中文摘要：

将多个低频微弱信号、高频信号和加性α稳定噪声共同激励的一类周期势系统作为研究模型,以平均信噪比增益（MSNRI）为性能指标,对α稳定噪声环境下周期势系统中的振动共振现象进行了研究,分别探究了α稳定噪声的特征参数α、对称参数β、加性噪声强度放大系数D、高频信号幅值B以及频率？对振动共振输出效应的影响.研究结果表明：1）在不同分布的α稳定噪声环境下,固定频率Ω（或幅值B）,当幅值B（或频率Ω）逐渐增大时,MSNRI-B（或MSNRI-Ω）曲线出现多个峰值,即存在多个B区间（或Ω区间）可诱导振动共振,并且这些区间不会随噪声分布参数α或β的变化而变化;2）当加性噪声强度放大系数D发生变化时,幅值B和频率？的共振区间没有随着D的变化而变化,表明只有高频信号能量向待测低频信号转移,噪声能量并没有向待测低频信号转移.另外当幅值B、频率Ω固定时,随着D的逐渐增大,依然可以实现微弱信号的检测,表明振动共振可以克服工业现场噪声强度不可调控的缺点.本文研究结果提供了一种新的微弱信号检测方法,在信号处理领域有着潜在的应用价值.

英文摘要：

A periodic potential system excited by multi-low frequency weak signals, the high frequency signal and additive a stable noise is constructed. Based on this model, the vibrational resonance phenomenon under a stable noise is investigated by taking the mean signal-noise-ratio gain （MSNRI） of output as a performance index. Then the influences of stability index α（0 〈 α ≤ 2）, the skewness parameterβ （-1 ≤β ≤ 1） of a stable noise, the amplification factor D and the high frequency signal amplitude B, and frequency Ω on the resonant output effect are explored. The results show that under the different distributions of a stable noise, the multi-low frequency weak signals detection can be realized by adjusting the high frequency signal parameter B or Ω to induce vibrational resonance within a certain range. When α （orβ） is given different values, the curve of MSNRI-B has multiple peaks with the increase of B for a certain frequency Ω, and the values of MSNRI corresponding to peaks of the curve of MSNRI-B are equal. So the intervals of B which can induce vibrational resonances are multiple, and the multiple resonance phenomenon turns periodic with the increase of B. Similarly, the curve of MSNRI-Ω also has multiple peaks with the increase ofΩ for a certain amplitude B, so the intervals ofΩ which can induce vibrational resonances are also multiple. The difference is that the multiple resonance phenomenon becomes irregular with the increase ofΩ. Besides, the resonance intervals of B andΩ do not change with a norΩ- Under the different values of amplitude factor D, the resonance intervals of B（or Ω） do not change with the increase of D, indicating that only the energy of the high frequency signal transfers toward the signals to be measured, and the energy of α stable noise does not transfer toward the signals to be measured. Besides, when B andΩ are fixed, it can still be realized to detect the weak signal with the increase of D, which shows that the weak signal detection method b