Application of Wavelet De-noising in Vibration Torque Measurement

Transcription

1 IJCSI Interntionl Journl of Computer Science Issues, Vol. 9, Issue 5, No 3, September Appliction of Wvelet De-noising in Vibrtion orque Mesurement Ho Zho 1 1 Jixing University, Jixing, Zhejing, CHINA Abstrct For vibrtion torque is the ey to the rottion system stte inspection nd fult nlysis, vibrtion torque test is implemented for no slot rotor three-phse synchronous when under no lod condition. While the vibrtion torque signl is nnihilted by lots of noise, de-noising scheme bsed on wvelet trnsform is constructed. he ctul signl is decomposed with wvelet Sym8, then processed by hlf soft threshold, nd reconstructed signl finlly. Simultion results indicted tht the method cn get rid of most of the high frequency noise, recover the fctulity nd improve the fitting nd generliztion cpbility of the dt, nd denoising effect is fr better thn the trditionl fst flourier trnsformtion. Keywords: Grting, Angulr Accelertion, FPGA, Speed-feed 1. Introduction Getting "correct nd true" signl plys n importnt role to the reliztion of utomtic control system, but becuse of different inds of errors, including mesurement error clcultion error instrument precision nd even the humn element, the mesurement dt exist noise unvoidbly. he noise cn led to the resolution nd ccurcy of mesurement system decrese, nd even cuses the true signl obliterted, therefore, eliminte the noise in mesurement dt become n importnt technology in dt processing nd ppliction. Signls re usully divided into the unstble signl nd stble signl, the idel tool to del with the stble signl is still Fourier nlysis, but the mjority ctul signl in ppliction is unstble, nd the suitble tool is wvelet nlysis. In recent yers, some experts pplied wvelet trnsform in de-noising nd obtined series of chievements. he spectrl reflectnce of soil ws mesured by ASD, then its first derivtive of spectr were cquired nd de-noised by the threshold de-noising method bsed on wvelet trnsform [1]. he vibrtion signls of vibrtory roller re processed by wvelet de-noising, the result eep the smoothness nd similrity of excittion signl []. Zhou Zuo-feng[3] proposes blind imge restortion lgorithm itertively using wvelet de-noising nd totl vrition regulriztion, the experimentl results show tht the proposed lgorithm chieves better performnce thn the existing lgorithms. Yng Zui-zhong[4] proposes method tht combines multiple wvelet trnsform with new threshold function, the method cn remove most rndom noise, extrct true signl nd improve the confidence level of the dt. A multi-scle imge enhncement lgorithm combining wvelet denoising is proposed by Xu Ying[5], nd experimentl results demonstrte tht the proposed lgorithm cn remove noises efficiently. A new de-noising lgorithm bsed on customized threshold function is proposed by Li Ji-sheng, the proposed de-noising lgorithm hs two thresholds, the lower threshold nd the upper threshold [6]. Wvelet threshold re used to denoise the signls by Xie Qi, the result indictes tht the method of threshold hs prcticl vlue in improving the precision nd creditbility of the instrument [7]. An integrted fult detection method bsed on wvelet de-noising nd feture vector selection-kpca (FVS-KPCA)ws developed[8], the results show tht the proposed method vil effectively improve the speed of fult detection. A vibrtion torque test for no slot rotor threephse synchronous is implemented when no lod in this pper. In order to decrese the noise in vibrtion torque signl, de-noising scheme bsed on wvelet trnsform is constructed. Simultion results indicted tht the method cn get rid of most of the high frequency noise, recover the fctulity nd improve the fitting nd generliztion cpbility of the dt, nd denoising effect is fr better thn the trditionl fst flourier trnsformtion. Copyright (c) 01 Interntionl Journl of Computer Science Issues. All Rights Reserved.

