基于空间栅格法的最大Lyapunov指数算法研究

An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method

最大Lyapunov指数是判断时间序列是否为混沌的一个重要判据,但传统方法求解的计算量很大,所需时间较长,导致在工程实际应用中受到限制.本文提出了基于空间栅格法的最大Lyapunov指数的改进算法,该方法将重构后的整个相空间进行分割,形成多个小空间,搜索邻近点时只需在其子空间内进行搜索,可以大大提高搜索速度.仿真实验表明改进的邻近点搜索方法无论在有噪声情况下还是在无噪声情况下都具有良好的鲁棒性,可以快速而有效地实现参考点邻域的搜索,极大的缩短了计算时间,且易于编程实现,使混沌信号特征指数的在线提取成为了可能.

The largest Lyapunov exponent is an essential criterion to judge whether the time series is chaos or not.However,the traditional methods are complex and time-consuing,which leads to the limitations in engineering application.An improved algorithm based on space grid method for estimating the largest Lyapunov exponent is presented.Firstly,the whole reconstructed phase space is divided into small spaces;then the points locating in these subspaces which are searched when the reference point exists;finally,the characteristic exponent is calculated.Simulation results show that neighborhoods are searched effectively,and the whole calculated time is reduced greatly.In practically,the algorithm is robust to reconstructed parameters,noise and data length,and it is easy to be programmed as well,which make exponents computed of chaos online possible.