强噪声背景下微弱冲击信号的检测
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摘要
针对机械环境噪声具有随机脉冲性以及传统测量指标对机械故障冲击信号识别不足的问题,提出了利用Levy噪声作为背景噪声,以峭度指标和互关联系数构造的峭度-互关联(kurtosis-intercorrelation,简称KI)联合指标作为冲击信号检测的新衡量标准,对非对称双稳态系统中冲击信号的检测进行了研究。首先,在理论上分析了Levy噪声驱动下非对称双稳态系统中粒子的跃迁密度函数和KI的构造方法;其次,研究了Levy噪声特征指数α为1.5时,系统输出KI值分别跟随系统参数a和非对称因子C的变化趋势;最后,将该方法应用到了工程实际机械故障冲击信号的检测之中。仿真与实验研究结果表明,与峭度指标作为冲击信号检测依据相比,KI可使系统输出的信号特征幅值提高一倍以上;系统输出KI值随C呈现先增大后减小的趋势,非对称因子C为0.54时,系统输出KI值比C为0时提高了7.02%。工程实例数据证明,该方法能够有效提取故障信号的时域和频域特征信息,可应用到实际机械故障的检测中去。
In view of the random impulse of the mechanical environment noise and the shortcoming of traditional measurement index for recognizing the impact signal of the mechanical fault,a new criterion(Kurtosis-Intercorrelation combined index,abbreviated as KI)using as the basis for detecting the impact signal,which is constructed with kurtosis index and cross correlation coefficient,is proposed,and the detection of impact signal in asymmetric bistable system is studied with utilizing Levy noise as background noise.Firstly,the transition density function of particles and the construction method of KI in asymmetric bistable system driven by Levy noise are theoretically analyzed.Secondly,the variation trend of the output KI value of the system with the system parameter a and the asymmetric factor C is studied respectively,when the Levy noise characteristic indexαis 1.5.Finally,the method is applied to the detection of the actual mechanical fault impact signal.The results of simulation and experiment show that,compared with the kurtosis index as an impact signal detection basis,KI can increase the signal characteristic amplitude of the output of the system more than one times.The output KI value of the system increases with the C first and then decreases.When the asymmetric factor C is 0.54,the output KI value of the system is increased by 7.02%than that of when C is 0.The engineering example data proves that the method can extract the time-domain and frequency domain feature information of fault signal effectively,and it can be applied to the actual mechanical fault detection.
In view of the random impulse of the mechanical environment noise and the shortcoming of traditional measurement index for recognizing the impact signal of the mechanical fault,a new criterion(Kurtosis-Intercorrelation combined index,abbreviated as KI)using as the basis for detecting the impact signal,which is constructed with kurtosis index and cross correlation coefficient,is proposed,and the detection of impact signal in asymmetric bistable system is studied with utilizing Levy noise as background noise.Firstly,the transition density function of particles and the construction method of KI in asymmetric bistable system driven by Levy noise are theoretically analyzed.Secondly,the variation trend of the output KI value of the system with the system parameter a and the asymmetric factor C is studied respectively,when the Levy noise characteristic indexαis 1.5.Finally,the method is applied to the detection of the actual mechanical fault impact signal.The results of simulation and experiment show that,compared with the kurtosis index as an impact signal detection basis,KI can increase the signal characteristic amplitude of the output of the system more than one times.The output KI value of the system increases with the C first and then decreases.When the asymmetric factor C is 0.54,the output KI value of the system is increased by 7.02%than that of when C is 0.The engineering example data proves that the method can extract the time-domain and frequency domain feature information of fault signal effectively,and it can be applied to the actual mechanical fault detection.
引文
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[17]Georgiou P G,Tskalides P,KyriakaKIs C.Alpha-stable modeling of noise and robust time-delay estimation in the presence of impusive noise[J].Multimedia IEEE Transactions on,1990,1(3):291-301.
[18]Rafal W.On the chambets-mallows-stuck method for simulating skewed stable random variables[J].Statistics&Probability Letters,1996,28(2):165-171.
[19]林敏,黄咏梅,方利民.双稳系统随机共振的反馈控制[J].物理学报,2008,57(4):2041-2047.Lin Min,Huang Yongmei,Fang Limin.The feedback control of stochastic resonance in bistable system[J].Acta Physica Sinica,2008,57(4):2041-2047.(in Chinese)
[20]Podlubny I.Fractional differential equations[M].[S.l.]:Mathematics in Science and Engineering,1999:41-121.
[21]曹衍龙,杨毕玉,杨将新,等.基于变尺度随机共振的冲击信号自适应提取与识别方法[J].振动与冲击,2016,35(5):65-69.Cao Yanlong,Yang Biyu,Yang Jiangxin,et al.Impact signal adaptive extraction and recognition based on a scale transformation stochastic resonance system[J].Journal of Vibration and Shock,2016,35(5):65-69.(in Chinese)
[22]经哲,郭利.基于广义相关系数自适应随机共振的液压泵振动信号预处理方法[J].振动与冲击,2016,35(16):72-78.Jing Zhe,Guo Li.Hydraulic pump vibration signal pretreatment based on adaptive stochastic resonance with general correlation function[J].Journal of Vibration and Shock,2016,35(16):72-78.(in Chinese)
[2]Hu Gang.Stochastic force and nonlinear systems[M].Shanghai:Shanghai Science and Technology Education Press,1994:10-19.
