Denoising of Discontinuous Lithium Battery Film Thickness by Wavelet and Sparse Decomposition

Transcription

1 Sensos & Tansduces, Vol. 75, Issue 7, July 4, pp Sensos & Tansduces 4 by IFSA Publishin, S. L. Denoisin of Discontinuous Lithiu Battey Fil Thickness by Wavelet and Spase Decoposition Gon CHEN, Xifan ZHU, Qinquan XU, Anchen XU, Hui YANG School of Electonic Infoation and Electical Enineein, Chanzhou Institute of Technoloy, Chanzhou, 3, China E-ail: ealchenon@sina.co Received: 7 June 4 /Accepted: 7 July 4 /Published: 3 July 4 Abstact: Thid wavelet-theshold ate-spase decoposition sinal pocessin de-noisin is pesent, fo the pupose of easuin discontinuous fil thickness of lithiu battey not dependent on the inheent fequency and scannin vibation fequency of C-dynaic scannin syste by lase sensos. Inoin of pioi knowlede, best atoic sequence is acquied by iteation unde diffeent scannin ode. The ethod keeps thickness of lithiu battey and ets id of noise caused by inheent fequency and scannin vibation fequency. Expeient shows that spase atchin pusuit (MP) which is easy and effective to use is oe effective than wavelet aloith detection accuacy (ean eo) eaches 5-7 μ. Copyiht 4 IFSA Publishin, S. L. Keywods: Sinal pocessin, De-noisin, Spase decoposition, Lithiu battey.. Intoduction Fil lithiu battey is widely used in autoobile, obile phone and othe eney fields. Real-tie easueent autoatically of lithiu battey thickness can be ealized by C-dynaic scannin syste based on lase senso (Fi. ), but scannin pocess of the syste is accopanied with static and dynaic eo includin echanical vibation noise, syste eo of C-dynaic scannin syste, dynaic eo of diffeent scannin velocity [-3]. Pefoance could be achieved hihly accuately based on ulti-esolution wavelet aloith. But natual fequency and vibation fequency ae acquied to decide coefficient of wavelet decoposition and econstuction coefficient [, ]. Spase decoposition poposed by Mallat and Zhan is hot ecently, which has been widely used in iae, video, edical sinal pocessin [4-]. Spase decoposition aloith is adapt to choose the appopiate basis functions to coplete sinal decoposition on the condition of lack of noise statistical chaacteistics, and et natual featues of the oiinal sinal fo edundancy dictionay []. Duin industial suoundins, spase decoposition aloith eads actual thickness as a pat of the spase coponent and the vibation noise as the esidual of fil thickness. Duin poduction fil of lithiu battey, fo discontinuous fil, fistly thid-wavlet aloith is pesent. Secondly, theshold judeent is ealized to et id of fil of aluinu fil. At last, scannin vibation noise is ovecoe by spase decoposition aloith and econstucts the eal fil of lithiu battey. The aloith is scae of inheent fequency and scannin vibation fequency of C-dynaic scannin syste, but it can adapt to diffeent scannin speed fo fil thickness easueent. 58

2 Sensos & Tansduces, Vol. 75, Issue 7, July 4, pp Fi.. Fil of Lithiu battey detection.. Multi-esolution Wavelet and Theshold Judent.. De-noisin by Thid Wavlet Aloith Fo G. CHEN [], when the lithiu battey poduction line and C type echanis ae unnin at the sae tie, thid-wavlet aloith and theshold judeent ae pesent to denoisin dynaic eo. In industial envionent ν () n = d s() n s() n can be epesented as the distibution of eal-tie includin the coatin fil and aluinu fil thickness, d is distance between the uppe and lowe senso, s ( ) n is distance between uppe senso between uppe fil, s ( n ) is distance between lowe senso between lowe fil, n is saplin value, n=,, N, N epesents the axiu of saplin data. Thid level wavelet decoposition is used. ν '( is thickness value afte filtein. The ulti-esolution decoposition pocess is done as: a ( = v( n = + 8 aj a k = n+ ( k) h ( k k N j(, k > N () whee aj ( n ) is the decoposition coefficient of thid wavelet in the low fequency, j is the level of wavelet decoposition, j =,, 3, h ( k is the discete function afte low-pass diital filte, the ane of function is h () ~ h (8), whee h () = , h () = , h (3) = , h (4) = , h (5) = , h (6) = , h (7) = , h (8) = a ( ) 3 n is fo foula (), which is done as: ( n ) a '( = a3( h ( n k) k= n ( 8) ( n ) a' ( = a '( h ( n k), k = ( n 8) ( n ) a '( = a' ( h ( n k) k= ( n 8) v'( = a '(, whee aj '( n ) is the wavelet econstuction foula. Fo Fi, peak of sinal is noisy fil distibution of lithiu battey, the othes ae fil distibution of aluinu. The fist and second level wavelet decoposition is liit to et id of fil distibution of aluinu. The fouth level wavelet aloith eads lithiu and aluinu fil distibuted altenately as peiodic noise. The esult can not eflect the eal lithiu battey fil distibution. The thid level wavelet filte is bette and can eflect the eal lithiu fil distibution. 59

