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一元及多元信号分解发展历程与展望

陈启明 文青松 郎恂 谢磊 苏宏业

陈启明, 文青松, 郎恂, 谢磊, 苏宏业. 一元及多元信号分解发展历程与展望. 自动化学报, 2024, 50(1): 1−20 doi: 10.16383/j.aas.c220632
引用本文: 陈启明, 文青松, 郎恂, 谢磊, 苏宏业. 一元及多元信号分解发展历程与展望. 自动化学报, 2024, 50(1): 1−20 doi: 10.16383/j.aas.c220632
Chen Qi-Ming, Wen Qing-Song, Lang Xun, Xie Lei, Su Hong-Ye. Univariate and multivariate signal decomposition: Review and future directions. Acta Automatica Sinica, 2024, 50(1): 1−20 doi: 10.16383/j.aas.c220632
Citation: Chen Qi-Ming, Wen Qing-Song, Lang Xun, Xie Lei, Su Hong-Ye. Univariate and multivariate signal decomposition: Review and future directions. Acta Automatica Sinica, 2024, 50(1): 1−20 doi: 10.16383/j.aas.c220632

一元及多元信号分解发展历程与展望

doi: 10.16383/j.aas.c220632
基金项目: 国家自然科学基金(62003298, 62073286), 云南省基础研究计划(202201AT070577)资助
详细信息
    作者简介:

    陈启明:浙江大学工业控制技术国家重点实验室博士研究生、阿里巴巴达摩院高级算法工程师. 主要研究方向为信号分解与时频分析, 控制系统性能评估. E-mail: chenqiming@zju.edu.cn

    文青松:阿里巴巴达摩院高级算法专家. 主要研究方向为时间序列异常检测与预测. E-mail: qingsong.wen@alibaba-inc.com

    郎恂:云南大学信息学院副教授. 分别于2014年和2019年获得浙江大学学士和博士学位. 主要研究方向为信号处理, 控制系统性能评估. 本文通信作者. E-mail: langxun@ynu.edu.cn

    谢磊:浙江大学教授. 分别于2000年和2005年获得浙江大学学士和博士学位. 主要研究方向为信号处理, 控制系统性能评估. E-mail: leix@iipc.zju.edu.cn

    苏宏业:浙江大学教授. 主要研究方向为控制理论与控制工程. E-mail: hysu69@zju.edu.cn

Univariate and Multivariate Signal Decomposition: Review and Future Directions

Funds: Supported by National Natural Science Foundation of China (62003298, 62073286) and Yunnan Fundamental Research Program (202201AT070577)
More Information
    Author Bio:

    CHEN Qi-Ming Ph.D. candidate at the State Key Laboratory of Industrial Control Technology, Zhejiang University, and senior algorithm engineer at the Damo Academy, Alibaba Group. His research interest covers signal decomposition & time-frequency analysis and control system performance evaluation

    WEN Qing-Song Staff algorithm engineer at the Damo Academy, Ali-baba Group. His research interest covers time series anomaly detection and forecasting

    LANG Xun Associate professor at the School of Information, Yunnan University. He received his bachelor and Ph.D. degrees from Zhejiang University in 2014 and 2019, respectively. His research interest covers signal processing and control system performance evaluation. Corresponding author of this paper

    XIE Lei Professor at Zhejiang University. He received his bachelor and Ph.D. degrees from Zhejiang University in 2000 and 2005, respectively. His research interest covers signal processing and control system performance evaluation

    SU Hong-Ye Professor at Zhejiang University. His research interest covers control theory and control engineering

  • 摘要: 现实世界中, 所获得的信号大部分都是非平稳和非线性的, 将此类复杂信号分解为多个简单的子信号是重要的信号处理方法. 1998年, 提出希尔伯特–黄变换(Hilbert-Huang transform, HHT)以来, 历经20余年的发展, 信号分解已经成为信号处理领域相对独立又具有创新性的重要内容. 特别是近10年, 多元/多变量/多通道信号分解理论方法方兴未艾, 在诸多领域得到了成功应用, 但目前尚未见到相关综述报道. 为填补这个空缺, 从单变量和多变量两个方面系统综述了国内/外学者对主要信号分解方法的研究现状, 对这些方法的时频表达性能进行分析和比较, 指出这些分解方法的优势和存在的问题. 最后, 对信号分解研究进行总结和展望.
  • 图  1  一个IMF的波形示意图

