IEEE Systems, Man and Cybernetics Magazine - January 2023 - 20
features by WPD, as shown in Supplementary Figure 1 available
at https://doi.org/10.1109/MSMC.2022.3218424. In this
article, we use the wavelet transform to preprocess the
bearing monitoring signals, and the change in energy distribution
is described by the energy entropy. The balanced
binary tree structure of Supplementary Figure 1
available at https://doi.org/10.1109/MSMC.2022.3218424 is
obtained by the WPD decomposition of the lower and
higher frequency bands [14].
In our previous work [15], a preprocessing model for
bearing feature extraction is proposed that uses wavelet
packet empirical mode decomposition to extract the feature
parameters. The bearing monitoring signal is processed
by the wavelet packet and then decomposed by the
empirical mode. In this article, the wavelet transform is
consistent with our previous work.
We use three-layer WPD to denoise and decompose the
collected vibration signal. Eight waveforms are obtained
and designated as
xt xt xt^^ fhh ^ h We use the energy
3
1
3
2
3
8
.
entropy to describe the change in the energy distribution.
The energy and the entropy of each subband can be calculated
as follows:
N
Et =
j
i
^ hh^ ^| hxt 2
n 1
j
i
=
where i j is the number of wavelet coefficients, and N
is the length of the signal
xt .^h The signal is decomj
i
posed
into j levels, resulting in j2 mutually orthogonal
subspaces. Mathematically, the signal frequency
component energy of node (J, n) can be calculated by
the following equation:
The output of each neuron is obtained from (4), where
f is the activation function. The activation function of
x1
y1∗
x2
Ey y 2=-^h|
rdjj
j
2
1
y2∗
x3
Input Layer
Multiple
Hidden Layers
(a)
Input x
Encoder
f
Code y
Decoder
g
Output x~
Reconstruction
Error J
https://www.doi.org/10.1109/MSMC.2022.3218424
https://www.doi.org/10.1109/MSMC.2022.3218424
https://www.doi.org/10.1109/MSMC
IEEE Systems, Man and Cybernetics Magazine - January 2023
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