Localization Algorithm for Acoustic Emission

Transcription

1 Avalable onlne at Physcs Physcs Proceda 3 (2010) 00 (2009) Internatonal Congress on Ultrasoncs, Unversdad de Santago de Chle, January 2009 Localzaton Algorthm for Acoustc Emsson V. Salnas a, *, Y. Vargas a,#, J. Ruzzante b, L. Gaete a. a Unversdad de Santago de Chle, Av. Ecuador 3493, Santago, Chle b Comsón Naconal de Energía Atómca CNEA, Av. General Paz 1499, San Martín Buenos Ares, Argentna Elsever use only: Receved date here; revsed date here; accepted date here Abstract In ths paper, an teratve algorthm for localzaton of acoustc emsson (AE) source s presented. The man advantage of the system s that t s ndependent of the ablty n the determnaton of sgnal level to trggerng the sgnal by the researcher. The system was tested n cylndrcal samples wth an AE localzed n a known poston; the precson n the source determnaton was of about 2 mm, better than the precson obtaned wth classc localzaton algorthms (~1cm). PACS: Zc; Le Keywords: acoustc emsson, teratve methods, NDT 1. Introducton Acoustc emssons (AE) are the stress waves produced by the sudden nternal stress redstrbuton of the materals caused by the changes n the nternal structure [1]. Internal-structure changes could be crack ntaton, crack growth, crack openng, crack closure, dslocaton movement, phase transformaton n monolthc materals, fber breakage and fber-matrx debondng n compostes. Most of the sources of AEs are damage-related; thus, the detecton and montorng of these emssons are commonly used to predct materal falure [2]. Besdes the applcatons of AE n research endeavors, AE has been wdely used n ndustres, ncludng the detecton of flaws or leakage n pressure vessels, tanks, and ppng systems. AE s also used to montorng the weldng and corroson progress. The dfference between the AE technque and other nondestructve evaluaton (NDT) s that AE detects the actvtes nsde the materals, so ths technque can be predct a falure, whle other NDT methods detect the flaw when the falure was created. Furthermore, AE only needs the sgnal from one or more relatvely small sensors on * Correspondng author. Tel.: E-mal address: vcente.salnas@usach.cl # Correspondng author. Tel.: E-mal address: yolanda.vargas@usach.cl do: /j.phpro

2 864 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) the surface of the structure or specmen beng examned. So the structure or specmen can be examnated n-servce or n laboratory operaton whle the AE system contnuously montorng the progressve damage [3]. The methods of locazaton are constructed through teratve and non teratve algorthms based on sgnals from the source and acqured by sensors located on the surface of the sample and the poston of these sensors. Based on the arrval-tme dfferences, observed n an array of three sensors, an exact soluton for the confguraton of three sensors n a planar surface was derved. The AE source s located at the ntersecton ponts of two hyperbolae curves Tobas [4]. Usng the dfferences n tme-of-arrval (TOA) from an AE source to three sensors [5], the poston of the source s calculated through the use of sphercal coordnates. M. Asty found that, the postons of the source, can have more than 1 value and t s needed to use fourth sensor to elmnate ths problem. In a smlar approach, Barat et al. [6] developed a mathematcal method for the calculaton of the coordnates of an AE source n cylndrcal surfaces usng the concept of geodesc, to fnd the path of the wave between 2 sensors on the surface. Dong-Jn Yoon [7], generalzed mathematcal formalsm for the path traveled by an acoustc wave n the surface of a structure s presented, and a drect method for the calculaton of the coordnates of an AE source on a cylndrcal surface by three sensors s evaluated. Based on the cross-correlaton of two sensor sgnals the dfference of the arrval tme s estmated accurately by calculatng the phase shft of the sgnals n the cross-correlaton. Two alternatve but equvalent procedures for the best estmaton of the source locaton, correspondng to the ellpse s centre for three or more mcrophone clusters are presented by B. V. Landau [8]. A novel localzaton method of the source poston generatng mpulsve perodc sgnals s proposed n [9], requrng a mnmum of three mcrophones to dentfy mpulsve sources n 2-D space, whle n 3-D space at least four mcrophones must be used. In ths paper, a method to fnd the coordnate of an AE source n a non dspersve materal usng TOA of N events n M sensors s presented. The number of sensor must be greater than sx f locaton n 3D s requred. The method suppose propagaton wave velocty constant n all drecton, ths velocty was determned by TOF before expermentaton. 2. Theorcal Arguments For the source localzaton, only geometrcal arguments were utlzed. If the poston of the sensors are determned by X (x,y,z ) and the source poston s X(x,y,z), the dstance from the source to the sensor can be obtaned from 2 2 D = (x- x) +(y- y) +(z- z) 2 (1) The arrval tme from the poston of the source to the sensor s gven by the equaton D= (t-t 1) (2) Where t s the arrval tme to sensor and t s the tme of event occurrence. The poston of AE source and the wave propagaton velocty can be obtaned solvng the system composed by equaton (1) and (2). In these formulae more unknown varables than equatons appear. To solve ths problem we do: D-D= (t-t ) (3) 1 1 Where, D 1 s D evaluated for =1, and =2, 3,..., m.. These equatons conduct to the followng relatons [10] e (ax+by+cz) d = - 2 D (4) d d 1 Where

