Intelligent location of two simultaneously active acoustic emission sources: Part II

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1 1 Itelliget locatio of two simultaeously active acoustic emissio sources: Part II Tadej Kosel ad Igor Grabec Faculty of Mechaical Egieerig, Uiversity of Ljubljaa, Aškerčeva 6, POB 394, SI-11 Ljubljaa, Sloveia arxiv:74.5v1 [cs.ne] 1 Apr 7 Abstract Part I describes a itelliget acoustic emissio locator, while Part II discusses blid source separatio, time delay estimatio ad locatio of two cotiuous acoustic emissio sources. Acoustic emissio (AE) aalysis is used for characterizatio ad locatio of developig defects i materials. AE sources ofte geerate a mixture of various statistically idepedet sigals. A difficult problem of AE aalysis is separatio ad characterizatio of sigal compoets whe the sigals from various sources ad the mode of mixig are ukow. Recetly, blid source separatio (BSS) by idepedet compoet aalysis (ICA) has bee used to solve these problems. The purpose of this paper is to demostrate the applicability of ICA to locate two idepedet simultaeously active acoustic emissio sources o a alumium bad specime. The method is promisig for o-destructive testig of aircraft frame structures by acoustic emissio aalysis. INTRODUCTION A commo goal of may o-destructive testig methods is to detect defects i materials. Acoustic emissio aalysis (AE) is a passive testig method used to locate ad characterize defects which emit soud[1]. There are may ways to deduce the locatio of a AE source from electrical sigals detected by a chai of sesors. The correspodig problems may be classified by the type of acoustic source mechaism as the locatio of a cotiuous emissio source, such as that geerated by a leak, or as the locatio of discrete emissio, such as a AE burst caused by a growig crack. This paper describes a method for processig cotiuous AE sigals to determie the time delay (T-D) betwee sigals ad thus to provide iformatio for locatio of AE sources. It should be poited out that applicatio of AE source characteristics, such as cout, cout rate, amplitude distributio, ad covetioal time delay measuremet, becomes meaigless whe dealig with cotiuous acoustic sources. The basic iformatio for AE source locatio cosists of T-D betwee stress waves detected at differet positios o a specime. I the case of oly oe active AE source, T- D of cotiuous acoustic waves ca be estimated usig the cross-correlatio fuctio (CCF) of sesor sigals described i Part I of this article[1], [7]. I the case of two (or Mauscript geerated: Jauary 31, 7 more) simultaeously active AE sources, this method is ot applicable, sice aalysis of the CCF leads oly to the T-D of the most powerful AE sigal. Detectio of simultaeously active idepedet AE source sigals therefore requires a more sophisticated approach. The purpose of our study was to fid a suitable method for processig a mixture of two simultaeously active cotiuous AE sigals to determie the T-D ad, related to this, the coordiates of both AE sources. We foud that the Blid Source Separatio (BSS) method solves this problem satisfactorily. BSS is a geeral sigal processig method ivolvig the recovery of the cotributios of differet sources from a fiite set of observatios recorded by sesors, idepedet of the propagatio medium ad without ay prior kowledge of the sources. BSS has already bee successfully applied i medicie, telecommuicatios, image processig etc[8]. However, it is also a promisig method for AE aalysis of aircraft structures, because AE sigals are ofte hidde i a mixture of sigals from various sources. BSS could extract the specific sigature of each AE source, which ca further be used for locatio ad characterizatio purposes, or to isolate AE sources from backgroud oise. We coducted experimets with BSS o a alumium beam o which two cotiuous AE sources were geerated simultaeously by air flow. METHODS I this sectio we explai two differet methods for time delay estimatio of AE sources. The first method is based o aalysis of the CCF ad is coveiet for T-D