Research On Time Series Prediction Technology Based On Nonlinear Dynamic System

Nonlinear dynamical system isa complex behavior which is produced by thedetermined dynamical systems.For a nonlinear dynamical system with known structure,a nonlinear dynamical system model can be established according to the dynamic characteristics.Most of the nonlinear dynamic systems are difficult to have an accurate mathematical model.However,based on the observed time series values,a nonlinear dynamical system model can be given approximately.The main contents of this paper are as follows.First,the stability and period-doubling bifurcation and chaos characteristics of nonlinear dynamical systems are studied.The focus of the study is the phase space reconstruction theory.The mutual information method and saturation correlation dimension method are used to get the parameters of phase space reconstruction respectively.The theory of phase space reconstruction is the foundation of thenonlinear prediction model.For the nonlinear dynamical system with known structure,the nonlinear dynamic system model is established according to the characteristics of the dynamic system.For the nonlinear dynamical system model which has the solved analytic equation,the particle swarm method is proposed to solve the model parameters.The simulation results show that the method has high precision.For the nonlinear dynamic system model which is difficult to solve,the Newmark and Wilson method used to solve the transient analysis of the nonlinear dynamic system model.The simulation results show that the method has high accuracy when the integration step is very small.For the nonlinear dynamical systems with unknown structure,the adaptive prediction model and local prediction model are studied.Volterra adaptive prediction model is established in the phase space.To improve the prediction accuracy of the model,the group intelligentgenetic algorithmis used in this paper.The best model parameters are are solved by cross,mutation and selection in this algorithm.Simulation results show that the proposed method can improve the study ability and it has faster convergence speed and higher prediction accuracy.A local linear prediction model based on particle filter optimization is established in the phase space.In the local linear prediction model,the neighboring points are selected based on euclidean distance and correlation coefficient.The model is established on the basis of the neighboring points.And the model parameters are optimized by the particle filter method.The simulation results show that the improved method has higher prediction accuracy than other models.