| Summary: | 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 <i>L</i><sub>2</sub>-norm with a damping coefficient <i>ε</i>, and mode number <i>K</i> is set adaptively in a recursive manner to ensure appropriateness. The penalty parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> 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.
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