一种分数阶随机共振系统的弱信号检测研究

在利用随机共振系统进行弱信号检测的研究中大多是以整数阶朗之万方程为主,针对分数阶随机共振的鲜有研究。对过阻尼分数阶朗之万方程的随机共振特性进行深入研究分析,对于分数阶朗之万方程求解这一难题,引入Oustaloup算法对其近似化,搭建分数阶朗之万方程的近似仿真模型,找出了产生随机共振的阈值,实现了对满足绝热近似理论的微弱信号的检测,且讨论了不同分数阶阶次和噪声强度对分数阶朗之万方程产生随机共振的影响。数值分析表明,在一定阶数时,分数阶朗之万方程可以产生随机共振,且对微弱信号的检测及放大效果明显好于整数阶。该研究拓展了朗之万方程随机共振的研究范围,在信号检测与处理以及通信领域有着重要的应用价值。

The research of weak signal detection based on a fractional stochastic resonance system

Most of the research of weak signal detection depend on stochastic resonance (SR) are integer Langevin equation. The characteristics of stochastic resonance (SR) system based on over-damped fractional Langevin equation (FLE) is deeply studied in this paper for a small amount of research of fractional stochastic resonance. For solving FLE, Oustaloup algorithmSare introduced for its approximation The threshold of the stochastic resonance has been found, and weak signal detection has been achieved which meet the adiabatic approximation theory. In addition, the effects of fractional order and noise intensitySon FLE are studied respectively. The numerical simulation results show that in a certain range of the order, FLE can generate stochastic resonance, and it is evident that the SNR gain in fractional Langevin equation is better than that in the integer order situation. The paper has important practical potential in the field of weak signal detection, processing and communication, which expands the research scope of stochastic resonance based on Langevin equation.