Novel Ensemble Analytic Discrete Framelet Expansion for Machinery Fault Diagnosis 1

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

Download "Novel Ensemble Analytic Discrete Framelet Expansion for Machinery Fault Diagnosis 1"

Γάδ Παπαφιλίππου
5 χρόνια πριν
Προβολές:

1 OURNAL OF MECHANICAL ENGINEERING Vol.50 No.17 Sep DOI /ME * , 3 ( ) -- () - TH17 Novel Ensemble Analytc Dscrete Framelet Expanson for Machnery Fault Dagnoss 1 CHEN Bnqang 1 ZHANG Zhousuo 2 ZI Yanyang 2 HE Zhengja 2, 3 (1. School of Physcs and Mechancal & Electrcal Engneerng, Xamen Unversty, Xamen ; 2. School of Mechancal Engneerng, X an aotong Unversty, X an ; 3. State Key Laboratory for Manufacturng Systems Engneerng, X an aotong Unversty, X an ) AbstractAs the celebrated mathematcal scope, the mult-resoluton analyzng capacty of wavelet transform (WT) plays an mportant role n condton montorng and fault dagnoss of mechancal equpment. However, t has proven that the effectveness of WT s hampered by several negatve factors, such as shft-senstveness, sgnfcant energy leaage, and the fxed dyadc frequency-sale pavng. Especally, the dyadc frequency-sale pavng creates nevtable defcency n dentfyng mechancal sgnatures located n transton areas of adjacent wavelet scales. A novel tme-sale analyss methodology, named as derved ensemble analytc framelet (DEAF), based on overcomplete wavelet tght frame, s proposed. The DEAF s developed based on the exstng dual tree complex wavelet transform (DTCWT). The DEAF starts from a selected DTCWT bass, and combnes t wth a hybrd augmented tree-structured flter-ban, whch results n quas analytc wavelet pacet decomposton (QAWPD). Wth the results of QAWPT, an ensemble wavelet pacet generatng strategy s appled such that an unprecedented mplct wavelet pacet tght frame (IWPTF) contanng pseudo dyadc wavelet pacets s obtaned. Wth the combnaton of QAWPD and IWPTF, the proposed DEAF can be derved whch possesses the frequency-sale pavng characterzed by contnued tme-frequency refnement of analyss centers. The proposed technque s appled to the mechancal sgnature analyss of an engneerng applcaton to valdate ts superorty compared wth the exstng methods. * ( )(2010ZX , 2011ZX )

2 Key wordsmechancal fault dagnossdual-tree complex wavelet transformanalytc framelet expansonaugmented tree- structured flter-bantranslaton nvarance [1-3] (Dscrete wavelet transform, DWT) (Fast Fourer transform, FFT) [1, 3] DWT [2, 4-7] Daubeches(DB) DWT [8-9] DB SymmeletCoflet () [10] (MW) [11] (Dual tree complex wavelet transform, DTCWT) [12-13] DWT DWT (Dyadc frequency-scale pavng, DFSP) DFSP [5-6, 14] : (Derved ensemble analytc framelet, DEAF) DFSP DEAF ( )() DEAF DEAF DTCWT (Quas analytc wavelet pacet transform, QAWPT) QAWPT (Implct wavelet pacet tght frame, IWPTF) QAWPT IWPTF DEAF DEAF DTCWT - DEAF DEAF 1 (Quas analytc wavelet transform, QAWT) ( Re Im ) QAWT ( ) QAWT () () () () () { ( t), ( t),, ( t) } (1) 1 1 () Re Im r Im Re () t { () t } (2) {1,2,, r} {} Hlbert Fourer {} Im ˆ ( ) ˆ j ( ) 0 Re j ( ) 0 Re ˆ r (3) j -1 [ π, π]

2014 9 79 () t h (2 t n) (4) () () () 2 0 h Z () t h (2 t n) 1 r (5) () () () 2 h Z () h0 () h r 1, 2 [12-14]

tree-structured flter-ban, ATSFB) 2( ) QAWT DFSP DWT 2 (Quas analytc wavelet pacet transform, QAWPT) QAWT r 1

5) (6) Fourer G ( ) jsgn( ) H ( ) (7) 0 0 H ( ) 0 h0 Z G ( ) 0 g 0 Z H0 ( ) G 0 ( ){ h 0 } { g 0 } H0( )= h0(

