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1 ARTMAP NETWORK AND WAVELET ANALYSIS FOR FLAWS CHARACTERIZATION M. C. Moisen 1,, H. Benítez 1, L. Medin* 1, E. Moreno 3, G. González 4, nd L. Leij 4 1 DISCA-IIMAS-UNAM, Méico D. F.; Méico UAG, Acpulco, Méico, 3 ICIMAF, L Hn, Cu, 4 CINVESTAV, Méico D. F:, Méico Astrct: Ultrsonic pulse-echo technique hs een successfully used in non-destructive testing of mterils. This method ims to chrcterize the propgtion pth nd/or to determine the physicl properties of reflectors in terms of their loction, size, orienttion, nd porosity. To perform ultrsonic non-destructive evlution (NDE), n ultrsonic pulsed wve is trnsmitted into the mterils using trnsmitting/receiving trnsducer. The spectrl nlysis of the ckscttered echoes hs een widely used for flws detection, frequency-shift estimtion, nd dispersive echoes chrcteristion. An innovtive methodology is presented in this pper, in order to chrcterise flws within the tested mteril A pttern recognition technique sed on ARTMAP network nd wvelet trnsform is used s digitl processing tool tht llows the geometry of flws eing determined. This technique consists of two non-supervised neurl networks nmed ART (Adptive Resonnce Theory) nd the Meicn ht wvelet trnsform. An luminium lock with three mn-mde defects of circulr geometries ws scnned, y moving single ultrsonic trnsducer long two perpendiculr pths, producing two reflectivity mps contining the flws informtion. The signl processing method proposed here used the received signls s follows: The totl set of signls ws split into two susets, depending on the scnning pth. The 10% of ech suset ws used to trin n ART network, vi the spectrl informtion produced y the Meicn ht wvelet nd the rest of them to vlidte the system. The ARTMAP network uild mp field, since flws re present in oth es, mp field reproduced the flws contour, sed on the proper selection of vigilnce nd lerning prmeters. Introduction: Ultrsonic flw detection is n importnt technique to ssure the qulity of mterils non-destructively. The gol for ultrsonic inspection is the detection, loction nd clssifiction of internl flws nd defects. However, the detection cpility is often limited y the interference noise produced y sctterers rndomly distriuted throughout the mteril. Spectrl nlysis is often dopted since the noise due to grin scttering ehiits vriility in time domin. Neurl networks re well suited to signl clssifiction in instrumenttion. They hve the ility to generlise nd produce result on the sis of incomplete dt. For neurl network to relily clssify defects the trining dtse must contin sufficient of ech type of defect for the trining opertion to e effective. Where the type of defect is initilly unknown it my lso e possile to use utomtic pttern clssifiction nd self-orgnising network to generte the pproprite output sttes [1]. ARTMAP is clss of neurl network rchitecture tht perform incrementl supervised lerning of recognition ctegories nd multidimensionl mps in response to input vectors presented in ritrry order []. ART stnds for Adptive Resonnce Theory nd ws introduced y Grosserg in The min feture of ll ART systems is pttern mtching process tht compres the current input with selected lerned ctegory representtion. ART is cple of developing stle clusters in response to ritrry sequences of input ptterns y self-orgnistion. ARTMAP etends the ART design to include oth supervised nd unsupervised lerning. In ARTMAP, the chosen ART ctegories lern to mke predictions in the form of mppings to output clsses. Minim lerning rule enles the fuzzy ARTMAP system to conjointly minimise predictive error nd mimise code compression or predictive generlistion.