estimatio of oe active cotiuous AE source as is described i Part I[1], [7], [1]. The CCF exhibits a peak whe the delay parameter compesates the T-D betwee the sesor sigals [1]. The T-D is thus determied by the positio of the highest peak of the CCF. The secod method is based o BSS algorithm ad is coveiet for T-D estimatio of two (or more) simultaeously active cotiuous AE sources[9]. Locatio of two simultaeously active AE sources was performed by a itelliget locator based o a geeral regressio eural etwork[5] as is described i Part I. Multichael Blid Source Separatio has recetly received icreased attetio due to the importace of its potetial

2 PSfrag replacemets applicatios[3]. It occurs i may fields of egieerig ad applied scieces, icludig processig of sigals from atea array, speech ad geophysical data processig, oise reductio, biological system aalysis, etc. It cosists of recoverig sigals emitted by ukow sources ad mixed by a ukow medium (material where waves propagate), usig oly several observatios of the mixtures. The oly assumptios made are the liearity of the mixig system ad the statistical idepedece of origial sigals. BSS methods may be classified i several ways. Oe possible classificatio that ca be made depeds o whether the mixtures are istataeous or covolutive [4]. Covolutive mixtures correspod to a mixig system with time depedet memory. They represet a more geeral case tha istataeous mixtures, ad they have i particular acoustic applicatios. Recetly, the priciple of idepedet compoet aalysis (ICA) was applied i BSS, ad it was foud to be a simple ad powerful tool[6]. This study deals with the separatio of two covolutively mixed idepedet cotiuous AE sigals by ICA ad the itelliget locator was used to locate two idepedet cotiuous AE sources based o T-D [5]. The mixig ad filterig processes of ukow iput sigals s j (t) may have differet mathematical or physical backgrouds, depedig o specific applicatios. I this paper, we focus maily o the simplest cases with sigals x i (t) liearly mixed i ukow statistically idepedet, zero mea source sigals s j (t). The compositio is expressed i matrix otatio as x = A s [8], where * deotes a covolutio, x = [x 1 (t),...,x (t)] T is the vector of sesor sigals, s = [s 1 (t),...,s (t)] T is the vector of source sigals ad A is a ukow full rak mixig matrix whose elemets are fiite ipulse respose (FIR) filters. We assume that oly vector x is available. The goal of ICA is to fid a matrix W, by which vector x ca be trasformed ito source sigals u = W x. PSfrag replacemets Matrix W is simply the iverse of A. However, whe oise corrupts the sigals, matrix W must be foud by a optimal statistical treatmet of the iverse problem. The optimal matrix W ca be estimated by a feed-forward eural etwork operatig i the frequecy domai. A learig algorithm with Amari s atural gradiet ca be writte as[1]: ũ = W x, W(τ + 1) = W(τ) + α W(τ) + η W(τ 1), W = [I ỹ ũ H ] W, ỹ = tah(r[ũ])+ı tah(i[ũ]), where α is the learig rate, η is the costat of learig, I is the idetity matrix ad the tilde represets a frequecy domai. The ICA algorithm rus off-lie ad proceeds as follows [11] (Fig. 1): 1) Pre-process the time-domai iput sigals, x(t): substract the mea from each sigal. ) Iitialize the frequecy domai umixig filters, W. 3) Take a block of iput data ad covert it ito the frequecy domai usig the Fast Fourier Trasform (FFT). 4) Filter the frequecy domai iput block, x, through W to get the estimated source sigals, ũ. 5) Pass ũ through the frequecy domai oliearity, ỹ. 6) Use W, ũ ad ỹ alog with the atural gradiet extesio [] to compute the chage i the umixig Fig. 1. pre-process x x(t) FFT update rule Block diagram of ICA algorithm iitialize umixig filters W filter tah ũ ỹ W filter, W. 7) Take the ext block of iput data, covert it ito the frequecy domai, ad proceed from step 4. Repeat this process util the umixig filters have coverged upo a solutio, passig several times through the data. 8) Normalize W ad covert it back ito the time domai, usig the Iverse Fast Fourier Trasform (IFFT). 