Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR.

中文翻译：

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三分噪声下强耦合达芬和范德波尔振荡器的随机共振和轴承故障诊断

弱信号检测是一个重要课题，在各个领域得到了广泛的研究。与其他信号处理方法不同，随机共振（SR）可以利用噪声来增强特征频率。受SR独特优势的启发，研究了强耦合的Duffing和Van der pol SR系统（SCD-VSR）。仿真结果表明，输出平均信噪比增加值（MSNRI）与三分噪声的不同跳跃值之间的关系呈现不同的奇数对称分布。还发现当范德波尔系统的阻尼系数较小时，可以观察到双SR现象。此外，随着 Duffing 系统阻尼系数的增加，输出响应会逐渐变得平滑。此外，较小的阻尼力耦合系数与较大的恢复力耦合系数相结合将获得更好的系统响应。在检测模拟信号的情况下，SCD-VSR 的 MSNRI 大于经典双稳态 SR 系统（CBSR）和耦合 Duffing SR 系统（CDSR）。此外，实验表明SCD-VSR可以获得更高的MSNRI和更好的检测效果，这意味着性能优于CBSR和CDSR。