2 ARTMAP [] network hs s min chrcteristic to perform incrementl lerning of recognition ctegories nd multidimensionl mps. This network is supervised neurl network ssocited to vector ctegories in order to construct mp. Two kinds of vectors re used, first vector is relted to first ART network (ART A ) nd it is identified s unknown vector. Second vector is relted to second ART network (ART B ) nd it is identified s predicted vector. Both ART networks perform mtching procedure in order to construct mp of those similrities etween selected vectors. The structure of this neurl network consists of two ART networks [3]. Ech ART network is independent in principle, lthough, first network modifies its vigilnce prmeter ccording to certin ehviour from MAP field. Both ART networks follow the pproch presented y Frnk et l. (1998) [4]. This scheme is shown in Fig. 1. Output Vector n W 11 W1 W 13 W 14 W 53 W5 W 54 W 5n W 1n W Input Vector, Neurons Arry Figure 1. ART Network The ide is to identify lredy clssified ptterns nd ctegorize new ptterns. This network is divided into two stges: ) ottom up (input-output) competitive lerning nd ) top-down (output-input) lerning. The network stores ptterns s sets of weights ssigned to the pths connecting the input units to ech of the output units. Presenttion of n input vector cuses the output units to e ctivted, the mount of ctivtion depending on the similrity etween the input vector nd the stored pttern. Finding the nerest neighour is simply mtter of deciding which output unit hs een ctivted the most. The weights tht connect ech output unit to the input units represent the typicl pttern of the clss to which the output unit elongs. The weights tht connect the input units to ech output unit represent the sme pttern, ecept tht their vlues re normlised. The networks lso hve mechnism for dding new ctegory units to the output lyer. This process is controlled y two prmeters: the vigilnce prmeter nd the lerning prmeter. The vigilnce prmeter, ρ, specifies how similr de input pttern is to e clssified s elonging to the sme ctegory, nd the lerning prmeter, η, controls the step size for weight djustments. The current input of the network is stted s A. This is normlized using the Euclidin medi defined y A A I = = A m (1) i i= 1 where m is the mth element of A. The new generted vector I is used to perform nother vector nmed s t sed on where w ij t j = m i= 1 is n element of weight mtri generted y previous pttern clssifiction. w i ij i ()

3 From t j element, new vector is performed, stted s T. This vector represents the interction etween the lredy known weight mtri nd the input vector. The mimum element from current t ecomes the winner for this input vector then the stge ottom-up is completed. The mimum vlue of current t is compred ginst to vigilnce prmeter ρ in order to determine if this current minimum vlue is closed to vigilnce prmeter. If this it so, the relted winning vector Wj is declred s representtive pttern of the input A. Afterwrds, W j is modified y ( new) W = ηi + 1 η W (3) where η is defined s lerning prmeter. J ( ) old Alterntively, if ρ t J then new pttern hs een identified. Then new vector W j is conctented to weight mtri. This new vector is the current input vector I. The selected network (ARTMAP Network) hs the peculirity of mp field construction tht represents the min chrcteristics of ny pttern comintion. This lgorithm consists of two ARTA networks integrted to mp field s shown in Fig.. J Field A MAP Field B ARTA A Mtch Trcking ARTA B Input Vector Trget Vector Figure. Structurl construction of ARTMAP Network Since the lgorithm performed y ech ART network hs een defined, it is importnt to define how the mp field is uild. In this cse oth output vectors (from ech ART network), nmed s y nd y respectively, re send to mp field. In there, the inde of the winner neuron from first neurl network is considered in order to select the respective vector from the relted weight mtri from mp field. Once the weight vector is selected, it is compred ginst output vector (y ) from ART B network. There re four possile cses with reltion to mp field selection. y w If Jth element from y nd Jth element from y re ctive If = w J J y 0 If Jth element from y If Jth element from y If Jth element from y then ρ is incresed until it is slightly lrger thn is ctive nd Jth element from y is not ctive nd nd Jth element from y Jth element from y re not ctive is not ctive is ctive < ρ y (5) 1 I wj I (6) where W is defined dimensionl correct with respect to vectors y nd y. This mtri (W ) is initilly declred y 1 s nd is modified ccording to results. (4) The ARTA networks hd een trined with time-scle informtion from the received signls. The time-scle process is sed on wvelet nlysis. Wvelet nlysis refers to collection of methods tht hve found incresing use in signls processing, imge nlysis, nd dt compression. The wvelet trnsformtion of time vrying signl (t) consists of computing coefficients tht re inner products of (t) ginst fmily of wvelets. These wvelets ψ, (t) re lelled y

