Study On Chaotic Time Series And Application In Runoff Forecast

Since chaotic systems are frequently encountered in various fields, research on chaotic systems thus has great practical significance. Deterministic chaos with some special characters brings two effects on its research, one is that the character of positive Lyapunov exponents is intrinsically associated with a loss of long term predictability, the other is that some good characters of chaotic behaviors provide creative opportunities for conventional science and are helpful to scientific studies in other fields.Chaos theory's application in hydrology and water resources system is studied in this paper. The paper consists of three parts: the chaotic characteristics of hydrological time series, the weight-dynamic local prediction model for hydrological time series and the local intervals method for hydrological time series. The major contents and research results are as follows:In the first part, the chaotic characteristics of hydrological time series from TengLongQiao and LanXi hydrological stations are researched. First, the theory and method of phase space reconstruction are studied as the basis of chaotic diagnosis and analysis. Emphasis is given on the chaotic characteristics, i.e., fractal dimension and maximal Lyapuonv exponent, and state space parameters, including time delay and reconstruct dimension, were calculated respectively. Fractal dimension was estimated by G-P saturation correlation dimension method, and maximal Lyapuonv exponent was calculated by two methods, namely, Rosenstein method. Time delay was chosen by using autocorrelation function method and mutual information method, while reconstruct dimension was obtained by G-P saturation correlation dimension method and false nearest neighbor percentage method. Then on the basis of phase space reconstruction, the paper applies many methods to chaotic diagnosis. Emphasis is given on the surrogates data method, which is firstly applied to chaotic hydrological time series. The results show there is more or less chaos in these hydrological time series.In the second part, the weight-dynamic local prediction model(NNWGDF) is studied in terms of the chaotic characteristics of hydrological evolution process, which introduces the neighbor's weight based on the dynamic local prediction model(NSCGDF) of the paper [45]. The NNWGDF model considers the neighbors' weight and generalized degrees of freedom, and the deciding condition of the optimal neighborhood is proposed. The NNWGDF model can determine the reasonable neighborhood in the each step prediction.In the third part, Based on conventional methods of local predicting chaotic time series, local intervals method is proposed. Here a new concept, interval neighboring points, is defined for building up a data list. The list for finding neighboring points is gradually established in the procedure of forecasting future values. It is convenient that all neighboring points are obtained from the list, instead of searching in history data. Also the method can continually update the list and supply new types of neighboring points for the list.In the end, the research works are summarized. And some further research directions are highlighted.