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26
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tem
s
o
r
b
atter
y
m
an
ag
em
e
n
t
s
y
s
tem
s
(
B
MS)
.
T
h
e
m
eth
o
d
s
in
[
4
]
–
[
8
]
h
a
v
e
b
e
en
im
p
r
o
v
ed
to
e
n
h
an
ce
R
UL
p
r
ed
ictio
n
ac
c
u
r
ac
y
.
Se
co
n
d
ly
,
d
ata
-
d
r
i
v
en
s
tr
ateg
ies,
s
u
ch
as
lo
n
g
s
h
o
r
t
-
ter
m
m
em
o
r
y
(
L
STM
)
n
etw
o
r
k
s
[
9
]
,
h
av
e
b
ee
n
ap
p
lied
t
o
R
UL
f
o
r
ec
asti
n
g
.
T
h
ese
n
etwo
r
k
s
ar
e
p
o
wer
f
u
l
to
o
ls
f
o
r
p
r
e
d
ictin
g
t
h
e
R
UL
o
f
lith
iu
m
-
io
n
b
atter
ies
b
e
ca
u
s
e
th
ey
e
x
ce
l
at
ca
p
tu
r
in
g
l
o
n
g
-
te
r
m
d
e
p
en
d
e
n
cies
in
tim
e
-
s
er
ies
d
ata.
B
y
an
aly
zin
g
h
is
to
r
ical
p
ar
am
ete
r
s
s
u
ch
as
v
o
ltag
e,
cu
r
r
en
t,
a
n
d
tem
p
e
r
atu
r
e.
L
S
T
M
ca
n
ef
f
ec
tiv
ely
m
o
d
el
b
atter
y
d
eg
r
a
d
atio
n
p
atter
n
s
an
d
p
r
e
d
ict
wh
en
a
b
atter
y
will
r
ea
ch
its
en
d
-
of
-
life
(
E
OL
)
.
H
o
wev
er
,
L
STM
s
f
ac
e
ce
r
tain
ch
allen
g
es,
s
u
ch
a
s
th
e
h
ig
h
n
u
m
b
e
r
o
f
h
y
p
e
r
p
ar
am
ete
r
s
th
at
n
ee
d
ca
r
ef
u
l
tu
n
in
g
.
Ad
d
itio
n
ally
,
th
ey
ar
e
o
f
ten
co
n
s
id
er
ed
'
b
lack
-
b
o
x
'
m
o
d
els,
p
r
o
v
id
i
n
g
lim
ited
p
h
y
s
ical
in
ter
p
r
etab
ilit
y
o
f
th
e
b
atter
y
'
s
in
ter
n
al
d
e
g
r
ad
atio
n
m
ec
h
an
is
m
s
co
m
p
ar
ed
to
m
o
d
el
-
b
ased
ap
p
r
o
ac
h
es.
T
h
e
m
eth
o
d
s
in
[
1
0
]
–
[
1
3
]
h
a
v
e
b
ee
n
im
p
r
o
v
e
d
to
en
h
an
c
e
R
UL
p
r
ed
ictio
n
ac
cu
r
ac
y
.
T
h
en
,
th
e
h
y
b
r
id
p
r
o
g
n
o
s
tic
ap
p
r
o
ac
h
es
[
1
4
]
–
[
1
6
]
co
m
b
in
e
th
e
p
h
y
s
ical
in
s
ig
h
ts
o
f
m
o
d
el
-
b
ased
m
eth
o
d
s
with
th
e
p
r
ed
ictiv
e
p
o
wer
o
f
d
ata
-
d
r
iv
en
s
tr
ateg
ies.
W
h
ile
th
ey
o
f
f
er
s
u
p
er
io
r
ac
cu
r
ac
y
an
d
im
p
r
o
v
e
d
r
o
b
u
s
tn
ess
ag
ain
s
t
u
n
ce
r
tain
ty
,
t
h
eir
im
p
lem
e
n
tatio
n
is
o
f
ten
h
in
d
er
ed
b
y
i
n
cr
ea
s
ed
ar
ch
itectu
r
al
co
m
p
lex
ity
a
n
d
h
ea
v
y
c
o
m
p
u
t
atio
n
al
r
eq
u
ir
e
m
en
ts
.
Alth
o
u
g
h
th
e
m
et
h
o
d
s
in
[
1
]
–
[
1
6
]
ar
e
b
ein
g
co
n
tin
u
o
u
s
ly
r
ef
in
ed
t
o
en
h
an
ce
ac
cu
r
ac
y
,
th
ey
o
f
ten
en
tail
h
ig
h
c
o
m
p
u
tatio
n
al
co
s
ts
.
Fu
r
th
er
m
o
r
e,
t
h
ese
m
o
d
e
ls
ty
p
ically
r
eq
u
ir
e
an
e
x
ten
s
iv
e
in
itial
tr
ain
in
g
p
h
ase
o
f
ten
ex
ce
ed
i
n
g
6
0
%
o
f
th
e
b
atter
y
’
s
life
cy
cle
r
en
d
e
r
in
g
th
em
im
p
r
ac
tical
f
o
r
R
UL
p
r
ed
ictio
n
d
u
r
in
g
th
e
ea
r
ly
s
tag
es o
f
r
ea
l
-
wo
r
ld
o
p
er
atio
n
.
Sin
g
u
lar
s
p
ec
tr
u
m
an
aly
s
is
(
SS
A)
is
an
ad
v
an
ce
d
tim
e
-
s
er
ies
d
ec
o
m
p
o
s
itio
n
tech
n
iq
u
e
wid
ely
u
tili
ze
d
in
f
ield
s
s
u
ch
as
f
in
an
ce
an
d
en
g
i
n
ee
r
in
g
.
As
a
n
o
n
-
p
ar
am
etr
ic
m
et
h
o
d
,
SS
A
o
f
f
er
s
h
ig
h
f
lex
ib
ilit
y
b
y
r
eq
u
ir
in
g
n
o
p
r
i
o
r
ass
u
m
p
tio
n
s
r
eg
ar
d
in
g
d
ata
d
is
tr
ib
u
tio
n
o
r
p
atter
n
s
.
Fu
r
th
er
m
o
r
e,
it
is
co
m
p
u
tatio
n
ally
ef
f
icien
t
d
u
e
to
its
r
elativ
ely
s
tr
aig
h
tf
o
r
war
d
m
at
h
em
atica
l
f
r
am
ewo
r
k
.
Fo
r
f
o
r
ec
asti
n
g
ap
p
licatio
n
s
,
r
ec
u
r
r
en
t
s
in
g
u
lar
s
p
ec
tr
u
m
an
aly
s
is
(
R
SS
A)
[
1
7
]
–
[
1
9
]
is
em
p
lo
y
ed
,
ex
ten
d
in
g
th
e
f
u
n
d
am
e
n
tal
p
r
in
cip
les
o
f
SS
A
to
en
ab
le
p
r
e
d
ictiv
e
m
o
d
elin
g
.
Similar
ity
-
b
ased
f
o
r
ec
asti
n
g
[
2
0
]
,
[
2
1
]
f
o
r
b
atter
y
R
UL
is
a
d
ata
-
d
r
i
v
en
a
p
p
r
o
ac
h
t
h
at
e
s
tim
ates
a
tar
g
et
b
atter
y
'
s
life
s
p
an
b
y
id
e
n
tify
in
g
an
d
lev
er
a
g
in
g
h
is
to
r
ical
p
atter
n
s
f
r
o
m
"r
ef
er
e
n
ce
"
b
atter
ies
th
at
h
av
e
r
ea
ch
ed
th
eir
E
OL
.
T
h
is
m
eth
o
d
is
p
ar
ticu
lar
ly
e
f
f
ec
tiv
e
f
o
r
s
m
all
-
s
am
p
le
p
r
o
b
lem
s
s
u
ch
as
wh
en
lim
ited
f
ailu
r
e
d
ata
is
av
ailab
le
f
o
r
a
n
ew
b
atter
y
ch
em
is
tr
y
b
y
u
tili
zin
g
tr
an
s
f
er
lear
n
in
g
o
r
p
atter
n
m
atch
in
g
tech
n
iq
u
es to
b
r
id
g
e
t
h
e
g
ap
b
etwe
en
h
is
to
r
ical
an
d
r
ea
l
-
tim
e
d
ata.
