TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 2592 ~ 2
5
9
8
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4885
2592
Re
cei
v
ed Se
ptem
ber 22; Re
vised O
c
to
ber 29, 20
13;
Accept
ed No
vem
ber 2
0
, 2013
0.345 At
tenuation Law of Vibration Signals during
Caving
LI Xu
1
*, GU Tao
2
1
Departme
n
t of Mechan
ics an
d Electron
ics Engi
neer
in
g,
No
rth Chin
a Institute of
Scienc
e and T
e
chno
log
y
,
East of Beijin
g
Yanj
iao, 1
016
0
1
, Chin
a, T
e
l:
+860
10
615
97
47
6
2
Departme
n
t of Computer En
g
i
ne
erin
g, North
Chin
a In
stitute
of Science a
n
d
T
e
chnolo
g
y
,
East of Beijin
g
Yanj
iao, 1
016
0
1
, Chin
a, T
e
l:
+861
88 0
119
30
11
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:gucnm@
1
6
3
.com
A
b
st
r
a
ct
T
o
study on th
e charact
e
risti
cs of
the vibrat
ion si
gn
als of
coal
a
nd sto
n
e
hitting the
ar
mor
plate
duri
ng cavi
ng, a hybri
d
alg
o
rit
h
m b
a
se
d on fi
rst order
forw
ard differenc
e a
nd w
a
velet tra
n
sform
mo
du
lu
s-
max
i
ma
metho
d
is
pres
ente
d
w
h
ich ca
n
be
u
s
ed
in th
e
lon
g
w
all top
co
al fa
ce. F
i
rst, in
ord
e
r to r
educ
e th
e
nois
e
int
e
rfere
n
ce, the
pre-pr
ocessi
ng
of the vibr
atio
n sig
nals
is d
one
b
y
the first ord
e
r forw
ard differ
e
n
c
e
meth
od. S
e
co
nd, the
w
a
vel
e
t transform
mo
dul
us-maxi
ma
meth
od
is
use
d
to
ana
ly
z
e
t
he r
e
sluts
of th
e
differenc
e for the post-
proces
sing of t
he
dat
a. F
i
nally, atten
uatio
n formul
a
is defin
ed i
n
th
e first-level d
e
t
a
il
s
(D1). W
e
can
learn by th
e
experi
m
ent
al
results that the hybr
id a
l
g
o
rith
m prov
ide
s
real-ti
m
e, hi
g
h
confid
enc
e id
e
n
tificatio
n
of co
al a
nd sto
ne b
y
ana
lysis
of th
e first-level
det
ails th
at has
a
pprox
imate 0.
3
4
5
attenuati
on
la
w
betw
een the w
a
velet
tra
n
sform
mod
u
l
u
s-maxi
ma (th
e
maxi
mu
m c
oefficie
n
t) an
d
th
e
w
a
velet transf
o
rm
mod
u
lus-
mi
ni
ma
(th
e
mini
mu
m c
oeffici
ent). Becaus
e
the w
a
velet tr
ansfor
m
mo
dul
us-
max
i
ma
’
s
absc
i
ssa a
nd th
e w
a
vel
e
t transfor
m
mo
du
lus-
mi
ni
ma
’
s
absc
i
ss
a are
ad
jace
nt
to each
other,
the
conce
p
t of Sin
gul
arity-po
int
Cou
p
le (SP
C
) is
defin
ed. Ba
sed u
pon th
e
a
ttenuati
on l
a
w
and the defi
n
e
d
conce
p
t, interf
erenc
e si
gn
als
can
b
e
eli
m
i
n
ated, vi
brat
i
o
n
sig
nals
ca
n
b
e
restor
ed,
an
d so
me
pred
ic
tion
w
o
rk can be do
ne.
Ke
y
w
ords
: 0.3
45 atten
uatio
n law
,
SPC, first
order forw
ar
d d
i
fference, w
a
ve
let transfor
m
modu
lus-
max
i
ma
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The
m
e
chani
zed
caving
coal
fa
ce
ha
s
bee
n explai
ned by Figure 1 in [1]. The key
techni
que du
ring caving i
s
how to de
cid
e
what time the tail supp
ort should be u
p
or do
wn. When
the tail sup
p
o
r
t is up, the
caving is
stop
ped. On
th
e contra
ry, it is caving. The
ca
ving oppo
rtun
ity
is controlled
by the coal
worke
r
’
s
ob
serving
and
hi
s expe
rie
n
ce
s at p
r
e
s
ent.
