高级搜索

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

自整定多元变分模态分解

郎恂 王佳艺 陈启明 何冰冰 毛汝凯 谢磊

郎恂, 王佳艺, 陈启明, 何冰冰, 毛汝凯, 谢磊. 自整定多元变分模态分解[J]. 电子与信息学报, 2024, 46(7): 2994-3001. doi: 10.11999/JEIT230763
引用本文: 郎恂, 王佳艺, 陈启明, 何冰冰, 毛汝凯, 谢磊. 自整定多元变分模态分解[J]. 电子与信息学报, 2024, 46(7): 2994-3001. doi: 10.11999/JEIT230763
LANG Xun, WANG Jiayi, CHEN Qiming, HE Bingbing, MAO Rukai, XIE Lei. Self-tuning Multivariate Variational Mode Decomposition[J]. Journal of Electronics & Information Technology, 2024, 46(7): 2994-3001. doi: 10.11999/JEIT230763
Citation: LANG Xun, WANG Jiayi, CHEN Qiming, HE Bingbing, MAO Rukai, XIE Lei. Self-tuning Multivariate Variational Mode Decomposition[J]. Journal of Electronics & Information Technology, 2024, 46(7): 2994-3001. doi: 10.11999/JEIT230763

自整定多元变分模态分解

doi: 10.11999/JEIT230763
基金项目: 国家自然科学基金(62003298, 62201495),云南省基础研究计划(202301AT070277),云南省重大科技专项(202202AD080005, 202202AH080009)
详细信息
    作者简介:

    郎恂:男,副教授,研究方向为智能信号处理、工业过程智能监测与控制、医疗信号处理与应用等

    王佳艺:女,硕士生,研究方向为自适应多元信号处理与时频分析

    陈启明:男,高级工程师,研究方向为自适应信号处理与时频分析等

    何冰冰:女,讲师,研究方向为医疗信号处理与应用

    毛汝凯:男,研究方向为工业过程智能监测与控制

    谢磊:男,教授,博士生导师,研究方向为医疗信号处理与深度学习、工业过程智能优化与控制等

    通讯作者:

    何冰冰 hebingbing@ynu.edu.cn

  • 中图分类号: TN911.7

Self-tuning Multivariate Variational Mode Decomposition

Funds: The National Natural Science Foundation of China (62003298, 62201495), Yunnan Fundamental Research Projects (202301AT070277), The Major Project of Science and Technology of Yunnan Province (202202AD080005, 202202AH080009)
  • 摘要: 多元变分模态分解(MVMD)作为变分模态分解(VMD)的多元扩展,在继承VMD优点的同时,也存在其分解性能很大程度上依赖于两个预置参数——模态数量K 和惩罚系数$ \alpha $的问题。为此,该文提出一种自整定MVMD(SMVMD)算法。SMVMD采取了匹配追踪法的思想,通过频域的能量占比和模态正交性分别自适应地更新K和$ \alpha $。对仿真信号与真实案例的分析结果表明,所提SMVMD方法不仅有效解决了原MVMD的参数整定问题,而且表现出以下优势,(1) 与MVMD相比,SMVMD抗模态混叠的能力更强,且对噪声和$ \alpha $值的变化都具有更好的鲁棒性。(2) 与多元经验模态分解、快速多元经验模态分解和多元变分模态分解这些经典算法相比,SMVMD算法的分解误差最小,分解效果最好。
  • 图  1  滤波器组特性

    图  2  X1(t)分解的噪声鲁棒性和$ \alpha $值鲁棒性

    图  3  SMVMD分解EEG信号的结果

    图  4  厂级振荡数据及SMVMD的分解结果

    图  5  基于SMVMD的厂级振荡检测结果可视化

    1  SMVMD算法

     初始化:$ \{ u_{k,c}^1(\omega )\} ,\{ \omega _k^1\} ,n \leftarrow 0 $
     令$ k = 1,{{\mathbf{r}}_1}(\omega ) = {\mathbf{x}}(\omega ) $
     while $ \left\| {{{\mathbf{r}}_{{k}}}(\omega )} \right\|_2^2/\left\| {{\mathbf{x}}(\omega )} \right\|_2^2 > \delta $ do
      令n=1,初始化中心频率$ \{ \omega _k^1\} $
       while $ \displaystyle\sum\limits_c {\dfrac{{||u_{k,c}^n(\omega ) - u_{k,c}^{n - 1}(\omega )||_2^2}}{{||u_{k,c}^{n - 1}(\omega )||_2^2}}} \gt \varepsilon $ do
        $ n \leftarrow n + 1 $
         for $ c = 1:C $ do
          $ u_{k,c}^{n + 1}(\omega ) \leftarrow \dfrac{{{r_{k,c}}(\omega )}}{{1 + 2\alpha _c^n{{(\omega - \omega _k^n)}^2}}} $
         end for
         $ \omega _k^{n + 1} \leftarrow \dfrac{{\displaystyle\sum\limits_c {\int\limits_0^\infty {\omega |u_{^{_{k,c}}}^{n + 1}(\omega ){|^2}{\text{d}}\omega } } }}{{\displaystyle\sum\limits_c {\int\limits_0^\infty {|u_{k,c}^{n + 1}(\omega ){|^2}{\text{d}}\omega } } }} $
         for $ c = 1:C $do
          $ \alpha _c^{n + 1} = \alpha _c^n\dfrac{{u_{k,c}^{n + 1}{{(\omega )}^*}u_{k,c}^{n + 1}(\omega )}}{{u_{k,c}^{n + 1}{{(\omega )}^*}{r_{k,c}}(\omega )}} $
         end for
        end while
      令$ {u_{k,c}}(\omega ) = u_{k,c}^{n + 1}(\omega ),{\omega _k} = \omega _k^{n + 1} $,同时更新
      $ {{\mathbf{r}}_{k + 1}}(\omega ) = {\mathbf{x}}(\omega ) - {{\mathbf{u}}_k}(\omega ) $
     end while
    下载: 导出CSV