T
h
e
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
m
eth
o
d
in
te
g
r
ates
s
im
ilar
ity
-
b
ased
f
o
r
ec
asti
n
g
an
d
r
ec
u
r
r
en
t
s
in
g
u
lar
s
p
ec
tr
u
m
an
al
y
s
is
in
to
a
h
y
b
r
id
f
r
am
ew
o
r
k
v
ia
a
weig
h
te
d
lo
g
is
tic
s
witch
in
g
m
ec
h
a
n
is
m
.
T
h
is
ar
c
h
itectu
r
e
f
ac
ilit
ates
a
d
y
n
am
ic
tr
an
s
itio
n
b
etwe
en
th
e
two
m
o
d
els,
g
u
id
ed
b
y
th
e
s
p
ec
if
ic
ch
a
r
ac
ter
i
s
tics
o
f
th
e
b
atter
y
d
eg
r
ad
atio
n
tr
ajec
to
r
y
.
B
y
e
m
p
lo
y
in
g
lo
g
is
tic
weig
h
tin
g
,
th
e
s
y
s
tem
ad
ap
tiv
ely
b
alan
ce
s
th
e
d
ata
-
d
r
iv
e
n
s
tr
en
g
th
s
o
f
R
SS
A
with
th
e
p
atter
n
-
m
atch
in
g
ca
p
ab
ilit
ies
o
f
th
e
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
,
th
e
r
eb
y
o
p
tim
izin
g
p
r
e
d
ictio
n
ac
cu
r
ac
y
ac
r
o
s
s
th
e
v
ar
io
u
s
s
tag
es o
f
th
e
b
atter
y
’
s
life
cy
cle.
Fu
r
th
e
r
m
o
r
e,
th
e
alg
o
r
ith
m
is
ch
ar
ac
ter
ized
b
y
co
m
p
u
ta
tio
n
al
ef
f
icien
c
y
,
m
a
k
in
g
it
h
ig
h
l
y
s
u
itab
le
f
o
r
in
teg
r
at
io
n
in
to
r
eso
u
r
ce
-
co
n
s
tr
ain
ed
b
atter
y
m
an
a
g
em
e
n
t sy
s
tem
s
.
Acc
u
r
ate
R
UL
esti
m
atio
n
is
a
cr
itical
en
ab
ler
f
o
r
th
e
s
ec
o
n
d
-
life
ap
p
licatio
n
o
f
lith
iu
m
-
io
n
b
atter
ies.
B
y
p
r
ec
is
ely
p
r
ed
ictin
g
th
e
r
em
ain
in
g
life
s
p
an
,
b
atter
ies
r
etir
ed
f
r
o
m
elec
tr
ic
v
eh
icles
ca
n
b
e
s
af
ely
an
d
ef
f
ec
tiv
ely
r
ep
u
r
p
o
s
ed
f
o
r
b
atter
y
en
er
g
y
s
to
r
ag
e
s
y
s
tem
s
o
r
g
r
id
s
tab
ilizatio
n
.
T
h
is
n
o
t
o
n
ly
m
ax
im
izes
th
e
ec
o
n
o
m
ic
v
al
u
e
o
f
th
e
b
atter
y
ass
ets
b
u
t
also
p
r
o
m
o
tes
a
cir
cu
lar
ec
o
n
o
m
y
b
y
r
ed
u
cin
g
p
r
em
atu
r
e
r
ec
y
cli
n
g
an
d
m
i
n
im
izin
g
e
n
v
ir
o
n
m
en
ta
l
im
p
ac
t.
T
h
e
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
m
eth
o
d
p
r
o
v
id
es
th
e
n
ec
ess
ar
y
p
r
ed
ictiv
e
in
s
ig
h
ts
to
ev
alu
ate
wh
eth
er
a
r
etir
ed
b
atter
y
is
v
ia
b
le
f
o
r
s
u
ch
s
ec
o
n
d
ar
y
u
s
e
ca
s
es.
I
n
th
is
p
ap
er
,
th
e
o
b
jectiv
e
is
to
p
r
ed
ict
th
e
i
n
itial
s
tag
e
o
f
R
UL
with
less
d
ata
b
y
in
clu
d
in
g
th
e
tim
e
-
s
er
ies
ap
p
r
o
ac
h
es.
W
e
p
r
o
p
o
s
e
C
W
S
-
R
SS
A
m
eth
o
d
m
o
d
el
a
co
m
b
in
in
g
,
s
im
ilar
ity
-
b
ased
an
d
R
SS
A
th
at
is
b
ased
o
n
an
a
v
er
ag
in
g
weig
h
t
.
T
o
co
m
p
a
r
e
th
e
p
e
r
f
o
r
m
an
c
e
o
f
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
m
o
d
el
u
s
in
g
v
a
r
io
u
s
ex
is
tin
g
alg
o
r
ith
m
s
f
o
r
in
f
o
r
m
ed
d
ec
is
io
n
-
m
a
k
in
g
in
th
e
b
att
er
y
ca
p
ac
ity
.
T
h
is
p
ap
er
co
n
s
i
s
ts
o
f
s
ix
s
ec
tio
n
s
,
wh
ich
is
o
r
g
an
ized
as
f
o
llo
ws.
Sectio
n
s
2
i
n
tr
o
d
u
ce
s
th
e
b
asic
th
eo
r
etica
l
k
n
o
wled
g
e
i
n
p
r
e
d
ictin
g
R
UL
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
ema
in
in
g
u
s
efu
l life
esti
ma
tio
n
fo
r
p
r
ed
ictive
b
a
tter
y
ma
in
t
en
a
n
ce
… (
C
h
u
tip
o
n
g
s
e
B
o
o
n
ya
kitma
itr
ee
)
1819
Sectio
n
3
p
r
o
p
o
s
es C
W
S
-
R
S
S
A
f
o
r
ec
asti
n
g
m
eth
o
d
.
Sectio
n
4
p
r
esen
ted
th
e
an
al
y
s
is
o
f
th
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
.
Sectio
n
5
a
n
d
s
ec
tio
n
6
g
iv
e
t
h
e
d
is
cu
s
s
io
n
an
d
co
n
clu
s
io
n
.
2.
RE
L
AT
E
D
WO
RK
2
.
1
.
Acc
ura
cy
o
f
f
o
re
ca
s
t
s
T
o
ev
alu
ate
t
h
e
ac
cu
r
a
cy
an
d
r
eliab
ilit
y
o
f
tim
e
s
er
ies
p
r
e
d
ictio
n
s
o
f
b
atter
y
ca
p
ac
ity
.
W
h
en
th
e
b
atter
y
is
in
u
s
e,
its
ca
p
ac
ity
will
d
ec
r
ea
s
e
to
7
0
%
o
f
its
f
u
ll
ca
p
ac
ity
[
2
2
]
en
d
-
of
-
life
f
o
r
m
ea
s
u
r
ed
(
)
an
d
en
d
-
of
-
life
f
o
r
p
r
e
d
icted
(
)
ar
e
g
iv
en
i
n
(
1
)
,
=
|
−
|
(
1
)
wh
er
e
d
en
o
tes
as
th
e
er
r
o
r
o
f
E
OL
.
T
h
e
b
atter
y
c
y
cles
f
r
o
m
th
e
cu
r
r
e
n
t
to
th
e
E
OL
ar
e
d
ef
in
ed
as
th
e
R
UL
.
R
UL
f
o
r
m
ea
s
u
r
ed
(
)
an
d
R
UL
f
o
r
p
r
ed
icted
(
)
as sh
o
wn
in
(
2
)
,
=
|
−
|
(
2
)
w
h
er
e
d
en
o
tes as th
e
er
r
o
r
o
f
R
UL
.
T
h
er
ef
o
r
e,
b
o
th
eq
u
atio
n
s
an
d
ar
e
eq
u
al
=
|
−
|
∗
100%
(
3
)
w
h
er
e
d
en
o
tes as th
e
p
er
ce
n
ta
g
e
o
f
e
r
r
o
r
o
f
E
OL
.
2.
2
.
RUL est
im
a
t
i
o
n
Dis
ch
ar
g
e
ca
p
ac
ity
is
a
k
e
y
f
ea
tu
r
e
th
at
ca
n
r
ef
lect
th
e
h
ea
lth
o
f
a
b
atter
y
.
T
h
e
d
ataset
was
u
s
ed
in
th
is
p
ap
er
th
at
is
p
r
o
v
id
e
d
b
y
th
e
NASA
Pro
g
n
o
s
tics
C
en
ter
o
f
E
x
ce
lle
n
ce
(
PC
o
E
)
[
2
3
]
.
T
h
e
d
ata
s
et
co
n
s
is
ts
o
f
f
o
u
r
b
atter
ies ar
e
n
u
m
b
er
ed
No
.
