AUTOMATED METHOD FOR STATISTICAL PROCESSING OF AE TESTING DATA

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1 AUTOMATED METHOD FOR STATISTICAL PROCESSING OF AE TESTING DATA V. A. Barat and A. L. Alyakrtsky Research Dept, Interuns Ltd., bld. 24, corp 3-4, Myasntskaya str., Moscow, 0000, Russa Keywords: sgnal processng, AE data classfcaton Abstract Acoustc emsson (AE) as a nondestructve testng method allows estmatng the condton of sophstcated ndustral objects, detectng defects at ther ntaton, and preventng development of such defects. The relablty of detecton and the accuracy of determnaton of AE source locaton depend on the correct nterpretaton of the AE testng results. Testng procedures of dfferent ndustral equpment are ntended for estmatng condton of the objects on the bass of AE parameters, whle the AE sgnals proper are not used n analyss as the prmary dagnostc data. We have developed the statstcal method of analyss to study the whole complex of measured data, both the AE parameters and sgnal waveforms. Ths method s based on the two-level clusterng of data, such as AE sgnals from separate channels, and "groups of sgnals" formed on the bass of the prmary clusterng. The algorthm allows the determnaton of the quantty of AE sources, and estmates the degree of ther danger wthout resortng to the prelmnary locaton. The zonal locaton s carred out after the determnaton of AE sources. It avods the so-called false locatons, whch consderably complcate the locaton map. On the bass of classfcaton results, one can correct the AE sgnal arrval tme, and such correcton makes t possble to mprove the accuracy of the AE source locaton. The characterstc property of the developed method s data processng n an automatc mode, wth mnmal operator nterventon. In ths case there s no need to employ a hgh-sklled operator. Snce the AE sgnals themselves are used for analyss, the obtaned results prove to be more relable than those obtaned when workng wth the AE parameters. The algorthm bult on the developed method has been successfully appled for processng data obtaned as a result of laboratory research of the corroson development, for studyng renforced concrete structures, and also as an addtonal nstrument for processng data of the ndustral AE testng. Introducton Each AE event defnes a unque process occurred at a certan pont of the test object. When AE sgnals propagate from the pont of emsson to a sensor, the waveforms are complcated due to conversons to dfferent modes of waves, multplcty of dstrbuton paths, and due to wave velocty dsperson by frequency. AE sgnals contan nformaton not only about the AE source event for ths sgnal, but n the hghest degree about parameters of acoustc and electrc path. In ths connecton constructon of the analytcal or even numercal dagnoss model for nterpretaton of AE sgnals appears to be an ntrcate and nontrval problem, the soluton of whch cannot be generalzed for the test equpment of dfferent types. Whle the data nterpretaton based on accurate dagnostc models appears to be dffcult, the statstcal analyss s a reasonable choce for carryng out the data nterpretaton and classfcaton wth the hgh certanty. At present the statstcal methods of data analyss are wdely appled both n ndustral AE systems and n laboratory research, and the applcatons are vared: data clusterng, correlaton analyss, and check of dfferent statstcal hypotheses. In ths paper the statstcal method of analyss enablng the automatc clusterng of AE testng data s presented. Ths method makes t possble to process bulk data obtaned as a result of the AE testng or durng the laboratory research n the absence of a pror nformaton. As a consequence of processng, the data are structured and organzed; each cluster formed as a result of analyss characterzes an AE source at a defnte stage of development EWGAE, Cracow UT

