A De-Noising Method for Track State Detection Signal Based on the Statistical Characteristic of Noise

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1 Journal of Transportaton Technologes, 204, 4, Publshed Onlne October 204 n ScRes. A De-Nosng Method for Track State Detecton Sgnal Based on the Statstcal Characterstc of Nose Lmng L, Xaodong Cha, Shubn Zheng, Wenfa Zhu College of Urban Ralway Transportaton, Shangha Unversty of Engneerng Scence, Shangha, Chna Emal: lmng0028@26.com, cxdyj@63.com, zhengshubn@26.com, zhuwenfa986@63.com Receved August 204; revsed 26 August 204; accepted 7 September 204 Copyrght 204 by authors and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY). Abstract Based on the statstcal characterstcs analyss of random nose power and autocorrelaton functon, ths paper proposes a de-nosng method for track state detecton sgnal by usng Emprcal Mode Decomposton (EMD). Ths method s used to nose reducton refactorng for the frst Intrnsc Mode Functon (IMF) component n accordance wth the random sort-accumulaton-average-refactorng" order. Sgnal autocorrelaton functon characterstcs are used to determne the cut-off pont of the domnant mode. Ths method was appled to test sgnals and the actual nertal unt sgnals; the expermental results show that the method can effectvely remove the nose and better meet the precson requrement. Keywords Track Inspecton, Long Wave Irregularty, Emprcal Mode Decomposton, De-Nosng. Introducton Tracks are the nfrastructure to tran safe operaton due to the uneven elastcty of track structure and ral base can cause ral lne long wave rregulartes [] [2]. Inerta method s the man techncal route n track detecton [3]-[6]. Usng strapdown nertal technology test track long-wave rough chronologcal, due to the nerta unt acceleraton sgnal collected contan more low frequency nose, easy to cause ntegrator saturaton, so we must do de-nosng processng frst before the ntegral on acceleraton sgnal. The complex sgnal can be decomposed nto level sgnals step by step (.e., to smooth the sgnal processng) based on the emprcal mode decomposton accordng to dfferent tme scales and get a seres of ntrnsc mode functon characterstcs of dfferent scales. Each IMF component contans a sgnal from low frequency to hgh How to cte ths paper: L, L.M., Cha, X.D., Zheng, S.B. and Zhu, W.F. (204) A De-Nosng Method for Track State Detecton Sgnal Based on the Statstcal Characterstc of Nose. Journal of Transportaton Technologes, 4,

2 frequency of dfferent ngredents and each frequency component that s ncluded n the frequency changes over the sgnal tself [7] [8]. So the EMD can be thought of as a space-tme flterng process based on sgnal extremum characterstc scale. Ths property s used n sgnal flterng analyss and nose reducton processng. In ths paper, through the statstcal characterstcs analyss of random nose power and autocorrelaton functon, we put forward the EMD de-nosng method based on nose statstcal characterstcs. Expermental results show that the method can effectvely suppress nose and mprove the track rregularty detecton accuracy. 2. The Prncple of Inertal Reference Method Detecton Inertal reference method [9] [0] measurng system s n the movng car, speed meter and gyroscope s used to establsh an nertal reference benchmark, through the measurements of these two knds of nertal components analytcal method to get a benchmark, and reuse dsplacement sensor or mage sensor measurement orbt relatve poston relatve to the benchmark, and get the relatve poston at the top of the ral n the nertal coordnate system. As shown n Fgure, under the same datum pont, accordng to the basc prncple of strap down nertal navgaton system [] [2], usng the angular velocty sgnal output by gyroscope, real-tme updatng the atttude matrx of the carrer, through the atttude matrx we can transform the acceleraton sgnal output from accelerometer nto the geographcal coordnate system, and can get the trajectory curve of three axs x, y, z n geographc coordnate system after two ntegral operaton for acceleraton sgnal. The curve of x, y, z respectvely represents projecton parameters of ral lnes n the vertcal plane and horzontal plane and vertcal plane, further combned wth results of the cross secton measurement system, ultmately get all the rregularty parameters we need [3] [4]. Through comparng the dfferent results to acqure the devaton, the deformaton can be calculated quanttatvely, so that the workers can repar the serous abrason tmely. Moreover, durng the actual measurement, what s manly concerned s the ral deformaton of vertcal and level plane, meanng the rregularty value of heght and drecton. 3. Emprcal Mode Decomposton Algorthm The basc method of emprcal mode decomposton: Through contnuous screenng, the complex sgnal s decomposed nto several ntrnsc mode functons IMF component whch are arranged from hgh to low frequency and the resdual term, as shown n Equaton (), the concrete process can be referred to [5]. n n () = = + x t IMF t r t r n s resdue component, representng average trend of the sgnal. And each IMF component respectvely contans dfferent frequency sgnal components from hgh to low. IMF t, IMF2 t, IMFn t After decomposton, each ntrnsc mode functon (IMF) must be met two condtons followng: ) Throughout the tme sequence, the number of passng zero s equal to the number of the pole or at best, a dfference; 2) At any pont, the mean value composed of local maxmum value upper envelope and lower local mnma envelope must be zero. Fgure. The mage of moton trajectory. 328

