基于增广Huber正则化稀疏低秩矩阵的旋转机械微弱故障诊断

Weak Fault Diagnosis of Rotating Machinery Based on Augmented Huber Regularized Sparse Low-rank-matrix Approach

在多重故障相互耦合和强烈背景噪声下,提取大型旋转机械中的复合微弱故障特征是一个难点,针对这一问题,提出一种新的基于增广Huber正则化稀疏低秩矩阵(augmented Huber regularized sparse low-rank-matrix,AHR-SLM)的旋转机械故障特征提取方法,以大型减速机齿轮箱复合微弱诊断为例。该方法借助于非凸罚正则化稀疏低秩矩阵的思想,通过引入增广Huber罚函数代替传统最小化L1-norm融合套索算法,建立正则化目标成本函数,推导所建立模型的严格凸性,同时讨论模型严格凸性前提下的模型参数最优取值问题,并利用前向–后向算法对所建立模型进行求解。仿真算例与大型减速机齿轮箱微弱故障诊断实例表明:该方法不仅能提取隐藏在强烈外界噪声中的复合微弱故障特征,而且改善传统最小化L1-norm融合套索算法在提取微弱故障冲击时产生的稀疏系数低估与故障频率丢失问题,以及变分模态分解与快速谱峭度图特征提取算法产生的能量衰减与故障频率丢失问题。

It is a challenging difficulty to accurately extract the weak fault characteristics of large rotating machinery under the environment of multiple faults coupling and strong background noise. In this paper, a novel weak multi-fault feature extraction methodology based on augmented Huber regularized sparse low-rank-matrix(AHR-SLM) was proposed,taking a large reducer gearbox as an example. Illuminated by the idea of nonconvex penalty regularization of sparse low rank matrix, in this paper, the augmented Huber regularized penalty function was introduced to substitute the L1-norm fused lasso optimization(LFLO), and the convexity of the proposed objective cost function(OCF) was proved via the non-diagonal characteristic of the matrix, meanwhile, the model parameters were discussed to guarantee the strictly convex property of objective cost function, besides, the solution of the proposed OCF was solved by the forward-backward algorithm(FBA).The diagnosis results of simulation case and large reducer gearbox with weak faults indicate that the proposed method not only extract multiple weak fault characteristics under heavy background noise, but also the underestimate of sparse coefficients and frequencies missed issues of LFLO method, as well as the energy attenuation and frequencies missed issues of variational modal decomposition and fast spectral kurtosis diagram(VMD-FSKD) are improved, respectively.