Chaotic Time Series Procession And Application

As a common natural phenomenon, chaos phenomenon is manifested by a nonlinear dynamical system determined by the complex behavior of an irregular movement. With the development of chaos theory, nonlinear time series analysis has been a hot research topic in the field of signal procession. It is widely encountered in various fields ranging from physics and mathematics to biology and others.The traditional timing diagrams and power spectrum analysis method can not determine whether the signal is chaos or randomness. Phase space reconstruction from a scale time series is the foundation of chaotic time series analysis. Embedding dimension and time delay parameters are important parameters of the phase space reconstruction. With the development of chaotic theory, nonlinear time series forecasting has been widely applied in many areas. There are many methods about modeling of nonlinear time series forecasting, mainly including the global and local method.In this paper, a new method based on binary particle swarm optimization algorithm is proposed to predict the chaotic time series. The improved algorithm searches for the optimal parameter values by minimizing the standard error of prediction based on binary particle swarm optimization to improve the prediction performance. In addition, the number of neighboring point is also one of the important parameters of the local prediction method, which determines the local prediction accuracy and computation amount. If the number of neighboring points is too many, it will increase not only the amount of calculation but also the number of false adjacent points, which has a great influence in predicting performance. Or if the number of neighboring points is too few options, the full information is not taken into account, which also has great influence in predicting performance. The number of adjacent points is usually the sum of embedding dimension plus one. In the improved local prediction model the number of neighboring points is increased in order to reduce the weight of the pseudo adjacent point, and is applied to analyze typical nonlinear time series.There are many training models for modeling of chaotic time series. Least Squares Support Vector Machine (LS-SVM) theory is a new classification and regression tool based on statistical learning theory, which has strong the generalization ability. The selection of the kernel function parameters has very important impact on the generalization ability. In this paper, particle swarm optimization is applied to search for the optimal parameters to minimize the prediction error. Simulation results proved high prediction accuracy and less computation of this method.This paper also proposed a multi-model fusion method. By fusing variety of chaotic time series prediction model with adaptive weighted fusion algorithm, the fusion data is much closer to the real value.The basic characteristic of chaotic systems is sensitivity to the initial value and immune to noise, which determines that weak signal can be detected by a chaotic system. The principle of Duffing system detecting the weak signal is described particularly in this paper, then the method about the amplitude and frequency of weak sinusoidal signals detection is discussed in detail in this paper. But single Duffing oscillator is sensitive to the signal whose frequency is in a very small range of the reference frequency, therefore it can not work when there are mutiple weak sine signal get involved. In this paper the Duffing oscillator arrays is introduced to resolve the problem and the results proved validity.