Research Of Nonlinear Noise Reduction Methods For Chaotic Time Series Including Noises

It is inevitable that the observed time series are contaminated by noises for all the nonlinear dynamical systems. The universal existence and destructiveness of noise conceals the internal dynamics properties, and influences the parameters calculation and prediction of univariate or multivariate time series. Therefore, it is necessary for us to study noise reduction methods for chaotic time series.For reflecting features of chaotic systems, including certainty, nonlinear and sensitivity of the initial state, this paper explores noise reduction methods on different backgrounds for own rules of chaotic signals and effects of noises. For chaotic time series with unknown dynamics characters and models, an improved method is proposed with introduction of nonlinear constraint conditions to the local projection method, and singular spectrum analysis is combined in the local neighborhood, which uses the main components representing the attractors to reconstruct the time series. The improved method overcomes problems that the traditional local projection can not fully character the nonlinear relationship of system. For chaotic time series with no knowledge of characters and enough length information, an improved dual-wavelet spatial correlation method is proposed for noise reduction. The expansion of discrete wavelet transform from using one wavelet to using two strengthens local characteristics of signals. For different features between signal and noise in different scales, an improved wavelet modulus maximum method is proposed. The approximate parts are handled by singular spectrum analysis, and the spatial scales relevancy is used for wavelet coefficients after modulus maximum analysis in different scales in order to reserve useful signals mixed in noises. For the choice problem of wavelet coefficients, an adaptive noise reduction method is proposed combining with self-learning of nonlinear threshold in neural network. This method solves the problem that the threshold function of the soft-threshold wavelet has a constant deviation in application and that of the hard-threshold wavelet is not continuous, and reduces the root mean square error of chaotic system.This paper considers the chaotic time series generated by Lorenz model and sunspot time series as research objects which are applied to simulation analysis, the experimental results show that the performances of the proposed methods are all effective for chaotic time series.