TELKOM
NIKA
, Vol.13, No
.3, Septembe
r 2015, pp. 8
94~903
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i3.2010
894
Re
cei
v
ed Ma
rch 9, 2
015;
Re
vised J
une
2, 2015; Accepted June 1
8
, 2015
Spatial–Temporal Anomaly Detection Algorithm for
Wireless Sensor Networks
Liu Xin
1,2
, Zhang Shaolia
ng*
1
1
School of Envi
ronme
n
t Scien
c
e and Sp
atia
l Informatics,
Ch
ina U
n
ivers
i
t
y
of Minin
g
an
d T
e
chnolog
y,
Xuz
h
o
u
Cit
y
,
Ji
angs
u Provi
n
ce, 2210
08, Ch
i
n
a
2
School of Med
i
cine Inform
atio
n of Xuz
h
o
u
Medic
a
l Co
lle
ge,
Xuz
h
o
u
Cit
y
,
Ji
angs
u Provi
n
ce, 2210
04, Ch
i
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fl
y
i
nsk
y
6
@
18
9.cn
A
b
st
r
a
ct
T
r
aditio
nal a
n
o
m
a
l
y detecti
on
alg
o
rith
ms can
not e
ffectively i
dentify spati
a
l
–
temp
ora
l
an
omalies i
n
wireless sensor networks (W
SNs), so we take the
CO
2
concentrati
on
obt
ain
ed
by W
S
N
s
as a
n
ex
a
m
p
l
e
and
pro
pose
a
spatia
l–te
mp
or
al a
n
o
m
aly d
e
t
e
ction
al
gor
ith
m
for W
S
Ns. F
i
rst, w
e
detecte
d outl
i
ers thr
o
u
g
h
the ad
aptiv
e th
resho
l
d. T
hen,
w
e
ex
tracted the e
i
ge
nva
l
ue
(avera
ge) of
th
e slid
in
g w
i
nd
o
w
to be detect
ed,
constructed
th
e spati
a
l
–
te
mp
oral
matrix for
the re
la
tio
n
sh
i
p
betw
e
e
n
n
e
i
ghb
orin
g n
o
d
e
s
in th
e sp
ecifi
ed
interva
l
, use
d
the fu
zz
y
cl
uste
ring
method
to
ana
ly
z
e
th
e ei
g
enva
l
ue
of ad
j
a
cent n
o
d
e
s in
spatia
l–te
mpo
r
al
correlati
on
an
d
classify th
e
m
, and
id
entifi
e
d
the a
b
n
o
rmal
leak
age
pro
b
a
b
ility
accord
in
g
to the r
e
sults
of
the cl
assificati
on. F
i
n
a
lly,
w
e
us
ed
rea
l
d
a
tasets to
verify this algorithm
an
d
ana
ly
ze the
p
a
ra
met
e
rs
selecte
d
. T
he results show
that the alg
o
rith
m has
a
hig
h
d
e
tection rate
a
nd a low
false
positiv
e rate.
Ke
y
w
ords
: w
i
reless se
nsor n
e
tw
orks, spatial–te
mp
oral a
n
o
m
a
l
y, data stre
am
Copy
right
©
2015 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
In recent yea
r
s,
wirel
e
ss
sensor n
e
two
r
ks
(WSNs) h
a
ve bee
n ap
plied in m
a
n
y
fields,
su
ch a
s
environmental
and
habitat monit
o
ring, o
b
je
ct and invento
r
y
tracking, h
e
a
l
th and medi
cal
monitori
ng, b
a
ttlefield ob
servation,
and
indu
st
rial
sa
fety and
con
t
rol [1]. However, the
dat
a
measured a
nd colle
cted
by WSNs is some
tim
e
s un
relia
bl
e because of the reso
urce
contai
nment
s of the no
de
s or
statu
s
cha
nge
s in
th
e m
onitorin
g
o
b
je
ct. Abno
rmal
data in
se
nso
r
netwo
rks can
be
divided
i
n
to ab
no
rmal
point
s
calle
d “outliers” a
nd a
bno
rmal
events
calle
d
“events” [2]. Abnorm
a
l poi
nts are a result of res
ource limitations
of WSNs an
d
sen
s
o
r
no
de
s in
poor e
n
viron
m
ents, whi
c
h
often lead to node failure
and therefore
result in abn
ormal dat
a [3].
Abnorm
a
l events [4] are of
ten descri
bed
as a se
rie
s
o
f
abnorm
a
l values in a d
a
ta
stream.
At pre
s
ent, th
e metho
d
s wi
dely u
s
ed i
n
sen
s
o
r
a
nom
aly dete
c
tion
are
mainly b
a
s
ed
on
several cate
gorie
s, in
clu
d
ing stati
s
tical model te
chnolo
g
y [5],
adja
c
ent de
g
r
ee te
chn
o
lo
gy,
wavelet an
alysis te
chn
o
log
y
[6], and cluster te
chn
o
lo
gy [7]. The method ba
se
d on the statisti
cal
model
is un
suitable fo
r
ab
norm
a
l di
strib
u
tion d
a
ta. T
he m
e
thod
b
a
se
d o
n
clu
s
tering
d
epen
d
s
o
n
the nu
mbe
r
of clu
s
te
rs.
The m
e
thod
s b
a
sed
on
adja
c
ent
deg
ree
technol
o
g
y and
wav
e
let
analysi
s
are complex.
The traffic forec
a
s
t
model [8] uses
the c
o
rrelati
on coefficie
n
t
of predi
cte
d
traffic
seq
uen
ce
s
and the a
c
tual flow se
quen
ce for
anomaly det
ection. The
spatial
–
tem
pora
l
correl
ation ch
ara
c
teri
stics of
the
sen
s
o
r
data
we
re
co
nsid
ere
d
in
[9
], which u
s
e
d
time an
d
spat
ial
correl
ation
s
to gene
rate o
u
tliers. Th
e lo
cal outlie
rs
are conve
r
g
ed
to sink fo
r th
e global o
u
tliers.
