加性和乘性三值噪声激励下周期势系统的动力学分析

周期势系统是一类在机械工程、物理、化学、神经生物等领域应用十分广泛的系统,其随机动力学特性的研究是非线性科学的一个热点和难点问题.三值噪声是真实噪声的典型模型, 不仅包含二值噪声和高斯白噪声情形,而且能更好地描述自然界中随机环境扰动的多样性,本文研究了由加性和乘性三值噪声驱动的周期势系统中概率密度的演化和随机共振.通过计算系统的平均稳态联合概率密度函数和瞬态联合概率密度函数,发现随着外周期力振幅的增大, 单自由度系统在多个稳态之间跃迁,其平均稳态联合概率密度具有多峰结构. 此外,利用随机能量法揭示了系统的随机共振,发现存在最优的噪声强度和外周期力振幅使得平均输入能量曲线存在一个极大值,即出现随机共振现象. 对于仅考虑加性噪声或乘性噪声激励的情况,平均输入能量曲线随噪声转迁率是否出现共振现象依赖于外周期激励振幅的大小.特别是仅考虑加性噪声的情形, 对于较小的外周期激励振幅,加性噪声转迁率诱导产生抑制共振现象, 而对于较大的外周期激励振幅,加性噪声转迁率诱导产生随机共振现象.      

Trichotomous noise induced stochastic resonance in a linear system

We investigate stochastic resonance in an underdamped linear system subjected to multiplicative trichotomous noise. We carry out the Shapiro?CLoginov formula to find the exact expression of output amplitude gain, and the impacts of the input signal frequency and noise parameters will be observed, such as noise switching rate or noise correlation time, noise amplitude and noise flatness. Then one can find the stochastic resonance for the proposed linear system.     

含时滞反馈与涨落质量的记忆阻尼系统的随机共振

针对具有记忆效应的欠阻尼系统, 存在时滞反馈与涨落质量, 本文主要研究了其输出稳态响应振幅的随机共振效应. 首先通过引入新变量和运用小时滞近似展开理论, 将具有非马尔科夫特性的原系统转化为等价的两维马尔科夫线性系统, 再利用Shapiro-Loginov公式和Laplace变换获得了系统响应的一阶稳态矩和稳态响应振幅的解析表达式. 结果表明: 当系统参数满足Routh-Hurwitz稳定条件时, 稳态响应振幅随质量涨落噪声强度、周期驱动信号频率以及时滞的变化均存在随机共振现象, 其中随机多共振现象也被观察到. 在适当范围内, 通过控制时滞反馈, 系统的随机共振效应随着时滞的增大而增强, 而较长的记忆时间及增大阻尼参数均对共振行为呈现抑制作用.有效调控时滞反馈与记忆效应的变化关系将有助于增强系统对周期驱动信号的响应强度. 最后, 通过数值模拟计算验证了理论结果的有效性.      

双稳系统中随机共振与相同步时间的相关性

研究了双稳系统的随机共振(SR)与输入输出之间的相同步相关性. 首先得到系统的输出信噪比(SNR)与输入输出之间的平均相同步时间的表达式,然后讨论了随机共振与输入输出之间的平均相同步时间之间的关系. 结果表明:(1)系统出现了随机共振现象,且平均相同步时间对噪声是敏感的;由于加性与乘性噪声的相互影响,随加性噪声强度的增加,输出信噪比及平均相同步时间曲线上首先出现抑制现象,然后出现峰值,并且, 减小乘性与加性噪声强度比率,可提高输出信噪比和增长平均相同步时间. (2)系统的随机共振与平均相同步时间达到最大值不同步出现,但平均相同步时间对输出信噪比是敏感的. 该结论为信号传输中利用随机共振原则改变系统工作环境提供了依据.      

随机共振系统输出的一种新的反演方法

随机共振是一种在非线性系统中噪声起促进作用的反直观的现象。近年来，这一现象被应用到信号处理领域，以前大部分关于随机共振的工作都集中在考虑受噪声污染的简谐信号或者数字信号，将考虑多频模拟信号，以获得随机共振在信号处理中的更多有价值的信息，还原型随机共振系统的输出一直是一个困难的问题，但是在信号比较简单，例如简谐模拟信号和数字信号的情况下，可以有一些比较简便的方法，对于多频模拟信号，系统输出的还原就会相应地变得比较复杂。在分析非线性系统输出波形畸变原因的基础上，提出了一种新的反演方法，这种方法包含一个简单的反演公式，跃迁区域（信号严重失真段）的线性插值和最小二乘法的多项式曲线拟合。仿真结果表明，在适当选择系统参数的基础上，应用上述的反演方法可以得到比较理想的结果。     

Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises

Bearing fault is the most likely to occur in mechanical fault, and stochastic resonance (SR), as a noise enhanced signal processing tool, can find mechanical faults as early as possible, so as to avoid larger problems. However, most of the existing research methods are based on the first-order Langevin equation. According to the previous studies of many scholars, the weak signal detection ability of the second-order system is better than that of the first-order system, and the coupled system also has better performance due to the addition of the control system. So, in order to detect the fault signal more easily, a second-order coupled tristable stochastic resonance system (SCTSR) based on the adaptive genetic algorithm (AGA) is proposed, it is an improvement on improving the first-order coupled tristable stochastic resonance system (FCTSR). First, based on the fourth-order Runge–Kutta algorithm (F-RK), the performances of monostable, bistable and tristable control systems to SCTSR are compared, it is verified that the monostable system has the best performance as SCTSR’s control system. Secondly, the equivalent potential function of SCTSR is derived, and the influences of each system parameters on it are researched. The output signal-to-noise ratio gain (SNRG) is chosen as a measure to verify that SCTSR’s performance is better than that of FCTSR, and the influences of parameters on SNRG are discussed. SCTSR and FCTSR are used to detect low-, high- and multi-frequency cosine signals combined with AGA. The simulation results are compared with the wavelet transform method, which proves the performance superiority of SR, and also prove that SCTSR is easier to detect weak signals and has a stronger de-noising ability. Finally, SCTSR and FCTSR are applied in bearing fault detection under Gaussian white noise and trichotomous noise. The results also prove that SCTSR can get larger peaks and SNRG, and it is easier to detect fault signals. This proves that SCTSR’s performance is superior that of other methods in bearing fault detection, and has better engineering application value.

     

双稳随机共振的信号恢复研究

针对双稳随机共振输出波形失真的问题,从还原粒子运动轨迹的角度提出了波形恢复公式.通过将其应用于双稳系统对无噪阈上信号的响应输出,揭示了由粒子跃迁经过系统拐点引起的轨迹突变,及其在恢复波形的表现形式.鉴于阈下随机共振系统中噪声的随机影响,引入级联双稳系统对残余噪声进行二次调节,同时采用参数调节的恢复系统对波形进行恢复.数值仿真表明,该法直接应用于系统输出,适合处理有限长的时间数据,可以有效地估计噪声背景下微弱信号的时域波形.      

Performance improvement of the stochastic-resonance-based tri-stable energy harvester under random rotational vibration

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.     

Effects of non-Gaussian noise on logical stochastic resonance in a triple-well potential system

In this paper, we have investigated the phenomenon of logical stochastic resonance in a trip-well potential system driven by a colored non-Gaussian noise. The effects of a non-Gaussian noise on logical stochastic resonance have been discussed, and we have found that the reliability of the logic operation is dependent on the parameter q that indicates the departure from Gaussianity. The reliable region in the parameter plane of correlation time τ and noise strength D appears and expands with the decrease of q. Furthermore, it has been found that the reliable region in the plane (q,D) expands with the increase of noise color. The phenomenon can be explained successfully by the approach of Fokker–Planck equation.     

有界随机噪声激励下一类非线性系统的共振与饱和现象

研究了二自由度非线性系统在有界随机噪声激励下,系统响应的共振与随机饱和现象。用多尺度法分离了系统的快变项,用线性化方法求出了系统响应幅值的一、二阶矩,并给出了系统优化设计的一些建议。数值模拟表明本文提出的方法是有效的。     

A piezoelectric energy harvester based on internal resonance

A vibration-based energy harvester is essentially a resonator working in a limited frequency range.To increase the working frequency range is a challenging problem.This paper reveals a novel possibility for enhancing energy harvesting via internal resonance.An internal resonance energy harvester is proposed.The excitation is successively assumed as the Gaussian white noise,the colored noise defined by a second-order filter,the narrow-band noise,and exponentially correlated noise.The corresponding averaged root-meansquare output voltages are computed.Numerical results demonstrate that the internal resonance increases the operating bandwidth and the output voltage.     

Stochastic resonance in coupled weakly-damped bistable oscillators subjected to additive and multiplicative noises

With coupled weakly-damped periodically driven bistable oscillators subjected to additive and multiplicative noises under concern,the objective of this paper is to check to what extent the resonant point predicted by the Gaussian distribution assumption can approximate the simulated one.The investigation based on the dynamical mean-field approximation and the direct simulation demonstrates that the predicted resonant point and the simulated one are basically coincident for the case of pure additive noise,but for the case including multiplicative noise the situation becomes somewhat complex.Specifically speaking,when stochastic resonance(SR) is observed by changing the additive noise intensity,the predicted resonant point is lower than the simulated one;nevertheless,when SR is observed by changing the multiplicative noise intensity,the predicted resonant point is higher than the simulated one.Our observations imply that the Gaussian distribution assumption can not exactly describe the actual situation,but it is useful to some extent in predicting the low-frequency stochastic resonance of the coupled weakly-damped bistable oscillator.     

