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Research of Nonlinear Noise Reduction Methods for Chaotic Time Series Including Noises

Author: LiuYunXia
Tutor: HanMin
School: Dalian University of Technology
Course: Systems Engineering
Keywords: Chaotic time series Local Projection Wavelet Transform Spatial Correlation Modulus maxima
CLC: O415.5
Type: Master's thesis
Year: 2008
Downloads: 205
Quote: 1
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Abstract


The actual observed time series of nonlinear dynamical systems always mixed with noise, widespread and destructive noise masks the inherent dynamic characteristics of the system, greatly influenced the the chaotic characteristic parameters univariate or more variables predictive accuracy. Therefore, the actual observed chaotic time series effective noise reduction has important significance. Order to fully reflect the uncertainty of chaotic systems, non-linear characteristics as well as the sensitivity of the initial state, the study starting from the chaotic signal its own laws, based on the impact of noise on chaos, to explore a different application context of chaotic time series drop The noise problem. Unknown system dynamics model of chaotic time series, this paper proposes a Local Projection noise reduction method based on non-linear constraints. The method by nonlinear constraints introduce local projection method, and in the local neighborhood of singular spectrum analysis, on behalf of the principal component of attractor to reconstruct the time series, overcoming the traditional local projection method can not fully characterize the intra-system the problem of the nonlinear relationship. Chaotic dynamics is unknown, the length of the information is not sufficient time sequence, based the dual wavelet airspace chaotic signal noise reduction method by single wavelet transform expansion dual wavelet transform, strengthen the signal localized. Has different characteristics according to the the chaos signal and noise performance, an improved wavelet modulus maxima noise reduction method, the method combined with singular spectrum analysis and scale correlation analysis, were transformed approximate coefficients and wavelet modulus great value analysis of the detail coefficients processing to improve the positioning accuracy of the chaotic signal. Nonlinear threshold for wavelet thresholding select the combination of neural networks self-learning research of one kind of adaptive selected to enhance wavelet detail coefficients of the method, to solve the actual in soft threshold method of universal threshold value applications seem too large and the presence of The continuous constant deviation as well as the threshold function of the hard threshold method, to improve the overall performance of the system, reduce the root mean square error of the system. This study known model Lorenz chaotic system and actual monthly sunspot time series observations as the research object, through its simulation analysis confirmed that the proposed method has better noise reduction effect.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Nonlinear physics > Chaos Theory
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