IEEE Computational Intelligence Magazine - August 2021 - 89

different random seeds. The evolutionary
process of GP and the classifier
training step only use the training set.
The fault diagnosis results of the test
sets are reported.
V. Results and Discussions
This section discusses and analyses the
fault diagnosis results obtained by MFCGPE
and the 19 comparison methods
on the three different datasets with a small
number of training samples. Table VII
lists the classification accuracy of the 20
methods, including the maximum
(Max) value, average (Avg) value and
standard deviation (Std) of the accuracy
of the 30 runs, where the best results of
each dataset are highlighted in bold.
Wilcoxon rank-sum test with a 5% significance
level is employed to evaluate
the significant difference in performance
improvement of MFCGPE compared to
a method. In Table VII, the " + " symbol
indicates that the performance of MFCGPE
is significantly better than the
comparison method. The summary of
the significance test results on each dataset
is listed in the last row of Table VII.
Rows 1-5 of Table VII list the classification
results of the five traditional
classifiers using raw signals amplitude
(RSA). It can be seen that the diagnosis
accuracy of these methods is very low.
On the NCEPU and CWRU datasets,
MLP achieves better results than KNN,
LR, SVM, and NB. Specifically, MLP
achieves an average accuracy of 22.01%
on NCEPU and of 21.92% on CWRU.
On the XJTU dataset, NB achieves a
NOR
-5
5
30
-30
0.04
Time (s)
0.08
0.04
ORF
0.08
50
-50
50
-50
0.04
Time (s)
FIGURE 11 Time domain waveform of vibration signals under four running conditions in XJTU.
TABLE VII Diagnosis accuracy (%) of MFCGPE and the comparison methods on the NCEPU, CWRU, and XJTU datasets.
ROW
METHOD
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
RSA+KNN
RSA+LR
RSA+SVM
RSA+NB
RSA+MLP
TDF
FDF
MDF
MMSDE
IMDE
GPS-TDF
GPS-FDF
GPS-TFDF
GPM-TDF
GPM-FDF
GPM-TFDF
OFE
GPSE
GPME
MFCGPE
OVERALL
MAX
16.67
17.04
16.67
17.41
31.85
79.26
82.96
88.15
87.78
91.11
90.74
92.59
94.81
94.44
95.92
97.03
89.25
95.55
98.51
100.0
NCEPU
AVG±STD
16.67±0.00+
17.04±0.00+
16.67±0.00+
17.41±0.00+
22.01±4.24+
79.26±0.00+
82.96±0.00+
88.15±0.00+
87.78±0.00+
91.11±0.00+
87.83±2.76+
89.42±3.78+
90.73±3.53+
92.37±1.94+
93.30±2.17+
94.56±2.35+
89.25±0.00+
93.84±1.56+
97.47±1.12+
99.56±0.30
19+
MAX
10.00
21.33
16.44
23.33
32.22
76.67
83.56
90.22
92.67
85.78
88.89
91.78
93.78
96.22
97.11
97.56
90.44
94.46
98.45
100.0
CWRU
AVG±STD
10.00±0.00+
21.33±0.00+
16.44±0.00+
23.33±0.00+
21.92±1.10+
76.67±0.00+
83.56±0.00+
90.22±0.00+
92.67±0.00+
85.78±0.00+
84.62±2.56+
87.52±3.08+
90.17±2.91+
93.37±2.42+
95.34±1.58+
96.16±1.76+
90.44±0.00+
92.81±1.45+
97.65±0.85+
99.23±0.67
19+
MAX
25.00
28.70
28.70
52.78
37.96
87.96
97.22
75.93
83.33
82.41
91.67
99.07
100.0
95.37
100.0
100.0
95.37
100.0
100.0
100.0
19+
0.08
0.04
CF
0.08
maximal and average accuracy of
52.78%, which is better than other classifiers.
Compared with these five methods,
MFCGPE achieves much higher
accuracy, i.e., over 99%, on the three
datasets. The results show that constructing
high-level features is very important
for fault diagnosis of rolling bearings.
Rows 6 to 10 of Table VII list the
classification results of the KNN classifier
using five different types of manually
crafted features (i.e., TDF, FDF, MDF,
MMSDE, and IMDE). It can be seen
IRF
XJTU
AVG±STD
25.00±0.00+
28.70±0.00+
28.70±0.00+
52.78±0.00+
31.45±3.26+
87.96±0.00+
97.22±0.00+
75.93±0.00+
83.33±0.00+
82.41±0.00+
88.22±3.71+
96.45±2.36+
96.67±3.37+
93.09±2.98+
97.87±2.36+
98.21±1.97+
95.37±0.00+
98.37±1.81+
99.02±1.09+
99.61±0.26
AUGUST 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 89
Amplitude (g)
IEEE Computational Intelligence Magazine - August 2021

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