TELKOM
NIKA
, Vol.11, No
.11, Novemb
er 201
3, pp. 6645
~6
650
e-ISSN: 2087
-278X
6645
Re
cei
v
ed Ap
ril 23, 2013; Revi
sed
Jun
e
22, 2013; Accepted July 2
4
,
2013
Safety Voting System Based on D-S Evidence Theory
Yue Xi, Feng Liu, Hongli Yuan, Dong
bo Pan*
Facult
y
of computer and infor
m
at
ion science, South
w
est Universit
y
, 2# T
i
ansheng Road,
Beibei Dist.,
Cho
ngq
in
g, Ch
ina, 40
07
15
*Corres
p
o
ndi
n
g
author, e-ma
i
l
*
: pand
b@s
w
u
.
edu.cn
A
b
st
r
a
ct
This thesis pr
opos
es a safety instrument
syst
em w
h
ich is base
d
o
n
D-S evide
n
ce theory,
inclu
d
i
n
g
sens
or, lo
gic v
o
tin
g
system an
d
ex
ecutio
n
unit. W
h
ile
the
l
ogic
v
o
ting
syste
m
c
oncl
udes
the
i
n
put
circuit, pr
ocess
o
r, outp
u
t circ
u
i
t an
d th
e
dia
g
nosis
mod
u
l
e
b
a
sed
o
n
D-S
e
v
ide
n
ce t
heory.
Accord
ing
to t
h
e
dia
gnos
is mod
u
le i
n
multi-ch
ann
el lo
gic voti
ng syst
em
and
calcul
ation b
a
s
ed on D-S ev
i
denc
e theory, th
e
interco
nnect
e
d
feedb
ack inf
o
rmati
on c
an i
m
pr
ove th
e re
l
i
abi
lity of the
dia
gnos
is.
T
h
e
r
efore, the saf
e
ty
instrum
e
nt system elaborated
in this thes
is c
an
achieve sys
tem’
s
se
lf-
d
iagnosis
function
under the pr
emise
of usin
g l
e
ss
h
a
rdw
a
re
equ
ip
me
nt a
nd
at th
e
mea
n
ti
me
a
c
quiri
ng
adv
an
tages
of low
c
o
st, relia
bil
i
ty a
n
d
high security.
Ke
y
w
ords
:
saf
e
ty instrument
system
, safety functi
on, D-S evidence th
eory, reliability
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Safety Ins
t
rument Sys
t
em (SIS), als
o
k
n
ow
n
as Sa
fety Interlocki
ng System, p
l
ays an
importa
nt part in alarming
and interlo
c
king in in
dustrial automati
c
co
ntrol, wh
ose fun
c
tion
is
impleme
n
ting
alarm sy
ste
m
, adjusting
or stop
ping
t
he machine
s
according to the testing results
from the
co
ntrol
system
s [
1
, 2]. SIS sha
ll execute
its
safety control
function
time
ly and
corre
c
t
l
y
to prevent or
redu
ce the o
c
curre
n
ce of dange
rou
s
a
c
cidents, where
a
s a
cci
dent
s will hap
pen.
At present, there are many
methods for
sa fety
instru
ment system
to achieve its safety
function, amo
ng whi
c
h pro
babili
stic met
hod is t
he m
o
st favorite way to measure security and
risk
assessm
ent, such as
Relia
bility Block Di
agram
(RBD) [3], Fa
ult Tree Anal
ysis
(FTA
) [4-6]
and M
a
rkov
Analysis (MA
)
[7-9] or M
a
rkov co
mbi
ned
with oth
e
r a
nalysi
s
[
10], and
so
on.
However, these m
e
thods
still hav
e
some uncertain fa
ctors in assessing.
The D-S evidence
theory a
r
o
s
e,
whi
c
h
wa
s first put forwa
r
d by
De
mpst
er in 1
967, fu
rther
pro
m
ote
d
and
develo
ped
by Shafer in 1976. D-S eviden
ce theo
ry acqui
re
s uni
que advanta
g
e
s to solve th
e uncertaintie
s
mentione
d ab
ove.
