A Transient Fault-signal Extraction Scheme for Bearing Compound
Fault Intelligent Diagnosis based on Vibration Signals
MIYAZAKI SHUUJI1, ZHI-QIANG LIAO2,3*, PENG CHEN2*
1Mitsubishi Chemical Corporation,
Okayama Prefecture Kurashiki city,
JAPAN
2Graduate School of Bioresources,
Mie University, Mie,
JAPAN
3Naval Architecture and Shipping College,
Guangdong Ocean University,
Zhanjiang,
CHINA
*Corresponding Authors
Abstract: - As a compound fault of bearing is characterized by complexity, disproportion, and interaction, its
fault diagnostic accuracy tends to decline sharply. To solve this problem, the present study proposes a transient
fault-signal extraction scheme for bearing compound fault intelligent diagnosis. First, the single fault vibration
and compound fault vibration signals are transformed into the time-frequency domain by wavelet transform.
Then, according to the normal condition signal, the transient fault signal of the single signal and compound
signal is extracted through the positive k sigma principle. Next, the single fault signal symptom parameters are
calculated to build the fault diagnostic model. Thereafter, the symptom parameters of the extracted compound
fault transient signal are brought into the diagnostic model to obtain the model output result. Finally, according
to the developed fault diagnosis discrimination criterion, the method can diagnose the compound fault
successfully. The effectiveness of the proposed method is validated by bearing fault vibration signals under
various conditions. The results show that the diagnostic method has superior performance in intelligently
diagnosing the bearing compound fault.
Key-Words: - Compound fault, Fault signal extraction, Wavelet transform, Positive k sigma principle.
Received: November 13, 2022. Revised: August 19, 2023. Accepted: September 23, 2023. Published: October 16, 2023.
1 Introduction
Bearings are among the essential components of
rotating machines. Due to their complex working
conditions,
bearing fault diagnosis is a significant
task in guaranteeing equipment safety and reducing
accidents, [1]. In many situations, compound faults
often appear as spalls or cracks on different
positions, [2]. Compared with fault diagnosis
methods that have been successfully used in single
faults, accurate diagnosis of compound faults has
not been effectively proven in theory. Bearing
compound fault is characterized by complexity,
disproportion, and interaction results in diagnostic
performance deterioration. Therefore, studying the
compound fault diagnosis is important.
Many studies have conducted compound fault
diagnosis of the rotating machine. With the
development of automation and information
technology, most methods are machine learning
algorithms. The bearing compound fault diagnosis
can be divided into two types: one is fault
characteristic frequency-based and the other is
discriminant model-based. The general process of
the fault characteristic frequency-based type is as
follows: the acquired signal is filtered first, and then
a signal is decomposed to extract or strengthen the
fault signal.
The method can identify the fault characteristic
frequency for fault diagnosis. Numerous compound
fault diagnosis strategies have been applied with this
method, [3], [4]. Empirical mode decomposition,
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[5], [6], empirical wavelet transform combined with
chaotic oscillator, [7], 1.5-dimension envelope
spectrum, [8], resonance and spectral kurtosis, [9],
[10], Hilbert transform demodulation analysis, [11],
and adaptive maximum correlated kurtosis
deconvolution, [12], have been successfully applied
with fault characteristic frequency-based approach.
This type of method needs to calculate the fault
characteristic frequency initially, which requires
knowing intrinsic information about the object, such
as size, rotation speed, and diameter. These factors
are difficult to identify in some unknown working
conditions. The general process of the discriminant
model-based method is as follows: collecting the
vibration signal in the fault state, extracting the fault
features, and building an effective discriminant
model for fault diagnosis through signal filtering
and feature extraction. Many different studies have
addressed compound fault diagnosis by this method.
Sparse non-negative matrix factorization combined
with support vector data description, [13], support
vector machine, [14], [15], [16], independent
component analysis, [17], principal component
analysis, [18], [19], and hidden Markov model, [20],
have been successfully applied in compound fault
diagnosis. In this method, the accuracy of the
discriminant model largely depends on the effective
extraction of features, but no perfect method can be
used to extract features in the compound fault signal
characterized by feature coupling. Motivated by this
problem, the present study developed an automatic
transient spectrum extraction scheme for bearing
compound fault diagnosis. Transient spectrum
extraction can effectively extract single and
composite fault features from signals, and the
extracted features have stronger fault representation
ability. Based on the transient spectrum extraction,
the compound fault diagnosis model has better
diagnostic ability.
