TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3777 ~ 37
8
5
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.5097
3777
Re
cei
v
ed
No
vem
ber 1
0
, 2013; Re
vi
sed
De
cem
ber 2
8
,
2013; Accep
t
ed Jan
uary 1
0
, 2014
Bayesian Neural Network of Rolling Force Prediction
for Hot-Strip Mill
Xiaodan Zha
ng
1
, Rui LI
2
, Yanliang
YE*
3
1
Electrical a
nd
Information En
gin
eeri
ng D
epa
rtmen
t, Beihua
Univers
i
t
y
, Jil
i
n
,
1320
13, P. R. Chin
a
2
School of Aut
o
matio
n
& Elec
trical Eng
i
ne
eri
ng, UST
B
, Beijing 10
00
83, P. R. Chin
a
3
Scientific Research Office
, Beihua Universit
y
, Jili
n,132013,
P. R. China
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: z1314
o
y
@1
6
3
.com
1
, lirui0
1
2
@1
63.com
2
, yy
lx
cy
@126.com*
3
A
b
st
r
a
ct
F
o
r obta
i
ni
ng
r
e
lativ
e
acc
u
rat
e
ro
lli
ng-
mi
ll
mode
l is
d
i
fficult
y by th
e s
i
mpl
e
math
e
m
atic
a
l
meth
od,
due to th
e co
mplexity of th
e a
c
tual pr
oducti
o
n
scen
e
an
d th
e no
n-li
near r
e
l
a
tions
hip
betw
een v
a
ria
b
les, t
h
is
pap
er firstly p
r
opos
es an i
m
prove
d
Bayes
i
an reg
u
l
a
ri
z
a
ti
on ne
ura
l
net
w
o
rk mod
e
l a
ccordi
ng to th
ese
me
asur
ed
data
of 15
80
pro
d
u
c
tion l
i
n
e
. In th
is mod
e
l,
the
p
aper c
onstruct
s
the i
m
prove
d
Bayesi
an
ne
ur
al
netw
o
rks by
the
intro
ductio
n
of b
o
u
n
d
ter
m
s th
at re
pre
s
ents the
n
e
tw
ork co
mpl
e
xi
ty in th
e
obj
e
c
tive
function. At las
t, the simul
a
tio
n
re
sult prov
es
the effectiven
ess and va
lid
ity of the mod
e
l
and the pr
ed
iction
accuracy of the
mod
e
l a
l
gor
ith
m
is sup
e
ri
or to the traditio
n
a
l
mo
de
l.
Ke
y
w
ords
:
hot
continu
ous ro
ll
ing, rol
lin
g force pred
ic
tion, n
eura
l
netw
o
rk, Bayesi
an re
gul
ari
z
a
t
i
on
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
The
characteristics of the
rolling process are non
-linear, large-del
a
y, strong
coupling
and p
a
ramet
e
r vari
ation.
Since
state p
a
ram
e
ters of
the co
ntrol
sy
stem a
r
e
co
n
s
tant chan
ge,
the
traditional
co
ntrol m
odel
cannot
well
ad
apted
due
to
i
t
s
sho
r
tcomi
n
gs. T
a
ki
ng i
n
to a
c
count
of t
h
e
learni
ng ne
ural netwo
rk, m
any st
udie
s
showed that p
r
edi
ctive cont
rol effect usi
n
g traditional
BP
algorith
m
or
LM algo
rithm,
whi
c
h u
s
e
n
eural
networks to cre
a
te ro
lling force m
o
del an
d u
s
e
on-
site mea
s
u
r
e
d
data for trai
ning an
d learning, is
rema
rkabl
e. Since
neural network traini
ng time is
usu
a
lly too long, and the sample data
contain
s
noi
se
, there are p
r
oblem
s of tra
i
ning times to
o
much o
r
the
network sca
l
e too large
and othe
r is
sue
s
, so it tend
s to make the netwo
rk to
remem
b
e
r
un
necessa
ry de
tails wh
en ne
ural net
wo
rk
t
r
ainin
g
. If the
noise incl
ude
d in the traini
ng
pro
c
e
ss of ne
twork data a
r
e recor
ded, the ne
w data may result in inco
rrect outp
u
t, that is to say
the
traditio
nal
neu
ral netwo
rk algo
rithm d
oes
not
have
good
ge
nerali
z
ation
fun
c
tio
n
, and
there i
s
a few p
r
oble
m
s
su
ch
a
s
t
he difficulty to control
com
p
lexity degre
e
of the
mo
d
e
l an
d the
difficulty
to
overcome
over-fitting
d
a
t
a
and so on [1].
