Abstract
Nonlinear time series denoising is the prerequisite for extracting effective information from observation sequence. An effective chaotic signal denoising method not only has a good signal-to-noise ratio (SNR) enhancement performance, but also can remain as a good unpredictable denoised signal. However, the inherent characteristics of chaos, such as extreme sensitivity to initial values and broadband spectrum, pose challenges for noise reduction of polluted chaotic signals. To address these issues, an adaptive smoothing multiscale morphological filtering (ASMMF) is proposed to reconstruct chaotic signals. In the process of noise reduction for contaminated chaotic signals, firstly, a multiscale morphological filter is constructed adaptively according to the multiscale permutation entropy (MPE) of morphological filter residuals, and the contaminated signals are filtered. Secondly, the weight coefficients of scale structural element are calculated by the residual sum of squares operation, and the chaotic signals are reconstructed. Finally, the resampled filter signals are smoothed by cubic B-spline interpolation operation. In the experiment, the Lorenz signal with white Gaussian noise, the measured sunspot, and the chaotic vibration signal are reconstructed by four comparison methods. The test results show that the proposed ASMMF method has obvious advantages in noise suppression and topological trajectory restoration.
Highlights
Chaos is a seemingly random irregular motion that occurs in a deterministic system [1]
In order to verify the effectiveness of proposed adaptive smoothing multiscale morphological filtering (ASMMF) for different chaotic signals, the existing empirical mode decomposition (EMD)-CIT [9], wavelet threshold (WT) [3], and AMMF methods are applied for comparison, and the noise suppression results of the Lorenz signals with different intensities of Gaussian white noises, the sunspot chaotic signals, and chaotic vibration signals are, respectively, shown
We have proposed an adaptive smoothing morphological filtering method for denoising contaminated chaotic signals. is algorithm solves the problem of top-weakening distortion in morphological filtering and can filter the signal in multilevel and multiscale adaptively
Summary
Chaos is a seemingly random irregular motion that occurs in a deterministic system [1]. Wang et al [13] further improved the cooperative filtering denoising method; the complexity of chaotic signals is analyzed and the optimal filtering parameters are adaptively selected according to the smallest permutation entropy (PE) [14]. Combined with the self-similar characteristics of chaotic signals, an adaptive smooth multiscale morphological filtering (ASMMF) method for chaotic signal denoising is proposed on the basis of existing algorithms. Within this scheme, the scale range of structural element is determined in accordance with the self-similarity of temporal waveform of chaotic signal.
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