n o e c n e r e f n o C l a n o it a n r e t n I 8 1 0
2 Communicaiton,NetworkandAritifcia lIntelilgence(CNAI2018) 8 7 9 : N B S
I -1-60595- 50 -5 6
r
o
f
d
o
h
t
e
M
k
r
o
w
t
e
N
l
a
r
u
e
N
F
a
u
l
t
D
i
a
g
n
o
s
i
s
o
f
A
n
a
l
o
g
C
ri
c
u
i
t
B
a
s
e
d
o
n
K
u
r
t
o
s
i
s
a
n
d
S
k
e
w
n
e
s
s
o
a
T
X E
I
1,*a
n
d
H
e
n
g
LI
21Schoo lofComputerScienceandEngineering,HunanUniverstiyofScienceandTechnology ,
a n i h C , 1 0 2 1 1 4 n a t g n a i X
2CollegeofForeignLanguage,Centra lSouthUniverstiyofForestryandTechnology,
, 4 0 0 0 1 4 a h s g n a h
C China
r o h t u a g n i d n o p s e r r o C * : s d r o w y e
K Analog cricuti, Fautl diagnosis, High-order cumulants, Informaiton fusion, Neura l k r o w t e n . .t c a r t s b
A This paper proposes the method of analog circui tfaul tdiagnosis based on high-order h t i w d e n i b m o c s t n a l u m u
c InformaitonFusion .I tisto extracttheorigina lvoltageand curren tsignals r i e h t e n i m r e t e d o t , t s e t r e d n u t i u c r i c e h t f o l a n i m r e t t u p t u o m o r
f kurtosis and skewness as faul t
d n a , s r o t c e v n e g i
e to impor tthem into improved BP neura lnetwork for faul tdiagnosis. As for f o n o i t c u r t s n o
c faul teigenvectors ,high-ordercumulantst echnique ,comparedt oPrincipalComponen t s i s y l a n
A (PCA) which is based on second order statistics ,pays more attention to information r e t f A . A C P y b d e t c e l g e
n Information Fusion isemployed to integratevoltagewith curren tasfaul t g i e s e k a m t i , s r o t c e v n e g i
e envectors show relatively comprehensive faul tinformation .Diagnosis d n a e t a r n o i t i n g o c e r r e h g i h e v a h y a w s i h t n i d e n i a g s r o t c e v n e g i e t l u a f t a h t y f i r e v r e h t r u f s e l p m a x e . y c a r u c c a s i s o n g a i d n o it c u d o r t n I o r p t s r i f s a w h c i h w , t i u c r i c g o l a n a f o s i s o n g a i d t l u a
F posedformilitaryi n1960’s,i san i nteresting
l l e w y r e v t o n s a w t n e m p o l e v e d s t i , y l e t a n u t r o f n U . y r o e h t t i u c r i c n i c i p o t h c r a e s e
r due to the
e h t , t i u c r i c g o l a n a f o y t i x e l p m o
c tolerance of analog faul tand some other related factors .Unti l t h t i w , y l t n e c e
r hedevelopmen tofartificia lintelligence ,someinteresting andusefu lresultsinother o t d e s u e r a s d l e i
f faul tdiagnosisofanalogcircuit ,whichmakesi tbecominganewi nterdisciplinary . a e h t s a h w o n t i u c r i c g o l a n a f o s i s o n g a i d t l u a f , y l t n a t r o p m i e r o
M dvantage of higher diagnosis
n i s l o h t n e m l a n o i t i d a r t e h t h t i w d e r a p m o c y t i x e l p m o c d e c u d e r y l t a e r g d n a n o i t a t u p m o c s s e l , y c a r u c c a e c n e g i l l e t n i l a i c i f i t r a f o t n e m y o l p m e e h t , e r o f e r e h T . s 0 7 9 1 d n a s 0 6 9
1 in faul tdiagnosis of analog
a e r o m d e t c a r t t a s a h t i u c r i
c ndmorer esearchers’i nterest .Somei nterestingr esultsint hisaspec tmainly , n o i t a m r o f s n a r t t e l e v a w , k r o w t e n l a r u e n y z z u f e d u l c n
i simulatedannealingalgorithm ,suppor tvector
n o o s d n a e n i h c a
m [ -9]1 .Simulated annealing hastheshortcomingsofslow convergen tspeed ,long
