CLASSIFICATION OF ULTRASONIC SIGNALS

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1 The 8 th Internatonal Conference of the Slovenan Socety for Non-Destructve Testng»Applcaton of Contemporary Non-Destructve Testng n Engneerng«September -3, 5, Portorož, Slovena, pp CLASSIFICATION OF ULTRASONIC SIGNALS V. Matz, M. Kredl, R. Šmíd Czech Techncal Unversty, Faculty of Electrcal Engneerng, department of Measurement, Techncká, Prague 6, 66 7, E-mals: matzv@feld.cvut.cz, kredl@feld.cvut.cz, smd@feld.cvut.cz ABSTRACT In ultrasonc defectoscopy t s very dffcult to detect flaw n materals wth coarse-gran structure. The ultrasonc sgnals measured on these materals contan echoes whch are very smlar to fault echo. These echoes arse from grans whch are contaned n materal. For detecton of flaw varous methods for suppressng of echoes from grans have to be used. In ths work we used the method for flterng of ultrasonc sgnal based on dscrete wavelet transform. For classfcaton of ultrasonc sgnals n A-scan we used pattern recognton method called support vector machnes. In ths study we classfy sgnals wth fault echo, echo from weld and back-wall echo. Ultrasonc sgnals were measured on materal used for constructng arplane engnes. The expermental results ndcate the performance of the proposed approach. Keywords: Ultrasonc testng, Dscrete wavelet transform, Support vector machnes. Introducton Ultrasonc non-destructve testng s part of non-destructve evaluaton whch offers to detect the undersurfaces flaws n the materals. The basc prncple of the ultrasonc testng s ultrasound whch uses the transmsson of hgh-frequency sound waves n a materal to detect a dscontnuty or to locate changes n materal propertes. The sound s ntroduced nto a materal and the reflectons (echoes) are receved from nternal mperfectons or from surface of the part. The receved sgnal conssts of echoes from flaw or surface and echoes from scatterng of coarse graned structure of materal. Nose, formed from scatterng of nhomogeneous mcro-structures has to be cancelled. Several technques have been proposed to reduce nose from sgnal. Splt spectrum processng, FIR flterng and dscrete wavelet transform were studed and the best method for flterng of ultrasonc sgnal were searched []. Among them dscrete wavelet transform gves very good results. Ths paper ntroduces an expermental study nvolvng measurement of ultrasonc sgnals wth consequent analyss and sgnal processng. Proposed processng of ultrasonc sgnals allows effcent flterng by whch t s possble to reduce the nose formed from scatterng and electronc crcutry. The frst secton descrbes the flterng of ultrasonc sgnal and ntroduces the basc analyss. For flterng method based on the dscrete wavelet transform called wavelet packets [] s used. In the next secton a method for classfcaton based on support vector machnes s ntroduced. The method support vector machnes s based on the maxmum of the mnmal length between 7

