Abstract: Rolling bearing vibration signal’s sparse representation over over-complete dictionary is a hot issue. In this paper, it proposes an improved method for MOD（Method of Optimal Direction） dictionary learning, which is applied to sparse representation of rolling bearing vibration signal. The core of this method is processing of dictionary learning, which is carefully constructed. In this processing, data is segmented with overlapping. In comparison with DCT, FFT and normal method, the transform coefficient is sparser, which is obtained by improved method. This method is applied in vibration signals processing based on compressed sensing. Compared with DCT and FFT in the same range of reconstruction error, the method requires less measure data, and less computational.

Key words: sparse representation, dictionary learning, rolling bearing, Method of Optimal Direction（MOD）

摘要： 基于过完备字典的振动信号稀疏表示是滚动轴承信号研究的新热点。提出一种改进MOD字典学习的算法，并用于滚动轴承振动信号的稀疏表示。该方法基于MOD（Method of Optimal Direction）训练学习过程，通过构造分段重叠训练矩阵，能够得到更为稀疏的变换系数。相对DCT、FFT和未改进的处理方法，该方法得到的变换系数更稀疏。将该方法应用到基于压缩感知的滚动轴承振动信号处理，在相同的重构误差范围内，该方法所需要的观测数更少，计算量更小。

关键词: 稀疏表示, 字典学习, 滚动轴承, 最优方向法（MOD）