5
,
No
.
6
,
No
.
7
an
d
No
.
1
8
,
r
esp
ec
tiv
ely
,
an
d
th
eir
ca
p
ac
it
y
ar
e
all
2
.
0
Ah
r
.
Fig
u
r
e
1
s
h
o
ws
th
e
s
tate
o
f
h
ea
lth
(
SOH)
o
f
b
atter
y
b
etwe
en
ca
p
ac
ity
,
ch
ar
g
e
an
d
d
is
ch
ar
g
e
cy
cle
th
at
co
n
s
is
ts
o
f
3
s
tag
es.
T
h
e
f
ir
s
t
s
tag
e
is
with
less
d
ata
f
o
r
p
r
ed
ictio
n
.
Fo
r
th
e
s
ec
o
n
d
s
tag
e,
th
er
e
is
n
o
p
r
ev
io
u
s
r
esear
c
h
to
p
r
ed
ict
R
UL
in
th
is
s
tag
e.
I
n
g
en
er
al,
in
f
o
r
m
atio
n
m
u
s
t
b
e
lear
n
ed
u
p
to
th
e
t
h
ir
d
s
tag
e
an
d
th
e
s
am
p
le
u
s
ed
f
r
o
m
SO
H
is
u
n
til
th
e
cu
r
r
en
t
tim
e.
T
h
en
,
th
e
p
r
e
d
ictio
n
s
am
p
le
o
f
SOH
tr
en
d
m
ee
ts
th
e
f
ailu
r
e
th
r
esh
o
ld
th
at
is
ca
lled
“e
n
d
-
of
-
life
(
E
OL
)
.
”
So
,
R
UL
is
d
ef
in
ed
b
y
cy
cles
b
etwe
en
th
e
cu
r
r
en
t
tim
e
an
d
E
OL
.
Fig
u
r
e
1
.
Stag
e
o
f
h
ea
lth
(
SOH)
o
f
b
atter
y
No
.
5
2.
3
.
RSSA
a
lg
o
rit
h
m
R
UL
p
r
ed
ictio
n
is
ch
allen
g
in
g
b
ec
au
s
e
o
f
th
e
c
o
m
p
lex
in
ter
ac
tio
n
s
b
etwe
en
d
eg
r
ad
atio
n
m
ec
h
an
is
m
s
an
d
ev
o
lv
in
g
b
att
er
y
tech
n
o
lo
g
ies.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
8
1
7
-
1
831
1820
Fo
llo
win
g
[
1
7
]
,
R
SS
A
h
as th
e
f
o
llo
win
g
s
tep
s
as
a.
Data
p
r
ep
ar
atio
n
: A
tim
e
-
s
er
ie
s
m
eth
o
d
is
tr
an
s
f
o
r
m
ed
in
to
a
tr
ajec
to
r
y
m
atr
i
x
.
As
{
=
(
,
…
,
+
−
1
)
,
=
1
,
…
,
=
[
1
,
.
.
.
,
]
=
(
,
)
,
=
1
,
(
4
)
w
h
er
e
is
s
am
p
les,
is
th
e
lag
g
ed
v
ec
to
r
s
o
f
win
d
o
w
len
g
th
,
is
tr
ajec
to
r
y
m
atr
ix
o
f
s
am
p
les,
is
win
d
o
w
len
g
t
h
(
1
<
<
)
,
is
a
s
eq
u
en
c
e
o
f
la
g
g
ed
v
ec
to
r
s
o
f
s
ize
b
y
f
o
r
m
in
g
=
−
+
1
,
is
len
g
th
s
am
p
les.
b.
Sin
g
u
lar
v
alu
e
d
ec
o
m
p
o
s
itio
n
(
SVD)
:
T
h
e
tr
ajec
to
r
y
m
atr
i
x
is
d
ec
o
m
p
o
s
ed
u
s
in
g
SVD,
wh
ich
y
ield
s
th
e
s
in
g
u
lar
v
alu
es a
n
d
v
ec
to
r
s
r
e
p
r
esen
tin
g
th
e
c
o
m
p
o
n
en
ts
o
f
th
e
d
ata.
c.
C
o
m
p
o
n
en
t
Selectio
n
:
B
ased
o
n
th
e
s
in
g
u
lar
v
alu
es
an
d
s
ig
n
al
o
f
r
elev
an
t
co
m
p
o
n
en
ts
s
elec
ted
wh
ile
d
is
ca
r
d
in
g
n
o
is
e
co
m
p
o
n
en
ts
.
d.
R
ec
o
n
s
tr
u
ctio
n
: T
h
e
s
elec
ted
co
m
p
o
n
en
ts
ar
e
u
s
ed
to
r
ec
o
n
s
tr
u
ct
th
e
o
r
i
g
in
al
tim
e
s
er
ies.
as
̃
=
∑
̂
(
)
=
1
,
=
1
,
…
,
(
5
)
w
h
er
e
̂
is
co
ef
f
icien
ts
o
f
̂
(
)
=
(
̂
1
(
)
,
…
,
̂
(
)
)
,
̃
is
a
co
m
p
o
n
en
t
o
f
a
tim
e
-
s
er
ies
th
at
ca
n
b
e
r
ec
o
n
s
tr
u
cted
.
e.
R
ec
u
r
r
en
t
f
o
r
ec
asti
n
g
:
T
o
f
o
r
e
ca
s
t
f
u
tu
r
e
v
alu
es,
th
e
last
f
ew
r
ec
o
n
s
tr
u
cted
v
alu
es
ar
e
u
s
ed
as
in
p
u
t
to
th
e
m
o
d
el,
an
d
th
e
p
r
o
ce
s
s
is
r
ep
e
ated
iter
ativ
ely
.
Α
=
1
1
−
2
∑
(
6
)
w
h
er
e
is
v
ec
to
r
lin
ea
r
r
ec
u
r
r
en
ce
r
elatio
n
with
co
e
f
f
icien
t
s
[
−
1
,
…
,
1
]
,
is
∑
2
∈
,
is
th
e
last
co
o
r
d
in
ate
o
f
an
d
is
th
eir
f
ir
s
t
−
1
co
o
r
d
i
n
ates,
=
{
1
,
…
,
}
,
is
s
elec
ted
co
m
p
o
n
e
n
ts
.
=
{
̃
,
=
1
,
…
,
∑
−
−
1
=
1
,
=
+
1
,
…
,
+
(
7
)
w
h
er
e
1
,
…
,
an
d
+
1
,
…
,
+
M
ar
e
tim
e
s
er
ies cr
ea
ted
b
y
R
SS
A
with
f
o
r
ec
asti
n
g
p
o
s
itio
n
.
2
.
4
.
Sim
ila
ri
t
y
-
ba
s
ed
a
pp
ro
a
ch
C
u
r
r
en
tly
,
m
o
s
t
esti
m
ates
o
f
R
UL
u
s
e
d
ata
s
et
o
f
b
atter
y
t
o
d
eter
m
in
e
f
u
tu
r
e
b
atter
y
ca
p
ac
ity
.
I
t
is
n
ec
ess
ar
y
to
u
s
e
a
lar
g
e
am
o
u
n
t
o
f
p
ast
b
atter
y
ca
p
ac
ity
d
ata
to
g
et
ac
cu
r
ate
r
esu
lts
.
T
h
er
ef
o
r
e,
in
th
e
b
eg
in
n
in
g
it
will
b
e
im
p
o
s
s
ib
le
to
esti
m
ate
th
e
R
UL
.
T
o
s
o
l
v
e
th
is
p
r
o
b
lem
,
th
e
s
im
ilar
ity
m
eth
o
d
[
2
0
]
ca
n
b
e
u
s
ed
to
h
elp
esti
m
ate
th
e
R
UL
.
a.
B
r
in
g
th
e
d
ata
to
f
in
d
th
e
r
ef
er
en
ce
d
ata
s
et
u
s
in
g
th
e
r
o
o
t m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
.
b.
Use th
e
o
b
tain
ed
r
e
f
er
en
ce
d
at
a
s
et
to
ad
ju
s
t th
e
o
f
f
s
et.
T
h
e
s
im
ilar
ity
m
eth
o
d
i
n
v
o
lv
e
s
b
y
co
m
p
a
r
in
g
a
v
ailab
le
d
ata
with
all
r
ef
er
en
ce
d
ata
t
o
f
in
d
th
e
m
o
s
t
s
im
ilar
d
ata.
T
h
er
e
ar
e
s
ev
er
al
m
eth
o
d
s
u
s
ed
.
