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基于小波包变换的自适应混沌信号降噪算法

刘云侠 贝广霞 蒋忠贇 孟强 时慧喆

刘云侠, 贝广霞, 蒋忠贇, 孟强, 时慧喆. 基于小波包变换的自适应混沌信号降噪算法[J]. 电子与信息学报, 2023, 45(10): 3676-3684. doi: 10.11999/JEIT221137
引用本文: 刘云侠, 贝广霞, 蒋忠贇, 孟强, 时慧喆. 基于小波包变换的自适应混沌信号降噪算法[J]. 电子与信息学报, 2023, 45(10): 3676-3684. doi: 10.11999/JEIT221137
LIU Yunxia, BEI Guangxia, JIANG Zhongyun, MENG Qiang, SHI Huizhe. Adaptive Noise Reduction Algorithm for Chaotic Signals Based on Wavelet Packet Transform[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3676-3684. doi: 10.11999/JEIT221137
Citation: LIU Yunxia, BEI Guangxia, JIANG Zhongyun, MENG Qiang, SHI Huizhe. Adaptive Noise Reduction Algorithm for Chaotic Signals Based on Wavelet Packet Transform[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3676-3684. doi: 10.11999/JEIT221137

基于小波包变换的自适应混沌信号降噪算法

doi: 10.11999/JEIT221137
基金项目: 全国金工与工训青年教师教学方法创新研究项目(2022JJGX-WKJY-40),山东科技大学2022年度在线课程建设项目(ZXK202242),山东科技大学2022年教育教学研究“群星计划”项目(QX2022M91)
详细信息
    作者简介:

    刘云侠:女,工程师,研究方向为智能控制和非线性信号处理

    贝广霞:女,工程师,研究方向为智能控制

    蒋忠贇:男,工程师,研究方向为信号处理

    孟强:男,工程师,研究方向为系统工程

    时慧喆:男,工程师,研究方向为电气工程

    通讯作者:

    蒋忠贇 skd994602@sdust.edu.cn

  • 中图分类号: TN911.2

Adaptive Noise Reduction Algorithm for Chaotic Signals Based on Wavelet Packet Transform

Funds: The National Metalworking and Engineering Training Young Teachers' Teaching Method Innovation Research Project (2022JJGX-WKJY-40), The 2022 Online Course Construction Project of Shandong University of Science and Technology (ZXK202242),The 2022 Education and Teaching Research “Stars Program” Project of Shandong University of Science and Technology (QX2022M91)
  • 摘要: 为了更好地体现混沌系统的内在特征,该文提出一种基于小波包变换的自适应混沌信号降噪算法。首先,该算法根据不同分解尺度小波包系数的相关性不同,确定了最佳分解层数;以对数能量熵为代价函数,得到了最优小波包基。然后,在局部邻域内对近似系数进行投影分析,利用神经网络梯度下降法对细节系数进行自适应选择。通过最小化损失函数,最大限度降低噪声对混沌信号的影响。最后,通过对来自Rossler混沌模型的状态变量进行仿真分析,证实了该算法对混沌信号降噪的优越性。
  • 图  1  基于小波包变换的自适应混沌降噪算法流程图

    图  2  自相关函数曲线

    图  3  误差平均值变化曲线

    图  4  相空间图

    图  5  自相关系数图

    图  6  信号功率谱

    表  1  不同噪声水平下的最优小波包基

    噪声水平(%)坐标轴近似系数细节系数
    5x, y$ s_3^1 $$ s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6,\;s_3^7,\;s_3^8 $
    10x, y$ s_3^1 $$ s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6,\;s_3^7,\;s_3^8 $
    20x, y$ s_3^1 $$ s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6,\;s_3^7,\;s_3^8 $
    35x, y$ s_3^1 $$ s_2^4,\;s_3^2,\;s_3^3,\;s_3^4,\;s_3^5,\;s_3^6 $
    60x, y$ s_3^1 $$ s_2^3,\;s_2^4,\;s_3^2,\;s_3^3,\;s_3^4 $
    90x$ s_3^1 $$ s_1^2,\;s_3^2,\;s_3^3,\;s_3^4 $
    y$ s_3^1 $$ s_2^3,\;s_2^4,\;s_3^2,\;s_3^3,\;s_3^4 $
    5~90z$ s_2^1 $$ s_2^2,\;s_2^3,\;s_2^4 $
    下载: 导出CSV

    表  2  SNR和RMSE对比表(x轴)

