Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 3,
J
une
2
0
1
4
,
pp
. 37
2~
37
7
I
S
SN
: 208
8-8
7
0
8
3
72
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Predi
c
ti
on of L
o
ad in Revers
e E
x
trusion Process
of Holl
ow
Parts using Modern Artifici
al Intelligence Approaches
M. Sh
ariat
P
a
nahi
*, N.
Mos
h
taghi Yaz
d
ani**
Departem
ent
of
M
echani
cal
Eng
i
neering
,
Univ
ers
i
t
y
of
T
e
hran
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 14, 2013
Rev
i
sed
Ap
r 3, 20
14
Accepted Apr 19, 2014
Extrusion is one of the important
processes to manufacture
and produce
m
ilitar
y
and ind
u
strial com
ponents. Desi
gning it
s tools is usually
associ
ated
with trial and
error and needs great
exp
e
rtise and adequate
experience.
Reverse extrusion process is k
nown as one of the common p
r
ocesses for
production of hollow parts with closed e
nds. The
significant load
required in
formation of
a
workpiece is on
e of
th
e
exist
i
n
g
constra
i
nts for
the
rev
e
rse
extrus
ion proces
s
.
This
is
s
u
e becom
e
s
rather diffi
cult es
pe
cia
l
l
y
f
o
r the parts
having thin walls since its
analy
s
is using finite elem
ent softwares is exposed
to som
e
lim
itati
ons. In this regard, a
ppl
ica
tion
of artifi
c
ia
l inte
l
ligen
ce for
predic
tion of
loa
d
in th
e r
e
verse
extrusion pro
ces
s will not
onl
y s
a
ve
tim
e an
d
money
,
bu
t also improve quality
fe
atur
es of the product. B
a
sed on th
e
existing d
a
ta and
methods suggested fo
r v
a
riation
s
of punching fo
rce th
rough
the rev
e
rs
e ex
tru
s
ion proces
s
,
the
s
y
s
t
em
is
tra
i
ne
d and then p
e
rfo
rm
ance of
the s
y
stem
is evalua
ted using the test data in th
is paper. Effi
ci
e
n
c
y
of th
e
proposed metho
d
is also assessed via co
mpariso
n
with
the results of others
.
Keyword:
in
tellig
en
t app
r
o
ach
es
p
r
ed
ictio
n of l
o
ad
reve
rse e
x
tr
usi
o
n
th
ird sim
u
latio
n
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
N.
M
o
sh
tagh
i Yazd
an
i,
Depa
rtem
ent of
M
ech
atroni
cs
,
Universit
y
of
T
e
hran Kish In
tern
ation
a
l C
a
m
pus
,
Ki
sh Isl
a
nd
,
I
r
a
n.
Em
a
il: n
a
v
i
d
.
m
o
sh
tag
h
i
@u
t.ac.ir
1.
INTRODUCTION
Ex
tru
s
ion
is a
si
m
p
le fo
rm
in
g
p
r
o
cess i
n
wh
i
c
h
a
p
r
eca
st b
illet is first pu
t in
cylin
d
e
r
o
f
t
h
e ex
tru
s
ion
mach
in
e. Th
en, th
is b
illet flo
w
s ou
tward
from th
e d
i
e th
at
i
s
in
d
i
rect con
t
act with
th
e cylin
d
e
r
b
y
ap
p
l
i
catio
n
of a
great load
whic
h is i
n
troduced
hy
dra
u
lically or m
echanically [1].
Figure
1. Reve
rse e
x
trusion
proces
s:
(1) die;
(2)
workpiece;
and
(3)
punc
h
Ext
r
usi
o
n i
s
m
a
i
n
l
y
di
vi
de
d i
n
t
o
t
h
ree g
r
ou
p
s
i
n
t
e
rm
s of d
e
fo
rm
ati
on an
d
t
y
pe of t
h
e
pr
ocess:
di
rect
ext
r
usi
o
n, i
ndi
r
ect
ext
r
usi
o
n,
3
3
3
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
37
2 – 3
7
7
3
73
In
di
rect
(f
o
r
w
a
rd
) ext
r
usi
o
n
,
t
h
e pu
nc
h an
d
t
h
e di
e ha
ve horiz
ontal positions
, whereas the m
a
terial
u
n
d
e
r d
e
fo
rm
atio
n
an
d th
e
pun
ch m
o
v
e
in
t
h
e sam
e
d
i
rectio
n
.
Th
e l
o
ad is
ap
p
lied to
end
o
f
t
h
e
b
illet with
th
e
metal flo
w
in
g
t
o
ward
th
e force. Th
ere is so
m
e
frictio
n
b
e
tween
th
e
b
illet an
d
t
h
e cylin
d
e
r su
rroun
d
i
ng
it. Th
is
technique has
an
a
dva
ntage
o
us
sim
p
le desi
gn and i
n
hot
direct e
x
tr
usion, t
h
e e
x
trude
d
workpiece c
a
n
be
easily co
n
t
ro
lled
and
coo
l
ed
.
Nev
e
rth
e
less, ex
isten
ce of
frictio
n
in
th
e con
t
act area b
e
tween
th
e b
illet an
d
th
e
cy
l
i
nder an
d
heat
gene
rat
e
d t
h
ere
o
f
,
fo
r
m
at
i
on of n
o
n
-
u
ni
fo
rm
m
i
crost
r
uct
u
re a
nd t
h
us n
o
n
-
uni
fo
r
m
properties along the ext
r
ude
d
workpiece,
greater deform
ation loa
d
in c
o
m
p
arison with non-direct e
x
trusi
o
n,
as well as
formation of i
n
ternal
de
fects
particularly
in
ex
isten
ce of frictio
n
,
in
tro
ductio
n
o
f
su
rface an
d
subsurface im
purities to the
wo
rkpiece,
appe
arance of funnel-sha
p
ed
ca
vi
t
y
at the end
of the billet and
thus,
ex
cessiv
e
th
ickn
ess
o
f
th
e remain
in
g b
illet as
scrap are
so
m
e
seriou
s d
i
sad
v
an
tag
e
s of th
e
d
i
rect ex
tru
s
ion
.