Acco
rd
in
g to the p
r
oj
e
c
t specifi
c
i
s
sues,
com
pari
ng
with the
BP a
l
gorithm,
LM
algorith
m
a
n
d
Bias alg
o
rith
m, this
pap
er propo
se
s
an
improved
Bia
s
method of n
e
u
ral n
e
two
r
k
predi
ction fo
r
the rollin
g fo
rce of the h
o
t rolling mill,
so
as to obtai
n the
better mathe
m
atical mo
de
l.
2.
The Principle of Bay
esia
n
Regulari
z
a
t
ion Neu
r
al Net
w
o
r
k
The m
e
thod
of Bayesi
a
n
re
gula
r
i
z
at
ion mai
n
ly
throug
h m
o
difying the
training
perfo
rman
ce
function
s of n
eural
network to impr
ove t
heir ma
rketin
g ca
pabilitie
s. Input variabl
es
are two categ
o
rie
s
in a
c
tua
l
system, on
e
can
be ob
se
rved, and th
e
other i
s
al
so
uncontroll
abl
e
and un
ob
se
rved. But the two varia
b
le
s have a
n
i
m
pact o
n
th
e output sy
stem. Let X be an
observabl
e v
a
riabl
e, X=[x1, x2…xn]. Then the
follo
wing
rel
a
tion
ship
between
the sy
stem o
u
tput
d and the inp
u
t x:
)
(
x
f
d
(1)
Whe
r
e f rep
r
ese
n
ts the ef
fect of the un
obser
vabl
e in
puts to the o
u
tputs in the
system;
rep
r
e
s
ent
s the rand
om vari
able with a di
stributio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3777 – 37
85
3778
The trai
ning
perfo
rman
ce
function
of ne
ural
network i
s
ge
ne
rally u
s
ing th
e me
a
n
sq
ua
re
error func
tion. As
s
u
ming the error func
tion E0 is
:
K
k
N
n
nk
nk
y
E
11
2
'
0
)
y
(
2
1
(
2
)
Whe
r
e N
represe
n
ts
the nu
mber of
sam
p
les,
K repre
s
ent
s the o
u
tput numb
e
r
o
f
neural
netwo
rk,
nk
y
represe
n
ts the ex
pecte
d output
,
nk
y
'
rep
r
e
s
ent
s the actu
al out
put of network.
Although the
function tha
t
make the above-
mentio
ned obje
c
tive function reach to
minimize has infinite, the
neural netwo
rk ha
s
lo
cal
minimum. Aiming at the above-mentio
ned
probl
em
s, it can be solve
d
by r
egula
r
ization theory wh
ich add
s a co
nstrai
nt term to obtain stabl
e
and
useful
so
lutions. In
ge
neral, if
F(x) i
s
smooth,
it
will h
a
ve the
interpol
ation
ability. Whe
n
the
netwo
rk weig
ht is
small, th
e network o
u
t
put is
smoot
her.
So usi
n
g
smo
o
thne
ss con
s
trai
nt
a
s
a
con
s
trai
nt term, it can effectively redu
ce
t
he network
weig
ht. Then the obje
c
tive function i
s
:
2'
2
11
1
11
()
22
WK
N
in
k
n
k
ik
j
Fw
y
y
()
()
WD
JF
J
F
(3)
3.
Impro
v
ed Ba
y
esian Regularization
Ne
ural Ne
t
w
o
r
k
Algorithm
Bayesian
ne
ural
net
works p
u
t the
probability di
stribution
of we
ight value
(t
hre
s
hol
d
value) i
n
the
whol
e
spa
c
e
as th
e
startin
g
poi
nt, co
nsi
ders the
pa
ra
meter
as a
ra
ndom va
ria
b
l
e
,
con
s
id
ers the
obje
c
tive function a
s
the li
kelih
ood fun
c
tion of trainin
g
data, and t
he rig
h
t de
ca
y
term
corre
s
p
ond
s to the
p
r
iori
proba
bility distri
b
u
tion
of the net
wo
rk pa
ram
e
ters, and inte
grati
on
the pri
o
r probability dist
ri
buti
on
assumption of the param
e
ters
, and the param
e
ters of
the
poste
rio
r
dist
ribution
can
be co
nsta
ntly adjus
ted a
fter the observing data
are given. T
he
predi
ction re
sults of Bayesia
n
neu
ral
network
are base
d
on
an average
of the posterio
r
distrib
u
tion of
the param
eters, a si
ngle
model is
ma
p
ped to a poin
t
in paramete
r
spa
c
e, an
d all
model
s a
r
e
mappe
d to th
e entire p
a
ra
meter
sp
ace, in o
r
de
r to
g
uara
n
tee
stro
ng g
ene
rali
za
tion
ability of the
network in theory [2].
