基于 Duffing 振子的信号频谱重构随机共振研究

摘要

The matching relation between signal characteristic frequency and sampling frequency has a restriction on the scale-varying stochastic resonance (SR)of a Duffing oscillator.Therefore,a signal pre-processing approach based on spectrum reconstruction was studied here,and a signal spectrum reconstruction SR method based on a Duffing oscillator was further proposed.This method introduced spectrum reconstruction parameters to realize the flexible varying of signal characteristic frequency.When combined with the scale varying and damping-ratio-adjustment methods,this method realized the large parametric SR of a Duffing system under any signal characteristic frequency and sampling frequency, thus its application in weak-signal detection was extended.Both numerical simulation and fault diagnosis example analysis verified the effectiveness of the proposed method.%针对信号特征频率和采样频率所要求的匹配关系对 Duffing 振子变尺度随机共振的限制，研究一种频谱重构的信号预处理方法，并进一步提出基于 Duffing 振子的信号频谱重构随机共振方法。该方法通过引入频谱重构参数实现信号特征频率的灵活转化，与变尺度方法和阻尼比参数调节方法相结合，可以实现任意信号特征频率和采样频率下的 Duffing 系统的大参数随机共振，从而扩展其在微弱信号处理中的应用。数值仿真和故障诊断实例分析均验证了该方法的有效性。