    降噪指标噪声水平(%)降噪前小波阈值降噪小波包阈值降噪本文算法降噪
    SNR
    526.115 834.414 234.223 634.681 2
    1020.095 228.880 628.507 329.632 4
    2014.074 623.581 522.568 624.660 0
    359.213 918.781 017.677 520.736 2
    604.532 214.898 411.920 317.144 2
    901.010 411.359 36.676 814.668 1
    RMSE
    50.174 20.067 00.068 50.065 0
    100.348 30.126 70.132 20.116 2
    200.696 60.233 20.262 00.205 9
    351.219 10.405 20.460 10.323 5
    602.089 80.633 60.892 70.489 2
    903.134 80.952 31.632 60.650 6
    下载: 导出CSV

    表  3  SNR和RMSE对比表(y轴和z轴)

    坐标轴降噪指标降噪前小波阈值降噪小波包阈值降噪本文算法降噪
    ySNR14.074 622.589 222.589 225.895 2
    RMSE0.639 30.239 90.239 90.208 4
    zSNR14.074 620.336 519.751 821.650 9
    RMSE0.310 00.150 70.161 20.129 6
    下载: 导出CSV

    表  4  信号的自相关函数值

    延迟时间(s)噪声水平(%)加噪信号小波阈值降噪小波包阈值降噪本文算法降噪
    150.995 00.997 30.997 30.997 4
    100.988 10.997 30.997 30.997 4
    200.961 50.997 30.997 20.997 4
    350.896 10.997 30.996 70.997 4
    600.752 70.996 70.981 40.997 5
    900.583 40.996 60.904 00.997 7
    250.989 10.991 50.991 50.991 6
    100.981 90.991 50.991 40.991 7
    200.954 20.991 40.991 00.991 7
    350.886 10.991 20.989 70.991 8
    600.736 80.989 30.970 60.992 1
    900.560 70.988 50.885 00.992 5
    550.953 20.955 60.955 50.955 9
    100.946 10.955 40.955 10.956 1
    200.918 90.954 90.953 30.956 6
    350.852 20.953 80.948 00.956 9
    600.705 80.943 90.919 60.958 4
    900.532 90.938 80.823 30.959 6
    下载: 导出CSV
  • [1] 黄丽莲, 姚文举, 项建弘, 等. 一种具有多对称同质吸引子的四维混沌系统的超级多稳定性研究[J]. 电子与信息学报, 2022, 44(1): 390–399. doi: 10.11999/JEIT201095

    HUANG Lilian, YAO Wenju, XIANG Jianhong, et al. Extreme multi-stability of a four-dimensional chaotic system with infinitely many symmetric homogeneous attractors[J]. Journal of Electronics &Information Technology, 2022, 44(1): 390–399. doi: 10.11999/JEIT201095
    [2] 金江涛, 许子非, 李春, 等. 基于深度学习与混沌特征融合的滚动轴承故障诊断[J]. 控制理论与应用, 2022, 39(1): 109–116. doi: 10.7641/CTA.2021.10177

    JIN Jiangtao, XU Zifei, LI Chun, et al. Rolling bearing fault diagnosis based on deep learning and chaotic feature fusion[J]. Control Theory &Applications, 2022, 39(1): 109–116. doi: 10.7641/CTA.2021.10177
    [3] 毛北行, 王东晓. 不确定分数阶高维混沌系统的自适应滑模同步[J]. 电子学报, 2021, 49(4): 775–780. doi: 10.12263/DZXB.20200316

    MAO Beixing and WANG Dongxiao. Self-adaptive sliding mode synchronization of uncertain fractional-order high-dimension chaotic systems[J]. Acta Electronica Sinica, 2021, 49(4): 775–780. doi: 10.12263/DZXB.20200316
    [4] 郭业才, 姚文强. 基于信噪比分类网络的调制信号分类识别算法[J]. 电子与信息学报, 2022, 44(10): 3507–3515. doi: 10.11999/JEIT210825

    GUO Yecai and YAO Wenqiang. Modulation signal classification and recognition algorithm based on signal to noise ratio classification network[J]. Journal of Electronics &Information Technology, 2022, 44(10): 3507–3515. doi: 10.11999/JEIT210825
    [5] LIU Yunxia, LU Xiao, PENG Wei, et al. Compression and regularized optimization of modules stacked residual deep fuzzy system with application to time series prediction[J]. Information Sciences, 2022, 608: 551–577. doi: 10.1016/j.ins.2022.06.088
    [6] KADAM S T, DHAIMODKER V M N, PATIL M M, et al. EIQ: EEG based IQ test using wavelet packet transform and hierarchical extreme learning machine[J]. Journal of Neuroscience Methods, 2019, 322: 71–82. doi: 10.1016/j.jneumeth.2019.04.008
    [7] LOU Shuting, DENG Jiarui, and LYU Shanxiang. Chaotic signal denoising based on simplified convolutional denoising auto-encoder[J]. Chaos, Solitons & Fractals, 2022, 161: 112333. doi: 10.1016/j.chaos.2022.112333
    [8] CHEN Yue and ZHANG Yu. Chaotic signal denoising using an improved wavelet thresholding algorithm[C]. 2021 International Conference on Communications, Information System and Computer Engineering, Beijing, China, 2021: 200–203.
    [9] 罗勇江, 杨腾飞, 赵冬. 色噪声下基于白化频谱重排鲁棒主成分分析的语音增强算法[J]. 电子与信息学报, 2021, 43(12): 3671–3679. doi: 10.11999/JEIT200594