2 Method Descrpton The clusterng of AE data s used rather frequently. However, dfferent methods of data processng pursue dfferent ams, and have specal features of mplementaton [4,5,7,8]. The key features of a gven method s, frstly, the possblty for data processng n an automatc mode wth mnmum operator s nvolvement and a mnmum number of settngs, and, secondly, the possblty to carry out the analyss of the heterogeneous dagnoss nformaton. The ntal data for algorthm realzng the gven method can be both the AE sgnals and also ther parameters computed under data acquston n on-lne mode. Even f the AE count rates are such that on techncal grounds an acquston of prmary dagnoss nformaton n full capacty s mpossble, more than half the AE sgnals can be substtuted for values of AE parameters (arrval tme, rse tme, energy, etc.) wthout loss of the processng accuracy. Start Formaton of classes of sgnals Groupng of sgnals relatng to the same AE event Formaton of classes of groups Are all AE-sgnals recorded? Calculaton of features for each class of groups Classfcaton of AE sgnals specfed by parameters Refnement of sgnals arrval tme correcton of locaton maps End Fg.. Flowchart of automated method of statstcal processng of AE data. Fgure shows the flowchart of the proposed method. The data are processed n two stages. At the frst stage the clusterng of AE sgnals takes place. The data recorded by each measurng channel are analyzed ndvdually. The correlaton coeffcent s used as a measure of smlarty of each par of sgnals. The classes of sgnals are formed at ths frst stage. Next, the classfed sgnals are combned n groups n such a way that one group wll nclude the sgnals of dfferent measurng channels, whch belong to the same AE event. The next stage of algorthm s the formaton of classes of groups ; to the same class of groups assgned are the groups wheren the sgnals recorded by one and the same class of sgnals correspond to the same classes of sgnals. The quantty and parameters of AE sources are estmated by the results of classfcaton of sgnal groups. When a part of AE sgnals s defned only by parameters, and waveforms are absent, the classes of sgnals and classes of groups are formed on the bass of ncomplete dagnoss nformaton. For classfcaton of AE sgnals, specfed only by ther parameters, each class of groups s characterzed by a set of features. The classfcaton n ths case s accomplshed on the bass of multdmensonal emprcal dstrbuton functon bult for the calculated features. Clusterng of Acoustc Emsson Sgnals For AE sgnal clusterng, t s necessary to determne a dstance measure [3]. In order that an estmaton error of AE parameters does not nfluence on the classfcaton result, the correlaton coeffcent r was used as a measure of smlarty of two sgnals; see Eq. (). The prelmnary analyss has shown that sgnals relevant to the same AE source and recorded by the same 77

3 measurng channel have a hgh correlaton coeffcent, whose value vares from 0.70 to 0.99 dependng on the nature of the AE generatng process. r = N! = N! = ( x " x) ( x " x)( y 2 N! = " y) ( y " y) 2 Usng the correlaton coeffcent as the dstance measure of AE sgnals, an automatc correcton of arrval tmes of sgnals, whch belong to the same cluster, can be carred out, because the cross-correlaton functon reaches ts peak at the tme correspondng to a dfference of arrval tmes of AE sgnals. When processng bulk data, the calculaton of correlaton coeffcents for all pars of sgnals requres a long tme; to speed up the data processng, a wavelet decomposton may be used, namely, a sgnal decomposton by wavelet packets [2]. The decomposton by wavelet packets s one of varety of the mult-resoluton analyss, and t s the sgnal decomposton on the bass of wavelets (n a general case by the Rss bass) specfed for a sequence of subspaces embedded to each other. w 2 n( x) = 2! h( k) wn (2t " k) w ( 2 n+ x) = 2! g( k) wn (2t " k), (2) k k where g( k) = (! ) h(! k) s defned by the type of wavelet functon. Under a dscrete wavelet transform the sgnal s decomposed nto a low-frequency component - approxmaton and a hgh-frequency component - detalng. At the next level both the approxmaton and the detalng are subject to further decomposton. So, at j-level of decomposton the 2 j coeffcents are calculated. In ths case the coeffcent (j, k) localzes energy wthn the frequency range (Eq. 3), where Ω 0 s the frequency correspondng to a half of the sample rate frequency & ' 0 ' 0 # (' = $ k, ( k + )!. (3) j j % 2 2 " As a rule, the AE sgnal energy s non-unformly dstrbuted on the spectrum, and often 3 or 5 coeffcents of cluster decomposton are suffcent for locaton of 95-99% of energy. Moreover, the dmenson of nformatonal components, as a rule, s at least four tmes smaller than the orgnal sgnal dmenson. The research has shown that the precse estmate of correlaton coeffcent based on the weghted sum of correlaton coeffcents of wavelet-packet decomposton components s 85%. Wth the clusterng of AE sgnals, the quantty of clusters s to correspond to the quantty of the assumed AE sources. In desgnng the clusterng algorthm, a partcular attenton was gven to the true determnaton of clusters quantty. For llustratng ths am, we suggested a two-stage clusterng dagram, as shown n Fg. 2; that s, the flowchart of clusterng algorthm. At the frst stage, a herarchcal agglomeratve algorthm wth complete lnk clusterng s appled. At the second step an teraton analyss s appled, the dstances between centers of mass of the clusters formed are calculated, and two clusters havng the maxmum and above-threshold dstance between the clusters centers are merged. Thereafter, the re-clusterng s accomplshed by the method of k-averages. When usng ths flowchart of clusterng algorthm, the clusterng s flexble and controllable; t uses two settngs the threshold value for sgnal addton to the cluster (at herarchcal clusterng) and the threshold value for the nter-cluster dstance. The settng values are selected on the bass of nformaton about the test object and the testng condtons. Clusterng of Groups of Acoustc Emsson Sgnals At the next stage of algorthm, the groups of sgnals relevant to the same AE event are analyzed. For formaton of such the groups analyzed are the arrval tmes of AE sgnals, the dffer- k () 78