2 IJCSI Interntionl Journl of Computer Science Issues, Vol. 9, Issue 5, No 3, September Wvelet nd Wvelet rnsform Set ( t) L( R) L ( R), it mens tht (t) is bsolutely integrble nd squre integrble, its flourier trnsform is ˆ ( ) ˆ ( ) stisfied the llowble condition: ˆ ( ) d, if (1) he () t is clled bse wvelet or mother wvelet, when this mother wvelet is stretched nd trnslted, we cn get wvelet sequence: 1 t b () ( ) b, t () he continuous wvelet trnsform of signl f () t is defined s: 1 t b Wf (, b) f( t) ( ) dt (3) In this formul: is scle fctor(corresponding to the frequency informtion); b is trnsltion fctor(corresponding to the time nd spce informtion); () t is wvelet function(bse wvelet or mother wvelet); () t is the complex conjugte of () t. In prcticl pplictions, the continuous wvelet trnsform need to be discreted, the discrete is to scle fctor nd trnsltion fctor b, not to time vrible t, if order, b n, we cn obtin discrete wvelet trnsform: W f ( n) f ( t) ( n) dt, n Z o ensure the precision of reconstructing signl, the wvelet function should meet the frmewor conditions:, n, n A f f B f (5) (4) In this formul, 0 A B, A nd B re the bounds of the frme. 3. Wvelet De-noising he signl de-noising bsed on wvelet is function pproximtion problem, it mens looing for the optiml pproximtion to the rel signl in the spce which expnded by wvelet function telescopic nd trnsltion ccording to certin stndrd. he principle of de-noising. he mthemticl model of one-dimensionl signl with noise cn be expressed s: f ( t) s( t) e( t), t 01,,n-1 (6) in this formul, f (t) is the signl with noise; s(t) is the rel signl; e(t) is the noise; is the coefficient level of noise. Becuse of signl nd noise on different scles of wvelet trnsform will presents different chrcteristics, so the process of eliminting noise is: Decomposition the signl with noise by wvelet trnsform firstly, becuse the noise usully be contined in high frequency detils, so, we cn process wvelet coefficients which corresponding noise in the form of the threshold or threshold, then reconstruct the signl nd chieve the purpose of signl de-noising. Steps of threshold de-noising. he steps of threshold de-noising re: (1). Signl decomposition with noise: Choose certin wvelet bse function nd wvelet decomposition level N, then decomposite the signl f (t) by wvelet with N lyers. (). Quntify the threshold vlue of high frequency coefficients: Choose quntifiction criteri of threshold, then implementing quntified threshold process to high frequency coefficients of ech lyer. (3). Reconstruct the signl: ICW ccording to the high frequency coefficients of 1 to N lyers nd the low frequency coefficients of N lyer, the coefficients re ll quntittive threshold. he determintion of wvelet bse nd Copyright (c) 01 Interntionl Journl of Computer Science Issues. All Rights Reserved.

3 IJCSI Interntionl Journl of Computer Science Issues, Vol. 9, Issue 5, No 3, September decomposition of lyer. he bsic chrcteristics of wvelet bse including symmetry, orthogonlity, vnishing moment nd compct support, we should compromise these chrcteristics when choosing wvelet bse. It cn be proved tht the wvelet with pproximte symmetry is optiml for de-noising [9]. According to the blnce, choose the sym8 wvelet s bsis function, its supports length of N 1, the order of vnishing moment is N, the sym8 with pproximte symmetry nd hs the highest vnishing moment for the given support width. For sym8 wvelet bsis, the decomposition lyers is 5 ccording to the formul (7)in reference[10]. he determintion nd quntifiction of threshold. o ensure the uthenticity nd the smoothness of signl, select the dptive threshold which bsed on the principle of Stein unbised lielihood estimte s the methods to del with the vibrtion torque signl with noise. he selected principle of soft threshold vlue estimtion which bsed on the Stein unbised lielihood estimtion (SURE) is getting its lielihood estimte for given thresholdt firstly, nd then minimize the lielihood function, lst receive the required threshold. he methods of threshold function to signl re two inds usully, hrd threshold vlue method nd soft threshold vlue method. Hrd threshold processing cn eep more locl edge fetures of rel signls, soft threshold processing cn produce more smooth results becuse it decomposites for wvelet coefficient. In order to combine the dvntges of ech other, we use the improved hlf soft threshold function []: signls nd detil signl of ech lyer re shown in figure nd 3 respectively. Fig.1 Actul smpling signl Fig. Approximtion signls of ech lyer 1 ) ( 1) (,( ) 1,( ),( ) 1 (7) 4. De-noising Experiment he ctul smpling vibrtion torque signl is shown in figure 1, the smpling frequency is 10 K, smple dt point is Decompositing the ctul signl with noise 5 lyers bsed on sym8 wvelet, the pproximtion Fig.3 Detil signls of ech lyer It is nown tht the detil signl d1 nd d is relted with noise, nd the detil signl d3 (especilly the d4) is ssocited with sine signl is presented in figure 3. Copyright (c) 01 Interntionl Journl of Computer Science Issues. All Rights Reserved.

