Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
11,
No.
2,
April
2021,
pp.
1697
1708
ISSN:
2088-8708,
DOI:
10.11591/ijece.v11i2.pp1697-1708
r
1697
Monitoring
of
solenoid
parameters
based
on
neural
netw
orks
and
optical
fiber
squeezer
f
or
solenoid
v
alv
es
diagnosis
Abdallah
Zahidi
1
,
Said
Amrane
2
,
Nawfel
Azami
3
,
Naoual
Nasser
4
1,2,3
INPT
Optics
Lab,
National
Institute
of
Posts
and
T
elecommunications,
Rabat,
Morocco
4
LDEDS,
F
aculties
of
Science
and
T
echnology
,
Hassan
Uni
v
ersity
1
st
,
Settat,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Apr
4,
2020
Re
vised
Aug
11,
2020
Accepted
Sep
30,
2020
K
eyw
ords:
EMS
Fluctuations
Monitoring
Neural
Netw
orks
Polarization
squeezer
ABSTRA
CT
As
crucial
parts
of
v
arious
engineering
systems,
solenoid
v
alv
es
(SVs)
operated
by
electromagnetic
solenoid
(EMS)
are
of
great
importance
and
their
f
ailure
may
lead
to
cause
une
xpected
casualties.
This
f
ailure,
characterized
by
a
de
gradation
of
the
per
-
formances
of
the
SVs,
could
be
due
to
a
fluctuations
in
the
EMS
parameters.
These
fluctuations
are
essentially
attrib
uted
to
the
changes
in
the
spring
constant,
coef
ficient
of
friction,
induc
tance,
and
the
resistance
of
the
coil.
Pre
v
enti
v
e
maintenance
by
con-
trolling
and
monitoring
these
parameters
is
necessary
to
a
v
oid
e
v
entual
f
ailure
of
these
actuators.
The
authors
propose
a
ne
w
methodology
for
the
functional
diagnosis
of
electromagnetic
solenoids
(EMS)
used
in
h
ydraulic
systems.
The
proposed
method
monitors
online
the
electrical
and
mechanical
parameters
v
arying
o
v
er
time
by
using
articial
neural
netw
orks
algorithm
coupled
with
an
optical
fiber
polarization
squeezer
based
on
EMS
for
polarization
scrambling.
First,
the
MA
TLAB/Simulink
model
is
proposed
to
analyze
the
ef
fect
of
the
parameters
on
the
dynamic
EMS
model.
The
result
of
this
simulation
i
s
used
for
training
the
neural
netw
ork.
Then
a
simulation
is
proposed
using
the
neural
net
tting
toolbox
to
determine
the
solenoid
parameters
(Re-
sistance
of
the
coil
R,
stif
fness
K
and
coef
ficient
of
fric
tion
B
of
the
spring)
from
the
coef
ficients
of
the
transfer
function,
established
from
the
model
step
response.
Future
w
ork
will
include
not
only
diagnosing
f
ailure
modes,
b
ut
also
predicting
the
remaining
life
based
on
the
results
of
monitoring.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Abedallah
Zahidi
National
Institute
of
Posts
and
T
elecommunications
A
v
enue
Allal
Al
F
assi,
Rabat,
Morocco
Email:
zahidiabdo@yahoo.fr
1.
INTR
ODUCTION
In
electromechanical
solenoids
(EMS),
also
called
electromagnetic
de
vices
(EMD),
dri
v
en
by
a
control
solenoid,
the
armature
is
positioned
by
balancing
the
electromagnetic
force
ag
ainst
that
of
a
return
spring.
The
y
are
relati
v
ely
an
ine
xpensi
v
e
construction
[1],
ha
v
e
a
simple
design
and
control
circuit,
require
li
ttle
ener
gy
for
control,
are
highly
reliable
[2],
these
electromagnetic
actuators
are
used
in
wide
range
of
modern
industrial
equipment
such
as
digital
actuator
arrays
[3],
v
ehicle
vibration
control
systems
[4],
g
as
v
alv
e
[5],
robotic
ma-
nipulators
[6],
positioners
[7],
anti-braking
systems
[8],
and
polarization
controllers
where
solenoids
are
used
as
mechanical
actuator
on
the
fiber
to
adjust
the
output
light
po
wer
[9].
