A quadratic penalty item optimal variational mode decomposition method based on single-objective salp swarm algorithm

•A mode mixing density is proposed to quantitatively measure the mode mixing severity between IMFs.•The optimal quadratic penalty item is obtained based on the SSA.•No prior knowledge is required for complex vibration signal. A quadratic penalty item optimal variational mode decomposition (VMD) method based on single-objective salp swarm algorithm (SSA) is proposed to alleviate the mode mixing of complex vibration signals. A novel frequency domain mode mixing density is proposed to quantitatively measure the mode mixing severity between intrinsic mode functions (IMFs). Then, an objective function is constructed by integrating correlation coefficient into frequency domain mode mixing density. Based on the SSA, the optimal quadratic penalty item is obtained through the objective function. The merits of this method are the alleviation of the mode mixing and maintenance of the signal fidelity for complex vibration signal without prior knowledge. Experimental results demonstrate the effectiveness of the proposed method.