TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 5729 ~ 5735
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.515
9
5729
Re
cei
v
ed
No
vem
ber 1
8
, 2013; Re
vi
sed
Febr
uary 19,
2014; Accept
ed March 6, 2
014
A Grey Relation Analysis Method to Vibration Fault
Diagnosis of Hydroelectric Generating Set
Wang Ruilian*
1
, Gao Shengjian
2
1
School of Ele
c
tric Po
w
e
r, No
rth Chin
a Univ
ersit
y
of W
a
ter
Reso
urces an
d
Electric Po
w
e
r
,
Z
hengz
ho
u
，
H
ena
n
，
Chi
n
a
2
School of Civi
l
Engi
neer
in
g a
nd Comm
unic
a
tion
，
North C
h
i
na Un
iversit
y
o
f
W
a
ter Resour
ces and El
ectri
c
Po
w
e
r
，
Z
hen
g
z
hou
，
He
na
n
，
Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 2002r
l
w
1
6
5
@
16
3.com
A
b
st
r
a
ct
Aiming to th
e
complex
i
ty of vibration fa
u
l
t c
ause,
the great many o
f
fault para
m
eters in
hydro
e
lectric g
ener
ating s
e
t, and the s
uper
i
o
rity of grey
rel
a
tion a
n
a
l
ysis for its no strict requ
ire
m
e
n
t to fault
sampl
e
cap
a
cit
y
and r
e
g
u
lar
i
ty, the w
e
ighte
d
grey re
latio
n
mo
de
l is b
u
i
l
t to lo
ok for the v
i
brati
on fa
ult type
.
T
he fu
zz
y
mat
r
ix'
s
transformation arit
hmeti
c
is used
to obtain the w
e
ig
ht vect
ors of the grey rel
a
tio
n
coefficie
n
t, thus the w
e
ighte
d
coeffici
ent i
s
the w
e
i
g
h
t
ed
g
r
e
y
rel
a
ti
on
mo
de
l
.
Th
e re
l
a
ti
on
coe
ffi
ci
ent
betw
een refer
ence se
qu
enc
e and co
mpar
e sequ
enc
e in
vibr
atio
n fault
samp
le is pr
o
v
ide
d
by synth
etic
arith
m
etic
of fu
zz
y
w
e
ig
ht to
dia
g
n
o
se th
e
vibrati
on fa
ult t
y
pe. T
he
grey
relati
on c
oeffici
ent w
e
ig
hted
b
y
fu
zz
y
synth
etic
arithmetic, w
h
ich is
not only
ma
de the est
a
blish
ed w
e
ig
ht
be a scie
n
tific basis, but als
o
ca
n
“sensitiv
e
”
hig
h
light the v
i
brati
on f
ault type
of hydroe
lectric
gen
eratin
g se
t. T
hus the pro
b
l
e
m
of look
ing f
o
r
every fault typ
e
s is better re
solve
d
. By ana
ly
z
i
ng th
e
prac
tical exa
m
ple, i
t
prov
ed that t
he w
e
ig
hted gr
e
y
relati
on
mo
del
in the p
a
p
e
r ca
n effectively
di
agn
ose th
e
vib
r
ation fa
ult typ
e
of hydr
oel
ectric gen
erati
ng
set
and it has
defin
it
e app
lica
b
il
ity.
Ke
y
w
ords
:
h
y
droe
lectric g
ener
ating s
e
t, vibratio
n, faul
t dia
gnos
is, grey relati
on
analys
is, matrix
transformation arithm
etic by fuzz
y rela
tionship, fu
z
z
y synth
e
t
ic arithmetic
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Hydro
e
le
ctri
c generating set is the most im
portant p
o
we
r equi
pm
ent of powe
r
station.
Whether it can run
safely
or not, will di
rectly
concern the norm
a
l operatio
n of the power
station
and th
e p
o
wer
system.
T
he vibration
of hydro
e
le
ctric gen
eratin
g set is inev
itable, but th
e
excessive vibration
will have a
great inf
l
uence on normal run life
of the unit, even can lead to
great d
e
st
ru
ctive acci
dent
s [1]. In ord
e
r to be
abl
e to qui
ckly
and a
c
curate
ly diagno
se t
h
e
vibration fa
ul
t, enoug
h vi
bration
fault
ch
aracte
risti
c
p
a
ramete
rs a
nd fa
ult types
data
of
hydrop
ower
gene
rating
set are
nee
de
d collect, a
n
d
the
sam
p
l
e
s
colle
cted
sho
u
ld b
e
a
c
tual
measured da
ta from some
a actual
unit
.
