Non-iterative denoising algorithm for mechanical vibration signal using spectral graph wavelet transform and detrended fluctuation analysis

Abstract

A novel non-iterative denoising technique combining spectral graph wavelet transform and detrended fluctuation analysis is proposed to solve the filtering problem of non-linear and non-stationary mechanical vibration signals. The vibration signal is firstly converted to a graph signal defined on the path graph. Then, the graph signal is decomposed into scaling function coefficients and spectral graph wavelet coefficients by spectral graph wavelet transform. Finally, the threshold is adopted to shrink the spectral graph wavelet coefficients, and the denoised signal is obtained via the inverse transform. Besides, an efficient criterion based on detrended fluctuation analysis is designed to select the decomposition level of spectral graph wavelet transform. The denoising performance of the presented approach for mechanical vibration signal has been thoroughly evaluated through analog signals compared with five conventional methods. The developed technique is then applied to denoise the vibration signal collected in hob fault experiments, and the influence of different optional parameters on the denoising performance is analyzed by single factor experiments. Experimental results indicate that the proposed approach can remove noise well and retain the fine signatures of signal as much as possible, and Euclidean weight function and Minimax threshold can achieve desired denoising capability when combined with soft threshold function or hard threshold function.