Levy噪声中EMD降噪的随机共振研究
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摘要
经验模态分解(empirical mode decomposition,EMD)降低噪声的同时也削弱信号能量,并会产生虚假信号,导致信号检测存在缺陷,针对这一问题,提出Levy噪声环境下经验模态分解随机共振检测方法。通过将含噪信号进行EMD分解,对分解后信号进行叠加取平均二次采样等处理方法,使其满足随机共振要求,利用自适应算法优化系统参数,进而使处理后信号能够在双稳系统中产生随机共振,达到精确检测的目的。理论分析及实验证明在Levy噪声下,此方法能实现同一特征指数下单频信号与多频信号检测,实验表明在单频信号信噪比为-28 dB情况下能有14 dB的提高,特征指数为1.8下多频信号5 Hz频谱幅值从311.8增加到724,10 Hz频谱幅值由138.9增加到143.2。此方法对在复杂噪声环境中降低剩余噪声能量同时,提高信号能量,减少虚假信号,相对于仅仅进行EMD分解无法判断信号成分,能更好的达到检测效果。
Empirical mode decomposition(EMD) method attenuates the signals' energy and generates false signals in decomposing signal noise,which leads to incorrect detection results.In order to solve this problem,a stochastic resonance method under Levy noise after denoised by EMD decomposition is presented in this paper.After decomposed by EMD,the noisy signals are handled by overlaying,averaging and resampling to meet the condition of stochastic resonance.An adaptive algorithm is used to optimize system parameters,and then the processed signal can generate stochastic resonance in bistable system to achieve precise detection.The theoretical analysis and experimental results prove that the method can detect single-frequency signal and multi-frequency signal under the same characteristic exponent with the Levy noise.The experimental results demonstrate that the SNR of single-frequency signal can increase 14 d B in the case of SNR of -28 d B.The spectral amplitude of the 5 Hz spectrum is increased from 311.8 to 724 and 10 Hz spectrum amplitude is increased from 138.9 to 143.2.This method that reduces the residual noise energy and false signal can improve the signal energy in a complex noisy condition.Compared to EMD decomposition which cannot determine the signal components,this method can achieve the detection effect better.
Empirical mode decomposition(EMD) method attenuates the signals' energy and generates false signals in decomposing signal noise,which leads to incorrect detection results.In order to solve this problem,a stochastic resonance method under Levy noise after denoised by EMD decomposition is presented in this paper.After decomposed by EMD,the noisy signals are handled by overlaying,averaging and resampling to meet the condition of stochastic resonance.An adaptive algorithm is used to optimize system parameters,and then the processed signal can generate stochastic resonance in bistable system to achieve precise detection.The theoretical analysis and experimental results prove that the method can detect single-frequency signal and multi-frequency signal under the same characteristic exponent with the Levy noise.The experimental results demonstrate that the SNR of single-frequency signal can increase 14 d B in the case of SNR of -28 d B.The spectral amplitude of the 5 Hz spectrum is increased from 311.8 to 724 and 10 Hz spectrum amplitude is increased from 138.9 to 143.2.This method that reduces the residual noise energy and false signal can improve the signal energy in a complex noisy condition.Compared to EMD decomposition which cannot determine the signal components,this method can achieve the detection effect better.
引文
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[14]张刚,宋莹,张天骐,等.Lévy噪声下一阶线性系统的弱信号复原分析[J].仪器仪表学报,2016,37(1):109-118.ZHANG G,SONG Y,ZHANG T Q,et al.Weak signal recovery analysis in first-order liner system under Lévy noise[J].Chinese Journal of Scientific Instrument,2016,37(1):109-118.
[15]王季,楼军伟,李贵子,等.EMD样本熵在滚动轴承信号复杂性度量中的应用[J].中国测试,2014(s1):45-48.WANG J,LOU J W,WANG G Z,et al.Application of EMD sample entropy in rolling bearing signal complexity measure[J].China Measurement&Test,2014(s1):45-48.