Fo
r
ex
am
p
le,
R
MSE
i
s
u
s
ed
to
f
in
d
th
e
s
m
a
lles
t
v
alu
e
to
s
elec
t
th
e
d
ata
s
et
as a
r
ef
er
en
ce
d
ata
in
R
UL
f
o
r
ec
ast.
=
√
1
∑
(
−
̅
)
2
=
1
(
8
)
wh
e
r
e
is
t
h
e
ca
p
ac
it
y
v
al
u
e
o
f
th
e
b
at
te
r
y
t
o
b
e
p
r
e
d
i
cte
d
.
̅
is
t
h
e
c
ap
ac
i
ty
o
f
t
h
e
b
a
tte
r
i
es
b
e
i
n
g
co
m
p
a
r
e
d
.
2
.
5
.
Weig
hte
d a
v
er
a
g
e
m
et
h
o
d
A
weig
h
ted
av
er
a
g
e
[
2
4
]
is
a
t
y
p
e
o
f
m
ea
n
th
at
g
iv
es
d
if
f
e
r
in
g
im
p
o
r
tan
ce
to
t
h
e
v
alu
es
in
a
d
ataset.
I
n
co
n
t
r
ast,
th
e
r
eg
u
lar
av
er
a
g
e,
o
r
ar
ith
m
etic
m
ea
n
,
g
iv
es th
e
eq
u
al
weig
h
t to
all
o
b
s
er
v
ati
o
n
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
ema
in
in
g
u
s
efu
l life
esti
ma
tio
n
fo
r
p
r
ed
ictive
b
a
tter
y
ma
in
t
en
a
n
ce
… (
C
h
u
tip
o
n
g
s
e
B
o
o
n
ya
kitma
itr
ee
)
1821
=
∑
=
1
∑
=
1
(
9
)
w
h
er
e
d
en
o
tes as a
weig
h
t,
is
th
e
n
u
m
b
er
o
f
ter
m
s
to
b
e
av
e
r
ag
ed
,
is
th
e
weig
h
ts
ap
p
lied
t
o
v
alu
es,
an
d
is
a
s
et
o
f
d
ata
v
alu
es to
b
e
av
er
ag
ed
.
2
.
6
.
Sig
m
o
ida
l f
un
ct
io
n
T
h
e
s
ig
m
o
id
al
f
u
n
ctio
n
[
2
5
]
,
as
g
iv
en
in
(
1
0
)
b
y
(
)
is
a
m
ap
p
in
g
o
n
a
v
ec
to
r
,
an
d
d
ep
en
d
s
o
n
two
p
ar
am
eter
s
an
d
0
as g
iv
en
b
y
(
)
=
1
(
1
+
−
)
(
1
0
)
T
h
e
lo
g
is
tic
f
u
n
ctio
n
,
as
g
iv
en
in
(
1
1
)
,
also
k
n
o
wn
as
th
e
s
ig
m
o
id
f
u
n
ctio
n
,
is
u
s
ed
i
n
lo
g
is
tic
r
eg
r
ess
io
n
to
m
ap
in
p
u
t
f
ea
t
u
r
es
to
p
r
o
b
a
b
ilit
ies.
T
h
e
s
i
g
m
o
id
f
u
n
ctio
n
is
a
m
ath
em
atica
l
f
u
n
ctio
n
th
at
p
r
o
d
u
ce
s
a
v
alu
e
b
etwe
en
0
a
n
d
1
,
wh
ich
is
th
e
r
an
g
e
o
f
p
r
o
b
ab
ilit
ies f
o
r
lo
g
is
tic
r
eg
r
ess
io
n
(
)
=
1
+
−
κ
(
−
)
(
1
1
)
w
h
er
e
is
th
e
g
ain
o
f
s
ig
n
al,
κ
is
th
e
s
lo
p
e
an
d
is
th
e
in
f
lectio
n
p
o
i
n
t.
3.
P
RO
P
O
SE
D
AL
G
O
R
I
T
H
M
Mo
s
t
p
r
ed
ictio
n
m
eth
o
d
s
[
1
]
–
[
1
6
]
n
ee
d
a
lar
g
e
a
m
o
u
n
t
o
f
d
ata
to
cr
ea
te
an
ac
cu
r
ate
m
o
d
el
u
s
u
ally
m
o
r
e
th
an
h
alf
o
f
th
e
b
atter
y
'
s
cy
cle
life
.
T
o
o
v
er
co
m
e
th
is
lim
itatio
n
,
we
p
r
o
p
o
s
e
a
s
im
ila
r
ity
-
b
ased
m
eth
o
d
th
at
en
ab
les
ea
r
ly
p
r
ed
ictio
n
s
tar
tin
g
f
r
o
m
j
u
s
t
1
0
%
o
f
th
e
b
atter
y
’
s
E
OL
.
Ou
r
ap
p
r
o
ac
h
o
f
f
er
s
a
s
im
p
le
an
d
ef
f
ec
tiv
e
way
to
esti
m
ate
th
e
R
UL
b
y
co
m
p
ar
i
n
g
th
e
p
r
esen
t b
atter
y
with
p
r
e
v
io
u
s
ly
co
lle
cted
d
atasets
.
T
o
en
a
b
le
r
ea
l
-
tim
e
esti
m
atio
n
o
f
th
e
R
UL
o
f
elec
tr
ic
v
eh
ic
les,
th
e
ca
lcu
latio
n
p
r
o
ce
s
s
m
u
s
t
b
e
b
o
th
s
im
p
le
an
d
f
ast.
T
h
er
ef
o
r
e,
th
e
R
S
SA
m
eth
o
d
,
o
r
ig
in
ally
u
s
ed
in
th
e
f
in
an
cial
in
d
u
s
tr
y
[
1
8
]
is
ad
o
p
ted
f
o
r
R
UL
p
r
ed
ictio
n
.
W
e
in
teg
r
ate
a
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
,
wh
ich
d
em
o
n
s
tr
ates
s
tr
o
n
g
f
o
r
ec
asti
n
g
p
er
f
o
r
m
a
n
ce
in
th
e
ea
r
ly
s
tag
e
with
th
e
R
S
SA
m
eth
o
d
,
wh
ich
p
e
r
f
o
r
m
s
b
etter
in
th
e
n
ex
t
s
tag
es.
I
n
ad
d
i
tio
n
,
R
SS
A
h
as
th
e
ad
v
an
tag
e
o
f
b
ei
n
g
s
ig
n
if
ican
t
ly
s
im
p
ler
an
d
f
aster
to
co
m
p
u
te
co
m
p
ar
ed
to
o
th
e
r
m
eth
o
d
s
.
T
wo
alg
o
r
ith
m
s
ar
e
co
m
b
in
e
d
u
s
in
g
an
av
e
r
ag
i
n
g
weig
h
t te
ch
n
iq
u
e.
W
e
p
r
o
p
o
s
e
co
m
b
in
e
d
weig
h
ted
s
im
ilar
ity
-
b
ased
an
d
r
ec
u
r
r
en
t
s
in
g
u
lar
s
p
ec
tr
u
m
a
n
aly
s
is
(
C
W
S
-
R
SS
A)
m
eth
o
d
th
at
co
n
s
is
ts
o
f
m
o
d
el
a
co
m
b
in
in
g
,
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
an
d
R
SS
A.
Ou
r
m
o
d
el
is
b
ased
o
n
an
av
er
ag
in
g
weig
h
t
as
s
h
o
wn
in
Alg
o
r
ith
m
1
an
d
Fig
u
r
e
2
.
C
W
S
-
R
SS
A
alg
o
r
ith
m
co
n
s
is
ts
o
f
f
o
u
r
m
ai
n
s
tep
s
.
a.
Pre
p
ar
atio
n
o
f
in
itial
p
ar
am
et
er
s
:
I
n
itial
p
ar
am
eter
s
,
in
clu
d
in
g
,
an
d
ar
e
d
er
iv
ed
f
r
o
m
th
e
d
ataset
o
r
d
atash
ee
t.
b.
Similar
ity
-
b
ased
ap
p
r
o
ac
h
:
T
h
e
in
p
u
t
s
am
p
le
is
co
m
p
ar
e
d
with
th
e
m
o
s
t
s
im
ilar
d
ata
in
th
e
d
atab
ase
to
esti
m
ate
th
e
R
UL
,
r
esu
ltin
g
in
an
o
u
t
p
u
t d
e
n
o
ted
as
′
.
c.
