IEEE Computational Intelligence Magazine - August 2021 - 81

1) A new program structure is developed
in MFCGPE to allow it to
construct high-level features from
multiple views. More importantly,
the number of constructed features
can be adaptively determined without
being pre-defined.
2) A new fitness function based on
accuracy and distance is proposed in
MFCGPE to enable the constructed
features to be accurate and discriminative
when the number of training
samples is small. The new fitness
function is able to maximize the
classification performance and the
inter-class distances of training samples,
and minimize the intra-class
distances of training samples.
3) An ensemble is created using the features
constructed by MFCGPE from
multiple views and using KNN to
make predictions for unseen test samples.
Using ensemble for classification
can further improve the generalization
performance, particularly when the
number of training samples is small.
4) A new intelligent diagnosis approach,
namely MFCGPE, is developed to
achieve effective fault diagnosis of rolling
bearings with the use of a small
number of training samples. MFCGPE
can achieve better results than 19 competitive
methods on three datasets. Specifically,
MFCGPE can achieve a
maximal and average accuracy of 100%
and above 99% on three fault datasets
with only five training samples per class.
The rest of this paper is organized as
follows: Section II briefly introduces the
GP algorithm and reviews its applications
on feature construction and fault diagnosis.
Section III describes the MFCGPE
approach in detail. Section IV designs the
experiments. The experimental results are
analyzed and compared in Section V. Section
VI further analyses the proposed
approach. Section VII presents conclusions
and future work.
II. Background and Related Work
A. Genetic Programming (GP)
Unlike other EC techniques such as
genetic algorithms (GAs) that have a
fixed-length representation, GP has a
End
FIGURE 2 Evolutionary process of GP.
variable-length representation [40]. An
individual of GP is typically represented
using a tree-based structure, as shown in
Figure 1. This example tree/program
consists of internal nodes (the functions
or operators selected from the function
set) and leaf nodes (the arguments or
constants selected from the terminal set).
This example tree can be mathematically
expressed as () (),yx
58 2'#
++
where +, ×, and ' (protected division,
return 0 if the divisor is 0) are the internal
nodes, and x, y, 2, 5, and 8 are the
leaf nodes. This equation can also be
treated as a newly constructed feature,
where x and y are two original features.
GP can automatically select functions
from the function set and terminals from
the terminal set to evolve the best trees
for solving a task via an evolutionary process.
Figure 2 shows the overall evolutionary
process of GP. First, a population
of computer programs are randomly initialized
in the search space. Then, each
individual (program) in the population is
evaluated using a fitness function and
assigned a fitness value. At each generation,
a new population of individuals are
Start
Initial Population
generated using genetic operators, i.e.,
Elitism, Crossover, and Mutation operators.
The Elitism operation is to copy the best
individuals from the current generation
to the next generation. A number of
individuals are selected based on their
fitness values via Tournament selection to
be used as parents to generate new
individuals using Crossover and Mutation
operators. The Crossover operation
is to exchange the subtrees of two
parents to generate new offspring.
The Mutation operation is to randomly
delete a subtree of the parent and
grow a new subtree from that node. The
new population of individuals are evaluated
and evolved generation by generation.
When a termination criterion is
+
÷
+
×
52 x
y
8
FIGURE 1 An example program of GP.
Generate New Population
Crossover
Fitness Function
No
Terminate
Yes
Best Individual
Mutation
Elitism
AUGUST 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 81
IEEE Computational Intelligence Magazine - August 2021

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