TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 11, Novembe
r
2014, pp. 76
9
7
~ 770
4
DOI: 10.115
9
1
/telkomni
ka.
v
12i11.63
44
7697
Re
cei
v
ed Ma
y 30, 201
4; Revi
sed Septe
m
ber
6, 2014
; Accepte
d
Septem
ber 30,
2014
Robustness Estimation of Wireless MEMS Vibration
Test under Harsh Environment
Chan
gjian Deng
Schoo
l of Auto
mation En
gi
ne
erin
g, Univers
i
ty of
el
ectronic
scienc
e an
d techno
log
y
of Ch
ina,
No.20
06, Xi
yu
an Ave, W
e
st Hi-T
e
ch Z
one, 611
73
1
Dep
a
rtment of Contro
l Engi
ne
erin
g, Chen
gd
u Univ
ersit
y
of Information T
e
chno
log
y
,
Che
ngd
u cit
y
Xuefu roa
d
bl
oc
k 1 No24, 6
102
25
E-mail: che
ngl
i
_dcj@
16
3.com
A
b
st
r
a
ct
Rob
u
stness
es
timati
on
is i
m
p
o
rtant issu
e to
ensur
e
stab
ility
,
relia
bil
i
ty, an
d
precis
ion
of
Wireless
MEMS vibrati
o
n test u
n
d
e
r h
a
r
sh e
n
viro
n
m
e
n
t stressin
g
.
Al
thoug
h th
e ro
b
u
stness
of vibr
ation
test is
li
mited
ma
inly
by the
embe
dde
d e
l
e
c
tronics a
nd s
ensors, h
o
w
to obtai
n pr
ecise
and r
o
b
u
st da
ta by usi
ng
en
erg
y
effective a
nd r
e
sourc
e
s co
nstrain
ed w
i
re
less
sensor
n
odes
is
still a prob
le
m.
Pa
per
uses
the mu
ltivari
a
t
e
uncerta
inty statistics method t
o
esti
mate ro
b
u
stness
of o
n
li
ne test data
un
der h
a
rsh e
n
vir
o
n
m
e
n
t, and u
s
e
s
F
i
sher infor
m
ation d
i
stanc
e to estimate trans
mittin
g
rob
u
stn
e
ss in its co
mp
licatio
n co
mmu
n
icati
on pr
oces
s
.
Experi
m
ents a
nd si
mulati
on
a
r
e des
ign
ed to
ana
ly
z
e
th
e ro
bustness
an
d
precis
e of w
i
rel
e
ss MEMS no
de
s
in nu
merica
l va
lue, resu
lts sho
w
estimatio
n
methods a
nd
mo
del ar
e effective.
Ke
y
w
ords
:
robustness, mult
ivariat
e
uncert
a
inty statistics, Cramer-Ra
o
l
o
w
e
r boun
d, F
i
sher infor
m
ati
o
n
distanc
e
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
Measuri
ng vibration i
s
very esse
ntial in
detecting
an
d diagn
osi
n
g
any deviatio
n
from
norm
a
l con
d
i
t
ions. The a
d
vantage of MEMS acce
l
e
rom
e
ters from conve
n
tional pie
z
oel
e
c
tri
c
accele
rom
e
te
rs a
r
e their
si
ze, ea
sy insta
llation, co
st and so o
n
.
In life cycle
analysi
s
, there a
r
e som
e
qua
litative
experime
n
ts result
s for
MEMS
accele
rom
e
te
rs in n
o
rm
al and ha
rsh work
situat
io
n. Ron Denton
repo
rted reli
ability result
s on
MEMS accel
e
rom
e
ters fro
m
field failu
re expe
rien
ce,
the MTBF
b
e
ing a
r
o
und
2,000,00
0 ho
urs
(aroun
d 5*10
-7h
-
1 for a
n
expone
ntial d
i
stributio
n of
failure
s) [1]. Andover
rep
o
rt
ed a failure rate
of 1.75
ppm
for MEMS
a
c
cele
rom
e
ters manufa
c
tu
re
d by MEMSI
C
[2].The
se
result
s
sho
w
t
hat
MEMS accel
e
rom
e
ters are high reliability devices
,
with low fai
l
ure rate. There have been
several studi
es [3-6] ad
dressing this i
s
sue for
irra
diation. COT
S
accel
e
ro
m
e
ters h
a
ve b
een
sho
w
n to su
rvive 1000 temperature
cycle
s
from -
6
5
°
C to +1
50°
C, as well as 3
0
,000 me
cha
n
ical
sho
c
ks of 2,0
00G. But there are not en
o
ugh test an
d analysi
s
of its robu
stne
ss.