    LUO Yongjiang, YANG Tengfei, and ZHAO Dong. Speech enhancement algorithm based on robust principal component analysis with whitened spectrogram rearrangement in colored noise[J]. Journal of Electronics &Information Technology, 2021, 43(12): 3671–3679. doi: 10.11999/JEIT200594
    [10] 郭文博, 林朗, 赵宏志, 等. 频谱共生干扰主动抑制技术研究[J]. 中国科学:信息科学, 2022, 52(10): 1915–1928. doi: 10.1360/SSI-2021-0160

    GUO Wenbo, LIN Lang, ZHAO Hongzhi, et al. Research on the active cancellation technology of spectrum symbiotic interference[J]. Scientia Sinica (Informationis), 2022, 52(10): 1915–1928. doi: 10.1360/SSI-2021-0160
    [11] MORADI M. Wavelet transform approach for denoising and decomposition of satellite-derived ocean color time-series: Selection of optimal mother wavelet[J]. Advances in Space Research, 2022, 69(7): 2724–2744. doi: 10.1016/j.asr.2022.01.023
    [12] 江莉, 尚文擎, 周军妮, 等. 一种用于地震信号分析的二阶挤压小波变换算法[J]. 电子与信息学报, 2021, 43(12): 3710–3717. doi: 10.11999/JEIT200753

    JIANG Li, SHANG Wenqing, ZHOU Junni, et al. A second-order squeezed wavelet transform algorithm for seismic signal analysis[J]. Journal of Electronics &Information Technology, 2021, 43(12): 3710–3717. doi: 10.11999/JEIT200753
    [13] JIANG Feibo, DONG Li, DAI Qianwei, et al. Using wavelet packet denoising and ANFIS networks based on COSFLA optimization for electrical resistivity imaging inversion[J]. Fuzzy Sets and Systems, 2018, 337: 93–112. doi: 10.1016/j.fss.2017.07.009
    [14] DASS R. Speckle noise reduction of ultrasound images using BFO cascaded with wiener filter and discrete wavelet transform in homomorphic region[J]. Procedia Computer Science, 2018, 132: 1543–1551. doi: 10.1016/j.procs.2018.05.118
    [15] CUI Huimin, ZHAO Ruimei, and HOU Yanli. Improved threshold denoising method based on wavelet transform[J]. Physics Procedia, 2012, 33: 1354–1359. doi: 10.1016/j.phpro.2012.05.222
    [16] GHANBARI Y and KARAMI-MOLLAEI M R. A new approach for speech enhancement based on the adaptive thresholding of the wavelet packets[J]. Speech Communication, 2006, 48(8): 927–940. doi: 10.1016/j.specom.2005.12.002
    [17] LU Yibin, LI Min, WU Biteng, et al. Denoising of pulse wave signal by wavelet packet transform[C]. 2021 IEEE International Conference on Robotics and Biomimetics, Sanya, China, 2021: 232–236.
    [18] ISLAM T, SHAHNAZ C, ZHU Weiping, et al. Rayleigh modeling of teager energy operated perceptual wavelet packet coefficients for enhancing noisy speech[J]. Speech Communication, 2017, 86: 64–74. doi: 10.1016/j.specom.2016.11.002
    [19] ZAHHAD M A, AHMED S M, and ABBAS S N. Biometrics from heart sounds: Evaluation of a new approach based on wavelet packet cepstral features using HSCT-11 database[J]. Computers & Electrical Engineering, 2016, 53: 346–358. doi: 10.1016/j.compeleceng.2016.05.004
    [20] DONG Wenyong and DING Hong. Full frequency de-noising method based on wavelet decomposition and noise-type detection[J]. Neurocomputing, 2016, 214: 902–909. doi: 10.1016/j.neucom.2016.06.072
    [21] SWAMI P D, SHARMA R, JAIN A, et al. Speech enhancement by noise driven adaptation of perceptual scales and thresholds of continuous wavelet transform coefficients[J]. Speech Communication, 2015, 70: 1–12. doi: 10.1016/j.specom.2015.02.007
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出版历程
  • 收稿日期:  2022-08-30
  • 修回日期:  2022-11-27
  • 网络出版日期:  2022-11-30
  • 刊出日期:  2023-10-31

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