algorithms
Article
Noise Reduction of Steel Cord Conveyor Belt Defect
Electromagnetic Signal by Combined Use of
Improved Wavelet and EMD †
Hong-Wei Ma, Hong-Wei Fan *, Qing-Hua Mao *, Xu-Hui Zhang and Wang Xing
School of Mechanical Engineering, Xi’an University of Science and Technology, Xi’an 710054, China;
[email protected] (H.-W.M.); [email protected] (X.-H.Z.); [email protected] (W.X.)
* Correspondence: [email protected] (H.-W.F.); [email protected] (Q.-H.M.);
Tel.: +86-029-8558-7170 (H.-W.F. & Q.-H.M.)
† This paper is an extended version of our paper published in the International Symposium on Computer,
Consumer and Control, Xi’an, China, 4–6 July 2016.
Academic Editor: Hsiung-Cheng Lin
Received: 17 July 2016; Accepted: 13 September 2016; Published: 26 September 2016
Abstract: In order to reduce the noise of a defect electromagnetic signal of the steel cord conveyor belt
used in coal mines, a new signal noise reduction method by combined use of the improved threshold
wavelet and Empirical Mode Decomposition (EMD) is proposed. Firstly, the denoising method based
on the improved threshold wavelet is applied to reduce the noise of a defect electromagnetic signal
obtained by an electromagnetic testing system. Then, the EMD is used to decompose the denoised
signal and then the effective Intrinsic Mode Function (IMF) is extracted by the dominant eigenvalue
strategy. Finally, the signal reconstruction is carried out by utilizing the obtained IMF. In order to
verify the proposed noise reduction method, the experiments are carried out in two cases including
the defective joint and steel wire rope break. The experimental results show that the proposed method
in this paper obtains the higher Signal to Noise Ratio (SNR) for the defect electromagnetic signal
noise reduction of steel cord conveyor belts.
Keywords: steel cord conveyor belt; signal noise reduction; wavelet; Empirical Mode
Decomposition (EMD)
1. Introduction
In the modern coal mine, the belt conveyor [1] is one of the important transport machines. Due to
the high strength of steel wire rope, the steel cord conveyor belt is widely used in the coal transportation.
However, the coal mine steel cord conveyor belt is usually subject to the alternating heavy load and
complicated conditions, so the safety of the steel cord conveyor belt is very important. If the steel cord
belt breaks, there will be undesired production interruption and large economic loss [2]. A typical steel
cord conveyor belt break is shown in Figure 1.
Electromagnetic testing is a common kind of steel cord conveyor belt defect detection method.
However, under the complicated coal mine working conditions, the defect electromagnetic signal
collected from steel cord conveyor belt usually contains a large amount of non-stationary noise which
makes the signal feature extraction difficult. Thus, for the steel cord conveyor belt the research of a
reliable signal noise reduction method is necessary. It is well known that the wavelet transform is a
common signal noise reduction method [3,4] and it has been used for the denoising of electromagnetic
signals [5–7]. For the steel cord conveyor belt, the wavelet transform was used to denoise the
electromagnetic signal with the steel wire rope break defect [8] and the corrected linear B-wavelet
method was proposed to improve the Signal to Noise Ratio (SNR) [9]. However, the wavelet transform
result can be affected by the selection of wavelet basis, decomposition level and threshold value [10].
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This
papervalue
will propose
improved
threshold
method
to reduce
themethod
signal distortion
threshold
[10]. Thisanpaper
will propose
anwavelet
improved
threshold
wavelet
to reduceand
the
unsmoothed
phenomenon
after
denoising
[11,12].
Furthermore,
the
defect
electromagnetic
signal distortion and unsmoothed phenomenon after denoising [11,12]. Furthermore, the signal
defect
of
coal mine steelsignal
cord of
conveyor
belt
is acord
kindconveyor
of complicated
signal, non-stationary
so the optimal
electromagnetic
coal mine
steel
belt is non-stationary
a kind of complicated
filtering
cannot
be
obtained
only
by
the
wavelet
method.
The
Empirical
Mode
Decomposition
signal, so the optimal filtering cannot be obtained only by the wavelet method. The Empirical(EMD)
Mode
method
need not(EMD)
select the
basisneed
function
can
adaptively
decompose
theadaptively
signal intodecompose
many Intrinsic
Decomposition
method
not and
select
the
basis function
and can
the
Mode
so Mode
it is very
suitable(IMFs),
for the so
noise
of non-stationary
[13,14].
signal Functions
into many(IMFs),
Intrinsic
Functions
it isreduction
very suitable
for the noisesignal
reduction
of
However,
the
EMD
is
usually
realized
by
directly
removing
the
high-frequency
functions,
which
can
non-stationary signal [13,14]. However, the EMD is usually realized by directly removing the
cause
these problems
suchwhich
as non-maximal
noiseproblems
removal such
rate and
loss of useful
signal.
In recent
high-frequency
functions,
can cause these
as non-maximal
noise
removal
rate
years,
some
effective
IMF
selecting
methods
were
proposed,
including
the
close
eigenvalue
[15],
and loss of useful signal. In recent years, some effective IMF selecting methods were proposed,
great
kurtosis
contribution
[16][15],
and great
large kurtosis
correlation
coefficient[16]
[17].and
However,
these IMFcoefficient
selection
including
the close
eigenvalue
contribution
large correlation
methods
are qualitative,
the actual
operation
the IMF selection
rationality
willthe
affect
noise
[17]. However,
these IMF in
selection
methods
are qualitative,
in the actual
operation
IMFthe
selection
reduction
effect.
