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中值互补集合经验模态分解

刘淞华 何冰冰 郎恂 陈启明 张榆锋 苏宏业

刘淞华, 何冰冰, 郎恂, 陈启明, 张榆锋, 苏宏业. 中值互补集合经验模态分解. 自动化学报, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c201031
引用本文: 刘淞华, 何冰冰, 郎恂, 陈启明, 张榆锋, 苏宏业. 中值互补集合经验模态分解. 自动化学报, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c201031
Liu Song-Hua, He Bing-Bing, Lang Xun, Chen Qi-Ming, Zhang Yu-Feng, Su Hong-Ye. Median complementary ensemble empirical mode decomposition. Acta Automatica Sinica, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c201031
Citation: Liu Song-Hua, He Bing-Bing, Lang Xun, Chen Qi-Ming, Zhang Yu-Feng, Su Hong-Ye. Median complementary ensemble empirical mode decomposition. Acta Automatica Sinica, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c201031

中值互补集合经验模态分解

doi: 10.16383/j.aas.c201031
基金项目: 国家自然科学基金(81771928, 62003298), 云南省基础研究计划重点项目(202101AS070031), 中国博士后科学基金资助项目(2020M683389)资助
详细信息
    作者简介:

    刘淞华:云南大学信息学院硕士研究生. 主要研究方向为数据驱动故障检测与诊断、微弱信号检测与处理. E-mail: liusonghuaYN@126.com

    何冰冰:云南大学信息学院博士研究生. 主要研究方向为超声平面波血流信号处理. E-mail: he_bing_bing123@126.com

    郎恂:云南大学信息学院讲师. 主要研究方向为数据驱动故障检测与诊断、时频分析和医学信号处理. 本文通信作者. E-mail: langxun@ynu.edu.cn

    陈启明:浙江大学控制科学与工程学院博士研究生. 主要研究方向为信号分解、时频分析和故障诊断. E-mail: chenqiming@zju.edu.cn

    张榆锋:云南大学信息学院教授. 主要研究方向为数字信号处理理论, 微弱信号检测和医学超声工程. E-mail: zhangyf@ynu.edu.cn

    苏宏业:浙江大学控制科学与工程学院教授. 主要研究方向为控制理论与应用, 复杂过程先进控制和优化技术, 先进控制软件开发及应用. E-mail: hysu69@zju.edu.cn

Median Complementary Ensemble Empirical Mode Decomposition

Funds: Supported by National Natural Science Foundation of P. R. China (81771928, 62003298), Key Project of Fundamental Research of Yunnan Province (202101AS070031) and China Postdoctoral Science Foundation (2020M683389)
More Information
    Author Bio:

    LIU Song-Hua Master student at the School of Information, Yunnan University. His research interest covers data-driven fault detection and diagnosis, weak signal detection and processing

    HE Bing-Bing Ph.D. candidate at the School of Information, Yunnan University. Her research interest covers ultrasonic plane wave blood flow signal processing

    LANG Xun Lecturer at the School of Information, Yunnan University. His main research interest covers data-driven fault detection and diagnosis, time-frequency analysis and medical signal processing. Corresponding author of this paper

    CHEN Qi-Ming Ph.D. candidate at the College of Control Science and Engineering, Zhejiang University. His main research interest covers signal decomposition, time-frequency analysis and fault diagnosis

    ZHANG Yu-Feng Professor at the School of In-formation, Yunnan University. His research interest covers digital signal processing theory, weak signal detection and medical ultrasound engineering

    SU Hong-Ye Professor at the College of Control Sci-ence and Engineering, Zhejiang University. His re-search interest covers control theory and application, complex process advanced control and optimization technology, and the software development and appli-cation of advanced control

