Research On Prediction And Improved Methods Of Chaotic Time Series

Chaos is a phenomenon widely existing in the nature. Chaotic dynamics system is essentially a kind of classical high-dimension complex non-linear dynamics system. Chaotic system is a deterministic system in itself, while, there is some randomization in internal system, and its internal randomization makes it extremely sensitive to the initial value, which finally leads to the action of the chaotic system ruleless and similarly stochastic phenomenon. This similarly stochastic chaos action is not formed by outside stochastic factor, nor acted by outside environment noises, but formed by the internal non-linear structure of the chaotic system. The variables which describe the changes of the chaotic system with the change of the time are called chaotic time series. In the real measurement, all chaotic time series values cannot be found, it is a long-time problem focused by the researchers who major in time series analysis how to utilize finite chaotic time series measurement value to form the dynamics characteristic of chaotic system of that series. The sensitiveness of the chaos for the initial value makes chaos widely applied in secret communication field, but there are still huge threats to the safety of the chaos secret communication system, formed by the short-time predictable property of the chaotic series, the degeneration phenomenon with the realizing chaotic system made by computer, short-period phenomenon and so on. Based on these situations, this thesis researches the prediction of the chaotic time series first, and then improves the chaotic series in the secret communication. The main research contents are as following:(1) In recent years, the methods, such as the radial neural network, Gauss process, recursive neural network, and support vector regression, are widely applied. But for the same method, the different parameter setting or different time series sampling makes a big difference of the prediction accuracy. How to improve the generalization ability of the prediction system is a difficulty of the research field. To this problem, this thesis will integrate adalines of different rules, learn the unknown sample by structuring the basic classifiers different among each other and the learning machine of adaptive dynamic selective basis, and then by combining the least square support vector machine, present a prediction method dynamically selecting integrated chaotic time series based on the least square support vector machine, which improves the prediction accuracy of the chaotic time series.(2) Support vector regression (SVR) algorithm is widely applied in prediction field of the chaotic time series because of its good model sparseness, but currently, the research on SVR algorithm mainly focuses on the modeling the single kernel function and the parameter optimization. However, in the real application, since the regularity implicated in all kinds of data is complex, it is difficult to use one single kernel function to act the regularity which changes sometimes steep, sometimes mild. In addition, since in real application, only finite real data can be obtained usually, so in the situation of less real data, it is difficult to precisely establish model with complex changing discipline by using the single support vector regression. In view of these situations, the thesis presents an algorithm of structuring polykaryon support vector regression by using the linear weighting of many kernel functions to form one mixed kernel function, and optimizes the parameters by the method of multiple-dimensioned escaping particle swarm optimizing united parameters. The experiment result shows that this method improves the chaos prediction accuracy and has good generalization ability.(3) With the wide application of the chaos theory in secret communication field, some researchers query the safety of the chaos secret communication, and the short-time predictable property, the degeneration and the short-time phenomenon of the chaos bring many indeterminate factors to the safety of chaos secret communication. Based on this situation, this thesis presents the dual K-L Transform method. This method can be experimented easily, calculate fast and improve the period and the complexity of the chaotic key series. The experiment verifies the effectiveness of this method and shows that it can be applied to the chaos secret communication system.