high quity imge of the object under test, which coud be cquired using high frequency eddy current inspection or nother NDE modity. Resuts bsed on the proposed technique, bsed on finite eement simution of eddy current inspection re presented, ong with suggested imge quity mesures to test the spectr s we s spti informtion of the trnsfusion imge. Keywords: NDE, Pused Eddy Current, Wveet Anysis, mge Fusion.. NRODUCON Eddy current (EC) techniques re widey used to inspection conductive mteris such s ircrft skin. Convention eddy current depend on hrmonic nysis in which

2 sinusoid ecittion is used. Due to the skin effect, high frequency ecittion with ow penetrtion depth is used for detecting surfce fetures, whie ow frequency vues re used to inspect subsurfce fetures. Singe-frequency ecittion hs thus imited mteri chrcteriztion cpbiities nd dt tht re more rigorous coud be obtined by enhncing the spectr informtion with techniques such s mutifrequency or swept frequency inspection. Brodbnd ecittion is so impemented with time-domin inspection using pused eddy current (PEC) methodoogy deveoped to improve the efficiency of eddy current testing in detecting corrosion nd deep fws. n PEC, n eectric puse is ppied to driving coi. he secondry mgnetic fied is recorded using n inductive coi or mgnetic sensor. Appiction empe is in inspecting fusege p joint muti-yer structure where ftigue crcks re not necessriy confined to the upper yer. Corrosion of the p spice tends to ter the stress stte nd shift the mimum stress to second or third skin yers skin [Giguere, 0]. Vrious techniques hve been deveoped to cst eddy current signs obtined using hrmonic s we s pused eddy current inspection dt in the form of C-scn imges [Udp, 0]. mges provide ntur wy of nyzing the eddy current sign. PEC provides so powerfu too to obtin informtion reted to vrious depths in mteri. Observtion time interv nd smping rte cn be used for "in-depth sicing" of conductive medi [Potnikiv, 07] nd [Potnikiv, 0]. his pper provides too to fuse prti eddy current informtion obtined from mesurements in both time domin (using PEC) nd prticur frequency domins nodes (with hrmonic nysis). he technique is bsed on imge fusion methods.

3 . ME-DOMAN AND FREQUENCY-DOMAN EDDY CURREN SGNAS Hrmonic eddy current sign provide informtion bout certin point in the spectrum, where time domin representtion is simpe sinusoid form. nformtion is obtined s compe phsor representing probe impednce. C-scn imges coud be obtined to refect mp of re prt, imginry prt, or the mgnitude of probe impednce vues. Pused eddy current sign hs rich informtion in time domins. Vrious fetures coud be etrcted from picked up secondry mgnetic fied in time domin such s mpitude, time to pek, or time to zero crossings. Figure presents n ecittion puse in both time nd frequency domins. he puse hs durtion of τ ms nd is repeted every 0 5 ms. he brs in Fig. -b re obtined using fst Fourier trnsform of the time domin sign nd the enveop represent the nytic Fourier spectrum V(f) mutipied by smping frequency f S, where V(f) is given s [Crson, 03] A f V(f) sinc () f p f p Where A is the mgnitude of the puse, nd f p /τ. t is pprent tht most of energy is concentrted in the ower frequency bnd, nd tht there re repeted nus in the spectrum. More insight into mteri chrcteristics coud be obtined by enrichment of the spectrum informtion vibe from PEC inspection with informtion tht might vibe t prticur spectrum nodes obtined using hrmonic eddy current inspection. 3

4 Normized Votge time (ms) () 0 Spectrum Mgnitude frequency (khz) (b) Fig.. ypic PEC ecittion puse in time domin () nd spectrum of frequency domin (b). 3. EDDY CURREN MAGE FUSON he concept of imge fusion is done ntury by the humn eye in fusing spectr coor informtion to enhnce perception of objects. Simir concept cn be dopted in fusion of eddy current imges. C-scn imges cquired either using PEC inspection with different time domin prmeters, or hrmonic eddy current t vrious frequencies cn be fused to obtin one coor imge. A simpe gorithm is to consider three of theses imges to be the RGB pnes of fse coor imge. he resuting imge tht is ugmented in spectr informtion coud further be enhnced by fusion with high spti resoution imge tht 4