R
SS
A
:
T
h
e
s
am
e
in
p
u
t
s
am
p
le
i
s
p
r
o
ce
s
s
ed
u
s
in
g
th
e
R
SS
A
alg
o
r
ith
m
to
o
b
tain
an
o
th
er
p
r
ed
ictio
n
r
esu
lt,
d
en
o
ted
as
.
d.
Fin
al
R
UL
p
r
ed
ictio
n
:
T
h
e
o
u
tp
u
ts
′
an
d
ar
e
co
m
b
in
ed
u
s
in
g
an
av
er
a
g
in
g
weig
h
t
to
p
r
o
d
u
c
e
th
e
r
esu
lt
̂
,
wh
ich
is
th
en
u
s
ed
t
o
esti
m
ate
th
e
f
in
al
R
UL
.
Alg
o
r
ith
m
1
.
Ma
in
C
W
S
-
R
S
S
A
alg
o
r
ith
m
I
n
p
u
t
:
=
(
1
,
…
,
)
̶
r
ep
r
esen
ts
th
e
b
atter
y
d
e
g
r
ad
atio
n
d
ata
o
f
E
V
r
ec
o
r
d
ed
u
p
t
o
d
ate
Ou
tp
u
t:
̶
R
em
ain
in
g
Usef
u
l L
if
e
(
R
UL
)
f
o
r
ec
asti
n
g
1
=
B
atter
y
Data
s
et(
s
elec
t m
ax
(
E
OL
)
)
2
=
in
t(
*
1
0
%),
=
in
t(
*
2
0
%),
ρ
=
0
.
5
3
=
L
o
g
is
ticf
u
n
ctio
n
(
ρ
,
)
4
while t
rue
5
do
6
=
R
ea
d
b
atter
y
d
e
g
r
ad
atio
n
d
ata
f
r
o
m
B
MS
7
=le
n
g
th
(
)
8
′
=
Similar
ity
B
ased
(
,
B
atter
y
D
ataset)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
8
1
7
-
1
831
1822
9
=
R
SS
A(
,
1
0
,
2
,
-
)
10
F
o
r
=
1
to
do
11
̂
=
(
(
)
∗
′
)
+
(
(
−
(
)
)
∗
)
12
=
f
in
d
(
̂
<
0
.
8
)
̶
8
0
% So
H
th
r
esh
o
ld
13
=
ab
s
(
−
)
14
Dis
p
lay
15
lo
o
p
S
i
m
i
l
a
r
i
t
y
-
ba
s
e
d
a
ppr
oa
c
h
R
S
S
A
W
e
i
ght
i
ng
+
D
a
t
a
s
e
t
O
f
b
a
t
t
e
r
y
s
c
a
p
a
c
i
t
y
p
r
e
p
a
r
e
i
n
i
t
i
a
l
p
a
r
a
m
e
t
e
r
Fig
u
r
e
2
.
Ov
e
r
v
iew
o
f
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
alg
o
r
ith
m
3
.
1
.
Appl
ied Sim
ila
rit
y
-
ba
s
ed
a
pp
ro
a
ch
Pro
ce
s
s
o
f
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
i
n
th
e
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
ap
p
r
o
ac
h
is
p
r
esen
ted
a
s
:
a.
C
o
m
p
ar
e
th
e
d
ata
with
t
h
e
ex
i
s
tin
g
d
ata
s
et
to
f
in
d
th
e
s
im
ilar
ity
u
s
in
g
R
MSE
v
alu
e
f
r
o
m
(
8
)
.
b.
T
h
e
b
atter
y
d
eg
r
a
d
atio
n
d
ata
was selec
ted
b
ased
o
n
th
e
lo
w
est R
MSE
v
alu
e
o
b
tain
ed
in
th
e
p
r
ev
io
u
s
s
tep
.
c.
T
o
en
s
u
r
e
th
at
th
e
f
o
r
ec
ast
d
a
ta
alig
n
s
with
th
e
latest
ac
tu
al
d
ata,
ad
ju
s
t
th
e
o
f
f
s
et
b
y
tak
i
n
g
th
e
last
d
ata
o
f
th
e
b
atter
y
to
b
e
f
o
r
ec
asted
an
d
d
e
d
u
ctin
g
t
h
e
d
ata
o
b
tain
e
d
f
r
o
m
d
ataset
at
th
e
s
am
e
p
o
s
itio
n
.
T
h
e
o
f
f
s
et
v
al
u
e
o
f
in
(
12
)
is
g
iv
en
b
y
.
=
−
̅
(
12
)
wh
er
e
is
th
e
ℎ
ca
p
ac
ity
v
alu
e
o
f
th
e
b
atter
y
t
o
b
e
p
r
e
d
icted
,
̅
is
th
e
ℎ
ca
p
ac
ity
o
f
th
e
b
atter
ies
b
ein
g
r
ef
er
en
ce
,
a
n
d
is
b
atter
y
ca
p
a
city
o
f
f
s
et
.
′
=
̅
+
(
13
)
Ad
ju
s
t
th
e
o
f
f
s
et
f
r
o
m
th
e
d
at
aset
u
s
in
g
th
e
v
alu
e
in
(
12
)
,
w
h
er
e
̅
is
th
e
ca
p
ac
ity
o
f
th
e
b
atter
ies
b
ein
g
c
o
m
p
a
r
ed
.
T
h
e
o
b
tain
e
d
d
ata
′
ca
n
b
e
u
s
ed
to
p
r
ed
ict
R
UL
b
atter
y
.
T
h
e
co
r
r
esp
o
n
d
in
g
p
s
eu
d
o
-
co
d
e
is
p
r
esen
ted
in
Alg
o
r
ith
m
2
.
Alg
o
r
ith
m
2
.
Similar
ity
B
ased
(
,
B
atter
y
Data
s
et)
:
I
n
p
u
t
:
̶
r
ep
r
esen
ts
th
e
b
atter
y
d
e
g
r
a
d
atio
n
d
ata
o
f
E
V
r
ec
o
r
d
e
d
u
p
to
d
ate
Ou
tp
u
t:
̶
p
r
e
d
ictin
g
b
atter
y
d
eg
r
ad
ati
o
n
d
ata
1
f
un
ct
io
n
Similar
ity
B
a
s
ed
(
,
B
atter
y
Data
s
et)
2
=
co
u
n
t(
B
atter
y
Data
s
et)
3
=le
n
g
th
(
)
4
f
o
r
=
1
to
5
f
o
r
=
1
to
6
(
)
=
r
m
s
e(
,
B
atter
y
Data
s
et(
))
7
[
m
in
Val,
m
in
I
d
x
]
=
m
in
(
)
8
=
(
)
-
B
atter
y
Data
s
et(
m
in
I
d
x
,
)
9
=
B
atter
y
Data
s
et(
m
in
I
d
x
)
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
ema
in
in
g
u
s
efu
l life
esti
ma
tio
n
fo
r
p
r
ed
ictive
b
a
tter
y
ma
in
t
en
a
n
ce
… (
C
h
u
tip
o
n
g
s
e
B
o
o
n
ya
kitma
itr
ee
)
1823
10
r
etu
r
n
11
end f
un
ct
io
n
3.
2
.
P
r
o
po
s
ed
t
un
ing
pa
ra
met
er
f
o
r
RSSA
Acc
o
r
d
in
g
to
f
o
r
ec
asti
n
g
in
e
co
n
o
m
ic
an
d
f
in
a
n
cial
tim
e
s
er
ies,
R
SS
A
ca
n
h
an
d
le
with
th
e
n
o
n
-
s
tatio
n
ar
y
d
ata
[
2
6
]
.
T
h
is
lead
s
u
s
to
ap
p
ly
R
SS
A
f
o
r
p
r
ed
ict
io
n
E
OL
b
atter
y
ca
p
ac
ity
b
y
p
er
f
o
r
m
in
g
s
tep
-
by
-
s
tep
ca
lcu
latio
n
u
s
in
g
s
h
o
r
t tim
e
s
er
ies.
So
,
R
SS
A
ca
lcu
lati
o
n
co
n
s
is
ts
o
f
f
o
u
r
m
ain
p
ar
ts
:
a.
C
alcu
late
eig
en
v
alu
es a
n
d
eig
en
v
ec
to
r
s
.
b.
C
r
ea
te
th
e
m
ain
co
m
p
o
n
en
ts
o
f
a
tim
e
s
er
ies.
c.
R
eb
u
ild
.
d.
E
s
tim
ate
th
e
R
UL
.
