RECONSTRUCTION OF IMPACT ON COMPOSITE AIRFOIL SEGMENT USING PIEZOELECTRIC SENSORS

Transcription

1 7th European Workshop on Structural Health Montorng July 8-, 204. La Cté, antes, France More Info at Open Access Database RECOSTRUCTIO OF IMPACT O COMPOSITE AIRFOIL SEGMET USIG PIEZOELECTRIC SESORS Robert Zemčík, Jan Bartošek, Zuzana Lašová, Tomáš Kroupa Unversty of West Bohema, Unverztní 8, Plsen, Czech Republc zemck@kme.zcu.cz ABSTRACT The presented study focuses on structural health montorng technque wth the goal to predct nduced damage and assess the resdual strength of mpacted structure. Heren, the prmary problem of mpact force reconstructon s nvestgated on an arfol segment (part of a propeller blade for a large fan) made of lamnated composte wth attached pezoelectrc transducers. The segment s made from carbon textle usng RTM technology. The reconstructon s based on deconvoluton method and transfer functons. The effcency of the proposed approach s tested for all mpact locatons used to calbrate the system, and also on several addtonal locatons. The nterpolaton of transfer functons s used to ncrease the accuracy of the reconstructon. KEYWORDS : force reconstructon, convoluton, nverse problem, Tkhonov regularzaton, experment. ITRODUCTIO The safety or functonalty of every structure can be sgnfcantly affected by defects. Therefore, they must be found pror to any catastrophc scenaro. These defects can be undetectable by vsual nspecton. Currently, they are detected by non-destructve technques lke ultrasonc, X- ray, con tappng or other methods [9], whch are tme and cost consumng and requre the constructon to be taken out of servce. In contrary, the condton of constructon can be evaluated durng operaton from measurements of sensors placed over the structure. Ths prncple s so-called structural health montorng. The dentfcaton of mpact force and mpact locaton s an mportant task of such systems and the deal dentfcaton method should dentfy the mpact force, or even the combnaton of mpact forces, on complex structures n real tme wth low dependence of operatng nose. The hdden defects are very common especally n modern composte materals, such as carbon fber renforced epoxy lamnates, that are wdely used thanks to ther hgh strength and stffness to weght ratos. ot only s the desgn process of structures whch contan parts from composte materals complcated due to effects such as non-lnear behavor [3], specfc damage behavor [9], and drectonal dependence of velocty of propagaton of stress waves [5], but, furthermore, compostes are hghly susceptble to transverse loadng, whch can cause delamnaton and cracks n matrx and thus sgnfcantly reduce the stffness or strength of the constructon [2]. The mpact dentfcaton problems have been studed by many researchers n recent years and several methods were proposed. The often used one s the nverson of forward problem, whch can be performed n tme, frequency or spectral doman. Drect deconvoluton s a well-known llcondtoned problem and ts results are strongly nfluenced by qualty of expermental data, approprateness of the mechancal model and robustness of employed algorthm. Many researches defne the problem rather as a mnmzaton of the dfference between measured and modeled responses of the mpacted structure. Addtonal terms and constrants are added to mnmzaton to regulate oscllatons n results. Copyrght Inra (204) 552

