Applied Acoustics 77 (2014) 195–203
Contents lists available at ScienceDirect
Applied Acoustics
journal homepage: www.elsevier.com/locate/apacoust
Rolling bearing diagnosing method based on Empirical Mode
Decomposition of machine vibration signal
Jacek Dybała a, Radosław Zimroz b,⇑
a
b
Warsaw University of Technology, Institute of Vehicles, ul. Narbutta 84, 02-524 Warsaw, Poland
Wroclaw University of Technology, Diagnostic and Vibroacoustic Science Laboratory, Pl. Teatralny 2, 50-051 Wroclaw, Poland
a r t i c l e
i n f o
a b s t r a c t
Keywords:
Rolling element bearings
Bearing diagnostics
Condition monitoring
Empirical Mode Decomposition (EMD)
Intrinsic Mode Function (IMF)
Combined Mode Function (CMF)
Rolling bearing faults are one of the major reasons for breakdown of industrial machinery and bearing
diagnosing is one of the most important topics in machine condition monitoring.
The main problem in industrial application of bearing vibration diagnostics is the masking of informative bearing signal by machine noise. The vibration signal of the rolling bearing is often covered or concealed by other structural vibrations sources, such as gears. Although a number of vibration diagnostic
techniques have been developed over the last several years, in many cases these methods are quite complicated in use or only effective at later stages of damage development. This paper presents an EMD-based
rolling bearing diagnosing method that shows potential for bearing damage detection at a much earlier
stage of damage development.
By using EMD a raw vibration signal is decomposed into a number of Intrinsic Mode Functions (IMFs).
Then, a new method of IMFs aggregation into three Combined Mode Functions (CMFs) is applied and
finally the vibration signal is divided into three parts of signal: noise-only part, signal-only part and
trend-only part. To further bearing fault-related feature extraction from resultant signals, the spectral
analysis of the empirically determined local amplitude is used. To validate the proposed method, raw
vibration signals generated by complex mechanical systems employed in the industry (driving units of
belt conveyors), including normal and fault bearing vibration data, are used in two case studies. The
results show that the proposed rolling bearing diagnosing method can identify bearing faults at early
stages of their development.
Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Rolling element bearings, also known as rolling bearings, are
widely used in rotary machinery systems. Rolling bearings fall
out of service for various reasons, such as unexpected heavy loads,
unsuitable or inadequate lubrication and ineffective sealing. The
components that often fail in rolling bearings are the rolling elements, the inner race and the outer race. Rolling bearings’ diagnostics is important for guaranteeing machine safety and production
efficiency. The damage of a bearing may cause the breakdown of
a rotary machine, leading to serious consequences. One of the
key issues in rolling bearing diagnostics is to detect the defect at
its early stage and alert the machine operator before it develops
into a catastrophic damage. Contrary to oil condition and thermal
state monitoring methods that detect damages of bearings at very
late stages of their development (close to catastrophic stages),
⇑ Corresponding author.
E-mail addresses: [email protected]
pwr.wroc.pl (R. Zimroz).
(J.
Dybała),
radoslaw.zimroz@
0003-682X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.apacoust.2013.09.001
vibroacoustic analysis detect most of the damages yet at much earlier stages of bearings’ technical degradation.
Rolling bearing is a complex vibration system whose components (e.g. rolling elements, outer race, inner race and cage) interact to generate complex vibration signal. When a fault on one
surface of a bearing element strikes another surface, an impact is
generated. The successive mechanical impacts (which are the result of the passage of the fault through the load zone) produce a
series of impulses observed in a bearing signal. These mechanical
impacts modulate the bearing signal at characteristic frequencies
depending on the localization of the defect, such as: Fundamental
Train (Cage) frequency (fFTF), Ball Spin Frequency (fBSF), Ball Fault
Frequency (fBFF = 2fBSF), Ball Pass Frequency Outer Race (fBPFO)
and Ball Pass Frequency Inner Race (fBPFI) [1,2]. Calculations of
the characteristic frequencies assume that the rolling elements
do not slide, but roll over the race’s surfaces. There is always some
slip and real characteristic frequencies differ from calculated characteristic frequencies by about a few percent [3].