4 scle nd time loction prmeters nd. In continuous wvelet trnsform, the wvelet corresponding the scle nd time loction is 1 t ψ, () t = ψ (7) where ψ, (t) is the mother wvelet, which cn e thought s ndpss function. The continuous wvelet trnsform (CWT) is given y [5] * CWT, = t ψ t dt (8) ( ) ( ) ( ) where * stnds for comple conjugtion. Wvelet series (WS) coefficients re smpled CWT coefficients. Time remins continuous ut time scle prmeters re smpled on dydic grid in the time-scle plne (,). A usul definition is C j, k CWT j j for j k Z (9) the wvelets re, in this cse,, =, =, = k j j ( t) = ( t k) ψ (10) j, k ψ nd the originl signl cn e recovered though the following formul t = C j ~ψ t () ( ), k j, k j Z k Z where ~ψ () t re lso of the form of ψ j,k (t) j,k A simple emple of wvelet with infinite support is the so-clled Meicn ht, defined y the second derivtive of Gussin function s d ψ () t = ( 1 t ) ep( t ) = ep( t ) = ψ 1, 0 () t (1) dt This wvelet hs ecellent loclistion in time nd frequency domins nd clerly stisfies the dmissiility condition. [6]. Results: All eperiments were crried out with Hydrophone scnning system (Specilty Engineering Assocites SEA, CA, USA), two Personl computers (Pentium II, 18 RAM), nd digitl oscilloscope (TDS-340 Tektroni, Oregon, USA). This system is le to control motor to move the ultrsonic trnsducer long the -is, y-is nd z-is with 10µm step. The system cn lso store the wveforms, clculte the prmeters nd disply grphicl representtion of the eperimentl dt. In typicl eperiment, the ultrsonic trnsducer nd the phntom re immersed in wter tnk (see Fig. 3), then the trnsducer is ecited producing pulse, the computer-controlled motor moves the trnsducer point y point, nd n oscilloscope records the corresponding signl from ech point nd stores it. The trnsmission nd triggering of the ultrsonic pulse of the trnsducer were controlled vi pulse-eco crd MATEC SR9000 (Mtec Instrument Compnies, MA, USA). The circulr Krutkrmmer (CR-RHP, GAMMA,.5X.50, BNC) ultrsonic trnsducer le to trnsmit pulse t.5 MHz hs een used. The phntom is n luminium lock of mm 3, with three mn-mde circulr flws digonlly locted. (11)

5 POSITIONING SYSTEM (yz) COMPUTER COMPUTER 1 ULTRASONIC PULSER PREAMPLIFIER DIGITAL OSCILLOSCOPE y ULTRASONIC TRANSDUCER WATER TANK Figure 3. Eperimentl Setup The proposed ARTMAP rchitecture ws pplied to simulted nd rel dt. The simultion of received signls nd the ARTMAP lgorithm hd een developed on MATLAB pltform. The ARTMAP lgorithm ws tested when the ARTA A nd ARTA B networks were trined with nd without wvelet informtion. In order to test the ARTMAP network lgorithm, simulted signls were used. Those signls with dditive white noise represent the scnned medium long nd y-is, where three point-inhomogeneities re digonlly locted. The received signls were split into two different sets: the first set is relted to the -is scnning direction nd the second to the y-direction, s shown in Figure 4. () () Figure 4 Simulted received signls: ) long -is nd ) long y-is. The ARTMAP lgorithm ws first pplied to the normlised (see eq. 1) received signls in order tht ARTA A nd ARTA B ptterns were computed nd the mp imge produced s shown in Figure 5. The lerning nd vigilnce prmeters vlues re shown in Tle 1 When the signls re wvelet trnsformed using the Meicn ht mother wvelet (eq. 1) nd normlised, the output ptterns of ARTA A nd ARTA B nd the utoregressive mp re shown in Figure 6. The min differences of ARTMAP outputs when the network is trined with nd without wvelet nlysis re: ) the noisy ptterns in Figures 5 nd 5 re clered when Meicn ht wvelet trnsform is included in the digitl process (see Figures 6 nd 6), nd ) the vigilnce prmeter of ARTA B is slightly diminished, reducing the numer of ptterns in the wvelet- ARTMAP network (see Tle 1). The sme digitl process ws pplied to rel dt. Two perpendiculr B-scns were mde cquiring two sets of received signls s shown in Figure 7. Ech signl ws wvelet trnsformed nd normlised to compute the input vector of ech ARTA networks. Those vectors generte the ptterns tht produce the mp of similrity mong them s shown in Figure 8. Since the rel dt is quite noisy, due to reflections coming from in-homogeneities, ottom of wter tnk, impurities, mong others, the numer of ptterns in ARTA A nd ARTA B is quite

