分数阶双稳系统随机共振现象研究及FPGA实现

Research on Stochastic Resonance Phenomenon of Fractional Bistable System and FPGA Implementation

相比整数阶微积分,分数阶对一些具有记忆依赖性以及空间相关性的复杂系统的描述更简明与贴合。利用分数阶微积分的这一优点并结合广义郎之万方程阻尼具有幂律衰减特性,选择合理的核函数,将整数阶郎之万方程推广至分数阶。以此为理论基础,提出了一种分数阶双稳态随机共振系统的FPGA实现方法。对该系统进行了仿真实验验证,仿真结果表明:在调节至合适的分数阶阶数时,系统可以产生随机共振现象,有效提高微弱信号的信噪比,并且存在一个最优分数阶阶次,使得系统输出信噪比增益最大。

The fractional order is more concise and accurate for the description of complex systems with memory dependence and spatial correlation,compared with the integer order calculus.It is observed that the damping has power-law attenuation characteristics,so a reasonable autocorrelation damping kernel function is selected.Combining the theory of fractional calculus and Langevin equation,the fractional Langevin equation can be derived.Then,a FPGA implementation method of fractional bistable stochastic resonance system is proposed based on this theory.Finally,a simulation experiment is performed to verify whether the system can generate stochastic resonance by changing the order of the fractional order.The results show that the system can generate stochastic with an appropriate fractional order,which can effectively extract the weak signal submerged by noise.And there is an optimal fractional order that maximizes the useful signal output gain.