This
paper
will
propose
a
new
kind
of
adaptive
IMF
selection
strategy
according
to
rationality will affect the noise reduction effect. This paper will propose a new kind of adaptive IMF
the
dominant
eigenvalues.
selection strategy according to the dominant eigenvalues.
Figure
1. Steel
break scene.
scene.
Figure 1.
Steel cord
cord conveyor
conveyor belt
belt break
Based on the above analysis, the new electromagnetic signal noise reduction method based on
Based on the above analysis, the new electromagnetic signal noise reduction method based on
the improved threshold wavelet and EMD with the dominant eigenvalue is proposed in this paper
the improved threshold wavelet and EMD with the dominant eigenvalue is proposed in this paper
and used for the coal mine steel cord conveyor belt testing. In Section 2, the basic theory of the
and used for the coal mine steel cord conveyor belt testing. In Section 2, the basic theory of the
proposed electromagnetic signal noise reduction method will be introduced. In Section 3, the test rig
proposed electromagnetic signal noise reduction method will be introduced. In Section 3, the test rig
and experiment will be carried out to verify the effect of the newly proposed method for the steel
and experiment will be carried out to verify the effect of the newly proposed method for the steel cord
cord conveyor belt defect detection.
conveyor belt defect detection.
2. Basic Theory of Signal Noise Reduction Method
2. Basic Theory of Signal Noise Reduction Method
2.1. Wavelet Noise Reduction Principle
2.1. Wavelet Noise Reduction Principle
The wavelet
wavelet threshold
processing
The
threshold noise
noise reduction
reduction method
method can
can be
be carried
carried out
out according
according to
to the
the processing
flow,
as
shown
in
Figure
2.
The
main
processing
steps
include
the
wavelet
basis
function
flow, as shown in Figure 2. The main processing steps include the wavelet basis function selection,
selection,
multi-scale
decomposition,
wavelet
threshold
selection
and
signal
reconstruction.
multi-scale decomposition, wavelet threshold selection and signal reconstruction.
2.1.1. Wavelet Basis Function Selection
The wavelet basis function has a great influence on the signal noise reduction effect. In order to
obtain a better denoised signal, the basis function having the similar waveform as the original signal
should be selected. Because the joint electromagnetic signal waveform is close to the dB8 wavelet basis
function, the dB8 wavelet basis is adopted in this paper.
2.1.2. Wavelet Multi-Scale Decomposition
The discrete wavelet basis function [18] is shown as Equation (1)
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j
ψ j,k (t) = a0 − 2 ψ( a0 − j t − kb0 )
(1)
where
a0 2016,
represents
the extension scale and b0 represents the time translation, usually a0 = 2, b03=
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9, 62
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11
Figure
noise reduction
reduction flow
flow chart.
chart.
Figure 2.
2. Wavelet
Wavelet threshold
threshold noise
2.1.1. Wavelet Basis Function Selection
Through the discrete wavelet transform, the original signal x (t) including noise is shown as
The wavelet
basis function has a great influence on the signal noise reduction effect. In order to
Equation
(2)
Z ∞
j
obtain a better denoised signal, the basis function
having
the similar waveform as the original signal
d j,k (t) =
x (t)2− 2 ψ(2− j t − k)dt
(2)
−∞
should be selected. Because the joint electromagnetic
signal waveform is close to the dB8 wavelet
basisThe
function,
dB8 wavelet
basis
adopted
in this paper.
Mallatthe
forward
transform
is is
shown
as Equation
(3) [19]

2.1.2. Wavelet Multi-Scale Decomposition
 c j,k = ∑ hk−2n c j−1,n
n
j = 1, 2, ···, J
 d j,k =[18]
The discrete wavelet basis function
∑ gis
k −shown
2n d j−1,nas Equation (1)
(3)
n
−
j
−j
(1)
ψ j , k (t ) signal,
= a0 2 ψ(daj,k
t − kb )
where c j,k is the smoothing signal of original
0 is the0detail signal of original signal, gn is the
impulse response of band-pass filter concerned with wavelet function, hn is the impulse response of
where a0filter
represents
extension
scale and b0 represents the time translation, usually
low-pass
concernedthe
with
scaling function.
a0 = 2 , b0 = 1 .
the discreteSelection
wavelet transform, the original signal x(t ) including noise is shown as
2.1.3.Through
Wavelet Threshold
Equation (2)
The wavelet threshold determination method includes the default, penalty, Birge-Massart, rigrsure
j
∞
−
rule, sqtwolog rule, heursure rule and minimaxi
rule,
and the threshold value can be defined by(2)
the
d j ,k (t) =  x(t)2 2 ψ(2− j t − k )dt
−∞
soft or hard strategy [20]. Based on the experimental
investigation, the Birge-Massart is applied in
this paper.
The Mallat forward transform is shown as Equation (3) [19]
 c j , k =  hk − 2 nc j −1,n

n
⋅⋅⋅, J as Equation (4)
j = 1,is2,shown
(3)
 signal after filtering
The reconstruction of smoothing
=
d
 j , k  g k − 2 n d j −1,n

n
c j−1,k = ∑ [hk−2n c j,n + gk−2n d j,n ]
(4)
where c j , k is the smoothing signal of original
signal, d j , k is the detail signal of original signal, g n
n
2.1.4. Signal Reconstruction
is theFirstly,
impulse
band-pass into
filtertime-frequency
concerned withdomain
waveletusing
function,
theThen
impulse
hn is(3).
theresponse
signal is of
decomposed
Equation
the
response
of
low-pass
filter
concerned
with
scaling
function.
reconstruction of denoised signal is realized by Equation (4).