Meanwhile, t
he MEMS
se
nso
r
s hol
d a
gre
a
t promi
s
e for th
e u
s
i
ng of
wirel
e
ss
sma
r
t
vibration me
asu
r
em
ent b
a
se
d co
nditio
n
monitorin
g
[7-14]. The robu
stne
ss o
f
the calibrati
on
pro
c
ed
ure un
der h
a
rsh en
vironme
n
t is
cru
c
ial fo
r the
potential pra
c
tical u
s
e
of multi-sen
s
or
and
singl
e se
nsor device
s
. MEMS accele
ro
meters
appli
e
d in the pap
e
r
are
ca
paciti
v
e base
d
MEMS
accele
rom
e
te
rs, it mea
s
ure cha
nge
s o
f
the
capa
citance betwee
n
a pro
o
f mass and a fi
xed
con
d
u
c
tive electro
de sepa
rated by a narrow g
ap [15].
As the MEM
S
sen
s
o
r
s of
embed
ded
el
ectro
n
ics
hav
e two
com
p
e
n
satio
n
me
an
s un
de
r
harsh
environ
ment. On
e i
s
environme
n
t co
mpe
n
satio
n
(system
e
r
ror);
the other is noise si
gn
al
filter which is stre
ssed b
y
harsh e
n
vironm
ent
(ra
n
dom error a
nd uncertai
n
ty). The pape
r is
focu
sed
on
th
e second
pro
b
lem. Robu
st
statisti
c i
s
sh
own
to b
e
u
s
eful to d
eal
with the u
n
cert
ain
data in
no
rm
al envi
r
onm
e
n
t [16-20]. Ba
sed
on
thi
s
,
pape
r
su
ppo
ses th
at the
collect
data
un
der
harsh
enviro
n
ment
contai
n "inform
a
tio
n
” of te
st
da
ta. And the f
i
she
r
info
rma
t
ion matrix a
nd
Cra
m
er-Rao
lowe
r bou
nd are ap
plied to analyze
ro
bustn
ess and
preci
s
e of vibration
sen
s
or
[21].
This pap
er a
ddre
s
se
s the
problem
of
robu
st
ne
ss e
s
timation of
wi
rele
ss MEMS
se
nsor
work
ing under hars
h
envir
onment. In sec
t
ion II, The formulation
of problem is introduc
e
d. In
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TELKOM
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KA
Vol. 12, No. 11, Novem
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14: 76
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7698
section III, th
e simulation method, experiment
result
s and discussi
on will be present. In section
IV, the conclu
sion i
s
given.
2. Problem Formulation
There a
r
e two main
pro
b
l
e
ms i
n
robu
stness
an
alysi
s
of
wirel
e
ss
sen
s
o
r
s un
de
r ha
rsh
environ
ment
(as
sh
own in
Figure 1). O
ne is mi
ssing
data processing i
n
co
mm
unication lay
e
r;
the other is
ro
bust un
ce
rtai
nty analysis u
nder h
a
rsh e
n
vironm
ent in
physic laye
r.
Figure 1. Two
Layers of
Wi
rele
ss Vib
r
ati
on Sensor
Ro
bustn
ess Ana
l
ysis
2.1. Robus
t Estimation P
r
oblem of Vibration Te
st
under Harsh
En
v
i
ronment
The vibratio
n sign
al model
unde
r ha
rsh env
iron
ment i
s
sh
own as fo
rmula (1):
,...)
,
,
(
'
,...)
