螺旋桨鸣音的混沌动力特性研究

利用混沌动力学方法研究螺旋桨鸣音信号时间序列,估计时间序列的相空间重构最佳参数,并提出其具有混沌动力特性,分析了系统拓扑维数的边界和生成系统所必须独立变量的个数,还计算分析了重构相空间中吸引子轨迹随时间演化的发散情况。分析计算结果表明:螺旋桨鸣音信号时间序列可以选取最佳延迟时间t_D=1、最小嵌入维数d_E=8进行相空间重构,其混沌吸引子的关联维数为5.1579、最大Lyapunov指数为0.0771,此研究结果可以为螺旋桨鸣音现象的进一步研究提供理论基础。 

Chaotic dynamics of propeller singing

Propeller singing signal time series has been examined by chaotic dynamics method,in order to demonstrate chaos character for the first time.The topological dimension of the system has been estimated,the number of independent variable has been confirmed,and the character of attractor trajectory has been described in reconstructed phase space. The results indicated that the propeller singing can be reconstructed by the optional delay time t_D = 1 and the minimal embedding dimension d_E=8 with a fractional correlation dimension D₂=5.1579 and a positive maximum Lyapunov exponent λ_tD=0.0771,so it may be a new approach based on chaos to study the propeller singing phenomenon.