5 coud be cquired t high frequency eddy current testing or even with different NDE modity such s rdiogrphy or utrsonic imging. his simpe three-imge fusion technique coud not be dequte with re industri eddy current imges. Advnced fusion pproches re presented net. 4. HS RANSFORM FUSON Ech of the three pnes of imge E defined s (ER, EG, EB) hree frequency eddy current imges re cquired either with PEC or hrmonic EC inspection. High spti resoution imge is so cquired which is genery rger in dimension thn other three imges. mge coud in gener be obtined with cquisition modity tht is different form eddy current. he fusion is done in the foowing four steps:. mges re co-registered.. For ech pie p in the imge, the HS trnsformtion is done s in [Gonzez- Audicn 06]. his trnsform, thus, eds to three imges:, H, nd S. 3. he histogrm of is mtched to tht of obtined imge to obtin new imge. his ccounts for differences reted to cquisition techniques. 4. mge is down-smped to the size of, to obtin imge. 5. mge is repced with. 6. nverse HS trnsform of (, H, S) is performed to obtin fused imge E (ER, EG, EB ). 5. SHF NVARAN WAVEE DECOMPOSON A probem ssocited with the bove method is the distortion in the spectr informtion, which is obtined on the epense of enhncing the spti resoution. One soution is to ppy the shift invrint wveet trnsform to obtin mutiresoution decomposition of imge. Mutiresoution wveet nysis permits the introduction of 5

6 6 detis between successive eves of sce or resoution. he wveet trnsform decomposes the origin imge into number of new imges with different degrees of resoution. n opposition to the spectr informtion provided by Fourier trnsform, Wveet nysis provides both spectr s we s spti informtion [Nunez, 99]. he wveet trnsform of distribution s(, ) cn be written s [Misiti, 07] R R d d b b s b C, ), ( ), ( ψ () R b R b R R R, {0}, {0},, ), ( Where nd re sce prmeters whie b, nd b re trnstion prmeters.. he bse function, b b ψ is the sced nd trnsted version of Mother Wveet ψ. he shift invrint wveet trnsform tht coud be obtined using á trous (with hoes) gorithm overcomes imge rtifcts [Wng, 05] nd [Fower, 05]. n this gorithm, imges nd re decomposed s foows [Prdhn, 06] d v h (3) d v h ' ' (4) Where represents the number of decomposition eves, nd nd represent the pproimtion mtrices of nd mtrices respectivey. he h, v, nd d mtrices re the deti imges decomposition t successivey higher sce. he pproimtion imge is dded to the deti imges of the imge. he inverse wveet trnsform is then obtined to obtin fused intensity imge w such tht w d v h (5)

7 he inverse HS trnsform is then ppied to ( w, H, S) to obtin the fused imge E (ER, EG, EB ). he vidity of the fused imge shoud be tested with quity metrics s described net. 6. MAGE QUAY MERCS wo quity metrics re impemented bsed on spectr s we s spti quity ssessments 0[Wng, 05] nd [Choi, 06]. he first imge quity metric QM is bsed on the spectr nysis nd is tken s the verge of the three corretion coefficients such tht ' QM C( E i E i ) (6) with i,, nd 3 for the three coor pnes in E nd E imges. he second imge quity metric MQ depends on spti quity ssessment bsed on structur simirity (SS) mesurement, introduced in [Wng, 04]. he metric is tken to be ' QM SS( '' ) (7) E i he presented fusion gorithms hve been tested using simuted resuts obtined with finite eement modeing described net. 7. COMPUAONA MODENG he differenti equtions for mgnetic vector potenti cn be written s A ν ( A ) ν ( A) σ σ V 0 (8) t σ A σ V 0 (9) t Where A is the mgnetic vector potenti nd V is the eectric scr potenti, nd σ is the conductivity. he reuctivity ν is the inverse of permebiity. 7

