摘要微弱信号检测是一种重要的技术，已经被广泛用于许多领域。与众多微弱信号处理方法不同的是，随机共振（SR）可以利用噪声实现对特征信号的检测。Van der Pol振子具有丰富的动力学性质，被广泛运用在混沌检测中。基于此，本文将Duffing与Van der Pol振子进行线性耦合，并添加微分项作为耦合系统的反馈以加强耦合强度，构建一种Duffing与Van der Pol强耦合系统，实验发现，该系统具有丰富的SR现象，且通过广义时间尺度变换，可以实现任意特征频率下的微弱信号检测。实验显示，强耦合系统比一般耦合系统具有更好的稳定性；在三值噪声背景下，该系统的输出平均信噪比增益（MSNRI）随着三值噪声状态值的变化呈现不同形式的对称分布；在被控系统中，随着阻尼系数的逐渐增强，输出响应将变得逐渐平滑；另外，在控制系统中，当阻尼系数很小时，系统输出将会出现二次共振现象，随着阻尼系数的增大，次级共振峰将逐渐减小直至消失，一级共振峰将逐渐增强，这是阱间共振完全取代了阱内，阱间联合共振的缘故。最后，借助遗传算法（GA）自适应参数寻优，与传统双稳以及耦合Duffing系统对比发现，所提系统具有更高的输出MSNRI。经测试，该系统对实际轴承故障信号也具有良好的检测效果，并且与传统双稳系统相比能更显著的消除边频信号干扰。
Abstract：Weak signal detection is an important technique, it is widely applied in various fields. Being different from other weak signal processing methods, stochastic resonance (SR) can utilize noise to detect characteristic signals.Van der Pol oscillator has rich dynamic properties,and is extensively applied in chaotic detection. Here, Duffing oscillator and Van der Pol oscillator were linearly coupled, and a differential term was added as the feedback of the coupled system for enhancing coupling degree to construct a Duffing-Van der Pol strongly coupled system. It was found with experiments that the system has rich SR phenomena,through the generalized time scale transformation, it can realize weak signal detection under arbitrary characteristic frequency. Experimental results showed that the strongly coupled system has better stability than the general coupled one does;under the background of trichotomous noise, the system’s output mean signal-noise ratio gain presents different symmetric distributions with variation of trichotomous noise state values;in the controlled system, with gradual increase in damping coefficient,the output response is gradually smooth; in the control system,when damping coefficient is very small, secondary resonance appears in the system output,with increase in damping coefficient,the second resonance peak gradually decreases until it disappears, and the first resonance peak gradually increases, this is because the well to well resonance completely replaces the joint resonance in and between wells.Finally, the genetic algorithm (GA) was used to do adaptive parametric optimization. It was found that compared with the traditional bi-stable and coupled Duffing systems, the proposed system has a higher output mean signal-noise ratio gain; after testing, the system has a good detection effect on the actual bearing fault signals, compared with the traditional bi-stable system, it can more significantly eliminate the side frequency signal interference.
张刚，吴瑕. 基于Duffing与Van der Pol强耦合系统的随机共振研究及轴承故障诊断[J]. 振动与冲击, 2020, 39(19): 266-276.
ZHANG Gang, WU Xia. Stochastic resonance and bearing fault diagnosis basedon a Duffing-Van der Pol strongly coupled system. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(19): 266-276.
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