2 EWSHM antes, France Jacqueln et al. [6] analyzed the deconvoluton n tme doman. The nfluence of sensors locaton and dfferent regularzaton methods were nvestgated. Smlarly, Gunawan et al. [8] used the tme doman. The mpact force was approxmated by cubc splne and the two-step B-splne regularzaton method was developed. On the other hand Yan and Zhou [3] used Chebyshev polynomals to represent the mpact force and the modfed genetc algorthm to solve the mnmzaton problem. Park and Chang [7] determned the system expermentally and nvestgated several types of mpacts. Martn and Doyle [] used the Fast Fourer Transform to swtch nto frequency doman and solved the deconvoluton drectly. Furthermore, Doyle [2] employed the wavelet deconvoluton and modelng wth FEA. Other researches preferred to work n spectral doman. Hu et al. [2] formulated the mnmzaton wth regularzaton parameter and constrant, whch was solved by quadratc programmng method. Moreover, dfferent types of sensors were compared and Chebyshev polynomals were employed to reduce the number of unknowns. Atobe et al. [4] used the gradent projecton method to solve the mnmzaton problem and compared the determnaton of the system by experment or by FEA. Fnally Sekne and Atobe [6] formulated the mnmzaton where multple mpacts can be dentfed. Another possblty s to defne the mnmzaton n recursve form n tme doman and to use flterng method to solve the nvestgated problem. Seydel and Chang [4, 5] used smoothng-flter method and nvestgated the nfluence of sensor locatons and boundary condtons. Smlarly, Zhang et al. [] mplemented smoothng-flter algorthm wth the possblty of real-tme computatons. The locaton of mpact wthn these methods s often estmated from the mnmzaton of the error between measured and modeled responses along the structure. Ths can be done by drect search methods [2] or by some other optmzaton technques [4]. Another possblty s to use the technques derved from methods used n acoustc emsson (AE) [0, 4], where the dfference n arrval tme of sgnal s determned and the locaton of mpact s estmated from velocty of waves. Unfortunately, the determnaton of exact tme of arrval n composte materal or complex structures s lmted because of the dsperson and reflecton of waves on boundares. The alternatve s calculaton of dstrbuton of energy n defned tme step and the determnaton of ts maxmum [7]. Totally dfferent approach s the determnaton of mpact force and force locaton from models based on neural networks [7]. The model s composed of parallel elements connected by defned relatons and traned by prelmnary tests. The output of the model s then set by learned behavor. The weakness of such approach s the necessty of learnng perod and uncertan reacton of model to not learned mpacts. The above cted works dffer n several features such as complexness of geometry, determnaton of the system model or the type and number of sensors. The mpact force was nvestgated on metal beam [], metal plate [2, 6, 8], composte plate [0, 2] or stffened composte plate [5, 7,, 2, 3, 4, 6]. The model of the system s defned analytcally [4,, 3] or determned by FEA [8, 2, 4, 6] or by experment [7, 4]. Sgnal s mostly obtaned from stran gauges [4, 6], accelerometers [, 2, 2], smple pezoelectrc sensors [2] or from sensor network [7, 3, 9, 20 and 22]. DISCRETE COVOLUTIO AD IVERSE PROBLEM The methodology used n ths work s based on the transfer functon approach. For a lnear system, ts response h to an nput f can be expressed by convoluton f * g = h () where g s so-called transfer functon and t represents the characterstcs of the system. In order to fnd the locaton of mpact and to reconstruct the tme dependence of the mpact force, t s necessary to perform two consecutve steps; a) a calbraton procedure,.e., to 553

3 EWSHM antes, France perform expermental measurements whle recordng the correspondng nput and response, and to calculate the transfer functons for all combnatons of mpact (calbraton) locatons and sensors, and b) a reconstructon procedure,.e. to reconstruct the force n each possble locaton for measured response for unknown mpact and to seek the mpact locaton by mnmzng the error of response reconstructon. Let us consder a system (a structure) wth K mpact locatons and L sensors. Frst, we measure the force n locaton and the correspondng response n sensor j. For dscrete system the nput and response sgnals, each consstng of samples (assumng constant tme ncrement t), can be wrtten as f = and T [ f, f2, K, f ] h =, (2) j T [ h, h2, K, h ] respectvely. The force vector can be rearranged to matrx [ ] for each performed mpact (or experment) m = M and then a global matrx system can be assembled for up to M subsequent mpacts as 0 L 0 M f 0 f f L m F f g f 2 g2 M M f g 23 g j h h 2 =, M h { m H j F M g M F 23 F j H j = M. (3) M H j 23 H j The system s then represented by all solutons for each combnaton of and j. However, each system of algebrac equatons n (3) s overdetermned and ll-posed. If we rewrte (3) concsely as Fg H (4) the soluton can be obtaned by varous methods, for example by smple pseudonverson, by mnmzng the resduum usng least squares method, by quadratc programmng technques or others [9]. onetheless, to avod unrealstc oscllatons of the soluton, t s advsable to use adequate regularzaton technque that mposes addtonal condton on the soluton. Heren, the Tkhonov regularzaton [8] mn 2 2 { Fg H + λ g } 2 (0) s used, where the addtonal term, compared to least square method, means that the norm of the soluton wll be mnmzed too. A proper choce of the parameter λ s needed to balance the rato between the standard resduum and the oscllatons. When all transfer functons g j are known, we can attempt to reconstruct the unknown nput sgnal from measured responses only. The response agan wth samples as n (2) s obtaned n all L sensors or only n a subset of sensors. ow, the transfer functon for each combnaton of and j must be rearranged to matrx [ ] and then a global system for all selected sensors can be assembled as 554

