IEEE Computational Intelligence Magazine - August 2021 - 83

inputs of classification algorithms for
fault diagnosis. We use the features constructed
from each view to feed three
classifiers/KNNs individually, which are
combined via majority voting to form
an ensemble to make a good prediction
for the unseen test set.
B. Program Structure
To enable MFCGPE to construct a flexible
number of high-level features, a
new program structure with the input,
feature construction, feature combination,
and output layers are developed
based on strongly-typed GP (STGP)
[51]. These layers are connected in a
bottom-up manner. Each layer has a
specific function and type constraint.
The input layer takes the original features
as inputs, which are the terminals
of GP. The feature construction layer
transforms the original features into
high-level features. The feature combination
layer combines multiple constructed
features into a vector to
comprehensively describe the sample.
The output layer returns the constructed
feature vector as outputs for fault
diagnosis. The tree depths of the input
and output layers are one, and those of
the feature construction and feature
combination layers are automatically
adjusted according to the given task.
Figure 4 shows the program structure
and an example program of MFCGPE,
respectively. This example program represents
a feature vector containing three
constructed features. The detailed
description of the operators and the terminals
will be described in the following
subsections.
C. Function Set
The function set of MFCGPE is composed
of two types of operators, i.e., the
feature construction operators and the
feature combination operators. Table I
lists the detailed information of the
function set. Four arithmetic operators
including +, −, ×, and ' are for feature
construction, where ' is protected by
returning 0 if the divisor is 0. The inputs
of +, −, ×, and ' operators are two features,
and the output of them is a new
feature. It should be noted that their
outputs/features can be further used for
feature construction. To achieve feature
combination, two new operators (FC2
and
FC )m
are designed to combine
multiple features into a vector, where
the inputs of FC2
the inputs of FCm
are two features, and
can be one feature,
one vector, or two vectors. The use of
these feature combination operators
enables MFCGPE to adaptively construct
multiple high-level features
without presetting the number of constructed
features.
D. Terminal Set
The terminal set of MFCGPE is composed
of the low-level features extracted
from the vibration signals. The
terminal sets for feature construction
from different views are different. For
View1 (only consider the time-domain
characteristics of rolling bearing signals),
Vibration Signal
S1
S2
Multi-View Feature Set
16 View1 Features
Sp
Sq
29 View3 Features
13 View2 Features
Step 1: Original Feature Extraction
Train Set
S1
Sm
. . .
. . .
. . .
. . .
Evolutionary Learning
GP1
GP2
GP3
Best Model
. . .
. . .
S1
Sn
. . .
. . .
Test Set
. . .
. . .
. . .
. . .
T1×16 F1×13 TF1×29
Tp×16 Fp×13 TFp×29
Tq×16 Fq×13 TFq×29
Step 2: Multi-View Feature Construction
Training Set and Test Set With the Constructed Features
Classifier 1
Classifier 2
Majority Voting
Final Diagnosis
Step 3: Ensemble Diagnosis
FIGURE 3 Overall structure of the MFCGPE fault diagnosis approach.
Classifier 3
AUGUST 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 83
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IEEE Computational Intelligence Magazine - August 2021

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