In
di
rect
(bac
k
w
ar
d
or
re
ve
rs
e) e
x
t
r
usi
o
n i
s
t
h
e sa
m
e
as t
h
e
direct e
x
trusion proc
ess e
x
cept
that the
p
u
n
c
h
is
fix
e
d
wh
ile th
e
d
i
e
m
o
v
e
s [2
]. Flow
o
f
th
e m
e
tal
is op
po
site to th
e lo
ad
app
licatio
n
.
M
o
reov
er, th
ere
is no friction
between the
billet and
its surrounding cylinde
r. Taki
ng in
to
account hollow sh
a
p
e of the
punch
in
th
e ind
i
rect
ex
tru
s
ion
pro
c
ess, th
er
e are
practically so
m
e
li
mitatio
n
s
in
term
s o
f
th
e lo
ad
as co
m
p
ared
to
th
e
di
rect
ext
r
usi
o
n. T
h
i
s
m
e
t
hod be
nefi
t
s
f
r
o
m
several
ad
v
a
nt
ages;
i
n
cl
ud
i
ng
20
-3
0% s
m
al
l
e
r l
o
ad re
qui
red i
n
com
p
ari
s
on
wi
t
h
t
h
e di
re
ct
ex
t
r
usi
o
n
owi
ng t
o
i
t
s
no
-f
ri
ct
i
o
n co
n
d
i
t
i
on, a
n
d t
e
m
p
erat
ure
on
o
u
t
e
r l
a
y
e
r
of t
h
e
b
illet is n
o
t
in
creased
b
ecau
s
e th
ere
is n
o
frictio
n
b
e
tween
t
h
e b
illet an
d
th
e cylin
d
e
r. As a resu
lt, d
e
formatio
n
will b
eco
m
e
un
ifo
r
m
an
d
form
at
io
n
of
d
e
fects an
d crac
ks on
co
rn
ers an
d surface of
th
e produ
ct wi
ll b
e
di
m
i
ni
shed
. T
h
e i
n
di
rect
ext
r
usi
on
pr
ocess
at
hi
gh de
f
o
r
m
at
i
on rat
e
s i
s
pos
si
bl
e esp
eci
al
l
y
for al
um
i
num
materials
wh
ich
are p
r
essed
with
d
i
fficu
lty.
Surface im
puri
ties of the billet do en
te
r the
final product
so that th
e funnel-shape
d ca
vity is not
form
ed due to existence of fri
ction.
But inste
a
d, these im
purities can also
appea
r
on surface of the workpiece
.
Li
fe of t
h
e de
f
o
rm
at
i
on t
ool
e
s
peci
al
l
y
i
nner
l
a
y
e
r of t
h
e cy
l
i
nde
r i
s
en
hanc
ed d
u
e t
o
e
x
i
s
t
e
nce o
f
t
h
e
fri
c
t
i
on.
In
di
rect
e
x
t
r
usi
o
n
ha
s s
o
m
e
di
sad
v
ant
a
ges i
n
spi
t
e
of
i
t
s
n
u
m
erous
ad
va
nt
ages,
i
n
cl
u
d
i
n
g
l
i
m
i
t
e
d def
o
r
m
at
i
o
n
load, less
facilities for c
o
olin
g the extruded
workpiece afte
r leaving the
die, lower
quality of outer surface of
t
h
e p
r
od
uct
.
Im
p
act ex
tru
s
io
n
acts b
y
p
e
rform
i
n
g
i
m
p
a
c
t
s in
wh
ich
d
i
e an
d
pun
ch
are p
o
s
itio
ned
v
e
rtically
and
th
e
p
u
n
c
h
im
p
acts on
the
b
illet to
g
i
v
e
sh
ape of th
e
d
i
e and
its su
rro
und
in
g cylin
d
e
r. Th
is form
in
g
pro
cess is
som
e
t
i
m
e
s kno
wn
as a
t
y
pe
of
f
o
r
g
i
n
g
pr
oces
ses.
Eco
nom
i
c
si
gni
fi
cance
of t
h
e i
m
pact
extrusi
on i
s
ass
o
ciated with effec
tiv
e app
licatio
n
of raw
material, redu
ced
labor co
sts, eli
m
in
atio
n
of in
term
ed
iate o
p
e
ration
s
, im
p
r
ov
ed qu
ality of th
e produ
ct, and
g
r
eat yield
wi
th
relativ
ely si
m
p
le to
o
l
s. So
m
e
ad
v
a
n
t
ages o
f
th
is m
e
th
od
are listed
b
e
low: sav
i
n
g
in
co
nsu
m
p
tio
n
of th
e raw m
a
t
e
rials sin
ce all
o
r
a m
a
j
o
r part o
f
th
e in
itial b
illet
is tra
n
sfo
r
m
e
d
to
the fin
a
l
pr
o
duct
an
d t
h
e am
ount
of
w
a
st
ed raw m
a
t
e
ri
al
i
s
negl
i
g
i
b
l
e
, red
u
ct
i
o
n or
el
im
i
n
at
i
on of
t
h
e fi
nal
m
achi
n
i
n
g
tools; exam
ples pre
p
are
d
by this
m
e
thod
provi
de accepta
ble dim
e
nsiona
l
tolerances a
n
d surface
roughne
ss
(3
5
0
-
7
5
0
µm
), so t
h
ey
are co
m
p
l
e
t
e
l
y
usabl
e
and ne
ed
no
fu
rt
he
r m
achi
n
i
ng,
usi
n
g l
e
ss expe
nsi
v
e m
a
teri
al
s i
s
p
o
s
sib
l
e, m
a
n
y
o
f
t
h
e p
a
rts, if m
a
n
u
f
actured
b
y
con
v
e
n
t
io
n
a
l m
ach
in
ing
techn
i
qu
es,
will n
eed
a series of
prel
i
m
i
n
ary
op
erat
i
ons
, l
i
k
e
r
o
l
l
i
ng,
d
r
awi
n
g a
nd et
c.
