Levy噪声下新型势函数的随机共振特性分析及轴承故障检测
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摘要
针对经典双稳随机共振(Classical Bistablestochastic Resonance,CBSR)系统的输出饱和性问题,构建了一种新型的分段非线性双稳随机共振(Piecewise Nonlinear Bistable Stochastic Resonance,PNBSR)系统,用所提的PNBSR系统在理论上和CBSR系统作了对比;然后以平均信噪比增益(MSNRI)为衡量指标,用量子粒子群算法进行参数寻优,深入的探究了在Levy噪声不同特征指数与对称参数情况下,PNBSR系统参数l,c,a,b和Levy噪声强度放大系数D对共振输出的规律。研究表明:相对于CBSR系统的输出信噪比,PNBSR系统的输出信噪比有4 dB的提高;并且发现在不同的Levy噪声分布作用下,通过调节系统参数l,c,a,b和噪声强度系数D均可诱导随机共振,且系统较好的随机共振区间不随α或β变化;最后将PNBSR系统应用于轴承故障检测,效果明显优于CBSR系统。
Based on the output saturation of classical bistable stochastic resonance, a new type of piecewise nonlinear bistable potential stochastic resonance(PNBSR) system was constructed. Firstly, the PNBSR system was compared with the CBSR systems in theory. Then, the mean signal-to-noise ratio gain was treated as an index to measure the stochastic resonance phenomenon. The quantum particle swarm algorithm was used to seek optimal parameters. The laws for the resonant output of piecewise nonlinear bistable system governed by l, c, a, b, and D of Levy noise were explored under different characteristic index α and symmetry parameter β of Levy noise. The results show that the output of the PNBSR system has increased 4 dB compared with the output signal-to-noise ratio of a classical bistable stochastic resonance(CBSR) system. And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under any α or β of Levy noise and D of Levy noise, and the best interval does not change with α or β. At last, the piecewise nonlinear bistable stochastic resonance system was applied to detect bearing fault signals, which achieves better performance compared with the classical bistable stochastic resonance system.
Based on the output saturation of classical bistable stochastic resonance, a new type of piecewise nonlinear bistable potential stochastic resonance(PNBSR) system was constructed. Firstly, the PNBSR system was compared with the CBSR systems in theory. Then, the mean signal-to-noise ratio gain was treated as an index to measure the stochastic resonance phenomenon. The quantum particle swarm algorithm was used to seek optimal parameters. The laws for the resonant output of piecewise nonlinear bistable system governed by l, c, a, b, and D of Levy noise were explored under different characteristic index α and symmetry parameter β of Levy noise. The results show that the output of the PNBSR system has increased 4 dB compared with the output signal-to-noise ratio of a classical bistable stochastic resonance(CBSR) system. And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under any α or β of Levy noise and D of Levy noise, and the best interval does not change with α or β. At last, the piecewise nonlinear bistable stochastic resonance system was applied to detect bearing fault signals, which achieves better performance compared with the classical bistable stochastic resonance system.
引文
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[22] LAI Z H,LENG Y G.Weak-signal detection based on the stochastic resonance of bistable duffing oscillator and its application in incipient fault diagnosis[J].Mechanical Systems & Signal Processing,2016,81:60-74.
[23] 王婕.基于随机共振和混沌理论的行星齿轮箱微弱信号检测方法研究[D].成都:电子科技大学,2014.
[24] 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):768.
[25] GUO W,ZHOU Z M,CHEN C,et al.Multi-frequency weak signal detection based on multi-segment cascaded stochastic resonance for rolling bearings[J].Microelectronics Reliability,2017,75:239-252.
[26] ZHANG H B,HE Q B,KONG F R.Stochastic resonance in an underdamped system with pinning potential for weak signal detection[J].Sensors,2015,15(9):21169-21195.
[27] QIAO Z J,PAN Z R.SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient[J].Measurement Science & Technology,2015,26(8):15-30.
[28] ZHANG J,ZHANG T.Parameter-induced stochastic resonance based on spectral entropy and its application to weak signal detection[J].Review of Scientific Instruments,2015,86(2):025005.
[2] COLLINA J J,CHOW C C,IMHOFF T T.Aperiodic stochastic resonance in excitable systems.[J].Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics,1995,52(4):R3321.
[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.
[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].杭州:浙江大学,2012.
[5] WANG Z Q,XU Y,YANG H.Levy noise induced stochastic resonance in an FHN model[J].Science China Technological Sciences,2016,59(3):371-375.
