IEEE Computational Intelligence Magazine - August 2021 - 80

have been developed for rolling bearing
feature analysis and fault diagnosis. These
methods extract various types of features
from the vibration signals and use traditional
classification algorithms to perform
fault diagnosis [10]. The commonly
used features include simple statistical
features of time-domain and frequencydomain,
and the non-linear evaluation
indicators, such as fractal dimension [11],
Lyapunov exponent [12], and entropybased
features [13]-[15]. Typically, a large
number of features are extracted to
describe the vibration signal and these
features may contain redundant or irrelevant
features, which may reduce the fault
diagnosis accuracy. Therefore, feature
selection methods, such as max-relevance
and min-redundancy [16], ReliefF [17],
Laplacian score [18], principal component
analysis [19], local discriminant
analysis [20], and margin fisher analysis
[21], have been employed to select a subset
of important features for effective fault
diagnosis. To further improve the fault
diagnosis performance, different classification
methods have been explored for
different tasks, including k-nearest neighbor
(KNN) [22], artificial neural network
(ANN) [23], extreme learning
machine (ELM) [24], and support vector
machine (SVM) [25]. However, these
methods typically contain several steps of
signal processing, feature design, feature
selection, and classifier learning. These
steps need to be appropriately connected
to achieve accurate fault diagnosis. In
addition, most of these steps require
domain expertise, which causes the diagnosis
method to be effective only on a
specific fault diagnosis task and unable to
be generalized to other even similar tasks.
Deep learning is an advanced machine
learning approach that has been applied
to fault diagnosis [26], [27]. Most deep
learning methods are based on neural networks
(NNs). Different types of neural
networks, such as deep belief networks,
sparse autoencoders, and convolutional
neural networks, have also been developed
for effective fault diagnosis [28]-
[30]. These methods can automatically
learn features from the vibration signals
and train classifiers for effective fault diagnosis.
However, the NN-based methods
often use a large number of training samples
to build models/classifiers for fault
diagnosis. In real-world scenarios, the
training samples are often difficult to
obtain and require extensive manual effort
to label. Furthermore, designing an effective
architecture for the NN model typically
requires
rich expertise in the
problem and NN domains. Therefore, it is
necessary to develop a new intelligent
fault diagnosis method that can achieve
good performance using a small number
of training samples.
Typically, the feature quality is important
for effective rolling bearing fault
diagnosis. Traditional methods use many
ways, such as signal processing, feature
selection, and feature learning, to improve
the quality of the extracted features [15],
[21], [25]. Feature construction is an
effective way to generate new informative
and high-level features from the
original low-level features [31]. As shown
in existing work [11]-[15], the features
of vibration signals can be extracted from
multiple views and each view represents
different characteristics. However, feature
construction, particularly constructing
features from multiple views, which can
create informative features to improve
the fault diagnosis, has not been extensively
explored in this field.
Evolutionary computation (EC) methods
ordinarily do not use extensive
domain knowledge to find solutions and
have been successfully applied to many
difficult problems [32]-[34]. Genetic programming
(GP) is an EC technique that
has been widely used as one of the most
popular feature construction methods [31],
[35]. Unlike other EC methods, which use
a fixed-length representation, GP has a
variable-length tree-based representation,
enabling it to automatically construct
high-level features from low-level features
in a more flexible way [35]. For feature
construction, GP typically evolves models
that consist of a set of operators (such as +,
− and ×) and the original features. The
original features are operated by these
operators and new features are then generated.
The tree-based solutions of GP
potentially have high interpretability to
provide insights into what features are
important for construction and why the
80 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
constructed features are effective. Owing
to these advantages, many GP methods
have been developed to feature construction
in various problems and achieved
promising results [36]-[38].
However, existing GP methods need
several improvements to construct effective
features for fault diagnosis using a
small number of training samples. First,
the features extracted from the vibration
signals can be multiple views, such as
time-domain view and the frequencydomain
view [39]. Each view represents
different characteristics of the data.
Existing methods often simply concatenate
all the features from different views,
which may not be effective. GP has seldom
been developed for constructing
high-level features from different views
(i.e., multi-view feature construction).
Second, existing fitness measures of GP
for feature construction often use classification
accuracy, which may cause the
overfitting issue, particularly when the
number of training samples is small.
Third, the generalization performance
of the features constructed by GP can
be further improved by constructing
ensembles of classifiers for classification.
However, this has seldom been explored.
Therefore, this paper develops a new GP
approach to address these limitations.
The goal of this paper is to propose a
new intelligent approach, i.e., multiview
feature construction based on GP
with the idea of ensemble learning
(hereafter called MFCGPE), to rolling
bearing fault diagnosis using a small
number of training samples. The proposed
approach is able to construct a
flexible number of high-level features
from every single view and build an
effective ensemble using the constructed
multi-view features to achieve high generalization
performance when the number
of training samples is small. The
performance of MFCGPE will be tested
on three datasets of varying difficulty
and compared with 19 competitive
methods. Further analysis will be conducted
to show the effectiveness of the
constructed features and the ensemble.
The main contributions of this
paper are summarized in the following
four aspects.
IEEE Computational Intelligence Magazine - August 2021

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