This l
ead
s to
the
low level of mining efficie
n
cy and auto
m
ation duri
n
g
caving. So it is of significance to study on
the techniq
u
e
for the tail suppo
rt cont
ro
lling. In
[1, 2], we have discu
s
sed the a
udio processi
ng
techn
o
logy. I
n
this pa
pe
r,
we
will
aim
at the vib
r
ation
sign
al p
r
o
c
e
s
sing
technol
o
g
y. Two
ki
nd
s o
f
techn
o
logy h
a
ve been a
d
o
p
ted re
spe
c
ti
vely in our instrument
s.
The alg
o
rith
m of static
coal
-rock int
e
rf
ace re
co
g
n
ition [3-6]
can n
o
t be
applied
approp
riately during
cavi
ng. It is essential to so
lv
e the cont
rol
ling of tail suppo
rt with the
techni
que
ad
opted b
a
sed
upon th
e dyn
a
mical
ide
n
tifi
cation
of coa
l
and
ro
ck
in
the process
of
caving. Fo
r a
c
curate
co
ntrolling, the en
vironme
n
tal requireme
nts
durin
g caving
sho
u
ld be ta
ken
int
o
ac
co
unt
spe
c
ially
.
E
x
p
e
rien
ce
s
of previous
studi
e
s
[1, 2]
sho
w
that it can
av
oid st
ron
g
noi
se
interferen
ce
usin
g digital
sign
al p
r
o
c
e
s
sing te
ch
niqu
e to p
r
o
c
e
s
s the vibration
sign
als of
coal
and sto
ne bu
mping the tra
n
sp
orting
coa
l
armor
plat
e. Based on
previous resea
r
ch result
s [1, 2],
the identification rul
e
is i
n
ve
stigated
using the first
orde
r forwa
r
d
differen
c
e
method a
nd
the
wavelet tran
sform mo
dulu
s
-maxima m
e
thod, an
d
the
0.345 atten
u
a
tion la
w of v
i
bration
si
gna
ls
is p
r
op
osed.
The
attenu
ation la
w
provides an
i
m
porta
nt ap
plicatio
n in
coal
mine
safety
prod
uctio
n
.
2. Cav
i
ng Signal and th
e
Signal Processing
Duri
ng the
whole p
r
o
c
e
ss
of caving, the
vibrat
ion
sig
nal whi
c
h i
s
caused by the
coal
and
stone
bumpi
ng the a
r
m
o
r plate i
s
sampl
ed by
vibration
sensor
with the spee
d 2
00k
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
0.345 Attenu
ation La
w of Vibration Sig
nals
Duri
ng Cavin
g
(LI Xu)
2593
sampl
e
s/
se
c. The so
und
n
o
ise
ha
s bee
n
elimin
ated
t
o
tally to the
sampled
vibration
sign
als.
T
he
caving
sign
al model can be
given by:
f(
t)
=
Vib_coal(t)+
Vib_rock(t)+
Vib_noi
se(t)
(1)
Whe
r
e Vi
b_
coal(t) is the vi
bration
si
gnal
of coal
fallin
g, Vib_rock(t
)
is th
e vibration
sign
al
of stone fallin
g, and Vib_n
oise
(t) is the
noise sig
nal.
In real-tim
e si
gnal a
c
qui
siti
on syste
m
, f(t) is comp
ose
d
of several signal
s listed i
n
(1)
or
maybe f(t) is a single si
g
nal merely. In orde
r
to re
duce the inte
rfere
n
ce of Vib_noi
se (t
), pre-
pro
c
e
ssi
ng of
data for f(t) is don
e by (2):
△
f(
k)
=f(k+
1
)-f(k)
(
2
)
Whe
r
e
△
is th
e first ord
e
r f
o
rward differe
nce o
perator.
