针对滚动轴承早期振动信号微弱且难以提取的问题，结合灰狼算法与变分模态分解（Variational mode decomposition，VMD）提出改进变分模态分解（Improved variational mode decomposition，IVMD）方法分解轴承故障信号，并基于快速谱峭度图（Fast kurtogram，FK）提取特征分量进行信号重构，采用深度学习与混沌理论对各故障轴承重构信号进行非线性分析，完成故障识别。在保留原故障信息整体几何结构的同时降低了特征数据复杂度，增强了故障状态分类能力。基于损伤轴承实验数据验证所提方法的有效性。结果表明：IVMD较VMD能更好地分解故障信号，快速谱峭度图可有效提取特征分量；采用IVMDFK进行信号前处理后，经卷积神经网络（Convolutional neural network，CNN）进行故障分类，准确率高达99.99%，远高于传统故障诊断方法；在强噪声环境下此方法仍可较好地进行故障分类，在-8dB噪声下准确率达到75.75%，具有良好的鲁棒性；同时，结合混沌相图与Lyapunov指数反映故障信号的混沌特性，随卷积层数增加Lyapunov指数逐渐减小，表明深度学习模型和混沌理论可从混沌序列中提取纯净特征信息，准确进行故障识别。

Aiming to identify the weak early vibration signals of rolling bearings and solve its extraction problem，an improved variational mode decomposition (IVMD) was proposed in this paper to decompose the bearing fault signals by combining grey wolf algorithm with variational mode decomposition (VMD). The feature components were extracted by fast kurtogram (FK) to reconstruct the fault signals. The nonlinear analysis of the reconstructed signals for each fault bearing was carried out by using deep learning and chaos theory，and fault identification was completed. The overall geometric structure of the original fault information was kept. Meanwhile，the complexity of feature data was reduced，and the fault state classification ability was enhanced. The effectiveness of proposed method was verified based on fault bearing experimental data. Results show that IVMD can decompose the fault signals better than VMD，and FK can extract the characteristic components effectively. After using IVMDFK for signal pre processing，convolutional neural network (CNN) is used for fault classification with an accuracy rate of 99.99%，which shows much higher accuracy than traditional fault diagnosis methods. Under strong noise environment，this method can still classify faults well，and the accuracy rate reaches 75.75% under -8 dB noise，which shows good robustness. Meanwhile，the combination of chaotic phase diagram and Lyapunov exponent reflects the chaotic characteristics of fault signals，and the Lyapunov exponent gradually decreases with the increasing convolution layers，which indicates that the deep learning model and chaos theory can extract pure characteristic information from chaotic sequences and accurately identify fault.

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