2 support vectors whch characterzes the features. Features are based on extracton of the basc mathematcal operatons as s root mean square, standard devaton or mean value. In the fnal secton system for classfcaton of ultrasonc sgnals s descrbed. Wth the system t s possble to classfy the three dfferent types of ultrasonc: clear sgnal, sgnal wth flaw and sgnal from weld.. Classfcaton of ultrasonc sgnals. System for measurement For classfcaton of ultrasonc sgnals hgh frequency ultrasonc system was used. For measurement of ultrasonc sgnals the transducer wth operaton frequency of MHz was used. The frequency MHz s the best compromse for detecton of flaw n coarse grany materal. For measurement the two types of materals (steel and coarse grany materal) were used. Steel and coarse grany materals were welded. The ultrasonc sgnals were measured n three dfferent places: place wthout flaw, place wth flaw and n the centre of the weld.. Flterng of ultrasonc sgnal Pre-processng of ultrasonc sgnals contans the ampltude normalzaton and flterng. For flterng of ultrasonc sgnal a method based on the dscrete wavelet transform (DWT) called wavelet packets (WP) s used. Ths method s very effcent n the tme doman. The ultrasonc sgnal n A-scan s measured and WP s used for the mprovement of the sgnal-to-nose rato. The wavelet transform s a multresoluton analyss technque that can be used to obtan the tmefrequency representaton of the ultrasonc sgnal. Flterng procedure s based on decomposton of sgnal usng DWT n N levels usng band pass flterng and decmaton to obtan the approxmaton and detal coeffcents. Next step s thresholdng of detal coeffcents and reconstructon of sgnal from detal and approxmaton coeffcents usng nverse transform (IDWT). The WP method s a generalzaton of wavelet decomposton that offers a larger range of possbltes for sgnal analyss. In wavelet analyss, a sgnal s splt nto an approxmaton and detal coeffcents. The approxmaton s then tself splt nto a second-level approxmaton and detal, and the process s repeated. In WP analyss, the detal coeffcents as well as the approxmaton coeffcents can be splted. Hard thresholdng was used for thresholdng detal coeffcents. Hard thresholdng can be descrbed as the process of settng to zero the elements whose absolute values are lower than the threshold. For thresholdng of detal coeffcents the local threshold value based on standard devaton was used [3]: Thr = k Dc Dc N ( ), () N = where k s coeffcent related to crest factor of fltered sgnal (crest factor s the rato of the peak value to the RMS value), Dc are detal coeffcents at each level, N s length of each set of detal coeffcents. Usually global threshold s used n WP flterng. In our study the local thresholdng was used nstead of global thresholdng. The threshold s computed from detal coeffcents at each level of decomposton. Then the computed threshold s used for thresholdng detal coeffcents at the same level. For examnaton of qualty of flterng sgnal-to-nose rato s computed: 8

3 where S ef F ef S ef SNR = log [ db ], () N ef s the root mean square value of the nosy part of the raw sgnal. s the root mean square value of an adequate part of the fltered sgnal..3 Support vector machnes The basc theory of SVM used n ths applcaton s frst presented detals can be found elsewhere [4]. The SVM maxmzes margn between classes whch ncreases generalzaton ablty. The classfcaton problem can be restrcted to consderaton of the two class problem wthout loss of generalty. In ths problem the goal s to separate the two classes by a functon whch s nduced from avalable problem. The goal s to produce a classfer that wll work well on unseen examples. The basc dea s lnear classfer that maxmzes the dstance between separatng hyperplane and the nearest data pont of each class. Consder the problem of separatng the set of tranng vectors belongng to two separate classes, wth hyperplane, n ( x y ),...,( x, y ), x R, y {,},, l l (3) w, x + b =. (4) The set of vectors s sad to be optmally separated by the hyperplane f t s separated wthout error and the dstance between the closest vectors to the hyperplane s maxmal. The parameters w, b n equaton (4) are constraned by, mn w, x + b =. (5) X Class Support vectors Class X Fg. : SVM Lnear classfer. The dstance d (w, b; x) of a pont x from the hyperplane (w, b) s, d w, x + b = (6) w ( w, b; x). 9

4 The am s to convert the problem nto a formulaton wthout constrants. Lagrange functon L s ntroduced, α Lagrange multplers, L L T ( w b, ) = w α ( w x ), α y + α. (7) í = = Once the Lagrange multplers for the optmal hyperplane have been determned the followng separatng rule can be used by expressng the optmal weght vector n terms of support vectors and the Lagrange multplers: L r r r f x sgn y x x + b, T ( ) α ( ) = support vectors (8) where x r are the support vectors, α are the correspondng Lagrange coeffcents, and b s the threshold constant. A Support Vector Machne maps the nput space nto a hgh dmensonal feature space and then constructs an optmal hyperplane n the feature space..4 Feature extracton For the feature extracton the characterstc propertes of ultrasonc sgnal have to be used. From the shape of ultrasonc sgnal whch was measured on dfferent place contans the fault and backwall echo, only the backwall echo or the sgnal from the center of weld the basc ampltude characterstcs were derved. The basc features nclude: mean value: root mean square value: standard devaton: absolute value: N x N = AVG =, (9) N x N = EFC =, () STD = x AVG N ( ), () N = N ABS = x. () = For the calculaton of descrptve features the back-wall echo was cut off. The average, root mean square a standard devaton value were computed from the back-wall echo and from the rest of the sgnal. The sgnal whch contans only the backwall echo has the smallest average value but n the opposte the sgnal measured n the centre of the weld has the hgher average value because the sgnal n the centre of the weld contans more echoes whch were caused by scatterng of the sgnal. The features of ultrasonc sgnal were put nto the SVM classfer and the hyperplane was computed. 3. Expermental results For measurement of ultrasonc sgnals two dfferent materals (steel and coarse graned metallc materal) were used. In all materals artfcal flaws were created, and two parts of these materals were welded. In case of coarse gran materal whch s used for constructon of arplane engnes 3

