Study On Chaos Theory's Application In Runoff Forecast

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 chaotic prediction models for hydrological time series and the chaotic optimization algorithm for fuzzy optimal selection neural network. The major contents and research results are as follows:In the first part, the choatic characteristics of hydrological time series from YiChang and CunTan hydrological stations are researched. First, the theory and methods of phase space reconstruction are studied as the basis of chaotic diagnosis and analysis. Emphasis is given on the correlation integral method, which is used to calculate the embedding parameters of phase space reconstruction of hydrological dynamic system. The correlation integral method can estimate both the time delay and the embedding window, and can avoid subjectivity in calculating the embedding window. Then, on the basis of phase space reconstruction, the paper applies many methods, such as the phase portrait method, the power spectrum method, the saturated correlation dimension method and the largest Lyapunov exponent method, to analyze the choatic characteristics of many hydrological time series from YiChang and CunTan hydrological stations. The results show there is more or less chaos in these hydrological time series.In the second part, the chaotic prediction models for hydrological time series are studied in terms of the chaotic characteristics of hydrological evolution process. First, the weight-dynamic local prediction model (NNWGDF) is presented, which introduces the neighbors' weight based on the dynamic local prediction model (NSCGDF) of the paper [37]. The NNWGDF model considers the neighbors' weight and generalized degrees of freedom, and the deciding condition of the optimal neighbourhood is proposed. The NNWGDF model can determine the reasonable neighborhood in the each step prediction. Second, the radial basis function network chaotic prediction model (CIFCA-ROLS) is proposed, which introduces the Cross Iterative Fuzzy Clustering Algorithm (CIFCA) based on the Regularized Orthogonal Least Squares Algorithm (ROLS) of the paper [51]. The CIFCA-ROLS model centralizes advantages of CIFCA and ROLS, which can decrease network scale and improve generalization performance. Third, the interval prediction of chaotic hydrological time series is firstly researched in this paper. The proposed interval prediction model which breaks through the traditional point prediction, can predict the interval of the future value under different interval risk from the interval predictionview.In the third part, the prediction model of fuzzy optimal selection neural network based on chaotic optimization algorithm is studied. In general, the weights of fuzzy optimal selection neural network are calculated by gradient-descended algorithm. Therefore, there exist the problems of slow convergence speed and local optimum. Since chaos movement has the characteristics of the interior stochastic, the ergodicity and the regulation, especially the ergodicity which can be used as the optimal mechanism to avoid local optimum, the paper applies the imitative scale chaotic optimization algorithm to learn the network parameters. To verify feasibility of the chaotic optimization algorithm, the cases of Yamadu hydrological station and Biliuhe reservoir for annual runoff forecast, is analyzed and discussed by three algorithms: the chaotic optimization algorithm, the genetic algorithm and the weight-adjusted BP algorithm. The results show that chaotic optimization algorithm is an efficient learning algorithm for fuzzy optimal selection neural network.