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Rolling bearing fault diagnosis method based on GJO–VMD, multiscale fuzzy entropy, and GSABO–BP...
typically demands extensive prior experi- component, thereby facilitating adaptation. For
ence and incurs high computational costs, more information, please refer to the article by
thereby reducing the influence of human Dragomiretskiy and Zosso. 17
subjectivity. Moreover, by integrating a
comprehensive evaluation factor method,
2.2. Selection of key decomposition
the IMFs’ features that are most sensitive
parameters for variational mode
to signals can be reliably selected, ensuring decomposition based on golden jackal
the accuracy of subsequent feature extrac- optimization
tion.
(ii) The MFE is capable of capturing the com- Based on the social interaction behavior and hunt-
plexity of a signal across multiple scales by ing behavior of golden jackals, a population intel-
computing its fuzzy entropy at each scale. ligence optimization method, GJO (also known
When applied to VMD-reconstructed sig- as Asian jackals), has been derived. The algo-
nals, MFE benefits from the effective sup- rithm mimics the process of individuals working
pression of noise and irrelevant compo- together and competing to discover the best an-
nents, enhancing the precision of entropy swer during golden jackals’ eating and hunting
calculation. The integration of VMD and activities. The article by Chopra and Ansari 21
MFE thus significantly improves the ro- provides a thorough description of the theory of
bustness and accuracy of signal feature ex- GJO.
traction.
2.2.1. Determining the fitness function
(iii) The MFE values computed at designated
scale factors are used as quantitative The fitness function plays a critical role in guid-
feature parameters and are subsequently ing the parameter optimization process of the
input into a Bo–XGBoost classification VMD algorithm through artificial intelligence-
model. This hybrid framework enables ac- based search algorithms. This function measures
curate classification of rolling bearing fault the effectiveness of the VMD in the current pa-
types. Compared with conventional fault rameter settings and subsequently updates the
classification models and signal decompo- parameters based on these results to enhance
sition techniques, the proposed method overall effectiveness. Envelope entropy evaluates
demonstrates superior diagnostic perfor- the degree of disorder in the signal and effectively
mance, even under small-sample condi- reflects the proportion of random components. A
tions. higher envelope entropy indicates a greater pres-
ence of random components, while a lower en-
In the following section, the basic theory is
velope entropy suggests a more ordered signal
explained in Section 2, the framework of the pro- 24
structure.
posed method is provided in Section 3, and Sec-
In the case of rolling bearing faults, periodic
tion 4 validates the performance of the GJO–
impacts generated by faults make the signal more
VMD in signal decomposition and correct selec-
orderly, leading to a reduction in envelope en-
tion of IMF components using the evaluation fac-
tropy. Compared to other fitness functions, en-
tor algorithm. In Section 5, the proposed method
velope entropy is an optimal choice due to its
is further applied in a real-world rolling bear-
stronger global search capability and robustness,
ing fault detection application. To conclude the
making it better suited to adapt to complex and
study, in Section 6, the main findings are summa-
rized. changing environments while also offering higher
optimization efficiency. 25 The envelope entropy is
determined to be the fitness function in this study,
2. Basic theory
as it not only ensures the proper combination of
2.1. Variational mode decomposition VMD parameters to achieve fidelity and reliabil-
algorithm ity of the decomposition results but also enhances
the robustness of the algorithm.
The VMD algorithm models the signal as a varia-
tional problem and iteratively updates each com-
M
ponent to obtain an optimal solution, extend- X
E(m) = − [p n (n) log 2p n (m)] (1)
ing the classic Wiener filter to multiple adap-
tive bands. The signal is decomposed into m=1
IMF components with different center frequen- M
X
cies and bandwidths, iteratively repeating the p n (m) = a n (m)/ a n (m) (2)
center frequency and bandwidth for each modal
m=1
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