[16]张淑清,翟欣沛,董璇,等.EMD及Duffing振子在小电流系统故障选线方法中的应用[J].中国电机工程学报,2013,33(10):161-167.ZHANG SH Q,ZHAI X P,DONG X,et al.Application of EMD and duffing oscillator to fault line detection in uneffectively grounded system[J].Proceedings of the CSEE,2013,33(10):161-167.
[17]张刚,胡韬,王颖.基于Melnikov函数Duffing系统微弱信号检测[J].电子测量技术,2015,38(1):109-112.ZHANG G,HU T,WANG Y.The weak signal detection based on duffing system and melnikov function[J].Electronic Measurement Technology,2015,38(1):109-112.
[18]赖志慧,冷永刚,孙建桥,等.基于Duffing振子的变尺度微弱特征信号检测方法研究[J].物理学报,2012,61(5):60-68.LAI ZH H,LENG Y G,SUN J Q,et al.Large parameter stochastic resonance of two-dimensional Duffing oscillator and its application on weak on weak signal detection[J].Acta Physica Sinica,2012,61(5):60-68.
[19]缑新科,马艳.多频信号的多尺度随机共振检测方法及应用[J].兰州理工大学学报,2015,41(5):91-94.GOU X K,MA Y.Multi scale stochastic resonance detection method of multi-frequency signal and its application[J].Journal of Lanzhou University of Technology,2015,41(5):91-94.
[2]赖志慧,冷永刚,范胜波.级联双稳Duffing系统的随机共振研究[J].物理学报,2013,62(7):69-77.LAI ZH H,LENG Y G,FAN SH B.Stochastic resonance of cascaded bistable duffing system[J].Acta Physica Sinica,2013,62(7):69-77.
[3]韩东颖,丁雪娟,时培明.基于自适应变尺度频移带通随机共振降噪的EMD多频微弱信号检测[J].机械工程学报,2013,49(8):10-18.HAN D Y,DING X J,SHI P M.Multi-frequency weak signal detection based on emd after de-noising by adaptive re-scaling frequency-shifted band-pass stochastic resonance[J].Journal of Mechanical Engineering,2013,49(8):10-18.
[4]苗晟,王威廉,姚绍文.Hilbert-Huang变换发展历程及其应用[J].电子测量与仪器学报,2014,28(8):812-818.MAO SH,WANG W L,YAO SH W.Historic development of HTT and its applications[J].Journal of Electronic Measurement and Instrumentation,2014,28(8):812-818.
[5]朱维娜,林敏.基于随机共振和人工鱼群算法的微弱信号智能检测系统[J].仪器仪表学报,2013,34(11):2464-2470.ZHU W N,LIN M.Weak signal intelligent detection system based on stochastic resonance and artificial fish swarm algorithm[J].Chinese Journal of Scientific Instrument,2013,34(11):2464-2470.
[6]冷永刚.双稳调参高频共振机理[J].物理学报,2011,60(2):1-7.LENG Y G.Mechanism of high frequency resonance of parameter-adjusted bistable system[J].Acta Physica Sinica,2011,60(2):1-7.
[7]赵文礼,刘进,殷园平.基于随机共振原理的中低频信号检测方法与电路设计[J].仪器仪表学报,2011,32(4):721-728.ZHAO W L,LIU J,YIN Y P.Medium-low frequency signal detection based on stochastic resonance principle[J].Chinese Journal of Scientific Instrument,2011,32(4):721-728.
[8]樊养余,李利品,党瑞荣.基于随机共振的任意大频率微弱信号检测方法研究[J].仪器仪表学报,2013,34(3):566-572.FAN Y Y,LI L P,DANG R R.Study on high frequency weak signal detection method based on stochastic resonance[J].Chinese Journal of Scientific Instrument,2013,34(3):566-572.