5 max max Max max the structure of materal s nhomogeneous and the measured ultrasonc sgnal contans the echoes from scatterng from grans. u/u Max a) b) c) t [ µ s] d) t [ µ s] u/u max e) t [s] µ f) Fg. : Ultrasonc sgnal of grany materal a) clear raw sgnal, b) fltered sgnal, c) raw sgnal wth fault echo, d) fltered sgnal wth fault echo, e) raw sgnal measured on weld, f) fltered sgnal measured on weld. For flterng of ultrasonc sgnals the wavelet packets method was used. In ths method the local threshold was used. It means that the threshold was computed n every detal coeffcents and these coeffcents were thresholded. Ths method gves the hghest suppressng of background nose whch s contaned n measured sgnal. Nose reducton n the depcted case for WP s SNR=7 [db]. The results of measured and fltered ultrasonc sgnals are n Fg.. For the successful classfcaton the nformatve features should be obtaned. The features were computed from the ampltude characterstcs and were mapped to the three classes. The class s related to the sgnal wthout flaw, the class to the place wth the flaw and the class 3 to the weld. For the tranng the dfferent algorthm of support vector machnes functons as Successve overrelaxaton (SOR), one-aganst-one decomposton (OAO), one-aganst-all decomposton (OAA) and sequental mnmal optmzer (SMO) were used. The dfferent functons were 3

6 ABS [ - ] combned wth the dfferent features. The results of dfferent features and functons are llustrated n Fg Sgnal EFC Sgnal [ - ] EFC Echo [ - ] a) Echo b) Sgnal AVG Sgnal [ - ] c).5. AVG [ - ] d) Fg. 3: Feature spaces wth dfferent functons and features a) OAO, b) SOR, c) OAA, d) SMO. The best results were obtaned wth one-aganst-one decomposton wth features of root mean square value of echo and rest of sgnal. All the three classes were separated and the performance of classfcaton was % (error rate %). The proposed algorthm for the classfcaton of ultrasonc sgnals s effcent n ultrasonc defectoscopy for automated detecton and classfcaton of flaws. 4. Conclusons In ths paper a new method for the classfcaton of ultrasonc sgnals s proposed. In the ultrasonc sgnals measured on materals wth coarse gran structure t s not possble to easly recognze the flaws. In ths case the method for flterng of ultrasonc sgnals based on the dscrete wavelet transform called wavelet packets was used. Ths method offers effcent flterng of ultrasonc sgnals. For the classfcaton of ultrasonc sgnals the support vector machnes was used. Wth ths method t s possble to classfy the sgnal wth back-wall echo, sgnal wth fault echo and sgnal measured on weld. The proposed method s useful for the automated classfcaton of ultrasonc sgnals n ndustry. 3

7 Acknowledgements The research of Classfcaton of ultrasonc sgnals was supported by the research program No. MSM "Research of Methods and Systems for Measurement of Physcal Quanttes and Measured Data Processng " of the CTU n Prague sponsored by the Mnstry of Educaton, Youth and Sports of the Czech Republc. 5. References [] Ercsson, L., Stepnsk, T.: Algorthms for suppressng ultrasonc backscatterng from materal structure, Ultrasoncs, Volume 4, ssue -8, pages , May. [] Paul S Addson: The Illustrated Wavelet Transform Handbook: Introductory Theory and Applcatons n Scence, Engneerng, Medcne and Fnance. Naper Unversty, Ednburgh, UK, 4, ISBN [3] Matz V., Kredl, M., Šmíd, R.: Sgnal-to-Nose Rato Improvement based on the Dscrete Wavelet Transform n Ultrasonc Defectoscopy. Acta Polytechnca. 4, vol. 44, no. 4, s ISSN -79. [4] Gunn, S., R.: Support Vector Machnes for Classfcaton and Regresson. Techncal Report, Unversty of Southampton, 998. [5] Vapnk, V.: Statstcal learnng theory. Wley, Chchester, GB,

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