Levy噪声下一阶线性系统的弱信号复原分析
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摘要
将Levy噪声与一阶线性随机共振SR系统相结合,采用Levy噪声模型和弱正弦信号模型,研究了不同Levy噪声环境下的调参广义随机共振现象及弱信号复原。首先分析了Levy噪声的特征指数α、对称参数β以及强度系数D对输入信噪比的作用规律;然后探究了不同分布的Levy噪声环境下一阶线性系统结构参数a的广义随机共振现象;最后提出了Levy噪声激励下线性系统高低频弱信号复原方法;研究结果表明:输入信噪比随α单调递增,随μ变化甚微,随D单调递减到一定程度后,不再减小保持定值;在Levy噪声作用下的一阶线性系统不能产生传统意义上的随机共振现象,但却存在互相关系数随结构参数a非单调变化的广义随机共振现象;在信号复原过程中,理论分析与实际仿真结果一致,证明所提复原方法准确可行,复原效果理想
Abstrct:The Levy noise is combined with first-order linear stochastic resonance(SR) system,Levy noise model and weak sinusoidal signal model are adopted.The parameter-adjusted generalized stochastic resonance phenomenon and weak signal recovery under different Levy noise environment are researched.Firstly,the influence laws of the characteristic index α,symmetric parameter β and intensity factor D of Levy noise on the noise distribution form and input signal-to-noise ratio of the first-order linear system are analyzed.Then,the generalized stochastic resonance phenomenon under different Levy noise distribution is studied by adjusting the first-order linear system parameter a.At last,the high and low frequency weak signal recovery methods of the first-order linear stochastic resonance system under Levy noise stimulation are proposed.The study results show that the input signal-to-noise ratio monotonically increases with the characteristic index a;and monotonically decreases with the intensity factorD to a certain value,then stays at the constant value;while β has little effect on the input signal-to-noise ratio.Under Levy noise,the first-order linear system does not generate traditional stochastic resonance phenominon;however,a parameter-adjusted generalized stochastic resonance phenomenon exists,in which the cross correlation coefficient nonmonotonically changes with the system parameter a.In the weak signal recovery process,the theoretical analysis results are consistent with the simulation results,which proves that the proposed recovery methods are feasible and accurate,and the achieved recovery effect is ideal.
Abstrct:The Levy noise is combined with first-order linear stochastic resonance(SR) system,Levy noise model and weak sinusoidal signal model are adopted.The parameter-adjusted generalized stochastic resonance phenomenon and weak signal recovery under different Levy noise environment are researched.Firstly,the influence laws of the characteristic index α,symmetric parameter β and intensity factor D of Levy noise on the noise distribution form and input signal-to-noise ratio of the first-order linear system are analyzed.Then,the generalized stochastic resonance phenomenon under different Levy noise distribution is studied by adjusting the first-order linear system parameter a.At last,the high and low frequency weak signal recovery methods of the first-order linear stochastic resonance system under Levy noise stimulation are proposed.The study results show that the input signal-to-noise ratio monotonically increases with the characteristic index a;and monotonically decreases with the intensity factorD to a certain value,then stays at the constant value;while β has little effect on the input signal-to-noise ratio.Under Levy noise,the first-order linear system does not generate traditional stochastic resonance phenominon;however,a parameter-adjusted generalized stochastic resonance phenomenon exists,in which the cross correlation coefficient nonmonotonically changes with the system parameter a.In the weak signal recovery process,the theoretical analysis results are consistent with the simulation results,which proves that the proposed recovery methods are feasible and accurate,and the achieved recovery effect is ideal.
引文
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[12]田祥友,冷永刚,范胜波.一阶线性系统的调参随机共振研究[J]物理学报,2013,62(2):20505.TIAN X Y,LENG Y G,FAN SH B.Parameter-adjusted stochastic resonance of first-order linear system[J].Acta Physica Sinica,2013,62(2):20505.
[13]冷永刚,田祥友.一阶线性系统随机共振在转子轴故障诊断中的应用研究[J].振动与冲击2014,33(17):1-5.LENG Y G,TIAN X Y.Application of a first-order linear system's stochastic resonance in fault diagnosis of rotor shaft[J].Vibration and Shock,2014,33(17):1-5
[14]李华锋,徐博侯.随机共振系统输出的一种新的反演方法[J].力学学报,2003,35(2):194-198.LI H F,XU B H.A new method to recover the signals obtained by stochastic resonance[J].Acta Mechanica Sinica,2003,35(2):194-198.
[15]罗琦,韦香,朱敏.基于双稳耦合系统的随机共振信号复原[J]华中科技大学学报:自然科学版,2013,41(7):71-75.LUO Q,WEI X,ZHU M.Stochastic resonance signals recovery based on bistable coupling systems[J].Journal of Huazhong University of Science and Technology:Natural Science Edition),2013,41(7):71-75.
