Research On Prediction Of Chaotic Time Series Using Neural Networks

In the nonlinear signal processing field, study based on chaos and Neural Networks(NNs) is a new emerging subject.Chaos is a kind of special motion form of the nonlinear dynamical systems, it is universal and have extremely complexities.Neural Networks have some special nonlinear feature such as associative memory, and it is quite fit for processing complex nonlinear system with high difficulty. So the way to solve Chaos time series based on the NNs is an effective method, and it enlarges the area for prediction study.In recent years, with neural networks theory is experiencing steady progress, prediction methods based on neural networks is offering. In this paper, chaotic time-series is predicted with neural networks methods, based on neural networks theory and phase-space reconstruc-tion theory. Comparison of integrated research has focused on the BP networks algorithm and improved BP networks algorithm, RBF networks algorithm, as well as Adaptive Neural Fuzzy Inference System(ANFIS).As a new information processing subject, it has much advantages. By nature, it is a massively parallel processing adaptive nonlinear system, with strong self-study ability, nonlinear regression, good associative memory ability, comparison ability, and good generalization. ANFISis a special NNs characterized in fast convergence rate, small error and few train data Is needed. It is a production of NNs combined with fuzzy inference system. In comparison with traditional method, it complements the both methods, giving a better prediction than a single NNs giving.In comparison with traditional prediction method, neural networks algorithm not only achieve global prediction, but also can implement local prediction. It is characterized in modeling the chaotic time-series by observing the historical data. And the modeled neural networks model can learn in line at the same time. Thanks to the neural networks modeling is flexible,one can construct the chaotic time-series direct model, that is a direct prediction relation can be made to origin and prediction of time-domain prediction. Besides, one can implement multi-step-prediction through iteration of one step predictor.The main research results of this paper are as follows:(1) Study on BP neural networks algorithm and five improved BP neural networks algorithm, as well as RBF neural networks algorithm.Besides, Fuzzy neural network has resulted based on fuzzy inference and neural network, study focus on ANFIS.(2) In order to verify effectiveness of the algorithm,one use Mackey-Glass chaotic time series, Lorenz chaotic time series, and other three chaotic time series to study the performance of standard BP networks algorithm model. Using BP neural networks model, RBF neural networks model and ANFIS model to simulate five chaotic time series, comparison study on all kinds of algorithm, simulation shows the result is very good. All of the algorithms modeled in this dissertation have good prediction ability. Moreover,.by comparison,ANFIS shows the better prediction performance than other single neural network.