Interfere
n
ce sign
als a
r
e
effectivel
y su
ppre
s
sed
by the cal
c
ulat
ion of
△
f(k), all the
vibration sig
n
a
ls have discrete
valu
es
b
y
analysi
s
of
the first orde
r forward diffe
ren
c
e. Fi
gure
1
is the
ori
g
inal
vibration
si
g
nal
stone
3 sa
mpled
du
ring
cavin
g
. Figu
re 2
is the first orde
r forward
differen
c
e results of sign
al stone
3.
Figure 1. Vibration Signal stone3
Figur
e 2. First Order F
o
rward Diffe
ren
c
e
Re
sult
Wavelet
ana
lysis i
s
a
powerful to
o
l
for n
u
me
ri
cal a
nalysi
s
and
ca
n
be very
comp
utationa
l efficient.
We
ado
pt the m
o
st
comm
onl
y use
d
o
r
thog
onal
wavelet
s
to do th
e p
o
s
t-
pro
c
e
ssi
ng of
the data. The orthog
onal
wavelet serie
s
app
roximati
on to a sign
al
f(t) is given b
y
:
)
(
...
)
(
)
(
)
(
,
1
,
1
,
,
,
,
t
d
t
d
t
S
t
f
k
k
k
k
k
J
k
J
k
k
J
k
J
J
(3)
Whe
r
e
)
(
t
is th
e scali
ng fun
c
tion,
)
(
t
is the wavelet funct
i
on. J is the numbe
r of
multire
s
olutio
n scale
s
and
k ra
nge
s fro
m
one to t
he numbe
r of co
efficients in t
he co
rrespon
ding
comp
one
nt.
The Sj,k
are
calle
d a
s
t
he ap
proximation
coeffici
ents, a
nd th
e dj,k
are the detail
coeffici
ents. Acco
rdi
ngly,
the
wavel
e
ts seri
es app
ro
x
i
mation of the origi
nal si
g
nal f(t) is
writ
ten
as:
f( t)
≈
S
J
(t)+
D
J
（
t
）
+…
+
D
1
(t)
(4)
W
h
er
e
)
(
,
,
t
S
S
k
j
k
k
j
j
,
k
k
j
k
j
j
t
d
D
)
(
,
,
; j=1,…,J
.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
-3
-2.
5
-2
-1.
5
-1
-0.
5
0
0.
5
x 1
0
4
S
a
m
p
l
ed poi
nt
V
i
br
at
i
ng v
a
l
u
e
0
500
1
000
150
0
20
00
2
500
300
0
35
00
4000
450
0
50
00
-2
.
5
-2
-1
.
5
-1
-0
.
5
0
0.
5
x 1
0
4
D
i
f
f
e
r
e
nc
e V
a
l
v
e
S
a
m
p
l
ed poi
nt
F
i
rs
t
or
der
f
o
r
w
ar
d di
f
f
e
r
enc
e
of
s
i
gnal
s
t
o
ne3
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2592 – 2
598
2594
Two
-
scal
e rel
a
tions i
s
give
n by:
z
n
n
t
n
t
)
(
)
(
)
2
(
2
1
(5)
P
o
st
-p
ro
ce
ssi
ng of
t
h
e d
a
t
a
f
o
r
△
f(k) i
s
done
by (6).
Here, the
ort
hogo
nal
wav
e
let db
5 i
s
use
d
to a
n
a
lyze th
e p
r
e-pro
c
e
s
sing
re
sults.
Db
5 wavelet i
s
the
comp
actly supp
orted
orthon
orm
a
l wavelet whi
c
h belong
s to the Daub
echi
es famili
e. Highe
r order Daub
ech
i
es
function
s a
r
e
not easy to
descri
be
with an analytic
al
expre
ssi
on. The orde
r of the Dau
b
e
c
hi
es
function
s d
e
n
o
tes the
num
ber
of vanish
ing mom
ents, or the
num
ber
of ze
ro
moment
s of t
h
e
wavelet func
tion.
11
[]
[
]
[
2
]
jj
m
dk
f
m
h
m
k
(6)
Whe
r
e h1[
k] is the high
-pa
ss filter for d
e
c
omp
o
sitio
n
.
