Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are ...Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.展开更多
Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resona...Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.展开更多
In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standa...In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered.The stationary probability density function(SPDF)of the harvester is obtained by the improved stochastic averaging.Then,with the adiabatic approximation theory,the analytical expression of signal-to-noise ratio(SNR)for the TEH is deduced to characterize stochastic resonance(SR).To enhance direct current(DC)power delivery from a rotational TEH,the influences of system parameters on SR is discussed.The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system.The TEH has higher harvesting performance under the optimal SR.That is,the optimal parameter combinations can induce optimal SR and maximize harvesting performance.Thus,the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.展开更多
Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system(CTSR), a novel ...Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system(CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system(PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time(MFPT), and output signal-to-noise ratio(SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency,and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.展开更多
In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced...In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.展开更多
在Levy噪声驱动下,以级联三稳态随机共振为模型,首先研究了不同特征参数、对称参数条件下输入信噪比随噪声强度D的变化;然后以谱峰值和平均信噪比增益为性能指标,针对高、低频信号级联三稳随机共振现象进行了研究;最后将其应用到轴承故...在Levy噪声驱动下,以级联三稳态随机共振为模型,首先研究了不同特征参数、对称参数条件下输入信噪比随噪声强度D的变化;然后以谱峰值和平均信噪比增益为性能指标,针对高、低频信号级联三稳随机共振现象进行了研究;最后将其应用到轴承故障检测中。研究表明,通过自适应算法选取最优参数a、b和c,可诱导级联三稳系统发生随机共振,从而实现对目标信号的检测。结果表明,特征参数越大,输入信噪比达到稳定状态需要的噪声强度越大,而对称参数几乎没有影响;选取相同的系统参数a=0. 5、b=0. 5、c=0. 8时,级联三稳系统的检测效果要比单级三稳系统有更好的随机共振输出,在小参数信号检测中,单级输出平均信噪比增益为25. 46 d B,第2级输出平均信噪比增益为28. 38 d B。此外,在轴承故障检测中级联三稳系统也显示出更好的检测效果。此系统对于微弱信号的检测具有重要的研究意义也有着良好发展前景。展开更多
为了探究三稳态压电振动能量采集器的动力学特性,以磁-机-压电耦合型三稳态压电振动能量采集器(tristable piezoelectric vibration energy harvester,简称TPVEH)为研究对象,利用磁荷法、力平衡和基尔霍夫定律分别建立了采集器末端磁铁...为了探究三稳态压电振动能量采集器的动力学特性,以磁-机-压电耦合型三稳态压电振动能量采集器(tristable piezoelectric vibration energy harvester,简称TPVEH)为研究对象,利用磁荷法、力平衡和基尔霍夫定律分别建立了采集器末端磁铁与外部磁铁之间的非线性磁力模型和系统集总参数动力学模型。仿真分析了磁铁间距、激励加速度幅值和频率等参数对采集器动力学特性和采集电压的影响。研制了三稳态压电振动能量采集器原理样机,搭建了实验测试平台,实验验证了仿真结果的正确性。研究结果表明,随着激励加速度幅值增大,能量采集器依次经历单稳态、双稳态和三稳态3种运动状态,且三稳态运动时的工作频带和输出性能(位移、速度和采集电压)比双稳态和单稳态时要高。展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.12072025)the Beijing Natural Science Foundation (Grant No.1222015)。
文摘Stochastic resonance(SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density(SPD)and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations(MCS) confirm the effectiveness of the theoretical results.
基金Project supported by the National Natural Science Foundation of China(Grant No.61371164)the Chongqing Municipal Distinguished Youth Foundation,China(Grant No.CSTC2011jjjq40002)the Research Project of Chongqing Municipal Educational Commission,China(Grant No.KJ130524)
文摘Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.
基金This work has been supported by the National Natural Science Foundation of China(Grant No.12072025)Beijing Natural Science 5 Foundation(Grant No.1222015)the Natural Science Basic Research Program of Shaanxi Province(Grant No.2022JQ-044).
文摘In this paper,the stochastic-resonance-based tri-stable energy harvester(TEH)is proposed to enhance harvesting performance under random rotational vibration.An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered.The stationary probability density function(SPDF)of the harvester is obtained by the improved stochastic averaging.Then,with the adiabatic approximation theory,the analytical expression of signal-to-noise ratio(SNR)for the TEH is deduced to characterize stochastic resonance(SR).To enhance direct current(DC)power delivery from a rotational TEH,the influences of system parameters on SR is discussed.The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system.The TEH has higher harvesting performance under the optimal SR.That is,the optimal parameter combinations can induce optimal SR and maximize harvesting performance.Thus,the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.
基金Project supported by the National Natural Science Foundation of China(Grant No.61771085)the Research Project of Chongqing Educational Commission,China(Grant Nos.KJ1600407 and KJQN201900601)the Natural Science Foundation of Chongqing,China(Grant No.cstc2021jcyj-msxm X0836)。
文摘Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system(CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system(PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time(MFPT), and output signal-to-noise ratio(SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency,and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.
基金Project supported by the National Natural Science Foundation of China(No.12072264)the Fundamental Research Funds for the Central Universities+3 种基金the Research Funds for Interdisciplinary Subject of Northwestern Polytechnical Universitythe Shaanxi Project for Distinguished Young Scholarsthe National Key Research and Development Program of China(No.2018AAA0102201)the Shaanxi Provincial Key R&D Program(Nos.2020KW-013 and 2019TD-010)。
文摘In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.
文摘在Levy噪声驱动下,以级联三稳态随机共振为模型,首先研究了不同特征参数、对称参数条件下输入信噪比随噪声强度D的变化;然后以谱峰值和平均信噪比增益为性能指标,针对高、低频信号级联三稳随机共振现象进行了研究;最后将其应用到轴承故障检测中。研究表明,通过自适应算法选取最优参数a、b和c,可诱导级联三稳系统发生随机共振,从而实现对目标信号的检测。结果表明,特征参数越大,输入信噪比达到稳定状态需要的噪声强度越大,而对称参数几乎没有影响;选取相同的系统参数a=0. 5、b=0. 5、c=0. 8时,级联三稳系统的检测效果要比单级三稳系统有更好的随机共振输出,在小参数信号检测中,单级输出平均信噪比增益为25. 46 d B,第2级输出平均信噪比增益为28. 38 d B。此外,在轴承故障检测中级联三稳系统也显示出更好的检测效果。此系统对于微弱信号的检测具有重要的研究意义也有着良好发展前景。
文摘为了探究三稳态压电振动能量采集器的动力学特性,以磁-机-压电耦合型三稳态压电振动能量采集器(tristable piezoelectric vibration energy harvester,简称TPVEH)为研究对象,利用磁荷法、力平衡和基尔霍夫定律分别建立了采集器末端磁铁与外部磁铁之间的非线性磁力模型和系统集总参数动力学模型。仿真分析了磁铁间距、激励加速度幅值和频率等参数对采集器动力学特性和采集电压的影响。研制了三稳态压电振动能量采集器原理样机,搭建了实验测试平台,实验验证了仿真结果的正确性。研究结果表明,随着激励加速度幅值增大,能量采集器依次经历单稳态、双稳态和三稳态3种运动状态,且三稳态运动时的工作频带和输出性能(位移、速度和采集电压)比双稳态和单稳态时要高。