8 For source regions, Eqution 7 becomes ν ( A ) ν ( A) (0) J s Where, J s is the current density in the source. he potenti functions cn be found by soving equtions (7-9), with the pproprite boundry conditions. he finite eement (FE) method is one of the best we known numeric methods tht cn be used to sove this probem. he FE does not offer soution to the diffusion eqution directy. nsted, the soution is obtined t discrete nodes in the soution region by formuting n energy function equivent to energy bnce of Equtions 8-0. A three dimension mode is buit to simute coi on top of met object with defects s shown in Fig.. he coi is designed to be of 0-mm outer rdius, 5-mm inner rdius, nd 5-mm height. he object is composed of uminum with 00-mm rdius nd 0mm thickness, nd the ift-off between the probe nd the object is of.-mm. Anysis is done under ANSYS environment, using eectromgnetic-circuit fied couping nysis. he strnded coi is modeed to be ecited from votge source. he eement mtri is represented s [Ansys] [0] [ CiA ] [0] A [ K AA ] [0] t 0 [0] [ K [ K Ai ii ] A 0 ] 0 V 0 () Where A is nod mgnetic potenti vector, nd i nod eectric current vector. K AA is the potenti stiffness mtri, K ii resistive stiffness mtri, K Ai is potenti-current couping stiffness mtri, nd C ia is inductive dmping mtri. he vector V 0 represents the ppied votge drop. hree crcks re modeed in the simution. A crcks hve the sme cross section of mm mm tht is pre to the object upper surfce. ype is surfce crck of 5 8

9 Fig.. Schemtic finite eement mode of the numeric eddy current inspection system. mm depth. ype crck is subsurfce crck of 3mm depth nd is present mm under the upper surfce of the object. ype crck is of mm depth nd is present t 3 mm from the top surfce. A number of 7385 mesh eements re generted for cceptbe ccurcy. he ecittion is ppied nd the mode is soved for vrious crck positions nd so corresponding to vrious ecittion frequencies. nfinite boundry eements re impemented to mode the surrounding infinite spce. wo formution cses re considered s foows: A. Anysis for sinusoid eddy current ecittion is obtined using FE hrmonic nysis. B. Pused eddy current is nyzed either using trnsient time domin nysis or series of hrmonic nysis. n the trnsient nysis, sufficienty sm time step is used nd time difference pproch is used in time. n the hrmonic nysis of PEC technique the FE mode is run to obtin mgnetic fu density B FE (f) corresponding to frequencies kf 0, where f 0 is the inverse of repetition period 0 nd k,,...n/, nd N is the tot number of time or 9

10 frequency smpes. Runs re ecuded for frequencies mfp where f P is the inverse of puse period τ nd m is n integer. he spectrum of mgnetic fu density is obtined s B( f ) V ( f ) B ( f ) () FE Negtive frequencies resuts re obtined s the conjugte of the simution resuts corresponding positive frequency. nverse Fourier trnsform of B(f) is invoked to obtin the time domin sign. Sequence vues of probe inductnce nd resistnce vues re recorded nd rrnged to obtin c-scn imges, which simutes n object with the three crck types described erier. Crck is on the right, crck is on the eft nd type 3 crck is in the midde. hirteen imges generted with 88 resoution. hree PEC imges re generted s we s ten hrmonic nysis imges, representing probe resistnce vues ( 5 imges ), probe inductnce vues ( 5 imges ) corresponding to frequencies of 00 Hz, khz, 0 khz, 00 khz, nd M Hz. Fig. 3 presents fused imges correspond to simpe RGB fusion technique, identifying three crcks t different depths. Fig. 4 is bsed on HS fusion with high-resoution imge generted t he estimted imge quity metrics of the imge in Fig. 4 were ccuted to be QM nd QM Empes of imge fusion with shift invrint wveet decomposition re presented in Fig. 5, nd Fig. 6, where Dubechies wveets of order 6 re used. he quity metrics were ccuted for imge in Fig. 5 to be QM nd QM Fig. 7 presents the pproimtion nd deti imges corresponding to imge, where the deti coefficients of re repced with those of imge '' shown in Fig. 8. 0

11 Fig. 3. Simpe fusion, with frequency domin imges nd one time domin imge. Fig. 4. Fusion obtined with HS trnsformtion.

12 Fig. 5. Fusion obtined with wveet decomposition, where the high spti resoution imge is frequency domin imge. Fig. 6. Fusion obtined with wveet decomposition s described, where the high spti resoution imge is time domin imge.