This meth
od
is applied o
n
ly to detect abnormal p
o
ints, but so
metimes, ab
norm
a
l se
qu
ence
detectio
n
h
e
l
p
s to
reveal
a
bnormal
even
ts that
oc
cu
r.
Thus,
the tim
e
seri
es of a
n
omaly det
ecti
on
wa
s m
o
re
val
uable
in [1
0],
whi
c
h
pro
p
o
s
ed to
ra
pidly
comp
are the
simila
rities of
two time
seri
es
based
on th
e Cheby
shev
co
efficient
a
nd fou
nd a
n
abn
orm
a
l time sequ
en
ce. The lite
r
at
ure
focu
sed o
n
o
u
tlier dete
c
tio
n
and a
singl
e time se
rie
s
of anomaly detectio
n
in the se
nsor d
a
t
a.
The spatial–t
e
mpo
r
al cha
r
acteri
stics of
the
se
nsor
whe
n
the a
b
norm
a
l event
occu
rre
d was
overloo
k
e
d
[11].
The obje
c
tive
of this study
is to identify the pheno
m
enon of CO
2
leakage by a
nalyzin
g
the abn
ormal
readi
ng
s of
sen
s
o
r
s.
Con
s
ide
r
ing th
e
analysi
s
of CO
2
data st
rea
m
s, we
analy
z
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Spatial–Tem
poral An
om
aly Dete
ction A
l
gorithm
for Wirel
e
s
s
Sen
s
or
Netw
or
k
s
(Liu Xin)
895
the sp
atial–te
mporal chara
c
teri
stics
of
e
a
ch se
nsor when CO
2
lea
k
s [12] an
d th
en identify the
abno
rmal
lea
k
ag
e effe
ctively. In this pa
per,
we
p
r
op
ose
the
spati
a
l–tempo
r
al
a
nomaly
dete
c
tion
(STAD) algorithm for WS
Ns
. Firs
t, 3
rules for the a
nomaly dete
c
tion of adapti
v
e threshold
value is
use
d
. Seco
nd, E
u
clid
ean
dist
ance is
empl
oyed to dete
r
mine th
e nei
ghbo
r no
de
and
extract the
m
ean of time
seque
nce with
in the sl
i
d
ing
wind
ow,
whi
c
h is the
eig
e
nvalue. Th
en,
a
fuzzy
similar
spatial
–
temp
oral mat
r
ix of the nei
gh
bor node i
s
con
s
tru
c
ted. Afterwa
r
d, the fu
zzy
clu
s
terin
g
alg
o
rithm i
s
u
s
e
d
to identify the ab
no
rmal
prob
ability m
odel. Fin
a
lly, the algo
rithm
is
verified u
s
in
g
a real d
a
taset, and the
d
e
tection
rate
(DR)
and
false po
sitive rat
e
(FP
R
)
of th
e
different para
m
eter setting
s are an
alyzed. Severa
l referen
c
e
s
for paramete
r
selectio
n in the
future are pro
v
ided.
2. Problem Descriptio
n
a
nd De
finition
2.1. Backg
ro
und
The g
r
e
enho
use
ga
s
CO
2
, which i
s
emitted by i
ndu
strial
pro
ductio
n
an
d
huma
n
activities, is g
r
adu
ally cau
s
ing global
wa
rming.
The e
a
rth’s e
n
viron
m
ent on whi
c
h people rely is
increa
singly deterio
ratin
g
.
Ca
rbo
n
ca
pture
and
st
ora
ge
(CCS) is
a technol
ogy
that
can
re
d
u
ce
the gree
nho
u
s
e effect of CO
2
by storing
the gas u
nde
rgroun
d.
The main ri
sk of
CCS is le
aka
ge.
Thus, to
mon
i
tor the
safet
y
of the CCS
system, va
ri
ous
monito
rin
g
technolo
g
ie
s
were u
s
ed
to
establi
s
h a th
ree
-
dime
nsi
o
nal monito
rin
g
system. Su
rface
CO
2
co
nce
n
tration monitori
ng
is one
of them. Iden
tifying the lea
k
ag
e cau
s
ed
by monito
ri
ng
data
colle
cte
d
by sen
s
ors
is the
re
sea
r
ch
target of the pape
r.
2.2. CO
2
Sensor
Acco
rdi
ng to
the gas diffusio
n
in the guidi
n
g
prin
ci
ples fo
r environmental ev
aluation,
while l
eakag
e occu
rs, the
con
c
e
n
tratio
n of CO
2
i
s
mainly affect
ed by the
wi
nd spee
d, wi
nd
dire
ction, an
d other
weat
her
con
d
ition
s
. The
r
ef
ore, after a co
m
p
reh
e
n
s
ive consi
deration
of
system m
onit
o
ring
re
quire
ments,
we
selecte
d
sen
s
ors for tem
p
eratu
r
e, hu
mi
dity, wind sp
eed
,
wind directio
n,
and CO
2
c
o
nc
en
tr
a
t
io
n.
T
h
e
C
O
2
concentratio
n
monitori
ng d
e
vice di
ag
ra
m is
s
h
ow
n
in
F
i
gu
r
e
1
.
Figure 1. CO
2
con
c
entratio
n
monitori
ng
system dia
g
ram
2.3. Experimental Set-up
To ide
n
tify the spatial–tem
por
al
charact
e
risti
c
s of the
CO
2
le
akage
, we d
e
si
gnat
ed eig
h
t
sen
s
o
r
s
at e
quidi
stan
ce o
f
the leaka
g
e
sou
r
ce,
and
each se
nsor i
s
lo
cated at t
he same h
e
ight
as the lea
k
a
g
e
sou
r
ces. Th
e layout of every
monitori
n
g
sen
s
o
r
is shown in Figu
re 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
9
30
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 894 – 903
896
Figure 2. Sensor layo
ut ma
p
As the lea
k
a
ge rate i
s
20
L/min and th
e lea
k
age ti
me is 1
5
min
,
the variatio
n of each
s
e
ns
or
is
sh
ow
n
in
F
i
g
u
r
e
3
.
