Study Of Noise Reduction On Chaotic Nonlinear Time Series And Its Application

Over the last couple of decades, chaos is widely found in the fields of communications, electronics, medicine, meteorology, hydrology, information science, physics and other natural sciences. Chaos is a seemingly random and irregular movement happening in a deterministic system. The chaotic signal is characterized by pseudorandom, wideband in the time-frequency domain and sensitive dependence on initial conditions. It has rich dynamics and extensively exists in non-linear dynamical systems. However, noise is always problematic in a practical situation. The presence of noise can greatly affect the analysis of the observed data from chaotic systems. For example, noise may obscure or even destroy the fractal structure of chaotic attractor, and noise may mislead the calculation of correlation dimension and Lyapunov exponents. Therefore, distinguishing chaos and noise accurately and improving signal to noise ratio of systems have been widely concerned as an important aspect in the research of chaos phenomenon.Based on recognition techniques of chaotic characteristic and noise, this paper has devoted to the research of noise reduction of chaotic non-linear time series and its application. The new based-chaos and based-wavelet denoising methods are proposed and applied to the proposed new chaotic secure communication scheme. The research in this paper involves the study of physics, information science, artificial intelligence, and mathematics and belongs in the cross research field. It mainly includes the following several parts:1) Based on chaotic theory of phase space reconstruction, a novel noise reduction method is presented. In the proposed approach, the attractor set is reconstructed by embedding the time domain signal onto a d-dimensional space through the method of delay reconstruction. Based on the reconstructed phase space, a matching pursuit (MP) approach is used to decompose the signal into linear expansion of waveforms to best match the signal structures. In order to show the validity of the approach in noise reduction, the chaotic signals generated by Lorenz model and the practical time series data obtained from chaos correlation optical time domain locator are used for performance analysis. Experimental results show the mean value of correlation peak-sidelobe level is decreased by9.5394.2) By combining discrete undecimated wavelet transform (UWT) with genetic algorithm (GA) an efficient enhancement algorithm for chaotic time series is proposed. The algorithm suppresses noise and extrudes dynamics for chaotic time series by the nonlinear gain operation with GA in UWT domain. GA is used to obtain the asymptotic optimal denoising threshold in the UWT domain without the accurate statistic properties of noise known in advance. The optimal nonlinear gain parameters can adaptively be also obtained by GA in the UWT domain. An efficient objective assessment measure, which combines information entropy, contrast measure, and signal to noise ratio (SNR), is proposed to assess the visual quality of enhanced chaotic time series. The proposed algorithm can efficiently suppress the additive gauss white noise (GWN) for chaotic time series while extruding the dynamics of chaos.3) Based on an improved center-based genetic algorithm (CBGA) in lifting wavelet framework, a new chaotic noise reduction approach is proposed to solve the problem of various kinds of noise source separation characterized by wide band power spectra when one of the sources is chaotic. This method intelligently adapts itself to various types of noise, and it weighs the preservation of dynamics and denoising through SNR and root mean square error (RMSE). This new method utilizes second-generation wavelets which can allow a faster implementation of wavelet transforms and provide a great deal of flexibility in the construction of biorthogonal wavelets compared with the classical wavelets. Computer simulations show that the approach is very effective in diminishing different kinds of noise, and performs better in terms of visual quality as well as quantitative metrics than existing algorithms.4) Gravitation Search Algorithm (GSA) has higher performance than GS in the selection of global optimization. By introducing a chaotic operation factor this paper puts forward to an improved gravitation search algorithm (IGSA) which reduces the premature convergence and the selection of local optimization in standard gravitational search algorithm. The IGSA is tested on the nonlinear filter modeling and compared with GSA and particle swarm optimization (PSO). The results confirm the high performance of the proposed IGSA in parameter estimation of nonlinear filter modeling.5) A chaotic secure communication scheme is proposed based on IGSA which minimizes premature convergence of GSA. The new secure chaotic communication scheme consists of an encoder, a chaotic filter, a chaotic receiver, and a decoder. In this scheme, an IGSA-based filter is applied to the proposed communication scheme to reduce channel noise. Computer simulations with the unified chaotic map are done to verify the feasibility of the proposed secure communication scheme. The results show that the proposed new scheme accurately estimates the states and information symbols, and provides a lower bit error rate (BER) than existing secure communication schemes.