    Fig.  1  Waveform diagram of an IMF

    图  2  EMD的筛分过程示意图

    Fig.  2  Schematic diagram of sifting process of EMD

    图  3  ITD分解过程示意图

    Fig.  3  Schematic diagram of ITD decomposition process

    图  4  EWT的模态频谱分割示意图

    Fig.  4  Schematic diagram of modal spectrum division of EWT

    图  5  VMD原理示意图

    Fig.  5  Schematic diagram of VMD principle

    图  6  NCMD频率解调过程示意图

    Fig.  6  Schematic diagram of NCMD frequency demodulation process

    图  7  EMD分解结果

    Fig.  7  The decomposition results of EMD

    图  8  VMD分解结果

    Fig.  8  The decomposition results of VMD

    图  9  NCMD分解结果

    Fig.  9  The decomposition results of NCMD

    图  10  多元/多通道/多变量信号分解领域术语的图形化解释

    Fig.  10  Graphical interpretation of terms in multivariate signal decomposition

    图  11  单变量ICMD分解多变量信号的结果

    Fig.  11  The decomposition results of multivariate signals by the univariate ICMD

    图  12  多变量ICMD分解多变量信号的结果

    Fig.  12  The decomposition results of multivariate signals by the multivariate ICMD

    图  13  BEMD的分解原理示意图

    Fig.  13  Principle of the decomposition of BEMD

    图  14  BEMD的两种二维包络的均值计算示意图

    Fig.  14  Schematic diagram of the calculation of the mean value of two envelopes of two-dimensional signal for BEMD

    图  15  二维局部极值点示例

    Fig.  15  Example of two-dimensional local extreme points

    图  16  双变量信号

    Fig.  16  Bivariate signal

    图  17  双变量信号的投影信号

    Fig.  17  Projection signal of bivariate signal

    图  18  双变量信号的局部均值

    Fig.  18  Local mean of bivariate signal

    图  19  多变量IMF

    Fig.  19  Multivariate IMF

    图  20  等角度采样

    Fig.  20  Uniform angle sampling

    图  21  Halton-Hammersley序列采样

    Fig.  21  Halton-Hammersley sequences based sampling

    图  22  MEMD的分解结果

    Fig.  22  The decomposition results of MEMD

    图  23  MVMD的分解结果

    Fig.  23  The decomposition results of MVMD

    图  24  MNCMD的分解结果

    Fig.  24  The decomposition results of MNCMD

    表  1  常见单变量信号分解方法归类总结

    Table  1  Classification and summary of common univariate signal decomposition methods

    方法名称作用域优点局限性
    FT频域经典方法, 理论完备, 简单高效仅适用于线性平稳信号
    STFT时频域经典方法, 简单高效窗函数选取问题, 分辨率固定
    WVD时频域经典方法, 理论完备不能处理交叉频率和多分量情况
    WT时频域经典方法, 理论完备母小波和尺度需人为指定
    EMD时域自适应性强, 适用于非线性和非平稳信号, 应用场景广泛噪声敏感, 模态混叠和端点效应问题严重, 缺乏理论基础
    EEMD时域自适应性强, 对信号间歇性鲁棒计算效率低, 重构误差大, 受辅助噪声参数影响大
    CEEMD时域对信号间歇性鲁棒, 计算效率和重构误差优于EEMD辅助噪声的参数会影响分解结果
    MEEMD时域对信号间歇性鲁棒, 噪声鲁棒性好, 模态分裂概率低计算效率低于EEMD
    MCEEMD时域噪声鲁棒性和分解完备性好、模态分裂概率低计算效率低于CEEMD
    LMD时域能处理非平稳信号噪声敏感、参数影响大
    ITD时域计算效率优于EMD, 易于实施在线计算噪声敏感、模态提取能力劣于EMD
    SST时频域能有效表征非平稳信号的时变调频特征在处理强、变信号时, 会产生较大误差且无法处理时频面
    交叉和重叠信号
    EWT频域数据驱动自适应划分频段噪声鲁棒性弱, 分辨率有限
    VMD频域噪声鲁棒性和采样频率鲁棒性好, 数学理论完善局限于处理窄带信号, 参数影响大
    NCMD时频域数学理论完善, 宽带信号处理能力强需要提前指定参数
    ICMD时频域宽带信号处理能力强, 计算效率高, 能处理交叉瞬时频率需要提前指定参数
    下载: 导出CSV

