Levy噪声驱动下指数型单稳系统的随机共振特性分析
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摘要
该文基于绝对值型和指数型势函数,构建了更一般的指数型单稳势函数,深入研究了Levy噪声驱动的指数型单稳系统,并总结出不同特征指数a和不同对称参数b下,指数型系统参数l和b,Levy噪声强度系数D对指数系统共振输出的作用规律。研究表明:在不同Levy噪声驱动下,通过调节参数l和b均可诱导随机共振(SR),且当b(或l)的取值越大时,产生较好随机共振效果l(或b)的区间越大,从而改善传统SR系统由于参数选择不当造成随机共振效果不佳的问题。此外,通过调节噪声强度系数D也能产生随机共振,且较好随机共振区间不随a或b变化;最后将指数型单稳系统应用于轴承故障检测,效果明显优于传统双稳系统。
Based on the absolute and exponential monostable potential, a generalized exponential type single-well potential function is constructed. The laws for the resonant output of monostable system governed by l and b, D of Levy noise are explored under different characteristic index a and symmetry parameter b of Levy noise. The results show that the stochastic resonance phenomenon can be induced by adjusting the exponential type parameters l and b under any a or b of Levy noise. The larger b(or l) is, the wider parameter interval of l(or b) can induce SR(Stochastic Resonance). The ESR(Exponential SR) system can solve the problem that the traditional system can not achieve SR due to the improper selection of parameters. The interval of D of Levy noise, which induces good stochastic resonance, does not change with a or b. At last, the proposed exponential type monostable is applicated to detect bearing fault signals, which achieves better performance compared with the traditional bisabled system.
Based on the absolute and exponential monostable potential, a generalized exponential type single-well potential function is constructed. The laws for the resonant output of monostable system governed by l and b, D of Levy noise are explored under different characteristic index a and symmetry parameter b of Levy noise. The results show that the stochastic resonance phenomenon can be induced by adjusting the exponential type parameters l and b under any a or b of Levy noise. The larger b(or l) is, the wider parameter interval of l(or b) can induce SR(Stochastic Resonance). The ESR(Exponential SR) system can solve the problem that the traditional system can not achieve SR due to the improper selection of parameters. The interval of D of Levy noise, which induces good stochastic resonance, does not change with a or b. At last, the proposed exponential type monostable is applicated to detect bearing fault signals, which achieves better performance compared with the traditional bisabled system.
引文
[1]EINSTEIN A.über die von der molekularkinetischen theorie der w?rme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen[J].Annalen der Physik,1905,17(8):549-560.
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[3]梁军利,杨树元,唐志峰.基于随机共振的微弱信号检测[J].电子与信息学报,2006,28(6):1068-1072.LIANG Junli,YANG Shuyuan,and TANG Zhifeng.Weak signal detection based on stochastic resonance[J].Journal of Electronics&Information Technology,2006,28(6):1068-1072.
[4]WANG Zhanqing,XU Y,and YANG H.Levy noise induced stochastic resonance in an FHN model[J].Science China Technological Sciences,2016,59(3):371-375.doi:10.1007/s11431-015-6001-2.
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[7]陆思良.基于随机共振的微弱信号检测模型及应用研究[D].[博士论文],中国科学技术大学,2015.LU Siliang.Models and applications of stochastic resonance based weak signal detection[D].[Ph.D.dissertation],University of Science and Technology of China,2015.
[8]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):95-102.doi:10.7498/aps.62.020505.TIAN Xiangyou,LENG Yonggang,and FAN Shengbo.Parameter-adjusted stochastic resonance of first-order linear system[J].Acta Physica Sinica,2013 62(2):95-102.doi:10.7498/aps.62.020505.
[9]袁季冬,张路,罗懋康.幂函数型单势阱随机振动系统的广义随机共振[J].物理学报,2014,63(16):242-252.doi:10.7498/aps.63.164302.YUAN Jidong,ZHANG Lu,and LUO Maokang.Generalized stochastic resonance of power function type single-well system[J].Acta Physica Sinica,2014,63(16):242-252.doi:10.7498/aps.63.164302.
[10]赖志慧,冷永刚.三稳系统的动态响应及随机共振[J].物理学报,2015,64(20):77-88.doi:10.7498/aps.64.200503.LAI Zhihui and LENG Yonggang.Dynamic response and stochastic resonance of a tri-stable system[J].Acta Physica Sinica,2015,64(20):77-88.doi:10.7498/aps.64.200503.
[11]GILBARG D and TRUDINGER N S.Elliptic Partial Differential Equations of Second Order[M].Berlin Heidelberg,Springer-Verlag.1977:469-484.
[12]CHAMBERS J M.Display and analysis of spatial data:NATO advanced study institute[J].Journal of the American Statistical Association,1976,71(355):768-769.doi:10.2307/2285621.
[13]WERON R.On the Chambers-Mallows-Stuck method for simulating skewed stable random variables[J]Statistics&Probability Letters,1996,28(2):165-171.doi:10.1016/0167-7152(95)00113-1.