. s r e t e m a r a p d n a s e u l a v l a i t i n i e h t o t e v i t i s n e s y r e v s i e c n a m r o f r e p m h t i r o g l a s t i d n a , e m i t n o i t u c e x e h c i h w n i , g n i m m a r g o r p c i t a r d a u q g n i s u y b r o t c e v t r o p p u s e h t s e v l o s ) M V S ( e n i h c a m r o t c e v t r o p p u S m e h t f o n o i t a l u c l a c e h
t -ordermatrix isinvolved .Whenthevalueofmisverybig ,i ttakesalo tof . x i r t a m e h t f o e g a r o t s d n a n o i t a t u p m o c e h t r o f y r o m e m e n i h c a m f o t n u o m a t a e r g a d n a e m i t g n i t u p m o c S e h t , s t i u c r i c g o l a n a f o s i s o n g a i d t l u a f e h t n i r e i f i s s a l c e h t s a d e s u s i M V S e h t n e h w , e c n e
H VM
e g r a l n o t n e m e l p m i o t d r a h y r e v s i m h t i r o g l
a -scaletraining samples .Moreover ,theclassicsuppor t e h t e v l o s o t e l b a c i l p p a t o n t u b , n o i t a c i f i s s a l c y r a n i b r o f d i l a v y l n o s i m h t i r o g l a e n i h c a m r o t c e v i t l u
m -classification problems .When fuzzy neura lnetwork is used for faul tdiagnosis of analog t n i o p r a l u g e r f o m e l b o r p e h t s a h d n a k r o w t e n e h t f o e r u t c u r t s e h t e n i m r e t e d y l d r a h n a c e n o , s t i u c r i c c i t a m o t u a d n a s e l u r y z z u f f o n o i t c a r t x e c i t a m o t u a e h t , n o i t i d d a n I . " n o i s o l p x e n o i t a n i b m o c “ t a z i m i t p o d n a n o i t a r e n e
e v o b a e h t g n i s u f
o -mentionedmethodt oanalogcircuitf aul tdiagnosisareasfollows .Firstly ,stimulus , y l d r i h T ; d e t c a r t x e e r a s l a n g i s t l u a f l a n i g i r o e h t , y l d n o c e S ; t s e t r e d n u t i u c r i c e h t o t d e i l p p a e r a s l a n g i s e r a s r o t c e v n e g i e t l u a
f constructed and then faults are identified .Among them ,the third step of e h t g n i t c u r t s n o
c faul teigenvectorsi st hekeyprocedure .Unfortunately ,mos toft hecurren tresults[ -9]1
t o n n a
c giveaverygoodanswerto thisstep .Thecommonly-used method ,in which origina lvoltage y b d e m r o f s n a r t t s r i f e r a s l a n g i s t l u a
f wavele ttransformation and then analyzed by using PCA,can f o t c e p s a e h t m o r f , r e v e w o H . t n e t x e e m o s o t n o i t a m r o f n i l a n i g i r o e h t f o s c i t s i r e t c a r a h c e h t n i a t n i a m , s c i t s i t a t s l a n g i
s principa lconstituentscomingfromPCAonlyi nvolvesecondorderstatistics .When s e l b a i r a v m o d n a r t u p n i e h
t obeyGaussiandistribution ,eachprincipa lcomponenti si ndependent .As n o n h t i w s e l b a i r a v m o d n a r r o
f -Gaussian distribution , the high-order statistics contain some e b t o n d l u o h s h c i h w n o i t a m r o f n
i neglected .In addition ,the information of single voltage signals c
a r t x
e ted bythismethodcannotmaximallyexpressthefaul tfeaturesofacircuit ,and thenthefaul t o t y r a s s e c e n s i t i , y c a r u c c a e h t e v o r p m i o t , e r o f e r e h T . y r o t c a f s i t a s t o n s e m i t e m o s s i y c a r u c c a s i s o n g a i d f s r o t c e v n e g i e t l u a f s a n o i t a m r o f n i f o e g n a r e d i w e k a
t orcircui tfaul tdiagnosis .Motivated by above
