小波域局部Laplace模型降噪算法及其在机械故障诊断中应用

Denosing Algorithm Based on Local Laplace Model in Wavelet Domain and Its Application in Mechanical Fault Diagnosis

提出一种基于小波域局部拉普拉斯模型的降噪算法。并将其成功应用于机械故障诊断中。降噪算法利用复小波变换幅值和相位的组合信息对信号奇异点具有更好的敏感特性,对各尺度上信号奇异点予以精确定位;根据各尺度上奇异点位置和一定宽度的邻域窗,将实小波分解的各尺度上小波系数分为两类:有效系数和无效系数。将奇异点邻域窗之外的无效系数直接置零;而对邻域窗内有效系数的统计分布进行拉普拉斯建模。在先验分布的基础上,运用最大后验概率估计从含噪小波系数中估计出真实信号的小波系数。利用信号小波系数的估计值来重构信号,便得到降噪信号。通过仿真试验和汽车驱动桥主减速器故障诊断实例分别对此算法进行分析和验证,结果表明,该算法均具有良好的降噪效果,可以有效地对主减速器中齿轮故障信号进行降噪。

A denoising algorithm based on local Laplace model in wavelet domain is proposed, and it is successfully applied in mechanical fault diagnosis. Magnitude-phase compounding information of complex wavelet transform is used to position singular points of signal on each level for its good sensitivity to singular points of signal. And then the coefficients of real wavelet transform are separated into two sorts by the certain neighborhood width and the positions of singular points on each level, the two sorts include effective coefficients and ineffective coefficients. And ineffective coefficients out of neighborhoods of singular points are directly set zero, while local statistical distribution of efficient coefficients in neighborhood is assumed to Laplace mode 1. And on the basis of prior distribution, maximum a posteriori （MAP） estimator is used to restore the wavelet coefficients to signal from the noisy observations. New wavelet coefficients are used for the reconstruction to the denoising signal. This algorithm is analyzed and certificated by simulation and automotive main reducer gear fault diagnosis example respectively. Analysis results show that this algorithm has good noise reduction effect, and can efficiently reduce the noise of gear fault signal in main reducer.