[3]Gammaitoni L,Marchesoni F,Menichellasaetta E,et al.Stochastic resonance in bistable systems[J].Physical Review Letters,1989,62(62):349-352.
[4]Zhou T,Moss F.Analog simulations of stochastic resonance[J].Physical Review A,1990,41(48):4255-4264.
[5]李晓龙,冷永刚,范胜波,等.基于非均匀周期采样的随机共振研究[J].振动与冲击,2011,30(12):78-84.Li Xiaolong,Leng Yonggang,Fan Shengbo,et al.Stochastic resonance based on periodic non-uniform sampling[J].Journal of Vibration and Shock,2011,30(12):78-84.(in Chinese)
[6]冷永刚,赖志慧.基于Kramers逃逸速率的Duffing振子广义调参随机共振研究[J].物理学报,2014,63(2):34-42.Leng Yonggang,Lai Zhihui.Generalized parameteradjusted stochastic resonance of Duffing oscillator based on Kramers rate[J].Acta Physica Sinica,2014,63(2):34-42.(in Chinese)
[7]Lai Zhihui,Leng Yonggang.Dynamic response and stochastic resonance of a tri-stable system[J].Acta Physica Sinica,2015,64(20):200503.
[8]Lévy P.Sur les intégrales dont leséléments sont des variables aléatoires indépendantes[J].Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze,1934(3/4):337-366.
[9]Zolotarev V M.On the representation of stable laws by integrals[J].Selected Translations in Mathematical Statistics and Probability,1964,71:46-50.
[10]贺利芳,崔莹莹.基于幂函数型双稳随机共振的故障信号检测方法[J].仪器仪表学报,2016,7:1457-1467.He Lifang,Cui Yingying.Fault signal detection method based on power function type bistable stochastic resonance[J].Chinese Journal of Scientific Instrument,2016,7:1457-1467.(in Chinese)
[11]焦尚彬,孙迪,刘丁,等.α稳定噪声下一类周期势系统的振动共振[J].物理学报,2017,66(10):100501.Jiao Shangbin,Sun Di,Liu Ding,et al.Vibrational resonance in a periodic potential system withαstable noise[J].Acta Physica Sinica,2017,66(10):100501.(in Chinese)
[12]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.Zhang Gang,Hu Tao,Zhang Tianqi.Characteristic analysis of power function type monostable stochastic resonance with Levy noise[J].Acta Physica Sinica,2015,64(22):72-81.(in Chinese)
[13]张刚,宋莹,张天骐.Levy噪声驱动下指数型单稳系统的随机共振特性分析[J].电子与信息学报,2017,39(4):893-900.Zhang Gang,Song Ying,Zhang Tianqi.Characteristic analysis of exponential type monostable stochastic resonance under Levy noise[J].Journal of Electronics&Information Technology,2017,39(4):893-900.(in Chinese)
[14]Li Jimen,Zhang Yungang,Xie Ping.A new adaptive cascaded stochastic resonance method for impact features extraction in gear fault diagnosis[J].Measurement,2016,91:499-508.
[15]Lei Yaguo,Qiao Zijian,Xu Xuefang,et al.An underdamped stochastic resonance method with stable-state matching for incipient fault diagnosis of rolling element bearings[J].Mechanical Systems&Signal Processing,2017,94:148-164.
[16]Liu Xiaole,Liu Houguang.Improving the bearing fault diagnosis efficiency by the adaptive stochastic resonance in a new nonlinear system[J].Mechanical Systems and Signal Processing,2017,96:58-76.
[17]Georgiou P G,Tskalides P,KyriakaKIs C.Alpha-stable modeling of noise and robust time-delay estimation in the presence of impusive noise[J].Multimedia IEEE Transactions on,1990,1(3):291-301.
[18]Rafal W.On the chambets-mallows-stuck method for simulating skewed stable random variables[J].Statistics&Probability Letters,1996,28(2):165-171.
[19]林敏,黄咏梅,方利民.双稳系统随机共振的反馈控制[J].物理学报,2008,57(4):2041-2047.Lin Min,Huang Yongmei,Fang Limin.The feedback control of stochastic resonance in bistable system[J].Acta Physica Sinica,2008,57(4):2041-2047.(in Chinese)
[20]Podlubny I.Fractional differential equations[M].[S.l.]:Mathematics in Science and Engineering,1999:41-121.
[21]曹衍龙,杨毕玉,杨将新,等.基于变尺度随机共振的冲击信号自适应提取与识别方法[J].振动与冲击,2016,35(5):65-69.Cao Yanlong,Yang Biyu,Yang Jiangxin,et al.Impact signal adaptive extraction and recognition based on a scale transformation stochastic resonance system[J].Journal of Vibration and Shock,2016,35(5):65-69.(in Chinese)
[22]经哲,郭利.基于广义相关系数自适应随机共振的液压泵振动信号预处理方法[J].振动与冲击,2016,35(16):72-78.Jing Zhe,Guo Li.Hydraulic pump vibration signal pretreatment based on adaptive stochastic resonance with general correlation function[J].Journal of Vibration and Shock,2016,35(16):72-78.(in Chinese)