In
h
ydraulic
systems,
these
electro-
magnetic
actuat
ors
are
comm
o
nl
y
used
in
three
basic
cate
gories
to
actuate
h
ydraulic
control
v
alv
es
directional-
J
ournal
homepage:
http://ijece
.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
1698
r
ISSN:
2088-8708
control,
flo
w-control,
and
pressure-control.
Directional-control
v
alv
es
are
used
to
connect
and
isolate
h
ydraulic
passages
by
simply
opening
a
nd
closing
a
communication
path.
Flo
w-control
v
alv
es
allo
w
v
ariable
flo
w
rate
control
to
a
component.
Finally
,
pressure-control
v
alv
es
re
gulate
v
ariable
pressure
to
a
h
ydraulic
component
[10].
Analysis
of
EMS
purposes
sho
w
that
to
impro
v
e
the
safety
and
the
performance
of
the
EMS
based
h
ydraulic
system,
t
he
re
gular
maintenance
strate
gy
of
these
electromechanical
solenoids
surely
reduces
f
ailure
rate
of
the
system
;
ho
we
v
er
,
it
brings
high
maintenance
cost
[11].
It
should
be
highlighted
that
emer
genc
y
modes
of
EMDs
a
re
not
only
results
of
f
aults
of
their
v
arious
elements
or
incorrect
personnel
acti
vities
during
EMD
manuf
acturing
and
operation,
the
y
are
also
possible
during
a
normal
operation
due
to
the
wearing
of
mating
surf
aces
of
friction
assemblies
or/and
fluctuation
in
its
parameters
[12,
13].
Therefore,
it
is
necessary
to
de
v
elop
an
ef
fecti
v
e
approach
for
EMS
diagnostics
and
operation
controls
in
order
to
map
the
f
ailure
and
the
reliability
of
the
EMS
based
on
the
solenoid
v
alv
es.
The
diagnostic
results
could
be
used
to
estimate
the
health
condition
of
the
solenoid
v
alv
es
and
predict
their
remaining
useful
life.
Additionally
,
the
s
olenoid
v
alv
es
coul
d
get
tim
ely
repaired
or
replaced
before
their
potent
ial
f
ailure
causes
an
y
system
breakdo
wn.
2.
PR
OBLEM
ST
A
TEMENT
Despite
the
high
reliability
and
the
e
xcellent
performance
of
solenoid
v
alv
es
in
v
arious
appli
cations,
their
f
ailure
may
result
in
se
v
ere
system
crash,
signficant
casualties
and
economic
losses,
especially
in
safety-
first
fields,
such
as
rail
w
ay
braking
system,
a
viation
engine,
and
nuclear
po
wer
plants
[14].
Ho
we
v
er
,
as
stated
in
some
pre
vious
w
orks
[15,
16],
the
EMS
dynamic
in
these
de
vices
is
go
v
erned
by
an
electromagnetic
force
that
increases
greatly
when
the
air
g
ap
is
near
zero.
This
nonlinear
beha
vior
,
together
with
ph
ysical
bounds
that
limit
the
motion,
causes
EMS
of
v
alv
es
to
be
s
ubject
to
strong
shocks
and
wear
that
often
result
in
early
f
ailures
[17],
these
f
ailures,
which
af
fects
the
dynamic
response
[18],
may
be
due
to
a
fluctuation
in
the
EMS
structure
parameters
[19]
or
the
electrical
and
mechanical
parameters
of
the
EMS
(v
ariations
in
inductance
and
resistor
of
the
coil,
changes
in
spring
constant
and
coef
ficient
of
friction)
[20,
21].
Other
studies
ha
v
e
sho
wn
a
deterioration
in
the
performance
of
EMS
based
system
in
presence
of
parametric
v
ariation
[12,
13],
e
v
en
for
the
best
control
solutions
[20].
Other
literatures
ha
v
e
also
re
v
ealed
that
f
ailure
of
solenoid
v
alv
es
can
also
occur
gradually
due
to
coil
b
urnout
of
EMS
related
to
mains
v
oltage
and
frequenc
y
,
spring
force
[22,
23];
and
that
the
resistance
of
the
coil
might
be
a
source
of
themo-mechanical
f
ailure
of
the
solenoid
v
alv
e
[24].
In
addition,
the
abo
v
e-mentioned
literature
pro
vides
the
parameters
which
characterize
the
f
ailure
of
the
solenoid
v
alv
es.
This
information
can
then
be
used
to
design
a
m
o
de
l
to
map
the
f
ailure.