,
,
(
)
(
1
H
T
t
f
H
T
t
f
t
(1)
f(t,T,H,…) is c
e
rtain tes
t
s
i
gnal, f’ (t,
T
,
H,…) is
uncertain
si
g
nal
come
fro
m
ha
rsh
environ
ment. Here
Γ
1
(
t) m
ean
s only test vibration value,
have not
tested temp
erature, humi
d
ity,
and othe
r env
ironm
ent influ
ence paramet
ers.
In the test scenari
o
, we te
st vibration, t
e
mpe
r
ature, humidity and
so o
n
sim
u
lta
neou
sly,
obtain
Γ
2(t,T,H,…) from formula (2).
,...)
,
,
(
'
,...)
,
,
(
,...)
,
,
(
2
H
T
t
f
H
T
t
f
H
T
t
(2)
To sim
p
lify the p
r
oble
m
, here
Supp
ose
Γ
2(t,T,H,…
) ha
s a
n
em
pirical di
strib
u
tion, the
qualitative ro
bustn
ess i
s
e
s
sentially eq
uivalent to weak
co
ntinuit
y
of
Γ
. As de
scribe
in formula
(
3
)-
(5)
.
Many of the
most co
mmo
n test statistics and e
s
timators d
epe
nd o
n
the sample
(x 1. . .
x
n,) only throu
gh the empi
ri
cal di
stributio
n function.
i
x
n
n
1
(3)
Whe
r
e
i
x
stand
s for the point
mass 1 at x.
That is,
)
(
)
,...,
(
1
n
n
n
F
x
x
(4)
If the limit in
probability exists:
)
(
lim
)
(
n
n
F
F
(5)
Then
Γ
is
Fisher cons
is
tent, or
(asympto
tic robu
stne
ss). Let:
,...)
,
,
(
,
2
H
T
t
y
i
i
(6)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Robus
t
ness
Es
timation of
Wireless
ME
MS Vi
bration
Test un
der
Harsh… (Ch
a
n
g
jian Deng
)
7699
Then Cram
er-Ra
o
ineq
uali
t
y is:
)
,
(
ln
)
(
]
)
)
(
ˆ
[(
;
1
2
2
2
2
i
i
i
i
i
i
i
i
i
i
x
a
y
y
p
a
p
dy
a
I
I
a
y
a
dy
e
and
I
e
(7)
Whe
r
e I is Fisher info
rmatio
n [21], ‘p’ is distributio
n of ‘a’.
For
Γ
2
(t, T, H,…) h
a
s
n
a
tive comp
o
nent of
un
ce
rtainty f’ (t, T, H,…), the
robu
st
estimation
p
r
oblem
of vibration te
st u
n
der ha
rs
h e
n
v
ironme
n
t is
multivariate
u
n
ce
rtainty ro
bust
statistics p
r
ob
lem.
2.2. Robust
Estimation P
r
oblem of Wi
reless
Data Transmitting
under Ha
rs
h En
v
i
ronment
In netwo
rk t
r
ansmitting, t
here
are pa
cket
lo
sing
ra
te owin
g to
attacks, envi
r
onment
influen
ce, en
d of battery powe
r
and
so
on.
In the pape
r,
wirel
e
ss sen
s
ors lo
sin
g
p
a
cket sto
c
h
a
stic p
r
o
c
e
ssi
ng is
sup
p
o
s
ed to be
Poisson p
r
o
c
essing.
The pa
per f
o
cu
se
s on t
w
o robu
st e
s
timation p
r
o
b
lems. O
ne
is ro
bu
st est
i
mations
occurre
d
in
u
n
ce
rtainty diff
erent
depl
oyment pla
c
e,
the oth
e
r is robu
st p
r
e
c
ise
estim
a
tion
s
of
10% uncertai
n
ty conne
ctivity (or pac
ket l
o
sin
g
rate
) in one no
de.
In the first situation, Fi
sher info
rmati
on
dista
n
ce
D is d
e
fined
to present
different
deployme
nt status. As sh
o
w
n in form
ula
(8).