We u
s
e
(7)
to do inverse wavelet trans
form [7], the firs
t-lev
e
l details
of
ᇞ
f(k) is
recon
s
tru
c
ted
,
shown in Figure 3.
11
'[
]
[
]
[
2
]
jj
m
f
kd
m
r
h
k
m
(7)
Whe
r
e
r_h
1
[k] is the hi
gh-pass filter fo
r re
c
o
ns
tr
uc
tion
.T
h
e
re
la
tion
s
h
ip
b
e
t
w
e
en
h
1
[
k
]
and r_
h1[k] is given by:
r_h
1
[k]=
(-1)
k
h
1
[N-1-K]
(8)
Figure 3. Coe
fficients in d1
by the
△
-W T
r
an
sform
Figure 4. Hig
h
-pa
s
s Filter f
o
r De
co
mpo
s
ition
Fi
gure 5. Hig
h
-pa
s
s Filter f
o
r Re
co
nst
r
u
c
tion
0
1
000
2000
30
00
4000
5000
6
000
-1
.
5
-1
-0
.
5
0
0.
5
1
x 1
0
4
d1
S
a
m
p
l
ed p
o
i
n
t
W
a
v
e
l
e
t
c
oef
f
i
c
i
ent
s
(
s
t
on
e3)
o
f
f
i
r
s
t
o
r
der
f
o
r
w
ar
d di
f
f
e
r
enc
e
1
2
3
4
5
6
7
8
9
10
-0.
8
-0.
6
-0.
4
-0.
2
0
0.
2
0.
4
0.
6
0.
8
D
e
c
o
m
pos
i
t
i
on h
i
gh
-pas
s
f
i
l
t
e
r
db5
1
2
3
4
5
6
7
8
9
10
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
R
e
c
o
ns
t
r
u
c
t
i
on hi
gh-
pas
s
f
i
l
t
er
db
5
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
0.345 Attenu
ation La
w of Vibration Sig
nals
Duri
ng Cavin
g
(LI Xu)
2595
The
high_
pa
ss filters fo
r de
com
positi
on a
nd
re
co
nstru
c
tion
a
r
e dete
r
min
e
d
by the
cha
r
a
c
teri
stics of the vibrati
on signal
s, the use
d
db5
wavelet’
s hi
gh_p
ass filters are
sho
w
n
in
Figure 4 and
Figure 5.
We
can find f
r
om Fig
u
re
2 and Fig
u
re
3 that
the unilat
e
ral
cha
r
a
c
te
ristics of the
data in
Figure 2 ha
s become bilat
e
ral data in F
i
gur
e 3 afte
r post-proces
si
ng of the data for
△
f(k). We
can
se
arch
o
u
t the Singul
a
r
ity-point [8, 9
]
Coupl
e
of th
e vibration
si
gnal
s in
D1 u
s
ing th
e wave
let
transfo
rm m
o
dulu
s
-m
axima metho
d
after the
sig
nal
has bee
n
reconstructe
d. We
d
e
fine (2),
(6),
and (7) as
th
e
△
-W tran
sf
orm. Th
e differen
c
e
of the
origin
al
sign
al is
con
s
tructed by the S
P
C’s
data rul
e
. Th
e rule
can b
e
used to elim
inate the inte
rfere
n
ce sig
n
a
ls, and to id
entify the falling
rock
from c
oal.
3. The Rule
of Co
efficien
ts in D1
3.1. The SPC and it’s Cha
r
acteristic
In orde
r to a
nalyze th
e problem of di
sti
ngui
shing
ro
ck from
co
al e
a
sily, we
defi
ne the
con
c
e
p
t of Singula
r
ity-poin
t
Couple (SP
C
) a
s
follows.
The maxim
u
m co
efficient
and the
mini
mum
coeffici
ent is
obtain
ed from
coefficient
s in
d1 afte
r the
sampled
signa
l ha
s b
een
d
one
by the
△
-W trans
f
orm.