3 After EMD decomposton we can get fnte IMF: Among them, the bg order correspondng to the low frequency component sgnals, s generally thought that lttle mpact nose n the low frequency components; Small order corresponds to the hgh frequency component sgnal, often assume that contans a sharp part of the sgnal and nose [6] [7]. The man dea of usng EMD method to deal wth the nose s that man energy of most polluted sgnals s concentrated n low frequency band, the farther the hgh frequences, t contans the less energy, so we can reconstruct sgnal partly by usng several IMF n low frequency, namely: N IMF ( t) x t = = K + (2) 4. An EMD De-Nosng Method Based on the Statstcal Characterstc 4.. Random Nose Power Statstcal Propertes For the length of N dscrete sgnal x( n ), the power calculaton formula s: 2 P N x x n N = = (3) If keep the ampltude of orgnal sgnal x (n) each element constant, to dsrupt ts locaton n order to get x (n), x (n) and x (n) can be determned power equal, namely, Px = P x, the sgnal power stays the same after a random sequence. The followng research s the changng rule of the nose power through random nose nt after the random sort-accumulatve-average. Stochastc schedulng random nose nt whch samplng ponts s 2048, totally 25 tmes repeated, after the tme random sort we can get the new nose n ( t ), supermpose n ( t ) and the n t whch s get from random sequence of - before, can obtan a new nose component: nose + j nt n t j= n = (4) + Computng the power of n ( t) by Equaton (3), then we can get a power sort frequency curve, as shown n Fgure 2. In Fgure 2, the power P n gradually reduced wth the ncrease of number of sortng number after the random sort-accumulaton-average ; when sortng number ncreased to a certan degree, the attenuaton speed of power P n became slow; when tend to be nfnte, P n wll be close to zero. Inspred by the above experments, we let the mf, mf 2, mf 3 component whch s obtaned after the EMD decomposton of the random nose nt random sort-accumulatve-average and compute power, the powersort frequency curve respectvely as shown n Fgures 3-(c). Expermental results show that the frst IMF component of random nose after EMD decomposton remans the approxmate random features, for the frst IMF component namely the mf, n accordance wth the random sort-average accumulatve the new nose power decreases wth the ncrease of number of random sequence. Fgure 2. Nose power-sort frequency curve. 329

4 Fgure 3. Nose IMF component power-sort frequency curve The Statstcal Feature of Random Nose Autocorrelaton Functon (c) The autocorrelaton functon of random sgnal s an average measure of the sgnal tme doman features, reflectng the sgnal related degree at two dfferent tmes t, t 2. Random sgnal xt autocorrelaton functon s defned as: (, ) Rx t t2 = E x t x2 t (5) The autocorrelaton functon of random nose nt and general sgnal xt can be calculated respectvely accordng to the Equaton (5), functon curve as shown n Fgure 4 and Fgure 5, respectvely. R ( τ ) ( 0) x ρ τ = (6) Rx where τ = t t2, represent tme dfference. The Fgure 4 and Fgure 5 show that although the normalzed autocorrelaton functon of random nose nt and xt can get maxmum value n zero, but outsde the zero pont s dfferent; For random nose nt, because of ts weak correlaton and randomness n every moment, so ts maxmum of autocorrelaton functon can get at zero, autocorrelaton functon at other ponts attenuaton quckly to small features; For the general sgnal xt, ts autocorrelaton functon does not have such features. Usng ths feature can determne the cut-off pont n the sgnal-to-nose rato (SNR) domnant mode The EMD De-Nosng Algorthm Based on Nose Statstcal Propertes Accordng to the statstcal characterstcs analyss of random nose power, autocorrelaton functon [8], put forward the EMD de-nosng algorthm based on nose statstcal characterstcs and use sort-accumulatonaverage-refactorng order to suppress the nose. Specfc steps are as follows: 330