The main contributions of this paper reflect in:
(1) The proposed positive k sigma principle can
extract single fault information from compound
signals effectively. (2) The discriminant model with
extracted single faults can reduce diagnostic
performance deterioration caused by compound
faults. Various experiments confirmed the efficacy
of this method.
The rest of this paper is organized as follows.
Section 2 introduces the bearing compound fault
diagnosis method and theory proposed in this paper,
which illustrates the positive k sigma principle to
extract transient spectra and discrimination criteria.
Section 3 uses the experiment platform data to
verify the proposed method. Section 4 provides a
summary of the conclusions.
2 Bearing Compound Fault Diagnosis
Strategy
The automatic transient spectra scheme of bearing
compound fault diagnosis covers condition
surveillance, the positive k sigma principle, the
discrimination model, and others. The process of the
proposed method is shown in Figure 1.
1. Wavelet Transform
Transform
signal to
time-
frequency
with WT
Data preprocessing
and calculate 7
symptom parameters
3. SVM training
4. SVM diagnosis
Select fault signal samples
to train with SVM
Use the trained model to
diagnose compound fault
Trained model
Training
Diagnosis
Compound
fault signal
Normal signal
Single state
（For training）
Compound fault and normal state
(For diagnosis)
2. Symptom parameters
calculate
Single faults
signal
Fig. 1: Process of proposed compound fault
diagnosis method
In the training stage, wavelet transforms (WT)
are used to transform vibration signals measured in
the normal state and single fault state (inner race,
outer race, and roller defects) to the time-frequency
domain. With normal state signals as reference
signals, the transient spectra of abnormal (fault)
states are detected. Each impulse wave corresponds
to one transient spectrum. Then, the frequency
domain symptom parameter method is used to
obtain symptom values. These symptom values are
synthesized as input and substituted into the support
vector machine (SVM) to establish a model from
symptom parameters to fault types.
In the diagnosis stage, condition surveillance is
performed by measuring vibration signals to reveal
the bearing condition first. Similar to the training
stage, the compound fault is transformed into the
time-frequency domain by WT. Then, the transient
spectra of abnormal components are extracted using
reference signals and the positive k sigma principle.
In these transient spectra, frequency domain
symptom parameters are used to obtain symptom
values. Then, the symptom values are substituted
into the SVM model, which is established in the
training stage. According to the model result, the
compound fault can be diagnosed through a
designed discrimination criterion.
2.1 Condition Surveillance
The proposed bearing diagnosis method has two
stages: one is condition surveillance (simple
diagnosis) and the other is precision diagnosis.
Before the diagnosis of compound faults, condition
surveillance is needed to judge the bearing
condition. Generally, for condition surveillance,
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statistical symptom parameters acquired from
vibration signals are used to monitor the mechanical
condition. These parameters have two types:
symptom parameters with dimensionality (e.g.,
mean and peak values representing signal
amplitude) and dimensionless symptom parameters
(e.g., skewness and waveform kurtosis, which
represent signal shape), [21].
In the first step of the proposed method, the
bearing condition must be diagnosed as either
normal or not. Kurtosis is one of the most effective
parameters to detect bearing abnormality. Kurtosis,
which has been successfully used to detect bearing
faults [22], is defined as
44
1
N
i
i
Kurtosis x N
(1)
where: µ = mean value
σ = standard deviation
N = length of signal xi
According to the experimental findings of
reference, [22], when the bearing vibration signal
kurtosis value exceeds five times the normal state
signal kurtosis, the bearing is abnormal. Thus,
kurtosis is employed for condition surveillance. It
only judges whether the bearing is normal or not,
and the further precise diagnosis employs the
proposed method.
2.2 Discrete Wavelet Transform
Compared with the fast Fourier transform, wavelet
transform, [23], [24] has good time-frequency
localization properties in signal processing and
characteristic of multi-resolution analysis. Given a
signal f(t), its discrete wavelet transform is defined
as
2
1
,2
2
jwt
wt j
j
tk
DWT j k f t d t
(2)
where: ψ(t) = mother wavelet
2j = scale parameter (inverse of frequency)
2jkwt = translation parameter
2.3 Positive k Sigma Principle Fault-
Transient Spectra Extraction Methodology
Using Eq. (2), i.e., wavelet transform computation,
we can obtain time-frequency domain signals of
each state for the training and diagnosis stages.
