1 11.1 1

1.2 21.3 3

1.4 4

1.5 4

2 72.1 7

2.2 8

2.2.1 8

22.2 g

2.3 11

2.3.1KI 11

2.3.21D 12

2.3.3 K ID12

2.41DKI 13

2.4.1 IDK13

2.42 15

2.5K ID 18

2.6 MK 20

2.6.1 20

2.6.2 (Components)21

2.6.3M]M 22

2.7 23

3 ......24

3.1 24

3.2 24

3.2.1 25

3.2.2 IDKI27

32.3 28

3.3 28

3.3.1 28

3.3.2 29

3.4 30

3.4.1 30

3.4.2 32

3.4.3 33

3.4.4 35

3.5 35

4

38

4.1 38

4.2 IDK39

4.2.1 39

4.2.2 40

42.3 IDK41

4.3 41

4.3.1 41

4.3.2 43

4.4 46

4.4.1 46

4.4.2 47

4.4.3 47

4.5 49

4.5.1 49

4.5.2 49

4.5.3 4g

4.6 54

1i

5 555.1 55

5.2 57

5.2.1MKI 57

5.2.2Mll 57

5.3 58

5.3.1MKI 58

53.2MKI 5g

5.4 61

5.4.1 61

5.4.2 65

5.5 66

6

676.1 67

6.2 67

6.2.1 67

62.2 68

6.2.3 6g

6.2.4 70

62.5 71

6.2.6 76

6.3 77

6.3.1 77

6.3.2 ID77

6.3.3 78

6.3.4 79

6.3.5 82

6.3.6 84

6.4 86

6.4.1 86

6.4.2 86

6.4.3 88

6.4.4 90

6.4.5 92

7 g37.1 937.2 g4

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10

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11

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12

fi(Xl,x2,,Xk)MK7(f1:f2)==Exlogf

2(Xl,X2,,k)

x2Xk)1il 1 dUk(2-8)

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.

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fi(fl( 2Xk)(xxXk))1ll 1idUdUk(2-9)

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(2'20)

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13

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(224)}

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. ,(1:2) (225) (2.26)

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. , , 1=0, =1 ,

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.

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-i{1gEii +(2)2-12}S{1 +( }

-S{ +( 2)2+3+( 2)2-}( )

14

.

, , , =8=2 ,

(228)

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. , ,1=2= ,

(2-28)}

D(ff2) 2}(2-3)

. ,ID(1:2) (2-29) (230)

)(fi2)II)(f1 2;)ID(fif2;2)(231)

. , , 1=O, =1 ,ID

9(1+ 33-22}(2-32)

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3

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15

k t .(2.33),

(235),k1 ,

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(k2,-12_1

2k2)( D(2-36)

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(k_'2_12k2)(237)

21-1)(2-38)

1 (239)

'(240)

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4 L.1(242)Wl

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k (Klk,II)k) . ,Wl,IDI1 2.2 .

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16

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17

2.5KlID

KI,ID, (223),(2-28) ,IDK

, , ,1(x)=f2(x)

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.

K ,

k1(1:2;On)R r(,)

19 ()194(2-43)

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KI .

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1D(fi:f2;On)RID(,)

.2+19(+)/2.(.+)191-(+)/2(2.44)21-(+)/22(+)/2

,Hl 3. Rn)(,)ID .

R1(,)RID(,) 2.3, 2.4 .

1 ,RKI(,)R)(,) , ,

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19

2.6 MKI

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k ( 1)k ( 2)

, fi(Xl,x2,,Xk),i-42N(ILi,i) ,

f( Xk)-1 12 )')(2- )

. ,1(iLil,lti2,,Ptik)k ,

i=(%),(,s=Z2,,k)k . ,

1 1b itr 9tr 12)t

, k MKI (2-18) ,

MKT(filf) fi( k)19 1i dUdUk

-i )Str ( 1)(2-11)'(2-46)

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,(246)

(fi )tr-1( )()'

.1,, i'.1' (2.47)22

. ,=1 2 .(247) ax ,

MH-2kKl(fi 2;)-k'1(2-48)

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. , ] .

1=2= , , ,

, .

