Page 112 - IJOCTA-15-4

Zhang et al. / IJOCTA, Vol.15, No.4, pp.649-669 (2025)
is based on the evaluation criteria in the time– Let τ denotes the scale factor. When τ = 1,
frequency domain, and its core is to ensure that y j (1) represents the original time series. For non-
the unique characteristics of each IMF component zero values of τ, the original sequence is seg-
are fully reflected and identified in the time do- mented into coarse-grained vectors y j (τ), each
main. At the same time, the algorithm also takes with a length of N/τ.
into account the relationship between these com- The fuzzy entropy of the sequence is then
ponents and the original signal in the frequency computed at each scale τ, and the resulting values
domain, thus ensuring the comprehensiveness and are referred to as the MFE.
accuracy of the analysis. Through this method, a
complex signal can be effectively decomposed into τ τ
MFE(x, τ, m, n, r, N) = FuzzyEn(y , m, n, r, N )
a series of IMF components with physical signif-
(9)
icance, providing a more accurate tool for signal
Due to the high complexity of vibration sig-
processing and analysis.
nals in rotating machinery and the diversity of
This procedure enhances the discrimination
fault types, a single-scale fuzzy entropy is insuffi-
by mitigating any impact of the interfering factors
cient to capture the full extent of the fault-related
and facilitating the identification of spurious IMF
information. The complexity and richness of fault
components that do not embed fault information.
characteristics cannot be effectively represented
Additionally, it mitigates the impacts of unrelated
at a single scale, leading to incomplete feature
modal components on fault information and min-
extraction. Therefore, this study employs MFE
imizes the influence of human factors associated as the method for signal feature extraction. 27 By
with the setting of threshold values, thereby en- analyzing the signal over multiple scales, MFE ef-
hancing the accuracy of fault feature extraction.
fectively overcomes the limitations of single-scale
approaches and provides a more comprehensive
characterization of the signal complexity under
various operating conditions.
2.4. Multiscale fuzzy entropy algorithm
By mapping the original signal into a high- 2.5. Golden sine
dimensional space, describing the signal’s com- subtraction-average-based
plexity using high-dimensional vectors within the optimizer–back-propagation neural
amplitude tolerance, and defining the similar- network
ity between the signals using a fuzzy function,
2.5.1. Subtraction-average-based optimizer
fuzzy entropy produces more accurate and real- algorithm
istic computation results. Nevertheless, the con-
An intelligent optimization technique based
ventional fuzzy entropy only uses one scale to de-
on mathematical principles is the subtraction-
scribe the signal complexity, which could result in
average-based optimizer (SABO) algorithm. Its
the loss of crucial signal information and compro-
fundamental idea is that the subtraction average
mise the precision of fault feature extraction. By
of the group members is responsible for updat-
extracting the signal’s fuzzy entropy value from ing the locations of fellow group members within
several scales, MFE can more thoroughly capture the search space. In addition to reducing reliance
the signal’s characteristic information, increasing on a particular candidate, the algorithm success-
the precision of defect diagnosis. 22
fully avoids settling into local optima, enhanc-
The specific calculation process of MFE is as ing its global search capability and optimization
22
follows : effectiveness. 28
Coarse-graining of the original sequence. For
the original time series (X i = {x 1 , x 2 , ..., x N }) of 2.5.2. Golden sine subtraction-average-based
length N, under the condition that the embedding optimizer
dimension (m) and the similarity tolerance (r) are The SABO algorithm updates particle positions
given in advance, the coarse-grained processing of using the subtraction average method. To avoid
the series is carried out. The new coarse-grained getting trapped in local optima, this study en-
vector is: hanced the SABO algorithm by leveraging the
advantages of the golden sine algorithm in global
optimization. In instances where the fitness val-
jτ ues of particles were stable across iterations in the
1 X N
yj(τ) = x i , 1 ≤ j ≤ (8) SABO algorithm, the golden sine algorithm is in-
τ τ
i=(j−1)τ=1 voked to adjust particle positions. The precise
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