Approaches
based
on
signal
processing
[25]
and
machine
learning
[26]
ha
v
e
been
proposed
in
the
lit
erature
to
diagnose
the
state
of
solenoid
v
alv
es
leading
to
the
de
v
elopment
of
a
sensor
to
detect
anomalies
[27]
or
a
method
for
grouping
f
ailures
[26].
None
of
these
approaches
gi
v
es
a
ph
ysical
e
xplanation
of
the
f
ailure
modes
related
to
the
solenoid
parameters
[28];
Other
models
based
on
the
mo
v
ement
of
the
armature
and
F
oucault
current
[2]
and
the
EMD
winding
current
curv
e
appearing
with
the
mo
v
ement
of
the
armature
[29,
30]
ha
v
e
been
de
v
eloped
for
diagnosis,
b
ut
none
of
these
models
does
treat
electrical
and
mechanical
parameters
as
a
source
of
f
ailure.
More
v
er
,
most
control
approaches
are
using
signals
such
as
the
coil
current
or
v
oltage
of
solenoid
to
monitor
the
parameters;
yet,
the
main
problems
in
such
approaches
are
that
the
detected
signals
ar
e
prone
to
interference
and
difcult
to
obtain
[31].
Other
w
orks
ha
v
e
been
limited
to
the
estimation
and
identication
of
a
single
solenoid
parameter
[32,
22].
In
this
w
ork,
the
authors
ha
v
e
de
v
eloped
a
ne
w
approach
for
the
diagnosis
of
an
EMS
actuator
in
solenoid
v
alv
e.
The
proposed
approach
is
based
on
a
ne
w
method
based
on
optical
fiber
polarization
controller
signal
feedback
coupled
with
articial
neural
netw
orks
model
(ANN)
for
monitoring
the
electrical
and
mechanical
EMS
parameters
(resistence
of
coil
R,
and
K,
B
respecti
v
ely
the
stif
fness
and
the
coef
ficient
of
friction
of
the
spring),
considered
in
this
approach
as
health
indices
to
characterize
the
f
ailure
of
the
solenoid
v
alv
e.
NN
has
the
adv
antages
of
controlling
comple
x
and
non-linear
systems
[33,
34],
has
high
accurac
y
of
prediction
capability
[35],
and
it
is
of
great
importance
to
find
the
high
speed
electromagnetic
switching
v
alv
e
[36].
3.
METHODOLOGY
OF
STUD
Y
This
paper
proposes
a
ne
w
methodology
using
optical
fiber
polarization
controller
signal
feedback
coupled
with
an
articial
neural
netw
orks
model
(ANN)
for
monitoring
the
solenoid
parameters
and
predicting
its
performance.
Figure
1
sho
ws
the
proposed
monitoring
process.
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
2,
April
2021
:
1697
–
1708
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
1699
Laser
1550nm
EMS
of
solenoid
v
alv
e
Sensor
of
armature
pressure
(Fiber)
Analyzer
Detector
(photodiode)
Neural
net-
w
ork
model
Storage
&
vie
wing
of
EMS
parameters
Figure
1.
Block
diagram
of
monitoring
process
In
the
proposed
struct
ure,
the
optical
fiber
polarization
controller
is
based
on
an
EMS
and
an
opti
cal
fiber
used
as
a
mechanical
force
sensor
of
the
EMS
armature.
This
force
induces
an
optical
birefringence
that
modifies
the
polarization
of
the
light
[9].
The
v
ariation
of
the
polarization
of
the
light
is
reflected
by
the
v
ariation
of
the
light
intensity
detected
by
a
photodiode
placed
at
the
output
of
the
optical
fiber
,
In
the
first
step,
a
mathematical
model
is
proposed
to
obtain
the
response
of
the
system.
Then,
this
model
is
identied
from
this
response
using
function
tfest
of
MA
TLAB/Simulink
[37]
to
determine
the
transfer
function
coef
ficient
of
the
system.
In
the
second
step,
the
ef
fect
of
solenoid
parameters
v
ariation
on
the
transfer
function
coef
ficient
is
analysed.
This
method
uses
simulation
electromagnetic
fiber
squeezer
based
polarization
controller
with
function
tfest
and
the
simulation
results
are
stored
in
a
te
xt
file
that
will
be
used
for
neural
netw
orks
training.
