IEEE Computational Intelligence Magazine - August 2021 - 82

satisfied, the evolutionary process stops,
and the best individual is obtained.
B. GP for Feature Construction
In recent years, many GP based feature
construction methods have been proposed,
in which the arithmetic and logical
operators are usually used as
the
function set, and the low-level features
are usually used as the terminal set.
Otero et al. [41] used information gain
ratio as the fitness function of GP to
construct features. Muharram et al. [42]
comprehensively compared four different
fitness functions based on information
gain in GP for feature construction.
Guo et al. [43], [44] used the Fisher criteria
and its improved version as the fitness
function of GP. Neshatian et al.
[45] proposed a multiple feature construction
method for symbolic learning
classifiers, where the constructed features
are evaluated by a fitness function
that maximizes the purity of the class
interval. The above methods belong to
the filter-based feature construction
methods. Guo et al. [36] proposed a
method based on GP and KNN to classify
EEG signals, which achieved a classification
accuracy of 99% on one
dataset. Bi et al. [37] proposed a GP
method combined with image-related
operators and SVM for image classification,
which obtained better accuracy
than the deep learning methods on
some datasets. Aslam et al. [38] combined
GP and KNN for automatic
modulation classification, and the method
achieved better classification performance.
The above methods belong to
the wrapper-based feature construction
methods. Tran et al. [46] developed a fitness
function using the classification
accuracy and a distance measure to
improve the performance of the constructed
features on high-dimensional
data classification tasks and discussed the
impact of the number of constructed
features on classification accuracy. Ma et
al. [47] designed a hybrid fitness function
that combined information gain
ratio and the error rate of a classification
algorithm, and proposed a feature construction
strategy that obtained multiple
high-level features using a single GP.
C. GP for Fault Diagnosis
To the best of our knowledge, GP has
rarely been applied to fault diagnosis of
mechanical equipment. In [48], GP was
used as a binary classifier for fault diagnosis
of rolling bearing. The classification
performance of GP with the use of
statistical features, spectral features, and
the combination of statistical and spectral
features are compared. The results
showed that the combined features
achieved better fault classification accuracy.
Guo et al. [49] proposed a GPbased
rolling bearing fault diagnosis
method, in which a fitness function
based on Fisher criteria was developed
to enable GP to construct the high
order of moments of vibration signals as
informative features. This method used
two classification algorithms for multiclass
fault classification. Xuan et al. [50]
proposed a gear fault diagnosis method
that combines GP and SVM, where a
distance measure based fitness function
was developed and the power spectral
features of vibration signals were used to
construct high-level features. These two
methods only construct a single feature
for fault diagnosis, which may not be
effective when the machine working
conditions become more complicated.
In summary, although these methods
successfully show that GP offers possibilities
for dealing with fault diagnosis,
there are still some problems that need
to be addressed. The GP based feature
construction methods in [45]-[47] have
discussed the effect of the number of
constructed features on classification
performance. However, these methods
set the number of constructed features
according to prior knowledge and multiple
trials, therefore the adaptability of
them is poor. The GP based fault diagnosis
method in [48]-[50] only used the
features of a single view for feature construction.
However, since the features of
different views have both internal relations
and interval differences, using only
single view features may ignore the
characteristics of the samples. Moreover,
these GP based fault diagnosis methods
use sufficient training data to construct
features and perform classification and
do not consider the scenario of a small
82 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
number of training samples. In general, a
small number of training samples can
not well represent the class distribution
information comprehensively and often
leads to poor generalization performance.
To address the above issues, this
paper proposes a new GP based fault
diagnosis approach (i.e., MFCGPE) to
adaptively construct a flexible number
of informative features from multiple
views for representing sample comprehensively,
and create an ensemble using
these constructed features for effective
fault diagnosis with the use of a small
number of training samples.
III. The Proposed Approach
In this section, the details of the MFCGPE
fault diagnosis approach will be
introduced, including the algorithm
overview, the program structure, the
function set, the terminal set, the fitness
function, and ensemble construction for
fault diagnosis.
A. Overview of MFCGPE
Figure 3 shows the overall structure of
MFCGPE to rolling bearing fault diagnosis
with a small number of training
samples. First, the collected vibration
signals of rolling bearings are transformed
into three different-view features
by calculating the statistical values
of time waveform and frequency spectrum.
The 16 time-domain features
(TDF), the 13 frequency-domain features
(FDF), and the combination of
TDF and FDF (named TFDF features)
are represented by View1, View2, and
View3, respectively. Second, the transformed
data set is divided into the training
set and the test set, and three
independent GPs are utilized to construct
high-level features of each singleview
feature set, respectively. The
program structure and the function set
used for feature construction from different
views are the same, but the terminal
set is different. Only the training set
is used for the evolutionary process of
GP to construct high-level features that
are expected to have a small intra-class
distance and a large inter-class distance
for effective fault diagnosis. Third, the
constructed features are provided as the
IEEE Computational Intelligence Magazine - August 2021

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - August 2021