20

,

1=2,=2 10 ,(2-46)

MKT(flf )-9 itr(ris)

9 i5i(2-49)

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.

2.6.2 t (Components)

MKzr(f1:2) ,n

On ,MKi(f1:2;On)=nMKr(1:f2) MKr(1:2) (246)

,

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(Wishart) . (247)

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.(2-50) ,

.

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1

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11 1b ss

,

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. ,S ,N=n-1 .

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MKT(fi:2;On)=nMKI(fi=f2)=MKT(fi:f2;7)+MKT(1:f2;S)

21

.

26.3MKI

MKI , k , ,

fi(x1,x2,,xk)'f2(xl,x2,,xk),MKT(1:2)=0 , ,1(xl,x2,xk)

2(1,x2,,Xk) MKI . k

1(Xl,x2,Xk) 2(1,2,,Xk) MK[

.

,MKT(fi:2) M(f1:2) ,2M(fi:f2)

k+k(k+1)/2X2 3. ,

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, ,

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, ,

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alna2n"

, ,

1=(ltil, 2,,`)(254)

illi12'

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1 2 ikk

. ,i=g2 , .

(246) MKf(1:2)

. , 3, 0.05 ,(252)

Rk()

(5) 2(5 ) 46(2-56)

. ,3 ,

22

MKI(ft:fr)R3(0.05)=8.46(257)

,fi(Xl,x2,Xk)f2(X1,X2,,Xk) . ,

, .

2.7

, ,

(1)KIID , , AE .

(2) ,ID .

(3) , .(4) , ,

.

23

3

3.1

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, . , ,

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(4) , .4 .

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24

1

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, ,AE

. 3.1 .

.

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, , ,3.2 , xx+x

25

tl+t2++tnP(x)=

T

. P(x) .

, ,

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f() tl+V+.'+tn 1m(x0

. (x)3.

,

Xi,(i-1-2>). , m ,[x,x+x]

P(x) (3-2)

. ,ni [x,x+x] , ni

{b,n,,,nm}n-N . x itl

P

P-fP PPm}P {3"

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+xT

x ______.1__9_L___

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li:iin-21

('t tn. tn

3.2

26

Referencefr(x)

Testft(x)

1

1

,11}ll,}1}/'"

KTT(R,T) 19

, , IDIDT(RT) (Pi-qi)19(36)

. m,ID K,ID ,.

3.2.3

2.4 , ,IDK . ,

. , , ,

D.Dyer 20.,

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KI .

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. ,

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, .

3.3

3.3.1

,

. ( ) ( )

(),() .

, ,

,(243) ,K RKT(,)

RKT(a ) 191 (1 )191

28

. ,(244) ID Rn)(,)

RD(,).2+19(+)/2.(.+)191-(+)/221-(+)/22(+)/2

.

, =0.1, .1 ,

RKr(,)=RKr(0.LO.1)1.758(37)

Rlz)(,)=RID(0.LO.1)=3.516(38)

. ,

Ki(fr:f,;On)RKr(0.=O.1)=1.758(39)

1D(fr:ft;On) Rn)(0.1,0.1)=3.516(310)

,() () ,

.

, , ,

f,(x) , ,

ft(x) ,ft(x)fr(x) IDKI . ,

, ,(243),(2-44) RKr(,),RID(,)

, 1DRID(,), RKT(,) ,

.

3.3.2

, .

, ,

.n xr

xr=[X,lx,2x.n]

, X.i f.i(x)G=1,,n) .

Xt ft(x) , X,i

XtW(f,i,ft)1Z)(fri,ft) ,(3-5),(36) . mID

K7==[IUIw Wn]

ll)=[11D2IDn]

,, ,

Kii=min(gy)(311)

IDi=min(ID)(312)

29

, , Xri Xt

, , HID

f,i(x) i .

, f,(x) fr(x) ,

KIID ruID . ,

mID , .3.4ID

.KI 3.4 .