There are two main groups of diagnosing techniques using
vibration signals: time-domain and frequency-domain analysis techniques. Traditional time-domain analysis calculates characteristic
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features from vibration signal waveform, such as root mean square,
skewness, kurtosis or crest factor and they have been applied with
limited success for rolling bearing diagnosing [4]. Kurtosis of vibration signal can be used to detect bearing faults at early stages of
their development [5]. The kurtosis is a statistical parameter based
on the fourth and the second moments of a signal, which is close to
3 for Gaussian noise and other stationary signals, but large for
impulsive signals containing series of impulses, such as a signal
generated by damaged bearing. However, precise nature of the
fault cannot be defined by the kurtosis analysis and for such information it is necessary to use a more sophisticated diagnostic method. The advantage of frequency-domain analysis, based on the
transformation of a signal in the frequency domain, is its ability
to easily identify certain spectral components of the signal. With
high frequency resonance analysis (also known as envelope analysis) it is possible to identify not only the occurrence of the bearing’s
fault, but also identify this fault, like damage in the outer race or in
the rolling element [1]. In short, the conventional Hilberttransform-based envelope detection is based on amplitude demodulation and consists of band-pass filtering and the Hilbert
transform. Defects in rolling bearings can be detected and localized
by discovering spectral components of vibration signal with the
frequencies (and their harmonics) typical for the fault.
Usually, bearing vibration signal is collected with an accelerometer installed on the bearing housing where the vibration sensor is
often subject to collecting active vibration sources from other
mechanical components of the machine. The vibration signal from
a bearing at an early stage of defect development may be masked
by machine noise, making it difficult to detect the fault by vibration analysis techniques [1,6]. Therefore, a method of diagnostic
signal extraction is needed to provide useful information regarding
the bearing condition. A number of techniques are described for
the separation of bearing signals from background signals which
mask it [7–10]. For some specific requirements (e.g. time-triggered
signal acquisition), not all of them can be always applied in industrial reality. Moreover, the effectiveness of some techniques depends in essential degree on proper values of a given technique’s
parameters (e.g. convergence factor, filter order), which must be
determined in an empirical study.
There are also more advanced techniques related to time frequency methods [11], especially wavelets [12] and dedicated approaches for signal enhancement using signal modeling [13,14]
or deconvolution technique [15]. Relatively new interesting approach is related to algorithms for searching for informative frequency band [31,33]. Diagnostics under non-stationary load and
operating speed condition is discussed in recent papers given by
different authors [9,11,21,30,32].
Empirical Mode Decomposition (EMD) has attracted attention
in recent years due to its ability to self-adaptive decomposition
of non-stationary signals. Recent publications on EMD [16–21]
show its advantages for non-stationary signals processing and confirm its effective application in many diagnostic tasks.
In this paper, an EMD-based approach for rolling bearing diagnostics is investigated. By using EMD a raw vibration signal is
decomposed into a number of Intrinsic Mode Functions (IMFs).
Then, a new method of IMFs aggregation into three Combined
Mode Functions (CMFs) is applied and finally the vibration signal
is divided into three parts of signal: noise-only part, signal-only
part and trend-only part. To further bearing fault-related feature
extraction from resultant signals, the spectral analysis of the
empirically determined local amplitude is used. To validate the
proposed method, raw vibration signals generated by complex
mechanical system employed in the industry (driving units of belt
conveyors), including vibration data of damaged and undamaged
bearings, are used in two case studies. The results show that the
proposed rolling bearing diagnosing method can identify the bearing faults at early stages of their development.
2. A brief look into Empirical Mode Decomposition (EMD)
Empirical Mode Decomposition (EMD) has been proposed by
Huang et al. [22]. This self-adaptive decomposition method decomposes any signal into empirical modes which represent different
oscillation modes embedded in the signal. Based on the EMD algorithm, any original signal xo(t) can be reconstructed by a linear
superposition of empirical modes:
xo tÞ ¼
n
X
ci ðtÞ þ rn ðtÞ;
ð1Þ
i¼1
where ci(t) is i-th empirical mode and rn(t) is the final residue after
the extraction of n empirical modes. Each empirical mode ci(t),
called Intrinsic Mode Function (IMF), fulfills the following two conditions [22]: (1) in the whole empirical mode, the number of mode
local extremes and the number of mode zero-crossings are equal or
differ at most by one and (2) at any point, the local average of upper
and lower envelope is zero.
