A Modified Complex Variational Mode Decomposition Method for Analyzing Nonstationary Signals with the Low-Frequency Trend

Abstract

Complex variational mode decomposition (CVMD) has been proposed to extend the original variational mode decomposition (VMD) algorithm to analyze complex-valued data. Conventionally, CVMD divides complex-valued data into positive and negative frequency components using bandpass filters, which leads to difficulties in decomposing signals with the low-frequency trend. Moreover, both decomposition number parameters of positive and negative frequency components are required as prior knowledge in CVMD, which is difficult to satisfy in practice. This paper proposes a modified complex variational mode decomposition (MCVMD) method. First, the complex-valued data are upsampled through zero padding in the frequency domain. Second, the negative frequency component of upsampled data are shifted to be positive. Properties of analytical signals are used to get the real-valued data for standard variational mode decomposition and the complex-valued decomposition results after frequency shifting back. Compared with the conventional method, the MCVMD method gives a better decomposition of the low-frequency signal and requires less prior knowledge about the decomposition number. The equivalent filter bank structure is illustrated to analyze the behavior of MCVMD, and the MCVMD bi-directional Hilbert spectrum is provided to give the time–frequency representation. The effectiveness of the proposed algorithm is verified by both synthetic and real-world complex-valued signals.

Research on the Rotor Fault Diagnosis Method Based on QPSO-VMD-PCA-SVM

“…Dragomiretskiy and Zosso (2014) proposed a completely nonrecursive signal decomposition method, the VMD algorithm. Compared with signal time-frequency domain analysis methods such as EMD, ensemble empirical mode decomposition (EEMD), and wavelet decomposition, VMD breaks away from the common thinking pattern of progressive recursive decomposition and transforms it into solving constrained variational problems, which can better analyze unbalanced signals and solve modal aliasing and adaptive problems (Liu and Tan, 2022;Miao et al, 2022;Song et al, 2022;Zhang et al, 2022).…”

“…Their safe and reliable operation state determines the safety and economic benefits of using mechanical equipment. Among all types of faults related to rotating machinery, the most obvious is the abnormal vibration of a rotor system (Liu and Tan, 2022;Miao et al, 2022;Song et al, 2022;Zhang et al, 2022). Therefore, it is important to improve the safe and efficient operation of mechanical equipment to fully explore the relationship between the rotor vibration signal and rotor system operation state.…”

Seismic Signal Analysis Based on Variational Mode Decomposition and Hilbert Transform for Ground Intrusion Activity Classification

“…Compared with EMD, the EEMD method and variational mode decomposition (VMD) method constructs the Wiener filter according to the center frequency of the component and takes the narrow-band property of the component into full consideration [ 31 ], so the frequency band of filtering is more concentrated, and the signal can be decomposed into components with coefficient characteristics adaptively [ 32 ]. With a solid theoretical foundation, the VMD method has been successfully applied in many fields such as seismic data analysis [ 33 , 34 , 35 ], Time-Varying system identification [ 36 ], structural health monitoring [ 37 , 38 ], Micro-Motion signal processing [ 39 ], fault detection and classification [ 40 ].…”

A Source Localization Method Using Complex Variational Mode Decomposition

“…Recently, a complex VMD (CVMD) method was proposed [29], which provides the opportunity for applying VMD to array signal processing. In particular, we have proposed a modified CVMD method in [30], which gives a natural extension for VMD to the complex domain. This paper applies the modified CVMD in far-field and near-filed sources localization, aiming to yield great performance with small computation.…”