The Study Of Noise Smoothing Methods On Chaotic Time Series

It is inevitable for the measured time series of all the nonlinear dynamical systems to be contaminated by noise. The presence of noise has broken the internal chaotic dynamics of these systems and influenced the prediction of univariate or multivariate series of chaotic time series. Therefore, it is necessary for us to study the noise smoothing methods of chaotic time series effectively.Studying on the observed chaotic time series such as annual runoff data of Yellow River, sunspots numbers and rainfall of Dalian coming from the nonlinear dynamic systems of hydrology, chronometer and weather, this paper explores the noise smoothing methods of chaotic time series on different backgrounds and objects. For the shorter length time series with no knowledge of chaotic characters, an improved wavelet transform method is proposed. This method decomposes the wavelet signals in detail and chooses different thresholds neatly according to the signal noise ratio on different scales. Simulation results indicate this method can identify the clear chaotic attractors and improve the signal ratio noise. Meanwhile, for the observed time series without enough information, this paper gives an optimized method based on local projection noise smoothing theory. The neural network is applied to predict the noise smoothing data as a main diagnostic tool to determine the optimal noise smoothing result. This method solves the problem of choice of neighborhood and iterations in general local projection method effectively. For the influence of noise, each neighborhood has its own dynamical characters in phase space of observed noisy chaotic time series and the general local projection method is restricted on neighborhood and local noise subspace. Therefore, on the basis of the above work, an improved local projection method is presented. This method can search the neighborhood adaptively according to practical situations. What is more, non-orthogonal projective approach is used to different neighborhoods in order to control the effect of the first or the last weight. Simulation result shows that the proposed method can better correct the position of data points in phase space and approximate the real chaotic attractor trajectories more closely.