T
h
e
,
v
alu
es
f
o
r
f
o
r
ec
asti
n
g
s
h
o
u
ld
b
e
u
s
ed
d
u
r
in
g
th
is
p
er
i
o
d
,
=
2
to
/
2
an
d
=
1
to
/
2
,
wh
er
e
is
n
u
m
b
er
o
f
s
am
p
les.
T
h
e
co
r
r
esp
o
n
d
i
n
g
p
s
eu
d
o
-
co
d
e
is
p
r
esen
ted
in
Alg
o
r
ith
m
3
.
Alg
o
r
ith
m
3
.
R
SS
A(
,
,
,
)
:
I
n
p
u
t
:
̶
in
p
u
t
d
ata
s
er
ies co
lu
m
n
v
e
cto
r
̶
n
u
m
b
er
o
f
r
ec
o
n
s
tr
u
cted
c
o
m
p
o
n
e
n
ts
in
p
u
t d
ata
s
er
ies to
b
e
d
ec
o
m
p
o
s
ed
to
̶
n
u
m
b
er
o
f
r
ec
o
n
s
tr
u
cted
c
o
m
p
o
n
e
n
ts
to
b
e
u
s
ed
f
o
r
th
e
f
o
r
ec
ast
̶
n
u
m
b
er
o
f
p
o
in
ts
to
b
e
f
o
r
e
ca
s
ted
Ou
tp
u
t:
̶
s
u
m
o
f
th
e
f
ir
s
t
r
ec
o
n
s
tr
u
ct
ed
co
m
p
o
n
en
ts
p
lu
s
p
o
in
ts
f
o
r
ec
asted
v
ia
f
ir
s
t r
ec
o
n
s
tr
u
cted
co
m
p
o
n
en
ts
1
f
un
ct
io
n
R
SS
A(
,
,
,
)
2
T
=
len
g
th
(
Y)
;
3
K
=
T
-
L
+
1
;
4
X
=
ze
r
o
s
(
L
,
K)
;
5
f
o
r
i =
1
:K
6
X(
:,i)
=
Y(
i:i
+L
-
1
)
.
'
;
7
[
U,
D]
=
eig
(
X*
X.
'
)
; %#
o
k
<N
ASGU>
8
U
=
f
lip
d
im
(
U,
2
)
;
9
V
=
ze
r
o
s
(
K,
L
)
;
10
f
o
r
i =
1
:L
11
V(
:,i)
=
X.
'
*
U(
:,i)
;
12
Z
=
ce
ll(L
,
1
)
;
13
Q
=
ze
r
o
s
(
K,
L
)
;
14
f
o
r
i =
1
:L
15
Z
{i}
=
U(
:,i)
*
V(
:,i)
.
'
;
16
Z
{i}
=
f
lip
d
im
(
Z
{i},
2
)
;
17
f
o
r
j =
(
-
L
+
1
)
:(
K
-
1)
18
Q(
L
+j,
i)
=
s
u
m
(
d
iag
(
Z
{i},
j)
)
/l
en
g
th
(
d
ia
g
(
Z
{i},
j)
)
;
19
Q
=
f
lip
d
im
(
Q,
1
)
;
20
A
=
ze
r
o
s
(
L
-
1
,
1
)
;
21
f
o
r
i =
1
:
22
A
=
A
+
U(
L
,
i)
*
U(
1
:L
-
1
,
i)
;
23
v
=
n
o
r
m
(
U(
L
,
1
:
));
24
A
=
A/(
1
-
v
^2
)
;
25
A
=
f
lip
d
im
(
A,
1
)
;
26
G
=
s
u
m
(
Q(
:,1
:
)
,
2
)
;
27
=
[
G.
'
,
ze
r
o
s
(
1
,
M)
]
.
'
;
28
f
o
r
i =
T
+
1
:T+
M
29
f
o
r
j =
1
:L
-
1
30
(
i)
=
(
i)
+
A(
j)
*
(i
-
j)
;
31
=
(
T
+1
:T+
M)
;
32
=
[
G.
'
,
.
'
]
.
'
;
33
r
etu
r
n
34
end f
un
ct
io
n
3
.
3
.
Av
er
a
g
ing
weig
ht
m
et
h
o
d
T
o
th
e
b
est
o
f
o
u
r
k
n
o
wled
g
e,
th
e
av
er
a
g
in
g
weig
h
t
[
2
7
]
is
s
u
g
g
ested
to
co
m
b
i
n
e
th
e
R
SS
A
an
d
Similar
ity
-
b
ased
ap
p
r
o
ac
h
.
T
h
e
weig
h
ted
ca
p
ac
ity
v
ec
to
r
̂
is
g
iv
en
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
8
1
7
-
1
831
1824
̂
=
{
⨀
′
}
+
{
(
1
−
)
⨀
}
(
1
4
)
wh
er
e
d
en
o
tes
t
h
e
weig
h
te
d
v
ec
to
r
,
y
is
ca
p
ac
itan
ce
v
ec
to
r
o
b
tain
ed
f
r
o
m
R
SS
A,
′
is
r
ef
er
en
ce
ca
p
ac
itan
ce
v
ec
to
r
,
a
n
d
̂
is
th
e
r
esu
ltin
g
weig
h
ted
ca
p
ac
itan
c
e
v
ec
to
r
,
T
h
e
o
p
er
ato
r
⨀
is
Had
am
ar
d
p
r
o
d
u
ct
,
an
elem
en
t
-
wis
e
m
u
ltip
licatio
n
o
f
two
m
atr
ices o
f
th
ese
d
im
en
s
io
n
al
an
d
1
is
a
v
ec
to
r
o
f
o
n
es is
s
am
e
s
ize
.
3
.
4
.
M
o
dified
lo
g
is
t
ic
f
un
ct
io
n
T
h
e
lo
g
is
tic
f
u
n
ctio
n
was
im
p
lem
en
ted
as
th
e
weig
h
t
f
u
n
cti
o
n
;
th
er
ef
o
r
e,
it
is
n
ec
ess
ar
y
to
ca
lib
r
ate
th
e
p
ar
am
ete
r
s
b
ef
o
r
e
u
s
e.
Sin
ce
th
e
weig
h
t
f
u
n
ctio
n
r
a
n
g
e
s
f
r
o
m
0
t
o
1
,
th
e
g
ain
(
)
is
s
et
to
1
.
R
eg
ar
d
i
n
g
th
e
s
lo
p
e,
as
illu
s
tr
ated
in
Fi
g
u
r
e
3
,
a
s
lo
p
e
v
alu
e
o
f
1
is
s
u
f
f
icien
t
to
en
s
u
r
e
a
s
m
o
o
t
h
tr
an
s
itio
n
b
etwe
en
alg
o
r
ith
m
s
.
I
n
th
e
in
itial
s
tag
e
,
th
e
o
u
t
p
u
t
o
f
th
e
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
is
u
tili
ze
d
.
T
o
en
s
u
r
e
th
e
c
o
r
r
ec
t
o
p
er
atio
n
o
f
(
1
4
)
,
th
e
s
lo
p
e
m
u
s
t
b
e
n
e
g
ativ
e.
B
y
s
u
b
s
titu
tin
g
=
1
an
d
κ
=
−
1
in
to
(
11
)
,
we
o
b
tai
n
th
e
r
esu
lts
s
h
o
wn
in
(
1
5
)
an
d
r
ep
r
esen
ted
b
y
th
e
r
ed
lin
e
i
n
Fig
u
r
e
4
.
(
)
=
1
1
+
(
−
)
(
1
5
)
wh
er
e
is
th
e
in
f
lectio
n
p
o
in
t.
As
s
h
o
wn
in
Fig
u
r
e
3
,
it
ca
n
b
e
o
b
s
er
v
ed
t
h
at
(
)
ap
p
r
o
ac
h
es
0
at
ap
p
r
o
x
im
ately
=
−
10
o
n
th
e
lef
t
an
d
ap
p
r
o
ac
h
es
1
at
ap
p
r
o
x
im
ately
=
10
o
n
th
e
r
ig
h
t,
wh
ic
h
ca
n
b
e
r
e
p
r
esen
ted
as
∈
[
−
10
,
10
]
an
d
∈
[
−
10
,
10
]
.
Fig
u
r
e
3
.
Dif
f
e
r
en
t in
f
lectio
n
p
o
in
t (
)
an
d
Dif
f
er
en
t Slo
p
e
(
κ
)
f
o
r
lo
g
is
tic
f
u
n
ctio
n
Fig
u
r
e
4
.