3.4

3.4.1

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Reference

Pattern

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ormal.nditinEccentiityMialignmnt

ReferenceIDKIDE][IDKI

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conditionN1.OLO28.424.031.825.9

13.7192.2030.1600.1053.2842.000Eccentricity

N23.221.01.01.020.519.o

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N75.073.47,95.3LO1.o

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TesN m1 2ace aceconditionawflaw

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Nr lItt774574 86245 669cnditionN1

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I=InformatiorgN:Normalized

34

, , .

, , 3 ID

3.8 . , ,(37) (38)R]r(0.LO.1)

Rm(0.1,0.1) . .K

RK7(0.1,0.1) , . ,ID

ueRID(,) , , Rn)(,)

. ,ID

.

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ID KI 3.9 . ,m

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, , , ,

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, 2 ,

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3.5

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. .

35

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1.0

0.O

NormalEccentricityMisalignment

conditionconditioncondition

3.8

8.0 KI

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40'RD(O901)-3516

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36

(1)IDm , .

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(3) ,ID , , , , , .

, ID ,

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.

37

4

4.1

, , ,

. , , ,

,, ,

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. . ,

,

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(4) , .4

38

4.2 IDKl

. , , ,

mID .

4.2.1

, , (

(). ()()

x() (4-)

. , , [z] 2 .(41)

ejtcos +jsin(ot(42)

,(4-1)

X()-L.x( atdt f-..X(t)intdt

=R()+jl()(43)

. R(),1() .

()n(4-4)

. (), . ,X()

lX()1-A()-R2()12()

, () , .

x()2, ,

P()-IX()12-R2()2()(45)

, . P()x(t)

, ()

, .

(1) :

39

f,P(f,)

81(46)

P(f,)itl

(2) fBV:

(f-fp)2P(fi)'"'n12(47)

Pitl

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.

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p(fi) ,

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s().P()(48)

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s(f).P(49)

P(fi)i"1

. S() .

,

Pr(f) P,() (4-8)

, ,4.1

40

lReferenceSr

Tests(O

ll/ /1/

Frequencyf

4.1

5,() St() .

4.2.3 IDKI

Pr() S,() P,(f) St() (2.

14),(217) ,

(SrSt) (f)1glllll(4- )

D(SrSt)()-S(f))1gi;'lil3((ff))df(4- )

. , , (3-5),(36)

KT(SrSt) b i(4-2)

D(SrSt) (Sr(fi)-St(fi))1 1(4-3)

. ,n . KTFIDF

, .

4.3

4.3.1

, ,

. ,

41

,

.

4.2 , x(t) X()

, . ,

Nrpm] , ,(f,=N/60[Hz])

nf,(n 1,2,) , . ,4.2

,

, 1.

4.2 S(f)

m ()

, S(f)

. , [0,fmx] .

;

,== '

5HzIKHz10Khz

, ,

,

1 ll il 1

4.2 [1]

42

E , [fi,f2, (E)

(E) ()df(4-4)

. IDF(S,:St;E),KIF(Sr:St;E) , . ,

1DF(sr:St;E),IF(sr=s,;E) . ,

1DF(S,:St),KTF(S,:St),Il)F(,:St;E),KlrF(S,:St;E)

.

4.3.2

(A)

,4.2

(HzIKHz), (11(Hz10KHz),(10KHz )3

. , ,

,

LD-Jilooo(()-St(f))1glllll(4-5)

MD o()-St())1glli(4-6)

()-St(f))1gl1(4-7)

. , , ,,

4.2 ,

.

(B)

(Sr()-St())1glll (4-8)

(Sr(f)-S(f)ili(4-9)

. ,, , ,

Af . RIDm

43

, .

.

(C)

, , , ,

.4.3 .

, ,

. , . , ,

. . ,

( ) [2].

(1) ( )

( (4- )

(2) ( )

(d1--cosD)(4- )

(3)( )

fb1 2(4-22)

b'-T ''T'"

.! 6

'!i

-laI- 1-",

ll '!

!

'

4.3

44

(4)( )

((4-23)

,fr [Hz],D ,d , [rad],Z .

,

(1)

(Sr(f)-St(f))1gllgl(424)

(2)

m (Sr(f)-St())1g (4- )

(4)m (Sr(f)-St(f))19llll(426)

(4)

cm (Sr(f)-St())1gllll(4-27)

. , ,

.