3 a x 1 x b y1 y c z1 z d ( t t1) e x 1 y 1z 1 ( x y z ) V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) The non-lnear system defned by (4) can be lnearzed by subtractng the equaton (4) evaluated for =2 from the equaton (4) [10]. Where f x f y f z h g 2,1,2,3 (5) a2 a f,1 2 t2 t b2 b f,2 2 t2 t c2 c f,3 2 t2 t g ( t2 t) e2 e h t t Wth 3, 4,..., m 2 In the equaton (5) t s assumed that the velocty v s known, n the present case, the velocty n the materal wll be unknown and calculated n each one of the teraton. The matrx form of equatons system s Axb Where f3,1 f3,2 f3,3 g 3w x h3 A, x y, b fm,1 fm,2 fm,3 g mw z h m Each new value of velocty calculated s compared wth the nput velocty (measured). Ths system gves the coordnates of the source and the propagaton velocty n the medum gven by w. (6)

4 866 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) Algorthm Fg.1 Flow dagram of development of the localzaton algorthm. Fgure (1) shows the flow dagram of the algorthm that begns wth the selecton of one AE event detected by all the sensors. The program s feed wth the coordnates of each sensor n any convenent system, accordng to the geometry. For the ntal confguraton t s necessary to feed the frst threshold to calculate a tentatve poston of source n x(0). Then the program realze the calculaton of the coordnates of the source and the propagaton velocty n the medum wth the lnear system of equatons (6), these calculatons are performed n computatonal platform. After calculatng the poston and velocty, the program performs a comparson between the velocty measured and calculated, f the dfference between both s greater than the tolerance (the tolerance s gven by the user, of course t depends on the technque used n the measurement of speed, the case treated n ths paper, the tolerance used was 10 m / s ), the system changes the frst threshold thus obtaned new tmes of arrval. The decson to ncrease or reduce the threshold s gven by the tendency of the velocty calculated, n the frst nstant the program lowers the threshold, f the value of the calculated velocty s far from the measured value.e., f the speed dfference ncreases, the program ncreased the threshold untl t converges, otherwse t contnues to declne untl fulfll the requrement of tolerance. Fnally, the program gves the coordnates of the source n the reference system chosen for the poston of the sensors. 3. Expermental Setup The algorthm was tested on samples of epoxy resn (Araldte) (fgure (2a)) whch has n ts nteror a pezoelectrc ceramc (Fgure (2b)), whch smulate the acoustc emsson. Because the cylnder s made wth semtransparent Epoxy resn s possble know the exact locaton of that source checkng the algorthm accuracy. The ceramc was excted wth a pulse of 475 [] for 9 [], emttng a pulse wth shape and duraton determned by ts

5 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) own mechanc characterstcs. In the fgure (3) the mpedance and phase curve for the pezoelectrc ceramc t s shown. The sample s a cylnder 5115 [] n dameter and 90 [] heght. Ceramcs s 243 [] wde, 346 [] long and 290 [] thck. For the recepton of sgnals, dfferental transducers (16 [] n dameter) t was used. The resonance frequency of the sensor was measured, gvng 137 []. Sgnals were acqured by the acquston card wth 2.5 [MHz] of samplng frequency. (a) (b) Fg.2 (a) Sample wth BNC connector adapted to the exctaton of ceramcs. (b) Ceramcs wthn the sample smulatng acoustc emsson. Fg.3 (+) Phase of the ceramcs used. () Impedance of the ceramcs used.

