二次采样随机共振的工程应用研究

Engineering Application Study of Twice Sampling Stochastic Resonance

研究了小参数随机共振 (SR)理论的克莱默斯 (Kramers)逃逸速率和罗伦兹 (Lorentzian)分布的噪声频谱特性 ,得出了只有在噪声能量集中的低频区域才能产生随机共振的论点。在此基础上 ,通过二次采样频率变换思想 ,成功地将小参数随机共振扩展应用到大参数的随机共振 ,从而实现了从强噪声中检测出弱信号的目的。大参数随机共振谱特性及其信噪比的进一步定量分析表明 ,提高采样频率可把弱信号移入噪声能量集中的低频区域 ,有利于产生可辨识的随机共振谱峰。

The Kramers escape rate and the characteristics of noise frequency spectrum distributing as Lorentzian form were investigated under the theory of small parameter stochastic resonance (SR), and the viewpoint of creating stochastic resonance only in the low frequency region where the noise energy has been concentrated was also obtained. On the basis of the investigation and through the methodology of twice sampling frequency transformation, the small parameter stochastic resonance is successfully expanded into the applications of the large parameter stochastic resonance, and hence a weak signal submerged in strong noise is detected. The further quantitative analysis of the power spectral characteristics of the large parameter stochastic resonance and its signal-to-noise ratio indicate that the increase of sampling frequency can move the weak signal into the low frequency region concentrated by noise energy, which is benefit to produce a distinguishable SR spectral peak. The real example of monitoring and diagnosis of electromotor faults proves the validity of the technique in practical applications.