低采样率下经验模态分解性能提升研究

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (17) : 185-190.

论文

低采样率下经验模态分解性能提升研究

黎恒1，李智2,3，莫玮1

作者信息 +

Performance improvement for empirical mode decomposition at low sampling rates

LI Heng1, LI Zhi2,3, and MO Wei1

Author information +

文章历史 +

摘要

经验模态分解(EMD)使用信号极值点的位置和取值信息进行分解，对采样率有较高的要求。针对EMD在低采样率下性能降低的现象，提出一种基于B样条拟合的信号局部均值计算方法。首先提取信号极值点出现的时刻作为尺度，然后通过对极值点时刻进行重新采样构造B样条节点，最后应用B样条最小二乘拟合方法直接计算局部均值。与EMD方法相比，本文方法不需要信号极值点的准确位置和取值，因此不容易受到低采样率的影响。对平稳信号和非平稳信号的仿真结果表明，该方法能在接近奈奎斯特频率的低采样率下获得较高的性能。与基于插值的解决方案相比，该方法的分离性能更好。

Abstract

Empirical mode decomposition (EMD) depends highly on the exact location and value of extrema, which requires a high degree of oversampling. Aiming at improving the performance of EMD under low sampling rates, a local mean estimation method based on B-spline approximation is proposed. Firstly, the location of extrema is extracted as the time scale. Then, the location is re-sampled to generate knots for B-splines. Finally, the local mean is computed directly based on B-spline least squares approximation. In compare with the existing EMD method, the exact location and value of extrema are not essential to the proposed technique. The efficiency of this technique is demonstrated using synthetic signals. Experiments show that the performance of the proposed method is not reduced even the sampling rate is close to the Nyquist rate. It also demonstrates that the proposed method is superior to existing interpolation methods in separation performance.

导出引用

黎恒1，李智2,3，莫玮1. 低采样率下经验模态分解性能提升研究[J]. 振动与冲击, 2016, 35(17): 185-190

LI Heng1, LI Zhi2,3, and MO Wei1. Performance improvement for empirical mode decomposition at low sampling rates[J]. Journal of Vibration and Shock, 2016, 35(17): 185-190

参考文献

[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, 1998, 454(1971): 903-995.
[2] 吴响, 钱建生, 王海燕. 微震信号多尺度非线性特征提取与辨识研究[J]. 仪器仪表学报, 2014, 35(5): 969-975.
WU X, QIAN J S, WANG H Y. Study on multi-scale nonlinear feature extraction and signal identification for microseismic signal[J]. Chinese Journal of Scientific Instrument, 2014, 35(5): 969-975.
[3] 王录雁王强张梅军李焕良赵玮. 基于 EMD 的滚动轴承故障灰色诊断方法[J]. 振动与冲击, 2014, 33(3): 197-202.
WANG Lu-yan, WANG Qiang, ZHANG Mei-jun, LI Huan-liang, ZHAO Wei. A grey fault diagnosis method for rolling bearing based on EMD [J]. Journal of vibration and shock, 2014, 33(3): 197-202.
[4] YANG Z, LING B W K, BINGHAM C. Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum[J]. Measurement, 2013, 46(8): 2481-2491.
[5] KOMATY A, BOUDRAA A -O, AUGIER B, et al. EMD-Based Filtering Using Similarity Measure Between Probability Density Functions of IMFs[J]. IEEE Transactions on Instrumentation and Measurement, 2014, 63(1):27-34.
[6] GOHARRIZI A Y, SEPEHRI N. Internal Leakage Detection in Hydraulic Actuators Using Empirical Mode Decomposition and Hilbert Spectrum[J]. IEEE Transactions on Instrumentation and Measurement , 2012, 61(2):36-378.
[7] LEI Y, LIN J, HE Z, et al. A review on empirical mode decomposition in fault diagnosis of rotating machinery[J]. Mechanical Systems and Signal Processing, 2013, 35(1): 108-126.
[8] Rilling G, Flandrin P. on the Influence of Sampling on the Empirical Mode Decomposition[C]// IEEE International Conference on Acoustics, Speech and Signal Processing. Toulouse:IEEE, 2006: 444-447.
[9] 肖瑛, 殷福亮. 解相关 EMD: 消除模态混叠的新方法[J]. 振动与冲击, 2015, 34(4): 25-29.
Xiao Ying, Yin Fuliang. Decorrelation emd: a new method of eliminating mode mixing[J]. Journal of vibration and shock, 2015, 34(4): 25-29.
[10] 王录雁, 王强, 鲁冬林等. EMD自适应三角波匹配延拓算法[J]. 振动与冲击, 2014, 33(4): 94-99.
WANG Lu-yan, WANG Qiang, LU Dong-lin, et al. A self-adaptive triangular waveform matching extension algorithm for EMD. Journal of vibration and shock, 2014, 33(4): 94-99.
[11] XU Z, HUANG B, ZHANG F. Improvement of empirical mode decomposition under low sampling rate[J]. Signal processing, 2009, 89(11): 2296-2303.
[12] ROY A, DOHERTY J F. Improved signal analysis performance at low sampling rates using raised cosine empirical mode decomposition[J]. Electronics letters, 2010, 46(2): 176-177.
[13] CHEN Q, HUANG N, RIEMENSCHNEIDER S, et al. A B-spline approach for empirical mode decompositions[J]. Advances in Computational Mathematics, 2006, 24(1-4): 171-195.
[14] 赵利强王建林于涛. 基于改进EMD的输油管道泄漏信号特征提取方法研究[J]. 仪器仪表学报, 2013, 34(12): 2696-2702.
ZHAO Li-qiang, WANG Jian-lin, YU Tao. Study on the extraction method for oil pipeline leakage signal feature based on improved empirical mode decompositio [J]. Chinese Journal of Scientific Instrument, 2013, 34(12): 2696-2702.
[15] KIM D, PARK M, OH H S. Bidimensional statistical empirical mode decomposition[J]. Signal Processing Letters, IEEE, 2012, 19(4): 191-194.
[16] UNSER M, ALDROUBI A, EDEN M. B-spline signal processing. I. Theory[J]. IEEE Transactions on Signal Processing, 1993, 41(2): 821-833.
[17] UNSER M. Splines: A perfect fit for signal and image processing[J]. IEEE Signal Processing Magazine, 1999, 16(6): 22-38.
[18] RILLING G, FLANDRIN P. One or two frequencies? The empirical mode decomposition answers[J]. IEEE Transactions on Signal Processing, 2008, 56(1): 85-95.