IEEE Computational Intelligence Magazine - August 2021 - 87

respectively. 07, 14, and 21 indicate
that the defect diameter is 0.007,
0.014, and 0.021 inches, respectively.
The vibration signals of driver-end
bearing under 1,797 r/min are collected
with a sampling frequency of
12,000 Hz. Similar to the NCEPU
dataset, the first 102,400 data points
of vibration signals under each running
condition are divided into 50
samples on average. Five samples of
each running condition are randomly
selected to form the training
set, and the remaining samples are
used as the test set. Table V lists the
detailed information of the CWRU
dataset. Figure 9 shows the time
domain waveform of vibration signals
under ten running conditions
in CWRU.
3) XJTU [55]: It is a run-to-failure
bearing fault dataset collected by
Xi'an Jiaotong University (XJTU),
in which the reason for fault occurrence
is the natural damage as the
running time increases. Figure 10
shows the used test rig of XJTU. In
the experiments, the vibration signals
of the test bearings are collected
with a sampling frequency of
25,600 Hz until the bearing fails,
and the time interval for each sampling
is one minute. The vibration
signals of the last two recorded data
file of the Bearing 2_1, Bearing
2_2, and Bearing 2_3 datasets are
used as the analyzed data. The fault
types are inner ring fault
(IRF),
outer ring fault (ORF), and cage
fault (CF). The signals of the first
two recorded data file of the Bearing
2_1 dataset is used as the normal
(NOR) vibration signals for
analysis. Every vibration signal
contains 32,768 data points and is
divided into 32 samples on average
for conducting the experiments.
Each sample contains 2,048 data
points. Five samples under each
running condition are randomly
selected to form the training set,
and the remaining samples are used
as the test set.Table VI lists the
detailed information of the XJTU
dataset. Figure 11 shows the time
NOR
IRF
50
-50
400
-400
400
-400
0.08
Time (s)
0.16
0.08
IOCF
200
-200
0.08
Time (s)
FIGURE 7 Time domain waveform of vibration signals under six running conditions in NCEPU.
domain waveform of vibration signals
under four running conditions
in XJTU.
B. Comparison Methods
To verify the effectiveness of MFCGPE,
four categories of competitive methods,
i.e., 19 methods, are employed for comparisons.
The first category includes five
different classification algorithms, i.e.,
KNN, SVM, Naive Bayes (NB), logistic
regression (LR), and multilayer perceptron
(MLP), which use raw signals
amplitude to train the classifiers for fault
classification. The second category are
KNN using five manually crafted features,
i.e., TDF, FDF, multi-domain features
(MDF) [25], modified multi-scale
symbolic dynamic entropy (MMSDE)
[14], and improved multi-scale dispersion
entropy (IMDE) [15], for fault clasTABLE
V Description of the CWRU dataset.
CLASS
LABEL
1
2
3
4
5
6
7
8
9
10
RUNNING CONDITION
Normal
Inner ring fault
Inner ring fault
Inner ring fault
Outer ring fault
Outer ring fault
Outer ring fault
Rolling element fault
Rolling element fault
Rolling element fault
DEFECT
SIZE (IN)
0.007
0.014
0.021
0.007
0.014
0.021
0.007
0.014
0.021
TRAINING
SAMPLES
5
5
5
5
5
5
5
5
5
5
TEST
SAMPLES
45
45
45
45
45
45
45
45
45
45
sification. The TDF and FDF features
have been described in Section III-D.
The numbers of features in MDF,
MMSDE, and IMDE are 37, 20, and 20,
respectively. The comparisons aim to
investigate whether the features constructed
by MFCGPE are more effective
for fault diagnosis than these manually
crafted features.
The third category contains six GP
based methods using TDF, FDF, and
TFDF (described in Section III-D) as
0.16
0.16
0.08
ORF
0.16
500
-500
0.08
ROCF
0.16
300
-300
0.08
REF
0.16
FIGURE 8 CWRU test rig.
AUGUST 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 87
Amplitude (m/s2)
IEEE Computational Intelligence Magazine - August 2021

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