联合可调Q因子小波变换子带选择和改进奇异值分解的混沌信号降噪算法
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冶金工业过程系统科学湖北省重点实验室,武汉科技大学

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N93

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国家自然科学基金(62173262); 武汉科技大学”十四五”湖北省优势特色学科(群)项目(2023C0204)


Denoising of chaotic signal based on Tunable Q Wavelet Transform subband selection and improved Single Value Decomposition
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Hubei Provincial Key Laboratory of Process Systems science for Metallurgical Industry

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    摘要:

    针对低信噪比和动力学系统参数未知的混沌信号降噪,提出了一种可调Q因子小波变换(TQWT)与改进奇异值分解(ISVD)相结合的混沌信号降噪新算法(TQWT-ISVD)。该方法利用TQWT对含噪混沌信号进行分解,根据最大小波熵理论和能量阈值规则将TQWT的子带准确分为信号子带和噪声子带两部分;对于噪声子带,采用ISVD对其进行降噪,达到初步降噪的目的,在ISVD中,采用奇异值子集标准差确定有效重构阶次从而提高噪声抑制效果。为了进一步去除噪声,对初步降噪后的信号进行TQWT重构,利用ISVD对重构后信号进行再次降噪,得到二次降噪后的混沌信号。采用TQWT-ISVD对Lorenz仿真信号和实测月太阳黑子数序列进行降噪处理,并与SVD降噪法、TQWT降噪法、自适应噪声集合经验模态分解阈值降噪法(CEEMDAN-WT)和多元集合经验模态分解最小二乘降噪法(MEEMD-LMS)进行对比,实验结果表明,TQWT-ISVD方法能够更有效地对混沌信号进行降噪。与对比方法中降噪效果最好的CEEMDAN-WT方法相比,Lorenz信号降噪后,本文方法的信噪比(SNR)提高了2.653 7%,均方根误差(RMSE)下降了19.202 4%,排列熵(PE)下降了4.975 7%;月太阳黑子信号降噪后,本文方法的相关系数提高1.531 7%,排列熵(PE)下降了19.877 5%。

    Abstract:

    Aiming at chaotic signal noise reduction with low signal-to-noise ratio and unknown dynamic system parameters, a new chaotic signal noise reduction algorithm (TQWT-ISVD), which combines tunable Q-factor wavelet transform (TQWT) and improved singular value decomposition (ISVD), is proposed. The chaotic signal with noise is decomposed by TQWT, and the subband of TQWT is divided into signal subband and noise subband according to maximum wave entropy theory and energy threshold rule. For the noise subband, ISVD is used to reduce its noise to achieve the purpose of initial noise reduction. In ISVD, the effective reconstruction order is determined by the standard deviation of the singular value subset to improve the noise suppression effect. In order to further remove noise, the signal after initial noise reduction is reconstructed by TQWT, and the reconstructed signal is denoised again by ISVD, and the chaotic signal after secondary noise reduction is obtained. TQWT-ISVD was used to denoise Lorenz simulation signal and measured sunspot number sequence. Compared with SVD method, TQWT method, complete ensemble empirical mode decomposition with adaptive noise and threshold denoising method (CEEMDAN-WT) method and modified ensemble empirical mode decomposition combined with least squares denoising method (MEEMD-LMS) method, the experimental results show that TQWT-ISVD method can denoise chaotic signals more effectively. Compared with CEEMDAN-WT method, which has the best noise reduction effect, after Lorenz signal noise reduction, the signal-to-noise ratio (SNR) of the proposed method is increased by 2.653 7%, the root mean square error (RMSE) is decreased by 19.202 4%, and the permutation entropy (PE) is decreased by 4.975 7%. After the denoising of the lunar sunspot signal, the correlation coefficient of the method is increased by 1.531 7%, and the PE is decreased by 19.877 5%.

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王文波,杨欣卢,喻敏. 联合可调Q因子小波变换子带选择和改进奇异值分解的混沌信号降噪算法[J]. 科学技术与工程, , ():

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  • 收稿日期:2023-08-02
  • 最后修改日期:2023-11-11
  • 录用日期:2023-12-02
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