Assu
ming th
e network
st
ructu
r
e
H i
s
giv
en (prim
a
rily the n
u
m
ber
of hid
den laye
r
neuron
s) a
n
d
the network
model di
=f
(xi,W,H) is given
.
In the abse
n
ce of the sa
mple data, th
e
prio
r di
stribu
tion of the
weig
hts
(thre
s
hol
d) i
s
)
,
|
(
H
w
p
; the po
sterio
ri di
strib
u
tion i
s
)
,
,
,
|
(
H
D
w
p
with the sam
p
le data set
}
,
{
N
N
d
x
D
. Ac
c
o
rding to the Bayes
i
an rule [3] is
:
)
,
,
|
(
)
,
|
(
)
,
,
|
(
)
,
,
,
|
(
H
D
p
H
w
p
H
w
D
p
H
D
w
p
(
4
)
W
h
er
e p
(
D
|
w
,
β
,H) represe
n
ts th
e
likeli
hoo
d
functio
n
,
p(D|
α
,
β
,H
) re
p
r
es
en
ts
norm
a
lization
factor, w re
pre
s
ent
s the
weig
ht value (thre
s
h
o
ld) v
e
ctor. Th
e kn
owle
dge o
n
the
weig
hts
distri
bution i
s
little
wh
en the
r
e
i
s
n
o
dat
a;
th
erefo
r
e th
e p
r
ior di
stributio
n is a ve
ry wi
de
distrib
u
tion. It can be co
nverted to a co
mpact po
steri
o
r distri
bution
when the da
ta are obtain
ed,
the weight va
lue only in a very small ra
nge will p
r
od
uce
con
s
i
s
te
nt with the performa
n
ce of the
netwo
rk m
ap
[4].
3.1. Prior Pr
obabilit
y
In the ab
sen
c
e of the
prior kno
w
led
g
e
of wei
ghts, p(w|
α
, H)
follows
the Gauss
distrib
u
tion th
at the mean is 0 and the v
a
rian
ce i
s
1/
α
[5]:
)
exp(
)
(
1
)
,
|
(
1
W
i
i
W
w
z
H
w
p
(
5
)
Thus, the val
ue of the normalizatio
n factor ZW(
α
) is:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Baye
sian
Ne
ural Netwo
r
k of Rolling Fo
rce Pre
d
ictio
n
for Hot-Stri
p Mill (Xiaoda
n Zhang
)
3779
2
1
)
2
(
)
exp(
)
(
W
W
i
i
W
dw
w
z
(
6
)
3.2. Approxi
m
ate Probabilit
y
Assu
ming
the
noi
se
smo
o
thing fu
nction
with a
Ga
uss
distrib
u
tion th
at the me
an i
s
0
an
d
the varian
ce
is 1/
β
produces the desi
red
output
d, for
a given input
x,
the observ
ed probability of
the output d:
K
k
n
nk
nk
n
n
H
w
x
y
d
H
w
x
d
p
1
2
)
)]
,
,
,
(
[
2
exp(
)
,
,
,
|
(
(
7
)
If each sa
mpl
e
indep
ende
n
t
ly selected d
a
ta,
N
n
D
D
n
n
J
z
H
w
x
d
p
H
w
D
p
1
)
exp(
)
(
1
)
,
,
,
|
(
)
,
,
|
(
(
8
)
The n
o
rm
alization fa
ctor
dD
J
z
D
D
)
exp(
)
(
,
K
k
N
j
nk
nk
D
c
y
J
11
2
)
(
2
1
, therefo
r
e,
2
)
2
(
)
(
N
D
z
. Where N is t
he input vect
or dime
nsi
on.
3.3. Optimized and Solv
ed
The Pri
o
r Probability functi
on and approximate
probability function
into
equation (8), we
can o
b
tain:
11
(
|
,
,
,
)
exp(
)
e
xp[
(
)
]
(,
)
(
,
)
DW
MM
p
wD
H
J
J
M
w
zz
(
9
)
Whe
r
e,
dw
J
J
z
W
D
M
)
(
)
,
(
.
If the sampl
e
data re
aches a
ce
rtai
n numb
e
r, the po
sterio
r distrib
u
tion
tends to
Gau
ssi
an distribution. If th
e poste
rio
r
distributio
n cu
rve simultane
ously satisfie
s the suffici
e
n
tly
narro
w an
d t
he
sha
r
ply e
noug
h pe
ak,
you can fu
rth
e
r
simplify th
e problem,
n
a
mely u
s
ing
the
Taylor expa
n
s
ion o
b
tain
)
,
(
M
z
.