  • 摘要: 针对经验模态分解(Empirical mode decomposition, EMD)系列方法存在的模态分裂(Mode Splitting, MS)问题, 本文提出中值互补集合经验模态分解(Median complementary ensemble EMD, MCEEMD)算法. 通过概率模型量化互补集合经验模态分解(Complementary ensemble EMD, CEEMD)的MS问题, 证明了使用中值算子替代算术平均算子对抑制MS的有效性. MCEEMD算法首先添加 对互补的白噪声至原信号中, 并经过EMD分解得到 组固有模态函数(Intrinsic mode functions, IMFs), 然后分别对其中互补相关的IMFs两两取平均得到 组IMFs, 最后使用中值算子处理上述 组IMFs得到输出结果. 对仿真信号与实测信号的分析结果表明, 本文提出的MCEEMD方法不仅有效抑制了CEEMD的MS问题, 而且避免了单一使用中值算子的两个缺点, 即: 1)分解完备性差和2) IMFs中存在毛刺现象.
  • 图  1  EMD分解噪声辅助信号得到的前5个互补IMFs

    Fig.  1  The first five complementary IMFs obtained from the noise-assisted signal through EMD

    图  2  互补IMFs(由噪声辅助信号得到)的${p_i}(f)$${r_i}(f)$曲线

    Fig.  2  The curves ${p_i}(f)$ and ${r_i}(f)$ corresponding to the complementary IMFs (obtained from the noise-assisted signal)

    图  3  互补IMFs(由噪声辅助信号得到)的${P_i}(f)$曲线

    Fig.  3  The curves ${P_i}(f)$ corresponding to the complementary IMFs (obtained from the noise-assisted signal)

    图  4  不同算子处理互补IMFs集合得到的$MSD(f)$

    Fig.  4  Curves of $MSD(f)$ obtained by processing the complementary IMFs with different operators

    图  5  MCEEMD算法框图

    Fig.  5  The block diagram of the MCEEMD algorithm

    图  6  不同集合尺寸下CEEMD、MEEMD和MCEEMD的$R(f)$曲线

    Fig.  6  $R(f)$curves for different ensemble sizes within CEEMD、MEEMD and MCEEMD

    图  7  MCEEMD、MEEMD和CEEMD在不同集合尺寸下的$SDR(N)$曲线

    Fig.  7  $SDR(N)$ curves for different ensemble sizes within CEEMD、MEEMD and MCEEMD

    图  8  四种方法分解仿真信号所得的前5个IMF

    Fig.  8  The first five IMFs obtained by decomposing the simulated signal by four methods

    图  9  MEEMD、MCEEMD分解结果中的${d_{\rm{2}}}$分量

    Fig.  9  The${d_{\rm{2}}}$mode in the decomposition results of MEEMD and MCEEMD

    图  10  四种方法分解结果的PSD

    Fig.  10  The PSD curves of the decomposition results from the four methods

    图  11  MCEEMD分解血流信号所得的前8个分量

    Fig.  11  The first 8 components of the blood flow signal decomposed by MCEEMD

    图  12  原始信号的频率归一化功率谱

    Fig.  12  The frequency normalized PSD of the original signal

    图  13  (a) ~ (d)分别对应EEMD、CEEMD、MEEMD、MCEEMD提取的血流成分频率归一化功率谱

    Fig.  13  (a) ~ (d) correspond to the frequency normalized PSD of the blood flow component extracted by EEMD, CEEMD, MEEMD, and MCEEMD, respectively

    表  1  四种方法的性能指标

    Table  1  Performance indicators of the four methods

    方法PCCRMSEPSD area ratio
    EEMD0.95680.30870.28%
    CEEMD0.99860.00310.21%
    MEEMD0.72931.29380.24%
    MCEEMD0.99800.16140.14%
    下载: 导出CSV

    表  2  四种方法的计算时间

    Table  2  Calculation time of the four methods

    方法EEMDCEEMDMEEMDMCEEMD
    计算时间14.32 s28.95 s14.58 s29.01 s
    下载: 导出CSV
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  • 收稿日期:  2020-12-13
  • 录用日期:  2021-05-28
  • 网络出版日期:  2021-07-09

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