2
1
)
](
[
)
(
min
))
|
(
),
|
(
(
2
1
t
t
ij
T
F
dt
dt
d
g
dt
d
x
p
x
p
D
i
(8)
Suppo
se d
a
ta tran
smitting
prob
ability of node
s
in different d
eploy
ment pla
c
e is similar,
the Kullback
Leible
r
diverg
ence is half o
f
Fisher info
rmation dista
n
c
e.
)
,
(
)
,
(
)
,
(
1
2
2
1
2
1
p
p
D
p
p
D
p
p
D
KL
KL
F
(9)
In the seco
nd situation,
the location
of
missing
data is defined to describe the
relation
shi
p
b
e
twee
n pre
c
i
s
e (o
r CRLB
) with missing
data. Then:
c
b
CRLB
n
n
)
(
lim
(10
)
b is location o
f
missing d
a
ta, n is numbe
r of transmitting data, c is
con
s
t.
3. Method
s a
nd Simulation Analy
s
is
To
solve
problems in section II, two
hypot
heses are introduced fi
rstly, and t
hen the
robu
st u
n
cert
ainty analy
s
is of vibration t
e
st i
s
p
r
o
p
o
s
ed a
nd
simul
a
ted, in th
e e
nd, ba
se
d o
n
the
noisy un
cert
ain sign
al
m
odel, robu
st
estim
a
tion probl
em of wirel
e
ss
dat
a
tra
n
smittin
g
is
analyzed an
d
simulated.
H
y
potheses
1:
the Packets lo
sin
g
during o
ne pe
riod un
der u
n
ce
rtain inte
rface is th
e
Poisson
stochasti
c process; and th
e Pa
ckets lo
sin
g
i
n
different d
e
p
loyment is
a
l
so the Poi
sson
stocha
stic proce
s
s.
H
y
potheses 2:
Harsh d
e
g
r
ee, or
different enviro
n
m
ent informati
on co
ntain n
a
tive test
error inform
ation in
Fi
sher informati
on in
equ
ality. For exam
ple, the
sa
me MEMS
chip,
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TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 76
97 – 770
4
7700
uncertainty a
nd deviation
of COS ap
pli
c
ation
have
sm
aller val
ue t
han it of ind
u
s
trial a
ppli
c
ati
o
n
;
uncertainty a
nd deviatio
n
of indu
stri
al
appli
c
at
ion
have
smalle
r value tha
n
it of automot
ive
electroni
cs; and un
certai
nty
of
auto
m
otive appli
c
ation
ha
s
sma
ller value
than it
of
harsh
appli
c
ation
s
.
3.1. The Vibration Tes
t
Design and Robustnes
s Analy
s
is unde
r Harsh Env
i
ronment
The first test
is to verify t
he vibratio
n
sign
al mod
e
l. He
re
we te
st vibration in
different
temperature,
humidity, and
in diffe
rent
p
l
ace.
T
a
b
l
e 1 is
temp
er
a
t
ur
e
tes
t
da
ta
,
F
i
g
u
r
e
2 sh
ow
n
test in hydroe
lectri
c station.
Table 1 p
r
e
s
ents test valu
e of two MEMS vibr
ation
sen
s
o
r
s in n
o
r
mal (2
0 º) a
nd col
d
(-
10º) temp
erature.
The first test
is to verify t
he vibratio
n
sign
al mod
e
l. He
re
we te
st vibration in
different
temperature,
humidity, and
in different p
l
ace. Ta
ble 1
is temperatu
r
e test data, fig.2 sho
w
n te
st
in hydroel
ect
r
ic station.
Table 1 p
r
e
s
ents test valu
e of two MEMS vibr
ation
sen
s
o
r
s in n
o
r
mal (2
0 º) a
nd col
d
(-
10º) temp
erature.
So it is reaso
nable to u
s
e
follow un
ce
rtain sig
nal mo
del und
er ha
rsh environm
e
n
t like
(3).