4 EWSHM antes, France 0 L 0 g f h g g f h M 2 2 = 2, 0 M M M g g2 L g f h { { Gj f H j G M f G 23 L G H = M. (5) H 23 L H The soluton can be performed for each possble (suspected) mpact locaton. Agan, the problem (5), wrtten concsely as Gf H, (6) s overdetermned and ll-posed. Moreover, as the mpact force s always non-negatve (assumng non-stckng mpact), addtonal nequalty constrant mght be advantageous [20]. In ths work, however, the Tkhonov regularzaton s used agan wthout the nequalty constrant. Hence, the soluton f s found from mn 2 2 { Gf H + λ f } 2. (7) To fnd the real locaton (or at least a good estmate) of the unknown mpact, t s necessary to seek the locaton whch produces the smallest error δ between the measured response (H) and the response (H ) reconstructed usng the correspondng soluton of (7) as G f H H = G f. (8) Therefore, the goal s to solve { δ }, δ H H mn. (9) = The soluton f whch mnmzes (9) can be sought by varous methods, however, n ths work, a brute-force search n all locatons was conducted to ensure that the global mnmum s found. Further, an attempt was made to ncrease the accuracy of the reconstructon by nterpolatng the neghborng transfer functons. Each sector (four locatons) between the calbraton mpact locatons was subdvded nto 5 5=25 subsectors. The transfer functons at locatons q nsde each sector are calculated usng standard approxmaton functons for soparametrc quadrlaterals as = ( g ), j = a, b, c d g (0) q j j, j where the numbers a, b, c, and d correspond to locatons defnng the gven sector and 555

5 EWSHM antes, France a c = = 4 4 ( ξ )( η ), b = ( + ξ )( η ), 4 ( + ξ )( + η ), = ( ξ )( + η ). d 4 () 2 EXPERIMETAL TESTS Composte arfol segment was loaded usng mpact hammer B&K 8204 n 77 locatons (one at a tme) regularly coverng rectangular area of dmensons mm on the upper skn (see Fgure and 2). Three mpacts (.e. M = 3) were performed n each locaton n accordance wth (3). The force was measured usng embedded force sensor. The sgnals from the hammer and from the pezoelectrc patches were recorded usng I CompactDAQ devce wth I 925 and I 9234 modules samples for each channel were recorded wth samplng frequency of 5.2 khz. The segment was composed of an omega-shaped spar and two skns, all made of carbon textle usng RTM (Resn Transfer Moldng). The three parts were glued together and also patched along the leadng and tralng edges. The segment was hanged usng a clamp on the spar as shown n Fgure. The sensors were pezoelectrc fol patches DuraAct P-876.SP wth appled shunt resstors (R = MΩ). The sensors were attached usng double sded adhesve tape. Fgure : Schema of segment wth sensors ( ), calbraton mpact locatons ( ), addtonal mpact locatons ( ), and photograph of segment wth apparatus (rght) ncludng sensors wth cables, acquston modules, mpact hammer and clamp for hangng. The blue lnes denote the actual borders of the mpacted area. 556

6 EWSHM antes, France Fgure 2: Measured and reconstructed force for mpact for [x, y] = [0, 300] mm. 3 RESULTS All 77 mpact locatons used for calbratng the system were dentfed exactly usng (7). An example of measured and reconstructed forces s shown n Fgure 2 for a selected locaton. Several methods were tested and compared also n terms of tme needed for soluton n Matlab. The effcency of the proposed approach s further shown on eght examples n Fgure 3 when the mpact occurred between the calbraton postons (see addtonal mpact locatons n Fgure ). The values of error δ were calculated usng (9). The correspondng mpact locatons are vsually compared wth the real locatons n the graphs. The maxmum dfference between real and dentfed mpact locaton was 25 mm (correspondng to the sze of the nterpolaton grd). The poston of the spar s vsble n the contours of the graphs as t creates boundares between areas wth dfferent elastc propertes. COCLUSIO The proposed method for mpact locaton dentfcaton and force reconstructon proved to provde results wth suffcent accuracy on curved composte structure and also wth only three sensors coverng nvestgated rectangular area. The future work wll focus on detaled optmzaton of placement of sensors and also on nterpolaton sector sze wth respect to specmen sze and shape or materal complexty. The nterpolaton used heren could be enhanced wth general optmzaton algorthm wthn each sector nstead of smple sector subdvson. 557

