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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. 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. 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. 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. 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}}_{\mathbf{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
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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

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