o s l a e w d n a , s i s o n g a i d t l u a f t i u c r i c g o l a n a o t n i n o i s u f n o i t a m r o f n i s e i l p p a r e p a p s i h t , s n o i s s u c s i d . e .i , n o i t a m r o f n i t n a t r o p m i r e h t o n a r e d i s n o
c electric curren tof analog circuit ,as an information r o f e c r u o
s faul teigenvectors construction .Thus faul teigenvectors aredetermined by voltageand h g i h g n i n i b m o c y b t i u c r i c g o l a n a f o d o h t e m s i s o n g a i d t l u a f a e s o p o r p e w n e h T . s l a n g i s t n e r r u
c -order
d o h t e m r u o f o e r u d e c o r p f e i r b e h T . n o i s u f n o i t a m r o f n i d n a s t n a l u m u
c isasfollows :wefirs tcollec t
d n a s i s o t r u k r i e h t e n i m r e t e d o t r e d r o n i l a n i m r e t t u p t u o m o r f s l a n g i s t n e r r u c d n a e g a t l o v l a n i g i r o n o i t a g a p o r P k c a B r o r r E e v o r p m i o t t u p n i s a d e s u e r a y e h t n e h t d n a , s r o t c e v n e g i e t l u a f s a s s e n w e k s u a f r o f k r o w t e n l a r u e n ) P B
( l tdiagnosis .Sof tfaul tdiagnosis of tested circuits shows tha tfaul t o t s e h c a e r y c a r u c c a s i s o n g a i d t l u a f d n a , e t a r n o i t i n g o c e r h g i h e v a h y a w s i h t n i d e n i a g s r o t c e v n e g i e n o n e s o n g a i d n a c t i ,r e v o e r o M . % 0 0
1 -linearcircui tfaultsandcatastrophicfaultssuccessfully ,which .t i u c r i c g o l a n a f o s i s o n g a i d t l u a f r o f d o h t e m e v i t c e f f e w e n a s e d i v o r p h g i
H -orde rCumulants ,Kurtossi ,andSkewness
h g i
H -ordercumulants(HOC)t echniquei sanewt echnologyrapidlydevelopedi nrecen tyears ,andas n i l a e d l o o t t n a t r o p m i n
a g with non-Gaussiansignals ,nonlinearsignalsandblind signals ,i tattracts h c i h w f o , s e g a t n a v d a f o s ’ t I . n o i t n e t t a g n i s a e r c n
i the unique is tha t i t can detec t nonlinear
i t i d n a , s l a n g i s e h t g n o m a s c i t s i r e t c a r a h c g n i l p u o c e h t t c a r t x e d n a s c i t s i r e t c a r a h
c s insensitive to
n a c d n a , e s i o n n a i s s u a
G abandont heeffectsofinterferenceofnoise .What’smore,t heoretically,i tcan f o l a n g i s t l u a F . y c a r u c c a n o i t a c i f i t n e d i d n a s i s y l a n a e h t e v o r p m i d n a , e s i o n e h t e t a n i m i l e y l e t e l p m o c e n i l n o n s i f l e s t i t i u c r i c g o l a n
a ar ,which makes faul tsigna linevitably noisy with the effects of d n a e r u t a r e p m e
t environment .Therefore ,it’s a better and applicable choice to use high-order t i h t i w l a e d o t s t n a l u m u c h g i
H -orde rCumulants
, n o i t c n u f c i t s i r e t c a r a h c e h t f o n o i t c u d o r t n i h t i
W high-ordercumulants Ck,t osinglerandomvariable , : s a d e n i f e d e b n a c 0 ) ( 1 k
k k k
d C d j ω ω ψ ω =
= k=1,2,…,n ( 1)
h c i h w n i ) ( n l )
(ω φ ω
ψ = ] ) ( p x e [ ) ( p x e ) ( )
(ω f x jωx dx E jωx
φ ∞
∞
− =
, e g a r e v a l a c i t s i t a t s r o f g n i d n a t s , s n o i t a t c e p x e d n a m e d f o r o t a r e p o n a s i } · {
E ψ(ω) and φ(ω)
d n a r f o n o i t c n u f c i t s i r e t c a r a h c d n o c e s e h t d n a t s r i f e h t s a y l e v i t c e p s e
r omvariablex.