In
the
last
step,
the
neural
netw
orks
model
is
proposed
to
estabish
the
solenoid
parameters
from
the
coef
ficients
of
the
transfer
function
set
from
the
step
response
of
the
fiber
squeezer
.
Finally
,
to
check
the
ef
ficienc
y
of
the
proposed
model,
a
prediction
error
is
calculated.
The
result
of
the
simulation
sho
ws
that
this
optical
fiber
squeezer
coupled
with
the
neural
netw
ork
model
is
v
ery
ef
ficient
to
monitor
the
EMS
parameters.
The
results
of
monitoring
will
be
used
in
a
future
w
ork
to
estimate
the
remaining
life
of
the
solenoid
v
alv
e.
4.
B
UILDING
THE
SIMULINK
MODEL
4.1.
Structur
e
and
equations
of
electr
omagnetic
fiber
squeezer
The
EMS
is
the
electromagnetic
actuator
that
e
x
erts
the
pressure
on
the
fiber
.
Its
structure
is
sho
wn
in
Figure
2.
Analyser
Detector
Laser
1550
Solenoid
Figure
2.
Scheme
of
using
the
electromagnetic
fiber
squeezer
The
magnitude
of
the
phase
dif
ference
of
tw
o
polarized
light
along
the
squeezing
axis
and
its
orthog-
onal
axis
can
be
e
xpressed
as
[38]:
=
6
e
5
F
d
(1)
and
the
light
po
wer
P
s
at
the
output
of
the
polarization
analyzer
according
to
scheme
of
Figure
2
is:
P
s
=
E
2
(2)
Monitoring
of
solenoid
par
ameter
s
based
on
neur
al
networks
and
optical
fiber
...
(Abedallah
Zahidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1700
r
ISSN:
2088-8708
where
E
=
A:
1
2
:E
(3)
A
=
e
j
(
m
+
2
)
0
0
e
j
(
m
2
)
!
(4)
P
s
=
E
2
=
P
0
2
(1
+
cos
)
(5)
where
P
0
is
the
input
light
intensity
.
4.2.
Mathematical
model
of
EMS
The
solenoid
refers
to
the
electromagnetic
actuator
.
It
is
used
to
e
x
ert
pressure
on
the
fiber
.
Its
struc-
ture
is
sho
wn
in
Figure
3.
Plunger
Coil
Figure
3.
Cross
section
of
EMS
The
mathematical
model
of
EMS
is
gi
v
en
[39]
by
e
xpression
as
(6):
m
d
2
x
(
t
)
dt
2
+
B
dx
(
t
)
dt
+
K
x
(
t
)
=
0
r
N
2
AI
2
(
t
)
2(
x
0
x
(
t
))
2
(6)
where:
x
(
t
)
:
Displacement
of
the
armature
in
(m),
I
(
t
)
:
The
electromagnet
coil
current
in(A),
A
:
the
cross
sectional
area
of
the
coil
in
(m
2
),
N
:
the
number
of
the
turns
of
the
coil,
0
:
P
ermeability
of
the
free
space
in
(H/m),
r
:
Relati
v
e
Permeability
of
the
die
lectric
materiel
between
the
coil
and
armature,
x
0
:
The
initial
air
g
ap
between
the
armature
and
the
backside
of
the
frame
in
(m),
m
:
Masse
of
the
armature
in
(Kg),
K
:
is
the
stif
fness
of
the
spring
in
(N/m)
and
B
:
System
damping
coef
ficient
in
(N.s/m).
The
equation
of
the
electrical
circuit
is
as
(7)
and
(8):
u
=
R
i
(
t
)
+
d
dt
[
L
(
x
)
:i
(
t
)]
(7)
u
=
R
i
(
t
)
+
L
(
x
)
di
(
t
)
dt
+
i
(
t
)
dL
(
x
)
dt
(8)
R
is
the
series
resi
stance
of
the
EMS
coil
and
L
(
x
)
is
the
inductance
of
the
coil
that
depends
of
the
air
g
ap
[39]:
L
(
x
)
=
0
r
x
0
x
(
t
)
(9)
The
balance
equation
of
the
force
acting
on
the
fiber
is
e
xpressed
as
[40]
m
d
2
x
(
t
)
dt
2
=
F
K
(
x
(
t
)
x
0
)
B
dx
(
t
)
dt
(10)
F
is
the
force
produced
by
the
magnetic
field
and
it
be
deri
v
ed
kno
wing
that
magnetic
system
is
linear
and
that
current
w
as
k
ept
constant
F
=
dw
t
dx
=
i
2
2
dL
(
x
)
dx
=
i
2
2
aL
0
(
a
+
x
)
2
(11)
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
2,
April
2021
:
1697
–
1708
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
1701
where
L
0
=
0
adN
2
g
and
a
,
d
,
g
parameters
depending
on
the
EMS.
