IEEE Computational Intelligence Magazine - August 2021 - 92

using the features constructed from
View1 for visualization, few points in the
NOR, IRF, and REF classes are overlapping,
and the other colored points are
gathered together and do not overlap.
Using the features constructed from
View2 for visualization, only a few points
in the IOCF and ROCF classes are overlapping.
Using the features constructed
from View3 for visualization, only a few
points in the ORF and ROCF classes are
overlapping. Compared with the original
features, these newly constructed features
have a good similarity among the same
class and have a big difference between
different classes. These visualization
results indicate that the constructed
features can effectively represent the
vibration signals in different running
conditions, which makes fault diagnosis
simpler and more accurate.
View1
1
2
3
4
5
6
04590 135 180 225 270
Sample Number
(a)
View3
1
2
3
4
5
6
04590 135 180 225 270
Sample Number
(c)
Ture
Predict
FIGURE 14 Diagnosis results on the NCEPU dataset using the constructed features of different
views and the constructed ensemble. (a) Diagnosis results of using the features constructed
on View1 (b) Diagnosis results of using the features constructed on View2 (c) Diagnosis
results of using the features constructed on View3 (d) Diagnosis results of using the constructed
ensemble.
1
2
3
4
5
6
45 90 135 180 225 270
Sample Number
(d)
1
2
3
4
5
6
04590 135 180 225 270
Sample Number
(b)
Ensemble
C. Diagnosis Results Using the
GP-Constructed Features and the
Constructed Ensemble
To analyze the effectiveness of the constructed
features of Figure 13(b) and
the built ensemble, Figure 14 shows
their diagnosis results and the results of
the built ensemble, where the blue box
represents the true label of the sample,
the red asterisks represent the predicted
label of the sample, and the class labels 1,
2, 3, 4, 5, and 6 represent the NOR, IRF,
ORF, REF, IOCF, and ROCF running
conditions, respectively. The overlap of
boxes and asterisks indicates that the
diagnosis is correct. No-overlapping of
boxes and asterisks indicates that the
diagnosis is wrong.
It can be seen from Figure 14(a) that
using the features constructed from
View1 for fault diagnosis will cause seven
View2
samples to be misclassified, where two
samples in the IRF class are identified as
the NOR class and five samples in the
REF class are identified as the IRF class.
Figure 14(b) shows the diagnosis results
of using the features constructed from
View2. It shows that two types of compound
faults are misclassified, i.e., two
samples in the IOCF class are classified
into the ROCF class and three samples
in the ROCF class are identified as the
IOCF class. Figure 14(c) shows the diagnosis
results of using the features constructed
from View3, where three samples
in the ORF class are identified as the
ROCF class. The diagnosis accuracy of
using the TDF, FDF, and TFDF based
constructed features are 97.40%, 98.14%
and 98.88%, respectively. The ensemble
diagnosis accuracy is obtained by integrating
the three diagnosis results via the
majority voting method and shown in
Figure 14(d), in which no samples are
misclassified. Obviously, the ensemble
strategy improves the diagnosis accuracy.
By analyzing the best models evolved
by MFCGPE, the feature construction
process is clearly displayed. In addition,
the visualization results and the diagnosis
results of the newly constructed features
are demonstrated for interpretability.
Owing to the program structure and the
new fitness function, MFCGPE constructs
a flexible number of diverse and
effective high-level features from different
views. The constructed features can
make the classification of different fault
types easier and more accurate. Owing
to the ensemble diagnosis strategy, MFCGPE
constructs multi-view features and
gains a higher diagnosis accuracy by
using an ensemble built from the features
constructed from different views.
VII. Conclusions
The goal of this paper was to develop a
new GP-based approach to achieving
effective fault types diagnosis of rolling
bearings using a small number of training
samples. This goal has been successfully
achieved by developing the
MFCGPE approach. A new GP program
structure, a function set, and a
terminal set were developed to enable
MFECPE to construct a flexible number
92 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
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IEEE Computational Intelligence Magazine - August 2021

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