[6] LIU Y,LIANG J,JIAO S B,et al.Stochastic resonance of a tri-stable system with α stable noise[J].Chinese Journal of Physics,2017,55(2):355-366.
[7] ZHANG H,HE Q,KONG F.Stochastic resonance in an underdamped system with pinning potential for weak signal detection[J].Sensors,2015,15(9):21169-21195.
[8] 孙虎儿,王志武.级联分段线性随机共振的微弱信号检测[J].中国机械工程,2014,25(24):3343-3347.SUN Huer,WANG Zhiwu.Weak signal detection based on cascaded piecewise linear stochastic resonance[J].China Mechanical Engineering,2014,25(24):3343-3347.
[9] 王林泽,赵文礼,陈旋.基于随机共振原理的分段线性模型的理论分析与实验研究[J].物理学报,2012(16):50-56.WANG Linze,ZHAO Wenli,CHEN Xuan.Theory and experiment research on a Piecewise-linear model based on stochastic resonance[J].Acta Physica Sinica,2012(16):50-56.
[10] 冷永刚,刘瑜,赖志慧,等.二阶线性系统调参共振的特征信号检测[J].振动、测试与诊断,2014(3):491-495.LENG Yonggang,LIU Yu,LAI Zhihui,et al.Characteristic signal detection based on the parameter-tuned resonance of the second-order linear system[J].Journal of Vibration,Measurement & Diagnosis,2014(3):491-495.
[11] GUO Y,SHEN Y,TAN J.Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise[J].Communications in Nonlinear Science & Numerical Simulation,2016,38:257-266.
[12] ROUSSEAU D,VARELA J R,CHAPEAU-BLONDEAU F.Stochastic resonance for nonlinear sensors with saturation.[J].Physical Review E Statistical Nonlinear & Soft Matter Physics,2003,67(2):021102.
[13] ZHAO W,WANG J,WANG L.The unsaturated bistable stochastic resonance system[J].Chaos An Interdisciplinary Journal of Nonlinear Science,2013,23(3):175.
[14] GONG M,GUO F.Phenomenon of stochastic resonance in a time-delayed bistable system driven by colored noise and square-wave signal[J].Chinese Journal of Physics,2011,49(2):655-663.
[15] CASADO-PASCUAL J,GOMEZ-ORDONEZ J,MORILLO M.Stochastic resonance:theory and numerics[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2005,15(2):026115.
[16] PAOLA M D,SOFI A.Approximate solution of the Fokker-Planck-Kolmogorov equation,Probab[J].Eng.Mech,2002,17:369-384.
[17] GAMMAITONI L,HANGGI P,JUNG P.Stochastic resonance[J].Reviews of Modern Physics,1998,70(1):223-287.
[18] 胡岗.随机力与非线性系统[M].上海:上海科学教育出版社,1994.
[19] MCNAMARA B,WIESENFELD K.Theory of stochastic resonance[J].Phys.Rev.A,1989,39:4854-4869.
[20] NGUYEN S D,NGUYEN Q H,CHOI S B.A hybrid clustering based fuzzy structure for vibration control-Part 2:An application to semi-active vehicle seat-suspension system[J].Mechanical Systems & Signal Processing,2015,56/57:288-301.
[21] WERON R.On the chambers-mallows-stuck method for simulating skewed stable random variables[J] Statistics & Probability Letters,1996,28(2):165-171.
[22] LAI Z H,LENG Y G.Weak-signal detection based on the stochastic resonance of bistable duffing oscillator and its application in incipient fault diagnosis[J].Mechanical Systems & Signal Processing,2016,81:60-74.
[23] 王婕.基于随机共振和混沌理论的行星齿轮箱微弱信号检测方法研究[D].成都:电子科技大学,2014.
[24] 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):768.
[25] GUO W,ZHOU Z M,CHEN C,et al.Multi-frequency weak signal detection based on multi-segment cascaded stochastic resonance for rolling bearings[J].Microelectronics Reliability,2017,75:239-252.
[26] ZHANG H B,HE Q B,KONG F R.Stochastic resonance in an underdamped system with pinning potential for weak signal detection[J].Sensors,2015,15(9):21169-21195.
[27] QIAO Z J,PAN Z R.SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient[J].Measurement Science & Technology,2015,26(8):15-30.
[28] ZHANG J,ZHANG T.Parameter-induced stochastic resonance based on spectral entropy and its application to weak signal detection[J].Review of Scientific Instruments,2015,86(2):025005.