耦合激励作用下动力学行为突变机理及其在微弱信号参数识别中的应用

The application of mutation mechanisms for nonlinear dynamic behavior in the identification of weak signal parameters is a new method of time domain detection. High dimensional autonomous system, piecewise nonlinear system and the non-smooth dynamic system will be constructed to detect the parameters of the weak signal by using the theoretical system of impulsive differential equation and nonlinear dynamics. The weak signal and noise are presented as harmonic excitation, impulsive excitation and random excitation. And based on the energy method and perturbation method, the new method is used to explore the approximate analytic expression of the periodic orbit and homoclinic (heteroclinic) orbit. Melnikov methods are developed to detect the mechanisms of coupled excitation(harmonic excitation, impulse excitation and random excitation) on the bifurcation and chaos threshold of high dimensional autonomous system, piecewise nonlinear system and the non-smooth dynamic system by introducing scale transformation, differential extreme principle and equivalent driving force. The optimization analysis and the probability density of dynamical transition are studied to improve the adaptability to non-smooth detecting system for weak signal. With the aid of Simulink、Multisim、LabVIEW and C, the theoretical results are applied to the development of electronic circuit design and application software. Hence, the soft and hardware platform for detecting the weak signal parameters are constructed, which lead to combine scientific theory with engineering applications effectively.

非线性动力学行为突变机理在微弱信号参数识别中的应用是一种时域检测新方法。拟借鉴高维非线性动力学和脉冲微分方程理论，构造特殊高维非自治系统、分段非线性系统和脉冲系统开展谐波、非谐波微弱信号参数识别。将微弱信号和噪声作为谐波激励、脉冲激励和随机激励，基于能量法和摄动法，构建能量动态新方法，探讨周期轨道、同(异)轨道的近似解析表达式。引入尺度变换、微分极值原理和等效策动力，发展Melnikov方法，探究耦合激励(谐波激励、脉冲激励、随机激励)对特殊高维非自治系统、分段非线性系统和脉冲系统分岔和混沌阈值影响的机理。开展最优化分析及动力学转迁概率密度的研究，提高参数识别系统对微弱信号的自适应性。借助Simulink、Multisim、LabVIEW和C等工具，将理论结果应用到电子线路设计和应用软件开发的实验研究中，构建微弱信号参数识别软、硬件平台，将科学理论和工程应用进一步有效结合。

早期故障微弱信号常淹没在强噪声环境中，其相对微弱性给故障诊断带来极大的挑战。非线性系统具有信号敏感性和噪声免疫性，利用非线性动力系统来检测微弱信号是目前的研究热点之一。非线性动力学行为突变机理在微弱信号参数识别中的应用是时域微弱信号参数识别的新方法，开辟了非线性动力学的应用新领域。本项目借鉴经典摆，光滑不连续振子等构建了高维非自治、分段非线性和脉冲非线性等多种非线性动力学数学模型。在摄动法和能量法的基础上，发展了非光滑系统的近似解析法，研究了所构建系统的复杂的动力学行为；利用非光滑Melnikov方法探讨了混沌阈值对自身参数的依赖性；基于随机动力学理论研究了噪声激励对所构建的非线性系统动力学行为突变的影响，确定不同功率的噪声作用下的混沌阈值。借助Matlab、Python、Ansys等多款仿真软件开展了数值仿真和实验研究，对理论结果进行了数值模拟，验证了理论结果的正确性和新方法的可行性。开展了应用研究，基于Multisim仿真软件设计了电子电路，搭建了用以描述系统的硬件电路；基于LabVIEW平台开发了微弱信号参数识别的应用程序，将科学理论与工程应用有效结合。科研成果：发表论文25篇，SCI期刊论文检索21篇，EI期刊论文检索3篇，中文核心论文检索1篇，授权国家发明专利2项。国内外学术合作交流：举办国内学术会议4次，参加国际会议5次，参加国内会议24次。人才培养：培养了3名博士（2人在读），9名硕士（1人在读）。

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