Figure 3. Con
c
entration variation of each
sen
s
or
Figure 3 sho
w
s that, wh
e
n
leakage o
c
curs,
only pa
rt of the sen
s
ors’ con
c
ent
ration
levels
cha
nge
s si
gnificantly, and the
con
c
entration
d
o
e
s n
o
t increa
se
contin
uou
s
ly but volatil
e
ly,
while the diffe
ren
c
e of co
ncentration d
e
te
cted
by the re
maining
sen
s
ors i
s
minimal
.
2.4. Particularit
y
of CO2 Anomaly
Ju
dgment
Many schol
a
r
s p
r
ovide
di
fferent definit
i
ons
of spati
a
l–tempo
r
al
anomaly. Th
e CO
2
c
o
nc
en
tr
a
t
io
n d
a
t
a
ob
ta
in
ed
b
y
W
S
N
mo
n
i
to
r
i
ng
ar
e s
lig
h
t
ly d
i
ffer
e
n
t
fr
om th
os
e
ob
ta
in
ed
b
y
gene
ral STA
D
. First, the
sen
s
o
r
d
a
ta
belon
g to the
data
strea
m
. Seco
nd, CO
2
con
c
e
n
trati
on is
deci
ded by di
ffusion, and t
he diffusio
n
o
f
CO
2
is influ
enced by win
d
spe
e
d, wi
n
d
dire
ction, a
nd
other facto
r
s. Moreove
r
, the respon
se
s of
dif
f
e
rent
se
nso
r
s v
a
ry
.
T
herefo
r
e, the particula
rity of a
CO
2
data st
re
am is a
s
follows:
1) Data
s
t
ream
The data st
ream ha
s ma
ny features,
su
ch
a
s
larg
e and contin
uou
s amou
nts of CO
2
,
rapidity, unpredicta
b
ility, in
freque
nt
sca
nning, and
concept drift char
a
c
te
risti
c
s [13]. In
gene
ral,
the re
se
arch
ers propo
se
d
landma
r
k wi
ndo
w, slid
i
n
g
wind
ow, a
n
d
attenuation
model
s a
c
cording
to the sco
pe
of different time ran
g
e
s
to
redu
ce
storag
e and comput
ational cost
s.
2) Abno
rmalit
y feature
The data
stre
am ca
nnot ef
fectively iden
tify
abnormal
leaka
g
e thro
ugh a
single
sen
s
o
r
analysi
s
of time se
rie
s
da
ta at a ce
rtai
n mome
nt or throug
h an
adja
cent sen
s
or
data a
n
al
ysis
becau
se
sin
g
le
sen
s
o
r
a
bnormality m
a
y be
cau
s
e
d
by
equip
m
ent failu
re. I
n
ad
dition, t
h
e
respon
se of
each se
nso
r
to con
c
entration is differe
n
t. In general, the CO
2
lea
k
ag
e ca
use
d
b
y
abno
rmality h
a
s certain gl
o
bal, dura
b
ility, and fuzzi
ne
ss featu
r
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Spatial–Tem
poral An
om
aly Dete
ction A
l
gorithm
for Wirel
e
s
s
Sen
s
or
Netw
or
k
s
(Liu Xin)
897
2.5. Definitio
n
of CO
2
L
eak
a
g
e
An
o
m
al
y
Definition 1.
Sliding win
d
o
w
: We
cho
s
e
a slidin
g win
dow m
odel t
o
rep
r
e
s
ent t
he data
strea
m
, an
d
assumin
g
th
at the
windo
w le
ngths is
W
, we us
ed
W
as
the time interval. The
observation value
in
W
time can b
e
expre
s
sed a
s
time se
rie
s
S
W
=<
s
1
=(
c
1
,t
1
), s
2
=(
c
2
,t
2
),…,
s
w
=(c
w
,t
w
)>
, w
h
er
e
s
i
re
prese
n
ts th
e v
a
lue
c
i
at the moment
t
i
. The schem
atic
fo
r
the
slid
ing
wind
ow i
s
sh
own in Fig
u
re
4.
Figure 4. Sch
e
matic of the
slidin
g wind
o
w
Definition
2.
CO
2
time
series
abn
orm
a
l point
s: Give
n a time
seri
es
within
the
slidi
n
g
wind
ow,
S
W
=<
s
1
=(
c
1
,t
1
), s
2
=(
c
2
,t
2
),…, s
w
=(c
w
,t
w
)>
. If the ne
wly
derived
ob
se
rvation valu
e
c
j
excee
d
s the t
h
re
shol
d, t
hen that point is abnormal.
Definition
3.
CO
2
l
e
a
k
a
n
o
m
alies:
We d
e
termin
ed th
e eig
envalu
e
of the
slidi
ng
wind
o
w
and the
neig
hbor no
de
n
of the sen
s
or to be d
e
tect
ed. We
obtai
ned the
cl
assification of
ea
ch
node a
s
a re
sult of the fuzzy cl
uste
ring
algor
ithm. T
he pro
bability
of the abnormal leakage
can
be re
pre
s
e
n
ted a
s
the rat
i
o of the nu
mber
of se
n
s
ors
with the
same
cla
s
s a
s
the no
de t
o
be
detecte
d amo
ng all the nod
es. The ratio of the thresho
l
d
T
is expre
s
sed a
s
follo
ws:
%
100
*
)
(
nT
C
count
Dev
,
(1)
W
h
er
e
Count
(C)
re
presen
ts the
num
be
r of
se
nsor n
ode
s in
the
same
cla
s
s a
s
the
nod
e to
be
detecte
d a
n
d
T
is the th
re
shol
d. Sen
s
o
r
no
de
s a
r
e
evenl
y dist
rib
u
ted, so the
con
c
e
n
tration
of
about 50% of
sen
s
o
r
s d
o
wnwin
d
are affected; the
r
ef
o
r
e, on the b
a
sis of prio
r exp
e
rien
ce,
we set
the value of
T
to 50%.