When th
e
vibration fa
ult is dia
gno
sed,
a scientific a
n
d
rea
s
on
able a
nalysi
s
meth
od is re
quire
d, so that the diagno
sis
co
nclu
sio
n
can
be pra
c
tical [2-3].
Becau
s
e
the
cau
s
e
of th
e vibration
is very
com
p
li
cated, a
nd t
he mutu
al couplin
g bet
ween
varieties of fault types, the vibration fa
ult diagno
sis
itself carrie
s
a lot of ambiguity. When the
vibration
fault
type i
s
lo
oki
ng fo
r, if
all
kinds
of
po
ssi
b
l
e fault types
are not accu
rately taken in
to
accou
n
t, the cau
s
e dia
gno
sed may be
wro
ng. Thu
s
the unne
ce
ssarily addition
al work to the
trouble
s
h
ooti
ng ca
n be brought, and e
v
en the stabl
e operation condition of th
e power stati
on
itself and the
whol
e po
wer
system
will be affected.
Grey
relatio
n
analy
s
is is
to mea
s
u
r
e
the cl
ose ex
tent of different facto
r
s b
y
their
developm
ent trend.
T
he
m
e
thod about
t
he sampl
e
ca
pac
ity a
nd
re
gularity a
r
e
n
o
t stri
ct requi
red,
and th
e
perce
nt of
conta
c
t
area
b
e
twe
e
n
the
co
ncl
u
si
o
n
obtai
ned
an
d the
a
c
tual
situation i
s
very
high [4]. Usu
a
lly, in applying the meth
o
d
of grey
rela
tion analy
s
is,
the algeb
rai
c
average
of the
correl
ation
coefficient
bet
wee
n
the
va
riou
s fa
ctors is
used to
determi
ne
their
ea
ch
other
clo
s
en
ess,
whi
c
h d
o
e
s
not consi
d
er the
re
lati
ve importa
n
c
e of th
e factors
and
who
s
e
con
c
lu
sio
n
s
are not convi
n
cin
g
enou
gh
. This
pape
r,
by using the
fuzzy and weighted ave
r
age
model
whi
c
h
is gen
eralize
d
fuzzy synth
e
tic arithm
etic [5] to diagn
ose the vib
r
a
t
ion fault types,
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 572
9 –
5735
5730
according
to t
matrix tran
sformatio
n
a
r
ithmetic by
fu
zzy relation
shi
p
[6] to
obtai
n the
wei
ghts of
every grey rel
a
tion co
efficie
n
t, which i
s
in
orde
r to increase the cred
ibility of diagnosi
s
.
2. Matrix Tra
n
sforma
tion
Arithme
t
ic b
y
Fuzz
y
Relationship
Assu
med in
n
indexes
or p
a
ram
e
ters a
m
ong m
targ
ets, a data m
a
trix is expre
s
sed with
X
=
（
x
ij
）
m×n
:
X
=
mn
m
m
n
n
n
m
ij
x
x
x
x
x
x
x
x
x
x
2
1
2
22
21
1
12
11
)
(
(
1)
The rel
a
tive importa
nce of every indexe
s
or pa
ram
e
ters
can b
e
sh
owe
d
with the weig
ht,
who
s
e
cal
c
ul
ation pro
c
e
ss is as follo
ws:
(1) T
he di
sta
n
ce
of every
indicator o
r
p
a
ram
e
ter
rela
tive to the op
timal and the
worst
possibl
e targ
et:
The dista
n
ce of every indicator or p
a
ra
m
e
ter rel
a
tive to the optimal possibl
e targ
et:
2
1
)
(
n
j
ij
j
ig
x
g
（
i
=1
，
2
，
…
，
m
；
j
=1
，
2
，
…
，
n
）
(
2)
The dista
n
ce of every indicator or p
a
ra
m
e
te
r relative to the wors
t poss
ible target
:
2
1
)
(
n
j
j
ij
ib
b
x
（
i=1
，
2
，
…
，
m
；
j=1
，
2
，
…
，
n
）
(3)
In the form
ul
as: the
opti
m
al target set
g
：
j
g
g
=
in
i
i
i
i
i
r
r
r
max
,
,
max
,
max
2
1
(i=1
，
2
，
…
，
m, j=1
，
2
，
…
，
n)
；
the
wors
t
target s
e
t
b
：
j
b
b
=
in
i
i
i
i
i
r
r
r
min
,
,
min
,
min
2
1
(i=
1
，
2
，
…
，
m, j=1
，
2
，
…
，
n).
