Singular value decomposition (SVD) methods have aroused wide concern to extract the periodic impulses for bearing fault diagnosis. The state-of-the-art SVD methods mainly focus on the low rank property of the Hankel matrix for the fault feature, which cannot achieve satisfied performance when the background noise is strong. Different to the existing low rank-based approaches, we proposed a simultaneously low rank and group sparse decomposition (SLRGSD) method for bearing fault diagnosis. The major contribution is that the simultaneously low rank and group sparse (SLRGS) property of the Hankel matrix for fault feature is first revealed to improve performance of the proposed method. Firstly, we exploit the SLRGS property of the Hankel matrix for the fault feature. On this basis, a regularization model is formulated to construct the new diagnostic framework. Furthermore, the incremental proximal algorithm is adopted to achieve a stationary solution. Finally, the effectiveness of the SLRGSD method for enhancing the fault feature are profoundly validated by the numerical analysis, the artificial bearing fault experiment and the wind turbine bearing fault experiment. Simulation and experimental results indicate that the SLRGSD method can obtain superior results of extracting the incipient fault feature in both performance and visual quality as compared with the state-of-the-art methods.

中文翻译：

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滚动轴承故障诊断的同时低秩和组稀疏分解

奇异值分解（SVD）方法引起了人们的广泛关注，以提取用于轴承故障诊断的周期性脉冲。最新的SVD方法主要针对故障特征的Hankel矩阵的低秩特性，当背景噪声很强时，它们无法获得令人满意的性能。与现有的基于低秩的方法不同，我们提出了一种同时用于轴承故障诊断的低秩和组稀疏分解（SLRGSD）方法。主要的贡献是，首先揭示了汉克矩阵同时具有的低秩和群稀疏（SLRGS）特性，以提高故障诊断方法的性能。首先，我们利用汉克尔矩阵的SLRGS属性作为故障特征。在此基础上，制定了正则化模型以构建新的诊断框架。此外，采用增量近端算法来实现平稳解。最后，通过数值分析，人工轴承故障实验和风机轴承故障实验，深刻地验证了SLRGSD方法增强故障特征的有效性。仿真和实验结果表明，与最新方法相比，SLRGSD方法在性能和视觉质量上都可以提取早期故障特征。人工轴承故障实验和风力发电机轴承故障实验。仿真和实验结果表明，与最新方法相比，SLRGSD方法在性能和视觉质量上都可以提取早期故障特征。人工轴承故障实验和风力发电机轴承故障实验。仿真和实验结果表明，与最新方法相比，SLRGSD方法在性能和视觉质量上都可以提取早期故障特征。