The decomposition effect of variational mode decomposition (VMD) mainly depends on the choice of decomposition number K and penalty factor α. For the selection of two parameters, the empirical method and single objective optimization method are usually used, but the aforementioned methods often have limitations and cannot achieve the optimal effects. Therefore, a multi-objective multi-island genetic algorithm (MIGA) is proposed to optimize the parameters of VMD and apply it to feature extraction of bearing fault. First, the envelope entropy (E_e) can reflect the sparsity of the signal, and Renyi entropy (R_e) can reflect the energy aggregation degree of the time-frequency distribution of the signal. Therefore, E_e and R_e are selected as fitness functions, and the optimal solution of VMD parameters is obtained by the MIGA algorithm. Second, the improved VMD algorithm is used to decompose the bearing fault signal, and then two intrinsic mode functions (IMF) with the most fault information are selected by improved kurtosis and Holder coefficient for reconstruction. Finally, the envelope spectrum of the reconstructed signal is analyzed. The analysis of comparative experiments shows that the feature extraction method can extract bearing fault features more accurately, and the fault diagnosis model based on this method has higher accuracy.

中文翻译：

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参数优化变分模式分解方法在滚动轴承故障特征提取中的应用

变异模分解（VMD）的分解效果主要取决于分解数K和惩罚因子α的选择。在选择两个参数时，通常采用经验方法和单目标优化方法，但是上述方法往往有局限性，不能达到最佳效果。因此，提出了一种多目标多岛遗传算法（MIGA）来优化VMD参数并将其应用于轴承故障特征提取。首先，包络熵（E _e）可以反映信号的稀疏性，而仁义熵（R _e）可以反映信号的时频分布的能量聚集度。因此，E _e和选择R _e作为适应度函数，并通过MIGA算法获得VMD参数的最优解。其次，采用改进的VMD算法对轴承故障信号进行分解，然后通过改进的峰度和Holder系数，选择故障信息最多的两个固有模式函数（IMF）进行重构。最后，分析了重构信号的包络谱。对比实验分析表明，特征提取方法可以更准确地提取轴承故障特征，并且基于该方法的故障诊断模型具有较高的准确性。