Analysis Of Characteristics Of Chaotic Time Series And Research Of Phase Space Reconstruction

As known to all, non-linear phenomenon results from all kinds of motions and therefore it permeates into each branch of nature science and society science since the chaos theory was first established, even, in general cases, complex dynamical system cannot set up determinate mathematical model. The major reason for this is our ignorance for unknown dynamical systems, such as the complexity and volatility of parameters and boundary conditions of dynamical systems etc. As for a group of data collected on the spot from an unknown dynamical system, we must analyze and determine its nonlinearity of the obtained time series firstly for nonlinearity is a necessary condition of chaos. Based on nonlinearity of time series, we undoubtedly should turn to studying chaotic characteristics of the data qualitatively and quantitatively as a following step, such as correlation dimension, the largest Lyapunov exponent, Kolmogrov entropy etc. Obviously, only qualitative analysis is not enough, especially for some complex nonlinear system such as biological system, finance system etc. In view of the imperfection of qualitative analysis, phase space reconstruction presents a new approach to quantitative analysis. In fact, only by quantitative analysis can we obtain the intrinstic and fundamental properties of the nonlinear dynamical system and can we resolve those difficult problems completely such as examination or diagnosis of system signal derived from complex nonlinear dynamical system.The research work of this thesis is part of the Natural Science Foundation of Liaoning Province named "the research of the prediction methods oriented complicated industrial objects". It creates model for prediction of silicon contents under drastically changing. Especially, it researches the methods of non-stationary time series prediction problem and prediction of silicon contents under drastically changing. Firstly, the techniques of non-linearity examination, chaotic characteristic and inspection procedure are reviewed, detailed surrogate data, the recurrence plot, correlation dimension and lyapunov exponent; Secondly, in view of single variable chaotic time series, the practical techniques of phase-space reconstruction used in chaotic time series analysis are introduced. Through the experiments, Validity of False Nearest Neighbors and Mutal Information are affirmed, solved the problem of Artificial assignment of embedding dimension and time delay; At last, aimed at the complexed non-stationary time series, this thesis brings forward a new method of phase space reconstruction called EMFS:firstly, decomposing the complicated non-stationary time series, then computering m andτand creating models for components separately to get several values and combining all the values, we can get final predict result. Compared with forecasted results which before and after the decomposition and the phase space reconstruction, forecast precision of this method has the obvious superiority.