A
ssu
me
t
hat
MP
w
is the wei
ght
value (thre
s
hold value
)
to
whi
c
h B i
s
th
e minimu
m value
co
rre
sp
o
nding. T
he T
a
ylor exp
a
n
s
ion of
)
(
w
M
in the
vicinity of
MP
w
is
:
)
)(
(
)
(
2
1
)
(
)
(
MP
MP
T
MP
MP
w
w
w
M
w
w
w
M
w
M
(
1
0
)
()
()
()
M
PD
M
P
W
M
P
Mw
J
w
J
w
()
DM
P
Jw
I
(11
)
Whe
r
e,
represents the seco
nd der
ivative,
therefore:
)]
(
exp[
)]}
(
{det[
)
2
(
)
,
(
2
1
2
MP
MP
W
M
w
M
w
M
z
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3777 – 37
85
3780
3.4. Approxi
m
ate Calculation of
Hes
s
ian Matrix
If you want to
optimize the
solutio
n
, the f
i
rst i
s
to
cal
c
ulate
Hessian
matrix
when
)
(
w
M
in the minimu
m point of
MP
w
. T
he formul
a (1
1) sh
ows that
the calculatio
n amount of
)
(
MP
D
w
J
is larg
e. Therefore,
Hessian
matrix
can b
e
furthe
r simplifie
d to improve com
puting spee
d.
Make
)
(
nk
nk
nk
c
y
, then:
}
{
11
K
k
N
n
i
nk
D
w
w
J
(13)
K
k
N
n
j
i
nk
nk
j
nk
i
nk
ij
MP
D
w
w
w
w
w
w
J
11
2
]
[
))
(
(
(
1
4
)
3.5. Dete
rmination of
H
y
per-p
a
rame
ters
α
and
β
Hyper-p
ara
m
eters
α
and
β
can be o
b
tai
ned by cal
c
ul
ati
ng the po
sterio
r distri
buti
on:
)
|
(
)
|
,
(
)
,
,
|
(
)
,
|
,
(
H
D
p
H
p
H
D
p
H
D
p
(
1
5
)
Assu
me that
the prio
r di
stribution
)
|
,
(
H
p
meet a very wi
de
distrib
u
tion fu
nction.
Be
c
a
us
e th
e
n
o
r
ma
liza
t
io
n fa
c
t
or
)
|
(
H
D
p
ha
s n
o
thing to
do
with
,
in the
ab
ove form
ula,
so the
proble
m
of obtaini
n
g
the maxim
u
m a po
ste
r
iori distri
bution
coul
d be
tran
sform
ed into
the
probl
em of
solving
m
a
ximum like
lihood fu
ncti
on. Becau
s
e the a
pproximate fun
c
tion
)
,
,
|
(
H
D
p
is the norm
a
l
i
zation fa
ctor
of the formula
(15), then:
)
,
,
,
|
(
)
,
|
(
)
,
,
|
(
)
,
,
|
(
H
D
w
p
H
w
p
H
w
D
p
H
D
p
(
1
6
)
Uniting the (8
) and (9), we
can o
b
tain:
)
(
)
(
)
,
(
)
,
,
|
(
W
D
M
z
z
z
H
D
p
(
1
7
)
For form
ula (7) takin
g
the logarith
m
:
l
n
(
(
|
,
,
)
()
()
l
n
l
n
(
2
)
22
WM
P
D
M
P
NN
pD
H
J
w
J
w
1
ln
{
d
e
t
[
(
)
]
}
ln
22
MP
W
Mw
(
1
8
)
If the charact
e
risti
c
value
of
)
(
MP
D
w
J
is
W
i
i
,...
2
,
1
},
{
, we can
obtain that t
h
e
cha
r
a
c
teri
stic value of
)
(
MP
D
w
J
is
}
{
i
by the formula (11). Also,
becau
se
D
J
is a
norm
a
l error t
e
rm, then:
1
ln{
d
et
[
(
)
]
}
l
n[
(
)
]
W
MP
i
i
dd
Mw
dd
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Baye
sian
Ne
ural Netwo
r
k of Rolling Fo
rce Pre
d
ictio
n
for Hot-Stri
p Mill (Xiaoda
n Zhang
)
3781
1
1
1
[(
)
]
W
MP
i
i
tr
M
w
(
1
9
)
Since
i
and
are propo
rtion
a
l, therefore
:
i
i
d
d
1
l
n
{
d
et
[
(
)]}
l
n
[
(
)
]
W
MP
i
i
dd
Mw
dd
11
1
11
[l
n
(
)]
WW
W
ii
i
ii
i
ii
d
d
dd
(
2
0
)
Re
spe
c
tively make th
e partial derivative of
A and B in the formula
(20) e
qual to
0, you
can g
e
t:
N
N
w
J
W
w
J
W
i
i
i
MP
W
W
i
i
i
W
i
i
MP
W
1
1
1
)
(
2
)
(
2
(
2
1
)
Therefore, th
e maximum p
r
omin
en
ce of
and
M
PM
P
can be o
b
tai
ned:
)
(
2
,
)
(
2
MP
D
MP
MP
W
MP
w
J
N
w
J
(
2
2
)
Figure 1. Bayesia
n
neu
ral
netwo
rk traini
ng flow chart
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TELKOM
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KA
Vol. 12, No. 5, May 2014: 3777 – 37
85
3782
Whe
r
e
γ
re
pre
s
ent
s the
numbe
r of
para
m
eter
s works in
redu
cing th
e
netwo
rk
perfo
rman
ce i
ndex functio
n
,
0,
W
.
