Variational mode decomposition (VMD) is a new method of signal adaptive decomposition. In the VMD framework, the vibration signal is decomposed into multiple mode components by Wiener filtering in Fourier domain, and the center frequency of each mode component is updated as the center of gravity of the mode’s power spectrum. Therefore, each decomposed mode is compact around a center pulsation and has a limited bandwidth. In view of the situation that the penalty parameter and the number of components affect the decomposition effect in VMD algorithm, a novel method of fault feature extraction based on the combination of VMD and particle swarm optimization (PSO) algorithm is proposed. In this paper, the numerical simulation and the measured fault signals of the rolling bearing experiment system are analyzed by the proposed method. The results indicate that the proposed method is much more robust to sampling and noise. Additionally, the proposed method has an advantage over the EMD in complicated signal decomposition and can be utilized as a potential method in extracting the faint fault information of rolling bearings compared with the common method of envelope spectrum analysis.

Rolling bearings play a crucial role in rotary machinery systems, and their operating state affects the entire mechanical system. In most cases, the fault of a rolling bearing can only be identified when it has developed to a certain degree. At that moment, there is already not much time for maintenance, and could cause serious damage to the entire mechanical system. This paper proposes a novel approach to health degradation monitoring and early fault diagnosis of rolling bearings based on a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and improved multivariate multiscale sample entropy (MMSE). The smoothed coarse graining process was proposed to improve the conventional MMSE. Numerical simulation results indicate that CEEMDAN can alleviate the mode mixing problem and enable accurate intrinsic mode functions (IMFs), and improved MMSE can reflect intrinsic dynamic characteristics of the rolling bearing more accurately. During application studies, rolling bearing signals are decomposed by CEEMDAN to obtain IMFs. Then improved MMSE values of effective IMFs are computed to accomplish health degradation monitoring of rolling bearings, aiming at identifying the early weak fault phase. Afterwards, CEEMDAN is performed to extract the fault characteristic frequency during the early weak fault phase. The experimental results indicate the proposed method can obtain a better performance than other techniques in objective analysis, which demonstrates the effectiveness of the proposed method in practical application. The theoretical derivations, numerical simulations, and application studies all confirmed that the proposed health degradation monitoring and early fault diagnosis approach is promising in the field of prognostic and fault diagnosis of rolling bearings.