Figure 2 shows the roller bearing vibration signal
time domain fault impulse waveform of the
abnormal state (Figure 2(a)) and the corresponding
impulse waveform frequency spectrum transformed
by WT in the time-frequency domain (Figure 2(b)).
0.01 0.02 0.03 0.04
0
0.1
0.2
0.3
0.4
0.5
Time (s)
IW(t)
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
-0.1
-0.05
0
0.05
0.1
(a) Time (s)
Amplitude
0.01 0.02 0.03 0.04
0
1
2
3
4
5x 104
(b) Time (s)
Frequency (Hz)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
+k
(c)
Fig. 2: Signals in time and time-frequency domains:
(a) vibration signal; (b) time-frequency; and (c) time
intensity of spectrum
To extract the transient spectra of the abnormal
bearing, we define time intensity Iw(t) of wavelet
frequency spectrum W(tk, fi) as follows:
2
1
=2
2
wt
jwt
Wj
j
jk
tk
I t f t
(3)
An example of Iw(t) is presented in Figure 2(c).
The value of µ+kσ exceeding reference state
(normal state) Iw(t) is normally used in selection to
extract the transient spectra of fault pulse from the
signals. Here, µ is the mean value of Iw(t), σ is the
standard deviation of Iw(t), and k is calculated by
1
=peaks
peaks
N
W peaks
i
i
k I N
(4)
where: Npeaks = the number of peaks in the reference
state (normal state)
2.4 Frequency-domain Symptom
Parameters
To reflect symptoms of the fault-pulse signal
transient spectrum as shown in Figure 2(c),
according to our previous study, [21], seven types of
frequency domain symptom parameters presented in
Eqs. (5–11) are used to represent symptoms of the
transient spectrum.
2
133
=NN
i i i
i N i N
p f S f S f
(5)
42
233
=NN
i i i i
i N i N
p f S f f S f
(6)
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22
33 3 3
=N N N
i i i i i
i N i N i N
p f S f f S f S f
(7)
4=pf
(8)
33
53
=N
i
iN
p f f S f N
(9)
44
63
=N
i
iN
p f f S f N
(10)
73
=N
i
iN
p f f S f N
(11)
here,
33
NN
i i i
i N i N
f f S f S f
2
3
=N
i
iN
f f S f N
where:
N
= the acquired signal length
f
= the frequency of the acquired signal
Sf
= signal frequency spectrum,
1,2,iN
.
The amplitude
sf
significantly influences the
value of such a symptom parameter. Before the
symptom parameters are calculated, both the
spectrum and symptom parameters should be
normalized.
/2
''
1
( ) ( ) ( )
N
f
s f s f s f
(12)
where:
()sf
= the spectrum of normalization
'()
i
i i p
p p p std
(13)
where:
i
p
: fault symptom parameter;
'
i
p
: fault symptom parameter of normalization;
p
: the mean value symptom parameter;
i
p
std
: the standard deviation symptom parameter.
2.5 Classification of Compound Faults by
SVM
SVM is a type of intelligent algorithm based on the
theory of statistical learning. As bearings have many
fault types, compound fault SVM is a multi-class
classification problem.
Based on the normal state of bearing, according
to Eqs. (5–11), single-fault symptom parameters are
i
jk
p
(j = 1–M, ki = O, I, R), k = O (outer race defect),
I (inner race defect), and R (roller defect). Their
instantaneous spectra and symptom parameters are
normalized. Seven symptom values are input
parameters to SVM and the fault type is the output.
After training the SVM model, compound fault
parameters Pjc (j = 1–M), where C indicates
compound faults, are substituted into the model to
identify the fault type.
2.6 Discrimination Criterion
Based on the SVM classification model, the model
output is used to identify the compound fault type.