from
(8)
we
can
write
di
dt
=
1
L
(
x
)
u
R
i
i
dL
(
x
)
dx
dx
dt
(12)
from
(10)
we
can
write
d
2
x
dt
2
=
1
m
F
K
(
x
x
0
)
B
dx
dt
(13)
Both
(1)
and
(5)
are
used
to
write:
P
s
=
P
0
2
1
+
cos
(
6
e
5
F
d
)
(14)
4.3.
Simulink
model
The
system
model
has
been
implemented
in
v
ersatile
softw
are
MA
TLAB
which
is
widely
used
in
control
engineering
around
the
w
ord.
This
simulation
is
used
to
ef
fecti
v
ely
determine
the
best
performance
of
the
dynamic
response
in
the
output
light
intensity
.
The
electrical
model
Simulink
which
models
(12)
is
represented
in
Figure
4(a);
while,
the
Simulink
mechanical
model
for
(13)
is
illustrated
in
Figure
4(b).
This
model
depends
on
the
intrinsic
parameters
of
the
EMS:
the
mass
m
of
the
armature,
the
coef
ficient
of
friction
B,
the
stif
fness
of
the
ress
ort
K,
the
resistance
and
the
inductance
of
t
he
coil
(R,
L).
The
Figure
4(c)
represents
the
optical
Simulink
model
for
(14).
(a)
(b)
(c)
Figure
4.
Simulink
models,
(a)
Electrical
model,
(b)
Mechanical
model,
(c)
Optical
model
Monitoring
of
solenoid
par
ameter
s
based
on
neur
al
networks
and
optical
fiber
...
(Abedallah
Zahidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1702
r
ISSN:
2088-8708
5.
PRINCIPE
OF
SIMULA
TION
5.1.
Monitoring
pr
ocess
flo
wchart
T
o
predict
and
monitor
the
EMS
parameters,
the
coef
ficients
of
the
transfer
function
obtained
from
the
step
response
of
the
fiber
squeezer
based
on
the
EMS
are
used
as
input
of
the
NN
model.
The
parameters
solenoid
R,
B
and
K
are
e
xpected
as
outputs
.
The
flo
wchart
of
the
monitoring
process
is
sho
wn
in
Figure
5.
Figure
6
proposes
the
architecture
of
the
ANN
model
and
T
able
1
illustrates
an
e
xample
of
identification
results
used
for
the
ANN
training.
Figure
5.
Monitoring
process
flo
wchart
Input
3
Hidden
lay
er
10
w
b
+
Output
lay
er
3
w
b
+
Output
3
Figure
6.
Neural
netw
ork
architecture
T
able
1.
Identification
result
for
neural
netw
ork
training
Indice
K
(N/m)
B(Ns/m)
R(
)
Num
Dun1
Dun2
Dun3
1
2998.5692
3.2177
11.8536
114.7376
1
16.2331
15095.4567
2
2168.9635
2.3559
12.8581
70.5311
1
11.8918
10931.6472
3
2521.0054
2.1333
13.6778
72.4483
1
10.7603
12681.9928
5.2.
Neural
netw
orks
ar
chitectur
e
The
NN
inputs
consist
of
a
matrix
of
order
10000
3
,
where
each
line
represents
a
set
of
coef
ficients
of
the
transfer
function
num,
dun2
and
dun3.
On
the
other
hand,
the
outputs
are
the
elements
of
a
matrix
of
the
same
order
as
the
inputs
where
each
line
e
x
emplifies
a
set
of
solenoid
parameters
(K,
B
and
R).
The
structure
also
contains
10
hidden
layers
chosen
by
def
ault
with
the
sigmoid
function
as
act
i
v
ation
function
and
3
output
layers
with
a
linear
acti
v
ation
function
as
sho
wn
in
Figure
6.
5.3.
Neural
netw
orks
training
5.3.1.
Identification
with
v
ariable
parameters
f
or
NN
training
First,
we
propose
a
mathematical
model
that
is
used
to
obtain
the
response
of
the
system.