If the maximum
c
oeffic
i
ent’s
absci
ssa a
n
d
the mi
nimu
m coefficie
n
t’s a
b
sci
s
sa
a
r
e
adja
c
ent
to ea
ch
othe
r, the Sing
ula
r
ity-
point
Cou
p
le
(SPC) i
s
d
e
fined. If th
e maximum
co
efficient’
s
ab
sci
ssa
a
nd the
mini
mum
coeffici
ent’s
absci
ssa are
not adjace
n
t to each
oth
e
r, it is not the SPC. The
local maxim
u
m
coeffici
ent’s
absci
ssa and
the local minimum co
efficient’
s
absci
ssa are not adjacent to each
other, the SPC is not co
nstructed either. The concept of
SPC is illustrated in Fi
gure 6.
Figure 6. The
Con
c
ept of SPC
3.2 The Appl
ication of SP
C
To get th
e
wavelet tran
sform mo
dulu
s
-m
axima a
n
d
the
wavele
t transfo
rm
modulu
s
-
minima, five
gro
u
p
s
of v
i
bration
si
gn
als
sam
p
led
duri
ng
cavi
ng a
r
e
analy
z
ed
by the
△
-W
transfo
rm. Ta
ble 1 give
s t
he maximum
coeffici
ent a
nd the mi
nim
u
m coefficien
t in D1
of every
grou
p sig
nal
s.
Table 1. The
Maximum Co
efficient and t
he Minimum
Coeffici
ent in D1
D1
C
o
a
l
1 C
o
a
l
-
s
t
o
n
e
S
t
o
n
e1
S
t
o
n
e2
S
t
o
n
e3
Vmax
3435.7
9579.4
11158
875.84
2941.5
9458.9
Vmin
-2235.1
-6243.1
-17036
-1330.9
-4508.2
-14529
The SPC i
s
f
ound
out in e
v
ery gro
up’
s
D1 o
w
in
g to the adj
acent
absci
ssa. In fact, the
SPC is
composed of the
maximu
m
co
efficient a
nd
the minimu
m
co
efficient b
y
the cal
c
ul
ation
and an
alysi
s
of every group’
s sig
nal.
The re
co
gni
ti
on rule fo
r
disting
u
ishing
rock fro
m
coal
durin
g
caving
ca
n be
give
n a
s
follo
ws
by invest
igati
ng the
ch
ara
c
teri
stic
of S
P
C corre
s
po
nding
to the falling material:
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TELKOM
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Vol. 12, No. 4, April 2014: 2592 – 2
598
2596
IF S
P
C
’
S
|V
m
a
x
|>
| V
m
i
n
|
COAL IS
FALLIN
G
ELSE SPC’S |
V
max|
<|
Vmin |
ROCK IS
FALLI
NG
ENDIF
3.3. The Atte
nuation L
a
w
of SPC
The attenuati
on perce
ntag
e formula i
s
d
e
fined a
s
follows:
ma
x
m
i
n
ma
x
m
i
n
||
|
|
%
|m
a
x
[
,
|
|
]
|
VV
VV
(
9)
The d
a
ta in
Table 1
is i
n
vestigated
by (9). T
able
2
pre
s
ent
s the
r
e i
s
an
app
roximate
0.345 attenu
a
t
ion law bet
ween the maxi
mum co
e
ffici
ent and the m
i
nimum coefficient in D1.
Table 2. The
Attenuation L
a
w of SPC in D1
The first-level det
ail coefficients
C
o
a
l
1
C
o
a
l
-
s
t
o
n
e
S
t
o
n
e1 S
t
o
n
e2 S
t
o
n
e3
av
e
r
ag
e
△
%
0.3494
0.3483
0.3450
0.3419
0.3475
0.34896
0.34684
Experimental
re
sults
sho
w
the avera
ge
value
of the
attenuation l
a
w is i
nde
pen
den
cy of
the falling altit
ude of
coal
a
nd rock. The
averag
e
valu
e is a
p
p
r
oxim
ate co
nsta
nt 0.345. Th
ere
are
no SPC and
0.345
atten
uation l
a
w to
interfe
r
en
ce
sig
nal
s an
d
to the
aftermath of vib
r
ation
sign
als a
c
cording to the in
vestigated re
sults.