2.2.
Improved
Threshold
Wavelet Method
2.1.3.New
Wavelet
Threshold
Selection
In
to improve
the determination
noise reductionmethod
effect and
reducethe
thedefault,
signal distortion,
an improved
Theorder
wavelet
threshold
includes
penalty, Birge-Massart,
threshold
wavelet
method
is proposed.
threshold
function
is shown
as Equation
(5) be
rigrsure rule,
sqtwolog
rule,
heursureThe
ruleimproved
and minimaxi
rule,
and the
threshold
value can
defined by the soft or hard strategy [20]. Based on the experimental investigation, the Birge-Massart
is applied in this paper.
2.2. New Improved Threshold Wavelet Method
In order to improve the noise reduction effect and reduce the signal distortion, an improved
threshold wavelet method is proposed. The improved threshold function is shown as Equation (5)
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
λ
)], A ≥ λ
sign( A)[( A −
2
(
B =  sign( A)[(| A| −A exp( λA2 − λ 2 ))], | A| ≥ λ
| A|exp(| A|2 −λ2 )
B= 
A
<
λ
0,
0, | A| < λ
2
(5)
(5)
where
is the
the wavelet
wavelet coefficient
coefficient after
after threshold
threshold processing,
where B
B is
processing, A
A is
is the
the wavelet
wavelet coefficient
coefficient after
after
decomposition,
λ
is
the
threshold
value.
decomposition, λ is the threshold value.
The
newly improved
improved threshold
threshold function
function curves
curves are
are shown
shown in
in Figure
Figure 3.
3. The
The hard,
hard, soft
soft and
and newly
The B
B
value
for
the
improved
method
is
situated
between
soft
and
hard
cases
so
that
the
estimated
value for the improved method is situated between soft and hard cases so that the estimated
wavelet
improved
kind
of of
threshold
processing
method
overcomes
the
wavelet coefficient
coefficient isisclose
closetotoA.A.This
This
improved
kind
threshold
processing
method
overcomes
discontinuity
at
λ
compared
to
the
hard
method
and
the
unavoidable
signal
deviation
compared
the discontinuity at λ compared to the hard method and the unavoidable signal deviation compared to
to
soft
method.
thethe
soft
method.
Figure 3. Three kinds of threshold function curve.
Figure 3. Three kinds of threshold function curve.
2.3. EMD Noise Reduction Method by Dominant Eigenvalues
2.3. EMD Noise Reduction Method by Dominant Eigenvalues
2.3.1.
2.3.1. Noise
Noise Reduction
Reduction Principle
Principle by
by EMD
EMD
The
EMD is
is to
todecompose
decomposethe
thesignal
signal
into
sum
a series
of IMFs
one residual
The EMD
into
thethe
sum
of aofseries
of IMFs
and and
one residual
term.term.
With
With
the increase
of decomposition
the frequency
of IMF
decrease,
so signal
the signal
filtering
the increase
of decomposition
orderorder
the frequency
of IMF
will will
decrease,
so the
filtering
can
can
be realized.
be realized.
Assuming
the EMD
EMD by
by Equation
Equation (6)
(6) can
can be
be carried
carried out
Assuming the
the input
input signal
signal is
is xx((tt)) ,, the
out to
to obtain
obtain all
all
IMF
and rnr(n (tt)). .The
Thesignal
signalafter
after noise
noise reduction
reduction can
can be
be obtained
obtained by
IMF components
components including
including ssii (tt)) and
by the
the
reconstruction of different IMF components.
n
x (t) =
∑ si ( t ) + r n ( t )
(6)
i =1
The EMD flow is shown in Figure 4. The main processing steps include the determination of
local maximum values and minimum values, cubic spline fitting of signal, mean value calculation of
envelope and extraction of IMF component.
2.3.2. New IMF Component Extraction Method by Dominant Eigenvalue
Because the actual noise is variable, the effective IMF component should be obtained by the
adaptive strategy. Therefore, the IMF component extraction method according to the dominant
eigenvalue is proposed and carried out by the following two steps:
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n
x(t ) =  si (t) + rn (t )
5 of 11
(6)
i =1
Calculate the eigenvalues λ1 , λ2 , ···, λn of each order IMF component si (t) and the residual
The EMD flow is shown in Figure
4. The main processing steps include the determination of
component rn (t) by the Singular Value Decomposition (SVD) [21].
local maximum values and minimum values, cubic spline fitting of signal, mean value calculation
2. Extract the effective IMF component by the Dominant Eigenvalue Method (DEM) [22].
of envelope and extraction of IMF component.
1.
Figure
Figure 4.
4. EMD
EMD flow
flow chart.
chart.
2.3.2. New IMF Component Extraction Method by Dominant Eigenvalue
The variation tendency demarcation point of the ratio Ki of adjacent singular eigenvalues is used
Because
the
actual noise
is variable,
the effective
IMF component
should be
obtained to
bythen
the
in this
paper to
determine
the boundary
between
the dominant
and non-dominant
eigenvalues
adaptive
strategy.
Therefore,
the
IMF
component
extraction
method
according
to
the
dominant
extract the effective IMF components. The expression of Ki is defined as Equation (7)
eigenvalue is proposed and carried out by the following two steps:
λi
1, 2,each
···, n −
1
(7)
1. Calculate the eigenvalues Kλi 1 =
order
IMF component si (t ) and the
, λλ
, ,,λi n= of
2
i +1
residual component rn (t ) by the Singular Value Decomposition (SVD) [21].