3 Sensos & Tansduces, Vol. 75, Issue 7, July 4, pp Fi.. Fil thickness of dynaic scannin and de-noisin data (fo top to botto)... Ipleentation of Lithiu Battey Fil Continuity by Theshold Judent Fil of aluinu is concluded in discontinuous lithiu battey fil. In ode to et id of useless fil, it needs to set theshold ate: ν ( ν '( < ν '( < else =, () Fo expeience, uppe theshold is set 7 μ and lowe one is μ []. d is epesented as: N d = v (, (3) N n = Fi. 3 (a) and Fi. 3 (b) ae thid wavelet and theshold judent unde diffeent scannin speed (4 μ/s, 34 μ/s). Fo Fi. 3, unde diffeent scannin speed of C-dynaic syste, lithiu battey fil continuity is ipleented, but vibation of fil distibution is obvious and dynaic noise is kept. In fact, vibation fequency unde diffeent speed shows 3 Hz, when saplin fequency is khz, bandwith of fouth wavelet is effective to keep eal fil fo eo noise. Othe ethod is accoplished to filte dynaic noise. Spase decoposition aloith is poposed fo de-noisin. 3. Matchin Pusuit Spase De-noisin In the pocess of iteative, spase decoposition is to choose the laest ato which is the inne poduct of sinal o sinal esidual, spase decoposition continues tackin and extactin the ato which is atch to the oiinal sinal and esidual sinal. In the calculation of the inne poduct selection of Gabo ato, it is vey lae, and if the lenth of the input sinal is too lae, the aount of calculation is even oe astonishin ) 薄薄薄薄 ( 微微 (a) saplin 采样采 value (b) Fi. 3. Contast between thid wavelet and theshold aloith. 6