(D)

,

, .

(1)

(Sr()-St()) gi (428)

(2)SD(Sr(f)-St())1gllll(429)

. ,fa ,fs , Z,

N[rpm]

= z

f=fa+f,(430)

45

.

,

, , , ,

.

4.4

4.4.1

,

. , ( )

E,, Et ,

,(),,() . , , ,

(243),(244) , ID R1(,),RID(,)

RKr( ) 19k+(1 )19

RD()-2 19f (1-gi'S6)191 2

.

, 0.1, 0.1 ,

RKI(,)=RKI(0.1,0.1)1.758(431)

Rll)(,)=RID(0.O.1)=3.516(432)

. ,,(), ()

,

KTF(SrSt;On)RKr(0.1,0.1)-1758(433)

1Z)F(Sr:St;On)Rn)(0.90.1)=3.516(4-34)

,,() ,() ,

.

,

, ,() ,

, St() ,St(f)S,(f) 1DF

KIF . , , (243)

(2.44) Ricr(,),RID(,)

46

1DFRID(,),KTFRKI(,) ,

.

4.42

(A)

, .

.(415) (417) ,,.

Il)=[LID,MII),HID]

. ID ., , , ,() ,) , ,

, , .

.

(B)

, .

, .

, ,(420) (423)

fi,f,fb,f . , .(424) (427)

OID, IID, BID

CID ,

ID=[o,),BII),D]

. ID

. , OID , , Sr(f)

S,(f) ,f+ .

, , [,f+f],

, , ,

.

4.4.3

, ,

, ,FFT . ,

47

,.4.4.

,

FFT

4.4

48

4.5

4.5.1

, . , (35) , 1700rpm, o , (AnritsuUM.

4A) , (TEAC) .

FFT ( CF-250)A/D GP.IB

.

, , , , 4 .

, 2.56[s, 25.6kHz . 4

4.5,4.6 .

.

4.5.2

,

. , , , ,

4 . ,

(410)(411) ,4

1DFKTF .

, , ,

1DF KiF 4.7 . ,(431) (432)

RKr(0.1,0.1) RID(0.1,0.1) . , 1DFkZF

, . , ,

1DFKTF, , RKT(O.90.1)Rn)(0.1,0.1)

, . ,

1DFK7F .

4.5.3

3 .

, ,

,4.3 .

,4.5 , , 4

49

8004

:0.02

0 .02.o.ca

[ioh8

llB892mO

O500010000

Frequen(ry[Hz]

(a)

[13]6

,4B8200

0500010000

Frequen(yz

(b)

1. 80.06O.0480.02omO500010000

Frequency[Hz]

(c)

60.01a20.005

00mO500010000

Frequency[Hz]

(d)

4.6

51

. , , FFT ,4.8 . (4-24) (4-26) 3 4

.1. 4.1 ,3 , 0, III). D , , , .

. ,ID

5.0.CrkiO fIDKI-p--CreionofKIID

4.ORII)(O.LO.1)=3516

3oR(0101)'

.}11 2.0-=1,758

1o,'.,

o.o;t.

NormalOuterraceInnerraceBaelementconditionawawaw

4.71DFKIF

4.1

OIDIIDBID

race 5.32L4

1errace3.83 2.1

Baelement8665.50tt 9

1

05

o105001000

Frequency[Hz]

(a)

20

10

omO5001000

Frequen(yz]

(b)

2010

oPtO5001000

Frequency[Hz]

(c)

15B10

5

, 1

Frequency[Hz]

(d)

4.8

53

4.6

, .

,

. ,

. .

(1) , .

(2)1DF UF .

(3) , .

54

5

5.1

, . ,

5.1 . , AE(Aooustic

Emission: , , ,

, ), , , , ,, , , ,

. , , ,

. ,

.

, , , , .

,

. , , . ,

, , , ,

,

, . , ,

(1) .

(2) , ,1 .

(3) , , .

.

55

5.1 [4]

AE ,X

AE, , ,X ,

,

: , ,AE

, ,AE , , ( ) ,SOAP( ) , ,AE

,AE

,

:= ,

, ,1 m

(MultivariateKuback-Leiblerinformation:

MKI) [17[18.