r o t c e v m o d n a r r o f s
A ( 1, 2, , )T
k
x x x
x= ,t hedefinitionofhigh-ordercumulantsi sdefinedas :
2
1 1
1
1
1 1 ,
, ,
1 0
1
1 0
) , , ( ) (
) , , ( n l ) (
k k
k
k
k
k
k
k
k
j C
j
γ γ γ
γ
γ γ γ
ω ω
γ γ
γ γ
ω ω
ω ω ψ
ω ω
ω ω φ
ω ω
= =
= =
∂ =
− =
∂ ∂
∂ −
∂ ∂
( 2)
, h c i h w n
I φ(ω1,,ωk)=E[exp(j(ω1x1++ωkxk))] , γ =γ1+γ2+γk . Especially , when
3 2
1 γ γ 1
γ = = = and γ =3 ,t hird-ordercumulanti smarkedas:
3 2 1 1
, 1 , 1
3x C cum(x,x ,x)
C = = )( 3 k
, y l l a r e n e
G -ordercumulanti sasfollow:
1 1
1
1, ) [ ( ), ( ), , ( )]
( k k
x
k cum xt xt x t
C τ τ − = +τ +τ − ( 4)
si s o t r u
K a Snd kewness
f
I {x(n)} isthestationaryrandomprocessofzeromean ,first-order ,second-order ,third- order ,and h
t r u o
f -ordercumulantscanbei llustratedas:
1
1x mx E{x(t)}
C = = )( 5
2x( ) E{x(t)x(t )} Rx(t)
C τ = +τ = )( 6
2 1
2 1
3x( , ) E{x(t)x(t )x(t )}
C τ τ = +τ +τ ( )7
3 2
1 3
2 1 4
1 3 2 2
3 1
1 2 3
} ) ( ) ( ) ( ) ( { ) , , (
) ( ) ( ) ( ) (
) ( ) (
x
x x x
x
x x
t x t x t x t x E C
R R R
R R R
τ τ
τ τ
τ τ
τ τ τ τ
τ τ
τ τ τ
+ +
+ =
− −
− −
− −
)( 8
n
I formula (7) ,ifτ1=τ2=0 , -1 D slice of third order cumulants can be obtained .I tis defined as l
a n g i s l a e r f o s s e n w e k
s {x(n)} and marked as { 3( )}
x E x t
S = . Similarly , in formula (8) , f
i τ1=τ2=τ3 =0 ,anotheri mportan tconcept ,kurtosis ,canbeobtained ,whichi sasfollow :
2 2 4()} 3 { ()}
{
x E x t E x t
K = −
x
R stands for autocorrelation .Based on the above definition ,we know tha tfirst-order and d
n o c e
s -ordercumulantsofrandomvariablexofGaussiandistributionarerespectivelyt hemeanand e
c n a i r a
v ofx ,andhigh-ordercumulantsofGaussianr andomvariablexi salwaysequalt ozero .Asfor s
s e c o r p m o d n a r n a i s s u a
G {x(n)},i tshigh-ordercumulantsarealwaysequalt ozeroaswel lwheni ts h
g i h t a h t d e c u d e d e b n a c t i , e r o f e r e h T . 2 s d e e c x e r e d r
o -ordercumulantsareno tsensitivet oGaussian
n e h W . s s e c o r
p outer noise is the gaussian colored one ,high-order cumulants can completely e
t a n i m i l
e theeffec tofnoiseandi mprovet heaccuracyofi dentificationanddiagnosisi nt heory.
s is o n g a i
D Principle
s o h c r e p a p s i h T . 1 e r u g i f s a d e w o l l o f s i e l p i c n i r p s i s o n g a i
s u l u m i t s a , y l t s r i F . s u l u m i t s e h t s a s l a n g i s y r o t a l u m i t
s isexertedonthecircui tundertest .Secondly ,
e h t g n i s u y b , y l d r i h T . t u p t u o e h t m o r f d e n i a t b o e r a t i u c r i c f o s l a n g i s t n e r r u c d n a e g a t l o v l a n i m r e t
x o b l o o t s i s y l a n
a ofhigh-ordercumulants ,kurtosisandskewnessoft ermina lsignalsaredeterminedas k
r o w t e n l a r u e n o t n i t u p n i e r a y e h t , y l l a n i F . s r o t c e v n e g i e t l u a f e h
t forfaul tdiagnosis.
