面向随机振动功率谱估计的小波变换去噪算法理论分析*

 针对随机振动功率谱通常存突变或间断现象，在小波去噪处理中，软阈值法使得估计信号在间断处较模糊, 且整体误差大，而硬阈值法在信号的间断点附近会产生伪Gibbs现象。通过对随机振动谱的统计模型进行分析，建立了对数域振动谱噪声的统计模型，并理论推导出根据噪声小波变换系数而设置的滤波阈值与小波变换尺度之间的非线性关系，为小波变换自适应阈值去噪提供依据，在此基础上提出了基于小波变换的振动谱估计自适应去噪通用算法，通过仿真对比实验，结果表明理论分析的有效性。

Theory Analysis of Wavelet Transform Denoising Algorithm for Stochastic Vibration Spectrum Estimation

Stochastic vibration spectrum always contains sudden changes and discontinuance.On a wavelet denoising process,the soft-threshold method will make the estimation signal ambiguous at the discontinuity point,while the hard-threshold method will cause pseudo-Gibbs phenomena around the signal’s discontinuity point.Through analysis on the statistic model of the stochastic vibration spectrum,a noise statistic model of numeric field vibration spectrum is established,and the nonlinear relationship between the filtering threshold-value and the wavelet transform scale is derived theoretically for providing a base for adaptive-threshold wavelet transform denoising.Finally,an universal adaptive denoising algorithm for vibration spectrum estimation based on wavelet transform is proposed.Simulation results show that the theoretical analysis is correct and the algorithm is good.