3. Algorithm Defini
tion an
d Main Ideas
Con
s
id
erin
g t
he p
a
rticula
r
ity of CO
2
lea
k
age, we ado
p
t
ed
fuzzy clu
s
tering algo
rith
m
[14]
to analy
z
e th
e spatial–tem
poral
correlati
on m
easur
e
m
ents of e
a
ch sen
s
or to
e
ffectively iden
tify
anomali
e
s.
Figure 5. STAD
pr
oc
ess
bas
e
d on fuzzy c
l
us
ter
i
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
9
30
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 894 – 903
898
Takin
g
into
accou
n
t the lightwei
ght requi
reme
nts
of sen
s
o
r
an
omaly dete
c
tion, we
divided th
e a
l
gorithm
into
two p
h
a
s
e
s
.
The first
stag
e u
s
e
s
the
sl
iding
wind
ow to ide
n
tify the
abno
rmal poi
nts. At the seco
nd
stag
e, the neighbo
r node i
s
de
termine
d
by extracting th
e
eigenvalu
e
of
the slidin
g wi
ndo
w.
Th
e fu
zzy
ch
aracte
ristic
matrix fo
r the
eig
enval
ue of th
e
slidi
ng
wind
ow
sp
eci
f
ies its n
e
igh
bor n
ode
s.
We u
s
e
d
fuzzy clu
s
te
ring
to identify abnormal le
akag
e
prob
ability. The pro
c
e
s
s of anomaly det
ection i
s
sh
o
w
n in Figu
re
5.
3.1. Abnorm
al Point Dete
rmination of
Time Seque
nce
The data
stre
am of CO
2
e
x
hibits a
stro
ng sea
s
on
al featur
e; to im
prove the
accura
cy of
detectio
n
thresh
old, ada
p
t
ive problem
s should
be
con
s
id
ere
d
. By analyzing
the time-varying
cha
r
a
c
teri
stics and di
stri
b
u
t
ion feature o
f
the CO
2
mo
nitoring d
a
ta, we co
ncl
u
de
d, on the basis
of the Cheb
yshev theorem of large
numbe
rs
a
nd ce
ntral li
mit theorem,
that the CO
2
con
c
e
n
tration
of the
data
st
ream
in th
e fi
xed sli
d
in
g w
i
n
d
o
w
c
o
n
f
orm to
no
r
m
a
l
dis
t
r
i
b
u
tion
(
p
ro
o
f
omitted). T
h
e
ne
wly de
rive
d ob
se
rvation
value i
n
the
slidin
g
windo
w
can
dete
r
m
i
ne its thresh
old
value acco
rdi
ng to the following rule
s.
3
rules: If we suppo
se that
)
,
(
~
2
N
X
, then the probability
of the normal observed
values di
strib
u
ted in
)
3
,
3
(
shou
ld be 99.74%
. Among them,
is the mean value of
the wind
ow a
nd
is the sta
n
dard d
e
viatio
n of the data within the wi
n
dow.
Thro
ugh
3
rul
e
s,
we
ob
se
rved that the
cha
n
ge
in th
e threshold
value, a
c
comp
anied
by the chan
g
e
in the mean
and stan
dar
d
deviation, ha
s strong ad
ap
tability.
3.2. Spatial–temporal Abn
ormal Judg
ment
As shown i
n
the p
r
ece
d
ing a
nalysi
s
, the
leakage determination is
unusual. T
h
e
eigenvalu
e
of
the multiple
sen
s
o
r
s i
s
n
e
eded fo
r the
spatial
and t
e
mpo
r
al
correlation a
naly
s
is.
The di
scu
ssi
on on
sele
cting the
eige
nvalue, det
e
r
mi
ning the
nei
g
hbor no
de
s, and STA
D
ba
se
d
on fuzzy clu
s
tering i
s
as foll
ows.
1) Sele
cting the abn
orm
a
l eigenvalu
e
To dete
r
min
e
the seque
nce simil
a
rity d
egre
e
of the
adja
c
ent n
o
des fo
r the
a
nomaly
detectio
n
sen
s
or,
we
u
s
ed
the di
stan
ce
of
the co
rre
spondi
ng
m
e
a
s
ureme
n
ts be
tween
the no
des
[2]. However,
we observed that
CO
2
le
a
k
ag
e cau
s
e
d
by
the ch
ang
e
in
the se
nsor doe
s not
h
a
ve
a one-to
-o
ne
relation
shi
p
, as sho
w
n in
Figure 6.
Figure 6. Co
mpari
s
o
n
ch
a
r
t of obse
r
va
tion data from
different se
nsors
Figure 6 sh
o
w
s that di
re
ctly
using the observation v
a
lue can cau
s
e a la
rge e
r
ror
DR.
Con
s
id
erin
g t
he
cha
r
a
c
teri
stics of
the
o
b
se
rved
valu
e of
CO
2
l
e
a
k
age,
we
ch
ose the
mea
n
v
a
lue
of co
ncentration to
de
scri
be the
chan
ge
cha
r
a
c
teri
stics of
the
observation
values withi
n
the
slidin
g wi
ndo
w, which
can
smo
o
then
th
e influen
ce
o
f
the insta
n
ta
neou
s
cha
n
g
e
s to
a
certa
i
n
degree.
2) Dete
rmini
n
g the neigh
bo
r node
The voting de
cisi
on was u
s
ed to identify the neighb
o
r
node [15]. A Voron
o
i diag
ram wa
s
use
d
to det
ermin
e
the
adja
c
ent no
d
e
[16]. To simplify the calcul
ation, in
this pap
er,
we
determi
ned t
he neig
hbo
r
node b
a
sed o
n
the fact tha
t
the Euclide
a
n
distan
ce i
s
less than a fi
xed
value
K
.
K
is
set a
c
cording
to the dista
n
c
e of a
se
nso
r
. The
sen
s
o
r
node to
be d
e
tected i
s
O
, the
c
o
or
d
i
na
te
po
s
i
tio
n
is
(
x
,
y
), the neig
h
bor no
de set to be determi
ned is
X
= {
X
1
,
X
2
,..