Then,
this
model
is
identified
from
this
response
using
identification
function
tfest
whose
syntax
is
sys=tfest(data,
np,
nz).
This
function
is
used
to
estimate
a
transfer
function
containing
nz
zeros
and
np
poles
from
the
inde
x
response
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
2,
April
2021
:
1697
–
1708
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
1703
(data)
of
the
Simulink
model
described
in
paragraph
4.3.
The
resulting
transfer
function
has
the
coef
ficient
(num,
dun2,
dun3),
and
can
be
e
xpressed
as
(15):
T
f
=
num
s
2
+
dun
2
s
+
dun
3
(15)
Secondly
,
in
order
to
obtain
the
system
transfer
function
for
dif
ferent
v
alues
of
the
solenoid
parame-
ters,
K,
B
and
R
are
v
aried
while
while
k
eeping
m=200
g
and
L=20
mH
since
the
y
are
not
lik
ely
to
v
ary
during
long-term
operation
of
the
solenoid.
The
v
ariation
interv
al
of
K
is
1000
to
3000
N/m
;
R
is
10
to
15
and
B
is
2
to
4
N.s/m.
The
inputs
of
the
Simulink
model
are
a
matrix
of
three
columns
and
n
ro
ws
of
random
v
alue
of
solenoid
parameter
.
The
random
v
ariation
between
the
max
and
min
v
alues
of
each
of
the
three
parameters
(K,
B
and
R)
is
obtained
by
using
the
function
rand
(n,1)
whose
syntax
is
as
(16):
par
ameter
=
(
max
{
min
)
r
and
(
n;
1)
+
min
(16)
where
parameter
is
K,
R
or
B,
and
n=
10
000.
The
follo
wing
Figure
7
represents
the
flo
wchart
which
allo
ws
to
obtain
the
dataset
and
T
able
1
sho
ws
an
e
xample
of
the
te
xt
file
results
obtained.
The
results
of
this
simulation
are
used
as
data
(num,
dun2,
dun3)
and
tar
get
(K,
B,
R)
for
training
the
neural
netw
ork
model
as
sho
wn
in
section
5.3.2.
Start
initialization
K,
B
and
R
te
xt
files
Opening
Sumlink
model
Identification
with
tfest
function
Coef
Tf*
te
xt
files
V
ariation
of
EMS
parameters
(K,
B,
R)
End
VSP*
End
Tf:
T
ransfer
function
VSP:
V
ariation
solenoid
parameters
Figure
7.
Identification
flo
wchart
5.3.2.
Neural
netw
orks
training
The
tar
get
of
neural
netw
ork
is
able
to
identify
and
predict
the
solenoid
parameters.
Data
from
step
response
and
neural
netw
ork
tar
get
are
used
to
search
weight
(w)
and
bias
(b).
W
eight
and
bias
are
obtained
by
entering
data
and
tar
get
in
MA
TLAB
program
by
using
Neural
Net
fitting
toolbox
which
of
fers
se
v
eral
training
functions.
The
updating
of
weight
and
bias
v
alues
during
netw
ork
training
is
performed
according
to
the
Le
v
enber
g-Marquardt
optimization
which
of
fers
f
aster
tracking
of
system
parameter
change
[41].
The
Le
v
enber
g-Marquardt
algorithm
is
an
ef
ficient
and
popular
damped
least
squre
technique.
This
algorithm
is
a
combinaison
between
the
steepest
gradient
descent
and
the
Gauss-Ne
wton
algorithms
[42].
The
acti
v
ation
function
at
the
output
of
the
HLs
is
the
sigmoid
function,
it
deli
v
ers
a
continuously
smoother
range
of
v
alues
between
0
and
1
and
is
less
e
xpensi
v
e
in
terms
of
calculation.
At
the
output
of
the
netw
ork,
the
acti
v
ation
function
is
linear
,
which
creates
an
output
signal
proportional
to
the
input.
During
the
searching
process
of
weight
and
bias,
the
dataset
is
subdi
vided
into
three
percent,
70%
for
training,
15%
for
the
test
and
15%
for
Monitoring
of
solenoid
par
ameter
s
based
on
neur
al
networks
and
optical
fiber
...
(Abedallah
Zahidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1704
r
ISSN:
2088-8708
v
alidation.