p
r
ior to
p
r
od
u
c
tion, wh
ile in
im
p
act ex
trusion
an
d
b
y
u
s
ing
a cylin
drical b
illet, th
e fin
a
l
p
r
odu
ct
can
b
e
p
r
od
u
c
ed
thro
ugh
o
n
e sing
le pro
c
ess, redu
ced
costs of
ware
h
ousi
ng;
t
h
i
s
m
e
t
hod i
s
per
f
o
r
m
e
d aut
o
m
a
ti
cal
l
y
, so t
h
e o
p
er
at
i
ons
of l
o
adi
n
g
,
unl
oadi
ng
an
d m
a
t
e
ri
al
s
handling are c
onsi
d
era
b
ly de
creased, sim
p
li
city o
f
th
e p
r
o
c
ess; th
is p
r
o
cess is really si
m
p
le su
ch
th
at m
a
n
y
o
f
t
h
e com
pone
nt
s are m
a
de jus
t
t
h
ro
ug
h o
n
e
st
ep an
d t
h
ere
i
s
no nee
d
t
o
i
n
t
e
rm
edi
a
t
e
st
eps, g
r
eat
pr
o
d
u
ct
i
on
capacity; sm
a
l
l pa
rts ca
n
be m
a
de m
o
re
t
h
an
50 workpiece
per m
i
nute and this
rate reac
hes up t
o
15
parts per
min
u
t
es fo
r th
e larg
er
p
a
rts,
bo
tto
m
th
ick
n
e
ss of th
e
p
r
o
d
u
c
t is in
d
e
p
e
n
d
e
nt o
f
its wall th
i
c
k
n
e
ss, cap
a
b
ility to
m
a
nufact
ure
p
a
rt
s wi
t
h
z
e
r
o
separat
i
o
n a
n
gl
e, p
r
o
v
i
d
i
n
g excellent
m
echanical prope
r
ties and m
a
king a s
i
ngl
e
part
fr
om
sever
a
l
com
pone
nt
s.
On
t
h
e
ot
her
h
a
nd
, t
h
e
fol
l
o
wi
n
g
i
t
e
m
s
m
a
y
be m
e
nt
i
one
d as
t
h
e
m
a
i
n
di
sad
v
a
n
t
a
ges
of
t
h
e i
m
pact
ex
tru
s
ion
:
th
is p
r
o
cess is so
m
e
ti
m
e
s u
n
eco
no
m
i
c
;
f
o
r
ex
am
p
l
e
p
r
odu
ctio
n
o
f
allo
yed
steels an
d
h
i
g
h
car
bon
steels is not econom
i
c because they bot
h
require a significa
n
t pres
sure and
several interm
ediate pressi
ng and
anneal
i
n
g o
p
er
at
i
ons,
i
m
pact
ext
r
usi
o
n
i
s
us
ual
l
y
l
i
m
i
t
e
d
t
o
pr
od
uct
s
o
f
cy
l
i
ndri
cal
,
s
q
uare
, hexa
g
o
n
a
l
an
d
ellip
tical sect
i
o
n
s
o
r
o
t
h
e
r sy
mmetrical g
e
o
m
etries with
h
o
llow
o
r
so
lid
cro
ss section
s
, ap
p
lication o
f
th
e
im
pact
ext
r
usi
on i
s
n
o
t
rec
o
m
m
e
nded f
o
r
m
a
nufact
uri
ng
of
f-ce
n
t
e
r
part
s ha
vi
n
g
di
ffe
r
e
nt
wal
l
t
h
i
c
k
n
e
ss si
nce
th
ey im
p
o
s
e asy
m
m
e
tric an
d an
iso
t
ro
p
i
c l
o
ad
s t
o
t
h
e tool du
ring th
e
fo
rm
in
g
p
r
o
cess, rati
o
o
f
leng
th to
d
i
am
e
t
er is limited
fo
r
b
o
t
h
th
e pro
d
u
c
t
and
th
e
b
illet itself, im
p
a
c
t
ex
tru
s
ion
p
r
o
cess is rath
er cap
ital
con
s
um
i
ng wi
t
h
i
t
s
equi
pm
ent
bei
n
g rel
a
t
i
v
el
y
expe
nsi
v
e
;
t
h
eref
ore, m
a
ss pr
o
duct
i
o
n
wo
ul
d
be nee
d
ed t
o
make the
proce
ss econom
i
cally feasible.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Prediction
of Load i
n
Reverse
Extrusi
o
n Pro
cess
of Hollow Parts using M
ode
rn
Artificial
…
(
N.M
.
Yaz
d
ani
)
37
4
2.
SIGNIFIC
ANC
E OF LOAD
IN
REVE
R
S
E E
X
TR
US
I
O
N
PR
OCES
S
In
di
rect
(
r
eve
r
se) ext
r
usi
on i
s
one
o
f
t
h
e m
o
st
im
port
a
nt
pr
ocesses i
n
t
h
e ext
r
usi
o
n p
r
ocess. E
x
act
am
ounts of pre
ssing loa
d
and capacity
are critical because
designing the di
e and
punc
h, determ
ination of the
fo
rm
i
ng st
eps,
and m
a
t
e
ri
al
s sel
ect
i
on al
l
dep
e
nd
o
n
i
t
.
The
r
e are n
u
m
e
rous
fact
ors
w
h
i
c
h
affect
t
h
e e
x
t
r
u
s
i
on
load, som
e
of t
h
e m
o
st i
m
portant of
which are m
a
terial and
properties of
t
h
e work
piece, initial cross se
ction
of
the work piece,
ratio
of fri
ction betwee
n the
s
u
rfaces
,
s
h
ape
of t
h
e
work piece a
n
d
punc
h, and tem
p
erat
ure
of t
h
e p
r
ocess.