5 Fgure 4. Nose and normalzed autocorrelaton functon. Fgure 5. Sgnal x (t) and normalzed autocorrelaton functon. Step : the EMD decomposton on nose sgnal y( t ), get N ntrnsc mode components IMF, and let the last trend tem quantty decomposed for the frst N IMF; Step 2: remember n( t) = mf ( t), x( t) = mf ( t), n ( t) nt N = 2 cumulate = ; Step 3: stochastc schedulng nt and get a new component n ( t ), namely n ( t) n ( t) n ( t) cumulate = cumulate + ; Step 4: repeat Step 3 R tmes, calculate the average of accumulaton to get a new nose domnant mode ncumulate ( t) nr ( t) = whch power s weaken; R + Step 5: get a new nose sgnal y ( t) = nr ( t) + xt whch sgnal-to-nose rato s mproved after the refactorng of nr ( t ) and xt ; Step 6: y ( t) should be consdered the orgnal polluton sgnal repeat Steps - 5 S tmes, get further suppressve nose sgnal y 2 ( t) ; Step 7: EMD decomposton on y 2 ( t) frst, then calculate the autocorrelaton functon of the N IMF component, based on the characterstcs of the autocorrelaton functon graphc judge the cutoff pont K of nose do- 33

6 mnant mode and the sgnal domnated mode; Step 8: global threshold selecton method on the nose domnant mode component ~ K wth the nose, namely: where ( ( ) ) 0, sgn mf j mf j T, mf j > T mf = mf j T mf t mf t to deal T = σ 2ln L s the threshold value of the th component mf ( t ), L s the length of sgnal, σ s the 2 L L j= K ~ N ; standard devaton of mf ( t ), namely σ = mf ( j) mf ( t) Step 9: refactorng on mf ( t) ~ mf K ( t) and mf + ( t) mf ( t), then we can get de-nosng sgnal y ( t) 5. Expermental Verfcaton 5.. Analog Sgnal Usng the method to deal wth the nose of x ( t ) and x2 SNR, among them, x ( t ), x2. t whch contans Gaussan whte nose n dfferent t results from the superposton of gauss whte nose of sgnal f t π = 2sn 20πt+ 4, t s 3dB, as shown n Fgure 6 and Fgure 6. To the EMD de- t, random sort-accumulaton-average on the frst mf component for R tmes, x t : R = 45, S = 3 ; 2 : 45, 3 2 whch SNR s mproved, as shown n Fgure 7 and Fgure 7. Contnue to the EMD decomposton on x ( t), x 2 ( t), and calculate the autocorrelaton functon of each mf component, as shown n Fgure 8 and Fgure 8. The random nose autocorrelaton functon statstcal propertes s used to select the SNR cut-off pont K = 5, global threshold selecton method on mf( t) ~ mf5( t ) to deal wth the nose and get mf ( t) ~ mf 5( t), refactorng on mf ( t) ~ mf 5( t) and mf6 ( t ) to get sgnal X (, as shown n Fgure 9; In the same way, select SNR cut-off pont K 2 = 5, refactorng and get sgnal X 2 ( t), as shown n Fgure 9. The dfference between X 2 ( t) at both ends n Fgure 9 and the orgnal X t s caused by the nherent defects endpont effect of the EMD decomposton algorthm. SNR of x ( t ) s 8 db, SNR of x2 composton of x ( t ) and x2 wth the rest of the mf component refactorng agan, contnue to repeat S tmes ( x ( t) R = S = ), then can get sgnal x ( t), x ( t) sgnal 2 Fgure 6. Nosy sgnals. 332