D . 1 e r u g i
F iagnosticschematic.
si s o n g a i
D Example
d a u q s i t i u c r i c s i s o n g a i
D po - ma p high-pass filter(seen in figure 2) , in which R1=R4=5kΩ ,
R2=R3=R5=R8=R9=R10=10kΩ ,R6=3kΩ,R7=4kΩ,C1=20nF ,C2=5nF ,andtheinpu tAC voltageVinis
. V 6
5 R
k 0 1 1
V
c a V 6
0 2
C n 5
8 R
k 0 1
n i V
9 R
k 0 1
0 0
0 1 R
k 0 1
A 3 U
8 9 7 A U
3 2
8
4
1
+
-+
V
-V
T U O
A 1 U
8 9 7 A U
3 2
8
4
1
+
-+
V
-V
T U O
A 4 U
8 9 7 A U
3 2
8
4
1
+
-+
V
-V
T U O
A 2 U
8 9 7 A U
3 2
8
4
1
+
-+
V
-V
T U O
6 R
k 3 1
C n 0 2
0
2 V
c d V 2 1
0
2 R
k 0 1
0 3 V
c d V 2 1
V
0
t u o V
3 R
k 0 1
1 R
k 5
7 R
k 4 4
R k 5
. 2 e r u g i
F Fourop-ampbiquadhighpassfilter.
t a h t s w o h s s i s y l a n a e h
T circui toutpu tVou tis more sensitiveto resistors R1 ,R4 ,R6 ,and R7and
s e c n a t i c a p a
c C1andC2.Within5%oft hecomponentt olerance,t hereare13statesi ncludingf ault-free
R n i s a i b e v i t a g e n d n a e v i t i s o p f o % 0 5 f o s e t a t s t l u a f t f o s d n a e t a t
s 1 ,R4 ,R6, R7, C1andC2.
e e r h
T -layerBPneura lnetworkwithsinglehiddenl ayeri susedasfaul tclassifier .Thenumberofi ts f o d e s o p m o c e r a s r o t c e v n e g i e t l u a f e h t , e r e H . s t n e m e l e r o t c e v n e g i e t l u a f f o r e b m u n e h t s i s r e y a l t u p n i
b m u n e h t o s , s i s r o t u k d n a s s e n w e k s t n e r r u c e h t d n a e g a t l o v t u p t u o e h
t ersofneuronsi nt hei npu tand
n a c s r o t c e v t u p t u O . s e t a t s t l u a f f o r e b m u n e h t g n i e b r e t t a l e h t , 3 1 d n a 4 y l e v i t c e p s e r e r a s r e y a l t u p t u o
s i h t s a d e n i f e d e
b — supposet hatt hereareMkindsofstatesse tupi nt hecircuit ,andnetworkoutpu t s
i a( 1,a2,….ai… a. j….aM) .Ift hecircuitl ocatesi nstatei ,andi faiisequalt oone,t heothersequalt o0 ,
. e
.i desiredoutpu tvectorsofnetworkare(0,0,….1,….0),t hent henumberofneuronsi nhiddenl ayers a
l u m r o f l a c i r i p m e y b d e n i m r e t e d e b n a
c 1[ 0]
0 1
1 h m n
n
m+ + ≤ ≤ + + (9) .
s n o r u e n t u p t u o f o r e b m u n e h t , ” n “ e l i h w , s n o r u e n t u p n i f o r e b m u n e h t r o f s d n a t s ” m “ , t i n I
t n e n o p m o c e h t f o e g n a r e c n a r e l o t % 5 n i h t i
W values ,Monte-Carloanalysishasbeendoneforeach . s e l p m a s g n i y f i t n e d i r o f s e m i t 0 4 d n a s e l p m a s g n i n i a r t r o f s e m i t 0 6 , s e m i t 0 0 1 r o f t i u c r i c e h t f o e t a t s
s i s o t r u k e h t s i 1 e l b a
T and skewnessdetermined withhigh-ordercumulantsin variousstatesofthe circui tand Table 2 shows the outpu tresults of neura lnetwork diagnosis .While Figure 3 is the
1 e l b a
T . Kurtosisandskewnessundervariousstates. s
s l a c t l u a
