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                    中值互補集合經驗模態分解

                    劉淞華 何冰冰 郎恂 陳啟明 張榆鋒 蘇宏業

                    劉淞華, 何冰冰, 郎恂, 陳啟明, 張榆鋒, 蘇宏業. 中值互補集合經驗模態分解. 自動化學報, 2021, 47(x): 1?13 doi: 10.16383/j.aas.c201031
                    引用本文: 劉淞華, 何冰冰, 郎恂, 陳啟明, 張榆鋒, 蘇宏業. 中值互補集合經驗模態分解. 自動化學報, 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

                    中值互補集合經驗模態分解

                    doi: 10.16383/j.aas.c201031
                    基金項目: 國家自然科學基金(81771928, 62003298), 云南省基礎研究計劃重點項目(202101AS070031), 中國博士后科學基金資助項目(2020M683389)資助
                    詳細信息
                      作者簡介:

                      劉淞華:云南大學信息學院碩士研究生. 主要研究方向為數據驅動故障檢測與診斷、微弱信號檢測與處理. E-mail: liusonghuaYN@126.com

                      何冰冰:云南大學信息學院博士研究生. 主要研究方向為超聲平面波血流信號處理. E-mail: he_bing_bing123@126.com

                      郎恂:云南大學信息學院講師. 主要研究方向為數據驅動故障檢測與診斷、時頻分析和醫學信號處理. 本文通信作者. E-mail: langxun@ynu.edu.cn

                      陳啟明:浙江大學控制科學與工程學院博士研究生. 主要研究方向為信號分解、時頻分析和故障診斷. E-mail: chenqiming@zju.edu.cn

                      張榆鋒:云南大學信息學院教授. 主要研究方向為數字信號處理理論, 微弱信號檢測和醫學超聲工程. E-mail: zhangyf@ynu.edu.cn

                      蘇宏業:浙江大學控制科學與工程學院教授. 主要研究方向為控制理論與應用, 復雜過程先進控制和優化技術, 先進控制軟件開發及應用. 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: 針對經驗模態分解(Empirical mode decomposition, EMD)系列方法存在的模態分裂(Mode Splitting, MS)問題, 本文提出中值互補集合經驗模態分解(Median complementary ensemble EMD, MCEEMD)算法. 通過概率模型量化互補集合經驗模態分解(Complementary ensemble EMD, CEEMD)的MS問題, 證明了使用中值算子替代算術平均算子對抑制MS的有效性. MCEEMD算法首先添加 對互補的白噪聲至原信號中, 并經過EMD分解得到 組固有模態函數(Intrinsic mode functions, IMFs), 然后分別對其中互補相關的IMFs兩兩取平均得到 組IMFs, 最后使用中值算子處理上述 組IMFs得到輸出結果. 對仿真信號與實測信號的分析結果表明, 本文提出的MCEEMD方法不僅有效抑制了CEEMD的MS問題, 而且避免了單一使用中值算子的兩個缺點, 即: 1)分解完備性差和2) IMFs中存在毛刺現象.
                    • 圖  1  EMD分解噪聲輔助信號得到的前5個互補IMFs

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

                      圖  2  互補IMFs(由噪聲輔助信號得到)的${p_i}(f)$${r_i}(f)$曲線

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

                      圖  3  互補IMFs(由噪聲輔助信號得到)的${P_i}(f)$曲線

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

                      圖  4  不同算子處理互補IMFs集合得到的$MSD(f)$

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

                      圖  5  MCEEMD算法框圖

                      Fig.  5  The block diagram of the MCEEMD algorithm

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

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

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

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

                      圖  8  四種方法分解仿真信號所得的前5個IMF

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

                      圖  9  MEEMD、MCEEMD分解結果中的${d_{\rm{2}}}$分量

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

                      圖  10  四種方法分解結果的PSD

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

                      圖  11  MCEEMD分解血流信號所得的前8個分量

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

                      圖  12  原始信號的頻率歸一化功率譜

                      Fig.  12  The frequency normalized PSD of the original signal

                      圖  13  (a) ~ (d)分別對應EEMD、CEEMD、MEEMD、MCEEMD提取的血流成分頻率歸一化功率譜

                      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  四種方法的性能指標

                      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%
                      下載: 導出CSV

                      表  2  四種方法的計算時間

                      Table  2  Calculation time of the four methods

                      方法EEMDCEEMDMEEMDMCEEMD
                      計算時間14.32 s28.95 s14.58 s29.01 s
                      下載: 導出CSV
                      360彩票
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                    • 收稿日期:  2020-12-13
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