Table 1. Te
st Value of Two
MEMS Vibration
Sensors in
Norm
al (20 º
)
and cold (-1
0
º)
T
e
mp
er
a
t
ur
e
x y
z
note
s
Normal tempe
r
at
ure-
node No1
0.00g
0.06g
0.88g
Rate 1/20
Rate 1/4
Rate 1/4
Var
y
da
ta/all dat
a
Change 0.0
1
g
Change 0.0
1
g
Change 0.0
1
g
Max-min value
Normal tempe
r
at
ure-
node No2
0.05g
0.02g
0.92
Rate 1/1.5
Rate 1/1.5
Rate 1/1.5
Var
y
da
ta/all dat
a
Change 0.0
5
g
Change 0.0
2
g
Change 0.0
8
g
Max-min value
Cold temperat
ur
e-
node No1
0.01g
0.13g
0.92g
Rate 1/20
Rate 1/4
Rate 1/4
Var
y
da
ta/all dat
a
Change 0.0
1
g
Change 0.0
1
g
Change 0.0
2
g
Max-min value
Cold temperat
ur
e-
node No2
0.12g
0.16g
0.95
Rate 1/1.5
Rate 1/1.5
Rate 1/1.5
Var
y
da
ta/all dat
a
Var
y
0.
1g
Var
y
0.
08g
0.08g
Max-min value
Figure 2. Wireless vibratio
n MEMS sen
s
ors in field
s
Δμ
;
μ
μ
)
σ
k
μ
x
Φ
(
ε
)
σ
μ
x
Φ
(
ε
)
(1
F(x)
i
i
i
(11
)
As the cha
n
ce (or variety)
measure is s
ub additive. That is, for any countabl
e se
quen
ce
of events
,...
,
2
1
, the
n
have:
1
1
}
{
}
{
i
i
i
i
ch
ch
(12
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Robus
t
ness
Es
timation of
Wireless
ME
MS Vi
bration
Test un
der
Harsh… (Ch
a
n
g
jian Deng
)
7701
Metho
d
1:
m
u
ltivariate un
certai
nty rob
u
s
t statisti
cs p
r
oble
m
in
wo
rst ca
se
analy
s
is, the
every environ
ment influe
nce facto
r
othe
r than te
mp
erature, robu
st
estimation
ca
n use formul
a
(12
)
, and m
e
anwhile the
resolvin
g ca
p
ability of robu
st statisti
cs i
s
inversely pro
portion
al to the
harsh de
gree
.
The
simul
a
tio
n
of m
e
thod
1 is u
s
e
(1
3)
as
no
rmal
ro
bust
statisti
cs, use
(11
)
a
s
in robu
st
harsh stati
s
tics. as sho
w
n i
n
Figure 2
)
(
)
(
)
1
(
)
(
k
x
x
x
F
(13
)
(a) An exam
p
l
e resolving capability of ro
bust
statistics in n
o
rmal e
n
viron
m
ent
(b) An exam
p
l
e resolving capability of ro
bust
statistics in h
a
rsh environ
ment
Figure 3. (a)
An example resolvin
g ca
pa
bility of
robust statistics in
norm
a
l enviro
n
ment; (b
) An
example reso
lving cap
ability of robus
t st
atistics in harsh environm
e
n
t
The CRLB of (13
)
had b
e
e
n
proved to b
e
(14
)
:
G
CRLG
CRLBc
)
2
1
(
(14
)
Theo
ry 1: the CRLB
c
’ of unce
r
tain si
gn
al
model und
er harsh e
n
vironm
ent have value
as sho
w
n in (15).
)
'
....
'
(
2
2
1
'
n
c
c
CRLB
CRLB
(15
)
Prove: sup
p
o
s
e
ˆ
is an esti
mation value
of
, the mean squ
a
re e
r
ror
of
ˆ
is
)
ˆ
(
2
M
.
2
2
)
ˆ
(
)
ˆ
(
E
M
(16
)
)
(
)
ˆ
var(
]}
)
ˆ
(
[
)]
ˆ
(
ˆ
{[
2
]
)
ˆ
(
[
)]
ˆ
(
ˆ
[
]
)
ˆ
(
)
ˆ
(
ˆ
[
)
ˆ
(
2
2
2
2
2
b
E
E
E
E
E
E
E
E
E
E
M
(17
)
The form
ula (17) is true onl
y
ˆ
is asym
ptotic unbi
ased e
s
timation.