In view of th
e
ch
ara
c
te
risti
c
s of D-S evi
den
ce the
o
ry
and th
e p
r
e
s
ent situ
ation
of safety
instru
ment system, this thesi
s
presen
ts a sa
fety instru
ment sy
stem ba
sed
on D-S evid
ence
theory, who
s
e metho
d
i
s
t
hat un
der the
multi-c
han
ne
l
logic
voting system struct
ure and
thro
u
g
h
prop
er calcul
ation, whet h
e
r inde
pend
e
n
t or inte
rlo
c
ked cha
nnel
s, the output re
sults will p
r
ov
ide
stron
g
evid
e
n
ce
s fo
r oth
e
r
cha
nnel
s.
The
s
e ev
id
ences
will fo
rm
some
ce
rtain or
un
ce
rtain
feedba
cks
so
as to improv
e system’
s
re
liability
and secu
rity, while
D-S eviden
ce theory exactl
y
provide
s
axio
m syst
em in
pro
c
e
s
sing
the
certai
nties and
un
ce
rta
i
nties. Th
erefore, the
safe
ty
instru
ment
system ela
b
o
r
at
ed in thi
s
the
s
is
ca
n a
c
hie
v
e system’
s
self-di
agn
osi
s
function
und
er
the
premise of
usin
g
le
ss hard
w
a
r
e eq
uipment and
at the mea
n
time acquiri
n
g
advanta
g
e
s
o
f
low cost, relia
bility and high
security.
2
．
D-S Ev
ide
n
ce Theor
y
2.1. Axiomatic Sy
stem of Ev
idence
D-S evid
en
ce theo
ry ca
n
be divide
d
into
proba
bility distributio
n functio
n
, li
kelih
ood
function
and
De
sp
ster evid
ence combin
ation rul
e
[11,
12]. Assum
e
Fra
m
e of
Di
scern
m
ent i
s
,
then function
:2
0
,
1
m
sat
i
sf
ies:
0
m
,
1
A
mA
is calle
d the basi
c
pro
babili
ty
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e-ISSN: 2
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TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 664
5 – 6650
6646
distrib
u
tion o
f
frame of di
scern
m
ent
.
A
,
()
mA
is the basic probability of
A
. The
meanin
g
of
()
mA
is:
i
f
A
and
A
, thus
()
mA
is the accu
rate tru
s
t deg
ree of
A
; and
if
A
, thus
()
mA
mean
s it doesn’t kn
ow ho
w to all
o
cate it.
As
for
A
, the
defined fu
ncti
on Bel
：
:2
0
,
1
m
by
()
BA
B
el
A
m
B
is
the reliability function
of
. A
s
f
o
r
A
,
pl
is call
ed
the li
kelih
ood
fun
c
tion of Bel
i
n
()
1
(
)
pl
A
B
e
l
A
,
The relation
of reliability functio
n
an
d li
kelih
ood fu
nction is that
()
Bel
A
and
()
pl
A
are
respe
c
tively referred to the
lower limit fu
nction a
nd th
e uppe
r limit functio
n
of
()
()
pl
A
B
e
l
A
.
2.2. Ev
idence Combina
t
ion
Even the
sa
me evid
ence
s
, du
e to
different
sour
ce
s, the p
r
ob
abili
ty assi
gnm
en
ts will
be
different. The
n
D-S eviden
ce the
o
ry p
u
ts forw
a
r
d to
usin
g o
r
thogo
nal meth
od t
o
co
mbin
e th
ese
function
s.
A
ssu
me
12
,,
,
n
mm
m
are the
basic
probabilit
y assi
gnment functions
of
2
, their
orthog
onal
12
n
mm
m
m
are:
1
()
0
()
(
)
,
i
ii
AA
in
m
mA
k
m
A
A
(1)
in whi
c
h
1
1
1(
)
i
ii
AA
in
km
A
.
