Feature analysis in frequency domain of Duffing system based on general local frequency

Tang, Youfu; Liu, Shulin; Lei, Na; Ruihong, Jiang; Liu, Yinghui

doi:10.7498/aps.61.170504

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…In the case of nonlinearity detection, some typical characteristics including Lyapunov exponents, correla-tion dimension, entropy, and complexity have been proposed and well applied. [9] Among them, the Lempel-Ziv complexity (LZC) has been extensively used to calculate the information content for time series analysis involving nonlinear dynamics, such as coding, data compression, and the generation of test signals. [10] The LZC is much better than the traditional spectral analysis and the time-frequency analysis, and can be used to detect the long-range correlations embedded in a nonstationary time series.…”

Section: Introductionmentioning

confidence: 99%

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

et al. 2013

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We study the correlation between detrended fluctuation analysis (DFA) and the Lempel-Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamic systems including a logistic map and a Duffing model are investigated. Moreover, the influence of Gaussian random noise on both the DFA and LZC are analyzed. The results show a high correlation between the DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent a and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.

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Section: Introductionmentioning

confidence: 99%

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

et al. 2013

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Chaos Phase Space Reconstruction Based on Symbolic Analysis and Multi-Component Conditional Entropy

Zhang

Jiang

et al. 2015

2015 International Conference on Computational Intelligence and Communication Networks (CICN)

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Denoising of contaminated chaotic signals based on collaborative filtering

Chen¹,

Liu²,

Wu³

et al. 2017

Acta Phys. Sin.

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Reconstructing chaotic signals from noised data plays a critical role in many areas of science and engineering. However, the inherent features, such as aperiodic property, wide band spectrum, and extreme sensitivity to initial values, present a big challenge of reducing the noises in the contaminated chaotic signals. To address the above issues, a novel noise reduction algorithm based on the collaborative filtering is investigated in this paper. By exploiting the fractal self-similarity nature of chaotic attractors, the contaminated chaotic signals are reconstructed subsequently in three steps, i.e., grouping, collaborative filtering, and signal reconstruction. Firstly, the fragments of the noised signal are collected and sorted into different groups by mutual similarity. Secondly, each group is tackled with a hard threshold in the two-dimensional (2D) transforming domain to attenuate the noise. Lastly, an inverse transformation is adopted to estimate the noise-free fragments. As the fragments within a group are closely correlated due to their mutual similarity, the 2D transform of the group should be sparser than the one-dimensional transform of the original signal in the first step, leading to much more effective noise attenuation. The fragments collected in the grouping step may overlap each other, meaning that a signal point could be included in more than one fragment and have different collaborative filtering results. Therefore, the noise-free signal is reconstructed by averaging these collaborative filtering results point by point. The parameters of the proposed algorithm are discussed and a set of recommended parameters is given. In the simulation, the chaotic signal is generated by the Lorenz system and contaminated by addictive white Gaussian noise. The signal-to-noise ratio and the root mean square error are introduced to measure the noise reduction performance. As shown in the simulation results, the proposed algorithm has advantages over the existing chaotic signal denoising methods, such as local curve fitting, wavelet thresholding, and empirical mode decomposition iterative interval thresholding methods, in the reconstruction accuracy, improvement of the signal-to-noise ratio, and recovering quality of the phase portraits.

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Feature analysis in frequency domain of Duffing system based on general local frequency

Cited by 3 publications

References 20 publications

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

Chaos Phase Space Reconstruction Based on Symbolic Analysis and Multi-Component Conditional Entropy

Denoising of contaminated chaotic signals based on collaborative filtering

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