[16]CHAMBERS J M,DAVIS J C,MCCULLAGH M J.Display and analysis of spatial data;NATO advanced study institute[J].Journal of the American Statistical Association,1976,71(355).
[17]WERON A,WERON R.Computer simulation of Levyα-stable variables and processes[M].Springer Berlin Heidelberg,1995,457:379-392.
[18]WERON R.On the Chambers-mallows-stuck method for simulating skewed stable random variables[J].Statistic&Probability Letters,1996,28(2):165-171.
[2]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.
[3]邱天爽,张旭秀,李小兵,等.统计信号处理—非高斯信号处理及其应用[M].北京:电子工业出版社,2004:140.QIU T SH,ZHANG X X,LI X B,et al.Statistical signal processing non-gaussian signal processing and its applications[M].Beijing:Publishing House of Electronics Industry,2004:140.
[4]黄家闽.稳定分布噪声背景下非线性系统的随机共振现象研究[D].浙江:浙江大学,2012.HUANG J M.Study on stochastic resonance in nonlinear systems driven by stable distribution noise[D].Zhejiang:Zhejiang University,2012.
[5]赵文礼,郭丽红.随机共振及其微弱信号的自适应检测[J]电子测量与仪器学报,2006,20(5):21-25.ZHAO W L,GUO L H.Stochastic resonance and adaptive signal detection[J].Journal of Electronic Measurement and Instrument,2006,20(5):21-25.
[6]赵文礼,田帆,邵柳东.自适应随机共振技术在微弱信号测量中的应用[J].仪器仪表学报2007,28(10):1787-1791.ZHAO W L,TIAN F,SHAO L D.Application of adaptive stochastic resonance technology in weak signal detection[J].Chinese Journal of Scientific Instrument,2007,28(10):1787-1791.
[7]陶志颖,鲁昌华,查正兴,等.基于单势阱随机共振的多频周期微弱信号检测[J].电子测量与仪器学报2014 28(2):171-176.TAO ZH Y,LU CH H,ZHA ZH X,et al.Multi-frequency periodic weak signal detection based on singlewell potential stochastic resonance[J].Journal of Electronic Measurement and Instrument,2014,28(2):171-176.
[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]焦尚彬,任超,李鹏华,等.乘性和加性稳定噪声环境下的过阻尼单稳随机共振现象[J].物理学报,2014,63(7):70501.JIAO SH B,REN CH,LI P H,et al.Stochastic resonance in an overdamped monostable system with multiplicative and additiveαstable noise[J].Acta Physica Sinica,2014,63(7):70501.
[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):210501.JIAO SH B,REN CH,HUANG W CH,et al.Parameterinduced stochastic resonance in multi-frequery weak signal detection with stable noise[J].Acta Physica Sinica,2013,62(21):210501.
[11]焦尚彬,杨蓉,张青,等.α稳定噪声驱动的非对称双稳随机共振现象[J].物理学报,2015,64(2):20502.JIAO SH B,YANG R,ZHANG Q,et al.Stochastic resonance of asymmetric bistable system with stable noise[J].Acta Physica Sinica,2015,64(2):20502.
[12]田祥友,冷永刚,范胜波.一阶线性系统的调参随机共振研究[J]物理学报,2013,62(2):20505.TIAN X Y,LENG Y G,FAN SH B.Parameter-adjusted stochastic resonance of first-order linear system[J].Acta Physica Sinica,2013,62(2):20505.
[13]冷永刚,田祥友.一阶线性系统随机共振在转子轴故障诊断中的应用研究[J].振动与冲击2014,33(17):1-5.LENG Y G,TIAN X Y.Application of a first-order linear system's stochastic resonance in fault diagnosis of rotor shaft[J].Vibration and Shock,2014,33(17):1-5
[14]李华锋,徐博侯.随机共振系统输出的一种新的反演方法[J].力学学报,2003,35(2):194-198.LI H F,XU B H.A new method to recover the signals obtained by stochastic resonance[J].Acta Mechanica Sinica,2003,35(2):194-198.
[15]罗琦,韦香,朱敏.基于双稳耦合系统的随机共振信号复原[J]华中科技大学学报:自然科学版,2013,41(7):71-75.LUO Q,WEI X,ZHU M.Stochastic resonance signals recovery based on bistable coupling systems[J].Journal of Huazhong University of Science and Technology:Natural Science Edition),2013,41(7):71-75.
[16]CHAMBERS J M,DAVIS J C,MCCULLAGH M J.Display and analysis of spatial data;NATO advanced study institute[J].Journal of the American Statistical Association,1976,71(355).
[17]WERON A,WERON R.Computer simulation of Levyα-stable variables and processes[M].Springer Berlin Heidelberg,1995,457:379-392.
[18]WERON R.On the Chambers-mallows-stuck method for simulating skewed stable random variables[J].Statistic&Probability Letters,1996,28(2):165-171.