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

doi:10.11999/JEIT230763

自整定多元变分模态分解

doi: 10.11999/JEIT230763

1.
云南大学信息学院昆明 650504
2.
浙江大学工业控制技术国家重点实验室杭州 310027
3.
云南云天化股份有限公司装备技术中心昆明 650000

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
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- HTML全文浏览量: 54
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- 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

Self-tuning Multivariate Variational Mode Decomposition

1.
School of Information Science and Engineering, Yunnan University, Kunming 650504, China
2.
State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, China
3.
Yunnan Yuntianhua Limited by Share Ltd, Kunming 650000, China

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

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 $值的变化都具有更好的鲁棒性。(2) 与多元经验模态分解、快速多元经验模态分解和多元变分模态分解这些经典算法相比，SMVMD算法的分解误差最小，分解效果最好。
- 多元信号处理 /
- MVMD /
- 自整定 /
- 匹配追踪法 /
- 鲁棒性
Abstract: The Multivariate Variational Mode Decomposition (MVMD), being an extension of the Variational Mode Decomposition (VMD), inherits the merits of VMD. However, it encounters an issue wherein its decomposition performance relies heavily on two predefined parameters, the number of modes (K) and the penalty factor ($ \alpha $). To address this issue, a Self-tuning MVMD (SMVMD) algorithm is proposed. SMVMD employs the notion of matching pursuit to adaptively update K and $ \alpha $ based on energy occupation and mode orthogonality in the frequency domain, respectively. The experimented results of both simulated signals and real cases demonstrate that the proposed SMVMD not only effectively addresses the parameter rectification problem of the original MVMD, but also exhibits the following advantages: (i) SMVMD displays superior resilience to mode-mixing compared to MVMD, along with enhanced robustness to both noise and variations in $ \alpha $-value. (ii) In comparison to the classical algorithms of multivariate empirical mode decomposition, fast multivariate empirical mode decomposition, and multivariate variational mode decomposition, SMVMD showcases the lowest decomposition error and the best decomposition effect.
- Multivariate signal processing /
- Multivariate Variational Mode Decomposition (MVMD) /
- Self-tuning /
- Matching pursuit method /
- Robustness

HTML全文

图 1 滤波器组特性

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图 2 X₁(t)分解的噪声鲁棒性和$ \alpha $值鲁棒性

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图 3 SMVMD分解EEG信号的结果

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图 4 厂级振荡数据及SMVMD的分解结果

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图 5 基于SMVMD的厂级振荡检测结果可视化

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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

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表 1 4种算法的SAD值

算法	MVMD	MEMD	FMEMD	SMVMD
SAD	858.30	854.64	993.42	226.11

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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
${\theta _{k,c}}$	u₂	1	1	1	1	1	1	0.491	0.419	0.493
SI	u₁	–	–	–	–	–	–	0.8936	0.8853	0.8769
SI	u₂	0.9117	0.8818	0.8814	0.8866	0.8361	0.8306	-	-	-

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