基于Shannon熵的自适应小波包阈值函数去噪算法研究  

A study on adaptive wavelet packet threshold function de-noising algorithm based on Shannon entropy

作　　者：周建[1] 向北平[1] 倪磊[1] 艾攀华 ZHOU Jian;XIANG Beiping;NI Lei;AI Panhua(Manufacturing Process Testing Technology Key Laboratory of the Ministry of Education,Southwest University of Science and Technology,Mianyang 621000,China)

机构地区：[1]西南科技大学制造过程测试技术教育部重点实验室,四川绵阳621000

出　　处：《振动与冲击》2018年第16期206-211,240,共7页Journal of Vibration and Shock

基　　金：国家重大科学仪器设备开发专项(2013YQ13042902)

摘　　要：小波包去噪算法的关键问题在于对信号进行去噪时,如何有效地消除噪声且尽可能地保留原始信号的小波包系数。传统阈值函数由于无可调节参数,其去噪形式固定,无法根据小波包分解系数的噪声成分自适应地进行调整,去噪效果有待提升。据此,将Shannon信息熵作为调节参数引入小波包阈值函数中,提出一种基于Shannon熵的自适应小波包阈值去噪算法,对信号进行小波包分解并计算最大分解尺度小波包系数的Shannon熵值,依据该值对阈值函数进行调整,以实现在强噪声背景下对小波包系数进行大尺度的收缩,而在弱噪声背景下实现阈值收缩的平滑过渡。采用该方法对仿真信号与轴承振动实验信号进行去噪分析,并与其它小波包阈值去噪算法相对比,结果表明该方法去噪效果更好且在滤除噪声的同时有效地保留了信号的原始特征。The key problem of the wavelet packet de-noising algorithm is effectively eliminating noise while retaining as many of the original signal wavelet packet coefficients as possible.Due to the lack of adjustable parameters and the fixed de-noising form,the traditional threshold function fails to adjust adaptively based on the noise contribution of wavelet packet decomposition coefficients,and the de-noising effects have yet to be improved.Therefore,Shannon entropy was introduced as the adjusting parameter in the wavelet packet threshold function.To shrink wavelet packet coefficients on a large scale under a strong noise background and a smooth transition for threshold shrinkage under weak noise background,an adjustable wavelet packet threshold de-noising algorithm based on Shannon entropy was proposed.The signal was decomposed by the wavelet packet method,and the Shannon entropy of wavelet packet coefficients in the largest decomposition dimension was calculated for the adjustment of threshold function.The de-noising analysis of the simulation signal,the bearing vibration experimental signal based on the method above,and other wavelet threshold de-noising algorithms show that the new method has a greater de-noising effect and effectively retains original features of the signal while removing noise.

关 键 词：Shannon熵 小波包去噪 阈值函数 振动信号 

分 类 号：TN911.72[电子电信—通信与信息系统] TH165.3[电子电信—信息与通信工程]