.,
X
n
}
,
the
coo
r
din
a
tes of
the
X
i
is (
x
i
,
y
i
), a
nd th
e dista
n
ce b
e
twee
n the n
o
de
s
X
i
an
d
O
is d
e
fined
as
follows
:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Spatial–Tem
poral An
om
aly Dete
ction A
l
gorithm
for Wirel
e
s
s
Sen
s
or
Netw
or
k
s
(Liu Xin)
899
2
2
)
(
)
(
)
,
(
y
y
x
x
O
X
dist
i
i
i
.
(2)
If the distance of dist (
X
i
,
O
) is less than
K
, then it b
e
com
e
s the
K
th neighbo
r
of
X
i
when
the value is
O
.
3) STAD ba
sed on fuzzy cl
usteri
ng
The data coll
ected by se
n
s
or n
ode
s ten
d
to
have certain spatial correlation
s
. G
enerally,
the relevan
c
e of
sp
ace
refers to th
e
data of
t
he n
ode
s related
to
the clo
s
e
physi
cal
l
o
ca
tion
cha
nge
ap
proximation. Howeve
r, CO
2
lea
k
ag
e
cau
s
ed
by th
e
spatial
co
rrel
a
tion h
a
s a
certain
particula
rity becau
se the
diffusion of
CO
2
in the
atmosp
here
is not
even
ly distributed
. In
prin
ciple, it i
s
sp
rea
d
do
wnwin
d
, but b
e
ca
use
of th
e influen
ce
o
f
atmosp
he
ric turbule
n
ce, the
wind i
s
not st
able an
d the
con
c
e
n
tration
chan
ge of
th
e re
spo
n
se of each
se
nsor
also diffe
rs.
No
stri
ct mathe
m
atical fo
rm
ulas are u
s
e
d
to d
e
termi
ne the
lea
k
a
ge. Th
e
sen
s
ors also
ca
nno
t
identify the status of lea
k
a
ge stri
ctly accordin
g to the relation
shi
p
b
e
twee
n dista
n
ce o
n
the ba
si
s
of the neigh
b
o
r no
de
s, so
we ne
ed to
combine
th
e fuzzy theory a
nd spatial–te
mporal variati
on
cha
r
a
c
t
e
ri
st
ic
s of
CO
2
diffusion
to ju
dge
the lea
k
a
ge p
r
oba
bility. Thi
s
study u
s
e
s
f
u
zzy cl
uste
rin
g
method
s to condu
ct the STAD. The st
e
p
s are de
scri
bed bri
e
fly as follows:
a)
The data a
r
e
prep
ro
ce
ssed
.
m
j
n
i
x
x
x
j
j
ij
ij
,...,
2
,
1
,
,...,
2
,
1
,
'
(3)
n
i
n
i
j
ij
j
ij
j
m
j
x
x
n
x
n
x
11
,...,
2
,
1
,
)
(
1
1
,
1
b)
The co
efficie
n
t of similarity between sample
s or va
riable
s
is
cal
c
ulate
d
, and the
fuz
z
y
s
i
milar
matrix is
c
o
nstruc
ted.
m
k
j
ik
m
k
i
ik
m
k
j
jk
i
ik
ij
x
x
x
x
x
x
x
x
r
1
2
1
2
1
)
(
)
(
(4)
m
k
m
k
jk
j
ik
i
x
m
x
x
m
x
11
,
1
1
c)
The fuzzy ari
t
hmetic is u
s
ed to tran
sf
o
r
m and
synth
e
si
ze the
si
milar matrix.
The
fuzzy eq
uival
ence matrix is gen
erate
d
.
d)
The fuzzy clu
s
terin
g
is con
ducte
d on th
e bas
i
s
of the
different levels of intercept
ion
for the fuzzy equivalen
c
e
matrix.
4. Steps of the Algorith
m
4.1.
O
v
er
v
i
e
w
o
f
the Alg
o
rithm
The
3
rule
s were
use
d
for
each sen
s
or
data
st
ream t
o
dete
c
t the
outliers. After the
outliers we
re
found, formul
a (2) was u
s
ed to det
ermi
ne the neigh
bor no
de
s, and the correl
ation
coeffici
ents o
f
the eigenval
ue we
re
cal
c
ulated by
formula (4
). The
n
, one can ju
dge whethe
r
any
abno
rmal mo
de occu
rs a
c
cording to def
inition 3.
4.2. Steps of the Algorith
m
1) Outlie
r det
ection
Algorithm inp
u
t: the point of C
i
to be detected
Algorithm out
put: whethe
r the point of C
i
is an outlie
r
The algo
rithm
steps a
r
e
sh
own a
s
follo
ws:
a) The info
rm
ation of each slidin
g wind
o
w
)
,
,
(
i
i
i
WID
is calculate
d
and re
co
rd
ed.
b) The varia
n
ce a
nd the
mean value i
s
used to cal
c
ulate
)
3
,
3
(
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
9
30
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 894 – 903
900
c) Th
e ob
serv
ed value of C
i
to be detecte
d is rea
d
.
d) If C
i
is not in the interval of
)
3
,
3
(
, it is judged as an a
b
no
rmal point.
(2) Abn
o
rm
al pattern r
e
c
o
g
n
ition
Algorithm in
p
u
t: the coo
r
di
nate po
sition
(
x
,
y
) of the
abno
r
mal
se
nso
r
; the sli
d
ing wi
ndo
w
numbe
r of
m
; and the thre
shold value
Algorithm out
put: abnormal
leaka
ge
a) Fo
rmula 2
is used to det
ermin
e
the ne
ighbo
r nod
e.
b) The fuzz
y
c
h
arac
teris
t
ic matrix
with
n
nod
es an
d t
he ei
genvalu
e of
m
s
lid
in
g w
i
nd
ow
s a
r
e
establi
s
h
ed.
c) A seri
es
of tran
sforma
tions i
s
co
nd
ucted
on the fuzz
y char
ac
ter
i
s
t
ics
matrix, and this
matrix is tran
sform
ed into
a fuzzy eq
uivalen
c
e matrix
.
d) The fu
zzy
equivalen
c
e
matrix is cla
s
sified a
c
cordi
ng to
.
e) The p
r
ob
a
b
ility of abnormal leakage i
s
determine
d according to formul
a 1.