The algorithm for the extraction of IMFs from original signal
xo(t) is called sifting process and it consists of the following steps
[23]:
Step 1: Define x(t) = xo(t) and r0(t) = xo(t).
Step 2: Define the maximum number of extracted IMFs.
Step 3: Identify all the local extremes (maxima and minima) of
x(t).
Step 4: Connect all the local maxima (respectively minima)
with a line known as the empirically determined upper envelope Emax(t) (respectively the lower envelope Emin(t)).
Step 5: Construct the mean of empirically determined upper
and lower envelope m(t) = 0.5(Emin(t) + Emax(t)).
Step 6: Define the detail (proto-IMF) as d(t) = x(t) m(t) and
replace x(t) by d(t).
Step 7: Repeat steps 3–6 until d(t) meets the IMF conditions and
the stoppage criterion of the sifting process is fulfilled, then
derive i-th IMF from d(t) and replace x(t) by ri(t) = ri–1(t) d(t).
Step 8: If the stoppage criterion of the signal’s decomposition is
fulfilled then finish the decomposition process; otherwise, go to
step 3.
The second IMF condition is too rigid to use, so it is necessary to
change it to implement the EMD. The local average of upper and
lower envelope must be close to zero according to some criterion.
The evaluation (how small it is) of the amplitude of the local average may be done in comparison with the amplitude of the corresponding mode. In [24] authors introduce a new criterion based
on the local mode amplitude a(t) = 0.5(Emax(t) Emin(t)) and the
evaluation function r(t) = |m(t)/a(t)|. In this paper, d(t) meets the
second IMF condition, when max(r(t)) < h (the coefficient h was
equal to 0.2).
A critical part of the EMD procedure is the stoppage criteria of
the sifting process and decomposition process. The stoppage criterion of the sifting process determines the point when sifting is
complete and a new IMF has been found. Two different stoppage
criteria of the sifting process were considered.
The first stoppage criterion of the sifting process is determined
by using a Cauchy type of convergence test [22]. If the two details
(proto-IMFs) from successive iterations are close enough to each
other, it is assumed that the last extracted detail is an IMF. The
normalized squared difference SDk between two successive details
dk1(t) and dk(t) during k-th iteration is defined as:
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X
2
½dk ðtÞ dk1 ðtÞ
t
X 2
SDk ¼
< TD;
dk1 ðtÞ
siftings. Typical values for S are in the 3–5 range [25]. In this paper,
S was equal to 5.
The sifting process stops when the replications of sifting procedure exceed the predefined maximum number. Selecting a maximum number of siftings prevents the sifting procedure from
locking in a never-ending loop. This number should be set large enough to guarantee that IMF is extracted. In this paper, the maximum number of siftings was 750. The sifting process also stops
when x(t) has less than two extremes (the signal must have at least
two extremes, one maximum and one minimum, to successfully
decompose the signal into IMFs).
ð2Þ
t
If this squared difference SDk is smaller than a predetermined TD
value, the sifting process will be stopped. In this paper, TD was
equal to 1e5. The used TD value was determined experimentally.
The second stoppage criterion of the sifting process is based on
the agreement of the number of zero-crossings and extremes. The
sifting process is stopped when the numbers of detail
zero-crossings and detail extremes are the same for S successive
i=0
ri (t ) = xo (t )
Original signal xo (t )
Start
x(t ) = xo (t )
Define the maximum number of
extracted modes, N
Identify all the local extremes of x(t )
NO
Are there enough
local extremes of x (t )?
Stop
YES
x (t ) = ri (t )
Construct the upper envelope Emax (t )
x (t ) = d (t )
and the lower envelope Emin (t )
YES
Have the siftings
been performed in the
required number?
m (t ) = 0.5·(Emin (t ) + Emax (t ))
d (t ) = x (t ) − m (t )
NO
Did d (t ) meet
the IMF conditions?
