The fault feature signal of rolling bearing can be characterized as the narrow-band signal with a specific resonance frequency. Therefore, resonance demodulation analysis is a powerful damage detection technique of bearings. In addition to the fault feature signal, the measured vibration signals carry various interference components, and these interference components become a serious obstacle of fault feature extraction. Variational mode extraction is a novel signal analysis method designed to retrieve a specific signal component from the composite signal. Variational mode extraction is founded on a similar basis as variational mode decomposition, while it shows better accuracy and higher efficiency compared with variational mode decomposition. In this study, variational mode extraction is introduced to the resonance demodulation analysis of bearing fault. As the results of variational mode extraction analysis are greatly influenced by the choice of two parameters, that is, the balancing factor α and the initial guess of center frequency ω_d, an optimized variational mode extraction method is further developed. First, a new fault information evaluation index for measuring the richness of fault characteristics of the signal, termed ensemble impulsiveness and cyclostationarity, is formulated. Second, the ensemble impulsiveness and cyclostationarity is used as the fitness function of particle swarm optimization to automatically determine the optimal values of α and ω_d. Finally, the validity of optimized variational mode extraction method is verified by simulated and experimental analysis, and the superiority of optimized variational mode extraction method is highlighted through comparison with two other advanced resonance demodulation analysis approaches, that is, the improved kurtogram and infogram. The analysis results indicate that optimized variational mode extraction method has a powerful capability of resonance demodulation analysis.

滚动轴承的故障特征信号可以表征为具有特定共振频率的窄带信号。因此，共振解调分析是一种强大的轴承损伤检测技术。除了故障特征信号之外，所测量的振动信号还携带各种干扰分量，这些干扰分量成为故障特征提取的严重障碍。变分模式提取是一种新颖的信号分析方法，旨在从复合信号中检索特定信号分量。变量模式提取的建立与变量模式分解的基础类似，但与变量模式分解相比，它具有更好的准确性和更高的效率。在这项研究中，变分模式提取被引入到轴承故障的共振解调分析中。由于变量模式提取分析的结果会受到两个参数（即平衡因子）的选择的极大影响α和中心频率的初始猜测ω _d，优化的变模式提取方法进一步发展。首先，制定了一种新的故障信息评估指标，用于测量信号的故障特征的丰富程度，称为整体冲动性和循环平稳性。其次，合奏冲动和周期稳定性被用作粒子群优化适应度函数来自动确定的最优值α和ω _d。最后，通过仿真和实验分析验证了优化的变模提取方法的有效性，并通过与改进的峰图和信息图这两种先进的共振解调分析方法进行比较，突出了优化的变模提取方法的优越性。分析结果表明，优化的变模提取方法具有强大的共振解调分析能力。