)
ˆ
var(
sat
i
sf
y
:
10
20
30
40
50
60
70
80
90
100
0
50
100
150
200
250
300
350
400
No
.
o
f
t
e
s
t
1/
r
e
s
o
lution
10
20
30
40
50
60
70
80
90
10
0
0
20
40
60
80
10
0
12
0
14
0
16
0
18
0
20
0
No
.
o
f
t
e
st
1/
re
s
o
l
u
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 76
97 – 770
4
7702
G
CRLG
CRLBc
value
CRLB
have
I
)
2
1
(
:
_
_
;
/
1
)
ˆ
var(
(18
)
So the
CRL
B
c’ of u
n
cert
ain
signal
m
odel
u
nde
r
h
a
rsh e
n
viron
m
ent have
value a
s
sho
w
n in (15
)
, the
)
'
....
'
(
2
2
1
n
is
come
from
)
(
2
b
Metho
d
2:
m
u
ltivariate un
certai
nty robu
st statisti
cs p
r
oblem in un
certain an
alysi
s
tools.
Multivariate data analysi
s
can incl
ude
a la
rge nu
mber of mea
s
ured varia
b
l
e
s, even
some va
riabl
es overl
ap (it
might be dep
ende
nt). As shown in Figu
re 4.
Figure 4. Factor Analysi
s
in
Multivariate Data Proc
ess
3.2. The Transmitting
Data Tes
t
Design a
n
d
Robus
tne
s
s
Analy
s
is
under Ha
r
s
h
En
v
i
ronment
In tes
t
des
i
gn, firs
t is
te
stin
g co
mmuni
ca
tion influen
ce
d by environ
ment, for tem
peratu
r
e
influen
ce th
e co
mmuni
cation ha
d b
een te
sted i
n
re
se
arch
before, i
r
radi
ation influe
n
c
e
comm
uni
cati
on had b
een t
e
sted [27] (a
s sho
w
n in Fig
u
re5
). Secon
d
is testing in
comm
uni
cati
on
proto
c
ol, ho
w much pa
cke
t
loss rate
ca
n be acce
pte
d
. Results sh
ow 10% pa
cket loss rate
is
rea
s
on
able.
Figure 5. The
Relation
ship
betwe
en Nucl
ear
Irradiatio
n and Received Signal Strength at
Different F
r
eq
uen
cy
5
5.
5
6
6.
5
7
4
4.
5
5
5.
5
6
4.
5
5
5.
5
6
6.
5
Te
m
p
Se
ct
or
hum
i
S
e
c
t
or
other S
e
ctor
2.
4
2.
41
2.
42
2.
4
3
2.
44
2.
45
2.
46
2.
4
7
2.
48
2.
49
-3
8
-3
6
-3
4
-3
2
-3
0
-2
8
-2
6
-2
4
-2
2
-2
0
S
i
g
n
a
l
F
r
e
que
nc
y,
G
H
z
R
e
c
e
i
v
e
d
Si
g
n
a
l
St
r
e
ng
t
h
,
d
B
m
Low
I
r
r
adi
at
i
on F
i
el
d
H
i
gh I
r
r
adi
at
i
on F
i
el
d
N
o
r
m
a
l
env
i
r
onm
ent
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Robus
t
ness
Es
timation of
Wireless
ME
MS Vi
bration
Test un
der
Harsh… (Ch
a
n
g
jian Deng
)
7703
Metho
d
1:
a
s
periodi
c data
has infinity numbe
r, so ha
ve Equation (19).
c
b
CRLB
n
)
(
(19
)
Suppo
se th
e
Packets l
o
si
n
g
du
ring
on
e
perio
d u
nde
r
uncertain
inte
rface
is the P
o
isson
stocha
stic p
r
oce
s
s; and
the Packets losing in
d
i
fferent depl
oyment is al
so the Poi
s
son
stocha
stic proce
s
s.
And sup
p
o
s
e
all acq
u
ire
d
d
a
ta tran
smit to the re
ceiver.
