Three-dimensional instantaneous orbit map for rotor-bearing system based on a novel multivariable complex variational mode decomposition algorithm

Full spectrum and holospectrum are homogenous information fusion technology developed for the fault diagnosis of rotating machinery and are often used in the analysis of the orbit of rotating machinery. However, both of the techniques are based on Fourier transform, so they can only handle stationary signals, which limits their development. By drawing inspiration from the approach of multivariate variational mode decomposition (MVMD) and the complex-valued signal decomposition, we propose a method called multivariate complex variational mode decomposition (MCVMD) for processing non-stationary complex-valued signals of multi-dimensional bearing surfaces in this work. In particular, the proposed method takes the advantages of the joint information between the complex-valued signals of multi-dimensional bearing surfaces, and owing to this property, we provide its three-dimensional instantaneous orbit map (3D-IOM) to present the overall perspective of the rotor-bearing system and also offer a high-resolution time-full spectrum (Time-FS) to display the forward and backward frequency components of all the bearing surfaces within a time-frequency plane. The effectiveness of the proposed method through both the simulated experiment and the real-life complex-valued signals are shown in this paper.