13 Fig. 7. Approimtion nd deti coefficients of imge. Dubechies wveets re used. Fig. 8. Approimtion nd deti coefficients of imge ''. Dubechies wveets re used. 3

14 8. CONCUSONS Enhncement of eddy current inspection in nondestructive evution ppictions is currenty directed into incresing sensitivity to subsurfce fws, whie mintining high spti resoution. Convention eddy current using singe-frequency ecittion hs imited mteri chrcteriztion cpbiities nd dt tht re more rigorous coud be obtined by ugmenting the spectr informtion with techniques such s mutifrequency or swept frequency inspection. Brodbnd ecittion is so impemented with timedomin inspection using pused eddy current PEC. PEC spectrum hs repeted nus nd the energy decys with increse of frequency. An gorithm, termed trnsfusion is presented bsed on fusing prti eddy current informtion obtined from PEC inspection with frequency nodes in the spectrum obtined by hrmonic inspection. he technique is bsed on imge fusion methods, in ccordnce with incresed interest in C-scn representtion of eddy current signs. Muti-spectr nd muti-tempor dt re pcked into the coor components of trnsfusion imge. Further enhncement coud be obtined by fusing this imge with high quity imge of the object under test, which coud be cquired using high frequency eddy current inspection or nother NDE modity. Resuts bsed on the proposed technique, impementing finite eement simution of eddy current inspection re presented, ong with suggested imge quity mesures to test the spectr s we s spti informtion of the trnsfusion imge. ACKNOWEDGMENS his reserch is funded by King Abduziz City for Science nd echnoogy (KACS), Reserch Grnt: -8. 4

15 REFERENCES [Ansys] ANSYS documenttions. [Crso, 03] A.B. Crson, et., Communiction Systems: An ntroduction to Signs nd Noise in Eectric Communiction, 4th Ed., McGrw Hi, Boston, 00. [Choi, 06] M. Choi, A New ntensity-hue-sturtion Fusion Approch to mge Fusion with rdeoff Prmeter, EEE rnsctions on Geoscience nd Remote Sensing, Vo. 44 (006), pges [Fower, 05] J. E. Fower, he Redundnt Discrete Wveet rnsform nd Additive Noise EEE Sign Processing etters, Vo. (005), pges [Giguere, 0] J.S.R. Giguere, et., Detection of Crcks Beneth Rivet Heds vi Pused Eddy Current echnique, Review of Progress in Quntittive Nondestructive Evution, D.O. hompson nd D.E. Chimenti, eds., Mevie, New York, AP, Vo. A, (00), pges [Gonzez-Audicn 06] M. Gonzez-Audicn, et., A ow Computtion-Cost Method to Fuse KONOS mges Using the Spectr Response Function of ts Sensors, EEE rnsctions on Geoscience nd Remote Sensing, Vo. 44 (006), pges [Misiti, 07] M. Misiti, et., Mtb Wveet oobo 4, User s Guide, [Nunez, 99] J. Nunez et., Mutiresoution-Bsed mge Fusion with Additive Wveet Decomposition, EEE rnsctions on Geoscience nd Remote Sensing, Vo. 37 (999) pges 04-. [Potnikiv, 0] Y.A. Potnikov, et., Defect Chrcteriztion in Muti-yered Conductive Components with Pused Eddy Current, Review of Progress in Quntititive Nondestructive Evution, D.O. hompson nd D.E. Chimenti, eds., Mevie, New York, AP, Vo. A, (00), pges [Potnikov, 07] Y.A. Potnikov, et., Enhnced Corrosion Detection in Airfrme Structures Using Pused Eddy Current nd Advnced Processing, Mteris Evution, Apri 007, pges [Prdhn, 06] P. S. Prdhn, et., Estimtion of the Number of Decomposition eves for Wveet-Bsed Mutiresoution Mutisensor mge Fusion, EEE rnsctions on Geoscience nd Remote Sensing, Vo. 44 (006), pges [Udp, 0]. Udp, nd. Eshfiey, WNSADS: A New too for Enhncing the Performnce of Eddy Current nspection of Aging Aircrft Whees, nvited Pper, Proceeding of he 5 th Joint NASA/FAA/DoD Conference on Aging Aircrft, Hytt-Orndo, Orndo, Forid September, 00. [Wng, 04] Z. Wng, et., mge Quity Assessment: From Error Visibiity to Structur Simirity, EEE rnsctions on mge Processing, Vo. 3 (004), pges [Wng, 05] Z. Wng, et., A Comprtive Anysis of mge Fusion Methods, EEE rnsctions on Geoscience nd Remote Sensing, Vo. 43 (005), pges