(2) T
he clo
s
e
ness of every
indicato
r or p
a
ram
e
ter rela
tive to the optimal target se
t
i
：
ib
ig
ib
i
(i=
1
，
2
，
…
，
m)
(4)
(3)
Jud
g
ment
matrix
S:
S
=
（
s
lj
）
n×n
=
l
j
（
l, j=1
，
2
，
…
，
n
）
(5)
(4)
Normali
z
e
judgment ma
trix to matrix
V:
V
=
（
v
lj
）
n×n
n
k
lk
lj
s
s
1
（
l, j, k =1
，
2
，
…
，
n
）
(6)
(5) T
he wei
g
h
t
of every indicator o
r
pa
ra
meter:
From the mat
r
ix V=
(vlj)n×
n to the matrix
U:
U
=(
u
1
，
u
2
，
…
，
u
n
)
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Grey
Relati
on Analysi
s
Method to Vibration F
ault Diag
no
sis of
Hydro
e
le
ctri
c… (Wang
Rui
lian)
5731
In the fo
rmul
a:
n
l
lj
j
v
u
1
, whic
h is
from the mat
r
ix V
after th
e matrix V i
s
a
dde
d
according to the col
u
mn.
The matrix U=(u
1
，
u2
，
…
，
un
) is no
rmali
z
ed a
nd
then the matri
x
ω
is obtaine
d:
ω
=(
ω
j
)
1×n
=
(
n
,
,
,
2
1
)
(8)
In the formula:
n
f
j
j
j
u
u
1
，（
j=1
，
2
，
…
，，
n
）
. The vec
t
or
n
,
,
,
2
1
T is the weig
ht of every indicato
r or p
a
rameter.
3. Gre
y
Relation Anal
y
s
is
The pro
b
lem
of "large sam
p
le and un
ce
rtainty"
that is
the large sam
p
le and a lot of data
but the lack of obvious
regul
arity ca
n be solv
ed
by using th
e theory of
prob
ability a
nd
mathemati
c
al
statistics. The probl
em of "cognitive
un
certai
nty" whi
c
h is the un
certainty of pri
o
ri
kno
w
le
dge a
bout the hum
an expe
rien
ce and
cog
n
itiv
e can b
e
pro
c
e
s
sed by fu
zzy math
ema
t
ical
theory. The
p
r
oble
m
of "little data a
nd u
n
ce
rtai
nty" which
ha
s no
e
x
perien
c
e
an
d little data can
use the g
r
ay system the
o
ry to be settled [7].
The g
r
ey
system the
o
ry
is that
any
system
in
a certain
ra
nge
and tim
e
, som
e
informatio
n is known, so
me inform
ation is u
n
kn
o
w
n. Grey rel
a
tion theo
ry is put forwa
r
d by
Professo
r De
ng Julo
ng [4], which is o
n
e
of the im
portant pa
rts
of grey
syste
m
theory. Grey
relation a
naly
s
is i
s
wid
e
ly use
d
in su
ch
fields as
nat
ural
scie
n
ce, so
cial scie
nce and e
c
on
o
m
ic
manag
eme
n
t and so on [8
-10]. The ba
sic prin
cipl
e of grey relation
analysi
s
is to disting
u
ish
the
relation
al ext
ent of m
any
para
m
eters
o
r
indi
cato
rs b
y
com
pari
ng t
he g
eomet
rical rel
a
tion
shi
p
of
data se
que
nces in the sy
stem. If the ge
ometri
cal
sha
pe of the data seq
uen
ce
s
curve in
syst
em
is closer,
it sugge
sts
t
hat the
rel
a
tion e
x
tent betwee
n
them i
s
g
r
e
a
ter, wherea
s the
sm
aller [8-
10]. Grey rel
a
tion deg
ree
is use
d
to describe t
he de
gree of the cl
ose relation
ship betwe
en the
factors in
system, to mea
s
ure
the
cha
nge extent of
system, a
n
d
can di
sting
u
i
sh the
relati
on
degree bet
we
en variou
s fa
ctors in syste
m
. The anal
y
s
is meth
od compa
r
ed
with other co
rrela
t
ion
analysi
s
met
hod such as mathematical statistics
, it is not only intuitive, h
a
s sim
p
le a
nd
conve
n
ient calcul
ation pro
c
e
ss, but also
not t
oo high about the typicality of
distri
bution re
gula
r
ity
and the data
cap
a
city in co
mpare se
que
nce.
