Abstract: In order to extract fault features of bearings accurately，a method of parameter optimized variational mode decomposition(VMD)based on genetic algorithm(GA)combining with 1.5-dimensional spectrum was proposed for the fault diagnosis of bearing. Firstly，taking envelope entropy of modal components in the VMD method minimum as the optimization goal，number of modal components and secondary penalty factor were optimized by employing genetic algorithm，and the two input parameters which can realize the optimal decomposition of VMD were determined. Then，a simulated signal and the inner ring faulty signal of a bearing were decomposed using the parameter optimized VMD method，and 1.5-dimensional spectrum diagrams of each modal component were plotted. The parameter optimized VMD method decomposed and gained four modal components which were consistent with the original components of the simulated signal. 1.5-dimensional spectrum eliminated the 10Hz frequency component which was not involved in the quadratic phase coupling. In the meantime，the proposed method in this paper extracted the first to sixth harmonics and the modulation frequencies of the motor’s rotating frequency with them below the 1kHz. It showed that parameter optimized VMD based on genetic algorithm can decompose complex signals into several modal components accurately，and 1.5-dimensional spectrum can detect quadratic phase coupling of signals effectively. Meanwhile，parameter optimized VMD based on genetic algorithm combined with 1.5-dimenaionl spectrum can extract inner ring fault features effectively，which verifies the effectiveness and practicability of the method proposed in the paper.

Key words: Variational mode decomposition；Genetic algorithm；Bearing；Fault diagnosis；1.5-dimentional spectrum

摘要： 为了准确提取轴承的故障特征，提出了一种遗传算法(GA)参数优化的变分模态分解(VMD)结合1.5维谱的轴承故障诊断方法。首先以VMD方法中模态分量的包络熵值最小为优化目标，利用遗传算法对模态分量个数和二次惩罚因子进行优化，确定这两个能使VMD实现最优分解的输入参数。然后利用参数优化的VMD方法对仿真信号和轴承内环故障信号进行分解，并做各模态分量的1.5维谱图。参数优化的VMD分解得到了与仿真信号原始分量相符的4个模态分量，1.5维谱剔除了未参与二次相位耦合的10Hz频率分量。同时在1kHz频率以下，运用本文方法提取了轴承内环故障特征频率的1至6倍频频率成分以及电机转频对它们的调制频率。由此表明，遗传算法参数优化的VMD可实现复杂信号的正确分解，1.5维谱可有效检测信号的二次相位耦合。同时，遗传算法参数优化的VMD结合1.5维谱能有效提取轴承内环故障特征，从而验证了本文方法的有效性和实用性。

关键词: 变分模态分解；遗传算法；轴承；故障诊断；1.5维谱