Dif
f
e
r
en
t p
e
r
ce
n
tag
e
s
o
f
th
e
in
f
lectio
n
p
o
in
t (
ρ
)
f
o
r
m
o
d
if
y
th
e
lo
g
is
tic
f
u
n
ctio
n
T
o
en
s
u
r
e
c
o
m
p
atib
ilit
y
with
b
atter
y
ca
p
ac
ity
d
eg
r
a
d
atio
n
c
u
r
v
es,
th
e
d
ata
is
f
ir
s
t
s
h
if
ted
to
th
e
r
ig
h
t
s
o
th
at
it b
eg
in
s
at
ze
r
o
,
wh
ich
ca
n
b
e
r
e
p
r
esen
ted
as
1
∈
[
0
,
20
]
an
d
1
∈
[
0
,
20
]
.
1
=
+
10
(
1
6
)
1
=
+
10
(
1
7
)
Su
b
s
eq
u
en
tly
,
th
e
tim
e
s
ca
le
is
ad
ju
s
ted
to
s
p
a
n
f
r
o
m
0
to
th
e
E
OL
,
e
x
p
r
ess
ed
as
2
∈
[
0
,
]
.
T
h
e
in
f
l
ec
tio
n
p
o
in
t is r
ed
ef
in
e
d
as a
p
er
ce
n
t
ag
e,
d
en
o
ted
b
y
ρ
,
b
y
n
o
r
m
alizi
n
g
th
e
tim
e
s
ca
le
to
th
e
r
an
g
e
ρ
∈
[
0
,
1
]
.
=
1
20
∗
(
1
8
)
ρ
=
1
20
(
1
9
)
B
y
s
u
b
s
titu
tin
g
(
1
6
)
in
to
(
1
8
)
an
d
(
1
7
)
in
to
(
1
9
)
,
th
e
eq
u
a
tio
n
s
f
o
r
an
d
ca
n
b
e
r
ea
r
r
a
n
g
ed
as
f
o
llo
ws.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
R
ema
in
in
g
u
s
efu
l life
esti
ma
tio
n
fo
r
p
r
ed
ictive
b
a
tter
y
ma
in
t
en
a
n
ce
… (
C
h
u
tip
o
n
g
s
e
B
o
o
n
ya
kitma
itr
ee
)
1825
=
20
−
10
(
2
0
)
=
20ρ
−
10
(
2
1
)
Su
b
s
titu
tin
g
(
2
0
)
a
n
d
(
2
1
)
in
to
(
1
5
)
y
ield
s
th
e
g
o
v
er
n
in
g
eq
u
atio
n
f
o
r
th
e
weig
h
t
f
u
n
ctio
n
.
T
h
e
lo
g
is
tic
f
u
n
ctio
n
is
th
en
u
tili
ze
d
to
f
ac
ilit
ate
a
s
m
o
o
th
tr
an
s
itio
n
b
etwe
en
th
e
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
a
n
d
th
e
R
SS
A
m
eth
o
d
.
C
o
n
s
eq
u
en
tly
,
th
e
weig
h
t v
ec
t
o
r
(
)
ca
n
b
e
e
x
p
r
ess
ed
b
y
.
=
(
)
=
1
(
1
+
20
(
−
ρ
∗
)
)
(
2
2
)
T
h
e
co
r
r
esp
o
n
d
i
n
g
p
s
eu
d
o
-
co
d
e
is
p
r
esen
ted
in
Alg
o
r
ith
m
4
.
Alg
o
r
ith
m
4
.
L
o
g
is
ticf
u
n
ctio
n
(
ρ
,
)
:
I
n
p
u
t
:
ρ
̶
p
er
ce
n
tag
es th
e
in
f
lectio
n
p
o
in
t
̶
n
u
m
b
er
o
f
weig
h
t
v
ec
to
r
Ou
tp
u
t:
̶
weig
h
t v
ec
t
o
r
1
f
un
ct
io
n
L
o
g
is
ticf
u
n
ctio
n
(
ρ
,
)
2
=
[
1
:1
:
]
3
=
1
/(
1
+
e
x
p
(
(
2
0
/
)
*
(
-
(
ρ
*
))))
4
r
etu
r
n
5
end f
un
ct
io
n
4.
SI
M
UL
A
T
A
T
I
O
N
R
E
SU
L
T
S
T
h
e
NASA
d
ataset
co
n
s
is
ts
o
f
f
o
u
r
b
atter
ies
as
No
.
5
,
6
,
7
an
d
1
8
f
r
o
m
4
lith
iu
m
-
io
n
ce
lls
with
n
o
m
in
al
ca
p
ac
ity
o
f
2
.
2
A
h
an
d
a
n
o
m
in
al
v
o
ltag
e
o
f
3
.
7
V
u
n
d
er
v
ar
io
u
s
ch
ar
g
e
an
d
d
is
ch
ar
g
e
p
r
o
f
iles
[
2
3
]
.
W
e
as
s
u
m
e
th
at
b
atter
ies
No
.
6
,
7
an
d
1
8
ar
e
u
s
ed
f
o
r
a
n
a
ly
s
is
u
s
in
g
th
e
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
alg
o
r
ith
m
,
th
en
th
e
r
esu
lts
ca
n
u
s
e
to
p
r
e
d
ict
th
e
b
e
h
av
io
r
o
f
b
atter
y
No
.
5
.
T
o
c
o
m
p
a
r
e
th
e
R
UL
p
r
e
d
ictin
g
p
er
f
o
r
m
a
n
ce
b
etwe
en
th
e
p
r
o
p
o
s
ed
C
W
S
-
R
SS
A
m
eth
o
d
an
d
th
e
ex
is
tin
g
m
et
h
o
d
s
.
T
h
is
r
esear
ch
w
o
r
k
s
th
at
is
u
s
ed
t
h
e
s
am
e
b
atter
y
d
ata
s
ets
co
m
p
ar
ed
ac
co
r
d
in
g
t
o
th
eir
p
r
ed
icti
o
n
p
e
r
f
o
r
m
an
ce
.
B
ec
au
s
e
th
e
p
r
ed
ictio
n
s
tar
t
a
n
d
s
to
p
th
r
esh
o
ld
s
wer
e
d
if
f
er
en
t
ac
r
o
s
s
th
e
p
r
ev
io
u
s
wo
r
k
s
.
R
elativ
e
er
r
o
r
was
u
s
ed
to
r
ep
r
esen
t
th
e
p
r
ed
ictio
n
p
er
f
o
r
m
an
ce
,
as d
ef
in
ed
b
y
(
3
)
.
Her
e,
is
th
e
p
r
ed
icted
R
UL
v
alu
e,
is
th
e
m
ea
s
u
r
ed
R
UL
v
alu
e,
an
d
is
th
e
r
elativ
e
er
r
o
r
.
B
atter
y
No
.
5
d
ata
wer
e
th
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
b
y
ex
is
tin
g
R
UL
p
r
e
d
ictio
n
m
eth
o
d
s
,
s
o
its
d
ata
s
et
was selec
ted
f
o
r
th
is
co
m
p
ar
is
o
n
.
T
o
s
elec
t
th
e
ap
p
r
o
p
r
iate
,
b
y
ex
p
er
im
en
tin
g
with
v
a
r
y
in
g
th
e
,
v
alu
es
an
d
in
clu
d
in
g
t
h
e
er
r
o
r
R
UL
v
alu
e
at
th
e
en
d
o
f
th
e
ch
ar
g
in
g
c
y
cle.
L
et'
s
tak
e
th
e
d
ata
s
et
o
f
b
atter
y
No
.
5
an
d
in
clu
d
e
er
r
o
r
R
UL
v
alu
es f
r
o
m
7
4
th
cy
cle
t
o
9
8
th
cy
cle.
Set
eq
u
al
to
2
to
5
0
an
d
eq
u
al
t
o
1
to
/
2
.
Fro
m
r
esu
lt in
Fig
u
r
e
5
,
we
ca
n
d
iv
id
e
i
n
to
2
ca
s
es a
s
:
C
ase
1
:
if
b
atter
y
h
as
n
o
th
e
r
eg
en
er
atio
n
,
th
e
m
in
im
u
m
r
el
ativ
e
er
r
o
r
is
r
eq
u
ir
e
d
.
T
h
e
p
a
r
am
eter
s
ca
n
s
et
at
=
1
,
≤
/
2
.
C
ase
2
:
if
b
atter
y
h
as
th
e
r
eg
en
er
atio
n
,
th
e
p
ar
am
eter
s
ca
n
s
et
at
2
≤
≤
10
an
d
10
≤
≤
30
to
f
i
n
d
t
h
e
m
in
im
u
m
r
elativ
e
e
r
r
o
r
.