3.1. Gre
y
Relational Degr
ee
Ordin
a
ry, g
r
e
y
relation
de
g
r
ee i
s
used
g
r
ey re
lation
coefficient to
e
x
press. G
r
ey
relation
degree
analy
s
is is t
o
a
s
sess the
grad
e of the
refe
ren
c
e
se
que
nce
by an
alyzing
the
relat
i
on
extent betwe
en the
reference
seq
u
e
n
ce
s
dat
a
a
nd the
com
pare
seq
uen
ce
s d
a
ta. T
he
cal
c
ulatio
n formula of rel
a
tion co
efficient
is:
)
(
max
max
)
(
)
(
max
max
)
(
min
min
)
(
j
j
j
j
j
i
j
i
i
i
j
i
i
j
i
i
(
9)
In the formula:
i
is the
re
lation de
gre
e
between t
he refere
nce
seq
uen
ce
s data
n
j
j
X
X
,
,
2
,
1
/
)
(
0
0
and
the
co
mpare
seq
u
e
n
ce
s
data
n
j
j
X
X
i
i
,
,
2
,
1
/
)
(
, and
)
(
)
(
)
(
0
j
X
j
X
j
i
i
，
i
=1
，
2
，
…
，
m
,
j
=1
，
2
，
…
，
n
.
is the
re
solutio
n
coefficient
whi
c
h i
s
in
the [0
，
1].
is smaller, the resolution power is
stro
n
ger, conversely, the resol
u
tion po
wer i
s
wea
k
e
r
, but the re
sol
u
tion
coeffici
ent h
a
s n
o
e
ffect
on the con
c
l
u
sio
n
of the
analysi
s
. In the
pape
r
= 0.5.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 572
9 –
5735
5732
3.2. The Wei
ghted G
r
e
y
Relatio
n
Deg
r
ee
To avoid mi
ssing
som
e
a
singl
e pa
ram
e
ter in
fo
rmati
on, and
con
s
ider the
effect of all
para
m
eters a
s
far as
po
ssib
le, the
"weighted
average m
odel
M
(
ο
，
+)" wh
ich i
s
the fu
zzy
synthetic a
r
it
hmetic g
ene
ralize
d
in engi
neeri
ng fu
zzy
mathematics is for synth
e
t
ic com
puting
in
the pa
pe
r to
weig
ht the
rel
a
tion
coeffici
ent. The
alg
o
r
ithm
com
pared
with oth
e
r mod
e
l of fu
zzy
synthetic com
puting
g
ene
ra
lized su
ch as
,
M
、
,
M
and
,
M
, the ad
vantage i
s
th
at
the weighte
d
average
mo
del i
s
relative
" sen
s
itiv
e ". The
synth
e
tic al
go
rithm i
s
not
only "ma
i
n
factors
highli
ghted", but
also
taken i
n
to a
c
c
ount
the oth
e
r factors [6]. Furthe
rmo
r
e, t
he
con
c
lu
sio
n
computed i
s
more
coin
cid
ent with
the
vibration chara
c
te
risti
c
of hydroele
c
t
r
ic
gene
rating se
t.
The
comp
re
hen
sive valu
e of wei
ghte
d
grey
relati
on de
gre
e
b
e
twee
n the referen
c
e
seq
uen
ce
s d
a
ta and th
e
comp
are seq
uen
ce
s data
is expresse
d with Y,
whose calculat
ion
formula i
s
:
Y
=
ω
ο
ξ
T
(
10
)
In the formula: “
ο
”is the
syn
t
hetic co
mput
ing
in "weig
h
ted avera
ge m
odel
M
(
ο
，
+)".That
is
j
j
y
i
n
j
i
1
.
ω
(
j
) i
s
the weig
ht of the
j
grey relatio
n
coefficie
n
t that is equal to
the
j
fault
cha
r
a
c
teri
stic param
eter.
Acco
rdi
ng to the maximum
of the relation
al degree wei
ghted, the co
rrespon
ding fa
ult
type can be i
dentified which is
the mo
st likely fault type.
4. The Vib
r
ation Fault Diagnosis
of H
y
droelectric Gen
e
r
a
ting Set Based on Gr
e
y
Relatio
n
al Degree
Analy
s
is
4.1. The Gen
e
ration a
nd Handling o
f
Sample Set
The fa
ult sam
p
le
set i
s
fro
m
the
rep
r
e
s
entativ
e cha
r
acteri
stic p
a
rameter of vib
r
ation fault
in the va
riou
s fault types when vib
r
ation
fault oc
cu
rs.