5. Experimental Verifica
tion and Anal
y
s
is
Con
s
id
erin
g t
hat no
sta
n
d
a
rd
datab
as
e
is cu
rrently available
for the
CO
2
lea
k
age te
st,
we an
alyze
d
the detectio
n
results of the
al
gorithm
with the real d
a
taset
s
of the CO
2
lea
k
ag
e
to
verify the effi
c
i
enc
y
of the STAD algorithm in this
s
t
udy.
5.1. Experimental Setup Des
c
ription
The expe
rim
ental data
s
et use
d
the field to
simulate the lea
k
age d
a
ta. The experime
n
tal
site
is at
the open sq
uare without
a
n
y
b
u
ilding
s
. The
monitori
ng d
a
t
e wa
s Septe
m
ber
21, 20
1
4
.
The l
e
a
k
age
rate
wa
s
20
L/min a
nd th
e lea
k
a
ge l
a
sted for 15
mi
n. The
hei
ght
of the
lea
k
a
g
e
sou
r
ce wa
s 1
m. The height of the mo
nitoring
p
o
int
was al
so 1
m
. The sen
s
ors
colle
cted
data
once every 2
0
s. The ra
ng
e of the wind
spe
ed was
from 0 m/s to 4
.
5 m/s.
The sensors we
re
0.6
m away from
the leakage source.
The
sensor di
strib
u
t
ion is sh
ow
n
in Figure 2.
Figure 7 depi
cts
each monito
ri
ng data curve
for
each of the eight se
nso
r
s.
Figure 7. CO
2
C
o
nc
e
n
t
ra
tion
c
u
r
v
e
5.2 Data Pro
cessing
As a
n
exa
m
p
l
e ba
se
d o
n
slidin
g
wind
o
w
le
ngth
L
of 10, th
e n
u
m
b
er of
wind
o
w
s that
need
to b
e
d
e
tected
is 10
and th
e n
u
m
ber
n
of nod
e
s
e
q
ual
s 8.
T
he cla
ssifi
cati
on
results of
the
fuzzy cl
uste
rs obtained a
r
e
sho
w
n a
s
foll
ows.
Table 1. Cla
s
sificatio
n
re
su
lts (M = 10, L
= 10)
Thres
hold
Num
b
er
Specific
Cate
go
r
y
=0.5
1
{device01,device02,device03,de
vic
e04,device05,
device06,dev
ice
07,device08}
=0.6
1 {device01,device02,dev
ice03,device04,device05,devic
e06,device0
7,device08}
=0.7
1 {device01,device02,dev
ice03,device04,device05,devic
e06,device0
7,device08}
=0.8
3 {device01},{d
e
vice02,device04,de
vi
ce05,device08},{devic
e03,device06,device07}
=0.9
4 {device01},{d
e
vice02,device04,de
vic
e05,device08},{device03,dev
ice06},
{
device07}
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
9
30
Spatial–Tem
poral An
om
aly Dete
ction A
l
gorithm
for Wireless
Sens
or
Networks
(Liu Xin)
901
The
re
sults i
n
Ta
ble
1
sh
ow th
at we
cannot
achiev
e the
cla
s
sification
effect
whe
n
the
value of i
s
too small. Th
e greater the
value of i
s
, the more accurate the
c
l
as
s
i
fic
a
tion is
.
Whe
n
L
is 10
and
M
i
s
10,
the test
re
sult
s a
r
e
the
sa
m
e
when
L
and
M
ar
e r
e
s
pec
tive
ly e
q
ua
l to
0.8 an
d 0.9.
To comp
are
the dete
c
tion
re
sults,
we
evaluate
the
perfo
rman
ce
of
the
alg
o
rit
h
m
wit
h
t
h
e
a
c
c
u
racy
of
t
h
e
cl
as
sif
i
cat
i
o
n
r
e
sult
s.
Wh
en t
h
e
cla
ssifi
cati
on n
u
mbe
r
i
s
3, the a
bno
rmal
sen
s
o
r
nod
es in this experi
m
ent are d
e
vice
s 02, 04, 0
5
, and 08.
We a
dopte
d
DR
and FP
R,
whi
c
h a
r
e
co
mmonly u
s
ed
in anom
aly d
e
tection
as
a
n
index
to measu
r
e th
e perfo
rman
ce of the algori
t
hm.
5.3. Result E
v
a
l
uation
1) DR
The com
p
lexi
ty of the algorithm is det
ermi
n
ed by the length an
d the numbe
r
of the
slidin
g wind
o
w
s in
clu
ded i
n
the cal
c
ulati
on. Thu
s
, we
analyzed the
length an
d nu
mber.
First, we a
nal
yzed the len
g
t
hs of the slid
ing
win
dows.
Becau
s
e thi
s
factor
can in
crea
se
the com
p
lexity of the calculatio
n, our analys
i
s
sh
ows that 10
0% of the anomalie
s ca
n be
identified wh
e
n
the sliding
wind
ow len
g
th of
L
is 10 and the numbe
r of
M
windo
ws is e
qual to
10.
Therefore, to
redu
ce the
comp
utationa
l comple
xity and compa
r
e
the DR of the algo
rithm, we
approp
riately decrea
s
e
d
the slidin
g wind
ow len
g
ths to
6 and 10.
Figure 8. DRs of different
wind
ow len
g
ths when
M
is
equal to 10
Figure 8 d
epi
cts that th
e
DR
wa
s 1
0
0
%
when
the l
ength
s
of the
slidin
g wi
nd
ows were
10 a
nd
8. Th
e DR
dro
ppe
d to 7
5
% wh
en the
len
g
th
s of th
e
slidin
g wi
ndo
ws
were
ch
ang
ed
to 6.
