基于互补自适应噪声的集合经验模式分解算法

蔡念; 黄威威; 谢伟; 叶倩; 杨志景

doi:10.11999/JEIT141632

基于互补自适应噪声的集合经验模式分解算法

doi: 10.11999/JEIT141632

基金项目:

国家自然科学基金(61001179, 61471132)，东莞市产学研合作项目(2013509104105)和广州市产学研协同创新重大专项(201508010001)

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出版历程
- 收稿日期: 2014-12-25
- 修回日期: 2015-06-15
- 刊出日期: 2015-10-19

Ensemble Empirical Mode Decomposition Base on Complementary Adaptive Noises

Funds:

The National Natural Science Foundation of China (61001179, 61471132)

摘要

摘要: 经验模式分解(EMD)及其改进算法作为实用的信号处理方法至今仍然缺少严格的数学理论。该文尝试从数学理论上分析集合经验模式分解和自适应噪声集合经验模式分解的重构误差，推导了总体残留噪声的计算公式。针对自适应噪声集合经验模式分解在每一层固有模态分量上仍然存在残留噪声的问题，在分解过程中添加成对的正负噪声分量，提出一种基于互补自适应噪声的集合经验模式分解算法。实验结果表明，相比于集合经验模式分解和自适应噪声集合经验模式分解，所提的方法能够明显地减少每一层固有模态分量中残留的噪声，拥有较好的信号重构精度和更快的分解速度。
- 经验模式分解 /
- 集合经验模式分解 /
- 自适应噪声集合经验模式分解 /
- 模态混叠
Abstract: Empirical Model Decomposition (EMD) and its improved algorithms are most useful signal processing methods. However, those methods still lack rigorous mathematical theory. This paper attempts to analyze mathematically the reconstruction errors for Ensemble EMD (EEMD) and EEMD with Adaptive Noises (EEMDAN). Moreover, the formulae of the residual noise are deduced step by step. There exists the residual noise in each intrinsic mode function during the EEMDAN. To suppress the residual noise, an improved ensemble empirical mode decomposition with complementary adaptive noises by adding pairs of positive and negative noises is proposed. The experimental results indicate that the proposed method can obviously reduce the residual noise in each intrinsic mode function compared with the EEMD and the EEMDAN, and it also has better signal reconstruction precision and faster signal decomposition.
- Empirical Model Decomposition (EMD) /
- Ensemble EMD (EEMD) /
- EEMD with Adaptive Noise (EEMDAN) /
- Mode mixing

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参考文献(22)

Huang N E, Shen Z, Long S R, et al.. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903-995.

Yang Z, Ling B W K, and Bingham C. Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum[J]. Measurement, 2013, 46(8): 2481-2491.

Yang Z, Ling B W K, and Bingham C. Fault detection and signal reconstruction for increasing operational availability of industrial gas turbines[J]. Measurement, 2013, 46(6): 1938-1946.

王玉静, 康守强, 张云, 等. 基于集合经验模态分解敏感固有模态函数选择算法的滚动轴承状态识别方法[J]. 电子与信息学报, 2014, 36(3): 595-600.

Wang Yu-jing, Kang Shou-qiang, Zhang Yun, et al.. Condition recognition method of rolling bearing based on ensemble empirical mode decomposition sensitive intrinsic mode function selection algorithm[J]. Journal of Electronics Information Technology, 2014, 36(3): 595-600.

Li H, Wang X, Chen L, et al.. Denoising and R-peak detection of electrocardiogram signal based on EMD and improved approximate envelope[J]. Circuits, Systems, and Signal Processing, 2014, 33(4): 1261-1276.

杨达, 王孝通, 徐冠雷. 基于多尺度极值的一维信号趋势项快速提取方法研究[J]. 电子与信息学报, 2013, 35(5): 1208-1214.

Yang Da, Wang Xiao-tong, and Xu Guan-lei. Research on 1D signal fast trend extracting via multi-scale extrema[J]. Journal of Electronics Information Technology, 2013, 35(5): 1208-1214.

白春华, 周宣赤, 林大超, 等. 消除 EMD 端点效应的 PSO-SVM 方法研究[J]. 系统工程理论实践, 2013, 33(5): 1298-1306.

Bai Chun-hua, Zhou Xuan-chi, and Lin Da-chao, et al.. PSO-SVM method based on elimination of end effects in EMD[J]. Systems Engineering-Theory Practice, 2013, 33(5): 1298-1306.

Lin D C, Guo Z L, An F P, et al.. Elimination of end effects in empirical mode decomposition by mirror image coupled with support vector regression[J]. Mechanical Systems and Signal Processing, 2012, 31: 13-28.

汤宝平, 董绍江, 马靖华. 基于独立分量分析的EMD模态混叠消除方法研究[J]. 仪器仪表学报, 2012, 33(7): 1477-1482.

Tang Bao-ping, Dong Shao-jiang, and Ma Jing-hua. Study on the method for eliminating mode mixing of empirical mode decomposition based on independent component analysis[J]. Chinese Journal of Scientific Instrument, 2012, 33(7): 1477-1482.

Shen W C, Chen Y H, and Wu A Y A. Low-complexity sinusoidal-assisted EMD (SAEMD) algorithms for solving mode-mixing problems in HHT[J]. Digital Signal Processing, 2014(24): 170-186.

Zheng J, Cheng J, and Yang Y. Partly ensemble empirical mode decomposition: an improved noise-assisted method for eliminating mode mixing[J]. Signal Processing, 2014(96): 362-374.

高云超, 桑恩方, 许继友. 分离EMD中混叠模态的新方法[J]. 哈尔滨工程大学学报, 2008, 29(9): 963-966.

Gao Yun-chao, Sang En-fang, and Xu Ji-you. A new method for separating mixed modes in empirical mode decomposition [J]. Journal of Harbin Engineering University, 2008, 29(9): 963-966.

Wu Z and Huang N E. Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in Adaptive Data Analysis, 2009, 1(1): 1-41.

Yeh J R, Shieh J S, and Huang N E. Complementary ensemble empirical mode decomposition: a novel noise enhanced data analysis method[J]. Advances in Adaptive Data Analysis, 2010, 2(2): 135-156.

Torres M E, Colominas M A, Schlotthauer G, et al.. A complete ensemble empirical mode decomposition with adaptive noise[C]. 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech, 2011: 4144-4147.

Wu Z and Huang N E. A study of the characteristics of white noise using the empirical mode decomposition method[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2004, 460(2046): 1597-1611.

Goldberger A L, Amaral L A N, Glass L, et al.. PhysioBank, Physio Toolkit and PhysioNet: components of a new research resource for complex physiologic signals[J]. Circulation, 2000, 101(23): E215-E220.

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