基于Shannon熵的自适应小波包阈值函数去噪算法研究

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (16) : 206-211.

论文

周建，向北平，倪磊，艾攀华

作者信息 +

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

ZHOU Jian,XIANG Beiping,NI Lei,AI Panhua

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文章历史 +

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。

Abstract

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.

导出引用

周建，向北平，倪磊，艾攀华. 基于Shannon熵的自适应小波包阈值函数去噪算法研究[J]. 振动与冲击, 2018, 37(16): 206-211

ZHOU Jian,XIANG Beiping,NI Lei,AI Panhua. A study on adaptive wavelet packet threshold function de-noising algorithm based on Shannon entropy[J]. Journal of Vibration and Shock, 2018, 37(16): 206-211

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