The variation tendency demarcation point of Ki is expressed as Equation (8)
2. Extract the effective IMF component by the Dominant Eigenvalue Method (DEM) [22].
Ki
The variation tendency demarcation
of 1,
the
ratio
is
∆i = point
,i =
2, ···
, n −K1i of adjacent singular eigenvalues(8)
Ki + 1
used in this paper to determine the boundary
between the dominant and non-dominant
eigenvalues
to then (8),
extract
the point
effective
components.
The expression
ofdemarcation
Ki is defined
as
For the Equation
the first
of ∆iIMF
less than
1.0 is the variation
tendency
point
Equation
(7)
of K .
i
From Equation (8), it can be seen that if λ∆m is smaller than 1.0, the corresponding eigenvalues λ1 ,
i
K i = the
, i = 1, 2,  , n − 1
(7)
λ2 , . . . , λm+1 are dominant. In other words,
λ i +1 components from IMF1 to IMFm+1 are effective.
2.3.3.The
New
Noise Reduction
Basedpoint
on the
Improved
Threshold Wavelet and EMD by
i is expressed as Equation (8)
variation
tendency Method
demarcation
of K
Dominant Eigenvalue
K
The newly proposed method by Δcombined
threshold wavelet and EMD
= i , i =use
1, 2,ofthe
, n −improved
1
(8)
i
K 1
with the dominant eigenvalue can be carriedi +out
according to the process shown in Figure 5. Firstly,
the improved
threshold(8),
wavelet
denoise
are carried
the IMF
component
than 1.0out
is in
thesequence,
variationthen
tendency
demarcation
For the Equation
the first
pointand
of EMD
Δ i less
is extracted. Secondly, the eigenvalue is calculated and then the dominant eigenvalue is obtained.
point of Ki.
Finally, the effective IMF component is determined and then the signal is reconstructed.
From Equation (8), it can be seen that if Δm is smaller than 1.0, the corresponding eigenvalues
λ1, λ2, …, λm+1 are dominant. In other words, the components from IMF1 to IMFm+1 are effective.
Dominant
2.3.3. New Eigenvalue
Noise Reduction Method Based on the Improved Threshold Wavelet and EMD by
Dominant
Eigenvalue
The newly proposed method by combined use of the improved threshold wavelet and EMD
with The
the dominant
eigenvalue
can be
out according
the process
shown in
Figureand
5. Firstly,
newly proposed
method
bycarried
combined
use of theto
improved
threshold
wavelet
EMD
the
improved
threshold
wavelet
denoise
and
EMD
are
carried
out
in
sequence,
then
IMF
with the dominant eigenvalue can be carried out according to the process shown in Figure 5.the
Firstly,
component
is
extracted.
Secondly,
the
eigenvalue
is
calculated
and
then
the
dominant
eigenvalue
is
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the improved threshold wavelet denoise and EMD are carried out in sequence, then the IMF
obtained.
Finally,
the
effective
IMF
component
is
determined
and
then
the
signal
is
reconstructed.
component is extracted. Secondly, the eigenvalue is calculated and then the dominant eigenvalue is
obtained. Finally, the effective IMF component is determined and then the signal is reconstructed.
Figure 5. Noise reduction flow chart of combined method of improved wavelet and EMD.
Figure 5. Noise reduction flow chart of combined method of improved wavelet and EMD.
Figure 5. Noise reduction flow chart of combined method of improved wavelet and EMD.
3. Verification of Noise Reduction Method by Combined Use of Improved Wavelet and EMD
3. Verification of Noise Reduction Method by Combined Use of Improved Wavelet and EMD
3. Verification
of Noise Reduction Method by Combined Use of Improved Wavelet and EMD
3.1.
Test Rig Setup
3.1. 3.1.
TestTest
Rig
Setup
Setupelectromagnetic test rig used for the steel cord conveyor belt was built in our
TheRig
defect
The
is conveyor
11.0
and
width
is in0.8
laboratory,
as
shown
in Figure
6a.used
defect
electromagnetic
rig
used
forlength
the cord
steel
cord m
conveyor
beltbuilt
was
built
in The
our
TheThe
defect
electromagnetic
test test
rig
forbelt
the
steel
belt was
ourm.
laboratory,
electromagnetic
testing
device
was6a.
installed
close
to the is
lower
surface
of width
the downward
belt,The
as
The mbelt
is
11.0
m
is 0.8testing
m.
laboratory,
as shown
Figure
as shown
in Figure
6a.
Thein
belt
length
is 11.0
andlength
width
0.8
m.
Theand
electromagnetic
device
shown
in
Figure
6b.
The
sensitivity
of
the
electromagnetic
transducer
is
0.5
V/Gs.
The
location
testing
devicesurface
was installed
close to thebelt,
lower
downward
as
was electromagnetic
installed close to
the lower
of the downward
assurface
shown of
in the
Figure
6b. Thebelt,
sensitivity
detection
resolution
isThe
0.1 mm,
and the
detecting
speed is 0 totransducer
8 m/s. Theisdata
transmission
rate is
shown
in
Figure
6b.
sensitivity
of
the
electromagnetic
0.5
V/Gs.
The
location
of the electromagnetic transducer is 0.5 V/Gs. The location detection resolution is 0.1 mm, and the
10
M/100 resolution
Mbps, theisworking
temperature
is −20speed
°C to
+55
°C,
andThe
humidity
is 95% RH.
The
detection
0.1 mm,
and
the
detecting
is 10
0 toM/100
8 m/s.
data
transmission
rate
is
detecting
speed
is 0 to is8 m/s.
