A Fusion Method of Fault Diagnosis Based on Nonlinear Spectral Analysis
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1 Fo eod o Fal ago Baed o olear Seral al Ra We ogzao a Sool o Elero ad Iorao Egeerg X'a Jaoog Uver X'a 749.R. a rwe@are.o za@.ed. oggag Zo a Zag ad Xeg Wag Sool o Elero ad Iorao Egeerg X'a Jaoog Uver X'a 749.R. a zlz_@a.o bra - leor o eod o e al dago baed o e olear eral aal reeed aer. B g eod or e al dago e o vele dag rg e o orao oe ro e GFRF Geeralzed Freqe Reoe Fo er eare ad e vbrao voe er eare o e rg ad e eral ewor ed o realze e o dago. Fall e eere rel dae a e reeed eod ee. Keword: al dago geeralzed reqe reoe o GFRF orao o vele dag rg olear e. Irodo Tere are a dere al dago eod or eaal e; e eral aal oe aog e. Te a dea o e eod o dagoe e e al b g FFT o aalze e reqe er o e o gal o e dagoed e. B e eod ee ol or e ae a e al a aeed. For oe ae e gradal age o e e old be ow a rg rede dee alre e. Tee age are all releed b e age o e olear reqe er o e e. I e reqe er age are eve o e age o e eaal roere a ee al dago eod or eaal e b g e olear eral aal eerge. Te olear eral aal o oba e geeralzed reqe reoe o GFRF ro e ad o gal o e dagoed e [5]. I rae dl o dagoe e e al ol b g e olear eral aal beae ere are oe drbae or e gal eare ad GFRF eao. ow a leor o dago eod baed o e olear eral aal rooed aer. Te ad o gal o e e are aled ad e GFRF' are eaed a beore. eawle aoer eor a e rooe ed o oba e oleear orao. Te e o dago realzed b g a eral ewor. ordg o dea a eere e or e al dago o a vele dag rg deged ad e eere rel dae a e o dago eod ee. Te aer orgazed a ollow: e eo devoed or e olear eral aal o e vele dag rg. Te al dago rle o e vele dag rg baed o e olear eral aal llraed eo. d e leor o dago eod baed o e olear eral aal reeed eo 4. I eo 5 e eere e roded ad e eere rel are alo ow. Fall e eo 6 e olo. olear eral aal or e vele dag rg. Geeralzed Freqe Reoe Fo For SISO e-vara aal olear e o a be rereeed b e Volerra ere a [7] d were { } are e Volerra e-doa erel or e geeralzed le reoe o. Tag Forer raor o above eqao eld oe a: F F
2 π d d were e -deoal Forer raor o or w are alled e geeralzed reqe reoe o GFRF'.e. F d e. 4 I lear a } { ad } { are all e oaraer odel o olear e. J a e le reoe o o lear e e a derbe e eeal roere o e olear e. Eeall or e SISO oloal olear e rereeed b a olear dereal eqao a: [ a ]... b. 5 e o rerve orla o GFRF' a be obaed a ollow b g e l-deoal Forer raor.[] 6 [. ] / B 7... { [ ] / [ B ] } / 8 were e ber o erao. d > > odd / eve /. b B a 9 B g 6 ~ 9 e eore GFRF ereo a be obaed or a SISO oloal olear e.. olear eral aal o dag rg oder a dag rg e vele aedg e. Uder oral ae e da eqao o e rg a be rereeed a:. ordg o 6 ~ 9 eo. e GFRF' o e oral rg a be allaed. I lear a ere ol order GFRF or e oral rg.e. ad o o. B we e rg beoe alre e ard or o araer.e. e b olear araer wll evdel aear. e e rg da eqao wold be wre a. For e above olear dereal eqao b g orla 6 ~ 9 e aalal ereo o e r order GFRF' a be obaed a ollow [ ] U were ordg o ee ereo or a red dag rg eoreal GFRF' agde lo a be obaed a ow Fg.
