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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: 国家自然科学基金资助项目(62003298),国家自然科学基金资助项目(62201495),云南省基础研究计划项目(202301AT070277),云南省重大科技专项项目(202202AD080005),云南省重大科技专项项目(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), The National Natural Science Foundation of China (62201495), Yunnan Fundamental Research Projects under Grant (202301AT070277), The Major Project of Science and Technology of Yunnan Province (202202AD080005), The Major Project of Science and Technology of Yunnan Province (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_0^\infty {\omega |u_{^{_{k,c}}}^{n + 1}(\omega ){|^2}{\text{d}}\omega } } }}{{\displaystyle\sum\limits_c {\int_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  3  归一化相关系数与稀疏指数

    模态x1x2x3x4x5x6x7x8x9
    ${\theta _{k,c}}$u10.4460.4970.3980.4410.3710.497111
    u21111110.4910.4190.493
    SIu1------0.89360.88530.8769
    u20.91170.88180.88140.88660.83610.8306---
    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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