A g
r
eat
n
u
m
b
er o
f
ex
pe
ri
m
e
n
t
al
, anal
y
t
i
cal
and
n
u
m
e
ri
cal
m
e
t
hods
ha
ve
been a
d
dres
sed
i
n
t
h
e
literatu
re to
stu
d
y
pred
iction o
f
lo
ad
in
ex
tru
s
i
o
n
p
r
o
cesses [3
]. Exp
e
ri
men
t
al
meth
o
d
s u
s
u
a
lly d
e
mo
n
s
t
r
ate
po
o
r
per
f
o
rm
ance i
n
re
prese
n
t
i
ng e
x
act
de
t
a
i
l
s
of t
h
e pr
ocess an
d ha
v
e
l
i
m
i
t
e
d appl
i
cat
i
ons. M
ean
whi
l
e
,
fi
ni
t
e
el
em
ent
and
fi
ni
t
e
di
ffe
rence m
e
t
hod
s
need
g
r
eat
co
m
put
at
i
onal
t
i
m
e
and
po
wer
f
u
l
com
put
ers
.
Am
ong
the existing a
n
alytical
m
e
thods,
uppe
r
bound the
o
ry is t
h
e
one whic
h gi
ves
relatively accurate a
n
s
w
ers in
a
sh
ort ti
m
e
b
y
its si
m
p
le f
o
rm
u
lizatio
n
,
ev
en
t
h
oug
h
th
e wo
rk
p
i
ece in
co
rpo
r
ates
m
a
n
y
co
m
p
l
e
x
ities.
M
acdo
r
m
o
t
t
et al
. [4]
ha
ve u
s
ed 8
basi
c el
em
ent
s
vi
a t
h
e abo
v
em
ent
i
one
d m
e
t
hod i
n
or
der t
o
p
r
edi
c
t
t
h
e l
o
a
d
requ
ired
in
fo
rg
ing
p
r
o
cess. Ou
t of th
em
, 4
rin
g
elem
en
ts
b
e
lo
ng
to
th
e
in
ward
fl
o
w
, wh
ile th
e o
t
h
e
r 4
ri
ng
el
em
ent
s
are re
l
a
t
e
d t
o
t
h
e
o
u
t
w
ar
d
fl
o
w
.
Ki
u
c
hi
et
al
. [
5
]
ha
ve
devel
ope
d a
m
e
t
hod
base
d
on
el
em
ent
a
l
upp
e
r
bo
u
n
d
t
ech
ni
q
u
e f
o
r si
m
u
l
a
ti
on
of
t
h
e m
e
t
a
l
form
i
ng
pr
ocesses
(e.
g
.
f
o
r
g
i
n
g)
, i
n
w
h
i
c
h st
rai
g
ht
f
o
r
w
ar
d
ele
m
en
ts h
a
v
e
b
een
u
s
ed
to
ob
tain
the form
ing
force.
Kim
et al. [6] have
esti
m
a
ted
th
e
material flo
w
in
the
fo
rgi
ng
pr
oces
s usi
n
g t
h
e el
e
m
ent
a
l
uppe
r
bo
u
nd m
e
t
hod
. The
r
eby
,
t
h
e
y
have bec
o
m
e
abl
e
t
o
p
r
edi
c
t
t
h
e
pre
f
orm
geometry as well as
the num
b
er
of
requ
ired
forg
i
n
g
step
s in
th
is
process
.
Bae et al. [7]
have
adopte
d
the elem
ental
uppe
r bound a
p
proach t
o
a
n
alyze and
ge
t
th
e lo
ad
n
eed
ed
for th
e
re
ver
s
e ext
r
usi
o
n
p
r
oces
s
three
dim
e
nsionally. The loa
d
increases
t
h
roughout the
workpiece
due t
o
grow
th
of t
h
e friction s
u
rfaces
at the
fin
a
l step and th
is reg
i
m
e
is in
ten
s
ified
at
th
e
fin
a
l step.
3.
KSTA
R ALG
O
RITH
M
This is an
exa
m
ple-base
d l
earne
r whic
h
classifi
es every new
record by
co
m
p
aring
it with
th
e
ex
istin
g
classified
record
s in
t
h
e d
a
tab
a
se. It
is assu
m
e
d
in
th
is alg
o
r
ith
m
th
at th
e si
m
i
lar ex
am
p
l
es h
a
v
e
th
e
sam
e
cl
asses. Tw
o basi
c c
o
m
ponent
s
of t
h
e exam
pl
e-ba
sed l
ear
ners a
r
e di
st
ance f
u
n
c
t
i
on an
d cl
ass
i
fi
cat
i
on
fun
c
tion
.
Th
e fo
rm
er d
e
term
i
n
es th
e sim
i
larity b
e
tween
exa
m
p
l
es an
d
th
e latter sh
o
w
s
ho
w sim
ilarit
y
o
f
th
e
exam
ples leads
to a
final class
for t
h
e
new exa
m
ple.
Kstar algo
rithm is
a
lazy
lea
r
n
e
r o
f
K-n
earest n
e
ig
hb
orh
o
o
d
learn
i
ng
which
u
s
es a fatig
u
e
criteri
on
to address
distance
or sim
i
la
rity of t
h
e e
x
a
m
ples to
each
othe
r. T
h
e
approac
h
a
d
opte
d
by this al
gorithm
to
m
easure t
h
e di
st
ance bet
w
ee
n t
w
o e
x
am
pl
es i
s
deri
ve
d f
r
o
m
i
n
form
at
i
o
n t
h
e
o
ry
. I
n
t
h
i
s
regar
d
, t
h
e di
st
anc
e
betwee
n two e
x
am
ples includes t
h
e c
o
m
p
lexity of c
o
n
v
e
r
t
i
n
g
o
n
e e
x
a
m
pl
e t
o
anot
he
r o
n
e
.
