Abstract: For the lack of atomic coherence analysis and the lack of optimal atomic selection in the learning dictionary， a G-KSVD dictionary learning methods was proposed based on effective singular components herein. The method comprised the following steps. First， the ACFPER was proposed based on the coherence of the signals. The singular component was screened to achieve the signal denoising and the updating of the dictionary atom, and the solution of the coefficient were realized by using a component containing more fault information. Thus， the purpose of enhancing the impact components in the signals was achieved. Then the algorithm reduced the feedback layers in order to cut down the time cost. Last， the validity and repeatability of the proposed method were verified by using the simulation signals and the actual bearing signals. The results show that the G-KSVD algorithm has good denoising effectiveness in the idoneity interval， furthermore the time cost is low. 

Key words: G-KSVD algorithm, autocorrelation function pulse energy ratio（ACFPER）, singular component, correlation function, energy operator

摘要： 针对传统学习字典中缺少原子相干性分析的问题和最优原子选择问题，提出了一种基于有效奇异分量的G-K奇异值分解（G-KSVD）字典学习方法。基于信号相干性提出自相关函数脉冲能量比（ACFPER），并以此为指标对奇异分量进行筛选，实现信号的降噪，利用包含故障信息较多的分量对字典原子进行更新和系数求解，从而达到增强信号中冲击成分的目的，并通过减少反馈层来降低时间成本。利用仿真信号和实际轴承信号对所提方法进行有效性及重复性的验证，结果表明，G-KSVD算法在有效区间内具有良好的去噪效果和较低的时间成本。

关键词: G-K奇异值分解算法, 自相关函数脉冲能量比, 奇异分量, 相关函数, 能量算子