    表  1  4种算法的SAD值

    算法MVMDMEMDFMEMDSMVMD
    SAD858.30854.64993.42226.11
    下载: 导出CSV

    表  2  归一化相关系数与稀疏指数

    模态 x1 x2 x3 x4 x5 x6 x7 x8 x9
    ${\theta _{k,c}}$ u1 0.446 0.497 0.398 0.441 0.371 0.497 1 1 1
    u2 1 1 1 1 1 1 0.491 0.419 0.493
    SI u1 0.8936 0.8853 0.8769
    u2 0.9117 0.8818 0.8814 0.8866 0.8361 0.8306 - - -
    下载: 导出CSV
  • [1] CHEN Qiming, LANG Xun, XIE Lei, et al. Multivariate intrinsic chirp mode decomposition[J]. Signal Processing, 2021, 183: 108009. doi: 10.1016/j.sigpro.2021.108009.
    [2] ZAHRA A, KANWAL N, REHMAN N U, et al. Seizure detection from EEG signals using multivariate empirical mode decomposition[J]. Computers in Biology and Medicine, 2017, 88: 132–141. doi: 10.1016/j.compbiomed.2017.07.010.
    [3] HAN G, LIN B, and XU Z. Electrocardiogram signal denoising based on empirical mode decomposition technique: An overview[J]. Journal of Instrumentation, 2017, 12(3): P03010. doi: 10.1088/1748-0221/12/03/P03010.
    [4] 王宇红, 高志兴. 改进多维本质时间尺度分解的厂级振荡检测[J]. 控制工程, 2022, 29(10): 1835–1840. doi: 10.14107/j.cnki.kzgc.CAC2020-1557.

    WANG Yuhong and GAO Zhixing. Plant-wide oscillation detection based on improved multivariate intrinsic time-scale decomposition[J]. Control Engineering of China, 2022, 29(10): 1835–1840. doi: 10.14107/j.cnki.kzgc.CAC2020-1557.
    [5] REHMAN N U and AFTAB H. Multivariate variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2019, 67(23): 6039–6052. doi: 10.1109/TSP.2019.2951223.
    [6] TANAKA T and MANDIC D P. Complex empirical mode decomposition[J]. IEEE Signal Processing Letters, 2007, 14(2): 101–104. doi: 10.1109/LSP.2006.882107.
    [7] RILLING G, FLANDRIN P, GONCALVES P, et al. Bivariate empirical mode decomposition[J]. IEEE Signal Processing Letters, 2007, 14(12): 936–939. doi: 10.1109/LSP.2007.904710.
    [8] REHMAN N U and MANDIC D P. Empirical mode decomposition for trivariate signals[J]. IEEE Transactions on Signal Processing, 2010, 58(3): 1059–1068. doi: 10.1109/TSP.2009.2033730.
    [9] REHMAN N and MANDIC D P. Multivariate empirical mode decomposition[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010, 466(2117): 1291–1302. doi: 10.1098/rspa.2009.0502.
    [10] ASGHAR M A, KHAN M J, RIZWAN M, et al. AI inspired EEG-based spatial feature selection method using multivariate empirical mode decomposition for emotion classification[J]. Multimedia Systems, 2022, 28(4): 1275–1288. doi: 10.1007/s00530-021-00782-w.
    [11] LANG Xun, ZHANG Yufeng, XIE Lei, et al. Detrending and denoising of industrial oscillation data[J]. IEEE Transactions on Industrial Informatics, 2023, 19(4): 5809–5820. doi: 10.1109/TII.2022.3188844.
    [12] HUANG Guoqing, PENG Liuliu, KAREEM A, et al. Data-driven simulation of multivariate nonstationary winds: A hybrid multivariate empirical mode decomposition and spectral representation method[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2020, 197: 104073. doi: 10.1016/j.jweia.2019.104073.
    [13] LANG Xun, ZHENG Qian, ZHANG Zhiming, et al. Fast multivariate empirical mode decomposition[J]. IEEE Access, 2018, 6: 65521–65538. doi: 10.1109/ACCESS.2018.2877150.
    [14] 蔡念, 黄威威, 谢伟, 等. 基于互补自适应噪声的集合经验模式分解算法[J]. 电子与信息学报, 2015, 37(10): 2383–2389. doi: 10.11999/JEIT141632.