M
eas
ure
m
ent
of
t
h
e com
p
l
e
xi
t
y
i
s
done i
n
t
w
o
st
eps:
fi
rst
,
a const
a
nt
set
of con
v
e
r
si
o
n
s i
s
defi
ne
d whi
c
h m
a
ps som
e
exam
pl
es
t
o
som
e
ot
her exam
pl
es. A pro
g
ram
for co
n
v
ersi
on
of exa
m
pl
e "a"
t
o
exam
pl
e "b" i
nvo
l
v
es a const
a
nt
set
of
con
v
e
r
si
o
n
s w
h
i
c
h st
art
s
w
h
i
c
h "a" an
d e
nds t
o
"b"
.
T
h
ese
pr
og
ram
s
are t
y
pi
cal
l
y
m
a
de by
ad
d
i
ng a
termin
atio
n
sign
to
each
string
. C
o
m
p
lex
ity
o
f
a program
i
s
g
e
n
e
rally d
e
fin
e
d
as leng
th
o
f
t
h
e sh
ortest
string
represe
n
ting it. Therefore, the
distan
ce bet
w
een t
w
o ex
am
pl
es i
s
l
e
ngt
h of t
h
e sh
o
r
t
e
st
st
ri
ng
whi
c
h con
v
e
r
t
s
t
w
o exam
pl
es t
o
o
n
e an
ot
he
r.
Thi
s
ap
pr
oac
h
conce
n
t
r
at
es
o
n
o
n
e co
n
v
ersi
on
(t
he s
h
o
r
t
e
s
t
one) am
ong a
l
l
t
h
e
pos
sible c
o
nve
r
sions
[8].
4.
SVM ALGO
RITHM
SVM is an
alg
o
rith
m
fo
r classificatio
n
of lin
ear an
d
non
lin
ear
d
a
ta. It in
itial
l
y u
s
es a n
o
n
lin
ear
map
p
i
ng
fo
r con
v
e
rsion
of th
e in
itial d
a
ta
to
h
i
gh
er
d
i
m
e
n
s
i
o
n
s
and
later lo
ok
s for th
e b
e
st h
y
p
e
r-p
l
an
e in
th
e
new
di
m
e
nsi
ons. T
h
i
s
hy
pe
r
-
pl
a
n
e i
n
cl
u
d
e
s
a deci
si
on
b
o
u
n
d
ary
w
h
i
c
h
separat
e
s rec
o
rds
of
one cl
as
s fr
o
m
ot
he
r cl
asses
.
The
dat
a
m
a
rk
ed as
bel
o
n
g
i
n
g t
o
di
ffe
rent
c
l
asses are
si
m
p
l
y
separat
e
d
by
a
hy
per
-
p
l
a
ne
wi
t
h
a
no
nl
i
n
ea
r m
a
ppi
n
g
. S
V
M
fi
n
d
s t
h
i
s
hy
per
-
p
l
ane usi
n
g s
u
p
p
o
r
t
vect
ors a
n
d m
a
rgi
n
s w
h
i
c
h are
defi
ned
by
t
h
e
support
vectors. T
h
ere
are
va
rio
u
s decisio
n
bo
u
nda
ries fo
r separatio
n o
f
t
h
e
data ass
o
cia
t
ed with e
v
ery
class.
Howe
ver, current researc
h
work aim
s
to find the
deci
si
on b
o
u
n
d
ary
or
t
h
e
se
pa
rat
i
ng hy
pe
r-
pl
an
e
wi
t
h
m
a
x
i
mu
m
m
a
r
g
i
n
(
i
.
e
.
ma
x
i
mu
m
ma
r
g
i
n
h
y
p
e
r
-
p
l
a
n
e
o
r
MMH) which
separates t
h
e data at greater a
ccuracy
an
d lower error.
A
d
a
ta is d
e
e
m
ed
lin
ear
wh
en it is se
pa
ra
bl
e by
usi
n
g a
l
i
n
ear d
eci
sio
n
bo
und
ar
y.
No d
i
r
ect
lin
e m
a
y sep
a
rate d
a
ta fro
m
d
i
fferen
t
classes wh
en
th
e
dat
a
i
s
n
o
n
l
i
n
ear
.
For
t
h
ose
dat
a
whi
c
h a
r
e se
pa
rabl
e
linearly, the support vectors are a subs
et of learni
ng rec
o
rds which a
r
e located on the margi
n
s. Ne
vert
heless
,
th
e pro
b
l
em
is a b
it d
i
fferen
t
fo
r th
e
no
n
lin
ear
d
a
ta.
Once t
h
e MMH and s
u
pport
vectors are
obt
ained, a
l
e
a
r
nt
SVM
w
o
ul
d
b
e
avai
l
a
bl
e. A
l
earnt
SVM
i
s
fo
un
d as a
f
unct
i
o
n
of s
u
p
p
o
r
t
vect
ors
,
t
e
st
reco
rds
,
co
n
s
t
a
nt
s an
d La
g
r
an
gea
n
pa
ram
e
t
e
rs ve
rsu
s
su
pp
o
r
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
37
2 – 3
7
7
3
75
vect
o
r
s
by
eq
u
a
t
i
ons
rel
a
t
e
d t
o
t
h
e
m
a
rgi
n
s
and
hy
per
-
pl
a
n
e fol
l
owe
d
by
rew
r
i
t
i
ng
o
f
t
h
em
by
Lag
r
an
gean
form
u
l
a an
d
solv
in
g th
is
p
r
ob
le
m
b
y
HHR con
d
ition
s
.
Th
e appro
a
ch
u
tilized
for a lin
ear SVM can
also
ex
tend
ed
fo
r creatin
g
a n
o
n
lin
ear
SVM. Su
ch
an
algorithm
of SVM can
get nonlinea
r
decision
boundary for t
h
e input s
p
ace.