In summa
ry, the Bayesia
n
neural network is an
iterative process, e
a
ch
iteration i
n
volves
three inferenc
es
[6]: the firs
t la
ye
r infe
rence is to
m
a
ximize
)
,
,
|
(
H
w
P
und
er the
co
nditi
ons
of
hyper-pa
r
am
eters; the se
con
d
layer infe
ren
c
e i
s
to optimize hyp
e
r-paramete
r
s
,
, and to infe
r
the most po
ssi
ble hype
r param
eter
s; the third layer infere
nce
is the signi
ficant deg
ree
of
cal
c
ulatio
n model, and
sel
e
ct the be
st model [7].
4. Simulation
In the theoret
ical an
alysi
s
, the pape
r ma
de a se
rie
s
of simulation e
x
perime
n
ts b
a
se
d on
the mea
s
u
r
e
d
data of a
1
580 h
o
t strip
mill pro
d
u
c
tio
n
line
whi
c
h
con
s
i
s
ts of
sl
ab yard, fu
rn
ace,
roug
hing
mill
group, fini
shing
mill, coi
ling m
a
chine
s
a
n
d
othe
r
equipm
ent. T
he
strip
de
si
gn
thickne
ss
of 1580
hot-rolli
ng mill is
1.2
mm~1
2
.7mm
and
width i
s
700mm
~
1
7
5
0
mm. The m
a
in
varieties in
clude lo
w-ca
rb
on ste
e
l, sili
con ste
e
l,
carbon-structu
r
al
steel
, mi
cro-alloy steel, lo
w-
alloy steel. The steel
stren
g
th cla
ss a
r
e
σ
b
≤
65kg/mm2,
σ
s
≤
50kg/mm2.
The seven ra
ck fou
r
-roll m
ill of 1580 finishin
g mill was a
rra
nge
d in tandem, th
e seven
mills refe
rred
to as F1 ~ F
7
, the distan
ce betwe
en e
a
ch
rack i
s
5
800mm. fou
r
rolle
r pairs (P
C)
mill, roll crossing
with unil
a
teral transm
issi
on form
. Four roller
pair-cross
(P
C) mill is used by
F2~F
7, the form of u
n
ilat
e
ral
cross-use drive i
s
a
dopted
by ro
ll. F1 ha
s th
e neg
ative roll
bendi
ng, F2~F7 has th
e po
sitive bendi
ng
[8].
To
cal
c
ulate
the rolling
sp
eed
and
rolling time
fram
e: According
to the
rule
of
volume
flow rate, taking into acco
unt the dista
n
ce of
the roughi
ng mill exports to th
e finishin
g m
ill
entran
c
e i
s
1
8
m, and the
distan
ce b
e
tween ea
ch ra
ck is 5.8m, Th
e two frame t
r
an
smi
ssi
on time
of the rolled p
i
ece in ea
ch can be cal
c
ula
t
ed, and
the total rolling time also can
be obtaine
d. The
results a
r
e sh
own in Ta
ble
1. The pre
-
se
t roll gap valu
es of ea
ch fra
m
e are
sho
w
n in Table 2.
Table 1. The
Rolling Sp
ee
d and Time of
Rolling Mill
Frame
w
ork
1
F
2
F
3
F
4
F
5
F
6
F
7
F
Rolling
speed(m/s)
0.867
1.4743
2.1825
3.0225
4.21
4.8672
5.176
Exit
speed(m/s)
6.1834
7.8959
8.8373
9.5083
11.8712
11.2095
8.2363
O
v
er
time
mill(s)
0.2222
0.1064
0.0651
0.0422
0.0301
0.0239
0.0199
Total time rolling(s)
0.2793
0.1161
0.0727
0.049
0.0364
0.0289
0.0253
Table 2. The
Pre-set Roll
Gap Value of
each Fram
e
Frame
w
ork
1
F
2
F
3
F
4
F
5
F
6
F
7
F
gap
value(mm)
16.584
9.296
5.95 5.165
3.649
3.711
3.596
The sele
ction
prin
ciple of the input an
d
out
put varia
b
les: the
r
e is a clea
r and
definite
relation
shi
p
t
hat p
r
od
uces a
gre
a
ter i
m
pact
bet
we
en the
sele
ct
ed va
riable
s
and th
e
studi
ed
output va
riabl
es
wh
en t
he
neural n
e
two
r
k va
riabl
es
are sele
cted; th
e sele
cted
variable
s
can
b
e
detecte
d or calcul
ated in the ac
tual produc
tion proc
es
s
[9].