F Faul t
e d o c
l a n i m o
n Faultyvalue Outpu tvoltage Outpu tcurrent s
i s o t r u
k skewness kurtosis skewness R1↑ F 1 5 k 7.5k 12.764 3.1430 1.5503 -0.4165
R1↓ F 2 5 k 2.5k 10.326 2.5693 0.5826 -1.4857
R4↑ F 3 5 k 7.5k 11.362 2.8921 2.0579 1.3586
R4↓ F 4 5 k 2.5k 16.248 3.8952 3.3825 2.7625
R6↑ F 5 3 k 4.5k 14.742 3.3895 2.9825 0.9956
R6↓ F 6 3 k 1.5k 13.267 3.0567 3.1624 2.5243
R7↑ F 7 4 k 6 k 14.876 3.2265 6.5622 3.5213
R7↓ F 8 4 k 2 k 9.4862 2.1837 5.0527 3.0845
C1↑ F 9 2 0n 3 0n 9.9887 2.4372 2.0547 1.3845
C1↓ F 10 2 0n 1 0n 8.9736 2.1536 1.2846 0.9645
C2↑ F 11 5 n 7.5n 15.283 3.2769 3.6257 1.9864
C2↓ F 12 5 n 2.5n 15.365 3.4435 5.0945 3.7536
l a m r o
N F 0 10.988 2.6321 3.1520 1.6251
0 100 200 300 400 500
0 1-4
0 1-3
0 1-2
0 1-1
0 10
0 11
s h c o p E 1 8 5
kc
al
B-l
ao
G
eul
B-gni
ni
ar
T
1 0 0 . 0 s i l a o G , 9 5 6 9 9 9 0 0 0 . 0 s i e c n a m r o f r e P
e r u g i
F 3. Convergencecurvesofneura lnetwork.
2 e l b a
T . Output nof eura lnetwork.
t l u a f e h t , t i u c r i c e v o b a e h t n i d e s u s i k r o w t e n l a r u e n t e l e v a w h t i w d e n i b m o c n o i s u F n o i t a m r o f n I
o f o s t n e i c i f f e o c t e l e v a W . d e g n a h c n u e d o
m utpu tvoltage and outpu tcurren tare inpu tinto neura l e
r a k r o w t e n l a r u e n e h t f o t u p t u o d n a e v r u c e c n e g r e v n o C . n o i t a c i f i t n e d i t l u a f r o f k r o w t e
n separately
e r u g i f n i n w o h
s 4 andt able3.
0
F F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10 F 11 F 12
3 0 0 0 .
0 0.0003 0.0003 0.0003 -0.0001 0.0003 0.0004 0.0003 -0.0033 0.0004 0.0003 0.0003 0.0003
8 0 9 0 .
0 0.9025 0.0908 0.0909 -0.0000 0.0909 0.0904 0.0909 0.0017 0.0903 0.0909 0.0909 0.0909
9 0 9 0 .
0 0.0910 0.9520 0.0911 0.0000 0.0911 0.0903 0.0911 0.0003 0.0901 0.0911 0.0911 0.0911
9 0 9 0 .
0 0.0907 0.0910 0.9620 0.0905 0.0906 0.0929 0.0905 -0.0017 0.0932 0.0904 0.0904 0.0904
1 0 0 0 .
0 0.0003 -0.0000 0.0006 0.9999 0.0004 -0.0022 0.0006 0.0012 -0.0025 0.0006 0.0006 0.0006
4 1 9 0 .
0 0.0913 0.0914 0.0911 0.0003 0.9570 0.0924 0.0912 -0.0065 0.0926 0.0911 0.0911 0.0911
3 1 9 0 .
0 0.0914 0.0912 0.0917 0.0002 0.0916 0.9840 0.0917 -0.0031 0.0893 0.0917 0.0917 0.0917
0 1 9 0 .
0 0.0909 0.0910 0.0907 0.0001 0.0908 0.0921 0.9696 -0.0021 0.0922 0.0908 0.0907 0.0908
-0.0001 -0.0003 0.0001 -0.0008 0.0002 -0.0005 0.0029 -0.0007 0.9981 0.0033 -0.0007 -0.0008 -0.000 7
2 0 9 0 .
0 0.0901 0.0902 0.0899 -0.0001 0.0900 0.0911 0.0899 0.0077 0.9865 0.0899 0.0899 0.0899
0 1 9 0 .
0 0.0912 0.0909 0.0915 0.0000 0.0913 0.0889 0.0915 0.0009 0.0886 0.9625 0.0915 0.0915
4 1 9 0 .
0 0.0914 0.0913 0.0916 0.0001 0.0915 0.0904 0.0915 -0.0042 0.09 03 0.0916 0.9758 0.0916
7 1 9 0 .
