利用欠阻尼二阶线性随机共振抑噪的模型设计及实现

Model design and realization about stochastic resonance of the under-damped second-order linear system represses noise

以经典力学模型——质量-阻尼-弹簧欠阻尼二阶线性系统为研究对象,当系统的阻尼系数和固有频率同时受乘性高斯噪声干扰时,利用此系统产生的随机共振来消除此类噪声.理论分析表明,欠阻尼二阶线性系统中存在随机共振现象,系统的平均输出幅度增益呈现非单调变化,不仅在一定条件下大于无噪声时的增益,而且调节适当的系统参数和噪声强度能够提高幅度增益.因此,采用可视化仿真软件SIMULINK建立仿真模型,并进行实例模拟.仿真进一步表明,通过调节适当的系统参数或噪声强度,使系统处于共振区域,就会把夹杂在噪声中的被测信号突现出来,从而实现了弱信号的检测,证实该方法消除乘性噪声的可行性和有效性.

With the classic mechanics model,quality-damping-spring coiling the under-damped second-order linear system for research object,when the damping coefficient and intrinsic frequency of the system were subject to multiplicative Gaussian white noise,this article studied detailedly that stochastic resonance of the under-damped second-order linear system were used to resolve multiplicative noise.Theoretical analysis showed that this system produced the phenomenon of stochastic resonance.The average output amplitude gain（OAG） of this system presented not-monotonous variety.Under certain conditions,OAG was greater than that of second-order linear system with no noise,and adjusted the appropriate system parameters and noise intensity could improve the output amplitude gain.Therefore,the article used visual simulation software SIMULINK to establish a linear system simulation map of stochastic resonance and simulate some examples.Simulation further shows that appropriate system parameters can achieve weak signal detection of under-damped second-order linear system in the noise background so long as the system is in the resonance region.So it confirms that this method resolves multiplicative noise feasibly and effectively.