    CAI Nian, HUANG Weiwei, XIE Wei, et al. Ensemble empirical mode decomposition base on complementary adaptive noises[J]. Journal of Electronics & Information Technology, 2015, 37(10): 2383–2389. doi: 10.11999/JEIT141632.
    [15] WANG Yanxue, LIU Fuyun, JIANG Zhansi, et al. Complex variational mode decomposition for signal processing applications[J]. Mechanical Systems and Signal Processing, 2017, 86: 75–85. doi: 10.1016/j.ymssp.2016.09.032.
    [16] ZOSSO D, DRAGOMIRETSKIY K, BERTOZZI A L, et al. Two-dimensional compact variational mode decomposition[J]. Journal of Mathematical Imaging and Vision, 2017, 58(2): 294–320. doi: 10.1007/s10851-017-0710-z.
    [17] 孟明, 闫冉, 高云园, 等. 基于多元变分模态分解的脑电多域特征提取方法[J]. 传感技术学报, 2020, 33(6): 853–860. doi: 10.3969/j.issn.1004-1699.2020.06.011.

    MENG Ming, YAN Ran, GAO Yunyuan, et al. Multi-domain feature extraction of EEG based on multivariate variational mode decomposition[J]. Chinese Journal of Sensors and Actuators, 2020, 33(6): 853–860. doi: 10.3969/j.issn.1004-1699.2020.06.011.
    [18] YAN Xiaoan, LIU Ying, XU Yadong, et al. Multichannel fault diagnosis of wind turbine driving system using multivariate singular spectrum decomposition and improved Kolmogorov complexity[J]. Renewable Energy, 2021, 170: 724–748. doi: 10.1016/j.renene.2021.02.011.
    [19] ZHANG Yijie, ZHANG Haoran, YANG Yang, et al. Seismic random noise separation and attenuation based on MVMD and MSSA[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5908916. doi: 10.1109/TGRS.2021.3131655.
    [20] CHEN Qiming, CHEN Junghui, LANG Xun, et al. Self-tuning variational mode decomposition[J]. Journal of the Franklin Institute, 2021, 358(15): 7825–7862. doi: 10.1016/j.jfranklin.2021.07.021.
    [21] CHEN Shiqian, YANG Yang, PENG Zhike, et al. Adaptive chirp mode pursuit: Algorithm and applications[J]. Mechanical Systems and Signal Processing, 2019, 116: 566–584. doi: 10.1016/j.ymssp.2018.06.052.
    [22] REHMAN N U and MANDIC D P. Filter bank property of multivariate empirical mode decomposition[J]. IEEE Transactions on Signal Processing, 2011, 59(5): 2421–2426. doi: 10.1109/TSP.2011.2106779.
    [23] LANG Xun, ZHANG Yufeng, XIE Lei, et al. Use of fast multivariate empirical mode decomposition for oscillation monitoring in noisy process plant[J]. Industrial & Engineering Chemistry Research, 2020, 59(25): 11537–11551. doi: 10.1021/acs.iecr.9b06351.
    [24] CHEN Qiming, WEN Qingsong, WU Xialai, et al. Detection and time–frequency analysis of multiple plant-wide oscillations using adaptive multivariate intrinsic chirp component decomposition[J]. Control Engineering Practice, 2023, 141: 105715. doi: 10.1016/j.conengprac.2023.105715.
    [25] YU Wanke, ZHAO Chunhui, and HUANG Biao. MoniNet with concurrent analytics of temporal and spatial information for fault detection in industrial processes[J]. IEEE Transactions on Cybernetics, 2022, 52(8): 8340–8351. doi: 10.1109/TCYB.2021.3050398.
    [26] LINDNER B, AURET L, and BAUER M. A systematic workflow for oscillation diagnosis using transfer entropy[J]. IEEE Transactions on Control Systems Technology, 2020, 28(3): 908–919. doi: 10.1109/TCST.2019.2896223.
    [27] CHEN Qiming, LANG Xun, LU Shan, et al. Detection and root cause analysis of multiple plant-wide oscillations using multivariate nonlinear chirp mode decomposition and multivariate granger causality[J]. Computers & Chemical Engineering, 2021, 147: 107231. doi: 10.1016/j.compchemeng. 2021.107231.
    [28] AFTAB M F, HOVD M, and SIVALINGAM S. Detecting non-linearity induced oscillations via the dyadic filter bank property of multivariate empirical mode decomposition[J]. Journal of Process Control, 2017, 60: 68–81. doi: 10.1016/j.jprocont.2017.08.005.
  • 加载中
图(5) / 表(3)
计量
  • 文章访问数:  240
  • HTML全文浏览量:  72
  • PDF下载量:  30
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-07-25
  • 修回日期:  2024-04-27
  • 网络出版日期:  2024-05-15
  • 刊出日期:  2024-07-29

目录

    /

    返回文章
    返回