There a
r
e
no
SPC an
d 0.3
45 atten
uatio
n la
w in th
e
seco
nd-l
e
vel d
e
tails
(D2) to
the fifth-
level details
(D5
)
by an
al
ysis of the
wave
let tra
n
s
form m
odul
us-maxima a
nd the wave
let
transfo
rm
mo
dulu
s
-mi
n
ima
,
sho
w
n
in
T
able
3 to
Ta
ble 6.
Ho
wev
e
r, the
tre
nd
of data
bet
ween
the maximum
and th
e mini
mum in
d3
a
nd in
d5
are
simila
r a
s
th
e tren
d in
d1
. There a
r
e n
o
obviou
s
rule
s betwee
n
the maximum an
d the minimu
m in d2 and i
n
d4.
Table 3. The
Maximum Co
efficient and t
he Minimum
Coeffici
ent in D2 (n
o SPC and 0.34
5
attenuation la
w)
D2
C
o
a
l
1 C
o
a
l
-
s
t
o
n
e
S
t
o
n
e1
S
t
o
n
e2
S
t
o
n
e3
Vmax
1138.5
2127.2
3605.8
348.35
1037.3
3326.3
Vmin
-1453.7
-2036.1
-3172.1
-455.12
-1021.7
-3342.7
Table 4. The
Maximum Co
efficient and t
he Minimum
Coeffici
ent in D3 (n
o SPC and 0.34
5
attenuation la
w)
D3
C
o
a
l
1 C
o
a
l
-
s
t
o
n
e
S
t
o
n
e1
S
t
o
n
e2
S
t
o
n
e3
Vmax
1184.6
2840.1
4878.8
301.14
1118.9
3551.7
Vmin
-1098.6
-2576.7
-5310.8
-362.83
-1261.3
-4020
Table 5. The
Maximum Co
efficient and t
he Minimum
Coeffici
ent in D4 (n
o SPC and 0.34
5
attenuation la
w)
D4
Coal1
Coal-stone
Stone1
Stone2
Stone3
Vmax
374.91
1078.7
2327.3
281.44
466.89
1532
Vmin
-396.36
-918.44
-2246.5
-285.41
-537.42
-1731.4
Table 6. The
Maximum Co
efficient and t
he Minimum
Coeffici
ent in D5 (n
o SPC and 0.34
5
attenuation la
w)
D5
Coal1
Coal-stone
Stone1
Stone2
Stone3
Vmax
380.24
979.85
1460.2
328.46
736.81
1005.4
Vmin
-370.54
-915
-1654.7
-359.56
-674.28
-1048.6
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TELKOM
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ISSN:
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046
0.345 Attenu
ation La
w of Vibration Sig
nals
Duri
ng Cavin
g
(LI Xu)
2597
Assu
ming
th
at the
Wf(u,
s
) i
s
the
vibration
sign
al f(t)’s
wavelet t
r
ans
f
orm, if the Wf(u,s)
obtain
s
the lo
cal maximum
value and th
e local mini
m
u
m value, (10
)
sho
u
ld be m
e
t as follows:
(,
)
0
wf
u
s
u
(10
)
Each el
emen
t of the set {u} ca
n be
ca
lculat
e
d
to meet the co
nd
ition of (10
)
. If the
Wf(u,
s
)
obtai
ns th
e gl
oba
l maximum v
a
lue(Vm
ax)
at the a
b
sci
s
sa
u0, the
g
l
obal mi
nimu
m
value(Vmin)
will be obtained at t
he abscissa v. The relationship
between u0 and v is given by:
0
1
vu
(11
)
Simultaneo
usly, (12) is e
s
tablished ap
proximately:
ma
x
m
i
n
ma
x
m
in
||
|
|
0.34
5
|m
a
x
[
,
|
|
]
|
VV
VV
(12
)
Signal filterin
g and predi
ction ca
n be do
ne by (11
)
an
d (12
)
.
4. Applica
t
ions
of the Atten
u
ation La
w
4.1. Filtering and Identifi
cation Mod
e
l
Other type
s o
f
vibration si
g
nals
can i
n
terfere
with th
e
norm
a
l re
co
g
n
ition of the vibration
sign
als of co
al and sto
ne
durin
g cavin
g
.