The
data
transmission
rateelectromagnetic
is
Mbps,
thesystem
working
temperature
detection
distance
50
mm
to
110
mm.
The
whole
testing
is
shown
in
10 ◦M/100 Mbps,
the working temperature is −20 °C to +55 °C, and humidity is 95% RH. The
◦
is −Figure
20 C to6c.+55
and humidity
is 95% RH.was
The installed
detectiontodistance
is 50the
mm to 110
mm.
The whole
TheC,magnetic
loading
magnetize
wire
detection
distance
is 50 mm
to 110module
mm. The whole
electromagnetic
testingsteel
system
is rope.
shownThe
in
electromagnetic
testing
is shown
in m
Figure
6c.
The magnetic
loading
module
installed to
operating
ofsystem
belt loading
was
set module
to 0.5
/s
byinstalled
a variable
frequency
inverter.
Thewas
data
Figure 6c. velocity
The magnetic
was
to magnetize
the
steel wire
rope.were
The
magnetize
the steel
rope. The operating
velocity
of belttransmitted
was set to 0.5
m/s
by a variable
frequency
collected
thewire
electromagnetic
testing
device
to inverter.
a computer
TCP/IP
operating by
velocity
of belt was set to
0.5 m/s
by a and
variable frequency
The by
data
were
inverter.
The
data
were
collected
by
the
electromagnetic
testing
device
and
transmitted
to
a
computer
protocol.
collected by the electromagnetic testing device and transmitted to a computer by TCP/IP
by TCP/IP
protocol.
protocol.
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(a)
(b)
(a)
(b)
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(c)
Figure
6. Electromagnetic
testingrig
rigof
ofsteel
steel cord
cord conveyor
Tested
belt
conveyor
prototype;
Figure
6. Electromagnetic
testing
conveyorbelt:
belt:(a)(a)
Tested
belt
conveyor
prototype;
(b) Installed electromagnetic testing device; (c) Electromagnetic testing system setup.
(b) Installed electromagnetic testing device; (c) Electromagnetic testing system setup.
3.2. Noise Reduction Evaluation Index
The main evaluation indexes of signal noise reduction effect mainly have the Signal-to-Noise
Ratio (SNR) and Root Mean Square Error (RMSE). The SNR is higher or RMSE is smaller, the noise
reduction effect is better.
(c)
Figure 6. Electromagnetic testing rig of steel cord conveyor belt: (a) Tested belt conveyor prototype;
(b) Installed
Algorithms
2016, 9, 62electromagnetic testing device; (c) Electromagnetic testing system setup.
7 of 11
3.2. Noise Reduction Evaluation Index
3.2. Noise Reduction Evaluation Index
The main evaluation indexes of signal noise reduction effect mainly have the Signal-to-Noise
main
indexes
signal
noise reduction
effect
mainly
have isthe
Signal-to-Noise
RatioThe
(SNR)
andevaluation
Root Mean
SquareofError
(RMSE).
The SNR is
higher
or RMSE
smaller,
the noise
Ratio (SNR)
andisRoot
Mean Square Error (RMSE). The SNR is higher or RMSE is smaller, the noise
reduction
effect
better.
reduction
effectthe
is better.
Assuming
original signal is x( n) , the signal after denoising is x '(n) , so the SNR Equation is
Assuming the original signal is x (n), the signal after denoising is x 0 (n), so the SNR Equation is

n x 2 (n)  

SNR = 10 log
(9)
∑ x2 (n) 2
  [ x(nn) − x '(n)]  


(9)
SNR = 10log  n
2 
∑ [ x (n) − x 0 (n)]
n
The RMSE Equation is
The RMSE Equation is
s1
RMSE = 1  [ x(n) − x '(n)]2 2
0
RMSE = n ∑
n [ x ( n ) − x ( n )]
n n
(10)
(10)
3.3.
3.3. Electromagnetic
Electromagnetic Signal
Signal Collection
Collection
The
The steel
steel cord
cord conveyor
conveyor belt
belt joint
joint structure,
structure, steel
steel wire
wire rope
rope break
break photo
photo and their respective
respective
corresponding
corresponding electromagnetic signals are shown in Figure 7.
Normalized amplitude
1
0.5
0
-0.5
-1
0
2000
4000
6000
8000 10000 12000 14000 16000
Sample points
(a)
(b)
Normalized amplitude
1
0.5
0
-0.5
-1
0
500
1000
1500
2000
2500
3000
Sample points
(c)
(d)
Figure
7. Joint
Jointand
and
break
of steel
cord conveyor
and responding
electromagnetic
signal:
Figure 7.
break
of steel
cord conveyor
belt andbelt
responding
electromagnetic
signal: (a) Internal
(a)
Internal
structure
of
conveyor
belt
joint;
(b)
Electromagnetic
signal
at
joint;
(c)
Steel
wire
structure of conveyor belt joint; (b) Electromagnetic signal at joint; (c) Steel wire rope break ofrope
belt;
break
of belt; (d) Electromagnetic
of wire
rope break defect.
(d) Electromagnetic
signal of wiresignal
rope break
defect.