This study proposes a discrimination method based
on cumulative percentage, which is defined as
follows:
We assume that Nx, x = 1,2,…,m is the number of
fault type output by SVM and m is the fault type. Nx
is ranked as N1≥N2…. ≥Nm≥0 individual percentage,
and pri is defined as
1
m
i i i
i
pr N N
(14)
The cumulative percentage of the first t type in
the sequence is defined as
111,2,
tm
t i i
ii
C N N t m
，
(15)
As compound faults are characterized by
multiplicity and coupling, some fault symptoms are
not sufficiently clear. The proposed method is
implemented to assess the number of single faults in
the compound faults. However, the existence of
noise, complex fault signals, and coupling features
lead to a condition in which the single fault cannot
be perfectly (100%) extracted from the compound
fault signal. Thus, dominant signals of single faults
are selected to diagnose compound faults. The
threshold Thr is provided to select t. If Ct≥Thr, then
the compound faults include the first t fault types.
Here, the threshold Thr refers to principal
component analysis theory: the percentage of the
cumulative sum over 80% can represent the main
information of the signal. Fault discrimination
operations are shown in the following steps:
Step 1: The diagnosis samples are brought into
the trained model of SVM and obtain the
classification result
i
N
.
Step 2: All
i
N
values are ranked from max to
min
12 m
N N N
.
Step 3: Cumulative percentage
11
=tm
i i i
ii
Pr N N
,
where
, 1,2,
i
Pr i m
is calculated.
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Step 4: Fault type is diagnosed; if
ir
Pr Th
, then
a fault type exists from 1 to i.
For example, given the SVM model fault type
output ranking of No>NI>NR, if (No+NI)/
(No+NI+NR )≥ Thr, the compound fault includes O
(outer race defect) and I (inner race defect). If (No)/
(No+NI+NR )≥ Thr, then only the outer race defect O
exists.
3 Experiment
3.1 Experimental Conditions
To verify the effectiveness and feasibility of the
proposed method, this study presents the results of
roller-bearing compound fault diagnosis tests
performed on a rotating experimental machine
facility (Figure 3). An experimental bench used for
fault diagnosis testing is provided and includes
loading equipment, a servo motor, and a rotor
system. The original vibration signals of each state
were measured by an accelerometer with a sampling
frequency of 100,000 Hz. Objects of diagnosis
include a single fault in Figure 4 (outer race defect,
inner race defect, and roller defect) and a compound
fault (inner race defect and outer race defect, inner
race defect and roller defect, and outer race defect
and roller defect) created by machining. The inner
race defect is 0.15 mm × 0.5 mm (depth × width),
the outer race defect is 0.15 mm × 0.5 mm (depth ×
width), and the roller defect is 0.15 mm × 0.5 mm
(depth × width). The accelerometer is installed in
the vertical direction of the bearing seat (1,500
revolutions per minute). The length of the
experiment data is 16,384.
Fig. 3: Experimental bench
Fig. 4: Fault bearing for test: (a) outer race defect,
(b) inner race defect, and (c) roller defect
This experiment adopts a compound fault that
includes inner race and roller defects as an object to
verify the effectiveness of the proposed method. If
the fault-state operating conditions of the bearing
experiment differ from the normal state, then the
diagnostic accuracy declines.
3.2 Condition Surveillance
Kurtosis analysis is used for condition surveillance.
According to theory, in the normal state, the kurtosis
value is near 3 and the probability distribution
follows the normal distribution. If the kurtosis value
exceeds 5 times the normal state, then faults exist in
the bearing. The farther the kurtosis value from 5,
the more serious the fault. This study adopts
vibration signals of the normal state, single fault,
and compound fault to calculate the time domain
kurtosis values. Results are provided in Table 1.
Table 1. Kurtosis Values of Each State
Type
Kurtosis Value
Normal state
2.869
Inner race defect state
109.2879
Outer race defect state
34.1227
Roller race fault state
253.4692
Compound fault state
74.84
As shown in Table 1, the normal state kurtosis
value is near 3. The kurtosis values of the inner race
defect, outer race defect, roller defect, and
compound fault are 109.2879, 34.1227, 253.4692,
and 74.84, respectively. All of these values are
larger than 5 times the normal state. This result
indicates the fault in measured vibration signals. To
allow a straightforward analysis, Figure 5 shows the
calculated probability density distribution of each
state.