时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

摆式调谐质量阻尼器因其便于安装、维修、更换,且经济实用,广泛应用于结构减振.它通过将摆的自振频率调谐到接近主系统的控制频率,使摆产生与主系统相反的振动,从而抑制或消除主系统的振动.本文通过对主系统无阻尼的被动减振系统和主系统有阻尼的时滞反馈主动减振系统进行多目标优化设计,实现了对主系统幅频响应曲线的等峰控制和共振峰与反共振峰差值的有效控制.首先,建立了时滞耦合质量摆动力吸振器减振系统的力学模型和振动微分方程,通过对主系统无阻尼的被动减振系统进行等峰优化,获得了减振系统的最优频率比和质量摆的最优阻尼比.对于主系统存在阻尼的被动减振系统,在该优化参数下主系统的幅频响应曲线等峰优化失效.其次,对于主系统存在阻尼的时滞反馈优化控制系统,采用CTCR方法得到了反馈增益系数和时滞的稳定区域.在保证系统稳定的前提下,通过调节反馈增益系数和时滞量两个控制参数能够实现对主系统幅频响应曲线的等峰控制.再次,对共振点处主系统振幅放大因子时滞敏感度和反馈增益系数敏感度进行分析,表明共振点幅值对反馈增益系数比对时滞更为敏感.最后,通过实验分别在频域和时域内对理论结果进行了验证.研究表明,通过采用时滞反馈对摆式调...     

Inverse stochastic resonance in Hodgkin–Huxley neural system driven by Gaussian and non-Gaussian colored noises

Inverse stochastic resonance (ISR) is the phenomenon of the response of neuron to noise, which is opposite to the conventional stochastic resonance. In this paper, the ISR phenomena induced by Gaussian and non-Gaussian colored noises are studied in the cases of single Hodgkin–Huxley (HH) neuron and HH neural network, respectively. It is found that the mean firing rate of electrical activities depends on the Gaussian or non-Gaussian colored noises which can induce the phenomenon of ISR. The ISR phenomenon induced by Gaussian colored noise is most obvious under the conditions of low external current, low reciprocal correlation rate and low noise level. The ISR in neural network is more pronounced and lasts longer than the duration of a single neuron. However, the ISR phenomenon induced by non-Gaussian colored noise is apparent under low noise correlation time or low departure from Gaussian noise, and the ISR phenomena show different duration ranges under different parameter values. Furthermore, the transition of mean firing rate is more gradual, the ISR lasts longer, and the ISR phenomenon is more pronounced under the non-Gaussian colored noise. The ISR is a common phenomenon in neurodynamics; our results might provide novel insights into the ISR phenomena observed in biological experiments.

     

A Theoretical and Experimental Implementation of a Control Method Based on Saturation

A novel approach for implementing an active nonlinear vibration absorber is presented. The absorber, which is built in electronic circuitry, takes advantage of the saturation phenomenon that occurs when two natural frequencies of a system with quadratic nonlinearities are in the ratio of two-to-one. When the system is excited at a frequency near the higher natural frequency, there is a small ceiling for the system response at the higher frequency and the rest of the input energy is channeled to the low-frequency mode.A working model of using saturation to suppress the vibrations of a rigid beam connected to a DC motor has been built. An electronic oscillator is built, and its frequency is set at one-half the frequency of the beam. The output from a sensor on the beam is multiplied by the output from the electronic oscillator and a suitable gain, and the result is used as the forcing term for the oscillator. At the same time, the output from the oscillator is squared and multiplied by a suitable gain, and that result is used as the input to the motor. The oscillator/actuator and the beam act as the two modes of a two-degree-of-freedom quadratically coupled system with a 2:1 autoparametric resonance. When the beam is excited by a harmonic force, its motion quickly becomes saturated, and most of the energy imparted to the beam by the harmonic force is transferred to the electronic circuit and from there to the actuator. Thus, the harmonic force is made to work against itself. As a result, the motion of the beam always remains small.     