This findin
g
shows that re
duci
ng the co
mputational
complexity is con
d
u
c
ted at
the expense
of
the DR.
Secon
d
, we
analyzed the
numb
e
r
of sl
iding
wind
ows. The
follo
wi
ng
comp
are
s
the DR
whe
n
the
slid
ing
windo
w
n
u
mbe
r
rang
e
s
fro
m
8
to
1
2
an
d the l
e
n
g
ths
of win
d
o
w
s are 6,
8,
and
10.
(a)
M
=6
(b)
M
=8
(c
)
M
=
10
Figure 9. Co
mpari
s
o
n
of the DR und
er
different win
d
o
w num
be
rs
and len
g
ths
Figure 9 sho
w
s that the i
n
sp
ectio
n
DR of
the eve
n
t anomaly d
e
tection b
a
se
d on the
fuzzy
clu
s
teri
ng is high
er
a
s
a
whol
e. Fi
gure
9(
a)
dep
icts that th
e
DR
de
crease
d
slig
htly whe
n
M
take
s 6
as it
s value. Figu
re
9(b
)
an
d 9
(
c)
depi
ct that th
e DR
can
rea
c
h 1
0
0%
whe
n
M
is greate
r
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
9
30
TELKOM
NIKA
Vol. 13, No. 3, September 20
15 : 894 – 903
902
than 8. Thi
s
finding
sug
g
e
s
ts that the len
g
ths of
the
sli
d
ing wi
ndo
w
s sho
u
ld have
a value of 8 o
r
large
r
in such
a situation; n
o
differen
c
e e
x
ists
in the DR in terms
of the number of windows
.
2) FPR
The FPRs sh
own in Fig
u
re
10 are
whe
n
the numbe
r of windo
w
s is from 8 to 12 and the
length
s
of the sliding
windo
ws a
r
e 6, 8, a
nd 10.
(a) M
=
6
(b) M
=
8
(c
) M=
10
Figure10. Co
mpari
s
o
n
of the FPRs und
er the
differe
nt numbe
rs of
windo
ws and
different
length
s
Figure 10
d
epict
s that t
he FP
R of t
he
event
an
omaly dete
c
t
i
on ba
se
d o
n
fuzzy
clu
s
terin
g
is
nearly 0 whe
n
the numb
e
r
of wind
ows is larg
er tha
n
10; whe
n
the numb
e
r o
f
wind
ows i
s
8,
the FP
R i
s
h
i
gher.
The
F
P
R in
crea
se
s sig
n
ifica
n
tly whe
n
the
len
g
th of the
sli
d
ing
wind
ows is 6.
In summa
ry, the algo
rithm
has hi
ghe
r DR and lo
we
r FPR as a
wh
ole for event
anomaly
detectio
n
. Fo
r the ano
mal
y
detection u
nder th
ese
e
x
perime
n
tal condition
s
, co
nsid
erin
g the
dual
deman
d of th
e DR
and the
FPR, we
sug
gest that
the l
ength
s
of win
dows
shoul
d
be 8 o
r
great
er
and the num
b
e
r of the dete
c
ted wi
ndo
ws shoul
d be 10
or gre
a
ter.
6. Conclusio
n
The tradition
al dete
c
tion
method,
whi
c
h ne
gle
c
ts th
e featu
r
e
of o
b
se
rvation va
lues an
d
usu
a
lly adopt
s the static th
reshold m
e
th
od, may
cau
s
e the FPR to be too high.
Con
s
id
erin
g the
temporal and
spatial
cha
r
a
c
teri
stics of
CO
2
lea
k
a
ge,
we p
r
op
ose
d
a STAD al
gorithm
ba
se
d on
fuzzy
clust
e
ri
ng. The alg
o
rithm is divide
d into
two st
age
s. First, the abn
orm
a
l
points fo
r every
sen
s
o
r
are id
entified usi
n
g
3
rule
s. Seco
n
d
, the eigenv
alue of
the sli
d
ing wi
ndo
w
are extra
c
ted
to create a
model b
a
sed
on the fu
zzy equivalen
c
e model to
o
b
tain the
cla
ssifi
cation
re
sults
unde
r differe
nt thresh
old
s
. This method
allows the
ide
n
tification of the abno
rmal
prob
ability. This
algorith
m
extend
s the a
p
p
licatio
n sco
pe of the fu
zzy clu
s
terin
g
algo
rithm. The
expe
rim
ental
results
sho
w
that the algorithm ha
s a
high DR
an
d a low FP
R. As a re
sult of the limited
con
d
ition
s
, th
e nu
mbe
r
of
the
simulatio
n
nod
es is le
ss and
the
pa
ra
meter
sel
e
cti
on i
s
too
sim
p
le,
whi
c
h only ve
rified the pe
rf
orma
nce of the metho
d
ini
t
ially. These finding
s shoul
d be verified
on
platform
s wit
h
a large
r
nu
mber of sen
s
or nod
es.
Ackn
o
w
l
e
dg
ements
The
p
ape
r was su
ppo
rted
by
the 12th Five
Year sci
ence a
nd te
chnolo
g
y supp
ort Plan
No. 201
1BAC08B0
3
, a proje
c
t fund
e
d
by the Priority Acade
m
i
c Prog
ram
Develo
pment
of
Jian
gsu High
er Edu
c
ation
Institutions u
nder G
r
a
n
t No. SZBF2011
-6-B3
5
.
Referen
ces
[1]
McDon
a
ld D
y
l
an, Sanch
e
z Ste
w
a
r
t Madria
Sanj
a
y
, et
al. A Surve
y
of Methods for F
i
nd
ing O
u
tli
e
rs
i
n
W
i
reless Se
ns
or Net
w
orks.
Journ
a
l of netw
o
rk and syste
m
s man
a
g
e
m
ent
. 2015; 23(
1): 163-1
82.