Accordingl
y,
the interfere
n
ce
sign
als
should b
e
filtered
before
coal o
r
stone di
stin
guished. The
r
e are seve
ral types of the interferen
ce signal
s du
ring
caving:
(1
) T
he first type:
The
sam
p
led
sig
nal
s a
r
e
cau
s
e
d
o
n
ly
by the
syste
m
noi
se
vibra
t
ion,
there is n
o
coal or sto
ne falling du
ring
caving.
(2
) T
he se
con
d
type: The vibra
t
ion signal
s a
r
e
cau
s
e
d
by the co
al or
ston
e bumpi
ng th
e arm
o
r pl
ate
.
The first
sa
mpled d
a
ta correspon
ds to
the
coal
or
stone
falling. The
seco
nd
sampl
ed data i
s
th
e rep
e
rcu
s
sio
n
of the first sampl
ed
sign
als.
Becau
s
e it d
oes
not corresp
ond to th
e actu
al mat
e
rial fallin
g, it belong
s to
the interfe
r
en
ce
sign
als. Th
e
s
e type
s of
interfer
en
ce
sign
als
are
analyzed b
y
the
△
-W tran
sform,
the
investigate
d
result
s
sho
w
there
a
r
e
no
SPC an
d
0.3
45 atten
uatio
n la
w i
n
the
s
e inte
rfere
n
ce
sign
als. Thu
s
, the 0.345 attenuatio
n law
can b
e
used to filter these i
n
terferen
ce si
gnal
s.
The identifica
t
ion model for coal an
d
sto
ne ca
n be de
scribe
d as foll
ows:
If 0.33 =<
△
% <
=
0.35
If
Vmax>abs(Vmi
n)
O
u
t ’Coal’
Else
Out ’Stone’
EndIF
Else
O
u
t ’Noise’
EndIF
The algo
rithm
provide
s
re
cognition rates in industri
a
l tests a
s
follo
ws.
Table 7. Re
cognition
Rate
s
Signal1 Signal2 Signal2 Signal2
recognition
rate
95.6%
96.3%
95.1%
97.1%
4.2. Restorin
g the Origin
al Signal
If the relationship of the SPC’s data h
a
s
bee
n kn
own to the vibration sig
nals of
coal an
d
stone d
u
rin
g
caving, the
origin
al sig
n
a
l
s ca
n
be re
store
d
by the data of the SPC and t
h
e
c
oeffic
i
ents
in D1.
The coefficie
n
ts in the first-level detail
s
are
sho
w
n i
n
Figu
re 3. T
o
re
store the
origin
al
sign
al, the data of the SPC is
re
se
rved; other dat
a in D1 is cl
eare
d
. Then
the sign
al stone
3
whi
c
h i
s
sh
o
w
n in Fi
gure
7 is recon
s
tru
c
ted by
the d
a
ta of the SPC an
d the ot
her laye
r wavelet
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TELKOM
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KA
Vol. 12, No. 4, April 2014: 2592 – 2
598
2598
coeffici
ents.
Comp
ari
ng F
i
gure 1 an
d
Figure 7, we kn
ow th
e absol
ute error is bet
wee
n
0.0065
724
~1
438.9. The re
store
d
sig
nal
fulfills the req
u
irem
ents.
Figure 7. The
Resto
r
ed Sig
nal ston
e3
5. Conclusio
n
In this pa
per the co
ncept
of the SPC is
defin
ed a
nd the atten
uation la
w of
SPC is
investigate
d
. The vibratio
n
signal
s of coal and
ston
e can b
e
di
stinguished
co
rre
ctly by the
attenuation l
a
w. If the maximum coef
ficient or
the
minimum co
efficient is known in D1,
the
predi
ction
wo
rk
ca
n b
e
do
n
e
by form
ula
(10
)
, and
the
origin
al
signal
s al
so
ca
n b
e
re
con
s
tructe
d.
Experimental
results
sho
w
that
the 0.345 attenuatio
n law i
s
the
ch
a
r
a
c
teri
stic of the sampl
e
d
vibration si
gn
als. It is of
signifi
can
c
e t
o
e
liminate the noi
se occurred du
ring
caving and
to
improve the a
u
tomatic
caving tech
nolo
g
y
.