3 Te a o GFRF' deao o oba e Volerra erel o e dagoed olear e ro ad o gal. For e dagoed dag rg e vbrao aelerao gal a e o ad boo o e rg w are reevel og o a e o ad gal o e rg old be ed o allae GFRF'. Te raewor dagra o GFRF' deao ow Fg.. a Te agde lo o order GFRF Fg. Fraewor dagra o GFRF' deao b Te agde lo o rd order GFRF Fg. e GFRF' o a red dag rg Tee lo ave ow a e age o GFRF' o e dag rg are obvo we all o al ae ro oral oe. So b aalzg e age o GFRF' o e dag rg e alre o dag rg a be dagoed well ad rl eor. Fal dago o e dag rg baed o olear eral aal Te rle o al dago baed o olear eral aal a be derbed a ollow. Frl e GFRF' eare daabae o e dag rg old be bl aordg o a lo o adard GFRF' ale daa. d e or e dagoed rg e vbrao aelerao gal a e o ad boo o e rg wold be rool aled o a e rre ad rd GFRF o e rg a be ole eaed ro ee aled daa. er e rre GFRF er eare ave bee eraed b g aer reogo eqe e rre ae o e rg a be dagoed edael. I dago e e are o ora: GFRF' deao eare erao ad aer reogo.. GFRF' Ideao Te rar ar o e deao e e deao algor. For ole alao e Volerra e doa erel are r eaed b g e rerve ll deoled LS adave deao algor [8] ad e e GFRF' are obaed b Forer raor.. Feare Erao er e GFRF' er ave bee obaed e al eare o e rg a be eraed ro e. log ere are a dere eare or eaal al dago or a raal e e avalable eare old be deered aordg o e alao evroe obe roere ad leeg oveee e. Beae o e ole o GFRF' er o olear e e GFRF' er eare old be eraed ro e agde o GRFR' er w are odered a ollow: For order GFRF ae. For d order GFRF ae r. 4 r For rd order GFRF ae
4 r. 5 r ordg o ~5 e GFRF' er eare o e dag rg a be eraed aer e GFRF' ave bee obaed. For e al dago baed o olear eral aal a lo o adard GRFR' er eare are eear w are ed o ra a aer laer. er e GFRF' er eare ave bee eraed e ae aer o e dag rg oral or alre a be laed b g aer reogo eqe.. aer Reogo Te a o aer reogo o la e ae aer o e dagoed rg aordg o e rre GFRF' er eare. Uall a B eral ewor a be ed a e aer laer. Te GFRF' er eare are ed a e o e ewor wle o dae e ae o e dagoed obe oral or al. T ewor be raed b g e adard er eare daa. T raed ewor a aoaall la e ae aer o e rg e rre GFRF' er eare are ed a e o e ewor w ave bee eraed ro e rre eared ad o gal. So e al dago o dag rg a be realzed. Or aal ad eere ave daed a e al dago a be realzed b g olear GFRF' eral aal eod or dag rg. I rae ere are oe dle or al dago ol b g e olear eral aal de o drbae e gal eare ad GFRF' eao. Irovg e vera o e al dago e leor o dago eod baed o e olear eral aal or dag rg wold be deged. 4 leor o dago eod baed o olear eral aal 4. Voe er eare o dag rg B dg e voe er o e rg vbrao we d ere are oe deree bewee e ower er eare o vbrao voe gal o oral dag rg w al oe. So ee voe er eare a be ed a aoer eare orao or e al dago o e dag rg. B aalzg voe er eare araeer are deed w a eel dg oral vbrao voe ad al oe e are ower er ea ower er ovarae σ ad ower er bareer G e reqe rage o 5~z. eoe e ower er o vbrao voe gal o dag rg b o ee eare araeer are deed a: ower Ser ea:. 6 ower Ser ovarae: σ [ ]. 