负刚度时滞反馈控制动力吸振器的等峰优化

相比于传统动力吸振器, 负刚度动力吸振器同时具有更好的减振能力和更宽的有效减振频带宽度, 为了进一步降低共振峰幅值, 在负刚度吸振器系统耦合时滞反馈控制. 对负刚度时滞反馈控制动力吸振器系统进行等峰优化设计, 优化设计的准则是:第一和第二共振峰的峰值相等; 同时兼顾两个目标, 一个目标是在优化时的最大共振峰幅值小于被动负刚度吸振器系统的反共振峰幅值, 另一目标是在优化时共振峰幅值与反共振峰幅值差小于被动吸振器系统. 接着, 通过设计和调节负刚度系数、吸振器阻尼系数和时滞反馈控制系数对控制系统进行等峰优化设计. 最后, 在降低幅值的同时, 分析结构参数对有效减振频带宽度的影响. 经过等峰优化之后, 选择本文的一组结构参数与两个典型的模型进行对比. 为了定量比较不同模型的降幅效果, 定义了减幅百分比, 研究发现在有效减振频带区间内减幅百分比超过40%以上. 结果表明, 通过等峰优化准则对结构参数进行优化设计和调节增益系数和时滞量, 共振峰幅值的减幅百分比也近似达到40%, 也可以调节增益系数和时滞量, 使得幅频响应曲线具有较宽的有效减振频带和较低的共振峰幅值与反共振峰幅值的差值.      

电磁力作用下发电机定子端部绕组的两自由度主共振

对压板松动时大型汽轮发电机定子端部单根绕组的两自由度主共振问题进行了研究．在给出定子端部绕组区域磁感应强度表达式、绕组所受电磁力以及与松动压板间摩擦力计算式的基础上,建立了研究绕组非线性电磁振动的力学分析模型．采用多尺度法对两自由度主、内共振问题进行求解,得到了稳态运动下的幅频响应方程和解的稳定性判定条件．通过算例,得到了反应系统跳跃现象和软硬特性的幅频响应曲线图,以及响应图、相图、Poincare映射图和频谱图,并阐述了系统可能存在的周期运动和锁模现象。     

Bounded noise enhanced stability and resonant activation

We investigate the escape problem of a Brownian particle over a potential barrier driven by bounded noise, which is different form the common unbounded noise. Some novel stochastic phenomena and results are founded. For weak frequency of bounded noise, the mean first passage time (MFPT) shows a non-monotonic dependence on the intensity of white noise. One remarkable behavior is the phenomenon of co-occurrence of noise-enhanced stability and resonant activation. Another novel finding is that the position of minimum of MFPT about frequency shows monotone non-decreasing or non-increasing function with the variation of amplitude of bounded noise, while the minimum of MFPT monotonously depends on the amplitude of bounded noise. More important, we uncover the relationship of the parameters of bounded noise which induce the occurrence of the phenomenon of resonant activation. Besides, resonant activation can also be induced by simplified bounded noise, called sine-Wiener noise. The behaviors presented in our work driven by bounded noise show distinctive features compared with the ones inspired by the common noise.     

谐波激励下斜拉桥面内非线性振动试验研究

斜拉桥拉索的振动问题一直是桥梁工程领域的研究热点。为揭示拉索大幅振动的力学机理，课题组建立了斜拉桥的全桥精细化模型，本文测试和研究了单频激励下的斜拉桥可能的非线性振动行为。首先，通过自由振动试验测试了模型的模态参数，并与两类有限元模型（OECS模型和MECS模型）进行对比，结果吻合良好。其次，试验研究了在单个竖向简谐激励下斜拉桥模型的非线性响应。研究发现：当激励频率与斜拉桥某阶全局模态频率接近时，主梁产生主共振，并引起多根长索产生大幅的参强振动；当激励频率与某根斜拉索面内一阶频率之比为1：2或者2：1时，可以观测到索中产生超谐波和亚谐波共振现象。     

基于压电纤维复合材料的旋转叶片主动控制

旋转叶片结构的振动失效占据了航空发动机整机故障的相当比重. 发展针对旋转叶片结构的减振技术对于减轻叶片重量, 提升叶片性能, 延长叶片寿命具有重要意义. 通过引入压电纤维复合材料(macro fiber composite, MFC)传感器和作动器, 研究预变形旋转叶片2:1内共振的主动控制. 建立考虑时滞效应的旋转叶片比例微分闭环控制系统运动方程. 通过摄动分析推导出受控叶片的演化方程, 并结合延拓法揭示速度增益、位移增益、时滞量等系统参数对受控系统稳态响应及稳定性的影响规律. 理论研究结果与数值结果得到相互验证. 研究发现时滞量对系统稳定性影响显著, 当时滞超过某临界值时, 演化方程原有的平衡点失稳, 闭环受控系统将缓慢进入一个大振幅的周期运动, 从而丧失控制效果. 位移增益存在一个范围使得系统出现多值稳态响应, 进而破坏了增益平面内系统稳定区和非稳定区域的直线边界. 不恰当的速度增益和位移增益会给受控系统引入新的共振. 研究结果为叶片结构的减振提供了理论基础.