    表  2  多元信号分解方法归类总结

    Table  2  Classification and summary of multivariate signal decomposition methods

    方法名称拓展方式优点局限性
    CEMD复数性质可处理复数信号实部虚部模态数量可能不一致
    RCEMD复数空间
    旋转概念
    复数空间中极值定义明确, 实部虚部模态一致局限于处理复数信号
    BEMD单位圆投影向量可分解双变量信号局限于处理双变量信号
    TEMD球面投影可分解三变量信号局限于处理三变量信号
    QEMD超球面投影可分解四变量信号局限于处理四变量信号
    MEMD高维空间投影适用于双变量及多变量信号分解投影向量的数量和方向敏感, 抗噪声能力差, 计算效率低
    FMEMD高维空间投影大幅提高了MEMD的计算效率投影向量的数量和方向敏感, 噪声鲁棒性略低于MEMD
    IMITD高维空间投影局部特征处理效果好, 计算效率高于MEMD投影向量的数量和方向会影响到基线提取
    DMITD高维空间投影投影向量鲁棒性优于IMITD运算效率低于IMITD
    MSST多变量振荡时频谱清晰, 适用于探索性数据分析不能直接重构模态
    MEWT多变量振荡可以重构模态需要有效的频谱分割, 来显示构造自适应小波滤波器组
    CVMD复数性质噪声和采样频率鲁棒性好局限于处理复数窄带信号, 参数影响大
    MVMD多变量调制振荡噪声和采样频率鲁棒性好, 模态之间信息泄露
    少, 自适应多变量最优维纳滤波器
    局限于处理窄带多变量信号, 参数影响大
    MNCMD多变量调制振荡可对时变多元信号进行分解复杂度高, 需要预估信号中的噪声水平和调整参数
    MICMD多变量调制振荡适用于宽带多元信号分解与时频分析, 计算复杂度低,
    参数鲁棒性好, 模态正交性强, 信息泄露少
    在强噪声条件下, 分解性能下降, 零频分量波动较明显
    下载: 导出CSV

    表  3  常见多元信号分解方法的适用场景

    Table  3  Applicable scenarios of common multivariate signal decomposition methods

    方法适用场景
    CEMD只适用于复数信号
    BEMD只适用于双变量信号
    MEMD适合分析信噪比高, 实时性要求低, 采样频率足够高, 模态频率间隔两倍以上的多元信号, 可以作为有效的探索性分析方法
    FMEMD适合分析信噪比高, 实时性要求高, 采样频率足够高, 模态频率间隔两倍以上的信号; 数据量大时, 建议采用FMEMD, 不采用MEMD
    IMITD适合分析局部特征明显, 实时性要求高, 采样频率足够高的多元信号
    DMITD适合分析通道间差异大, 实时性要求低, 采样频率足够高的多元信号
    CVMD只适用于具有窄带性质的复数信号
    MVMD适用于分量频率范围不重叠的窄带多元信号, 处理宽带信号效果非常有限
    MNCMD适用于宽带多元信号, 但计算复杂度较高
    MICMD适用于宽带多元信号和时频曲线有交叉的多元信号, 计算复杂度较低
    下载: 导出CSV
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  • 收稿日期:  2022-08-09
  • 录用日期:  2022-12-19
  • 网络出版日期:  2023-05-22
  • 刊出日期:  2024-01-29

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