De
velopment of this approa
c
h
has t
w
o m
a
i
n
st
eps:
i
n
t
h
e fi
rst
st
ep, t
h
e i
n
put
dat
a
i
s
t
r
an
sfer
red t
o
one
hi
g
h
er
di
m
e
nsion
usi
n
g a no
n
l
i
n
ear
map
p
i
ng
. Th
ere are a larg
e
nu
m
b
er of non
lin
ear m
a
p
p
i
ng
s at
th
is step
which
can
b
e
u
tilized
for th
is
p
u
rpo
s
e.
Once the
data were m
a
pped to a space of
highe
r dim
e
nsi
ons, the sec
o
nd step will
search the ne
w spa
ce for
th
e lin
ear sep
a
ratin
g
h
y
p
e
r-p
lan
e
. Fin
a
lly, an
op
ti
m
i
zatio
n
p
r
ob
lem
o
f
seco
nd
d
e
gree will b
e
o
b
t
ain
e
d
wh
ich
can be s
o
l
v
ed
by linear SVM
form
ul
a. The
MMH found i
n
the
new s
p
ac
e
i
s
i
ndi
cat
i
v
e of
a no
nl
i
n
ea
r hy
pe
r-
plane i
n
the ini
tial space [9].
5.
XC
S
A
L
G
O
R
I
T
H
M
An e
x
t
e
n
s
i
v
e r
a
nge
o
f
l
earni
ng al
go
ri
t
h
m
s
are em
pl
oy
ed either supe
rvis
ed or
not in t
h
e conte
x
t
of
m
achi
n
e l
earni
ng t
o
st
o
p
t
h
e
m
achi
n
e fro
m
searchi
ng a
l
a
rge vol
um
e of i
n
f
o
rm
at
i
on an
d dat
a
. It
furt
her
sug
g
est
s
a pat
t
ern w
h
i
c
h ca
n be use
d
f
o
r
t
h
e predi
c
t
a
b
l
e (cl
a
ssi
fi
cat
ion a
nd re
g
r
es
si
on
) or
descr
i
pt
i
v
e
(cl
u
st
eri
n
g
)
act
i
ons
. Tec
h
ni
q
u
e
s w
h
i
c
h
w
o
rk
base
d
o
n
ru
les
are
known as
the m
o
st fam
ous m
achine lea
r
ni
ng
m
e
t
hods
, si
nce
t
h
ey
are
m
o
re com
p
rehe
nsi
b
l
e
i
n
com
p
ari
s
on
wi
t
h
ot
her
t
echni
que
s t
h
a
n
ks t
o
t
h
e
ap
pr
o
ache
s
they comm
only adopt.
They
use a
l
i
m
i
t
e
d set
of
“act
i
on”
an
d “c
o
n
d
i
t
i
on”
r
u
l
e
s t
o
s
h
ow
a sm
all
co
nt
ri
b
u
t
i
o
n
of
t
h
e
w
hol
e
so
lu
tion
sp
ace. The co
nd
ition
s
ad
dress a
p
a
rt
o
f
th
e
p
r
o
b
l
em
d
o
m
ain
,
wh
ereas th
e actio
n
s
ind
i
cate th
e
d
ecision
b
a
sed o
n
t
h
e sub-
pr
ob
lem
s
sp
ecified by the c
o
ndit
i
on. Basically,
the classification system
s include a
set o
f
ru
les in wh
ich
ev
ery
ru
le is an
approp
riate so
luti
on for t
h
e target problem
.
These classi
fications
g
r
adu
a
lly b
ecome effectiv
e
b
y
app
licatio
n o
f
a rei
n
fo
rce
m
en
t p
l
an
wh
ich
h
a
s
g
e
n
e
tic alg
o
r
ith
m
s
on
its
separat
o
rs
.
The
fi
rst
cl
ass
i
fi
cat
i
on sy
st
em
was pr
o
p
o
s
ed by
Hol
l
a
nd
i
n
o
r
de
r t
o
w
o
r
k
f
o
r b
o
t
h
t
h
e i
n
di
vi
dual
pr
o
b
l
e
m
s
and cont
i
n
u
ous
p
r
o
b
l
e
m
s
(LC
S
). T
h
i
s
l
ear
ni
ng system
cla
ssifies an
exa
m
ple of the machine
learning
whic
h com
b
ines temporal di
ffe
renc
es and lear
n
e
r’s sup
e
rv
ision
s
with
gen
e
tic alg
o
rith
m
an
d
so
lv
es
sim
p
l
e
and di
f
f
i
c
ul
t
pr
o
b
l
e
m
s
. Acc
o
r
d
i
n
g t
o
t
h
e su
pe
rvi
s
i
on s
u
ggest
e
d
by
Hol
l
a
nd
, t
h
e LC
S uses a
si
ngl
e
property (calle
d power) for
each
of t
h
e cl
assifiers.
Po
wer of a se
pa
rator
de
notes a
f
fectability of it and is
exclusi
v
ely de
termined by
percenta
ge
the
answer c
o
rrela
t
es
with
th
e ex
p
ected
resu
lt
s. The
s
e criteria are
characte
r
ized by
pri
n
ciples
o
f
su
perv
isor
y
tr
ain
i
n
g
.
Fro
m
th
e first in
trodu
ctio
n
o
f
th
e
m
a
in
lear
n
i
ng
classificatio
n
system
s
(LCS), so
m
e
o
t
h
e
r typ
e
s of
t
h
e LC
S are pr
op
ose
d
so fa
r i
n
cl
u
d
i
n
g XC
S.
B
e
fore 1
9
95
whe
n
t
h
e ext
e
nde
d cl
assi
fi
ca
t
i
on sy
st
em
w
a
s not
d
e
v
e
l
o
p
e
d
yet, ab
ility o
f
a cl
assificatio
n
sy
ste
m
to
fin
d
pro
p
e
r an
swers i
n
th
e
reinforcemen
t syste
m
o
f
th
ese
classifiers
was
of m
a
jor concern. T
h
ere
b
y, basic a
n
d
sim
p
le classification system
s were c
h
ange
d to
m
o
re
accurate
decision m
a
king fa
ctors.