9) Covolve the time domai umixig filters, W, with x to get the estimated sources. EXPERIMENTS We performed experimets with two idepedet cotiuous AE sources o a alumium bad of dimesios mm 3. Reflectios at the ed of the bad were reduced by wrappig the eds i putty. The testig area was o the logitudial axis i the middle of the bad, where 3 holes of diameter mm ad mutual separatio 1 mm were prepared as show i Fig.. Fig.. 1 φ mm AE geeratio by air flowig through the hole l bad air flow Two AE sesors were mouted 1 mm away from the termial holes, that is.4 m from each other. The origi of the coordiate system was i the middle of the bad ad the testig area exteded from 1.1 m to +1.1 m. AE sigals were excited by two idepedet air jets flowig through the holes. The source positio was arbitrarily selected at +1 mm ad +8 mm. Air jets were formed by two ozzles of diameter 1 mm usig pressure 7 bar. The experimetal setup cosisted of the test specime (alumium bad), two AE sesors (piducers), two AE sources (air jets), two amplifiers, a digital oscilloscope (A/D coverter) ad a computer (BSS module, locator, plotter) as show i Fig. 3. Three experimets were performed : (1) T-D estimatio usig a CCF of two AE sigals that were ot simultaeously active; () T-D estimatio usig a CCF of two AE sigals which were simultaeously

3 3 placemetsactive ad (3) T-D estimatio of AE sigals usig ICA. Locatio of sources, based o T-D, by the itelliget locator was performed i all three cases. specime sesor AE source amplifier A/D coverter blid source separatio locator PSfrag plotter replacemets Rx1x Fig. 3. Experimetal set-up PSfrag replacemets Rx1x rag replacemets rag replacemets I the first experimet oly oe air jet was activated for a particular measuremet. I the secod experimet both air jets were activated. Sesor sigals were liear covolutive mixtures of two idepedet cotiuous AE sources as show i Fig. 4. The auto-correlatio R 11, R ad cross-correlatio fuctios R 1, R 1 were calculated from sesor sigals. Oly oe T-D of two sigals ca be estimated from the highest peak i both CCF, regardless of the umber of idepedet AE sources o the test specime as show i Fig. 5. This meas that a CCF ca ot be used for automatic T-D estimatio of multiple AE sigals o the test specime. The CCF exhibits various peaks which belog to various idepedet AE sources, but it is ussually impossible to relate these peaks to correspodig coordiates of AE sources. x1(t) x(t) t [ms] (a) Sesory sigal # t [ms] PSfrag replacemets R x1 x PSfrag replacemets R x1 x R x x 1 Rxx1 Rxx Fig. 5. Auto- ad cross-correlatio fuctios of sesory sigals; dow-arrow marks the highest peak AE sources ad two sesors, the compoets of A are four FIR mixig filters, as show i Fig. 6. There are two direct, a ad two cross mixig filters a 1, a 1. The first idex of the filter represets the umber of the sesor, while the secod idex represets the umber of the source. The positio of the highest peak of the cross FIR filters determies the T- D betwee two sigals from two sesors. If we substract the coordiate of the highest peak of a direct mixig FIR filter from the coordiate of the highest peak of cross filter a 1 we obtai the T-D of first idepedet AE source, sice each of the highest peaks i the FIR filters belogs to differet idepedet AE sigals. (b) Sesory sigal # Fig. 4. Mixtures of two idepedet cotiuous AE sources aquired by two sesors I the third experimet the ICA algorithm was used to solve this problem satisfactorily. The ICA algorithm results i demixig FIR filters which extract the idepedet source sigals from sesory sigals. By ivertig the demixig filters W we obtai mixig filters A. I the case of two idepedet RESULTS The results of T-D estimatio of two cotiuous idepedet AE sources are show i Fig. 7. Three experimets were doe. I the first experimet, the T-D was estimated by a CCF of two AE sources which were ot active simultaeously as marked by. Locatios of these two sources estimated by the itelliget locator were +181 mm ad +784 mm. The secod experimet was performed with both AE sources active simultaeously. T-D were also estimated by a CCF. The highest peak

