非平稳信号分析的广义解析模态分解方法

doi:10.3969/j.issn.0372-2112.2016.06.029

电子学报 ›› 2016, Vol. 44 ›› Issue (6): 1458-1464.DOI: 10.3969/j.issn.0372-2112.2016.06.029

非平稳信号分析的广义解析模态分解方法

郑近德¹, 潘海洋¹, 程军圣²

1. 安徽工业大学机械工程学院, 安徽马鞍山 243032;
2. 湖南大学汽车车身先进设计制造国家重点实验室, 湖南长沙 410082

收稿日期:2015-04-14 修回日期:2015-06-20 出版日期:2016-06-25
- 通讯作者:
- 郑近德
- 作者简介:
- 潘海洋 男,1989年生于安徽宿州,硕士,现为安徽工业大学机械工程学院助教.研究方向为模式识别与机械设备故障诊断.E-mail:pansea@sina.cn;程军圣 男,1968年生于湖南永州,博士,现为湖南大学教授,博士生导师.主要从事机械故障诊断、动态信号分析与处理等方面的研究.E-mail:signalp@tom.com;chengjunsheng@hnu.edu.cn
- 基金资助:
- 国家自然科学基金 (No.51375152,No.51505002); 安徽省高校自然科学基金项目 (No.KJ2015A080)

Generalized Analytical Mode Decomposition for Non-Stationary Signal Analysis

ZHENG Jin-de¹, PAN Hai-yang¹, CHENG Jun-sheng²

1. School of Mechanical Engineering, Anhui University of Technology, Maanshan, Anhui 243032, China;
2. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, Hunan 410082, China

Received:2015-04-14 Revised:2015-06-20 Online:2016-06-25 Published:2016-06-25
- Supported by:
- National Natural Science Foundation of China (No.51375152, No.51505002); Program of Natural Science Foundation for Colleges and Universities in Anhui Province (No.KJ2015A080)

摘要/Abstract

摘要：

现有的非平稳信号分析方法都有各自不同的缺陷,短时傅里叶变换的时频分辨率受不确定性原理的限制,希尔伯特黄变换存在端点效应和模态混叠,易导致模糊的时频分布;解析模态分解只适合分析频率恒定的多分量信号;针对包含多个时变模态、特别是频谱重叠的非平稳信号,本文提出了一种新的信号分析方法——广义解析模态分解(Generalized Analytical Mode Decomposition,GAMD).GAMD通过广义傅里叶变换将时变频率转换为频谱可分的,采用解析模态分解对其分解,再对得到的单分量信号进行逆广义傅里叶变换即可得到原始信号的分量.因此,GAMD非常适合分析时变的非平稳信号.通过仿真信号将GAMD与短时傅里叶变换和希尔伯特黄变换等方法进行了对比,结果表明GAMD方法的分解效果更精确,时频分辨率更高.

关键词: 时频分析, 广义傅里叶变换, 解析模态分解, 经验模态分解, 非平稳信号

Abstract:

The existing methods for analyzing non-stationary signal all have different defects.The time-frequency resolution of short-time Fourier transform is limited by the uncertainty principle.The boundary effect and mode mixing of Hilbert-Huang transform often result in an unclear time-frequency distribution.Analytical mode decomposition is only suitable for analyzing multi-component signal with constant frequencies.For the multi-component signal with time-varying frequencies, especially when the spectrum overlaps, a method termed generalized analytical mode decomposition (GAMD) is proposed for analyzing these signals.In GAMD, generalized Fourier transform is used to convert the time-varying frequencies to constant ones without overlapping in spectrum and then the analytical mode decomposition is adopted to handle the transformed signal.Lastly, the inverse generalized Fourier transform is used to demodulate the obtained mono-components.Hence, GAMD is very suitable for analyzing time-varying non-stationary signals.The proposed GAMD method is compared with short-time Fourier transform and Hilbert-Huang transform through analyzing simulation signals and the results indicate that GAMD possesses more accurate decomposing results and higher time-frequency resolution.

Key words: time-frequency analysis, generalized Fourier transform, analytical mode decomposition, empirical mode decomposition, non-stationary signal

中图分类号:

TN911.7

郑近德, 潘海洋, 程军圣. 非平稳信号分析的广义解析模态分解方法[J]. 电子学报, 2016, 44(6): 1458-1464.

ZHENG Jin-de, PAN Hai-yang, CHENG Jun-sheng . Generalized Analytical Mode Decomposition for Non-Stationary Signal Analysis[J]. Acta Electronica Sinica, 2016, 44(6): 1458-1464.

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非平稳信号分析的广义解析模态分解方法

Generalized Analytical Mode Decomposition for Non-Stationary Signal Analysis

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