Warped Variational Mode Decomposition With Application to Vibration Signals of Varying-Speed Rotating Machineries

Recently, a powerful signal processing technique called variational mode decomposition (VMD) has drawn a great interest in various applications. The VMD assumes that the signal components are narrowly banded and separated in the frequency domain. Therefore, it cannot analyze wideband nonstationary signals with spectrum-overlapped components. To address this issue, a novel scheme called warped VMD (WVMD) is proposed in this paper. The WVMD includes the following steps. First, the phase function of a certain signal component is accurately estimated by optimizing a spectrum concentration index. Next, the time-warping principle is used to transform the original signal to a warped one in the phase coordinate where the spectrums of the components are well separated. Then, the conventional VMD can be used to effectively decompose the warped signal. Finally, the obtained signal components (of the warped signal) can be taken back to the time coordinate by the inverse warping operation. The WVMD works well in noisy environments and can even decompose signals with very close components. The effectiveness of the WVMD is validated by some simulated signals, a bat echolocation signal, and applications to real-life vibration signals of a rotor test rig and a hydroturbine.