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Rolling bearing fault diagnosis method based on GJO–VMD, multiscale fuzzy entropy, and GSABO–BP...























































            Figure 3. A flowchart illustrating the steps in the proposed fault diagnosis method
            Abbreviations: BP: Back propagation; GJO: Golden jackal optimization; GSABO: Golden sine
            subtraction-average-based optimizer; IMF: Intrinsic mode functions; VMD: Variational mode decomposition.



















                                 Figure 4. Time-domain waveform of the simulated signal y(t)


            the fault characteristic frequency proved challeng-  the GJO algorithm. Specifically, the search range
            ing. Therefore, the VMD method was employed       for K was set to [2, 7], and for α, it is set to [100,
            to decompose the aforementioned signal. 29        5000]. Envelope entropy was adopted as the fit-
                                                              ness function to guide the optimization of both
                During the VMD decomposition process, the
                                                              parameters.
            key parameters—K and α—were optimized using
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