混沌振动Lyapunov特征指数重构演化矩阵算法

发布时间：2018-05-01 15:36

本文选题：演化矩阵 + 切空间　；参考：《哈尔滨工程大学学报》2017年05期

【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。
[Abstract]:In order to solve the problem that it is difficult to describe the dynamic characteristics of chaotic orbits in different directions in phase space during the calculation of Lyapunov exponent, this paper studies the construction method of mapping matrix in chaotic reconstructed phase space. The algorithm expression of Lyapunov characteristic exponential evolution matrix in phase space reconstruction of chaotic vibration measured time series is derived, and the stretching and folding effect of tangent space cascade matrix on the neighborhood of reference point during orbit evolution is analyzed. It is revealed that the direction of eigenvector is the direction of neighborhood deformation, and the value of singular value corresponds to the magnitude of neighborhood stretching and compression in the direction of feature. An augmented matrix including mapping range and domain is constructed, and the error of calculation process is analyzed by perturbation method. The results show that the reconstructed evolutionary matrix algorithm can effectively extract the maximum Lyapunov exponent of chaotic time series. The experimental device of nonlinear chaotic vibration is designed, and the validity of the method is verified.
【作者单位】：海军工程大学动力工程学院;
【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)
【分类号】：O415.5

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