基于Hankel矩阵与奇异值分解降噪方法的齿轮故障诊断研究

摘要

Hankel matrix is combined with Singular Value Decomposition(SVD)for denoising the fault signal of gear using MATLAB software,in order to reduce noise in signals and improve Signal to Noise Ratio(SNR), so that to highlight the information feature of fault. The composed of measurement signal with noises of Hankel matrix was divided into two uncorrelated spaces,real signal space and noise space, and three different singular value selection methods respectively difference spectrum of singular value, mean value of eigenvalue and median of singular value were chosen to be applied, after processing the singular value matrix of two space, then reconstructed signal to reduce noise of measurement signal. The calculations and images show the denoising results of three differ-ent singular value selection methods,through which obtains that the median value of singular value method has the best denoising effect for broken teeth fault signal of gear.%将Hankel矩阵与奇异值分解相结合对齿轮故障信号进行降噪处理,并应用MATLAB软件实现,来降低信号中的噪声,提高信噪比,从而凸显故障的信息特征.首先将含噪的测量信号构成的Hankel矩阵分解成两个互不相关的空间——真实信号空间与噪声空间,采用3种不同的奇异值选择方法,即奇异值差分谱方法、特征均值方法以及奇异值中值方法,对两个空间的奇异值矩阵处理后,再重构信号,实现降低测量信号噪声的目的.利用计算数据和图像说明不同奇异值选择方法的降噪效果,得出奇异值中值方法对齿轮断齿故障信号降噪效果最佳.