2.3 Basic
Algorithm
(1) It is kn
own
that: if
we
a
s
sum
e
fram
e
of disce
r
nm
en
t of some
field is
12
{
,
,
...,
}
n
SS
S
, propo
sition
A
、
B are the sub
s
et
s of
, and the infere
n
c
e rul
e
sh
all be:
,
if
E
t
h
e
n
H
C
F
Among which
E
,
H
are th
e lo
gic g
r
ou
ping
s of the prop
o
s
ition,
CF
is the certai
nty
factor, a
nd
i
c
means credibility.
For any proposition
A
,
the ce
rtainty factor
CF
of credibility
A
s
hall satis
f
y:
(a)
0,
1
i
ci
n
(b)
1
1
i
in
c
(2) Evide
n
ce
De
scription:
assum
e
m
is the defined basi
c
probability assignment
function of
2
, then it shall m
eet the followi
ng co
ndition
s during
cal
c
ul
ation:
(a)
({
}
)
0
,
ii
mS
S
(b)
1
({
})
0
1
i
in
mS
(c
)
1
()
1
(
{
}
)
i
in
mm
S
(d)
()
0
,
,
1
0
m
A
A
and
A
o
r
A
among whi
c
h
A
means the f
a
ctor n
u
mb
ers of pro
positi
on
A
.
(3) Ina
c
curate Inferen
c
e M
odel
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TELKOM
NIKA
e-ISSN:
2087
-278X
Safety Voting
System
base
d
on D-S E
v
iden
ce The
o
ry (Yue Xi)
6647
(a) Supp
ose
A
is on
e p
a
rt
propo
sition
of re
gula
r
co
ndition, u
nde
r the
conditi
on of
eviden
ce
E
, th
e matchin
g
d
egre
e
of pro
p
o
sition
A
and e
v
idence
E
is
:
1
(,
)
0
if
E
A
MD
A
E
Ot
he
r
w
i
s
e
，
，
(2)
(b) T
he defini
t
ion of part propo
sition A in regula
r
condi
tion is:
(,
)
(
)
CE
R
M
D
A
E
f
A
3. Safet
y
Ins
t
rumen
t
Sy
st
em Model ba
sed on D-S Ev
idence Theor
y
Safety instru
ment sy
stem,
whi
c
h i
s
ba
se
d
on
D-S
eviden
ce the
o
ry, incl
ude
s se
nsor,
logic voting
system and ex
ecutio
n unit. While the lo
gi
c voting syste
m
con
c
lud
e
s
the input circuit,
pro
c
e
s
sor, ou
tput circuit an
d the diagn
osis m
odul
e ba
sed o
n
D-S e
v
idence theory. Accordi
ng to
the diagn
osi
s
mod
u
le in
multi-chann
el logi
c votin
g
system
an
d cal
c
ulatio
n
based on
D-S
eviden
ce the
o
ry, the intercon
ne
cted feedba
ck in
formation ca
n improve the reliability of the
diagn
osi
s
.
The follo
wing
Figure 1 a
n
d
Figu
re 2
are SIS
traditio
nal logi
c voti
ng sy
stem
structu
r
e
s
.
Take 1
oo1 a
nd 1oo2 for
example. As it is show
n in Figure 1, the 1oo1
syst
em is the typical
inse
cu
re sy
stem stru
cture wit
hout re
dun
dan
cy and failure mod
e
protection. Whil
e in Figure 2
,
1oo2
syste
m
has t
w
o in
de
pend
ent logi
c solve
r
s. In
o
r
de
r to di
sco
nne
ct the sy
stem relia
bly, the
two outp
u
t ci
rcuits
ado
pt the method
of
seri
al
conn
ection. This
system not only
provide
s
a
lo
w
possibility of ineffectiveness, but
also increases the possibility of fail safety circuit, whi
c
h helps
to improve the reli
ability of the sy
stem.