The
e
v
aluation
of
the
model
is
measured
using
three
e
v
aluation
performances
which
are
the
mean
square
error
(MSE),
the
coef
ficient
of
correlation
(R)
and
error
histogram.
The
optimization
technique
applied
in
the
ANN
model
training
seeks
to
optimize
the
we
ights
and
biases
of
the
ANN
structure
by
minimizing
rhe
mean
square
error
(MSE).
The
training
results
are
ill
ustrated
in
Figure
8(a)
which
represents
the
con
v
er
gent
curv
e
of
the
MSE
according
to
the
epochs,
error
histogram
and
coef
ficient
of
the
correlation
between
the
output
and
the
tar
get
that
respecti
v
ely
illustrated
in
Figure
8(b)
and
Figure
8(c).
0
200
400
600
800
1000
1000 Epochs
10
-4
10
-2
10
0
10
2
10
4
10
6
Mean Squared Error (mse)
Best Validation Performance is 6.6317e-05 at epoch 1000
Train
Validation
Test
Best
(a)
0
2000
4000
6000
8000
10000
12000
Instances
Error Histogram with 20 Bins
-0.06544
-0.05807
-0.0507
-0.04333
-0.03596
-0.02858
-0.02121
-0.01384
-0.00647
0.000902
0.008274
0.01564
0.02302
0.03039
0.03776
0.04513
0.0525
0.05987
0.06724
0.07462
Errors
Zero Error
(b)
500
1000
1500
2000
2500
Target
500
1000
1500
2000
2500
Output ~= 1*Target + -1.9e-06
Regression R=0.99
Y=T
Fit
Data
(c)
Figure
8.
T
raining
performance,
(a)
The
con
v
er
gent
curv
e
of
the
MSE,
(b)
T
raining
error
histogram,
(c)
T
raining
coef
ficient
of
correlation
5.4.
Monitoring
r
esult
and
pr
ediction
err
or
The
prediction
and
monitoring,
of
the
EMS
parameters
are
achie
v
ed
through
the
data
acquisition
(num,
dun2,
dun3)
from
the
step
response
of
the
optical
fiber
polarization
controller
based
on
EMS.
These
data
are
used
as
inputs
of
the
NN
model
in
order
to
find
the
parmeters.
The
predicted
solenoid
parameters
M,
B
and
K
obtained
from
the
transfert
function
coef
ficient
are
illustred
in
the
T
able
2.
Figure
9
sho
ws
the
structure
of
the
minotoring
process.
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
2,
April
2021
:
1697
–
1708
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Elec
&
Comp
Eng
ISSN:
2088-8708
r
1705
T
able
2.
Predicted
parameters
testing
result
NN
input
Solenoid
parameter
num
dun2
dun3
K(N/m)
B(Ns/m)
R(
)
T
est1
74.23
18.28
5683
1101.8
3.60
8.90
T
est2
137.86
14.03
14010
2775.5
2.76
10.40
T
est3
59.12
16.21
10871
2159.5
3.22
14.03
Figure
9.
The
model
architecture
for
EMS
monitoring
process
5.5.
Model
perf
ormance
testing
The
e
v
aluation
of
the
model
performance
is
done
according
to
the
flo
wchart
of
the
Figure
10
by
using
data
not
utilized
for
the
model
training.
The
parameters
found
are
used
as
inputs
of
the
Simulink
model
to
find
the
predicted
v
alue
of
transfer
function
coef
ficients.
These
v
alues
are
compared
to
the
current
v
alues
:num,
dun2
and
dun3
to
finally
calculate
the
prediction
error
.
The
model
performance
t
esting
structure
is
illustrated
in
Figure
11.
Figure
10.
Performance
testing
flo
wchart
Monitoring
of
solenoid
par
ameter
s
based
on
neur
al
networks
and
optical
fiber
...
(Abedallah
Zahidi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1706
r
ISSN:
2088-8708
Figure
11.
The
detail
model
performance
testing
5.6.
Results
and
discussion
T
able
1
illustrates
the
result
of
the
mathematical
model
identification
of
the
system
proposed
for
training
using
the
tfest
function
for
dif
ferent
v
alues
of
the
parameters
K,
B
and
R.
It
is
clear
from
this
table
that
if
the
stif
fness
of
t
h
e
spring
K,
the
coef
ficient
of
friction
B
and
the
resistance
of
the
solenoid
coil
R
v
ary
,
the
coef
ficients
of
the
transfer
function
characterizing
the
model
dun2
and
dun3
also
v
ary
,
this
v
ariation
af
fects
the
performance
of
the
h
ydraulic
system
based
on
solenoid
v
alv
e.