Fault
type
s
a
nd cha
r
a
c
teri
stic pa
ramete
rs
colle
cted mu
st have defini
t
e universality and practi
cability, and can accu
rately
identify the fault
types of hydroele
c
tric g
e
n
e
rating
set. In sampl
e
set, characte
risti
c
paramete
r
s include vibra
t
ion
amplitude
pa
ramete
rs,
also vibration
freque
ncy p
a
rameters, an
d
even the flu
c
tuating
pre
s
sure
para
m
eters.
Becau
s
e
the
s
e
pa
ramete
rs h
a
ve
different phy
sical
dimen
s
ion
s
, i
n
o
r
de
r to
en
sure
that the fault diagn
osi
s
an
alysis
ca
n be
accompli
sh
ed
su
ccessfully, all of the pa
rameters h
a
ve
to
be normali
ze
d.
The
n fault
ch
ara
c
teri
stic p
a
ram
e
ter dat
a in th
e m
fau
l
t type is sup
posed,
whi
c
h
ca
n u
s
e
the followin
g
formul
a to be norm
a
lized b
e
comi
ng the
data in the [0, 1]:
j
j
ij
j
ij
b
g
x
g
r
(
11
)
In the formula: the “
ij
x
” is
from the formula (1), the “
j
g
” is from (2
) an
d the “
j
b
” is
from
(3). At the s
a
me time,
i
=1
，
2
，
…
，
m
；
j
=1
，
2
，
…
，
n
.
4.2. The Wei
ght Dis
t
ribution of
Fault
Char
acteristi
c Parameter
s
The rel
a
tive importa
nt extent of fault c
hara
c
te
risti
c
para
m
eters
can be exp
r
e
s
sed in
weig
ht. After all of the
ch
a
r
acte
ri
stic
parameter
s are
norm
a
lized,
their wei
ght can
b
e
allo
cat
ed
throug
h the followin
g
cal
c
ulation.
The
dista
n
ce
of the fa
ult ch
ara
c
teri
stic p
a
ram
e
te
rs
relative to the mos
t
lik
e
ly fault type is
obtaine
d tho
ugh u
s
ing th
e formula
(2
) and the di
st
ance rel
a
tive to the least
likely fault type
though
u
s
ing
the
form
ula (3).
Th
e clo
s
e
ness of
the
fa
ult ch
ara
c
te
ri
stic
paramete
r
s rel
a
tive to t
h
e
most likely fault type can
be obtai
ned
by the form
ul
a (4
) an
d the
n
the judg
me
nt matrix ca
n
be
from the form
ula (5). After the judgme
n
t matrix
is pro
c
e
s
sed by the formula (6
) and (7), an
d
is
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Grey
Relati
on Analysi
s
Method to Vibration F
ault Diag
no
sis of
Hydro
e
le
ctri
c… (Wang
Rui
lian)
5733
norm
a
lized
b
y
the formul
a (8), th
e
weight di
stri
bu
tion vecto
r
o
f
every fault
ch
aracte
risti
c
para
m
eters can be gotten.
4.3. The Wei
ghted G
r
e
y
Relatio
n
Deg
r
ee bet
w
e
e
n
the ne
eding
Diagno
sis Fault Sample
s
and Ch
arac
teristic Para
meters
Vibration
faul
t cha
r
a
c
teri
sti
c
p
a
ramete
rs in th
e
com
m
on fa
ult type a
r
e
ch
osen
, whi
c
h
con
s
titute
a
comp
are seq
uen
ce.
T
he needi
ng diag
nosi
s
fa
ult sample
s are
sele
cted
a
s
t
he
referen
c
e se
quen
ce. Both
of the sequ
ences a
r
e
no
rmali
z
ed by the formula (11) an
d then
the
relation
coefficient b
e
twe
e
n
the n
eedin
g
diag
no
sis f
ault sa
mple
s
and the
com
pare
sequ
ence is
gotten. The relation co
efficient is weig
hted by
usin
g the formula
(10), and th
en the weig
h
t
ed
grey
correl
ation value
is
o
b
tained. F
r
o
m
the we
ight
ed g
r
ey relation nu
meri
cal
value, the f
ault
types of vibra
t
ion unit can
be judg
ed.
5. Example Analy
s
is
Freq
uent faul
t of hydro-ge
nerato
r
u
n
its
is
cho
s
en a
s
the fault type set. The
set
inclu
de
the roto
r imb
a
lan
c
e
F
1
, th
e roto
r mi
sali
gnment
F
2
,
d
y
namic or st
atic scratche
s
F
3
, defle
ct
ed
vortex ban
d
in draft tube
F
4
and K
a
rman vortex
street
F
5
. Ro
tational fre
q
u
ency of
unit
is
s
u
pp
os
e
d
f
0
.