(1) MKI .

(2)MKI i1

.

(3) .

.

56

5.2

52.1MKI

, ,AE k .

,

.

, N(,) ,k fr(Xl,x2,,Xk)

N(.,,),k ft(Xl,x2,,Xk)N(PL,,t) ,

f(1 k) 1112 '))(51)

. ,'=,X'=(1,X2,,Xk)k ,1=(,1, 2,_,rk)k

,i=(iis),(,s=92,,k)k

,x' 1 x [19][20].

2 ,1 m ,k

k MKI

MK(f ft)f( )191 ll duk

-i (;' ;1)itr71( Zt)(1)t(5-)

. , ' ( ) .

(5.2)MKI .1 2

, . 1

, ( ) . , 1 ,

,k=1 ,(52)

MKT(frft )-i (5-3)

( ;) ( ( )

. 1 ,1 m(MKI)

.

5.2.2MKI

2.6.3 , .

MK[ k , ,

57

fr(x1x'.Xk)-f(Xix) MKT(frf`) , ,fr(1, ,)ft(x1x2 Xk) MKI . k

fr(XlX2Xk)f,(X1X2,,Xk) N4KI

.

MKT(,ft) Mlu^(frft) ,2MKT^(f.f,) k+k(k+1)/2 2

]v-k 1) ,

Ho:ft(X1,X2,,Xk)=fr(Xl,X2,,Xk)

H1:f,(Xl,X2,,Xk)fr(Xl,X2,,Xk)

, ,

) 2(k(k+1,+2))

H1. ,

R()-i2 kk(1))(5-)

, Rk()k MK .

, ,

(fr:ft)

(5-2) MKT^(,:f,) . , 3, 0.05 ,(55) Rk()

(5) 2(5 )46

. ,3 ,

MKT(fr:f,)R3(0.05)=8.46(57)

,f,(X1,X2,Xk)f,(Xl,2,,Xk) ,

. ,

MKT(r:f)

VibrationsignalSoundsignalAEslgnal

X X X/Vtsfmeanvlues1-(,1,2,1i3)i

Calculatingl C ian bices`(ijs)( -923)i

}.. . ""tt./tt.t`o ".'.""nt-" `'

."'-M=wx. ''L' "tttL'. ' '1

lculgMKf(,ft)1

bgll (;i;i)i;1)yi..."!'-v.ttrt.}.y ''.t-'t`.' '..th"

i!Condiodgemetl

f')Rk() )Rk()1

'. v .t ..'=y:tT"J.t."':-t" 7' "'t.`"'. - ' ' t''"

./

:lus.

5.1

60

5.4

5.4.1

, . 5 .2 . , ,

AE , .5.3 . AE , 50mm] . , , , , 4 . 5.4 . , 1200rpm, 50kHz,

AE 500[kHz . 1 6

,1 65000 .3 5.2

,

, , ,

AE ,5.5 5.8 .

5.2

AnritusBO517

Anritsuuv4A KynceNR .35

TEACRD101T

RIONUC29'

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RIONUN04

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NFAE9902as

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61

lJ,

"

1'^

.

5.2

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62

11

(a)(b)

5.4

05

500.OlO.02003004005

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002

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0001002003004005Tlmesec

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920oo

9< _200001002003004005

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5.5 , AE

63

8:0 .2 .4

0.OlO.020.030 .040.05Mrrersecl

(a)

ovO.05

o

0.5

oo

.500.OlO.020.030.040,05

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(a)

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(b)

20

_2.000.010.020.030.040.05

Timesec

(c)AE

5.8 , AE

5.4.2

, AE

, , AE , , ,

4 .

MKI 5.9 .

R3(0.05) , . ,

, , R3(0.05)

, . ,

, .

65

R(0.05)=&46

NormalconditionO.22582.8369

0uterraceflaw :.k,

Ballelementflaw s}t'71 .3243

1nnerraceflawlZO922

020406080

ValueofMKI

5.9

5.5

, 1 (1 ) ,2 .

, ,

. , , . , , AE ,

, . .