4 IJCSI Interntionl Journl of Computer Science Issues, Vol. 9, Issue 5, No 3, September Quntify the high frequency coefficients of the ech lyer with hlf soft threshold, de-noising with soft threshold vlue estimtion which bsed on the Stein unbised lielihood estimtion (SURE), the reconstruction signl is shown in figure 4. And we now tht this de-noising method cn remove the most noise in vibrtion torque signl. In order to vlidte the superiority of wvelet de-noising, deling with the ctul vibrtion torque signl with noise by FF, the results is s shown in figure Conclusion Fig.4 De-noising signls by wvelet Fig.5 De-noising signls by FF A de-noising method bsed on wvelet trnsform is constructed in this pper, ccording to the denoising experiment to the vibrtion torque signl,. his method cn eep the smooth nd the similrity of signl better while compred with trditionl fst flourier trnsform. And the results indicted tht the method cn get rid of most of the high frequency noise, recover the fctulity nd improve the fitting nd generliztion cpbility of the rel signl. his pper proposes high precision speed feedbc type ngulr ccelertion mesurement system bsed on FPGA nd SCM, the mesuring principle nd method of system re introduced in detils. According to the experiments results, the system could overcome the error when system speeds up. he mesurement system hs short responding time nd high precision, we expect it will be used widely. Acnowledgment his study ws supported by Jixing Science nd echnology Reserch Project (number is 01AY101) nd Zhejing Provincil Deprtment of Eduction Scientific Reserch Project (number is Y01608). References: [1] Liu Wei, Chng Qing-rui, Guo Mn, Xing Dongxing nd YUAN Yong-sheng, Extrction of First Derivtive Spectrum vi Wvelet De-Noising, Spectroscopy nd Spectrl Anlysis, Vol. 31, No. 1, 011, pp [] Yi Fei, Co Yun-wen, Appliction nd Reserch of Wvelet De-noising in the Dt Processing of Vibrtory Roller, Journl of CHONGQING JIAOONG University (Nturl Sciences), Vol. 30, No. 1, 011, pp [3] Zhou Zuo-feng, Shui Peng-lng, Blind Imge Restortion Algorithm Itertively Using Wvelet De-noising nd otl Vrition Regulriztion, Journl of Electronic nd Informtion echnology, Vol. 30, No. 1, 008, pp [4] Yng Hui-zhong, Zhong Ho nd Ding Feng, Signl de-noising bsed on multiple wvelet trnsform nd its ppliction in soft mesurement, Chinese journl of Scientific instrument, Vol. 8, No. 7, 007, pp [5] Xu Ying, Hong Zhi, Study of Multi-Scle Enhncement Algorithm for Hz Imges Combining Wvelet De-noising, Chinese journl of Sensors nd Actutors, Vol. 4, No. 3, 011, pp [6] LI Ji-sheng, Hung Wen-qing nd DAi Yu-xing, Wvelet -bsed power qulity disturbnces denoising by customized thresholding, Power System Protection nd Control, Vol. 36, No. 19, 008, pp [7] Xie Qi, Chen Wei-yi, Luo Yun nd Li Lu, Appliction of Wvelet De-noising to Detection System for Fire Control System, Journl of Gun Lunch nd Control, No. 1, 011, pp [8] Zho Xio-qing, Wng Xin-ming, A FVS- KPCA Method of Fult Detection Bsed on Wvelet De-noising, Control nd Instrument in Chemicl Industry, Vol. 37, No. 1, 010, pp [9] Donoho D L, Johnstone I M, Adpting to unnown smoothness vi wvelet shringe, Journl of the Americn Sttisticl Assocition, Vol. 90, No. 43, 1995, pp Copyright (c) 01 Interntionl Journl of Computer Science Issues. All Rights Reserved.

5 IJCSI Interntionl Journl of Computer Science Issues, Vol. 9, Issue 5, No 3, September [10]Hll P, Ptil P, On the choice of smoothing prmeter threshold nd trunction in nonprmetric regression by nonliner wvelet methods, Journl of the Americn Sttisticl Assocition, Vol. 58, No., 1996, pp Mr. Zho received the mster degree in control theory nd control engineering from Zhejing University of echnology in 010. he is engged in the reserch wor of motor nd its testing. Copyright (c) 01 Interntionl Journl of Computer Science Issues. All Rights Reserved.