Referen
ces
[1]
LI X
u
, GU T
a
o.
New
T
e
chni
que of Disti
ng
uishi
ng R
o
ck from C
oal B
a
s
ed on Statistic
a
l Ana
l
ysis of
W
a
velet T
r
ansf
o
rm
. Proc. SPIE 2009; 7
343:
P734
30A.
[2]
GU T
ao, LI X
u
.
N
e
w Eq
ui
pmen
t o
f
D
i
s
tin
g
u
i
sh
i
n
g
Ro
ck from C
o
al
Ba
se
d on
Sta
t
i
s
ti
cal
Ana
l
ysi
s
o
f
Fa
st
F
ourier T
r
ansf
o
rm.
Glob
al C
o
ngress o
n
Intell
ige
n
t S
y
stems.
2009; P2
69-2
73.
[3] AVTOMA
T
G
O
R
MASH
(SU).
Coal-r
ock interf
ace mon
i
ng
method.
Pate
nt Numb
er: SU89
191
4-b.
[4]
Asfahan
i J, B
o
rsaru M. L
o
w
-
activit
y
s
pectr
omet
ric g
a
mm
a-ra
y l
ogg
in
g techn
i
qu
e for d
e
lin
eati
on
of
coal/rock i
n
terfaces in dr
y b
l
a
s
t holes.
Appl
ie
d Rad
i
atio
n an
d Isotopes.
20
07; 65(6): 7
48-
755.
[5]
YU Feng-y
ing, T
I
AN
Mu-qin, HU J
i
n-fa. C
o
al-rock Int
e
rfac
e Rec
o
g
n
itio
n
Based
on
N
e
u
r
al N
e
t
w
ork
.
Mecha
n
ica
l
En
gin
eeri
ng & Au
tomati
on.
20
07
; 8: 4-6. (in Chi
nese)
[6]
YU Shi-
jia
n. Wavel
e
t Multi-
Re
soluti
on A
nal
ys
is of
W
eak
Refl
ected W
a
v
e
F
r
om T
he Interfa
c
es Of Co
a
l
Seam And Strata.
Chin
ese J
ourn
a
l of Rock Mecha
n
ics an
d
Engin
eeri
ng.
2
005; 24(
18): 3
224-
322
8. (in
Chin
ese)
[7]
S Mall
at. A th
eor
y for
multir
esol
ution
si
gna
l d
e
comp
ositi
o
n: the
w
a
v
e
let
repres
entati
o
n
.
IEEE Trans
.
Patt. Anal. and Mach. Intell.,
1989; 11(
7): 674
-693.
[8]
S Mall
at, W
L
H
w
an
g. Sin
g
u
l
arit
y
detecti
on
and
proc
essin
g
w
i
th
w
a
ve
let
s
.
IEEE Trans. Info.
T
heor
y
,
199
2; 38(2): 61
7-64
3.
[9]
Vivek Kum
a
r, Mani Me
hra.
W
a
velet o
p
timi
zed fini
t
e
differ
ence m
e
thod
u
s
ing i
n
terp
olati
ng
w
a
v
e
l
e
ts for
solvin
g sin
gul
a
r
l
y
p
e
rturb
ed pr
obl
ems.
Journ
a
l of W
a
velet T
heory a
nd Ap
pl
icatio
ns
. 200
7; 1(1): 83-9
6
.
[10]
CJ Kice
y
,
CJ
Len
nard. U
n
iq
ue reco
nstructi
on
of ban
d-l
i
m
ited sig
nals
b
y
a Ma
ll
at-Z
hon
g
w
a
ve
let
transform algorithm.
F
ourier A
nalysis
and A
p
pl.
, 1997; 3(
1): 63-8
2
.
0
50
0
10
00
1
500
200
0
250
0
30
00
3500
4000
4500
500
0
-3
-2.
5
-2
-1.
5
-1
-0.
5
0
0.
5
x 1
0
4
S
a
m
p
l
ed po
i
n
t
V
i
br
at
i
n
g
v
a
l
u
e
S
t
o
ne3 R
e
s
t
ored
S
i
gn
al
Evaluation Warning : The document was created with Spire.PDF for Python.