YES
Has the stoppage criterion
of the sifting process been fulfilled?
NO
YES
i=i+1
ci (t ) = d (t )
ri (t ) = ri −1 (t ) − ci (t )
NO
Is ri (t ) a meaningful component
of xo (t ) regarding value level?
Stop
YES
YES
NO
i<N
Fig. 1. EMD algorithm flow chart.
NO
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The stoppage criterion of the decomposition process determines
how many components will be extracted from the signal. The
decomposition process can be stopped finally by any of the following predetermined criteria: (1) the maximum absolute value of the
remaining residue ri(t) is smaller than tolerance level (ri(t) should
be a meaningful component of the original signal regarding value
level); (2) the predefined number of empirical modes has been extracted (here 20). Here the first stoppage criterion of the decomposition process is described by the following relationship:
maxðjr i ðtÞjÞ < br ðmaxðxo ðtÞÞ minðxo ðtÞÞÞ;
ð3Þ
where ri(t) is i-th remaining residue, xo(t) is the original signal (the
object of decomposition) and br is the tolerance coefficient (here:
br = 0.01). The decomposition process is also stopped when next
IMF cannot be extracted.
In order to clarify the decomposition process, Fig. 1 shows the
flow chart of the applied EMD algorithm.
3. Method of IMFs identification and aggregation
Empirical Mode Decomposition is an iterative process of separating complicated signal into a finite number of IMFs. The successive IMFs include signal components from different frequency
bands ranging from high to low frequency. Therefore, EMD corresponds to an adaptive (data-driven) filtering [26].
In its assumption, the EMD method decomposes the signal
into a set of orthogonal IMFs [22]. In practice, the degree of
orthogonality among the IMFs is average and the energy leakage
between IMFs is severe. One of the major problems in EMD is the
mode mixing, by which IMFs will lose their physical meaning.
Mode mixing indicates that a single IMF contains several intrinsic oscillation modes, or that a single intrinsic oscillation mode
resides in several neighboring IMFs [27]. Mode mixing makes
that the analysis of EMD results is difficult. Some method of
combining neighboring IMFs into the so-called Combined Mode
Function (CMF) may be an effective way to increase EMD efficiency [19].
The method of IMFs aggregation proposed herein is based on
the assumption that the IMFs derived by EMD will be divided generally into three classes of IMFs: noise-only IMFs, signal-only IMFs
and trend-only IMFs. The problem is to assign each IMF to the
appropriate IMFs class. Typically, the noise is captured by IMFs of
low indices and the trend is captured by IMFs of high indices. Some
methods of identification of noise-only and trend-only IMFs are
presented in the literature [28,29]. They are based on the empirically observed energy and mean of signal components. The proposed method of IMFs identification is based on Pearson
correlation coefficient of each IMF and the empirically determined
local mean of the original signal. The empirically determined local
mean of the signal is defined as:
mðtÞ ¼ 0:5 ðEL ðtÞ þ EU ðtÞÞ
ð4Þ
where EL(t) is the empirically determined lower envelope of the signal and EU(t) is the empirically determined upper envelope of the
signal. The IMFs of low indices with low value of Pearson correlation
coefficient are identified as the noise-only IMFs. The IMFs of high
indices with low value of Pearson correlation coefficient are identified as the trend-only IMFs. Remaining IMFs are identified as the signal-only IMFs.
A noise-only part of signal and a signal-only part of signal are
created as the sum of the noise-only and as the sum of the signal-only IMFs, respectively. A trend-only part of signal is created
as the sum of the trend-only IMFs and the final residue.
4. Application of proposed rolling bearing diagnosing method –
two case studies
4.1. Machine and experiment description
Mining machines seem to be a special class of machines
with complex structure, high-power, time-varying load, etc.