3 () t h (2 t n) (4) () () () 2 0 h Z () t h (2 t n) 1 r (5) () () () 2 h Z () h0 () h r 1, 2 [12-14] KINGSBURY DTCWT ( r 1) [12] SELESNICK [13] QAWT [14] r 2 DFSP r DFSP QAWT( r 2 ) Mallat (Augmented tree-structured flter-ban, ATSFB) 2( ) QAWT DFSP DWT 2 (Quas analytc wavelet pacet transform, QAWPT) QAWT r 1 DTCWT 1 QAWPT QAWPT 2.1 SELESNICK DTCWT - Re () t Im () t h0 g 0 g n h n (6) ( ) 0 0 ( 0.5) (6) Fourer G ( ) jsgn( ) H ( ) (7) 0 0 H ( ) 0 h0 Z G ( ) 0 g 0 Z H0 ( ) G 0 ( ){ h 0 } { g 0 } H0( )= h0( )exp( j ) Z (8) G0( )= Z g0( )exp( j ) (9) DTCWT QAWPT DTCWT [15] DTCWT DTCWT ( 2) [15]DB9MV8 (Common factorzaton, CF) CF18 [16] [15] 18 DTCWT s() t

4 s() t 0.5cos(2π30 t) cos(2π85 t) 1.5cos(2π170 t) cos(2π340 t) 0.5cos(2π700 t) t[0,1.024] f 2000Hz L 2048 s 85 Hz170 Hz340 Hz 4 D 2 D 3 D 4 s () t cos(2πf t) t [0, 1.024] (10) s() t D Cd {, s} D Cd {, s} ( d ( ) d ) ( s ( ) s ) Z 2 2 [ d ( ) d] [ s ( ) s] Z Z f 2 fs /2 2 ˆ ˆ 0 f ED { } D( f) d f D( f) df (11) (12) (11)(12) Symmlet-18 h10 Re h11 Re Symmlet-18 h Im 01 h11 Im Im Re h10 h0 ( n 1) (13) Im Re h11 h11 ( n 1) (14) DTCWT DTCWT Q-Shft18 Re Re Im Im { h0, h1, h0, h1 } 2 DTCWT DTCWT QAWPT Q-Shft18 3 Re Re Im Im { h0, h1, h0, h1 } Q -Shft18 DB9 MV8 CF Q-Shft18 DB9 MV8 CF Q-Shft18 ([15] 23 ) 2.2 DTCWT [14] QAWPT 13 4 ( 2) QAWPT 3 DTCWT DTCWT { f 0, f 1 ( n )} Re 0 (15) f h 0 f n h n (16) ( ) Re 1 1 ( ) Z F 0 ( ) F 1 ( ) 4 4 QAWPT

5 QAWPT QAWPT 2 DTCWT QAWPT (1) 5 3 QAWPT () 4 QAWPT DTCWT (3) DTCWT [12] DTCWT QAWPT 7 7 QAWPT DTCWT 6 QAWPT DTCWT 7 QAWPT QAWPT (2) 6 ( 3 )QAWPT DTCWT 2 DFSP QAWPT DFSP 3

6 (1) QAWPT QAWPT { x } ( ) QAWPT x 2 P ( x) { D 1 2} (17) 4 P (2) (1) ( x) 1) D B { 0, 1,, 2, 1 log n n nm nm m 2 + 1} (18) B m1 m n (19) 0 2) B { 0, 1,, 2, 1 log n n n m n m m 2 + 1} (20) B B nm m1 nm mod( nm nm 1,2) 0,1,, 2 3) B (21) P( x) { D 1 2} (22) m1 m n (23) 0 (3) P( x) D 1 D 2 P( x) D (24) { } (Implct wavelet pacet, IWP) 21 2 I D D (25) 2 I ( x) { I () n 1 2 1} (26) 3 IWPTF QAWPT IWPTF DFSP 3 IWPTF QAWPT IWPTF QAWPT 0.5 f s f s 2 f 1 f 1 s 2 IWPTF 8 25 QAWPT I ( x) 8 IWPTF(25 )- 4 3 IWP QAWPT - IWPTF ( )() IWPT (1) QAWPT ( ) ( ) ( ) ( ) ( ) x n D n D n D n D n D D D D D D D D D D D D D I D (27) IWPTF QAWPT s

2014 9 83 (2) 9 3 IWPTF IWP e, () t IWP IWPTF

QAWPT - 10 I 10 QAWPT IWPTF QAWPT IWPTF 1)

(28) 2,1 3,2 4,4 2,2 fs /4 10 DEAF - 2) IWPTF I

1 2050 11 ( 65/22) 4 11 4 ( 11 14) 281.3 r/mn(4.

