Variational mode decomposition (VMD) has been applied in the field of rolling bearing fault diagnosis because of its good ability of frequency segmentation. Mode number
K
and quadratic penalty term
α
have a significant influence on the decomposition result of VMD. At present, the commonly used method is to determine these two parameters adaptively through intelligent optimization algorithm, namely, the parameter-adaptive VMD (PAVMD) method. The key of the PAVMD method is the setting of an objective function, and the traditional PAVMD method is prone to overdecomposition or underdecomposition. To solve these problems, an improved parameter-adaptive VMD (IPAVMD) method is proposed. A new objective function, the maximum average envelope kurtosis (MAEK), is proposed in this paper. The new objective function fully considers the equivalent filtering characteristics of VMD, and squared envelope kurtosis has good antinoise performance. In the optimization method, this paper uses an improved particle swarm optimization (PSO) algorithm. The MAEK and PSO can make sure the IPAVMD method reaches the best complete decomposition of the signal without an underdecomposition or overdecomposition problem. Through the analysis of simulation data and experimental data, the performance of the IPAVMD and the traditional PAVMD is compared. The comparison results show that the proposed IPAVMD has better performance and stronger robustness than the traditional method and is suitable for both single-fault and multiple-fault cases of rolling bearings. The research results have certain theoretical significance and application value for improving the fault diagnosis effect of rolling bearings.
In recent years, many studies on variational mode decomposition (VMD) have mainly focused on choosing the number of modes and balancing parameter, while less research focuses on the internal properties of VMD. This paper proposes an adaptive single-mode VMD (ASMVMD) method based on the convergence characteristics of VMD and the adaptivity of particle swarm optimization (PSO). Firstly, we study the convergence characteristics of single-mode VMD and find that the U-shaped convergence region related to fault impact is very wide in the whole frequency domain. Secondly, based on the characteristics of the U-shaped convergence region, a new population position initialization strategy is proposed. Finally, the improved PSO is used to optimize the initial center frequency and balancing parameter of single-mode VMD. The effectiveness of the proposed method is verified by analyzing the simulated signal and wheelset bearing fault signals. Compared with the fast kurtogram and Autogram, it is shown that ASMVMD has a stronger capability of fault feature extraction.
Aiming at the difficulty of accurate diagnosis of wheelset-bearing system composite faults, a multi-fault feature extraction method based on self-adaptive variational mode extraction (SAVME) was proposed. Variational mode extraction (VME) can extract a specific sub-signal from a multi-component signal. The key to the success of this algorithm is to determine appropriate initial parameters in advance, including initial center frequency (ICF) and penalty factor. To determine the key parameters of VME adaptively, the convergence characteristics of VME are analyzed deeply, and the VME convergence tendency diagram is proposed creatively according to the trend of the iterative curve of the center frequency (CF) of the desired mode. By analyzing the test signal with the VME convergence tendency diagram, the number of main latent sub-signals in the test signal and the ICF of each sub-signal corresponding to the VME can be determined efficiently. Then, according to the position of the ICF of each sub-signal in the frequency domain, the empirical formula of the penalty factor is used to quickly obtain the appropriate penalty factor. The proposed SAVME method not only improves the parameter selection adaptability of the traditional VME algorithm but also extends the VME algorithm to the field of multi-fault diagnosis. By analyzing the simulated signal and two experimental signals, the effectiveness of the SAVME algorithm is verified. Compared with the fast kurtogram (FK) method and the adaptive variational mode decomposition (VMD) method, the proposed method is more accurate and superior in the multi-fault feature extraction of the wheelset-bearing system.
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