4 4 frag replacemets a PSfrag replacemets estimated positio ˆl [m] correlatio fuctio ICA ICA frag replacemets a1 actual positio l [m] Fig. 7. Results of locatio of two cotiuous idepedet AE sources. Symbols: AE sources obtaied by ICA; estimated AE sources obtaied by cross-correlatio fuctio i two steps, whe just oe of two AE sources was active at time of measuremet; estimated AE sources obtaied by cross-correlatio fuctio whe two AE sources were active simultaeously; prototype AE sources required for locatio usig itelliget locator; distributio of actual sources. frag replacemets a 1 frag replacemets a 1 a 1 a1 a Fig. 6. Mixig filters obtaied by ICA of sesory sigals; dow-arrow marks the highest peak positio correspods to the source locatio marked by ad was +784 mm. The third experimet was performed usig ICA for T-D estimatio ad locatio by itelliget locator. The result is marked by. Estimated positios of this two sources were +179 mm ad +784 mm respectively. If we compare the coordiates of both idepedet AE sources estimated by the first experimet ad by the third experimet, we fid a good correspodece. If we compare estimated AE source coordiates with actual coordiates, which were +1 mm ad +8 mm respectively, we observe a slight disagreemet due to experimetal error. Experimetal error is about 3% regardig the distace betwee sesors. Absolute error i this case is 79 mm ad 16 mm respectively. The results also deped o the umber ad distributio of prototype sources marked by, which are essetial for operatio of the itelliget locator. If the umber of prototype sources is icreased, locatio error is reduced. I our case the prototype sources were distributed alog the beam from 1.1 m to +1.1 m separated by.1 m, so that systematic error of the locator was set to several procets. DISCUSSION AND CONCLUSION CCF is applicable to T-D estimatio oly i the case of oe active AE source. The goal of our research is to develop a ew method to estimate T-D betwee AE sigals i the case of multiple simultaeously active cotiuous AE sources. We have show that, for this purpose, ICA is a applicable optio. ICA fids a liear coordiate system (the umixig filters) such that the resultig sigals are statistically idepedet. This is a advatage of ICA over CCF. It represets a ew approach to processig of AE data ad further expads the applicability of AE aalysis i the field of o-destructive testig. I machies or i a idustrial eviromet, multiple sources are usually active Simultaeously, ofte represetig evirometal disturbaces. The correspodig complex sigals are ot directly applicable to characterizatio of particular sources. However, separatio of cotributios by ICA aalysis i fact represets a kid of filterig, icreasig the applicability of filtered sigals to characterizatio of sources i complex eviromets. Future research will be focused o locatio of multiple AE sources o two-dimesioal ad three-dimesioal specimes. REFERENCES [1] Amari, S.-I. 1998, Natural gradiet works efficietly i learig, Neural Computatio 1, [] Amari, S.-I., Cichocki, A. Yag, H. H. 1996, A ew learig algorithm for blid sigal separatio, i D. Touretzky, M. Mozer M. Hasselmo, eds, Advaces i Neural Iformatio Processig Systems, Vol. 8, MIT Press, Cambridge MA, pp [3] Burel, G. 199, Blid separatio of sources: A oliear algorithm, Neural Networks 5, [4] Deville, Y. Charkai, N. 1997, Aalysis of the stability of timedomai source separatio algorithms for covolutively mixed sigals, i Iteratioal Comferece o Acoustics, Speech, ad Sigal Processig, pp [5] Grabec, I. Sachse, W. 1997, Syergetics of Measuremet, Predictio ad Cotrol, Spriger-Verlag, Berli. [6] Hyvarie, A. Oja, E., Idepedet compoet aalysis: algorithms ad applicatios, Neural Networks 13, [7] Kosel, T., Grabec, I. Mužič, P., Locatio of cotiuous acoustic emissio sources geerated by air flow, Ultrasoics 38(1 8), [8] Lee, T.-W. 1998, Idepedet Compoet Aalysis, Theory ad Applicatios, Kluwer Academic Publishers, Bosto etc.

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