[14]张刚,胡韬,张天骐.Levy噪声激励下的幂函数型单稳随机共振特性分析[J].物理学报,2015,64(22):72-81.doi:10.7498/aps.64.220502.ZHANG Gang,HU Tao,and ZHANG Tianqi.Characteristic analysis of power function type monostable stochastic resonance with Levy noise[J].Acta Physica Sinica,2015,64(22):72-81.doi:10.7498/aps.64.220502.
[15]ZHANG Haibin,HE Qingbo,and KONG Fanrang.Stochastic resonance in an underdamped system with pinning potential for weak signal detection[J].Sensors,2015,15(9):21169-21195.doi:10.3390/s150921169.
[16]QIAO Zijian and PAN Zhengrong.SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient[J].Measurement Science&Technology,2015,26(8):15-30.doi:10.1088/0957-0233/26/8/085014.
[2]BENZI R,SUTERA A,and VULPIANI A.The mechanism of stochastic resonance[J].Journal of Physics A,1981,14(11)453-457.doi:10.1088/0305-4470/14/11/006.
[3]梁军利,杨树元,唐志峰.基于随机共振的微弱信号检测[J].电子与信息学报,2006,28(6):1068-1072.LIANG Junli,YANG Shuyuan,and TANG Zhifeng.Weak signal detection based on stochastic resonance[J].Journal of Electronics&Information Technology,2006,28(6):1068-1072.
[4]WANG Zhanqing,XU Y,and YANG H.Levy noise induced stochastic resonance in an FHN model[J].Science China Technological Sciences,2016,59(3):371-375.doi:10.1007/s11431-015-6001-2.
[5]GITTERMAN M.Classical harmonic oscillator with multiplicative noise[J].Physica A Statistical Mechanics&Its Applications,2005,352(s 2/4):309-334.doi:10.1016/j.physa.2005.01.008.
[6]郑俊,林敏.基于双共振的微弱信号检测方法与试验研究[J].机械工程学报,2014,50(12):11-16.doi:10.3901/JME.2014.12.011.ZHENG Jun and LIN Min.Experimental research of weak signal detection method based on the dual-resonance[J].Journal of Mechanical Engineering 2014,50(12):11-16.doi:10.3901/JME.2014.12.011.
[7]陆思良.基于随机共振的微弱信号检测模型及应用研究[D].[博士论文],中国科学技术大学,2015.LU Siliang.Models and applications of stochastic resonance based weak signal detection[D].[Ph.D.dissertation],University of Science and Technology of China,2015.
[8]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):95-102.doi:10.7498/aps.62.020505.TIAN Xiangyou,LENG Yonggang,and FAN Shengbo.Parameter-adjusted stochastic resonance of first-order linear system[J].Acta Physica Sinica,2013 62(2):95-102.doi:10.7498/aps.62.020505.
[9]袁季冬,张路,罗懋康.幂函数型单势阱随机振动系统的广义随机共振[J].物理学报,2014,63(16):242-252.doi:10.7498/aps.63.164302.YUAN Jidong,ZHANG Lu,and LUO Maokang.Generalized stochastic resonance of power function type single-well system[J].Acta Physica Sinica,2014,63(16):242-252.doi:10.7498/aps.63.164302.
[10]赖志慧,冷永刚.三稳系统的动态响应及随机共振[J].物理学报,2015,64(20):77-88.doi:10.7498/aps.64.200503.LAI Zhihui and LENG Yonggang.Dynamic response and stochastic resonance of a tri-stable system[J].Acta Physica Sinica,2015,64(20):77-88.doi:10.7498/aps.64.200503.
[11]GILBARG D and TRUDINGER N S.Elliptic Partial Differential Equations of Second Order[M].Berlin Heidelberg,Springer-Verlag.1977:469-484.
[12]CHAMBERS J M.Display and analysis of spatial data:NATO advanced study institute[J].Journal of the American Statistical Association,1976,71(355):768-769.doi:10.2307/2285621.
[13]WERON R.On the Chambers-Mallows-Stuck method for simulating skewed stable random variables[J]Statistics&Probability Letters,1996,28(2):165-171.doi:10.1016/0167-7152(95)00113-1.
[14]张刚,胡韬,张天骐.Levy噪声激励下的幂函数型单稳随机共振特性分析[J].物理学报,2015,64(22):72-81.doi:10.7498/aps.64.220502.ZHANG Gang,HU Tao,and ZHANG Tianqi.Characteristic analysis of power function type monostable stochastic resonance with Levy noise[J].Acta Physica Sinica,2015,64(22):72-81.doi:10.7498/aps.64.220502.
[15]ZHANG Haibin,HE Qingbo,and KONG Fanrang.Stochastic resonance in an underdamped system with pinning potential for weak signal detection[J].Sensors,2015,15(9):21169-21195.doi:10.3390/s150921169.
[16]QIAO Zijian and PAN Zhengrong.SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient[J].Measurement Science&Technology,2015,26(8):15-30.doi:10.1088/0957-0233/26/8/085014.