4 Start Herarchcal clusterng wth clusters mergng as per the complete lnk rule No Is the mnmum dstance between centers of clusters less than the threshold one? Yes Clusters mergng Reclusterng by the method of k-average Fg. 2. Flowchart of two-stage clusterng algorthm of AE sgnals. ence of recordng tme of the frst and last sgnals n the group should not exceed the specfed value, whch s determned by the rato of ts maxmum overall dmenson and mnmum velocty of acoustc wave propagaton expermentally measured for the gven test object. An AE sgnal beyond the tme wndow s ntal AE sgnal for the next group. To the same class of groups assgned are the groups wheren the sgnals recorded by the same measurng channels correspondng to the same classes of sgnals. The study of algorthm has shown that for assgnng the group of sgnals to one or other class t s suffcent that the classes of sgnals concde at least for two channels n the group. The membershp of classes of groups can be also defned for AE sgnals, even wth no nformaton about the AE sgnal waveform. For ths purpose, each class of groups obtaned s characterzed by the values of features lsted below representng a medan of dstrbuton for each class. Numbers of three channels wth mnmum tme of sgnal arrval {n_t, n_t 2, n_t 3 } Numbers of three channels wth maxmum sgnal ampltude {n_a, n_a 2, n_a 3 } Maxmum value of sgnal ampltude n the group A max Rato of ampltudes of sgnals recorded by channels n_t 2 and n_t, and also n_t 3 and n_t {A 2 & A 3 } The sgnal group belongng to one or other class s defned smlarly to the k-averages method, by the mnmum dstance between the features, characterzng each class of groups and the group of features to be analyzed. The classes of groups obtaned by such a manner characterze the potental AE sources wth a hgh degree of probablty. The quantty of classes of groups corresponds to the quantty of AE sources; the numbers of channels, by whch the sgnals wth the mnmum arrval tme are recorded, defne the number of locaton zone. The quantty of groups n each class and the energy of AE sgnals ncluded nto the group can defne the degree of danger of AE source. Results and Dscusson The practcal examples can vsually confrm the effectveness of the present method. To research regulartes of AE n concrete, a seres of experments was carred out. On a concrete cube wth a -m sde length, eght AE sensors were placed, one at each vertex. The AE sensors were used both for AE measurement mode and as a pulser for the smulaton of AE sources. To llustrate advantages of the present method, two of the experments were selected. Experment llustrates the case when the AE sources are not found because of mechancal nose and mpacts. There are two AE sources, a pulser that smulates a growng defect, and a hammer that smulates mechancal nose of equpment. Fgure 3а shows the result of volume locaton of 79