[2]
Shah
id N, IH
Naqvi, SB Q
a
i
s
ar. Char
acteri
sti
cs and cl
ass
i
ficatio
n
of outl
i
er det
ection te
chni
ques fo
r
w
i
rel
e
ss se
nso
r
net
w
o
rks
in
h
a
rsh e
n
viro
nm
ents: a surv
e
y
.
Artificial Inte
lli
genc
e Rev
i
ew
. 201
5; 43(
2):
193-
228.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Spatial–Tem
poral An
om
aly Dete
ction A
l
gorithm
for Wirel
e
s
s
Sen
s
or
Netw
or
k
s
(Liu Xin)
903
[3]
Hua
nhu
an C, Jian H, Kai W
,
et al. Research
o
n
W
S
Ns fault detec
tion metho
d
b
a
sed o
n
nod
e
similar
i
t
y
.
Transducer and Mic
r
osystem
Tec
h
nology
. 20
14; 33(4): 10-
13.
[4]
Shah
id N, IH
Naqvi, SB Qa
i
s
ar. Real T
i
me
Energ
y
Efficient Approach to Ou
tlier & eve
n
t detectio
n
in
w
i
reless sens
or net
w
o
rks.
IEEE International
Confer
enc
e
on Communic
a
tion system
s
. 20
1
2
; 162-1
66.
[5]
Qiu
y
an
Y. Res
earch
on
Min
i
n
g
Meth
od
of Mi
ne Pr
oba
bil
i
sti
c
Stream D
a
ta.
Chi
n
a
Un
ivers
i
ty of Min
i
n
g
and T
e
ch
no
log
y
. 2011.
[6]
Z
h
i
y
ua
n L, Qi
uzhi Z
,
Yon
g
k
un W
,
et al.
W
a
velet An
al
ysis-Base
d Re
al-time A
noma
l
y
Detecti
o
n
Algorit
hm for
W
i
reless S
ens
or N
e
t
w
ork.
J
ourn
a
l
of N
a
n
jing
N
o
r
m
al
U
n
iversity (
N
atu
r
al Sci
enc
e
Editio
n).
201
4; 37(1): 87-
92.
[7]
Kim Ho
ng
ye
on
, Min Ju
n-Ki. A
n
Ener
g
y
-Effici
ent Outlier
Det
e
ction B
a
se
d o
n
Data
Cl
usteri
ng i
n
W
S
Ns.
Internatio
na
l Journ
a
l of Distri
buted Se
nsor
Netw
orks
. 201
4.
[8]
Z
heng
ho
ng
X,
Z
hanfu
X, Z
h
i
y
ang C. A
n
Ano
m
al
y De
tecti
o
n
Appro
a
ch Bas
ed o
n
T
r
affic Predicti
on a
n
d
Correlation Coeffi
cient for W
S
N.
Microelectr
o
n
ics & Co
mp
uter
. 2009; 7: 21
4-21
6.
[9
]
An
ro
ng
X
,
Ming
L
.
An
o
m
aly
r
ead
ing
detecti
on al
gorit
hm in
W
S
N.
Applicat
ion R
e
se
arch o
f
Computers
.
201
0(9): 34
52-
345
5.
[10]
Qi
T
,
Xuej
un L
.
Outlier T
i
me
Series D
e
tecti
on Bas
ed o
n
W
S
N.
Journal
of T
r
ansducti
o
n
T
e
chn
o
lo
gy
.
201
3(1): 95-
99
.
[11]
Yu Genj
ian, W
eng k
unp
en
g. In
trusio
n detect
i
on tec
hno
lo
g
y
of la
yere
d
w
i
r
e
less se
nsor
n
e
t
w
o
r
k b
a
sed
on Age
n
t.
T
E
LKOMNIKA Indones
ian J
ourn
a
l of Electrica
l
Engi
neer
in
g
. 2013; 11(
8): 423
8-42
43.
[12]
Sano
F
u
min
o
ri
, Akimoto K
e
i
g
o, W
ada
Ke
nic
h
i.
Impacts of different diffusi
on
sc
enar
ios
for
mitig
a
tio
n
techno
lo
g
y
opti
ons a
nd of mo
del r
epres
entat
ions r
egar
din
g
rene
w
a
b
l
es i
n
termittenc
y o
n
eval
uatio
ns o
f
CO
2
emissions
reductio
n
s.
Cli
matic C
h
a
nge
.
201
4; 123(
3-4)
: 665-67
6.
[13]
Kumar Ashok
PM, Vaide
h
i
V. Anomal
ous
Event
Detecti
on in T
r
affic Vide
o Base
d
on Se
que
ntia
l
T
e
mporal Patterns of Sp
atia
l
Interval Eve
n
t
s
.
KSII Transactions on Inter
net and Infor
m
ation system
s
.
201
5; 9(1): 169
-189.
[14]
Weilin
Li, P
a
n
Fu, Erqin Zh
a
ng. Ap
plic
ation
of fr
actal dim
ensi
ons and
fu
zz
y
cl
usteri
ng to
tool
w
e
a
r
monitori
ng.
T
E
LKOMNIKA Indon
esia
n Jour
nal
of Electric
al
Engin
eeri
n
g
. 2
013, 11(
1): 187
-194.
[15]
Ying
hui Qi
u, C
hao
Liu. Mo
del
ling
an
d stimul
ation
of target trackin
g
an
d loc
a
lizati
on
in
w
i
r
e
less se
ns
o
r
net
w
o
rk.
Technical Ga
z
e
tte
.
201
4; 21(2): 23
3-24
5.
[16]
Yan W
,
Yuchun P, Hui W
.
Based o
n
Vo
rono
i
and Info
rmation e
n
trop
y sp
atial Outli
e
rs Detectio
n
Algorit
hms.
Co
mp
uter Eng
i
n
e
e
rin
g
and D
e
si
gn
. 201
0; 18: 3
998-
400
0.
Evaluation Warning : The document was created with Spire.PDF for Python.