Aiming at non-stationary signals with complex components, the performance of a variational mode decomposition (VMD) algorithm is seriously affected by the key parameters such as the number of modes $K$, the quadratic penalty parameter $\alpha$ and the update step $\tau$. In order to solve this problem, an adaptive empirical variational mode decomposition (EVMD) method based on a binary tree model is proposed in this paper, which can not only effectively solve the problem of VMD parameter selection, but also effectively reduce the computational complexity of searching the optimal VMD parameters using intelligent optimization algorithm. Firstly, the signal noise ratio (SNR) and refined composite multi-scale dispersion entropy (RCMDE) of the decomposed signal are calculated. The RCMDE is used as the setting basis of the $\alpha$, and the SNR is used as the parameter value of the $\tau$. Then, the signal is decomposed into two components based on the binary tree mode. Before decomposing, the $\alpha$ and $\tau$ need to be reset according to the SNR and MDE of the new signal. Finally, the cycle iteration termination condition composed of the least squares mutual information and reconstruction error of the components determines whether to continue the decomposition. The components with large least squares mutual information (LSMI) are combined, and the LSMI threshold is set as 0.8. The simulation and experimental results indicate that the proposed empirical VMD algorithm can decompose the non-stationary signals adaptively, with lower complexity, which is O(n²), good decomposition effect and strong robustness.

Early fault features of large-scale and low-speed mechanical equipment with heavy duty are weak and exhibit strong non-stationary characteristics. The adaptive extraction and identification of highly relevant important features from such signals has attracted significant attention. In this study, a novel empirical variational mode decomposition and exact Teager energy operator are proposed to explore valuable information. To highlight the fault impact signal representation, we use the exact energy operator to enhance the weak-impact components in the early fault signal. The proposed binary mechanism effectively distinguishes irrelevant features based on the adaptive decomposition parameter construction strategy. Therefore, interference features are easily removed from similar mixed signals, and the independent mode features are determined. The experimental results of the simulation and collected data are compared with those obtained with existing signal decomposition methods, and the superiority of the proposed method, owing to its better modal distinction and less time consumption, is verified.

For large rotating machinery with low speed and heavy load, the incipient fault characteristics of rolling bearings are particularly weak, making it difficult to identify them effectively by direct signal processing methods. To resolve this issue, we propose a novel approach to detecting incipient fault features that combines signal energy enhancement and signal decomposition. First, the structure of a conventional Teager algorithm is modified to further increase the energy of the micro-impact component and hence the impact amplitude. Then, a kind of composite chaotic mapping is constructed to extend the original fruit fly optimization algorithm (FOA) framework, improving the FOA’s randomness and search power. The effective intrinsic mode functions (IMFs) are determined by searching for the optimal combination values of the key parameters of the variational mode decomposition (VMD) with the improved chaotic FOA (ICFOA). The kurtosis index is then used to select the IMFs that are most relevant to the fault characteristics information. Finally, the sensitive components are analyzed to identify multiple early fault characteristics and determine detailed information about the faults. Moreover, the approach is evaluated by a simulation signal and a measured signal. The comprehensive evaluation indicates that the approach has clear advantages over other excellent methods in extracting the incipient fault feature information of the equipment and has great potential for application in engineering.

The variational mode decomposition (VMD) method has been widely applied in the field of mechanical fault diagnosis as an excellent non-recursive signal processing tool. The performance of VMD depends on its inherent prior parameters. Searching for the key parameters of VMD using intelligent optimization algorithms poses challenges for the internal essence and fitness function selection of intelligent optimization algorithm. Moreover, the computational complexity of optimization is high. Meanwhile, such methods are not competitive in evaluating orthogonality between intrinsic mode functions and the reconstruction error of the signal as a joint indictor for the termination of decomposition. Therefore, this paper proposes a new auto-regulative sparse variational mode decomposition method (ASparse–VMD) to achieve accurate feature extraction. The regularization term of the VMD handles sparsification by constructing an L₂-norm with a damping coefficient ε, and mode number K is set adaptively in a recursive manner to ensure appropriateness. The penalty parameter $\alpha$ is dynamically selected according to the number of modes and sampling frequency. The update step τ of the VMD algorithm is set using the signal-to-noise ratio to ensure the singleness and orthogonality of the modal components and suppress mode aliasing. The experimental results of the simulation signal and measured signal demonstrate the effectiveness of the proposed strategies for improving the inherent defects of VMD. Extensive comparisons with state-of-the-art methods show that the proposed algorithm is more effective and practical for hybrid feature extraction in mechanical faults.