6 lrge, compred to the ptterns produced when simulted dt is used in the digitl process. Also the vigilnce nd lerning prmeters re vried s shown in Tle 1. Figure 5. Ptterns nd imges of ARTMAP process: ) ARTA A, ) ARTA B, c) contour, nd d) imge of. Figure 6. Ptterns nd imges produced y ARTMAP-wvelet process: ) ARTA A, ) ARTA B, c) contour, nd d) imge of. Discussion: Present results show how this composite lgorithm cn overcome noise presence inherent to those processed signls. In fct, there re severl vriles to e considered such s the selection of the mother wvelet, the vigilnce nd lerning prmeters nd the structure of the network itself. It hs found, on simultion nd eperimentl sis, tht Meicn ht wvelet presents suitle results respective to the noise inherent in the studied signls. Figure 5c nd Figure 6c depicted clerly the intersections of selected ptterns from ARTA networks. It is importnt to highlight tht this intersections re defined s prt of the construction of the mp within the ARTMAP

7 network. This mp does not produce those intersections ecuse the sptil reltionship of the input signls, it is constructed sed on similr loctions of the ptterns. () () Figure 7. B-scn eperimentl dt: () long -is nd ) long y-is Figure 8. ARTMAP output for rel dt: ) ARTA A ptterns, ) ARTA B ptterns, c) contour nd d) imge of the digitl process result. Prmeter () () (c) ρ η ρ η ρ Tle 1. ARTMAP prmeters vlues when normlised input vectors re: ) rw signls nd ) normlised wvelet trnsformed signls. Conclusions: This pper hs presented novel pproch for non-destructive testing sed on comined lgorithm of wvelet trnsform nd ARTMAP network. The utoregressive mp is uilt considering the following: ) the orthogonl chrcteristic of the two B-scn, nd ) the selected neurl network tht hs the dvntge of mp construction y the intersection of common ptterns.

8 When simulted signls with dditive white noise re used s input vector of the ARTA networks the numer of pttern due to noise is reduced when the signls re wvelet trnsformed, however the resulting mp is not clerly ffected. However if rel dt is the input vector the numer of ptterns produced y the ARTA networks is drsticlly diminished when Meicn ht is pplied to the received echoes. Even though tht this numer is lrger thn 000 for the ARTA A cse. It cn e reduced, therefore the time consuming process, if the echoes coming from the fces nd ottom of the phntom re neglected. This technique hs presented not only flw loction it hs produced flw chrcteristion s result of mp construction. This my enhnced the ide of multidimensionl pttern recognition. Further studies re pursued in terms of NDT utonomous procedure where the ARTMAP network cn seprte severl types of flws s well s determine certin geometric chrcteristics of them. Alterntively, further work is pursued in order to incorporte wvelet decomposition chrcteristics into ARTMAP lerning procedure s well s mp construction. References: [1] Mrgrve F. W., Rigs K., Brdley D. A., Brrowcliffe P., The Use of Neurl Network in Ultrsonic Flw Detection, Mesurement 5, pp , [] Crpenter G. A., Grosserg S., Mrkuzon N., Reynolds J. H., Rosen D. B., Fuzzy ARTMAP: A Neurl Network Architecture for Incrementl Supervised Lerning of Anlog Multidimensionl Mps, IEEE Trns. Neurl Network 3, pp , 199. [3] Crpenter G. A., Grosserg S., The ART of Adptive Pttern Recognition y Self- Orginizing Neurl Network, IEEE Computer 1, pp , [4] Frnk T., Kriss K. F., Kuhlen T., Comprtive Anlysis of Fuzzy ART nd ART-A Network Clustering Performnce, IEEE Trns. Neurl Network 9, pp , [5] Aky M., Time Frequency nd Wvelets in Biomedicl Signl Processing, IEEE Inc., New York, 1998 [6] Denth L., Wvelet trnsforms & their pplictions, Birkhuser, Boston 00.