非线性系统的变尺度随机共振与振动共振及其相互作用机理研究

Based on the nonlinear and stochastic vibration theory, we investigate the re-scaling stochastic resonance and vibrational resonance and their interaction mechanism in some typical nonlinear systems under the excitations of strong noise and weak high-frequency character signal. We aim at revealing interesting dynamical phenomena and developing effective analytical methods. Through the theoretical investigations, we will propose the re-scaling vibrational resonance definition and develop the vibrational resonance theory. After making clear the interaction mechanism between the re-scaling stochastic resonance and the vibrational resonance, we aim to master the way that controlling and improving the re-scaling stochastic resonance by the vibrational resonance. By introducing the fractional-order calculus, we will study the re-scaling stochastic resonance and vibrational resonance in the fractional-order nonlinear systems. Through using the optimization algorithms, we will obtain the optimal output of the system, and then obtain the optimal nonlinear model for the re-scaling stochastic resonance. In the nonlinear response framework, we will study the stochastic resonance and vibrational resonance that occurs at the excitation frequency, the subharmonic frequencies, the superharmonic frequencies, and the combination frequencies. It will extend the original theoretical framework. By proposing the re-scaling aperiodic stochastic resonance, we will extract the weak aperiodic signal in the strong noise background. Through the experimental studies, we will design new types of hardware stochastic resonance simulation circuits. It will improve the efficiency for extracting the weak character signal and verify the validity of the theoretical analysis.

本项目基于非线性及随机振动理论，研究强噪声、微弱高频特征信号激励下非线性系统的变尺度随机共振与振动共振及其相互作用机理，旨在揭示丰富的动力学现象，发展有效的动力学分析方法。通过理论研究，拟提出变尺度振动共振概念，发展振动共振理论；弄清变尺度随机共振与振动共振的相互作用机理，掌握利用振动共振控制与增强变尺度随机共振的方法；引入分数阶微积分理论，在分数阶非线性系统中研究变尺度随机共振与振动共振，通过优化算法分析系统的最优输出，解决变尺度随机共振系统模型的优化设计问题；在非线性响应理论体系下，研究系统在信号频率、次谐频率、超谐频率及组合频率处的随机共振与振动共振，扩展原有的理论体系；提出变尺度非周期随机共振概念，解决强噪声背景下微弱非周期信号的提取问题。通过实验研究，设计出提取微弱特征信号的新型随机共振硬件电路模拟系统，提高微弱特征信息的提取效率，验证理论分析的正确性。

基于非线性及随机振动理论，研究了非线性系统的变尺度随机共振与振动共振及其相互作用机理，揭示了丰富的动力学现象，发展了有效的动力学分析方法，解决了强噪声背景下滚动轴承故障特征信息提取问题。通过理论研究，提出了归一化变尺度随机共振和振动共振理论。弄清了变尺度随机共振与振动共振的相互作用机理，得到了利用振动共振控制与增强随机共振的方法。通过研究多种非线性系统模型引起的最优共振响应，解决了变尺度随机共振系统模型的优化设计问题。在非线性响应理论体系下，研究了非线性频率处的随机共振与振动共振，扩展了原有的理论体系。提出了变尺度非周期随机共振概念，解决了强噪声背景下微弱非周期信号的提取问题。通过实验研究，在强噪声背景下提取了多种工况下的滚动轴承微弱特征信息，实现了变尺度随机共振理论在旋转机械故障诊断领域的应用价值。本项目共发表SCI论文26篇，EI论文3篇，出版专著2部，授权国家发明专利2件，软件著作权1个，参加学术会议5次，作大会特邀报告1次，培养研究生12名。获得中国煤炭工业协会二等奖1项，建立了滚动轴承故障实验数据库。本项目完成并扩展了任务书中的研究内容，为后续研究工作的深入开展打下了坚实的基础。