(1)1 , .

(2) , .

(3) , .

66

6

6.1

. , ,

. , ,, ,1

. ,

, . ,

, ,

.

, ,

22[23.,

, ., , ( )

, , ( ) ,

.

6.2

6.2.1

, . , ,

67

. , , ( , ) , . ,

(1) , , .

(2) , , .

(3) , , .

(4) , , .

.

, ,

,

,

(lnformationDivergence:ID) (KullbackLeiblerInformation:H) .

, . ,

(1) ID m .(2) ( , ).

(3) , .

6.2.2

,(),

ft(x) , KIID

,

KTT(f ft)()19(6-)

iD(f f,).frl(f(x)-f())19

.

, , P()

, . ,

68

s(f)-Jif.;ifll[,fidf(63)

,S() , .S() , mID,

KT(" ,()1gl1(6 -)

ID(SrSt) () st())1g1(6 -)

.

( ) E,, ( ) Et , (),(), Sr(f),St(f) , ,, , , 0.1, 0.1 ,(243),(244)

R1(0.1,0.1)=1.708(6-6)

Rn)(0.1,0.1)=3.516(67)

. ,fr(x),ft(x) ,KTT(fr:f`)RKr(O.90.1)=1708(6-8)

17F(fr:ft)RK1(0.1,0.1)1.708(69)

1Z)T(fr:f,)RID(0.1,0.1)=3.516(610)

1DF(Sr:St)Rm(0.1,0.1)=3.516(6,11)

,f,(x)f,(x) ,

.

, , ,

fr(x) ,

, (x) , f,(x)f,(x) mK

. , , ,(243),(2.44)

RKT(,),RID(,) .

1DRID(,),kiRKi(,) , .

62.3

, , ( ) (

) [24]. .

(1) ( ) : .

, ,

.

69

(2) ( ) : , .

2 RKf(,),Rm(,) ,

. ,, , , . ,, .

Po=1 (6 12) , , . , ,

. 0.4, 0.1 ,

Rf(O.4,0.1)0.551(613)

Rll)(0.4,0.1)=1.099(614)

. ID ,

, ,R1(O.4,0.1),RID(O.4,0.1) .

, 0.2, 0.1 ,

Rcr(0.2,0.1)=1.146(615)

Rn)(0.2,0.1)=2.428(616)

. IDKI ,

, ,Ru(0.2,0.1),RID(0.2,0.1)

.

6.2.4

, ,

f,(x) , ,

f,(x) , (61),(62) 1Z)TIUT . ,

, IDT

. , .

, (63)

,(6.4),(65) 1DF,IUF ,

.

, ,IDmRKt(O.4,0.1),RID(O.4,0.1) ,

, . ,IDK

Ru(O.2,0.1),RID(O.2,0.1) , . ,IDm

Rir(00,1),RID(O.40.1) , ,

, .

70

6.2.5

,

.

, , f,(x) O,1 , , ,

, . ,

y(t)-K"2'tOf'i(2!ft)N(t)(617)

. ,. ,

,N(t) 0, 1 .

, ,fn1500[z], 0.1 ,K1 0.3

. 1200rpm], 51.2[kHz,

25600, 3 .

6.1,6.2 . ,6.3

(RMS) . , ,

. ,

.6.4 IDm .

,H . , ,ID . ,6.5

IDK .IDm

. , ID IDK

.

, , fr(x) 0,

2 . , 11.5 .

.

y(t)-Ki(,)N(t)(618)

. ,fr ,N(t) 0,

. , , K1 O.2

1200rpm], 512[Hz, 4096,

3 .

6.6,6.7 .

71

2o

2

54-RMSDangerLevel

- RMSCaution]Level

3

2

1

01530

me[month

6.3 ( )

4--InformationMvengence

e4-Kubadk-lteiblerInformation

R3--IDDangerLevelP- IDCautionLeve1

2- K[DngerLv1.9KCautionLevel

1

01530

Timemonth]

6.4 ( )

4:= n3= 119- K[DangerLevel

2MCaut'onLevel

1"-

01530

Temonth

6.5 ( )

73

2

o.2