Abstract
Currently, study on the relevant methods of variational mode decomposition (VMD) is mainly focused on the selection of the number of decomposed modes and the bandwidth parameter using various optimization algorithms. Most of these methods utilize the genetic-like algorithms to quantitatively analyze these parameters, which increase the additional initial parameters and inevitably the computational burden due to ignoring the inherent characteristics of the VMD. From the perspective to locate the initial center frequency (ICF) during the VMD decomposition process, we propose an enhanced VMD with the guidance of envelope negentropy spectrum for bearing fault diagnosis, thus effectively avoiding the drawbacks of the current VMD-based algorithms. First, the ICF is coarsely located by envelope negentropy spectrum (ENS) and the fault-related modes are fast extracted by incorporating the ICF into the VMD. Then, the fault-related modes are adaptively optimized by adjusting the bandwidth parameters. Lastly, in order to identify fault-related features, the Hilbert envelope demodulation technique is used to analyze the optimal mode obtained by the proposed method. Analysis results of simulated and experimental data indicate that the proposed method is effective to extract the weak faulty characteristics of bearings and has advantage over some advanced methods. Moreover, a discussion on the extension of the proposed method is put forward to identify multicomponents for broadening its applied scope.
Highlights
Variational Mode Decompositionvariational mode decomposition (VMD) is a new technique for adaptive signal decomposition with nonrecursively sifting structure, which can divide a real-valued signal f(t) into K meaningful modes uk(t), k ∈ (1, 2, . . . , K). e overall framework of VMD is a variational constraint model, which minimizes the bandwidth of each estimated mode
[4, 5], wavelet transform [6], spectral kurtosis-based method [7,8,9,10], time-frequency analysis [11, 12], and the adaptive signal decomposition methods [13, 14]
The time-frequency representation (TFR) of the raw mechanical signal is obtained by short-time Fourier transform (STFT). en, the envelope negentropy spectrum (ENS) is constructed based on the results of TFR. ird, use the variational mode decomposition (VMD) method to extract the faulty modes on the basis of initial center frequency (ICF) located by ENS
Summary
VMD is a new technique for adaptive signal decomposition with nonrecursively sifting structure, which can divide a real-valued signal f(t) into K meaningful modes uk(t), k ∈ (1, 2, . . . , K). e overall framework of VMD is a variational constraint model, which minimizes the bandwidth of each estimated mode. VMD is a new technique for adaptive signal decomposition with nonrecursively sifting structure, which can divide a real-valued signal f(t) into K meaningful modes uk(t), k ∈ E overall framework of VMD is a variational constraint model, which minimizes the bandwidth of each estimated mode. Assume that each mode has a finite bandwidth with its individual CF, the optimization algorithm of alternating direction multiplier method [31] is adopted to solve the variational constraint model. E model of VMD is constructed as. L(uk, ωk, λ) is solved by the alternate direction multiplier method to search its saddle point. E optimization process mainly contains that the meaningful modes and their CFs are updated by modulating each mode to the corresponding baseband. The detailed procedure of VMD is written as follows. In which ε is the tolerance value of the converging judgment that is set as 10− 7 typically
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