Now,
it is firmly believed t
h
at the
XCS is able to sol
v
e eve
n
m
o
re
com
p
licated problem
s with no nee
d
to
further adjust the param
e
ters. As
a
result, it is
c
u
rr
ently accounted
for
the m
o
st succe
ssful lea
r
ni
ng s
y
ste
m
.
6.
IMP
R
O
V
ED X
C
S
In t
h
e s
u
g
g
est
e
d m
e
t
hod,
fi
r
s
t
l
y
t
h
e l
i
m
i
t
e
d set
of t
r
ai
ni
n
g
dat
a
i
s
com
m
onl
y
appl
i
e
d
fo
r am
endi
n
g
ch
aracteristics o
f
ru
les con
s
ists o
f
pred
ictio
n, pred
iction error and
fitne
ss. Thi
s
i
s
d
one
by
m
eans of t
h
e
fo
llowing
relatio
n
:
Up
dat
i
n
g
pre
d
i
c
t
i
on a
n
d
p
r
e
d
i
c
t
i
on e
r
r
o
r
If e
x
pi
<
1/
β
t
h
en Pi =Pi +
(
R
-Pi) / e
x
pi,
ε
i=
ε
i+(|
R-Pi|-
ε
i) / expi
(1)
If e
x
pi
≥
1/
β
t
h
en Pi =Pi +
β
(R-Pi)
,
ε
i=
ε
i+
β
(|
R-Pi|-
ε
i) (2)
Upd
a
ting
fitn
ess:
If
ε
i <
ε
0 th
en
k
i
=1
(
3
)
If
ε
i
≥
ε
0 t
h
en
ki
=
β
(
ε
i/
ε
0)
–
γ
(4
)
Fi = fi+
β
[(
k
i
/
∑
k
j
) – fi]
(5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Prediction
of Load i
n
Reverse
Extrusi
o
n Pro
cess
of Hollow Parts using M
ode
rn
Artificial
…
(
N.M
.
Yaz
d
ani
)
37
6
In t
h
ese
relations
,
β
is learnin
g
rank
,
γ
is
powe
r of law
accuracy,
ε
is
p
r
ed
ictio
n error, ex
p is law
expe
rim
e
nt, P
is law pre
d
iction, R is reward receive
d fr
om environm
ent, k is law accu
racy and
f is fitness. i
in
d
e
x
also
ind
i
cates nu
m
b
er of law in
set
of ru
les.
In
t
h
e
ne
xt
p
h
a
s
e f
o
r
de
vel
o
pi
ng
va
ri
et
y
i
n
s
e
t
of
dat
a
,
se
ve
ral
co
u
p
l
e
s
we
re sel
ect
ed
as
p
a
rent
s
fr
om
am
ong
t
h
e
fi
el
ds t
h
at
di
spl
a
y
t
h
e pa
rt
of e
x
i
s
t
i
ng dat
a
c
o
n
d
i
t
i
on
usi
n
g t
h
e m
e
t
hod
o
f
“
S
t
o
cha
s
t
i
c
sel
ect
i
on
with
rem
a
in
d
e
r”², and
n
e
w
data co
nd
itio
n sectio
n
is cr
eated
u
s
ing
in
termed
iate cro
s
sov
e
r m
e
th
od
wh
ich
are
ap
p
lied
on
th
e
field
s
of
p
a
rents. In
t
h
is m
e
th
o
d
, th
e
q
u
a
n
tity o
f
each
of the co
nd
itio
nal variab
les is ob
tain
ed
fro
m
th
e fo
llowing
relatio
n
:
a
i
=
α
(a
i
F
)+(
1
-
α
)( a
i
M
) (
6
)
in
wh
ich
a
i
is th
e qu
an
tity o
f
co
nd
itio
n
a
l
v
a
riab
le o
f
i in
n
e
w d
a
ta, a
i
F
is th
e qu
an
tity o
f
co
nd
itio
n
a
l
varia
b
le i in
the
first
pare
nt
(fat
h
er
),
a
i
M
is th
e
q
u
a
n
tity of co
nd
ition
a
l v
a
riab
le
o
f
i
in
th
e seco
nd
p
a
ren
t
(m
ot
her) a
n
d
α
i
s
t
h
e c
o
ef
fi
ci
ent
o
f
pare
nt
s pa
rt
ne
rshi
p
wh
ich
are
d
e
term
in
ed
in
ad
ap
tiv
e
form
. New
d
a
ta
sect
i
on pe
rf
o
r
m
a
nce i
s
al
so pr
o
duce
d
u
s
i
n
g a n
o
n
-
l
i
n
ear
m
a
p
p
i
ng
of
co
nd
itio
n
a
l
vari
ables area to a
r
ea of
per
f
o
r
m
a
nce w
h
i
c
h a
r
e c
r
eat
e
d
by
usi
n
g t
h
e
exi
s
t
i
n
g
dat
a
.
Di
ve
rsi
f
y
i
n
g
t
h
e exi
s
t
i
n
g dat
a
cont
i
n
ues
up
t
o
wh
ere l
ear
ni
n
g
st
o
p
co
n
d
i
t
i
on
(f
or e
x
a
m
pl
e, whe
n
perce
n
t of syste
m
correct ans
w
ers t
o
the tes
t
data reach
to a pre-determ
ined t
h
res
h
old) is satisfied aided
by
com
p
l
e
t
e
d dat
a
[
11]
.
7.
RESULTS
A
N
D
DI
SC
US
S
I
ON
Ex
peri
m
e
nt
s [10]
wa
s sel
ect
ed i
n
rel
a
t
i
o
n
wi
t
h
t
h
e re
ve
rs
e ext
r
usi
o
n p
r
ocess
of al
um
inum
part
s i
n
or
der t
o
c
o
m
p
are effi
ci
ency
of t
h
e m
odel
s
devel
ope
d by
t
h
e ab
ovem
e
nt
i
one
d al
g
o
ri
t
h
m
s
. The dat
a
ext
r
act
ed
fr
om
t
h
ese exp
e
ri
m
e
nt
s cont
ai
ns som
e
24
0
dat
a
ent
r
i
e
s
,
o
u
t
o
f
w
h
i
c
h
2
0
0
ent
r
i
e
s are
r
a
nd
om
l
y
sel
e
cted f
o
r
train
i
ng
with
t
h
e
rem
a
in
in
g
bein
g
cho
s
en
for testin
g.
