基于分段幂函数的LMD方法及其在轴承故障诊断中的应用

局域均值分解是一种将复杂的多分量信号分解为若干个乘积函数的方法,每个PF分量为一个单分量调频调幅信号。传统LMD算法对所有极值点集利用滑动平均的方法计算局域均值函数和局域包络函数,易造成过平滑现象,运算量增大,并影响分解精度。本研究对传统LMD方法进行了改进,采用分段幂函数法分别计算上下极值点集的包络线,得到的包络线具有良好的光滑性和稳定性,进而计算局域均值函数和局域包络函数,避免了传统方法过平滑现象,提高了运算效率与精确度。通过对仿真信号分析和轴承故障诊断实验,结果验证了本研究所设计方法的有效性。

The Local Mean Decomposition Method Based on Piecewise Power Function and Its Application in Bearing Fault Diagnosis

Local Mean Decomposition（LMD） is a method of decomposing a complicated multi-component signal into several production functions（PF）.Each PF is a single-component frequency and amplitude modulation signal.Traditional LMD algorithm employs the moving average method to obtain the local mean function and local envelope function of extreme point sets.However,it can easily cause the over-smoothness,time-consuming computation and low accuracy.Therefore,the traditional LMD algorithm is improved in this paper.Firstly,the piecewise power function is suggested for the envelop lines of upper and down extreme point sets,respectively.The obtained envelope lines have good smoothness and stability.And then,these two envelope lines can be adopted to calculate the local mean function and local envelope function.This improved LMD method not only avoids the over-smoothness phenomenon,but also improves the operational efficiency and accuracy.Finally,the presented method is validated by the comparison of the simulation signal with the bearing fault diagnosis experiment results.