基于马尔科夫链理论的改进的最大Lyapunov指数混沌预测法

Improved Maximal Lyapunov Exponent Chaotic Forecasting Method Based on Markov Chain Theory

针对很多文献都一直规避的基于最大Lyapunov指数的混沌预测会出现两个预测值的问题,引入马尔科夫链改进最大Lyapunov指数的混沌预测方法。改进的方法将时间序列的斜率作为状态变量,并根据马尔科夫链建立状态转移矩阵,判定预测值演化方向,进而根据混沌动力学系统的演化规律选择最优的预测值。最后利用渝武高速公路的交通流数据进行验证,结果表明了改进算法的可行性和有效性。

Forecasting of chaotic time series based on maximal Lyapunov exponent may bring two results,and few litera- tures have studied on it. The paper introduced Markov chain to improve it. The improved method makes the gradient of time series as state variables, builds the state transition matrix on the basis of Markov chain which will be used to verify the evolution direction of the forecasting results, and then chooses the best prediction value based on the evolution of dynamical chaotic systems. At last,the paper verified the improved forecast model using the traffic flow data of Yuwu Highway. The result shows that the improved maximal Lyapunov exponent forecasting method is valid and feasible.