7 ower Ser Bareer: G. 8 We e dag rg worg vbrao voe gal eared b rooe ed o e dag rg ad e ee eare araeer are eraed ro e ower er o e eared voe gal. Baed o e GFRF' er eare orao ad voe er eare orao o e dag rg e leor o dago eod or dag rg rooed. 4. Te rle o e leor o al dago o e dag rg Te rle o e leor o dago eod baed o e olear eral aal eqe ow Fg. I gre a a ad v are reevel e vbrao aelerao gal a e o ad boo ad vbrao voe gal o e dag rg. Tee gal are ed o era e GFRF' er eare ad e voe er eare. Te GFRF' er eare daabae ad e voe er eare daabae are bl aordg o e adard ale daa o e dag rg w ed o ore e oralzed adard GFRF' er eare daa ad e oralzed voe er eare daa. d ee daa are ed o ra a B eral ewor w ed a e o dago odle o a a eel realze e al dago or e dag
5 rg. Te ode ber o e laer e o e ber o e GFRF' er eare araeer ad e ber o voe er eare araeer e o laer a ode w reevel deoe e oral ae ad al ae o e dag rg. d e ode ber o dde laer deered b e rag rel. er e eral ewor a bee raed g a realze e o al dago o e dag rg. We e dag rg worg e rre GFRF' er eare ad e voe er eare are ole eraed ro e gal a a ad v b g oe eod gve eo.. ad 4.. d e ee eare araeer are ed a e o e o eral ewor aer e are oralzed ad e o o e eral ewor dae e rre ae o e dag rg. Fg. e rle o leor o al dago baed o olear eral aal or dag rg 5 Eere e ad rel We ave obaed e eqeal aal or ae ro Saa roval Govere ad a eere e a bee bl or e al dago o dag rg w e o dago eqe baed o e olear eral aal. Te eere eqe ow Fg 4. Te dag rg oe o e aedg e o ST ad wo d o eor are ed.e. aelerao eor ad voe eor. Te dago rle a bee llraed eo 4.. Te B eral ewor ed a e o dago odle a 8 ode o ode ad dde ode. Te eere r ae ave bee ed. Tere are oral good rg ad al rg. Te are dvded o gro.e. e oral gro ad e al gro. We ae deedel eere or ever rg o 5 gro o adard ale er daa are obaed. d e e B eral ewor raed b g ee er eare daa ad e raed ewor ed o realze o al dago o e dag rg. Te eere rel ave ow a e leor o dago eod or dag rg baed o e olear eral aal ee dago reo a aeved 7%. Fg 4 e eere eqe o o al dago e o e dag rg 6 olo T aer ree a o al dago eod or e dag rg w baed o e olear eral aal eqe. Te orreodg eere e a bee bl. Te vald o eod a bee llraed b e aal ad eere. Te eod rovde a ew al dago eqe or eaal e.
6 Reeree [] S.. Bllg ad K.. Tag Seral al or olear e ar I: araer olear Seral al eaal Se ad Sgal roeg o : [] S.. Bllg ad K.. Tag al or olear e ar II: Ierreao o olear Freqe Reoe Fo eaal Se ad Sgal roeg o: [] ogzao a Lq Wag Xaoqa Tag ad Ygog ag Ideao o oaraer GFRF odel or a la o olear a Se orol Teor ad lao ee Joral Vol.66: [4] R.J. Ko.L. o l-eor o baed dago or rbe blade al va aral eral ewor. Iellge Egeerg Se Trog ral eral ewor. Vol. :4-7 ov. 99. [5] Yog L ogzao a ad Weq X e al olear Seral al ad I lao Fal ago Joral o X'a Jaoog Uver Vol.49:-5. [6] B. Wdrow R.G. Wer R.. Baer Laered eral e For aer Reogo IEEE Traao o o See ad Sgal roeg Vol. 67: [7]. Seze Te Volerra ad Weer Teore o olear Se. Wle 98. [8] Ra We ogzao a ll eoled Volerra dave Fler T Eleroa Sa ee Joral Vol
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