The 1oo2
D
system in Fi
gure 3 co
ntains two
independent
electri
c
p
a
ssa
ges a
nd dia
g
nosti
c ch
ann
els. If
the output cha
nnel
detec
t
s
a pot
ential dan
gerous
failure, the system will automatically break the
circ
uit in order to make
sure the actuator in a
safe state. Th
e system’
s
di
agno
stic fun
c
tion wh
i
c
h u
s
es ”refe
r
en
ce
” method to d
i
agno
se
syste
m
reflect
s
in ev
ery ch
ann
el. 1oo2
D
syste
m
not only
can tolerate safety failure,but also da
n
ger
failure. Wh
en
it checks the
first critical f
a
ilu
re, the sy
stem will deg
rade to 100
1
D
’s fun
c
tion
and
by onlin
e m
a
i
n
-tainin
g
, the
syste
m
can
return to
1oo
2D
structu
r
e.
Figu
re
4 i
s
t
he 1
oo2
sy
stem
stru
cture with
D-S diag
no
si
s
tech
nolo
g
y mentione
d ab
ove.
Figure 1. Typical 1o
o1 System Structu
r
e
in
Logi
c Voting System
Figure 2. Typical 1o
o2 System Structu
r
e
in
Logi
c Voting System
Furthe
r, logic voting syste
m
adopts 1
o
o
2
st
ru
cture. And the diagn
o
s
is mo
dule b
a
se
d on
D-S evide
n
ce
theory incl
ud
es stat
e-spa
c
e ident
ificatio
n modul
e, function mo
dule
and calculatio
n
module.
a)
Acco
rdi
ng to
dual chan
nel
st
ru
cture, stat
e-spa
c
e id
ent
ificat
ion mo
d
u
le dete
r
mine
s the state
and
spa
c
e, which
will com
pose a fra
m
e
of discernme
n
t
. And these state
s
will a
ll together
comp
ose to a serie
s
of fra
m
e of discern
m
ents:
,1
,
0
,
0
,
1
；
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TELKOM
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Vol. 11, No
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er 201
3: 664
5 – 6650
6648
b)
Acco
rdi
ng to the reliability, function est
ablishe
s mod
u
les an
d ba
si
c pro
bability assignm
ent
function by
frame of
discernm
ent
:2
[
0
,
1
]
m
, and la
st gets the ba
sic
p
r
oba
bility
assignm
ent.
Figure 3. Typical 1o
o2
D
System Stru
cture in
Logi
c Voting System
Figure 4. 1oo
2 System Structure with D-S
Diag
no
sis
For chan
nel o
ne:
12
{1}
(
|
)
x
mP
A
A
(3)
__
12
{0
}
(
|
)
x
mP
A
A
(4)
__
12
12
{0
,
1
}
(
)
(
)
x
mP
A
A
P
A
A
(5)
For chan
nel two:
21
{1
}
(
|
)
y
mP
A
A
(6)
__
21
{0
}
(
|
)
y
mP
A
A
(7)
__
21
2
1
{0
,
1
}
(
)
(
)
y
mP
A
A
P
A
A
(8)
c) Accordi
ng
to
probabilit
y assignm
ent, cal
c
ulation module calc
ulates the orthogonal. It will first
cal
c
ulate
1
{}
{}
xy
xy
km
m
, and then
{}
m
, thereby obtaining reliability measure.
The advanta
ge of this system is that safety
instrum
ent system which i
s
based
on D-S
eviden
ce the
o
ry ado
pts th
e Moo
N
logi
c
voting syst
em
from D-S self
-diag
n
o
s
is te
chn
o
logy. It has
taken full u
s
e
of redun
dant
line of evide
n
ce fu
n
c
tion,
whi
c
h can p
r
odu
ce
s stron
g
feedba
cks t
o
the
inp
u
t sig
nal co
rre
ctly outputting an
d
st
ren
g
theni
ng the
out
pu
t relia
bility. Compa
r
ed
to t
h
e
MooN lo
gic v
o
ting system
of non-di
agn
osi
s
tech
nol
o
g
y, this can
signifi
cantly improve the ri
ght
output
sign
al
relia
bility an
d dia
gno
stic
coverage.