Displacem
ent of t
h
e
punc
h,
coeffici
ent of
friction, diam
eter of t
h
e
punc
h, ci
rcum
ferential dia
m
eter
of t
h
e di
e
p
o
l
y
go
nal
,
a
n
d n
u
m
ber of si
de
s
of t
h
e w
o
rk
pi
e
ce are t
a
ke
n as
i
n
p
u
t
va
ri
abl
e
s of t
h
e
pr
obl
e
m
, whi
l
e
the punchi
n
g l
o
ad is c
onsi
d
ered to be
the
output.
Fi
gu
re
2.
Pract
i
cal
t
e
st
i
ng o
f
t
h
e
reve
rse e
x
t
r
usi
o
n
pr
ocess
A co
m
p
ariso
n
b
e
tween
th
e th
ree trained algo
rith
m
s
g
i
v
e
s th
e
fo
llowing
resu
lts.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
37
2 – 3
7
7
3
77
Tabl
e 1. Pre
d
i
c
t
i
on of
l
o
a
d
i
n
reve
rse
e
x
t
r
usi
o
n
p
r
ocess
Algor
ith
m
Kstar
SVM
Im
pr
oved
xcs
XCS
Accur
a
cy 83.
9%
91.
4%
92.
8%
88.
6%
8.
CO
NCL
USI
O
N
R
e
verse e
x
t
r
u
s
i
on i
s
a com
m
on
pr
ocess f
o
r
m
a
nufact
u
r
i
n
g h
o
l
l
o
w
pars
wi
t
h
cl
ose
d
en
ds an
d t
h
u
s
has num
e
rous
applications in diffe
re
nt industries. Th
e significant
loa
d
requi
red
for forming the workpiece is
one
o
f
t
h
e m
a
in
dra
w
backs
o
f
t
h
e
re
ver
s
e e
x
t
r
usi
o
n
pr
oce
ss.
A l
o
a
d
p
r
e
d
i
c
t
i
o
n
sy
st
em
i
s
de
vel
o
pe
d i
n
t
h
i
s
research
b
a
sed on
t
h
e info
rmatio
n
g
a
th
ered fro
m
rev
e
rse
ex
tru
s
ion
forge an
alysis an
d artificial in
tellig
en
ce
alg
o
rith
m
s
. Th
ese resu
lts m
a
y p
r
op
erly con
t
ribu
te to
improve the reverse extrusion proce
ss consi
d
eri
n
g
accuracy
of ea
ch
of them
in the test
phase
(a
s summ
arized in Ta
ble
1).
REFERE
NC
ES
[1]
Yang, D. Y., Kim, Y. U. and
Lee, C. M
.
(1992). “Analy
sis
of center-shifted back
ward
extrusion
of eccentric tub
e
s
using round pun
ches”,
Journal o
f
Materials Processing Technolo
g
y
, Vol. 33
, PP.
289-298.
[2]
Bae, W. B
.
and
Yang, D. Y. (19
93)
. “An upper bound analy
s
is
of the backward
extrusion of tub
e
s of complicated
intern
al shap
es f
r
om round billets”.
Journal of M
a
terials
Processing Technolog
y
,
Vol. 36
, PP. 157
-173.
[3]
Bae, W. B. and
Yang, D. Y
.
(19
93). “An analy
s
is of b
ackward
extrusion of in
ter
n
ally
cir
c
ular-sh
a
ped tub
e
s from
arbitr
aril
y
-
shap
ed billets b
y
th
e upper bound m
e
thod”.
Journal o
f
Materials Processing Technology,
Vol. 36, PP.
175-185.
[4]
R.P Macdormott and A.N Bpunchley
. An elemen
tal upp
er bound
techn
i
que for general use
in forg
ing analy
s
is Pro
c
15 M.T.D.R Con
f
, (2002)
.
[5]
M. Kiuchi and Y. Murata.
Stud
y
on application
of UBET to
nonaxis
y
mmetric f
o
rging Adv.
Technol. of plasticity
,
vol. I
,
pp
9, (200
5).
[6]
Kim Y.
H,
“Computer
ai
ded
per
f
o
rm process”,
J.
of Mat
t
.
T
ech
, 4
1
(1994) p 105
.
[7]
W.B. Bae, An analy
s
is of back
ward extrusion
of in
tern
ally
cir
c
ular
shap
ed
billets b
y
upper-bo
und method,
J o
f
material processing technolog
y
, (
1993), 36
, pp
17
5.
[8]
I. H. W
itten and
E. Frank; Data
Mining (Practi
c
a
l
Mach
ine L
earn
i
ng Tools and Techniqu
es, San Francisco: Morg
an.
Kaufmann, 2007
.
[9]
J. Han
and M. Kamber; Data Mining Concepts
and Te
chniques
,
_San Francisco
:
Morgan Kaufmann, 2006
.
[10]
Ebrahimi, R., “Analy
sis of Rev
e
rse Forge Extrusion for
Manuf
actur
ing Hollow Parts”, Master of Science Th
esis,
Shiraz Univ
ersity
, 1997
, (in
Pers
ian).
[11]
M. Shariat Pan
a
hi, N. Moshtagh
i Yazdan
i, An I
m
proved
XCSR
Classifier S
y
s
t
em fo
r Data Mining with Limited
Train
i
ng Samples,
Global
Journal of S
c
ience,
Engineering
and Technology
, (IS
SN : 2322-2441)Issue 2, 2012
,
pp.
52-57.
Evaluation Warning : The document was created with Spire.PDF for Python.