7 (2) 9 3 IWPTF IWP e, () t IWP IWPTF DTCWT QAWPT IWPTF ( ) 5 9 IWPTF (3 ) (3) - 4 QAWPT - 10 I 10 QAWPT IWPTF QAWPT IWPTF 1) IWPTF QAWPT 10 QAWPT IWPTF IWP I, I, I,, I, (28) 2,1 3,2 4,4 2,2 fs /4 10 DEAF - 2) IWPTF I I ( 1) I ( 65/22) ( 11 14) r/mn(4.688 Hz) Hz DEAF DEAF L 4 xn ( ) n0.05l x 4 L 1 x Kx [] 3 (29)

8 s Z nterval (s) (30) Z pnon f pnon 12 L x x x x x ANTONI [17-18] DEAF 13a 240 Hz 160 Hz 13b 13c s Hz Hz

9 (1) (2) DTCWT QAWPT IWPTFIWPTF IWPTF DTCWT (3) QAWPT IWPTF DEAF DEAF QAWPT IWPTF [1]. [M]2007. HE ZhengjaZI YanyangZHANG Xnng. Modern sgnal processng and engneerng applcaton[m]. X an X an aotong Unversty Press2007 [2] GAO R XYAN R Q. WaveletsTheory and applcatons for manufacturng[m]. HedelbergLondonSprnger [3] MALLAT S G. A wavelet tour of sgnal processng[m]. MassachusettsAcademc Press1999. [4] WANG S BHUANG W GZHU Z KTransent modelng and parameter dentfcaton based on wavelet and correlaton flterng for rotatng machne fault dagnoss[]. Mechancal Systems and Sgnal Processng (4) [5] CHEN B QZHANG Z SSUN Cet al. Fault feature extracton of gearbox by usng overcomplete ratonal dlaton dscrete wavelet transform on sgnals measured from vbraton sensors[]. Mechancal Systems and Sgnal Processng [6] HE W PZI Y YHE Z et al. Tunable Q-factor wavelet transform denosng wth neghborng coeffcents and ts applcaton to rotatng machnery fault dagnoss[m]. Scence Chna Technologcal Scences201356(8) [7] WANG GAO R XYAN R Qet al. Current envelope analyss for defect dentfcaton and dagnoss n nducton motors[m]. ournal of Manufacturng Systems (4) [8] PENG Z KACKSON R RCHU F Let al. On the energy leaage of dscrete wavelet transform[]. Mechancal Systems and Sgnal Processng200923(2) [9] WANG Y XHE Z ZI Y Y. Enhancement of sgnal denosng and multple fault sgnatures detectng n rotatng machnery usng dual-tree complex wavelet transform[]. Mechancal Systems and Sgnal Processng (1) [10] SWDLDENS W. The lftng schemea constructon of second generaton wavelets[]. SIAM ournal on Mathematcal Analyss199629(2) [11] STRELA VHELLER P NSTRANG Get al. The applcaton of multwavelet flterbans of mage processng[]. IEEE Trans. Sgnal Processng19998(4) [12] KINGSBURY N G. Complex wavelets for shft nvarant analyss and flterng of sgnals[]. Appled and Computatonal Harmonc Analyss [13] SELESNICK I WBRARNIUK R GKINGBURY N G. The dual tree complex wavelet transform[]. IEEE Sgnal Processng Magazne200522(6) [14]. [] (9) CHEN Bnqang ZHANG Zhousuo HE Zhengja. Enhancement of wea feature extracton n machnery fault dagnoss by usng double densty dual tree complex wavelet transform[]. ournal of Mechancal Engneerng (9) [15]. [] (3)7-12. CHEN BnqangZHANG ZhousuoGUO Tnget al. Tme-frequency doman constructon of dual tree complex wavelets for assembly clearance detecton of gear

10 chans[]. ournal of X an aotong Unversty (3)7-12. [16] SELESNICK I W. The desgn of approxmate Hlbert transform pars of wavelet bases[]. IEEE Transactons on Sgnal Processng200250(5) [17] ANTONI. Fast computaton of the urtogram for the detecton of transent faults[]. Mechancal Systems and Sgnal Processng200721(1) [18] WANG DPETER T WTSUI K L. An enhanced urtogram method for fault dagnoss of rollng element bearngs[]. Mechancal Systems and Sgnal Processng (1-2) ()1986 E-malmung.cbq@stu.xjtu.edu.cn 1964 E-malzzs@mal.xjtu.edu.cn 2012/2013 * (E-mallangl@tsnghua.edu.cn) (ESP) 30% 2012 ESP ESP ESP 70% ESP (VSEKF) ESP 2. (1) (2) ESP * (ICFDM2014)

Σχετικά έγγραφα

Sydney 2052, Australia.

Sydney 2052, Australia. ΕΛΕΓΧΟΣ ΚΑΤΑΣΤΑΣΗΣ ΤΩΝ ΜΗΧΑΝΙΚΩΝ ΥΠΟΣΥΣΤΗΜΑΤΩΝ ΣΤΑ ΓΕΩΡΓΙΚΑ ΟΧΗΜΑΤΑ, ΒΑΣΙΣΜΕΝΟΣ ΣΤΗΝ ΣΥΝΤΗΞΗ ΤΩΝ ΧΑΡΑΚΤΗΡΙΣΤΙΚΩΝ ΤΩΝ ΟΝΗΣΕΩΝ. Κατέρης,. Μόσχου, Ι. Γράβαλος 2, Ν. Sawalh 3, Θ. Γιαλαµάς 2, Π. Ξυραδάκης 2,