Al
so,
comp
are
d
to the
Moo
N
D sy
stem
with
diagn
osi
s
te
chnolo
g
y, D-S
self-diagn
osi
s
tec
hnol
ogy
can
re
duce t
he chan
nel d
i
agno
si
s ci
rcuit,
almost a
c
qui
re the perfo
rm
ances of Moo
ND
system
a
nd at the me
an time red
u
ce the addition
al
failure ri
sk, improvin
g system’s reli
abilit
y and se
curit
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Safety Voting
System
base
d
on D-S E
v
iden
ce The
o
ry (Yue Xi)
6649
4. Case
Anal
y
s
is
This
part u
s
e
s
1o
o2 lo
gic
stru
cture a
s
a pref
erred
case to
elab
orate the p
r
in
ci
ple of
safety voting system
with
D-S evide
n
ce algo
rithm. For ea
ch
ch
annel, the
r
e
are two defin
ite
states {
r
eli
a
ble}, {un
r
elia
ble} an
d on
e i
ndefinite
state {un
k
nown}. Wh
e
n
{reli
able}
and
{unreliabl
e} a
r
e ex-p
resse
d
in ch
ann
el one, cha
nnel
two will
give
the sam
e
con
c
lu
sion, whi
c
h
is
descri
bed
a
s
{1},
{0}.
Wh
ile {u
nknown
}
is ex
presse
d in
ch
ann
el one,
ch
ann
el two
will
gi
ve
oppo
site con
c
lu
sion, which denote in {
0
,1}, and vice
versa.
Assu
me
cha
nnel o
ne’s
reliability is 9
5
%,
and cha
nnel two’s i
s
90%. Adopti
ng 1o
o2
stru
cture, the corre
c
t outp
u
t signal’
s
re
liability
is 85
.5%, while a
dopting 1
oo2
D, the co
rre
ct
output sig
nal
’s reli
ability is above 9
9
.
5%. The
failure p
o
ssibili
ty of using D-S dia
gno
si
s
techn
o
logy can be calcula
t
ed as follo
we
d (su
ppo
se th
e two ch
ann
e
l
s are in
dep
e
ndent):
For chan
nel o
ne:
12
1
{
1
}
(
|
)
(
)
95%
x
mP
A
A
P
A
(9)
__
12
{
0
}
(
|
)
0.
5%
x
mP
A
A
(10)
__
12
1
2
{0
,
1
}
(
)
(
)
4
.
5
%
x
mP
A
A
P
A
A
(11)
For chan
nel two:
21
2
{1}
(
|
)
(
)
9
0
%
y
mP
A
A
P
A
(12)
__
21
{0
}
(
|
)
0
.
5
%
y
mP
A
A
(13)
__
21
21
{0
,
1
}
(
)
(
)
9
.
5
%
y
mP
A
A
P
A
A
(14)
so:
1
{}
{}
{
1
}{
1
}
{
1
}{
0
,
1
}
{
0
}{
0
}
{
0
}{
0
,
1
}
{
0
,1
}
{
1
}
{
0
,1
}
{
0
}
{
0
,1
}
{
0
,
1
}
0.
99
075
xy
xy
xy
xy
x
y
x
y
xy
xy
xy
km
m
mm
mm
m
m
m
m
m
m
mm
mm
(15)
then:
{1
}
{1}
{
}
{
}
1
(
{
1}
{1}
{
0
,
1}
{1}
{
1}
{
0
,
1
}
)
0.
99075
0.
9949
5
3
xy
xy
xy
x
y
x
y
mk
m
m
mm
m
m
mm
(16)
{0
}
{0
}
{
}
{
}
1
(
{
0
}
{0
}
{
0
,
1
}
{0
}
{
0
}
{0
,
1
}
)
0.
990
75
0
.
00
073
2
xy
xy
xy
x
y
xy
mk
m
m
mm
m
m
m
m
(17)
{0
,
1
}
{0
,
1
}
{
}
{
}
1
({
0
,
1
}
{
0
,
1
}
)
0.
99075
0.