3.4. Denoising Analysis of Defect Signal
3.4.1. Noise Reduction of Joint Electromagnetic Signal
The conveyor belt joint electromagnetic signal containing the noise is shown in Figure 8a,
the noise includes 10 dB Gaussian white noise and non-stationary noise with frequency and amplitude
modulations, the noise function is shown in Equation (11). Figure 8b is the normalized spectrum
diagram of joint electromagnetic signal with noise, it can be seen that the noise function has the same
frequency band with the signal before denoising. The denoised result by the improved threshold
3.4.1. Noise Reduction of Joint Electromagnetic Signal
The conveyor belt joint electromagnetic signal containing the noise is shown in Figure 8a, the
noise includes 10 dB Gaussian white noise and non-stationary noise with frequency and amplitude
modulations,
Algorithms 2016, 9,the
62 noise function is shown in Equation (11). Figure 8b is the normalized spectrum
8 of 11
diagram of joint electromagnetic signal with noise, it can be seen that the noise function has the
same frequency band with the signal before denoising. The denoised result by the improved
wavelet is wavelet
shown inisFigure
result
by combined
of improved
wavelet
and
threshold
shown8c,
in while
Figurethe
8c,denoised
while the
denoised
result byuse
combined
use of
improved
EMD
is
shown
in
Figure
8d.
wavelet and EMD is shown in Figure 8d.
f noise =
= (0.2
0.20.2
⋅ sin(2
⋅ cos(2
0.20.2
⋅ sin(2
f noise
(0.2++
·sin(⋅2pi· pi⋅ 3·3⋅ t·))
t))·
cos(2⋅ pi
· pi⋅ ·55⋅·tt++0.2
0.2⋅ sin(2
·sin(2⋅ pi
· pi⋅ ·66⋅·tt))))++
·sin(⋅2pi· pi⋅ 2·2⋅ t·)t)
0.4
1
Amplitude
Signal amplitude
2
0
-1
-2
0
2000
4000
6000
8000
0.3
0.2
0.1
0
0
10000 12000 14000 16000
10
20
(a)
0.5
0
-0.5
4000
6000
8000
10000 12000 14000 16000
1
Signal amplitude
signal after denosing
original signal
2000
40
(b)
1
-1
0
30
Frequency/Hz
Sample points
Signal amplitude
(11)
(11)
signal after denoising
original signal
0.5
0
-0.5
-1
0
2000
4000
6000
8000
10000 12000 14000 16000
Sample points
Sample points
(c)
(d)
Figure
8. Comparison
joint electromagnetic
electromagnetic signal:
signal: (a)
Figure 8.
Comparison of
of two
two noise
noise reduction
reduction methods
methods for
for joint
(a) Joint
Joint
electromagnetic
signal
with
noise;
(b)
Normalized
spectrum
diagram
of
joint
signal;
(c)
Denoised
electromagnetic signal with noise; (b) Normalized spectrum diagram of joint signal; (c) Denoised result
result
by improved
threshold
wavelet;
(d) Denoised
result
by combined
use of improved
threshold
by improved
threshold
wavelet;
(d) Denoised
result by
combined
use of improved
threshold
wavelet
wavelet
and
EMD.
and EMD.
Based on the experimental investigation, the wavelet basis function is selected as dB8, the
Based on the experimental investigation, the wavelet basis function is selected as dB8,
threshold determination strategy is Birge-Massart, and the wavelet decomposition level is six. The
the threshold determination strategy is Birge-Massart, and the wavelet decomposition level is six.
eigenvalues of 11 IMF components are λ i , the ratio K i and Δ i is shown in Table 1.
The eigenvalues of 11 IMF components are λi , the ratio Ki and i is shown in Table 1.
Table
of joint
joint signal.
signal.
Table 1.
1. IMF
IMF component,
component, eigenvalue
eigenvalue and
and ratio
ratio of
IMF
Component Eigenvalue
Eigenvalue
λ i λi
IMF
Component
IMF1
IMF
IMF
1 2
IMF
IMF2 3
IMF4
IMF3
IMF5
4
IMF
IMF
6
5 7
IMF
IMF
IMF
IMF
6 8
IMF
7 9
IMF
IMF
IMF8 10
IMF11
29.62
17.61
29.62
14.34
17.61
12.19
14.34
10.45
12.199.36
10.458.91
9.362.55
8.910.60
0.054
2.55
0.00073
λi
λ
K i = Ki i = λi+1
λ i +1
1.68
1.68 1.23
1.23 1.18
1.17
1.18
1.12
1.17 1.05
1.12 3.50
1.05 4.21
3.5011.21
73.43
4.21
—
K i Ki
Δ i =∆i =
K
K i +i1+1
1.37
1.04
1.37
1.008
1.04
1.04
1.008
1.06
1.04
0.30
1.06
0.82
0.38
0.30
0.15
0.82
—
0.38
—
According to Table 1, ∆6 is smaller than 1.0. Thus, the selected IMF components are IMF1 to
IMF7 . The reconstruction result of seven IMF components is shown in Figure 8d, and two denoising
methods are compared, as shown in Table 2. According to Table 2 and Figure 8c,d, the proposed
0.054
0.00073
IMF10
IMF11
73.43
—
—
—
According to Table 1, ∆6 is smaller than 1.0. Thus, the selected IMF components are IMF1 to
9 of 11
result of seven IMF components is shown in Figure 8d, and two denoising
methods are compared, as shown in Table 2. According to Table 2 and Figure 8c,d, the proposed
method obtained by combined use of the improved wavelet and EMD has the better noise
method obtained by combined use of the improved wavelet and EMD has the better noise reduction
reduction effect for the non-stationary strong-noise joint electromagnetic signal and the SNR is
effect for the non-stationary strong-noise joint electromagnetic signal and the SNR is bigger.
bigger.
Algorithms
2016,
9, 62
IMF
7. The
reconstruction
Table 2. Comparison of two denoising methods for joint signal.
Table.2 Comparison of two denoising methods for joint signal.