[9]张宇,吕海峰,赵远,等.基于非线性系统随机共振的多频弱信号检测[J].吉林大学学报,2007,25(1):68-72.ZHANG Y,LV H F,ZHAO Y,et al.Detection of multifrequency weak signal based on stochastic resonance of nonlinear system[J].Journal of Jilin University,2007,25(1):68-72.
[10]焦尚彬,任超,黄伟超,等.α稳定噪声环境下多频微弱信号检测的参数诱导随机共振现象[J].物理学报,2013,62(21):34-43.JIAO SH B,REN CH,HUANG W CH,et al.Parameter-I nduced stochastic resonance inmulti-frequency weak signal detection withαstable noise[J].Acta Physica Sinica,2013,62(21):34-43.
[11]王世芳,邓永菊,吴涛.随机共振技术检测强色噪声中弱信号的研究[J].武汉工程大学学报,2008,30(4):123-126.WANG SH F,DENG Y J,WU T.Study on the application of stochastic resonance for detection weak signal from color noises[J].Journal of Wuhan Institute of Technology,2008,30(4):123-126.
[12]李娟娟,许勇,冯晶.Duffing系统中Lévy噪声诱导的随机共振与相转移[J].动力学与控制学报,2012,10(3):278-282.LI J J,XU Y,FENG J.Lévy noise induced stochastic resonance and phase transition in duffing system[J].Journal of Dynamics and Control,2012,10(3):278-282.
[13]顾仁财,许勇,郝孟丽,等.Lévy稳定噪声激励下的Duffing-van der Pol振子的随机分岔[J].物理学报,2011,60(6):157-161.GU R C,XU Y,HAO M L,et al.Stochastic bifurcations in Duffimg-van der Pol oscillator with Lévy stable noise[J].Acta Physica Sinica,2011,60(6):157-161.
[14]张刚,宋莹,张天骐,等.Lévy噪声下一阶线性系统的弱信号复原分析[J].仪器仪表学报,2016,37(1):109-118.ZHANG G,SONG Y,ZHANG T Q,et al.Weak signal recovery analysis in first-order liner system under Lévy noise[J].Chinese Journal of Scientific Instrument,2016,37(1):109-118.
[15]王季,楼军伟,李贵子,等.EMD样本熵在滚动轴承信号复杂性度量中的应用[J].中国测试,2014(s1):45-48.WANG J,LOU J W,WANG G Z,et al.Application of EMD sample entropy in rolling bearing signal complexity measure[J].China Measurement&Test,2014(s1):45-48.
[16]张淑清,翟欣沛,董璇,等.EMD及Duffing振子在小电流系统故障选线方法中的应用[J].中国电机工程学报,2013,33(10):161-167.ZHANG SH Q,ZHAI X P,DONG X,et al.Application of EMD and duffing oscillator to fault line detection in uneffectively grounded system[J].Proceedings of the CSEE,2013,33(10):161-167.
[17]张刚,胡韬,王颖.基于Melnikov函数Duffing系统微弱信号检测[J].电子测量技术,2015,38(1):109-112.ZHANG G,HU T,WANG Y.The weak signal detection based on duffing system and melnikov function[J].Electronic Measurement Technology,2015,38(1):109-112.
[18]赖志慧,冷永刚,孙建桥,等.基于Duffing振子的变尺度微弱特征信号检测方法研究[J].物理学报,2012,61(5):60-68.LAI ZH H,LENG Y G,SUN J Q,et al.Large parameter stochastic resonance of two-dimensional Duffing oscillator and its application on weak on weak signal detection[J].Acta Physica Sinica,2012,61(5):60-68.
[19]缑新科,马艳.多频信号的多尺度随机共振检测方法及应用[J].兰州理工大学学报,2015,41(5):91-94.GOU X K,MA Y.Multi scale stochastic resonance detection method of multi-frequency signal and its application[J].Journal of Lanzhou University of Technology,2015,41(5):91-94.