We
can
know that there are
many factors affecting the ro
lling pressure changes by the
mechani
sm analysi
s
of the rollin
g process
and pri
o
r
experience,
such as the ent
rance thi
c
kness
of rolled pl
ate, exit thickn
ess,
red
u
ctio
n rate, rolli
ng
temperature,
rolling
spe
e
d
, roll diam
eter,
chemi
c
al
co
mpositio
n co
ntent
an
d so
on.
Acco
rd
in
g to th
e
scen
e me
asure
d
data, the
det
ermin
e
para
m
eters o
f
each layer i
s
as follo
ws:
The input lay
e
r: the C cont
ent , the Si cont
ent, the Mn conte
n
t, the Cu co
ntent, the entry
thickne
ss
(H), outlet thickn
ess (h
1), rolli
ng width
(B), the rolling te
mperature
(T
), the rolling ti
me
(t1), reduction ratio
(e1).T
he output lay
e
r:
the rolling force
(P).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Baye
sian
Ne
ural Netwo
r
k of Rolling Fo
rce Pre
d
ictio
n
for Hot-Stri
p Mill (Xiaoda
n Zhang
)
3783
The n
u
mb
er
of neu
ron
s
i
n
the in
put lay
e
r i
s
1
0
, the
numbe
r
of n
euro
n
s in th
e
output
layer is 1.
4.1. The Prediction Rolling Force o
f
BP Neur
al Net
w
o
r
k
In the pap
er,
610 g
r
ou
ps’
norm
a
lized d
a
ta are
u
s
ed
as the t
r
ainin
g
sa
mple
s; a
variabl
e
learni
ng
rate
BP algorith
m
is
used to
train th
e
net
work.
The
tra
n
s
fer fun
c
tion
of between
the
input layer an
d the hidden l
a
yer ado
pts the hyperbo
lic S-shap
ed tra
n
sfer fun
c
tion
; the neuron
of
the output layer uses the n
euro
n
linea
r tran
sfer
fun
c
tion. The frequ
ency of the learnin
g
pro
c
e
ss
is 50, the trai
ning time is 5
000 an
d the e
x
pected e
r
ror is set to 1e-0
04.
Figure 2
shows the error
of the BP al
gorithm
forecasting
rolling fo
rce and the actual
value, and th
e error of the
cal
c
ulate
d
value of
rolling f
o
rce and the
actual valu
e. The ab
sci
ssa
is
the sampl
e
-p
oint; the vertical axis is t
he er
ror val
ue. As can
be see
n
, the use of neural
netwo
rks, the
forecastin
g error valu
es
of usi
ng BP
neural net
works i
s
bet
wee
n
[-200, 30
0], but
the traditiona
l calculation
errors is bet
wee
n
[-600,4
00]. Namely the forecasti
ng rollin
g force
fitting curve o
f
BP neural network is g
o
o
d
. Therefo
r
e, the predi
ction
accura
cy of rolling force can
be improved
by the use of neural network model.
Figure 2. The
Rolling Fo
rce Fitting Curv
e of BP Algorithm Predictio
n
4.2. The For
ecas
ting Mo
del of Lev
e
nberg- M
a
rqu
a
rdt Alg
o
rith
m
In the same
para
m
eter
se
ttings, 610 g
r
oup
s’ normali
zed d
a
ta set
610 as the t
r
ainin
g
sampl
e
s, Lev
enbe
rg
-Ma
r
q
uardt alg
o
rith
m is used to train the net
work.
Figure 3. Fitting Cu
rve of L-M Algorithm
As can
bee
n
see
n
, L-M alg
o
rithm fo
re
ca
sting
by
the rolling fo
rce a
nd the
actu
al
value of
the error, the
predi
ction
error va
lue
s
of the mod
e
l usi
ng the LM al
g
o
rithm is
bet
wee
n
[-20
0, 200],
whi
c
h
erro
r i
s
sm
aller tha
n
the e
rro
r
of th
e tra
d
itional
BP algo
rithm. Ho
weve
r,
we foun
d th
at the
netwo
rk
pre
d
i
c
tion a
c
curacy is not guaranteed
whe
n
the numbe
r
of hidden n
o
des
cha
nge
s in
experim
ents.