Method
Method
Before
denoising
Before
denoising
Improved
threshold
wavelet
Improved
threshold
wavelet
Combined use of improved threshold wavelet and EMD
Combined use of improved threshold wavelet and EMD
SNR
(dB)(dB)
SNR
−2.72
−2.72
5.027
5.027
11.63
11.63
RSMERSME
0.36 0.36
0.17 0.17
0.069
0.069
3.4.2. Noise
Noise Reduction
Reduction of
of Electromagnetic
Electromagnetic Signal
Signal with
with Wire
Wire Rope
3.4.2.
Rope Break
Break
2
0.08
1
0.06
Amplitude
Signal amplitude
The conveyor
conveyor belt
belt steel
steel wire
wire rope
rope break
break electromagnetic
electromagnetic signal
signal containing
containing the
the noise
noise is
is shown
shown in
in
The
Figure 9a,
white
noise
and
non-stationary
noise
withwith
frequency
and
Figure
9a, the
the noise
noiseincludes
includes1010dB
dBgaussian
gaussian
white
noise
and
non-stationary
noise
frequency
amplitude
modulations,
the
noise
function
is
shown
in
Equation
(11).
Figure
9b
is
the
normalized
and amplitude modulations, the noise function is shown in Equation (11). Figure 9b is the
spectrum diagram
of wire
ropeof
break
signal with noise,
can be
seenitthat
normalized
spectrum
diagram
wireelectromagnetic
rope break electromagnetic
signalit with
noise,
canthe
be noise
seen
function
has
the
same
frequency
band
as
the
signal
before
denoising.
The
denoised
result
by
the
that the noise function has the same frequency band as the signal before denoising. The denoised
improved
threshold
wavelet
is
shown
in
Figure
9c,
while
the
denoised
result
by
combined
use
of
result by the improved threshold wavelet is shown in Figure 9c, while the denoised result by
improved use
wavelet
and EMD
is shown
Figure
combined
of improved
wavelet
andinEMD
is 9d.
shown in Figure 9d.
0
-1
-2
0
500
1000
1500
2000
2500
0.04
0.02
0
0
3000
10
20
Sample points
(a)
0
-0.5
1000
1500
Sample points
(c)
2000
2500
3000
Signal amplitude
Signal amplitude
signal after denoising
original signal
0.5
500
40
(b)
1
1
-1
0
30
Frequency/Hz
signal after denosing
original signal
0.5
0
-0.5
-1
0
500
1000
1500
2000
2500
3000
Sample points
(d)
Figure
methods
forfor
wire
rope
break
electromagnetic
signal:
(a)
Figure 9.
9. Comparison
Comparisonofoftwo
twonoise
noisereduction
reduction
methods
wire
rope
break
electromagnetic
signal:
Electromagnetic
signal
with
noise
of
wire
rope
break;
(b)
Normalized
spectrum
diagram
of
wire
(a) Electromagnetic signal with noise of wire rope break; (b) Normalized spectrum diagram of wire
rope
rope break;
break; (c)
(c) Denoised
Denoised result
result by
by the
the improved
improved threshold
threshold wavelet;
wavelet; (d)
(d) Denoised
Denoised result
result by
by combined
combined
use
use of
of improved
improved wavelet
wavelet and
and EMD.
EMD.
The eigenvalues of 11 IMF components are λ i , the ratio of K i and Δ i is shown in Table 3.
The eigenvalues of 11 IMF components are λi , the ratio of Ki and ∆i is shown in Table 3.
According to Table 3, ∆6 is smaller than 1.0. Thus, the selected IMF components are IMF1 to IMF7.
The reconstruction result of seven IMF components is shown in Figure 9d, two denoising methods are
compared, as shown in Table 4. According to Table 4 and Figure 9c,d, the proposed method obtained
by combined use of the improved wavelet and EMD has the better noise reduction effect for the
non-stationary strong-noise wire rope break electromagnetic signal and the SNR is bigger.
Algorithms 2016, 9, 62
10 of 11
Table 3. IMF component, eigenvalue and ratio of wire rope break signal.
IMF Component
Eigenvalue λi
IMF1
IMF2
IMF3
IMF4
IMF5
IMF6
IMF7
IMF8
IMF9
IMF10
IMF11
25.28
20.20
16.87
14.57
12.99
11.99
11.36
2.28
0.13
0.0025
3.35 × 10−15
Ki =
λi
λi + 1
∆i =
1.25
1.20
1.16
1.12
1.083
1.056
4.98
17.54
54.24
7.46 × 1011
—
Ki
Ki+1
1.045
1.034
1.035
1.034
1.025
0.21
0.28
0.32
7.27 × 10−11
—
—
Table 4. Comparison of two denoising methods for wire rope break signal.
Method
SNR(dB)
RSME
Before denoising
Improved threshold wavelet
Combined use of improved threshold wavelet and EMD
−0.76
6.42
7.08
0.34
0.14
0.13
4. Conclusions
Aiming at the denoising problem of the non-stationary strong-noise defect electromagnetic signal
for coal mine steel cord conveyor belt, a new kind of combined use of the improved threshold wavelet
and EMD with the dominant eigenvalue is proposed. The new kind of belt defect electromagnetic
signal denoising method is introduced and verified by two groups of experimental test including
joint defect and wire rope break. The experimental results show that the proposed method with the
dominant eigenvalue can obtain the effective IMF components according to the original signal feature,
and has a better noise reduction effect than the improved threshold wavelet only. Therefore, the newly
proposed method in this paper can be used for the noise filtering of steel cord conveyor belt defect
electromagnetic signal in order to provide a good base for further signal feature extraction in the future.