5 the AE sources. Indcatons dstrbuted over the whole feld of locaton are generated by the mechancal nose source or hammer blows. As the hammer mpacts are made manually, the relevant sgnals have dfferent waveforms. In ths case, determnaton of the arrval tme by the threshold method entals the dfference n arrval tme errors. The errors of arrval tme determnaton dffer n ther meanng and sgn for the sgnals wth dfferent waveforms. Ths s one of the possble reasons for the dstrbuton of source locatons. Applcaton of the statstcal method of data analyss allows not only formng the class of groups of AE mpulses emtted by the smulator, but also pontng out as an ndependent class the sgnals relevant to the hammer blows. Table а shows the results of operaton; the attrbutes gven n ths table conform to the lst of class of group features. The names of features n Table comply wth the prevous lst of features. Each lne of the table characterzes one "class of groups". а) b) Fg. 3 Locaton results. a) Experment, b) Experment 2. Table а AE class data 2 classes Class Q-ty of A max n_t n_t 2 n_t 3 No. Class Elements Table b AE class data 6 classes Class Q-ty of A max n_t n_t 2 n_t 3 No. Class Elements In Experment 2, there are sx AE sources n all. Two types of acoustc waves were generated at three postons on the concrete cube surface by means of a pulser and a Hsu-Nelsen source. Fgure 3b shows the three locatons of the AE sources. Durng the statstcal processng of data, applcaton of the present method can gve sx classes of events correspondng to two dfferent sources of AE at three ponts on the test object surface, as shown n Table b. There are two "classes of groups" n each locaton zone, whch s defned by the channels number {n_t, n_t 2, n_t 3 }. One more useful mplementaton of the present method s structurng and data compresson. The data structurng s realzed due to replacement of the AE sgnals beng analyzed by the "classes of sgnals" and "classes of groups". Thus, the quantty of the nformaton under analyss s reduced consderably. For example, durng expermental AE studes from pttng corroson growth, several hundred thousand sgnals were recorded; after the statstcal analyss of data n an auto-mode wthout pre-processng about 20 representatve classes of "groups of pulses" descrbng dfferent stages of corroson damage development were defned [6]. In practcal AE applcatons, t s effectve to use automated method of statstcal analyss for processng of the AE montorng data, especally when t s necessary to analyze changes n the

6 structure of AE sgnals recorded for any length of tme, and also n the case of testng sophstcated ndustral facltes, for whch the constructon of an acceptable locaton scheme appears to be dffcult. Concluson In ths paper descrbed s an automated statstcal analyss method of AE data, whch makes t possble to structure the AE test data through parttonng nto dfferent clusters or the groups of sgnals, characterzng the dfferent AE sources. The key features of the gven method are, frstly, the possblty to process data n an automatc mode wth mnmum nvolvement of operator and a mnmum number of settngs, and, secondly, the possblty to carry out the analyss of the heterogeneous dagnoss nformaton. Based on the results of statstcal analyss, t s possble to specfy the quantty of AE sources, to carry out ts zone locaton, and to get addtonal evaluaton of the danger crteron wthout resortng to the prelmnary locaton. When usng the correlaton coeffcent as a measure of proxmty under cluster analyss of AE sgnals, we can carry out an automatc correcton of sgnal arrval tmes belongng to the same clusters, because the cross-correlaton functon reaches ts peak at the pont of tme correspondng to the dfference of arrval tmes of AE sgnals. References. V.A. Barat, A.L. Alyakrtsky. Statstcal method for processng of AE sgnals and ther parameters for ncreasng of relablty of the testng results. Proceedng of the 7th Russan- Internatonal Scentfc-Technologcal Conference on Non-Destructve Testng and Dagnostcs. Ekaternburg, (on the CD-ROM) 2. Ingrd Daubeches, Ten lectures on wavelets, SIAM, Phladelpha, Ajvazyan S.A., Buhshtaber V.M., Enjukov I.S., Meshalkn L.D., Appled statstcs n 3 parts, 989. (n Russan) 4. L.N. Stepanova, A.E. Kareev. Development of a method for the dynamc clusterng of AE sgnals for ncrease of accuracy of ther localzaton, Control Dagnostka, 2003, 6, pp (n Russan) 5. A. A. Anastassopoulos, T. P. Phlppds. Clusterng Methodologes for the evaluaton of AE from Compostes, Journal of Acoustc Emsson, 3, (/2), 995, Yu.S. Popkov, A.L. Alyakrtsky, E.Yu. Sorokn, D.A. Terentyev. AE method for determnaton of pttng corroson depth and montorng of defect propagaton rate. the Proceedng of EW- GAE Vallen VsualAE. The standard n Acoustc Emsson software. Vallen-Systeme GmbH AE-Studo. NPF Daton. 8

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