4 Sensos & Tansduces, Vol. 75, Issue 7, July 4, pp Fo a lae aount of calculation, teplateatchin pusuit spase de-noisin is poposed. Fist, best atoic sequence teplate is built by spase decoposition unde vaious ode of scannin. Secondly, at the iven ode, fil thickness data is atch to the best atoic sequence to de-nosin. Althouh best ato is not extacted to calculate by eans of iteation, the ato is to be the next best one. Copaed with MP aloith, this aloith eliinates ties of iteation. Teplate-atchin pusuit aloith aises the possibility of vaious sinal s lenth and eatly ipoves the pefoance. Fi. is a flow chat of the fast spase de-noisin based on teplate- atchin pusuit []. The steps ae as follows: Step : Tain best atoic sequences and constuct teplate unde diffeent ode. Step.: Define ove-coplete dictionay D= { }( =,,, M ) in Hilbet space, =, t u γ () t = ( )cos( vt+ w), (4) s s whee defines as iteation ties, M defines as iteation teination value. () t = e π t is the Gaussian window function and γ = (, s uvw,, ) ae the tie-fequency paaetes. The function γ () t is centeed at u and its eney is ostly concentated in a neihbohood of u whose size is popotional to s. The space of tie-fequency paaetes can be j j j discetized as γ = ( a, pa Δu, ka Δv, iδ w), with a =, Δ u = /, Δ v = π, Δ w = π /6, < j lo N, p< N j+, k j + <, i to fo the so called Gabo dictionay. Hee N is the nube of saples in fae. Step.: Define easued data as x( n ), n =,, N fo static and dynaic industial envionent. N defines as lenth as sinal. Define x( = R x, n,, = N, sinal. Step.3: Select the best ato Rx is oiinal esidual o D by MP aloith to ake Rx, axiu, et the esidual Rx= Rx Rx,. Select the best ato by MP aloith, and et the esiduals Rx= Rx Rx,, R x = R x R x,! aain. Step.4: Define coheent atio λ( R x) = sup R x, R x which deceases D with the inceasin of iteation. If set to one conveence value, iteation will end up to M th and et M + th esidual sinal M + M M R x = R x R x, M. In ode to ensue the M coheent atio eaches the set, the iteation value adds up to M + ties. Step.5: Save and constuct teplate libay, the best ato defines as { l, l, l, l G } l = M M +, l =,, L, L is the nube of teplate unde vaious ode. Step : De-noise unde iven suoundin. Step.: Input easued data xx( n ), n =,, N unde soe kind of ode. Set xx( = Rxx. Step.: Select the pope paaete l fo the teplate libay and et G l. The best atoic sequences ae involved in the iteation l l R xx = R xx R xx,, =,, MM. MM is defined as iteative ties, MM < M +. Step.3: Finally MM l l MM+ yn () = R xx, + R xx n =,, N is = ot, Define yn ( ) as econstucted de-noisin sinal. 4. Expeiental Results Fo diffeent scannin speed of C-dynaic syste, contast is epesented between thid wavelet-judeent-spase decoposition (aloith ) and thid wavelet-judeent-foth wavelet (aloith ). Fi. 4 is coheent atio conveence value when nube of iteation is chanin. Fi. 5(a) shows fil thickness afte th iteation ties when speed by aloith, Fi. 5(b) shows fil thickness afte 8th iteation ties when speed by aloith. Fi. 5(c) and Fi. 5(d) show esult by aloith unde vious speed. Whee coheent atio is.4. Fo Tables -, deviation at least is educed by % and % eduction in ean vaiance with thid wavelet-theshold-spase decoposition. Readin ean deviation as the accuacy of easue, scannin pecision can achieve 5-7 μ fo C-dynaic scannin syste. Expeient shows that the foth wavelet aloith and wavelet function ae decided by natual vibation fequency of C-dynaic scannin syste, but spase decoposition aloith just only depends on the expeience to deteine eneal spase decoposition iteative stoppin citeia. Unde diffeent scannin speed this ethod can achieve hihe accuacy of de-noisin. Althouh the spase aloith of ean deviation and deviation is slihtly hihe than foth wavelet aloith, but in the lack of pio knowlede, the aloith has oe obvious advantae than taditional aloith. 6

5 Sensos & Tansduces, Vol. 75, Issue 7, July 4, pp coheent atio 3 scannin speed scannin speed iteation ties Fi. 4. Iteation value unde two kinds of scannin speed. Mode Scannin speed Scannin speed Table. Contast by diffeent aloiths. Befoe pocessed (μ) eo Afte pocessed (wavelet) (μ) eo Table. Contast by diffeent aloiths (a) Mode Scannin speed Scannin speed Afte Pocessed (spase) (μ) eo Entance (%) (spase) eo % % % % (b) 5. Conclusion C-dynaic scannin syste will cause natual fequency and dynaic noise which will seiously affect the easued thickness duin discontinuity poduction of lithiu battey fil. Taditional thid wavelet-judent-foth wavelet aloith depends on above fequency. Spase decoposition aloith is atchin with coponent of noise, continuous tackin and extactin atoic. The aloith can atch the oiinal sinal which is the eal fil thickness distibution of lithiu battey fil. ) 薄薄薄薄 ( 微微 (c) (d) Fi. 5. Contast between both aloiths. Acknowledeents This wok was financially suppoted by the Jiansu Natual Science Foundation (BK345), Chanzhou Key Laboatoy of Optoelectonic Mateials and Devices (3694). Refeences []. J. F. Zhou, Reseach on eos analysis and pecision contol in hih-pecision convexity easueent with lase fo thin sheet, Cental South Univesity, Chansha, 6, pp []. G. Chen, X. F. Zhu, Q. Q. Xu, et al, Multi-esolution wavelet in discontinuous coatin thickness easueent, Contol Enineein of China, Vol., Issue, 3, pp [3]. C. Wan, Bin Zhao, Reseach of thin plate thickness easueent based on sinle lens lase tianulation, Lase Technoloy, Vol. 37, Issue, 3, pp [4]. S. Mallt, Z. Zhan, Matchin pusuits with tiefequency dictionaies, IEEE Tansactions on Sinal Pocessin, Vol. 4, Issue, 993, pp

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