Fig. 5: Probability distribution of each state
As presented in Figure 5, according to the
standard normal distribution, the probability
-5 0 5
0
0.2
0.4
Standard normal distribution -5 0 5
x 10-3
0
0.02
0.04
Normal state
-0.2 0 0.2
0
0.5
Inner race flaw -0.05 0 0.05
0
0.2
0.4
Outer race flaw
-0.1 0 0.1
0
0.5
1
Roller flaw -0.2 0 0.2
0
0.5
1
Compound fault
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distribution of the normal state follows the normal
distribution. The probability distributions of the
inner race, outer race, and roller defects deviate
from the normal distribution. The more apparent this
deviation, the more apparent the fault. Compared
with the normal distribution, the compound fault
kurtosis value deviates from the normal distribution.
3.3 Extraction of Transient Spectra using
WT
Considering the characteristics of vibration signals,
this study adopts Gabor wavelet ψ(t) to transform
signals to the time–frequency domain.
=it
t g t e
(16)
where: gσ(t)is referred to as the Gaussian window
function defined as
2
2
4
1
=2
t
g t e
(17)
where: σ = the standard deviation (factor width)
µ = the mean value (time factor)
Through WT operations, time–frequency
diagrams of a normal state, single fault state, and
compound fault state are obtained. The example of
the inner race defect result is shown in Figure 6.
In Figure 6, (a) shows vibration signals acquired
by the experiment, (b) shows some data of the time
domain signals intercepted from (a), (c) shows the
time–frequency contour diagram of the wavelet
spectrum obtained by WT, and (d) shows the time
intensity of the wavelet spectrum. As presented in
Figure 6, the fault pulse in the vibration signal time
domain has a corresponding fault symptom transient
spectrum in the time–frequency domain. The time-
intensity of Iw(t) of this point exceeds the time
intensity when no pulse signal exists. With the
normal state as a reference, the positive k sigma
principle µ+kσ of Iw(t) is used as the method to
select fault-signal transient spectra. According to
experiment results, µ+6σ has been used to extract 88
transient spectra from a single inner-race defect,
µ+4σ has been used to extract 118 transient spectra
from a single outer-race defect, µ+3σ has been used
to extract 104 transient spectra from a single roller
defect, and µ+3σ has been used to extract 153
transient spectra from a compound fault.
Obtained transient spectra have been normalized
and then, symptom parameters in Eqs. (5–11) are
used to obtain symptom values of the transient
spectra, followed by normalizing of symptom
parameters using Eqs. (12–13).
After the operations mentioned, the data obtained
can be used to establish the classification model and
identify and diagnose the compound faults.
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
0
0.5
1
1.5
Time (s)
(d)
IW(t)
0.2 0.4 0.6 0.8 1 1.2
-0.2
-0.1
0
0.1
0.2
Time (s)
(a)
Amplitude
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
-0.2
-0.1
0
0.1
0.2
Time (s)
(b)
Amplitude
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
0
1
2
3
4
5x 104
Time (s)
(c)
Frequency (Hz)
+6
Fig. 6: Fault signal time domain and time–frequency
domain (inner race defect)
3.4 Diagnosis of Compound Faults
In this section, SVM is used to establish a roller-
bearing diagnosis model. Based on this built model,
the compound fault can be classified. Some
symptom parameters of the SVM model training
part are inner race defect: 1(type), outer race defect:
2(type), and roller defect: 3(type). Diagnosis parts
(compound faults) are presented in Table 2.
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Table 2. Diagnosis samples
State
Fault
type
No.
P1
…
P7
Fault
type
Train-
ing
Inner
1
0.802
…
2.373
1
…
…
…
…
1
60
0.048
…
3.338
1
Outer
61
1.212
…
2.912
2
…
…
…
…
2
120
0.864
…
2.684
2
Roller
123
0.877
…
3.936
3
…
…
…
…
3
180
1.098
…
3.163
3
Diagno-
sis
Com-
pound
181
2.47
…
0.774
Un-
known
…
…
…
…
Un-
known
333
0.343
…
2.86
Un-
known
Here, the SVM model uses RBF as the kernel
function. In the training stage, 60 symptom
parameter samples of each state of the inner race
defect, outer race defect, and roller defect (total of
180 samples) are taken to train the SVM model.