Then u
s
e (1
3
)
as no
rmal signal, (11
)
as robu
st sign
al
, Figure 5 sh
ow Possio
n missi
ng
data is alm
o
st random, an
d the missing
data incr
ea
se uncertainty,
the mean va
lue almo
st ha
s
no ch
ang
e.
Metho
d
2:
B
a
si
cally, Fish
er info
rmatio
n di
stan
ce
D (8
)-(9) ha
s
simila
r me
ani
ng
with
clu
s
ter an
alysis of uncertai
n
data (o
r to do cross-vali
dation).
As sh
own in
pape
r [28], re
liable e
s
timati
ons
of
cla
ssifi
er a
c
cura
cy u
s
ing
cross-val
i
dation
techni
que
s a
nd finite-si
z
e
data sampl
e
s sho
w
s: the
more
accu
rat
e
is
a mod
e
l
indu
ced f
r
om
a
small am
ount
of real-wo
r
ld
data, the less reli
able a
r
e
the values o
f
simultane
ou
sly mea
s
ured
cro
s
s-vali
dati
on estimate
s.
Figure 6. The
Relation
ship
betwe
en Rob
u
st Missing S
i
gnal an
d its Mean Valu
e
4. Conclusio
n
This pap
er
p
r
esents
ro
bu
stne
ss analy
s
is of
wi
rele
ss MEMS vibration sen
s
ors un
de
r
harsh
enviro
n
m
ent. In se
nsing layer,the
robu
st un
ce
rta
i
nty analysi
s
of sen
s
o
r
sho
w
s th
e
statisti
c
resolution
of test data i
s
in
verse
propo
rtional to
the
h
a
rsh de
gree,
and the
Fish
er info
rmatio
n is
a function
with harsh e
n
vironment
statu
s
. In comm
u
n
icatio
n layer, the mean value of test d
a
ta
influen
ced by
Possion missing data
i
s
almost ran
d
o
m
,
and
the
more missin
g
data numb
e
r
increa
se
s the
uncertainty v
a
lue of te
st d
a
ta, but
the
mean valu
e h
a
s al
most
no
cha
nge. It is
also
sho
w
n
that Fi
she
r
i
n
form
ation di
stan
ce
D h
a
s
similar mea
n
ing
wit
h
cl
uste
r
anal
ysis
of u
n
cert
ain
data.
Ackn
o
w
l
e
dg
ements
This a
r
ticle i
s
su
ppo
rted
by “Chin
a
-Ca
nada
Joint Rese
arch Proj
ect” (proj
e
ct
numbe
r:
2009
DFA1
21
00) an
d Majo
r Proje
c
t of Education Dep
a
rtment in Sicha
n
(13
Z
20
4). For
supp
o
r
t,
contri
bution
s
to discu
s
s
we would li
ke
to than
k
the
rest of
M
C
C (mobil
e
com
puter ce
nter)
o
f
UESTC.
Referen
ces
[1] Denton
R.
S
e
nsor
re
li
abi
lity impact on pre
d
ictive mai
n
te
nanc
e
pr
ogr
a
m
c
o
sts
. W
ilc
oxon
Res
earc
h
Report, http://
w
w
w
.
w
i
lc
o
x
o
n
.com/kno
w
d
esk/
W
P
MT
BF
.pdf.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 76
97 – 770
4
7704
[2] Andov
er
N
D
S.
Ingeg
neri
a
s
e
l
e
cts MEMSIC'
s
ther
mal
acc
e
l
e
ro
meter f
o
r u
s
e in
the
i
r OEM vehic
l
e
anti-
theft system
s
. Broad
ba
nd T
e
chno
log
y
Ltd. Rep
o
rt. 2004.
[3]
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w
a
l
d
LP
, et al. R
adi
ati
on effects
on
surf
ace micr
o
m
achi
ned
com
b
driv
es a
nd
microen
gi
nes
,
IEEE Transactions on Nuclear
Science
.1
99
8; 45(6): 278
9–
2
798.
[4]
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d
s L,
e
t
al. Ra
di
ation
Resp
ons
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a
MEMS Acc
e
ler
o
meter: an Electrostatic
Force.
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ansactio
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r
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adi
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han
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EMS): RF
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enn
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ghe
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he Proce
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