Photographs of investigated machine working in the mining company are presented in Fig. 2. Depends on the design (required
power for driving of belt conveyor), belt conveyor driving station
might consist of one up to four drive units with 630 or 1000
[kW] power each. In case discussed here, two drive units are used
(note blue housing of electric motors in Fig. 2). In Fig. 3a the
scheme of the drive unit for a belt conveyor is shown. The drive
unit consists of an electric motor, a coupling and two stage gearbox, that are connected with a pulley. The pulley (Fig. 3b) consists
of a shaft, two bearings and the coating covered by rubber (to increase friction between the pulley coating and the belt). Often between the gearbox and the pulley a rigid coupling is used (see
Fig. 3c).
The purpose of the diagnostic experiment was to acquire vibration signal from the pulley and the assessment of the condition of
the pulley’ bearing (see Fig. 3a). The location of accelerometer is
shown in Fig. 3d: the sensor has been mounted using screw, in horizontal direction. Based on the bearing geometry and the shaft’s
rotational speed, the characteristic defect frequencies of rolling
bearings were calculated, namely: fFTF = 0.51 Hz, fBSF = 4.45 Hz,
fBFF = 8.90 Hz, fBPFO = 12,34 Hz, fBPFI = 16.06 Hz. Several signal acquisition sessions have been performed. For each measurement the
signal was acquired with the following parameters: sampling frequency fs = 19,200 Hz, duration T = 2.5 s. More information about
machine and diagnostic experiment can be found in other papers
concerning diagnostics of these machines [9,13].
Two vibration signals generated by the drive unit, including
vibration data of undamaged and damaged bearings, are used in
two case studies. Due to rigid connection between gearbox and
pulley, a serious participation of gearbox vibration in acquired
vibration signal has been noticed. Energy of signal components related to gear meshing frequency completely masks the signal of
interest –- the signal from the rolling bearing. Amplitude spectra
of acquired vibration signals are presented in Fig. 4. Fig. 5 presents
amplitude spectra of Hilbert-transform-based envelopes of vibration signals. Mean values were removed from the envelopes.
4.2. Decomposing of vibration signals
First, the EMD method is used to decompose the vibration signals. The decomposition results are presented in Figs. 6 (the first
case – undamaged bearing) and 7 (the second case – damaged
bearing). The results of IMFs identification are presented in Figs. 8
(the first case – undamaged bearing) and 9 (the second case – damaged bearing). Figs. 10 (the first case – undamaged bearing) and 12
(the second case – damaged bearing) present the waveforms of the
Fig. 2. A general view on belt conveyor driving station.
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Fig. 3. Diagnosed object: (a) scheme, (b) pulley with bearing housing mounted on shaft, (c) view on joint of output shaft in gearbox with pulley, and (d) view on sensor
location on pulley [9].
the first case
[m/s2]
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
800
900
1000
700
800
900
1000
the second case
[m/s2]
0.6
0.4
0.2
0
0
100
200
300
400
500
600
f [Hz]
Fig. 4. Amplitude spectra of vibration signals (the first case/undamaged/ – top, the second case/damaged/ – bottom).
the first case
0.4
[m/s2]
0.3
0.2
0.1
0
0
50
100
150
200
250
300
200
250
300
the second case
0.4
[m/s2]
0.3
0.2
0.1
0
0
50
100
150
f [Hz]
Fig. 5. Amplitude spectra of envelopes of vibration signals (the first case/undamaged/ – top, the second case/damaged/ – bottom).
