[1] Wei Dongdong, Tang Wencheng,. A method for constraining the end effect of EMDbased on sequential similarity detection and adaptive filter [J]. Journal of Southeast University (English Edition), 2021, 37 (1): 14-21. [doi:10.3969/j.issn.1003-7985.2021.01.003]
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A method for constraining the end effect of EMDbased on sequential similarity detection and adaptive filter(
)
基于序贯相似性检测和自适应滤波的EMD端点效应处理方法
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 37
- Issue:
- 2021 1
- Page:
- 14-21
- Research Field:
- Mechanical Engineering
- Publishing date:
- 2021-03-20
Info
- Title:
- A method for constraining the end effect of EMDbased on sequential similarity detection and adaptive filter
- 基于序贯相似性检测和自适应滤波的EMD端点效应处理方法
- Author(s):
- Wei Dongdong; Tang Wencheng
- School of Mechanical Engineering, Southeast University, Nanjing 211189, China
- Keywords:
- empirical mode decomposition(EMD); end effect; sequential similarity detection; adaptive filter
- PACS:
- TH17;TH165.3
- DOI:
- 10.3969/j.issn.1003-7985.2021.01.003
- Abstract:
- Aimed at the problem of the end effect when using empirical mode decomposition(EMD), a method for constraining the end effect of EMD is proposed based on sequential similarity detection and adaptive filter. The method divides the signal into many wavelets, and it changes the initial wavelet length to select the best initial wavelet that has the minimum error and maximum number of matching seed wavelets, and the wavelet slopes are used for pre-matching and secondary matching to speed up the matching speed. Then, folded self-adaptive threshold is used to select multiple seed wavelets, and finally the end waveform is predicted and expanded according to the adaptive filter method. The proposed method is used to analyze the non-stationary nonlinear simulation signal and experimental signal, and it is compared with the mirror extension and RBF extension methods. The orthogonality index and similarity index of the EMD results of the extended signal after the proposed method are better than those of the other methods. The results show that the proposed method can better constrain the end effect, and has certain validity, accuracy and stability in solving the end effect problem.
- 针对经验模态分解时存在的端点效应问题, 提出了一种基于序贯相似度检测和自适应滤波的方法来抑制EMD的端点效应.该方法将信号分成多个子波, 通过改变初始子波的长度来选择误差最小、匹配种子子波个数最大的最佳初始子波, 并利用子波斜率进行预匹配和二次匹配, 以提高匹配速度.然后利用对折方式自适应调整阈值选择多个种子小波, 最后根据自适应滤波方法对端点波形进行预测和扩展.利用该方法对非平稳非线性仿真信号和实验信号进行了分析, 并与镜像拓延法和RBF拓延法进行了比较, 该方法拓延后信号的EMD结果正交指数和相似指数优于其他方法.结果表明, 该方法能较好地抑制端点效应, 对解决端点效应问题具有一定的有效性、准确性和稳定性.
References:
[1] 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. DOI:10.1098/rspa.1998.0193.
[2] Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: The Hilbert spectrum[J]. Annual Review of Fluid Mechanics, 1999, 31(1): 417-457. DOI:10.1146/annurev.fluid.31.1.417.
[3] Bi F R, Ma T, Wang X. Development of a novel knock characteristic detection method for gasoline engines based on wavelet-denoising and EMD decomposition[J].Mechanical Systems and Signal Processing, 2019, 117: 517-536. DOI:10.1016/j.ymssp.2018.08.008.
[4] Nie Z H, Shen F, Xu D J, et al. An EMD-SVR model for short-term prediction of ship motion using mirror symmetry and SVR algorithms to eliminate EMD boundary effect[J]. Ocean Engineering, 2020, 217: 107927. DOI:10.1016/j.oceaneng.2020.107927.
[5] Zhang X J, Huo Y, Wan D S. Improved EMD based on piecewise cubic hermite interpolation and mirror extension[J]. Chinese Journal of Electronics, 2020, 29(5): 899-905. DOI:10.1049/cje.2020.08.005.
[6] Yang J P, Li P Z, Yang Y F, et al. An improved EMD method for modal identification and a combined static-dynamic method for damage detection[J]. Journal of Sound and Vibration, 2018, 420: 242-260. DOI:10.1016/j.jsv.2018.01.036.
[7] Wang J, Liu W Y, Zhang S. An approach to eliminating end effects of EMD through mirror extension coupled with support vector machine method[J]. Personal and Ubiquitous Computing, 2019, 23(3/4): 443-452. DOI:10.1007/s00779-018-01198-6.
[8] Hao R J, Li F. A new method to suppress the EMD endpoint effect[J]. Journal of Vibration, Measurement and Diagnosis, 2018, 38(2): 341-345. DOI:10.16450/j.cnki.issn.1004-6801.2018.02.019. (in Chinese)
[9] Shao C X, Wang J, Fan J F, et al. A self adaptive method dealing with the end issue of EMD[J]. Acta Electtonica Sinica, 2007, 35(10): 1944-1948.(in Chinese)
[10] Su D L, Zheng H P. A boundary extension method for empirical mode decomposition end effect[J]. Journal of Aeronautics, 2016, 37(3): 960-969.(in Chinese)
[11] Xu Z F, Liu K. Method of empirical mode decomposition end effect based on analysis of extreme value symbol sequence[J]. Journal of Vibration, Measurement & Diagnosis, 2015, 35(2): 309-315.(in Chinese)
[12] Rong Q B. Research on EMD method for improving end effect and suppressing modal mixing [D]. Tianjin: Tianjin University, 2017.(in Chinese)
[13] Wald A. Sequential analysis[M]. New York: Wiley, 1947.
[14] Chen H X, Shang Y F, Sun K. Multiple fault condition recognition of gearbox with sequential hypothesis test[J].Mechanical Systems and Signal Processing, 2013, 40(2): 469-482. DOI:10.1016/j.ymssp.2013.06.023.
[15] Qian G B, Dong F, Wang S Y. Robust constrained minimum mixture kernel risk-sensitive loss algorithm for adaptive filtering[J].Digital Signal Processing, 2020, 107: 102859. DOI:10.1016/j.dsp.2020.102859.
[16] Zhu L F, Song C T, Pan L Z, et al. Adaptive filtering under the maximum correntropy criterion with variable center[J].IEEE Access, 2019, 7: 105902-105908. DOI:10.1109/ACCESS.2019.2932201.
[17] Li Y, Fang Z B, Wei Y F. Suppressing end effect of EMD based on local polynomial regression[J]. Journal of University of Science and Technology of China, 2014, 44(9): 786-792.(in Chinese)
[18] Huang N E, Wu M L C, Long S R, et al. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis[J].Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 2003, 459(2037): 2317-2345. DOI:10.1098/rspa.2003.1123.
[19] Han J P, Qian J, Dong X J. A method using mirror extension and RBF neural network to deal with end effect in EMD[J]. Journal of Vibration, Measurement & Diagnosis, 2010, 30(4): 414-417.(in Chinese)
Memo
- Memo:
-
Biographies: Wei Dongdong(1996—), male, graduate; Tang Wencheng(corresponding author), male, doctor, professor, tangwc@seu.edu.cn.
Foundation item: The National Natural Science Foundation of China(No. 51675100).
Citation: Wei Dongdong, Tang Wencheng. A method for constraining the end effect of EMD based on sequential similarity detection and adaptive filter[J].Journal of Southeast University(English Edition), 2021, 37(1):14-21.DOI:10.3969/j.issn.1003-7985.2021.01.003.