Additionally, 24 symptom parameter samples of
each state are taken as test samples to test the
model. After the model training, the 153 symptom
parameters calculated from the compound fault state
are used as diagnosis samples to diagnose the
compound fault, as shown in Table 3.
Table 3. Sample setting of the SVM model
Fault type
Training
samples
Test
samples
Training
state
Inner
60
24
Outer
60
24
Roller
60
24
Diagnosis
state
Compound
No
153
(for
diagnosis)
All single-fault (inner race, outer race, and roller
defects) training samples are used to train the SVM
model. Then, testing samples of all single faults are
used to test the trained model. The model test
accuracy is defined as:
%
correctSampl
Accuracy testingSampl
es
es
(18)
The model test results are presented in Figure 7.
Fig. 7: Accuracy of a test sample of the SVM model
(I: inner, O: outer, and R: roller)
As shown in the results, output result accuracy
reaches 95.83%, thereby indicating the good
performance of the training model and the
successful establishment of mapping from fault
symptom parameters to fault types. Based on this
trained model, symptom parameters of compound
fault are substituted into the model to verify the type
of compound fault.
Substituting the 153 calculated compound fault
symptom parameters into the built SVM model, we
find that the output of the model belongs to three
types (I: inner race defect, O: outer race defect, and
R: roller defect). According to Eq. (14), NI is 38 and
its percentage PI is 24.84%; NO is 19 and its
percentage PO is 12.42%, and NR is 96 and its
percentage PR is 62.74%. Based on the ranking of a
percentage from maximum to minimum, and using
Eq. (15), the cumulative percentage of each fault
state (CI, CO, and CR) has been calculated, with
results shown in Figure 8.
Fig. 8: Fault type in compound fault
According to the results, the fault types are
ranked as follows: roller, inner race, and outer race
defects. As the data in the table show, the
cumulative percentage of the second (fault types:
roller defect and inner race defect) is 87.58%, which
indicates the inner race and roller defects in the
compound fault. This result is consistent with the
experimental facility, indicating the effectiveness of
the proposed method.
020 40 60 80
I
O
R
Sample
Test fault sample type
Accuracy = 95.83%
Observed
ISVM prediction
Misjudged
Inner race fault: 24.84%
Roller fault: 62.74%
Outer race fault: 12.42%
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To further prove the effectiveness of this method,
we have tested three types of single fault (inner race,
outer race, and roller defects) and another type of
compound fault (outer race defect + roller defect).
Verification results are presented in Table 4.
As shown in Table 4, if the diagnostic proportion
of a certain type of fault in the signal exceeds 95%,
it indicates that there is only one type of fault. For
composite faults, according to the method
mentioned in Section 2.6, the cumulative percentage
of extracted faults is 89.54%, exceeding 80%,
indicating that it is a compound fault and proving
that the diagnosis is effective.
Table 4. SVM fault diagnosis in single fault and
compound faults
N
o.
Classifica-
tion of fault
Classified
correctly
Misjudged
datasets
Accur
-acy
(%)
1
I
NI :21 (I)
1 (others)
CI:
95.23
2
O
No :24 (O)
0
Co:
100
3
R
NR: 22 (R)
1 (others)
CR:
95.45
4
O and R
NR+O: 124
(O and R)
13 (others)
CR+O:
89.54
(I: inner race defect, O: outer race defect, R: roller
defect.)
3.5 Diagnosis of Compound Faults
To further prove the effectiveness and advancement
of this proposed method, we employed the
conventional method for comparison with the
developed method. The main steps of the
conventional method are the following: (1) dividing
the compound fault vibration signal by N signal
subsets, (2) every signal subset attracts frequency
domain symptom parameters according to Eqs. (5–
11), (3) the symptom parameters are placed in the
SVM model by single fault symptom parameters,
and (4) the discrimination criterion is used to
calculate the diagnosis accuracy. The results are
shown in Table 5.
The results in Table 5 show that the conventional
method was used in single-fault diagnosis, and the
diagnosis accuracy approximates the proposed
method. When the conventional method was used in
the compound fault of the roller bearing, the
conventional method had a low accuracy (the
cumulative percentage of the outer race defect and
roller defect is 56.45%). These results show that the
proposed method can reduce the diagnostic
performance deterioration caused by compound
faults in roller bearing diagnosis.
