The bearing fault feature detection and extraction from vibration signals are of great significance in mechanical fault diagnosis and machine condition monitoring. Sparse optimization focusing on different domains is one effective tool to extract weak fault feature from strong background noise. To unbiasedly detect fault features, one sparse model is constructed on the time–frequency domain, and Minimax Concave penalty is implemented on the matrix elements and singular value vector simultaneously to enhance accuracy. However, the performance of algorithm settling with the sparse model usually descends owing to non-convex objective function configuration or unsuitable parameters. Therefore, we propose a Moreau Envelope Alternating Direction Method of Multipliers algorithm to improve the solution process of the sparse model. During the solution process, one Moreau Envelope term is acted on Augmented Lagrangian function to ensure convergence and accelerate the convergence rate of iterative calculation. The iterative updating steps of variables are formulated, and the convergence of the proposed algorithm is proved by the Kurdyka–Łojasiewicz property. Simulated and practical experiments are conducted to validate the effectiveness and superiority of proposed method.

中文翻译：

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莫罗包络稀疏优化提取轴承故障特征的新方法


轴承故障特征检测和振动信号提取对于机械故障诊断和机器状态监测具有重要意义。针对不同领域的稀疏优化是从强背景噪声中提取弱故障特征的一种有效工具。为了公正地检测故障特征，在时频域上构建了一种稀疏模型，并同时对矩阵元素和奇异值向量实施最小最大凹罚分以提高准确性。然而，稀疏模型求解的算法性能通常会因目标函数配置非凸或参数不合适而下降。因此，我们提出一种Moreau Envelope Alternating Direction Method of Multipliers算法来改进稀疏模型的求解过程。求解过程中，对增广拉格朗日函数作用一个莫罗包络项，保证收敛，加快迭代计算的收敛速度。制定了变量的迭代更新步骤，并通过 Kurdyka-Łojasiewicz 性质证明了该算法的收敛性。通过仿真和实际实验验证了该方法的有效性和优越性。