IEEE Computational Intelligence Magazine - August 2021 - 88

NOR
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FIGURE 9 Time domain waveform of vibration signals under ten running conditions in CWRU.
FIGURE 10 XJTU test rig.
the input features to construct highlevel
features. The constructed features
are used as the inputs of the KNN classifier
for fault classification. Two types
of GP based methods are used, i.e., the
TABLE VI Description of the XJTU dataset.
CLASS LABEL
1
2
3
4
RUNNING CONDITION
Normal
Inner ring fault
Outer ring fault
Cage fault
GPS methods (using GP to construct a
single feature) and the GPM methods
(using GP to construct multiple features).
The fitness function of these
methods is the same as MFCGPE. The
comparisons can investigate the effect
of the number of constructed features
on diagnosis accuracy. The GPS/GPMTDF,
GPS/GPM-FDF, and GPS/
GPM-TFDF methods use the TDF,
FDF, and TFDF features for feature
construction, respectively. According to
[46], the number of features constructed
by the GPM based methods is the
same as the number of the classes in
the dataset. For example, GPM-TDF,
GPM-FDF, and GPM-TFDF construct
10 new features for classifying the
CWRU dataset with 10 classes. The
comparisons aim to investigate whether
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TEST SAMPLES
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MFCGPE can outperform other GP
based feature construction methods
that construct features.
The fourth category of the comparison
methods are three ensemble diagnosis
methods (i.e., OFE, GPSE, and
GPME). These methods use three
KNNs as base classifiers and the majority
voting algorithm to build an ensemble.
In OFE (i.e., ensemble using the
original features), the TDF, FDF, and
TFDF features are fed into three KNNs,
respectively. In GPSE (i.e., ensemble
using the features constructed by GPS),
the features constructed by GPS-TDF,
GPS-FDF, and GPS-TFDF are fed into
three KNNs to build an ensemble. In
GPME (i.e., ensemble using the features
constructed by GPM), the features constructed
by GPM-TDF, GPM-FDF, and
GPM-TFDF are fed into three KNNs,
respectively. The comparisons aim to
investigate whether MFCGPE can beat
the ensemble diagnosis methods that use
the original features and the features
constructed by GP.
C. Parameter Settings
In MFCGPE, the GP related parameters
are common settings and refer to those
in [56]. The population size and the
maximal number of generations are set
as 100 and 50, respectively. The rates of
crossover, mutation, and elitism are set as
0.8, 0.19 and 0.01, respectively. The tree
depth is between 2-6. The tree generation
method is ramped half-and-half.
The tournament selection with size 5 is
used to select parents for crossover and
mutation operations. The parameters of
the GP based comparison methods are
the same as MFCGPE.
The GP based methods are implemented
using DEAP [57] and the classification
algorithms are implemented
using scikit-learn [58]. The number of
the neighbors in KNN is set as 3
according to [22]. The parameters in
the classification algorithms are the
default values of the scikit-learn package.
The parameter values of the methods
using manually extracted features
are set according to [14], [15], [25].
Each method has been executed 30
independent runs on each dataset with
88 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
Amplitude (m/s2)
IEEE Computational Intelligence Magazine - August 2021

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