Acknowledgments: The work was financially supported by the China National Natural Science Fund
(No. U1361121), the Specialized Research Fund for the Doctoral Program of Higher Education of China
(No. 20136121120010) and the Scientific Research Program Funded by Shaanxi Provincial Education Department
(No. 16JK1508).
Author Contributions: Hong-Wei Ma proposed the research topic and organized the research work,
Hong-Wei Fan and Qing-Hua Mao wrote the manuscript, Qing-Hua Mao, Xu-Hui Zhang and Wang Xing
performed the experiment and data processing.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
Sawicki, M.; Zimroz, R.; Wylomanski, A.; Stefaniak, P.; Zak, G. An automatic procedure for multidimensional
temperature signal analysis of a SCADA system with application to belt conveyor components. Procedia Earth
Planet. Sci. 2015, 15, 781–790. [CrossRef]
Huang, M.; Pan, H.S.; Hu, C.; Wei, R.Z. A system for real-time monitoring and protecting of steel-cord belt
conveyors. J. China Univ. Min. Technol. 2006, 5, 673–679. (In Chinese)
Schillaci, T.; Barraco, R.; Brai, M.; Raso, G.; Bortolotti, V.; Gombia, M.; Fantazzini, P. Noise reduction in
magnetic resonance images by wavelet transforms: An application to the study of capillary water absorption
in sedimentary rocks. Magn. Reson. Imaging 2007, 25, 581–582. [CrossRef]
Zhou, Z.J.; Wen, Z.J.; Bu, Y.Y. Application study of wavelet analysis of ultrasonic echo wave noise reduction.
Chin. J. Sci. Instrum. 2009, 2, 237–241.
Algorithms 2016, 9, 62
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
11 of 11
Jin, T.; Que, P.W. Applying wavelet theory to eliminate noise of magnetic flux leakage inspecting.
J. Transduct. Technol. 2003, 1, 260–262. (In Chinese)
Han, W.H. A new denoising algorithm for MFL data obtained from seamless pipeline inspection. Russ. J.
Nondestruct. Test. 2006, 3, 184–195. [CrossRef]
Mao, Q.H.; Ma, H.W.; Zhang, X.H. Steel cord conveyor belt defect signal noise reduction method based
on a combination of wavelet packet and RLS adaptive filtering. In Proceeding of the IEEE International
Symposium on Computer, Consumer and Control, Xi’an, China, 4–6 July 2016.
Song, D.L.; Xu, D.G.; Wang, W.; Wang, Y. The application of wavelet analysis in nondestructive testing of
wire ropes. Chin. J. Sci. Instrum. 1997, 2, 150–154.
Zhang, D.L.; Xu, D.G. Data compression and feature extraction of broken wires signal based on B-wavelet.
Chin. J. Sci. Instrum. 1998, 3, 249–254.
Zhang, Q.; Zhou, X.F.; Wang, J.; Guo, Q.G. Ultrasonic signal denoising based on improved EMD. J. Nanjing
Univ. Posts Telecommun. 2016, 2, 49–55. (In Chinese)
Poornachandra, S. Wavelet-based denoising using subband dependent threshold for ECG signals.
Digit. Signal Process. 2008, 1, 49–55. [CrossRef]
Cui, H.M.; Zhao, R.M.; Hou, Y.L. Improved threshold denoising method based on wavelet transform.
Phys. Procedia 2012, 33, 1354–1359.
Guo, C.C.; Wen, Y.M.; Li, P.; Wen, J. Adaptive noise cancellation based on EMD in water-supply pipeline
leak detection. Measurement 2016, 79, 188–197. [CrossRef]
Li, L.M.; Chai, X.D.; Zheng, S.B.; Zhu, W.F. A denoising method for track state detection signal based on
EMD. J. Signal Inf. Process. 2014, 4, 104–111.
Cui, F.X.; Xu, L.L.; Zheng, X.T. A new method for noise reduction based on EMD and SVD subspaces
reconstruction. J. Shaoyang Univ. 2014, 4, 12–17. (In Chinese)
Huang, M.; Wang, C.F.; Li, H.M.; Yao, C.W. Application of EMD noise reduction and wavelet transform in
bearing fault diagnosis. J. Acad. Armored Force Eng. 2013, 3, 39–43.
Zhang, X.Y.; Xie, F.; Qiao, T.Z.; Yang, Y. Denoising algorithm for metal magnetic memory signals based on
EEMD and improved semi-soft wavelet threshold. J. Taiyuan Univ. Technol. 2015, 5, 592–597. (In Chinese)
Ghods, A.; Lee, H.H. Probabilistic frequency-domain discrete wavelet transform for better detection of
bearing faults in induction motors. Neurocomputing 2016, 188, 206–216. [CrossRef]
Shi, H.S.; Wang, Q.M. Design and experimental Mallet method based on the SURF thresholding denoisings.
Compu. Digit. Eng. 2014, 4, 739–742. (In Chinese)
Wang, G.X.; Chen, L.; Guo, S.; Peng, Y.; Guo, K. Application of a new wavelet threshold method in
unconventional oil and gas reservoir seismic data denoising. Math. Probl. Eng. 2015, 2015, 969702. [CrossRef]
Zhao, X.Z.; Ye, B.Y. Singular value decomposition packet and its application to extraction of weak fault
feature. Mech. Syst. Signal Process. 2016, 70–71, 73–86. [CrossRef]
Liu, J.C.; Wang, H.H.; Zhang, Y. New result on PID controller design of LTI systems via dominant eigenvalue
assignment. Automatica 2015, 62, 93–97. [CrossRef]
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(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).