Ho
we
v
er
,
the
coef
ficient
dun1
is
k
ept
constant
it
is
equal
to
1.
The
Figure
8(a)
sho
ws
the
con
v
er
gence
curv
e
of
MSE
which
illustrates
the
e
v
olution
of
the
NN
training.
Moreo
v
er
,
it
can
be
observ
ed
from
this
figure
that
suitable
weights
and
biases
of
the
NN
model
are
found
in
the
end
of
the
iteration
with
a
better
MSE
v
alue
which
is
around
6,63.10
6
.
In
addition,
the
impro
v
oment
of
the
model
performance
might
be
realized
by
increasing
the
number
of
iterations
(epochs)
in
order
to
minimize
the
MSE.
The
Gaussian
form
of
the
error
histogram
in
Figure
8(b)
and
the
v
alue
of
coef
ficient
of
correlation
between
outputs
and
tar
gets
during
the
test
illustrated
in
Figure
8(c)
sho
w
the
high
quality
of
training
result.
On
the
other
hand,
according
to
the
results
obtained
from
the
performance
test
model
of
Figure
9
along
with
those
illustrated
on
the
T
able
2,
it
is
clear
that
the
predicted
v
alues
of
K,
B
and
R
are
in
e
vident
agreement
with
the
test
v
alues
obtained
by
the
model
of
the
Figure
11
and
which
are
illustrated
in
T
able
3.
What’
s
more,
and
generally
,
the
training
result
is
less
accurate
compared
to
the
training,
ho
we
v
er
,
from
the
testing
performance
gi
v
en
in
the
T
able
3
and
the
relat
i
v
e
prediction
error
illustrated
in
T
able
4.
Thus
it
is
pro
v
en
that
the
training
performance
of
Le
v
enber
g-Marquardt
algorithm
is
able
to
control
and
predict
the
solenoid
parameters,
and
that
the
proposed
neural
netw
ork
monitoring
w
as
successfully
implemented.
T
able
3.
Simulink
model
testing
result
Solenoid
parameters
Simulink
model
outputs
K(N/m)
B(Ns/m)
R(
)
num
dun2
dun3
T
est1
1101.8
3.60
8.90
74.73
18.34
5684
T
est2
2775.5
2.76
10.40
137.74
14.05
14010
T
est3
2159.5
3.22
14.03
58.97
16.21
10870
T
able
4.
The
test
result
prediction
error
Actual
v
alues
(NN
input)
Predicted
v
alues
(simulink
model
output)
Relatif
prediction
error
num
dun2
Dun3
num
dun2
dun3
num
dun2
Dun3
T
est1
74.23
18.28
5883
74.73
18.34
5684
0.67%
0.30%
0.01%
T
est2
137.86
14.03
14010
137.74
14.05
14010
0.08%
0.13%
0%
T
est3
59.12
16.21
10871
58.97
16.21
10870
0%
0%
0.003%
6.
CONCLUSION
In
this
article,
a
model-based
approach
for
detecting
f
aults
in
electromagnetic
solenoi
d
of
v
alv
es
w
as
proposed.
The
model
is
based
on
ANN
coupled
with
an
optical
fiber
polarization
squeezer
signal
feedback.
During
a
v
oltage
step,
the
coef
ficients
of
the
transfer
function
of
the
mathematical
model
are
determined
from
the
step
response
of
the
actuator
model.
Then,
the
parameters
of
the
EMS,
sele
cted
as
the
health
indices
of
the
solenoid
v
alv
e,
are
determined
from
the
ANN
model.
The
results
of
this
model
ha
v
e
been
v
erified
through
simulation
on
MA
TLAB/Simulink.
The
propose
d
neural
netw
orks
model
has
satisf
actory
performance
of
prediction
and
has
met
the
monitoring
requirement.
Thus,
this
contrib
ution
pro
vides
a
no
v
el
approach
on
f
ault
diagnostics
in
h
ydraulic
systems.
It
consists
only
of
softw
are
and
optical
fiber
.
Additionally
,
e
xpensi
v
e
Int
J
Elec
&
Comp
Eng,
V
ol.
11,
No.
2,
April
2021
:
1697
–
1708
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