7 Fgure 7. De-nosng results of test sgnals. Fgure 8. Each mf component of normalzed autocorrelaton functon of x ( t) and x ( t) Through the smulaton experments analyss: under the condton of low sgnal nose rato (SNR), the EMD de-nosng algorthm based on random nose statstcal characterstcs stll can obtan good de-nosng effect The Experment Results Analyss Experment system uses XW-IMU5250 tny mechancal nertal devce of Bejng StarNeto Technology Development Co., Ltd. In the experments for loadng of the nertal measurement unt testng the car through an analog lne segments, and then collect the nertal measurement unt acceleraton along x, y, z axs among the car movement. Frst of all, usng the average flterng method to elmnate the acceleraton sgnal contaned n the drect current; ths method s appled to the actual nertal unt sgnal nose processng then. The waveform and spectrum dagram of de-nosng before and after as shown n Fgures 0-2. Integral operaton on x, y, z axs acceleraton sgnal after de-nosng, and through the atttude matrx transforms the movement nformaton of vehcle coordnates to geographc coordnates, and get the car s trajectory, the expermental results and the actual test vehcle by ral sectons as shown n Fgure 3, error range wthn ±0.5 mm

8 Fgure 9. De-nosng result of the proposed method. 6. Concluson Fgure 0. The waveform and spectrum dagram of de-nosng before and after of x axs acceleraton sgnal. In ths paper, by usng the random nose power, autocorrelaton functon statstcal characterstcs, a knd of sutable for low SNR sgnal de-nosng method s put forward. The method can get the frst component of the IMF after EMD decomposton on nose sgnal, n accordance wth the random sort-accumulaton-averagereconstructon order. We can get a reconstructon sgnal whose nose power s sgnfcantly weaken and sgnal power constant frstly, and then do EMD decomposton agan for the reconstructed sgnal, and determne the cut-off pont of sgnal-to-nose domnant mode by usng sgnal autocorrelaton functon characterstcs, realze the fnal de-nosng sgnal reconstructon. Test results show that n low sgnal nose rato (SNR) the method for de-nosng effect s obvous. At the same tme, good performance of nertal measurement unt n the treatment of orbtal state detecton sgnal provdes a new thought for the future of nertal measurement unt sgnal processng. Acknowledgements The project s jontly supported by Natonal Natural Scence Foundaton of Chna (Grant No ), the 334

9 Fgure. The waveform and spectrum dagram of de-nosng before and after of y axs acceleraton sgnal. Fgure 2. The waveform and spectrum dagram of de-nosng before and after of z axs acceleraton sgnal. Fgure 3. Expermental platform orbt and space dsplacement curve after two ntegrals. Shangha Tertary Educaton Specalzed Fund for Plannng to Support Young Teacher's Tranngs (ZZGJD2007), the Natural Scence Foundaton of Shangha (2ZR42300), the Scence and Technology Commsson of Shangha Muncpalty Key Support Project ( ), and the Shangha Graduate Educaton Innovaton Project n Layout and Constructon Project (3sc002). References [] Lu, Z.X., Su, Y.C. and L, H. (2007) Super Track Long-Wave Irregularty Detecton System Desgn. Chna Measurement &Testng Technology, 33, 6-8. [2] Zheng, S.B., Ln, J.H. and Ln, G.B. (2007) Maglev Track Long-Wave Irregularty Detecton Based on Inerta Method and Its Implementaton. Journal of Electronc Measurement and Instrument, 2, [3] Chen, D.S. and Tan, X.Y. (2008) Chna s Hgh-Speed Ral Track Detecton Technology Development. Ralway Engneerng, 2, [4] Weng, S.D. (990) GJ-3 Track Detecton System Development and Applcaton. Chna Ralway Scence,, [5] Xu, G.Y., Cu, W. and Jang, Y. (2000) GJ-4 Track Inspecton Car and Its Effect on Transportaton Safety. Chna Ralway, 9, [6] Zhao, G., Lu, W.Z. and Chen, D.S. (2004) GJ-5 Track Inspecton Car Independent Research and Development of the 335

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