For exa
m
ple,
taking
the 3
0
hidde
n no
de
s, the training
of the net
wo
rk i
s
com
p
let
ed
to achi
eve th
e accu
ra
cy of
9.9356
e-005
at step
150.
But we fou
n
d
the p
r
edi
ctio
n erro
r is quit
e
0
10
20
30
40
50
60
70
80
90
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
Fittin
g
curve of L
-
M al
g
orithm
Sa
m
p
le
p
o
in
t
P
r
edi
ct
A
ct
ual
For
c
e
（
KN
）
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3777 – 37
85
3784
large and the rolli
ng forc
e predi
ction
curve deviates
signifi
cant
ly
from the act
ual rolling force
values
wh
en
the re
st data
of 90 g
r
oup
s
were u
s
ed to
detect. Thi
s
i
s
du
e to exce
ssive
emph
a
s
is
on traini
ng p
r
eci
s
io
n, leav
ing the d
e
si
g
n
of the
net
work i
s
la
rge
,
resulting in
more
po
werful
netwo
rk fu
nct
i
on map
p
ing,
resulting in e
x
cessiv
e ad
a
p
tation phe
no
menon. Thi
s
i
s
the limitatio
ns
of LM
algo
rit
h
m: The
a
ccura
cy of th
e
netwo
rk
trai
ni
ng o
b
je
ctives ca
nnot
be
d
e
termin
ed, th
e
error i
s
set to
o sm
all in
ord
e
r to th
e la
ck
of traine
d net
work
gen
erali
z
ation
and
th
e low preci
s
io
n;
Erro
r that be set too larg
e will ea
sily lead
to excessiv
e gene
rali
zati
on and n
on-v
e
rsatility.
4.3. Ba
y
esian Regulari
z
a
t
ion Neu
r
al Net
w
o
r
k M
o
de
In the same
para
m
eter
se
ttings, Bayesi
an neu
ral n
e
twork a
d
d
s
the con
s
traints of the
squ
a
re
d wei
g
hts and the n
u
mbe
r
of valid para
m
eter
i
n
netwo
rk tra
i
ning obje
c
tive function. T
he
training
Resul
t
s: MSE = 0.0058, SSE = 1.3961.
Figure 4 shows the comparing
error
curve of t
he forecast rolling force of Bayesian
netwo
rk a
nd t
he a
c
tual
rolli
ng fo
rce. As
can
be
en
se
e
n
, the
pre
d
icti
on e
r
ror ba
si
cally di
stri
but
ed
in [-20
0, 200]
, but the tra
d
i
t
ional calculat
ion e
rro
r di
stribution in
[-60
0, 400]. Fig
u
re 5
sho
w
s th
e
curve of the predi
ctive roll
ing
force and
the measu
r
e
d
value. We can see the fitting degre
e
is
good f
r
om th
e graph. T
herefore, t
he accura
cy
of
Baye
sian neu
ral n
e
tworks can establi
s
h a
g
ood
Rolling fo
rce predi
ction m
o
del.
Table 3. The
Traini
ng Result Contra
st o
f
Three Network M
odel
N=4 N=5
N=6 N=7 …
N=26
Variable learning
rate BP
MSE 0.0145
0.0097
0.0094
0.0092
0.0059
SSE
3.4744
2.3212
2.2665
2.1998
1.4190
Levenberg
-
Marq
uardt
MSE 0.0084
0.0076
0.0068
0.0052
9.9363e-0
0
7
SSE
2.0068
1.8203
1.6262
1.2371
2.3847e-0
0
4
Ba
y
e
sian regula
r
ization
MSE 0.0109
0.0078
0.0071
0.0058
0.0026
SSE
2.6058
1.8818
1.7015
1.3961
0.6196
Figure 4. Erro
r Cu
rve of Bayesi
an Netwo
r
k
Predictive Rolling
F
o
rce
Figure 5. Curve of Bayesian Ne
twork Predictive Rolling Force
Usi
ng Baye
si
an neu
ral n
e
t
work an
d int
r
odu
cin
g
the
poste
rior
probability of statistics
allows the n
e
twork to avoid falling into local extre
m
e and to re
duce the trai
ning time. In the
experim
ent, each trai
ning
time, the error in
dicator
a
nd the
netwo
rk
perfo
rma
n
ce valu
es of
the
Bayesian
ne
ural
network
training
mod
e
l are re
latively stable.
