基于关联噪声的静态系统中随机共振和相干共振研究

In this project,we protocol to study stochastic resonance(SR), coherence resonance(CR) and the relationship between them with the help of static systems driven by correlated noise. We derive the analytic expression of the output signal-to-noise ratio(SNR) by applying the SNR theory and cyclostationary theory of SR in static systems. And we get the analytic expression of the input-output normalized cross covariance(NCC) by using the mutual information theory. Then we analyse SR and CR by employing SNR and NCC respectively. Moreover, we will investigate the condition under which SR and CR will appear in the static systems driven by correlated noise, then we will discuss the effects on SR and CR of the noise intensity and the correlation intensity between noises and other parameters, also we will investigate the mechanism on SR and CR of correlated noise in static systems. On this basis, we compare the differences between SR and CR, and build bridge between them by adopting a new index—input-output coherence function of the system. This project can expand and perfect the SR theory in static systems, and it also provide theoretical basis for improving the output SNR in realistic sensor systems by using these theories.

本项目拟研究关联噪声驱动下静态系统中的随机共振和相干共振现象以及它们之间的相关性。基于静态系统随机共振的信噪比理论和循环平稳理论,推导输出信噪比的解析表达式。应用互有信息理论推导系统输入和输出之间标准化协方差的解析表达式。分别由输出信噪比和输入和输出之间标准化协方差分析系统的随机共振和相干共振现象。揭示关联噪声驱动下系统出现随机共振和相干共振的条件，讨论噪声强度、噪声之间的关联强度等参数对随机共振和相干共振的影响，进一步探索关联噪声驱动下静态系统出现随机共振和相干共振的内在机理。在此基础上，综合比较随机共振和相干共振之间的异同，提出一种新的指标--系统输入和输出之间的相关函数在这两种现象之间建立关联性。通过本项目的研究，进一步发展和完善静态系统中的随机共振理论，为将这些结论应用到实际的传感器系统中，提高系统的输出信噪比提供理论依据。

本项目对静态线性和非线性传感器系统、双稳态系统中的随机共振现象及其相关问题进行了深入研究，主要内容和结论如下：.1.研究了静态系统中的随机共振现象。针对一类并联非线性传感器系统，当系统输入信号为周期信号时，应用信噪比理论得到了输出信噪比的表达式；当输入信号为非周期信号时，根据互相关信息理论得到了系统输入与输出之间标准化时间平均协方差的表达式，进而分析了噪声对系统输出信噪比和输入与输出之间标准化时间平均协方差的影响。.2. 研究了双稳态系统中随机共振现象和输入与输出之间平均相同步时间的相关性，从相同步角度解释随机共振现象产生的机制。