0 1000 2000 3000 4000 5000 6000 7000 8000 0
1-3
0 1-2
0 1-1
0 10
0 11
s h c o p E 9 3 0 8
kc
al
B-l
ao
G
eul
B-gni
ni
ar
T
1 0 . 0 s i l a o G , 7 7 7 9 9 9 0 0 . 0 s i e c n a m r o f r e P
e r u g i
F 4. Convergencecurveofneura lnetwork.
3 e l b a
T . Output fo n ue ra lnetwork.
0
F F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10 F 11 F 12
4 0 2 0 .
0 -0.1368 -0.0057 -0.0577 0.0447 0.0463 0.0740 0.0192 -0.0092 -0.0187 0.0926 0.0610 -0.0912
1 3 9 1 .
0 0.4644 0.0015 -0.0392 0.1517 0.0962 -0.0432 -0.0010 -0.0324 -0.0151 -0.0240 0.0099 0.0816
5 1 0 .
0 7 -0.0707 0.9973 -0.0811 -0.0063 0.1484 -0.0418 0.0200 0.0217 0.0053 0.0086 0.0317 0.0660 -0.0076 -0.2087 0.0065 0.9314 0.0470 0.2454 0.0114 -0.0008 -0.0191 0.0845 0.0430 0.0360 0.0715
-0.1203 0.1033 0.0075 0.0199 1.0080 -0.0181 0.0299 -0.0149 -0.0143 0.0618 0.0552 0.0506 0.0025
0 3 4 2 .
0 0.1097 -0.0005 0.0798 -0.0593 0.9493 -0.1375 -0.0055 0.0270 0.0035 0.0862 0.0528 0.0917
7 0 5 3 .
0 0.0076 0.0015 0.0429 0.0553 -0.2127 0.9364 -0.0002 0.0254 0.0230 0.0065 0.0116 0.0826
1 2 2 0 .
0 0.0137 -0.0027 0.0067 -0.0266 -0.0147 0.0043 0.9997 -0.0064 0.0274 0.0932 0.0031 0.0047
-0.0075 -0.0195 0.0023 -0.0099 -0.0129 0.0700 -0.0319 -0.0055 1.0187 0.0327 0.0045 0.0630 0.0702
5 2 1 0 .
0 0.0247 0.0425 -0.0694 0.0032 0.0862 0.0089 -0.0487 0.0523 0.99 70 0.0128 0.0412 -0.0825
7 9 5 0 .
0 -0.3589 0.0261 0.0028 0.0712 -0.0037 -0.0310 0.0062 0.0062 0.0080 1.0025 0.0060 0.0120
-0.0642 0.0589 0.0052 0.0672 -0.0014 0.0216 0.0481 0.0756 -0.0893 0.0059 0.0815 0.98 90 0.1123 1
6 7 1 .
0 0.0569 0.0027 0.0038 0.0591 0.0682 0.0952 0.0384 0.0059 0.0640 0.0720 0.0806 0.99 25
b s e c n e r e f f i d e h t t a h t d e c it o n e b n a c t i , 1 e l b a t m o r
F etweenkutorsisandskewnessofoutpu tvotlageand
h g i h e h t o t s e t u b i r t n o c h c i h w , s n o it i d n o c t l u a f s u o i r a v r e d n u e l b a r e d i s n o c e r a s l a n g i s t n e r r u c
r o t c e v n e g i e t l u a f f o n o it a n i m i r c s i
d composedbyt hesefourvaluesandt hehighi denitficaitonrateforfaul t e
r u g i f m o r f n e e s e b o s l a n a c s i h T . s i s o n g a i
d 3 andt able2 .Theneura lnetworkt rainingconvergeswtihin y
c a r u c c a s i s o n g a i d t l u a f d n a s p e t s 0 0 0
1 ofneura lnetwork is up to 100% in table2 ,whlie diagnosis s i t e l e v a w h ti w s l a n g i s t n e r r u c d n a e g a tl o v g n i s o p m o c e d y b d e t c a r t x e s r o t c e v n e g i e t l u a f f o y c a r u c c a
1 F t l u a F f o s i s o n g a i d s u o e n o r r e e h t d n a k r o w t e n l a r u e n f o s p e t s e c n e g r e v n o c e r o m s ti r o f , r o i r e f n
i .