6 868 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) The sensors were dstrbuted to produce the best coverage of the volume n queston. An ensemble of 12 sensors dstrbuted n 3 rngs of 4 sensors on the surface of the sample was mounted. The sgnals recved by the 12 sensors are shown n the fgure (4). It can be apprecated n fgure 4 that the frst transducer detectng any sgnal s the channel fve sensor. Sold vaselne was used to couple the sensor wth the sample. Fg.4 Sgnals receved n the 12 postons sorted by tme of arrval.

7 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) Results To assess the computng velocty of dfferent methods to solve the lnear system dfferent algorthms were tested; the results are shown n table I. Method Accuracy (mm) Nº Iteratons Gauss-Sedel Lnsolve Jacob Gauss Analyzng the results suppled by the tested algorthms, the method obtanng greater accuracy s Lnsolve. The dfference between the actual poston and the calculated postons s 2.033[mm]. In fgure (5) the convergence of ths method t s shown. Fg.5 Convergence of the method accordng to the teratons calculated by Lnsolve method.

8 870 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) Progress Locaton Algorthm Z coordnate X coordnate Y coordnate Fg.6 Progress of the algorthm, outlned the soluton n each teraton (dots) n the vcnty of the real poston (damond). To better understandng of the process, n fgure (6) the results of poston source obtaned n the teratons t s shown. The blue dots represent susesve postons calculated, where the frst teraton s the frst pont of the left and the next are goes to the rght. The red damonds represent the true poston of the source (PZT ceramc). The green contour represents the sample surface. In each teraton the computed soluton s closer to the true poston of the source, whch confrms the results shown n the convergence curve presented n fgure (5). 5. Concluson A new approach to solve the problem of localzaton of acoustc emsson source n 3D s presented. Localzaton algorthm s evaluated n homogeneous meda where the speed of propagaton remans constant n all drecton. The poston of the sensors s arbtrarly selected by the researcher dependng of the geometry of the sample. Wth ths technque t s possble to fnd the tme n whch the event happened, ths s easly obtaned by replacng the poston found n equaton (1) and (2). The presented technque mproves the locaton of AE source n approxmately one magntude order. Aknowledgements Ths work was supported by FONDECYT project of the Chlean Government. References [1] GOST (State Standard) : Acoustc Emsson. Terms, Defntons, and Symbols, [2] Masayasu Ohtsua,U, Y. Kamnagab, Muzo C. Munwamb Expermental and numercal crack analyss of mxed-mode falure n concrete by acoustc emsson and boundary element method Constructon and Buldng Materals 13_ ]64 [3] A. Berkovts and D. Fang, Study of Fatgue Crack Characterstcs by Acoustc Emsson, Eng. Fracture Mech., 51 (3) (1995), pp [4] A. Tobas, Acoustc emsson source locaton n two dmensons by an array of three sensors, Non-destr. Test 9I (1976) 912. [5] M. Asty, Acoustc emsson source locaton on a sphercal or plane surface, NDT Internat. 11 (5) (1978) [6] P. Barat, P. Kalyanasundaram, Baldev Raj, Acoustc emsson source locaton on a cylndrcal surface, NDT&E Internat. 26 (6) (1993) [7] Dong-Jn Yoon, Young H. Km, Oh-Yang Kwon, New algorthm for acoustc emsson source locaton n cylndrcal structure, J. Acoust. Emss. 9 (4)(1992)

9 V. Salnas et al. / Physcs Proceda 3 (2010) Vcente Salnas / Physcs Proceda 00 (2010) [8] B.V. Landau, M. West, Estmaton of the source locaton and the determnaton of the 50% Probablty zone for an acoustc source locatng system (SLS) usng multple systems of 3 sensors, Appl. Acoust. 52 (1) (1997) [9] Y.-C. Cho, Y.-H. Km, Impulsve sources localsaton n nosy envronment usng modfed beam formng method, Mech. Systems Sgnal Process. 20 (6) (2006) [10] Maochen Ge, Analyss of source locaton algorthms Part I: Overvew and non-teratve methods, J. Acoustc Emsson, 21 (2003) 14-24