Standard sa
mple of vibra
t
ion sp
ect
r
um
su
ch a
s
(0.1
8~0.2
0
)
f
0
、
(1/6~
1
/2)
f
0
、
f
0
、
2
f
0
and 3
f
0
are cho
s
e
n
as f
ault paramet
ers,
stand
ard sam
p
le of
vibration a
m
plitude a
r
e
the
relation
shi
p
betwe
en vibration amplit
u
de and rotate spe
ed exp
r
esse
d in
C
1
, the relationship
betwe
en vib
r
ation a
m
plitu
de a
n
d
the l
oad
expresse
d in
C
2
, the
relation
ship
b
e
twee
n vib
r
at
ion
amplitude
an
d the
pressu
re
of the
spi
r
al case
exp
r
essed
in
C
3
and
th
e relati
onship betwe
en
vibration am
plitude with t
he flow exp
r
essed in
C
4
. Both of the samples
cons
titute a c
o
mpare
seq
uen
ce aft
e
r they are
norm
a
lized, whi
c
h is
sho
w
n in the Ta
ble 1. The n
eedin
g
diagn
osi
s
sampl
e
[2-3]
from
a hydro
p
o
we
r station unit
con
s
titutes
th
e refere
nce
sequ
ence, whi
c
h
is
shown
in the Table 2
.
Table1. Stan
dard Sam
p
le
Paramete
rs o
f
Vibration Fa
ult
if
Vibratio
n fa
ult
t
y
p
e
is
And
V
i
bra
t
io
n f
a
ult c
h
aract
eris
tic para
met
e
rs a
r
e
And
S
t
an
dard s
a
mple
of
v
i
brati
on s
p
ect
rum is
And
st
a
n
d
a
r
d
sa
m
p
l
e
o
f
v
i
b
r
ati
on a
m
pli
t
ude is
(0.18~0.20
)
f
0
(0.18~0.20
)
f
0
f
0
2
f
0
3
f
0
C
1
C
2
C
3
C
4
F
1
0.01
0.11
0.95 0.04
0.13 0.96
0.12 0.07
0.03
F
2
0.01
0.03
0.70 0.96
0.81 0.98
0.96 0.52
0.46
F
3
0.06
0.07
0.91 0.53
0.49 0.97
0.02 0.03
0.14
F
4
0.09
0.96
0.06 0.02
0.01 0.09
0.95 0.02
0.08
F
5
0.95
0.05
0.12 0.09
0.04 0.03
0.04 0.01
0.97
Table 2. Ne
e
d
ing Di
agno
ses Sampl
e
Param
e
ters of Set Vibration Fault
(0.18~0.20
)
f
0
(0.18~0.20
)
f
0
f
0
2
f
0
3
f
0
C
1
C
2
C
3
C
4
0.01
0.02
0.94 0.05 0.10 0.89 0.13 0.15
0.09
The di
stan
ce
of every fault cha
r
a
c
teri
stic
pa
ram
e
ter rel
a
tive to the most likely fault
type
：
ig
= [
1.6120
1.9216
1.5727
1.2808
1.6479
1.6427
1.2707
1.8115
1.8517
]
T
The di
stan
ce
of every fa
ult cha
r
a
c
teri
stic p
a
ramet
e
r relative to
the lea
s
t likely fault
type
：
ib
= [
1.0695
0.5137
1.3413
1.6591
0.9361
1.0817
1.4719
0.9576
0.9443
]
T
The cl
osene
ss of every fa
ult cha
r
a
c
teri
stic
pa
ram
e
ter rel
a
tive to the most likely fault
type set
：
i
=[
0.3988
0.2109
0.4603
0.5643
0.3623
0.3970
0.5367
0.3458
0.3377
]
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 572
9 –
5735
5734
The judg
ment
matrix of every fault chara
c
teri
stic pa
ra
meter
：
S
=
1.0000
0.5289
1.1541
1.4150
0.9083
0.9955
1.3456
0.8671
0.8468
1.8907
1.0000
2.1821
2.6753
1.7173
1.8822
2.5442
1.6394
1.6010
0.8665
0.4583
1.0000
1.2261
0.7870
0.8626
1.1660
0.7513
0.7337
0.7067
0.3738
0.8156
1.0000
0.6419
0.7035
0.9510
0.7513
0.5984
1.1010
0.5823
1.2706
1.5578
1.0000
1.0960
1.4815
0.9546
0.9323
1.0045
0.5313
1.1593
1.4214
0.9124
1.0000
1.3517
0.8710
0.8506
0.7432
0.3931
0.8577
1.0515
0.6750
0.7398
1.0000
0.6444
0.6293
1.1533
0.6100
1.3310
1.6319
1.0475
1.1481
1.5519
1.0000
0.9766
1.1810
0.6246
1.3629
1.6710
1.0727
1.1756
1.5891
1.0240
1.0000