n o is u l c n o C
h g i h h t i w , r e p a p s i h
T -ordercumulantscombinedwithI nformationFusion ,attemptst ocopewithfaul t s
s e n w e k s d n a s i s o t r u k h g u o r h t n w a r d s r o t c e v n e g i e t l u a f h t i w , t i u c r i c g o l a n a f o s l a n g i
s offaul tsignals ,
k r o w t e n l a r u e n P B o t n i m e h t s t u p n i d n
a for faul tdiagnosis . Diagnosis examples show tha tfaul t e h t d n a e t a r n o i t i n g o c e r h g i h e h t r o f t n e r e f f i d y l t n a c i f i n g i s e r a y a w s i h t n i d e t a r e n e g s r o t c e v n e g i e
k c i u
q BPnetwork convergence .So itsdiagnosis accuracy rateishigherthan tha tof othergenera l n
a w e n a s e d i v o r p h c i h w , s d o h t e
m deffectivewayforbotht heconstructionoffaul teigenvectorsand .t
i u c r i c g o l a n a f o s i s o n g a i d t l u a
f
s t n e m e g d e l w o n k c A
f s a w k r o w s i h
T inancially supported by ScientificResearch Fund of Hunan Provincia lEducation t
n e m t r a p e
6 6 3 1 5 E . o N t n a r
G ,the Nationa lNatura lScience Funds of China for Distinguished Young Scholar .
7 2 7 5 2 9 0 5 . o N t n a r G r e d n u
s e c n e r e f e R
] 1
[ JinYu,LiuHong.Faul tdiagnosisofanalogcircui tbasedonwavele tneura lnetwork J[ .] Chinese ,t
n e m u r t s n I c i f i t n e i c S f o l a n r u o
J 2007,28(9),1600~1603.
] 2
[ ZhuWenji ,HeYigang .Neura lNetworkBasedSof tFaul tDiagnosisofAnalogCircui tWith s
e c n a r e l o
T [J] .TransactionsofChinaElectrotechnica lSociety,2009,24(11),184~191. ]
3
[ TangJingyuan ,Sh iYibing ,ZhangWei .Analogcircui tfaul tdiagnosisbasedonsuppor tvector e
l b m e s n e e n i h c a
m .[ J] ChineseJourna lofScientificInstrumen,t2008,29(6),1216~1220. ]
4
[ Bing Long , Jianguo Huang , Shulin Tian Leas t squares suppor t vector machine based g
o l a n
A -Circui tFaul tDiagnosis using wavele ttransform as preprocessor [C]. Communications , .
8 0 0 2 S A C C C I , 8 0 0 2 , s m e t s y S d n a s t i u c r i
C Fujian,China.2008:1026~1029.
] 5
[ XieYongle ,LiXifeng .AMethod to LocateParametricFaultsinAnalogIntegratedCircuits[J] . .
s r o t c u d n o c i m e S f o l a n r u o
J 2008,29(3),598~605.
] 6
[ BaoruHan ,HengyuWu.BasedonCompac tTypeofWavele tNeura lNetworkToleranceAnalog s
i s o n g a i D t l u a F t i u c r i
C [C]. Information Engineering and ComputerScience ,2009 ,ICIECS 2009. ,
n a h u
W China,2009:1~4. ]
7
[ HeWuming ,Wang Peiliang. Analog Circui tFaul tDiagnosis Based on RBF Neura lNetwork m
h t i r o g l A O S P y b d e z i m i t p
O [C]. Intelligen tComputation Technologyand Automation(ICICTA) , .
0 1 0
2 Changsha ,China,2010:628~631. ]
8
[ XieYongle .ACorrelationAnalysisApproachBasedFaul tDiagnosisofAnalogVLSICircuits .[ J] .
s r o t c u d n o c i m e S f o l a n r u o J e s e n i h
C 2007,28(12),1999~2005.
] 9
[ L iMu ,He Yigang ,Yuan Lifen .Faul tDiagnosis of Analog Circui tBased on Wavele tNeura l m
h t i r o g l A n o i t u l o v E l a i t n e r e f f i D s o a h C d n a s k r o w t e
N [C]. Electrica land Contro lEngineering
0 1 0 2 , ) E C E C I
( .Wuhan ,China,2010:986~989. 1
[ 0] T. Deliyannis ,Y. Sun ,J.K. Fidler1999Continuous-TimeActiveFilterDesign(BocaRaton ,FL: p
) s s e r P C R