Table 5. Results of proposed and conventional
methods
N
o.
Classifica
-tion of
fault
Classified
correctly
Proposed
method
accuracy
(%)
Conven-
tional
method
accuracy
(%)
1
I
NI : 21 (I)
CI : 95.23
CI:
95.23
2
O
No : 24 (O)
Co : 100
Co:
95.85
3
R
NR : 22 (R)
CR : 95.45
CR :
95.45
4
O and R
NR+O: 124
(O and R)
CR+O :
89.54
CR+O:
56.45
(I: inner race defect, O: outer race defect, R: roller
defect.)
3.6 Different Fault Severity in Compound
Faults
When the compound fault vibration signal has
different fault-severity bearing components, the
proposed method's efficacy depends on the fault
degree. If the positive k sigma principle can extract
the transient spectra of all the single faults, then
different fault-severity bearing components can be
diagnosed using the developed method. If the
positive k sigma principle cannot extract certain
transient spectra, then the slight fault (which was
not extracted) can be regarded as a noise signal and
does not affect the operation, and the compound
fault cannot be effectively diagnosed.
The following experiments are conducted to
verify our findings. Two compound fault roller-
bearing vibration signals are observed: the first
compound fault signal composed of inner race
defect is 0.15 mm × 0.5 mm (depth × width) and the
roller defect is 0.05 mm × 0.3 mm (depth × width).
The roller defect severity is slight compared with
the inner race defect. The second compound fault
signal is composed of the outer race defect 0.15 mm
× 0.3 mm (depth × width) and roller defect 0.15 mm
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DOI: 10.37394/23202.2023.22.74
Miyazaki Shuuji, Zhi-Qiang Liao, Peng Chen
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× 0.5 mm (depth × width). The results of the
positive k-sigma principle of the developed method
are shown in Figure 9.
0.2 0.4 0.6 0.8 1 1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time (s)
IW(t)
Outer race flaw and Roller flaw
+3
(a)
0.2 0.4 0.6 0.8 1 1.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time (s)
IW(t)
Inner race flaw and Roller flaw
+4
(b)
Fig. 9: Different fault-severity diagnosis results:
(a) compound fault: outer race and roller defects;
(b) compound fault: inner race and roller defects
After the operation by the SVM model, in the
compound fault, the percentage of the outer race
defect is 86.36%. If larger than 80%, then the roller
defect cannot be accurately diagnosed. The reason is
that the roller defect degree is slight and cannot
extract the single fault (roller defect) feature by the
positive k sigma principle. In the compound fault,
the cumulative percentages of the inner race and
roller defects are 92.91% (roller defect: 49.61% and
inner race defect: 43.31%). The compound fault
diagnosis result is correct. Therefore, when the
severity of a single fault in a composite fault signal
is different, the positive k sigma principle can
extract the transient spectrum of a single fault as a
feature. If the transient spectrum cannot be extracted,
it is considered a noise signal.
4 Conclusion
An automatic transient-spectra extraction scheme
was developed to reduce diagnostic performance
deterioration caused by compound faults in roller
bearing diagnosis. The single fault features were
extracted from the compound fault vibration signal
by a positive k sigma principle. The created
diagnosis discrimination criterion is the ratio of the
single components to the multiple components
estimated by understanding the relationship between
the single and compound faults. The developed
method was verified through various conditions of
the defective roller bearing by the SVM model. The
experimental results indicated that the developed
method was superior to the conventional method in
compound fault diagnosis.
In the future, this method can be applied to other
rotating machines, such as in the diagnosis of gear
faults. At the same time, the complexity and time
consumption of the developed method have to be
considered in future research.
Acknowledgment:
This work was supported by a program for scientific
research start-up funds of Guangdong Ocean
University.
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DOI: 10.37394/23202.2023.22.74
Miyazaki Shuuji, Zhi-Qiang Liao, Peng Chen
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Volume 22, 2023
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed to the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This work was supported by a program for scientific
research start-up funds of Guangdong Ocean
University.
Conflict of Interest
The authors have no conflict of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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DOI: 10.37394/23202.2023.22.74
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E-ISSN: 2224-2678
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Volume 22, 2023