After the jud
g
ment mat
r
ix is no
rmali
z
e
d
, t
he wei
ght
distrib
u
tion
vector of
eve
r
y fault
cha
r
a
c
teri
stic param
eter is
expre
s
sed
：
ω
=
0.10347
0.19564
0.08966
0.07494
0.11392
0.10394
0.07690
0.11934
0.12230
The g
r
ey rela
tion co
efficie
n
t betwe
en t
he sta
nda
rd
sampl
e
a
nd t
he ne
edin
g
d
i
agno
si
s
sampl
e
is exp
r
esse
d
：
0.3481
0.7705
0.8393
0.3534
0.8868
0.9216
0.3643
0.9400
0.3333
0.9792
0.7833
0.3643
0.3701
0.8393
0.9400
0.3481
0.3333
0.8545
0.9038
0.7966
0.8103
0.8545
0.5465
0.4947
0.9400
0.9038
0.9038
0.5595
0.5595
0.3615
0.8393
0.3983
0.3406
0.6620
0.9792
1.0000
0.8868
0.8545
0.9792
0.8704
0.9400
0.9792
0.9792
0.8393
1.0000
i
The wei
ghted
grey relatio
n
degree
：
i
y
= [
666227
.
0
679241
.
0
790307
.
0
633394
.
0
918471
.
0
]
T
It can
be
se
e
n
from
the
n
u
meri
cal
valu
e in th
e
weig
hted relation
degree, the
vibration
fault or the v
i
bration fa
ult cau
s
e
of the po
wer
pla
n
t unit is dia
gno
sed
as "rotor imb
a
lan
c
e",
who
s
e
con
c
lu
sion
is con
s
istent with th
e l
i
terature [3],
and
co
nsi
s
te
nt with th
e
actual fault
cau
s
e
of
the po
wer station.
T
he diagn
osi
s
co
nclu
sio
n
sho
w
s that th
e d
i
agno
si
s met
hod
de
scribe
d i
n
the pa
pe
r
ca
n effectively j
udge
the
vibration faul
t
type from th
e f
ault type
set,
also
sh
ows t
hat
the method can be ap
plied
to fault diagnosi
s
of hydro
e
lectri
c ge
ne
rating set.
6. Conclusio
n
(1) By coll
ecting commo
n
or typi
cal vi
bratio
n
fault
of hydro
e
le
ctric
gen
eratin
g set a
s
sampl
e
, norm
a
lizin
g the ch
ara
c
teri
stic
p
a
ram
e
ters da
ta in the sam
p
le and th
e n
eedin
g
diag
n
o
si
s
sampl
e
, both
of the fault sa
mples be
com
e
the bi
gge
r
the po
ssible, t
hus it i
s
e
a
sy
to find the g
r
ey
relation coeffi
cient.
(2) T
he wei
g
ht of vibration fault chara
c
te
ri
stic pa
ra
meters ca
n b
e
gotten thro
ugh the
method of fuzzy matrix tran
sform
a
tion, which
can
n
o
t only sho
w
th
at vibration fault is fuzzi
ne
ss,
but also the
concl
u
si
on is
more p
e
rsua
sive if it
is com
pare
d
with th
e traditional a
nalytic hierarchy
pro
c
e
ss fo
r its rigo
ro
us ma
thematical
cal
c
ulatio
n.
(3) Vibration
fault cau
s
e of hydroele
c
tri
c
gener
ating set is very complex, vibration fault
para
m
eters is a g
r
e
a
t man
y
. The p
ape
r
sele
ct the
we
ighted
grey
relational
an
alysis,
whi
c
h
can
effectively reflect rel
a
tive importa
nce of fault char
act
e
risti
c
pa
ram
e
ters,
can ta
ke into accou
n
t
all
of the fault p
a
r
amete
r
s a
s
many a
s
p
o
ssible,
can
al
so indi
cate th
a
t
the metho
d
of weig
hted
g
r
e
y
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Grey
Relati
on Analysi
s
Method to Vibration F
ault Diag
no
sis of
Hydro
e
le
ctri
c… (Wang
Rui
lian)
5735
relation
al
a
n
a
l
ysis ba
sed o
n
fuzzy synthetic
u
s
e
d
in f
ault diag
no
si
s of hyd
r
o
e
le
ctri
c ge
ne
rating
s
e
t is
more prac
tical.