1.5
2
0.5
1
1.5
2
2.5
0
0.5
1
1.5
2
2.5
c13 (t)
c16 (t)
0.2
-0.2
0.05
-0.05
0
0.5
1
1.5
2
2.5
0
0.5
1
1.5
2
2.5
c3(t)
0
1.5
2
0.2
-0.2
0.1
-0.1
-0.04
0.5
-0.5
2.5
0.5
1
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-2
2.5
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c11 (t)
0
1
2
-2
2.5
c8(t)
1
0.5
c6(t)
0
c14 (t)
c7(t)
0.5
1
-1
0.05
-0.05
0.1
-0.1
2.5
c9(t)
2
0.4
-0.4
c12 (t)
1.5
0.5
-0.5
0
c10 (t)
1
c5(t)
0.5
c17 (t)
c4(t)
0
0.2
-0.2
c15 (t)
0.1
-0.1
0.02
-0.02
c18 (t)
c2(t)
J. Dybała, R. Zimroz / Applied Acoustics 77 (2014) 195–203
c1(t)
200
0.02
-0.02
r (t)
c19 (t)
t [s]
0.02
-0.02
0
0.5
1
1.5
2
0.1
0.05
2.5
0
0.5
1
t [s]
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t [s]
0
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c8(t)
0
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c13 (t)
0.2
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c14 (t)
1
-1
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-0.05
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c6(t)
2.5
c9(t)
2
0
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0
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c7(t)
1
-1
c16 (t)
c10 (t)
c2(t)
0.5
-0.5
c4(t)
c1(t)
Fig. 6. Decomposition of the first original signal (the first case – undamaged bearing)/19 empirical modes (IMFs) ci(t) [m/s2] and final residue r(t) [m/s2]/.
0.01
-0.01
r (t)
t [s]
t [s]
0.08
0.02
0
0.5
1
1.5
2
2.5
t [s]
Pearson correlation coefficient (PCC)
Pearson correlation coefficient (PCC)
Fig. 7. Decomposition of the second original signal (the second case – damaged bearing)/18 empirical modes (IMFs) ci(t) [m/s2] and final residue r(t) [m/s2]/.
0.7
0.6
0.5
0.4
0.3
0.2
Noise-only
part
Signal-only
part
Trend-only
part
0.1
0
PCC threshold = 0.02
0
2
4
6
8
10
12
14
16
18
20
Number of empirical mode (IMF)
Fig. 8. IMFs identification of the first original signal (the first case – undamaged
bearing).
0.6
0.5
0.4
0.3
0.2
0.1
Noise-only
part
Signal-only
part
0
Trend-only
part
PCC threshold = 0.02
0
2
4
6
8
10
12
14
16
18
Number of empirical mode (IMF)
Fig. 9. IMFs identification of the second original signal (the second case – damaged
bearing).
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[m/s2]
Original signal; kurtosis = 3.44
2
-2
0
0.5
1
1.5
[m/s2]
Noise-only part of signal;
2
2.5
2
2.5
2
2.5
2
2.5
kurtosis = 2.59
0.2
-0.2
0
0.5
1
1.5
[m/s2]
Signal-only part of signal
2
-2
0
0.5
1
1.5
[m/s2]
Trend-only part of signal
0.1
-0.3
0
0.5
1
1.5
t [s]
Fig. 10. Parts of the first original signal (the first case – undamaged bearing).
[m/s2]
Original signal
0.5
0
0
100
[m/s2]
x 10
200
300
400
500
600
700
500
600
700
500
600
700
500
600
700
Noise-only part of signal
-4
5
0
0
100
200
300
400
[m/s2]
Signal-only part of signal
0.5
0
0
100
200
300
400
[m/s2]
Trend-only part of signal
0.05
0
0
100
200
300
400
f [Hz]
Fig. 11. Amplitude spectra of parts of the first original signal (the first case – undamaged bearing).
vibration signals and the waveforms of the noise-only, signal-only
and trend-only parts of the vibration signals. Figs. 11 (the first case
– undamaged bearing) and 13 (the second case – damaged bearing)
present the amplitude spectra of the vibration signals and the
amplitude spectra of the noise-only, signal-only and trend-only
parts of the vibration signals.
4.3. Analysis of vibration signals and their parts
Kurtosis analysis of the raw vibration signals does not deliver
any diagnostic information. The kurtosis values of the raw vibration signals (3.44 in the first case and 3.10 in the second case)
are similar and their low level does not indicate any bearing fault.
[m/s2]
Original signal; kurtosis = 3.10
2
-2
0
0.5
1
1.5
[m/s2]
Noise-only part of signal;
2
2.5
2
2.5
2
2.5
2
2.5
kurtosis = 27.44
1
-1
0
0.5
1
1.5
[m/s2]
Signal-only part of signal
2
-2
0
0.5
1
1.5
[m/s2]
Trend-only part of signal
0.2
0
0
0.5
1
1.5
t [s]
Fig. 12. Parts of the second original signal (the second case – damaged bearing).
