基于相干累积量分段正交匹配追踪方法的轴承早期故障稀疏特征提取

Initial Fault Identification of Bearing Based on Coherent Cumulant Stagewise Orthogonal Matching Pursuit

低速重载机械出现早期故障时,振动信号中体现故障特征的微冲击成分具有稀疏性。根据振动动力学模型建立的故障信号过完备冗余字典,能实现对振动信号的稀疏逼近。分段正交匹配追踪(Stagewise orthogonal matching pursuit,StOMP)在正交匹配追踪(Orthogonal matching pursuit,OMP)的基础上,采用框架的思想对信号进行稀疏分解,不但克服了OMP方法导致的过匹配现象,也提高了算法的收敛速度,但在计算残差在子原子库的表示时计算量很大。基于相干累积量的StOMP方法根据故障信号过完备字典中各原子的相关性,分析了内置相干累积量和外置相干累积量的关系,并通过故障信号在字典中的内、外置相干累积量的值快速确定原子的位移因子和频率因子,进而为StOMP方法提供更为高效的子原子库选取策略,最后结合原子淘汰算法对影响不大的原子进行筛选,最终选出最能稀疏表示信号的一组原子。

The fault signal from the low-speed and heavy-duty machinery contains weak impulse signal and presents sparsity which can represent the feature of initial fault.The redundant dictionary is built according to the dynamic model of mechanical vibration can sparse approximate the impulse signal best.Stage-wise orthogonal matching pursuit is based on the orthogonal matching pursuit and uses the method of frame to decompose signal,which can overcome the matter of overmatching by orthogonal matching pursuit,and can also improve the convergence rate.But this method is complex to compute the presentation of the residual in the sub-library.As the coherent cumulant of two atoms in a set is larger than that not in a set,the shift factor and frequency factor can be confirmed efficiently,then a thin sub-library can be constructed for stage-wise orthogonal matching pursuit.Combining with elimination algorithm to delete the redundant atoms can get a set of atoms which can approximate signal more accurate and sparser.