Referen
ces
[1]
Z
H
ANG Lipin
g
,
SUN Meifen
g, W
A
NG
T
i
e
s
hen
g.
Applic
ation of a no
vel
RBF
algor
ithm to fault
dia
gnos
is of h
y
dro-turb
ine g
e
n
e
ratin
g
unit.
Jo
urna
l of Hydro
e
lectric En
gin
e
e
rin
g
. 200
9; 28
(6): 219-2
24.
[2]
LI Chaos
hu
n, Z
H
OU Jianz
hon
g, XIAO Jian, et al.
Vibratio
n F
ault Diag
nos
is of Hydro
e
lectr
i
c
Generati
ng U
n
it Using Gravit
ation
a
l Se
arch
Based Ker
n
e
l
Clusteri
ng M
e
thod
. Proc
ee
din
g
s of the
CSEE. 2013; 3
3
(2): 98-1
04.
[3]
AN
Xu
eli, Z
H
O
U
Jia
n
zh
on
g, L
I
U Li,
et al. V
i
b
r
at
ion
fault
di
a
gnos
is for
h
y
dr
aulic
g
e
n
e
rator
un
its bas
e
d
on e
n
trop
y
w
e
i
ght theor
y
an
d
informati
on fu
sion tec
hno
lo
g
y
.
Auto
mation
of Electric Po
w
e
r System
.
200
8; 32(2
0
): 78-82.
[4]
DENG Jul
ong.
Gre
y
pred
icti
on a
nd
an
d d
e
cisio
n
a
n
a
l
ysi
s
. Huazh
o
n
g
Univers
i
t
y
of
Scienc
e a
n
d
T
e
chnolog
y Pr
ess, Chin
a.19
8
6
.
[5]
MA Z
h
ipen
g, YUAN Jia
ngu
o, SHI Yun
y
un, e
t
al
. Gre
y
Deci
sion Mo
del for
F
l
ood Co
ntrol
of Casca
d
e
Reserv
oirs B
a
sed
on Stoc
ha
stic
W
e
ight As
signm
ent meth
od.
W
a
ter R
e
s
ources
an
d P
o
w
e
r
. 2
0
09;
27(1): 77-
80.
[6]
HUANG Jia
n
y
u
an. F
u
zz
y
set a
nd its app
lic
ation.
Nin
g
x
ia P
e
opl
e'
s Educati
o
n Press. Chin
a
.
1999.
[7]
F
eng Y
i
fen
g
. C
o
mpar
ed t
he
C
a
lcul
atio
n M
e
th
ods
of Gra
y
C
o
rrelati
on.
J
our
nal
of Xi
an
gfan
Vocati
on
al
and T
e
ch
nic
a
l
Coll
eg
e
. 10(3)
21-2
2
, 201
1.
[8]
LIU Yun
pen
g,
W
A
NG Ling, GUO W
e
n
y
i, et a
l
.
Influenc
e of
Enviro
nmenta
l
F
a
ctors on L
e
a
k
age C
u
rre
nt
of ±80
0
kV L
i
ne Insu
lators
at Hig
h Altitu
des Bas
ed
o
n
Gre
y
Re
lati
on An
al
ysis.
H
i
g
h Vo
l
t
age
Engi
neer
in
g
. 2013; 39(
2): 318
-323.
[9]
T
A
N Chun, CHEN Jia
npi
ng,
QUE Jinshen
g, et al.
Anal
ysis of represe
n
t
ative elem
ent
ar
y
vo
lum
e
for
rock mass b
a
s
ed o
n
3
D
fract
u
re n
u
meric
a
l
net
w
o
rk m
o
d
e
l
and
gre
y
s
y
st
em theor
y
.
S
H
UILI XUEBAO.
201
2; 43(6): 70
9-71
6.
[10]
LIU F
e
n
g
, W
E
I Guang
hui. F
u
zz
y o
p
timizati
on
of
h
y
dr
aul
ic
proj
ect sch
em
e b
a
sed
on
im
prove
d
gr
e
y
relati
on an
al
ys
i
s
.
Journal of H
y
droe
lectric En
gin
eeri
n
g
. 20
1
2
; 36(1): 10-2
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.