7 EWSHM antes, France Fgure 3: The contours of reconstructon error δ and comparson of locaton of real mpact ( ) and locaton dentfed usng nterpolated data ( ) for all 8 tested mpacts between calbrated data. 558

8 EWSHM antes, France ACKOWLEDGEMETS Ths work was supported by grant projects GA P0//0288 and SGS REFERECES [] Martn MT, Doyle JF. Impact force dentfcaton from wave propagaton responses, Internatonal Journal of Impact Engneerng 8 (996), [2] Doyle JF. A wavelet deconvoluton method for mpact force dentfcaton, Expermental Mechancs 37 (997), [3] Kroupa T, Laš V, Zemčík R. Improved nonlnear stress-stran relaton for carbon-epoxy compostes and dentfcaton of materal parameters. Journal of composte materals, 20, vol. 45, n. 9, [4] Seydel R, Chang FK. Impact dentfcaton of stffened composte panels: I. System development, Smart Materals and Structures 0 (200), [5] Seydel R, Chang FK. Impact dentfcaton of stffened composte panels: II. Implementaton studes, Smart Materals and Structures 0 (200), [6] Jacqueln E, Bennan A, Hameln P. Force reconstructon: analyss and regularzaton of a deconvoluton problem, Journal of Sound and Vbraton 265 (2003), [7] Park J, Chang FK. System dentfcaton method for montorng mpact events, Proc. SPIE 5758 (2005), [8] Gunawan FE, Homma H, Kanto Y. Two-step B-splnes regularzaton method for solvng an ll-posed problem of mpact-force reconstructon, Journal of Sound and Vbraton 297 (2006), [9] Laš V, Zemčík R. Progressve Damage of undrectonal Composte Panels, Journal of Composte Materals, 42(), (2008). [0] Kudu T, Das S, Martn SA, Jata KV. Locatng pont of mpact n ansotropc fber renforced composte plates, Ultrasoncs 48 (2008), [] Zhang B, Zhang J, Wu Z, Du S. A load reconstructon model for advanced grd-stffened composte plates, Composte Structures 82 (2008), [2] Hu, Fukunaga H, Matsumoto S, Yan B, Peng XH. An effcent approach for dentfyng mpact force usng embedded pezoelectrc sensors, Internatonal Journal of Impact Engneerng 34 (2007), [3] Yan G, Zhou L. Impact load dentfcaton of composte structure usng genetc algorthms, Journal of Sound and Vbraton 39 (2009), [4] Atobe S, Kuno S, Hu, Fukunaga H. Identfcaton of Impact Force on Stffened Composte Panels, Transactons of Space Technology Japan 7 (2009), 5. [5] Červ J, Kroupa T, Trnka J. Influence of prncpal materal drectons of thn orthotropc structures on Raylegh-edge wave velocty. Composte structures 92 (200), , ISS: [6] Sekne H, Atobe S. Identfcaton of locatons and force hstores of multple pont mpacts on composte sogrd-stffened panels, Composte Structures 89 (2009), 7. [7] LeClerc JR, Worden K, Staszewsk WJ, Haywood J. Impact detecton n an arcraft composte panel A neural-network approach, Journal of Sound and Vbraton 299 (2007), [8] Hansen P. C.: Regularzaton Tools, umercal Algorthms 46 (2007), [9] Laš V, Zemčík R, Kroupa T, Bartošek J. Proceda Engneerng, 48, , 202. [20] Laš V, Kroupa T, Bartošek J, Zemčík R. Impact force reconstructon for structural health montorng of composte beam, Acta Mechanca Slovaca 5 (2), 6 3, 20. [2] Wllams KV, Vazr R, Poursartp A. A physcally based contnuum damage mechancs model for thn lamnated composte structures, Internatonal Journal of Solds and Structures, 40 (2003), [22] Zemčík R, Laš V, Kroupa T, Bartošek J. Reconstructon of Impact on Textle Composte Plate Usng Pezoelectrc Sensors, Proceedngs of the 9th Internatonal Workshop on Structural Health Montorng 203, Chang FK (ed.), Structural Health Montorng 203, Vol., ,