202
J. Dybała, R. Zimroz / Applied Acoustics 77 (2014) 195–203
[m/s2]
Original signal
0.4
0.2
0
0
100
200
300
500
600
700
500
600
700
500
600
700
500
600
700
Noise-only part of signal
x 10-4
[m/s2]
400
5
0
0
100
200
300
400
[m/s2]
Signal-only part of signal
0.4
0.2
0
0
100
200
300
400
[m/s2]
Trend-only part of signal
0.02
0
0
100
200
300
400
f [Hz]
Fig. 13. Amplitude spectra of parts of the second original signal (the second case – damaged bearing).
[m/s2]
x 10
-3
the first case
1
0
0
50
100
150
200
250
300
200
250
300
the first case
[m/s2]
0.01
0.005
0
0
50
100
150
the second case
[m/s2]
0.01
Harmonic Cursor = 12.7 Hz
0.005
0
0
50
100
150
200
250
300
f [Hz]
Fig. 14. Amplitude spectra of the empirically determined local amplitudes of the noise-only signals parts (the first case/undamaged/ – top and middle, the second case/
damaged/ – bottom).
The kurtosis values of the noise-only signals parts are significantly
different (2.59 in the first case and 27.44 in the second case). High
value of the noise-only signal’s part indicates that in the second
case some bearing fault occurs. The precise nature of the fault cannot be defined by the kurtosis analysis and for such information it
is necessary to use a more sophisticated diagnostic method.
In order to perform a detailed fault-related analysis of signals,
the spectral analysis of the empirically determined local amplitude
of a signal is used. The empirically determined local amplitude of
the signal is defined as:
aðtÞ ¼ 0:5 ðEU ðtÞ EL ðtÞÞ;
ð5Þ
where EU(t) is the empirically determined upper envelope of the
signal and EL(t) is the empirically determined lower envelope of
the signal. In order to conduct the spectral analysis, mean value
was removed from the empirically determined local amplitude.
Amplitude spectra of the empirically determined local amplitudes
of the noise-only signals parts are presented in Fig. 14.
The discovery of high-amplitude spectral components of the
empirically determined local amplitude indicates that in the second case some bearing fault occurs. The basic frequency of those
spectral components equals 12.7 Hz and corresponds (with 3% tolerance) to Ball Pass Frequency Outer Race (fBPFO). The significant
coincidence between these frequencies enables, with high proba-
bility, the identification of this defect as the bearing outer race
defect.
5. Conclusions
The paper presents the rolling bearing diagnosing method
based on Empirical Mode Decomposition, a new method of IMFs
aggregation into three parts of raw vibration signal and the analysis of the noise-only signal’s part. The analysis of the noise-only
signal’s part provided herein is a two-stage process that involves
the kurtosis analysis and the spectral analysis of the empirically
determined local amplitude of this signal’s part.
Two case studies on the raw vibration signals generated by
complex mechanical systems employed in the industry were
conducted and the analysis demonstrated that the proposed rolling
bearing diagnosing method can identify the bearing faults. The
bearing fault at early stage of its development was detected by
using the kurtosis analysis of the noise-only signal’s part even
when the bearing vibration signal was completely masked by machine noise. This fact showed that the proposed method of the
noise-only signal’s part creation is very useful and important from
the diagnostic point of view.
J. Dybała, R. Zimroz / Applied Acoustics 77 (2014) 195–203
The precise nature of the bearing fault was defined by the spectral analysis of the empirically determined local amplitude of the
noise-only signal’s part. The discovery of high-amplitude spectral
components of the empirically determined local amplitude enabled the identification of this defect, because the basic frequency
of those spectral components was typical for the defined bearing
fault. Therefore, it has been demonstrated that the presented
method of the empirical determination of the local amplitude is
diagnostically useful and equivalent to the Hilbert-transformbased envelope detection method.
[14]
[15]
[16]
[17]
[18]
Acknowledgements
[19]
This paper was financially supported by Polish State Committee
for Scientific Research 2010–2013 as research Project no. N504
147838 (R. Zimroz).
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