螺旋桨鸣音的混沌动力特性研究

Chaotic dynamics of propeller singing

利用混沌动力学方法研究螺旋桨鸣音系统时间序列,估计时间序列的相空间重构最佳参数,并首次提出其具有混沌动力特性,还进一步分析了系统拓扑维数的边界和生成系统所必须地独立变量的个数,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:螺旋桨鸣音系统时间序列可以选取最佳延迟时间tD=1、最小嵌入维数dE=8进行相空间重构,其混沌吸引子的关联维数为5.157 9、最大Lyapunov指数为0.077 1,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。

The time series of a propeller singing system was processed by use of chaotic dynamics method.The topological dimension of the propeller singing system was estimated,the number of independent variables was confirmed,and the characters of attractor trajectory were described in reconstructed phase space.The results indicate that the propeller singing can be reconstructed by the optional delay time tD=1 and the minimal embedding dimension dE=8 with a fractional correlation dimension D2=5.1579 and a positive maximum Lyapunov exponent λtD=0.0771.The investigation gives a new approach based on chaos to study the propeller singing phenomenon.