IEEE Computational Intelligence Magazine - August 2021 - 84

the terminal set contains 16 statistical
features
+
TT ,116 which are extracted
through performing the simple mathematical
calculation on the amplitude of
the raw vibration signals [25]. Table II
lists the terminal set used under View1,
where s(i) represents the time signal,
and N represents the number of the signal
data points. TT
116
+
represent the
vibration signal's mean value, standard
deviation, square root amplitude, absolute
mean value, skewness, kurtosis,
Output
Output
FC2
Feature Combination
Feature Construction
Input
+
×
T T8
1
T5
×
T14 T3
FIGURE 4 Program structure of MFCGPE (left) and an example program (right) that can be
evolved by MFCPGE.
TABLE I Function set of GP.
SYMBOL
INPUT
+
−
×
'
FC2
FCm
2 Features
2 Features
2 Features
2 Features
2 Features
2 Vectors or 1 Vector/Feature
TABLE II Terminal set corresponding to View1.
SYMBOL
T1
FORMULA
N
1 si
i
=1
N / ()
T2
T3
T4
T5
T6
T7
T8
N- 1 i =1
1
1 / [( )]si T 2
-
N
1
eo/N i =1
N
si
1 / si
N i =1
N
()
1 / si
N i =1
N
(( ))3
1 / si
N i =1
N
(( ))4
1 / si
N i =1
N
(( ))2
ma ()x si
()
T12
T13
T14
T15
T16
2
T11
T
T
+
T5
-
T4 T14
2
÷
×
T T7
FCm
-
÷
T9 T11
variance, maximum value, minimum
value, peak-to-peak value, waveform
index, peak index, pulse index, margin
index, skewness index and kurtosis
index, respectively.
For View2 (only consider the frequency-domain
characteristics of rolling
bearing signals), the terminal set contains
13 statistical features
FF ,113
+
which are extracted through performing
the mathematical calculation on the
amplitude of frequency spectrum that
was obtained through Fast Fourier
Transform for the vibration signals [25].
Table III lists the terminal set used
under View2, where ()
fj represents the
frequency spectrum of time signal s(i),
M represents the number of spectrum
lines, and Aj
represents the frequency
value of the jth spectrum line. F1 represents
the energy of the vibration signal
in frequency-domain, FF
25
613
the position variation of the main frequency
band, and FF
OUTPUT
1 Feature
1 Feature
1 Feature
1 Feature
1 Vector
1 Vector
DESCRIPTION
Addition
Subtraction
Multiplication
Protected division
Concatenation
Concatenation
+ represent the
concentration and dispersion of the frequency
spectrum.
For View3 (considering both the timedomain
and frequency-domain characteristics
of rolling bearing signals), the terminal
set contains 29 features (TF TF
129) com+
posed
by the features of View1 and View2,
where the features TF TF
116 are equal to
+
the features TT
tures TF TF17
113
+
tures FF
SYMBOL
T9
T10
FORMULA
mi ()n si
TT
-
4
2
F
T
F
T
T
T
2
8
4
8
3
8
()T
T
5
7
()T
T
6
7
89
116
+ in View1, and the fea29
are equal to the fea+
in View2. There are two
3
2
reasons for using TDF features and FDF
features to form the multi-view features.
One is that the extraction of TDF and
FDF features is simple statistical calculations,
while the extraction of the time-frequency
domain features typically needs
complicated signal processing operations
and manual participation. The
other is that [48] shows that using the
combination of the TDF and FDF features
for feature construction is effective
for constructing new features. Different
from most of the existing works, the
proposed method constructs features
from these three views, individually,
which aims to generate a group of
effective and diverse features to comprehensively
describe a sample. The
effectiveness and diversity of the constructed
features can also improve the
84 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
+ represent
IEEE Computational Intelligence Magazine - August 2021

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