0
04315
xy
xy
mk
m
m
mm
(18)
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 664
5 – 6650
6650
Therefor, the
relia
ble
out
put si
gnal
o
f
1oo2
of D-S self-dia
gn
osi
s
te
chn
o
logy is
99.495
3%, which
is
signifi
cantly b
e
tter
than n
o
n
-
di
a
gno
sis techn
o
logy of
1oo
2 an
d i
s
clo
s
e to
the 1oo2
D structure with di
agno
si
s circui
t.
5. Conclusio
n
This th
esi
s
h
a
s
pro
p
o
s
ed
a safety voting sy
stem b
a
sed on
D-S ev
iden
ce the
o
ry
. Whe
n
applie
d into case, the follo
wing
con
c
lu
si
ons
can b
e
drawn:
(1)
To ac
hieve the
s
a
fety sec
u
rity func
tion,
the
safety inst
rume
nt system
can
provide axio
m
system in p
r
ocessin
g
the feedba
cks of
channel
s’ ce
rtaintie
s and uncert
a
inties. And
according to
the chann
el
s’ interlo
c
ked
f
eedbacks and ba
sed o
n
the calcula
t
ion of D-S
eviden
ce the
o
ry, it will improve the reli
a
b
ility of diagnosi
s
.
(2)
Safety voting system
can achi
eve system’s self-di
a
gnosi
s
func
tion, improving SI
S’ reliability.
Case analysi
s
has
shown that its output
signal
reliability is obv
iously better than non-
diagn
osi
s
structure and i
s
clo
s
e to structure with dia
g
nosi
s
ci
rcuit.
(3)
The cost of
safety voting system re
du
ce
s co
mpa
r
ing
with traditio
n
a
l system
s.
And it use
s
fewer
hardwa
r
e eq
uipme
n
ts to ac
hieve
the expecte
d
safety func
ti
on. In the existing safety
instru
ment
system, logi
c voting sy
stem is
ei
ther
without self
-diag
n
o
s
is m
e
ch
ani
sm,
or
having comp
licated dia
g
n
o
stic
circuit, whi
c
h re
sult
s in high co
st. Therefore,
the safety
instru
ment
sy
stem
elab
ora
t
ed in
this th
esi
s
c
a
n ac
hie
v
e
s
y
s
t
e
m
’s
s
e
lf-d
ia
gn
os
is fu
nc
tio
n
unde
r the premise
of usi
ng less ha
rd
ware
equi
pm
ent and at the mea
n
time acq
u
irin
g
advantag
es o
f
low co
st, high availability and security.
Ackn
o
w
l
e
dg
ements
We a
r
e g
r
atef
ul to our
colle
ges
and
cla
s
smate
s
Ya Li,
Xiaoge Zh
an
g and Xinyan
g Den
g
who
intro
d
u
c
ed u
s
to
ma
ny of the to
pic
discu
s
se
d in thi
s
pa
per. T
han
ks
are
due
to
any
anonymo
us referee
for co
mments that
help
ed in
crease the
su
bject
s
covere
d in thi
s
p
a
p
e
r
.
Partial finan
-cial
sup
p
o
r
t from the
Na
tional Hi
gh
Tech
nolo
g
y
Re
sea
r
ch a
n
d
Devel
opm
ent
Program of
Chin
a (No. 2
012AA04
110
1), the Fu
n
d
a
mental Re
search
Fo
und
s for the
Ce
ntral
Universitie
s
(No. XD-JK20
13C029
) ar
e also g
r
atefull
y
ackn
owl
edg
ed.
Referen
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Internatio
na
l E
l
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n
ica
l
Commissi
on.
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08.
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unction
al S
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al/Electro
nic/
Progra
mmabl
e
Electronic Saf
e
ty Relate
d Systems
. Genev
a
:
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[2]
Internatio
na
l
Electrotech
n
ic
al C
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mmissi
o
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51
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.
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Sa
fety Instrumented
System
s for the Process Industry Sector
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neva: IEC Pres
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n
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n
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Evaluation Warning : The document was created with Spire.PDF for Python.