When th
e
si
ze
of the n
e
twork
0
10
20
30
40
50
60
70
80
90
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
Sam
p
le
p
oi
n
t
Pr
edic
t
A
ct
u
a
l
Force
（
KN
）
0
10
20
30
40
50
60
70
80
90
-
200
-
100
0
100
200
S
a
mp
le
p
o
int
Fo
rce
（
KN
）
E
r
r
o
r cur
v
e of Bayesian networ
k pr
edictive r
o
lling for
c
e
Cur
v
e of Bay
e
sian networ
k pr
edictive r
o
lling for
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Baye
sian
Ne
ural Netwo
r
k of Rolling Fo
rce Pre
d
ictio
n
for Hot-Stri
p Mill (Xiaoda
n Zhang
)
3785
increa
se
s, it did not a
ppe
a
r
the p
hen
om
enon
of "ove
r-fit", which
avoids t
r
ying to
cho
o
se the b
e
st
approa
ch to
d
e
termin
e net
work
si
ze. In
the sa
me
p
a
rameter
settin
g
s, Ta
ble 3
shows the t
r
ai
ning
results of ta
king the
different type o
f
hidden n
o
d
e
s by contra
st variabl
e-le
arnin
g
rate
BP
algorith
m
, L-M optimizatio
n algorith
m
a
nd Bayesia
n
regula
r
ization
algorith
m
.
In the same p
a
ram
e
ter settings, Tabl
e 3 sho
w
s the tra
i
ning re
sult
s of taking the different
type of hidde
n node
s by contra
st
variab
le-lea
rnin
g rat
e
BP algorith
m
, L-M optimi
z
ation al
go
rithm
and Bayesi
an
regula
r
i
z
atio
n algorith
m
.
The
comp
arin
g the results
sho
w
that L
-
M algo
rithm n
eed to
cal
c
ul
ate the Jacob
i
n matrix
and the
He
ssian m
a
trix, and la
rge
r
st
orag
e spa
c
e.
Whe
n
the n
u
mbe
r
of pa
rameters i
s
very
large, L-M al
gorithm may not
be pra
c
ti
cal.
In
a
dditi
on, the a
pproximation p
r
eci
s
ion
of ne
ural
netwo
rk train
ed by train f
unctio
n
for le
arnin
g
samp
l
e
s i
s
ve
ry hi
gh, it is
ea
sy to re
alize "o
ver-
match" fo
r th
e sam
p
le d
a
ta point
s. But for non
-le
a
rning
sampl
e
s (such
as validation le
arni
ng-
effect sampl
e
), the
approxi
mation error
will appe
ar a singular
phenomeno
n that
decreased and
then risen al
ong with the
incre
a
ses in
the num
be
r of neural n
e
twork trai
ni
ng, whi
c
h ca
nnot
guarantee th
e gene
rali
zati
on ability of the network.
Ho
wever, trai
ner a
d
d
s
the
weight
s of the
netwo
rk to th
e pe
rform
a
n
c
e fun
c
tion,
se
lect the
optim
um weight
s a
nd threshold
s
gro
u
p
s
so
ca
n
redu
ce
the
weig
ht range
in
ord
e
r to
make
th
e
ne
twork
output
sm
oothe
r, e
a
se
the
la
ck of
gene
rali
zatio
n
cap
ability, and en
su
re
that t
he Bayesia
n
train
i
ng network is stability
and
robu
stne
ss.
5. Conclu
sion
Based o
n
the backg
rou
n
d
of a 1580mm hot
strip
mill produ
ction line, This pape
r
descri
b
e
s
the
stru
cture a
n
d
functio
n
of
mode
rn
h
o
t rolling
control
system, p
u
t forward the m
u
lti-
level
control strategy and resear
ch on the finishing
mill model
based on LEVEL
2.
Considering
the net
work
stability using the BP al
gorithm
is
poor and the generaliz
ati
on ability is
low,
Bayesian
ne
ural n
e
two
r
ks is introdu
ced into t
he
con
s
trai
nt in the tradition
a
l
neural function
according
to
the comple
xity of the actual
produ
ction
site. Combine
d
with the n
on-li
nea
r
cha
r
a
c
teri
stics of the vari
able
s
, highe
r pre
c
is
io
n n
eural n
e
two
r
k predi
ction
model ha
s b
een
obtaine
d ba
sed on the
me
asu
r
ed
data.
At last, St
udy and the exp
e
rime
ntal re
sult found that
the
predi
ction
a
c
curacy
of the
optimized m
odel h
a
s bee
n sig
n
ifica
n
tly improve
d
, a
nd the
stabilit
y of
its network, the traini
ng
speed
and th
e
gene
rali
zatio
n
ca
pabilitie
s are
su
peri
o
r
to the traditio
nal
netwo
rk n
e
u
r
al netwo
rk.
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ya
n
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