混沌振动Lyapunov特征指数重构演化矩阵算法  

A reconstruction evolution matrices algorithm based on Lyapunov characteristic exponent of chaotic vibration

作　　者：刘树勇[1] 位秀雷[1] 方远[1] 杨庆超[1] 

机构地区：[1]海军工程大学动力工程学院,湖北武汉430033

出　　处：《哈尔滨工程大学学报》2017年第5期746-751,共6页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(5157942);国家自然科学基金青年基金项目(51509253)

摘　　要：针对Lyapunov指数计算过程中,邻近点对演化难以有效刻画混沌轨道在相空间不同方向的动态特性问题,本文研究了混沌重构相空间中映射矩阵的构造方法,推导了混沌振动实测时间序列重构相空间中Lyapunov特征指数演化矩阵算法表达式,分析了轨道演化过程中切空间级联矩阵对参考点邻域的拉伸折叠作用,揭示其特征向量方向是邻域变形的方向、奇异值大小对应特征方向上邻域拉伸和压缩的大小。构造了包含映射值域和定义域的增广矩阵,通过微扰法分析了计算过程的误差。计算结果表明,应用重构演化矩阵算法能够有效提取混沌时间序列最大Lyapunov指数。设计了非线性混沌振动实验装置,证实了该方法的有效性。The reconstruction map matrix o! chaotic phase space is studied since the dynamical characteristics o! the chaotic orbit at different directions are discovered by the nearest orbit ineffectively,and the formulation of Lyapunov exponent based on evolution matrices in reconstructed phase space is derived. It explains that in the process of orbit evolution,the stretch and fold of the neighbor is the rotation operation of the cascade matrices and the fluctuation of the singular value of the reconstructed tangent space matrices. The S V D matrix of the reconstructed tangent space plays important role on the system dynamical behavior characteristic. The eigenvector direction is the deformation di-rection of the neighbor,and the stretch extent corresponds to the eigenvalue. The augmented matrix including range and definition domains is constructed,and the computation error is analyzed with perturbation. Numerical results show that the presented algorithm is useful to extract the maximal Lyapunov exponent of the chaotic time series. The experi-mental rig is designed and the Lyapunov exponent of the measured signal is computed with the method effectively.

关 键 词：演化矩阵 切空间 投影算子 混沌 重构相空间 LYAPUNOV指数 混沌振动 

分 类 号：TN911[电子电信—通信与信息系统]