R
an
g
e
o
f
v
alu
es
an
d
will
d
ep
en
d
o
n
th
e
ty
p
e
o
f
b
atter
y
a
s
m
o
d
el,
b
r
an
d
an
d
ca
p
ac
ity
.
T
o
f
in
d
an
d
v
alu
es,
it m
u
s
t f
in
d
th
e
m
f
r
o
m
d
ata
s
ets o
f
ea
ch
ty
p
e
.
B
y
p
r
ed
ictin
g
R
UL
o
f
b
atter
y
No
.
5
in
Fig
u
r
e
5
was
u
s
ed
d
at
a
o
f
b
atter
y
No
.
7
as
a
g
u
id
eli
n
e.
Fig
u
r
e
6
s
h
o
ws
r
elatio
n
s
h
ip
o
f
s
im
i
lar
ity
-
b
ased
ap
p
r
o
ac
h
,
R
SS
A,
av
er
ag
in
g
weig
h
t
wh
en
ρ
=
0
.
53
in
(
2
2
)
.
W
e
f
o
u
n
d
th
at
if
th
e
weig
h
t
in
d
o
tted
lin
e
is
clo
s
e
to
ze
r
o
,
t
h
e
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
in
b
o
ld
lin
e
is
u
s
ed
.
T
h
en
,
th
e
weig
h
t
in
cr
ea
s
es
g
r
ad
u
ally
u
n
til
clo
s
ed
to
o
n
e,
th
e
R
SS
A
m
eth
o
d
in
d
ash
lin
e
is
u
s
ed
.
I
t
is
n
o
ticed
th
at
if
th
e
i
n
ter
s
ec
tio
n
p
o
in
ts
b
etwe
en
R
SS
A
an
d
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
d
eter
m
in
es
th
e
in
f
lectio
n
p
o
in
t (
0
)
f
o
r
l
o
g
is
tic
f
u
n
ctio
n
in
(
1
1
)
.
I
t w
ill
b
e
clo
s
e
to
th
e
m
i
n
im
u
m
r
elativ
e
e
r
r
o
r
.
T
h
e
p
ar
ticle
f
ilter
is
u
s
ed
to
p
r
ed
ict
R
UL
o
f
b
atter
y
No
.
5
wit
h
r
ec
o
v
e
r
y
o
f
b
atter
y
ca
p
ac
ity
.
I
n
th
e
2
nd
s
tag
e,
n
ee
d
m
o
r
e
s
am
p
les
f
o
r
R
UL
p
r
ed
ictio
n
.
I
f
th
e
d
ata
is
b
ig
g
er
th
an
,
th
e
r
esu
lt
is
m
o
r
e
ac
cu
r
ac
y
.
Fro
m
th
e
ex
p
er
im
en
t
o
f
R
UL
f
o
r
ec
asti
n
g
u
s
in
g
R
SS
A,
s
o
m
e
p
r
o
b
lem
s
wer
e
f
o
u
n
d
in
th
e
2
nd
s
t
ag
e
o
f
f
o
r
ec
asti
n
g
.
T
h
er
ef
o
r
e,
it
is
n
ec
ess
ar
y
to
f
in
d
o
th
er
m
eth
o
d
s
to
h
elp
p
r
e
d
ict
in
th
e
2
nd
s
tag
e
th
at
will
g
iv
e
b
etter
r
esu
lts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
8
1
7
-
1
831
1826
Fro
m
th
e
s
tu
d
y
it wa
s
f
o
u
n
d
th
at
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
is
u
s
ed
to
f
in
d
th
e
s
im
ilar
ity
o
f
s
ig
n
als.
T
h
er
ef
o
r
e,
we
tr
y
to
u
s
e
it in
R
UL
f
o
r
ec
a
s
tin
g
.
Fig
u
r
e
5
.
Su
m
er
r
o
r
R
UL
b
atter
y
No
.
5
u
s
e
R
SS
A
let
=
2
50
an
d
=
1
/
2
.
Fig
u
r
e
6
.
R
elatio
n
s
h
ip
o
f
Similar
ity
-
b
ased
ap
p
r
o
ac
h
,
R
SS
A,
W
A
Similar
ity
-
b
ased
ap
p
r
o
ac
h
ca
n
b
e
u
s
ed
as
a
g
u
id
elin
e
f
o
r
p
r
e
d
ictin
g
R
UL
in
th
e
2
nd
s
tag
e.
T
h
er
ef
o
r
e,
th
is
m
eth
o
d
will
s
o
lv
e
th
e
we
ak
p
o
in
ts
o
f
R
SS
A.
T
h
er
ef
o
r
e
,
th
e
two
m
eth
o
d
s
h
av
e
b
ee
n
co
m
b
in
ed
b
y
u
s
in
g
av
er
ag
in
g
weig
h
t.
Fig
u
r
e
7
s
h
o
ws
th
e
co
m
p
a
r
is
o
n
m
o
d
el
o
f
b
atter
y
N
o
.
5
,
wh
ich
co
n
s
is
ts
o
f
th
e
PF
,
th
e
s
im
ilar
ity
-
b
ased
ap
p
r
o
ac
h
,
R
SS
A
an
d
C
W
S
-
R
SS
A.
T
h
e
co
m
p
ar
is
o
n
m
o
d
el
u
s
es
th
e
d
ata
in
th
e
s
ec
o
n
d
an
d
th
ir
d
s
tag
es,
wh
er
e
th
e
2
nd
s
tag
e
u
s
es 1
3
cy
cles a
n
d
th
e
3
rd
s
tag
e
u
s
es 9
8
c
y
cles.
(
a)
(
b
)
Fig
u
r
e
7
.
C
o
m
p
a
r
is
o
n
m
o
d
el
o
f
b
atter
y
No
.
5
p
r
o
v
id
e
d
b
y
N
ASA
in
(
a)
p
r
ed
ictio
n
s
tar
ts
at
2
nd
s
tag
e
an
d
(
b
)
p
r
ed
ictio
n
s
tar
ts
at
3
rd
s
tag
e
W
e
co
m
p
ar
e
ea
ch
alg
o
r
ith
m
u
s
in
g
d
if
f
er
e
n
t
am
o
u
n
ts
o
f
s
a
m
p
les.
Fro
m
Fig
u
r
e
7
(
a)
in
t
h
e
2
nd
s
tag
e,
th
e
am
o
u
n
t
o
f
lear
n
in
g
d
ata
is
v
er
y
s
m
all
u
s
in
g
o
n
ly
1
3
cy
cles
th
at
ar
e
u
s
ed
to
g
en
er
at
e
p
r
ed
ictio
n
s
.
T
h
e
C
W
S
-
R
S
SA a
lg
o
r
ith
m
ca
n
p
r
ed
ict
with
r
elativ
e
er
r
o
r
o
f
1
9
.
8
%.
W
h
ile
u
s
in
g
h
ig
h
d
ata,
th
e
R
UL
v
alu
e
will b
e
m
o
r
e
ac
c
u
r
a
te
.
F
r
o
m
F
ig
u
r
e
7
(
b
)
,
in
th
e
3
rd
s
t
ag
e,
t
h
e
am
o
u
n
t
o
f
l
ea
r
n
i
n
g
d
a
ta
is
v
e
r
y
b
i
g
,
u
s
i
n
g
9
8
c
y
cl
es
t
o
g
e
n
e
r
a
t
e
p
r
e
d
i
c
t
i
o
n
s
.
T
h
e
C
W
S
-
R
SS
A
al
g
o
r
i
t
h
m
a
c
h
i
e
v
es
n
e
ar
-
p
e
r
f
e
c
t
a
c
c
u
r
a
c
y
w
it
h
a
n
e
g
l
ig
i
b
l
e
r
e
l
a
ti
v
e
e
r
r
o
r.
Similar
ly
,
we
test
with
an
o
th
er
d
ataset
f
r
o
m
MI
T
-
Stan
f
o
r
d
[
2
8
]
.
Fig
u
r
e
8
s
h
o
ws
an
o
t
h
er
b
atter
y
d
ataset
u
s
in
g
No
.
1
p
r
o
v
id
ed
b
y
MI
T
-
Stan
f
o
r
d
.
T
h
e
d
ataset
c
o
n
tain
s
m
ea
s
u
r
em
en
ts
f
r
o
m
1
2
4
lith
iu
m
-
io
n
ce
lls
Evaluation Warning : The document was created with Spire.PDF for Python.