Automated system for weak periodic signal detection based on Duffing oscillator

Abstract

The periodic signals that have predictable and deterministic characteristics are used in the analysis and modelling of dynamical systems in diverse fields. These signals can be detected as the weak signals within the time series obtained from the measurable processes of dynamical systems. The Duffing oscillator is effective in detecting weak periodic signals with a very low signal‐to‐noise ratio. In this study, the authors present a method to automate the weak periodic signal detection of the Duffing oscillator using a quantitative index for the classification of the periodic and non‐periodic signals. In this method, the authors use the wavelet scale index as the quantitative index in the classification of signals. Thus, they are able to plot the wavelet scale index spectrum of the Duffing oscillator where the frequency values of the weak periodic signals correspond to near‐zero wavelet scale index parameters. First, the authors perform simulations using the method and detect weak periodic signals embedded in noise. Then, they employ two electroencephalogram signals to demonstrate the feasibility of the proposed method in the empirical data. Lastly, they compare the method to the periodogram power spectral density estimate based on fast Fourier transform.

Windowed scalogram entropy: wavelet-based tool to analyze the temporal change of entropy of a time series

“…Using the windowed scalogram of a time series (17), the windowed scale index [23] determines the wavelet scale index parameter [19,[24][25][26][27] changing over the course of a time series to provide temporal insight to the analyzed signal. For a time series f centered at time t with time radius the windowed scale index in the interval [ ] is given as [23] (…”

An improved method of weak signal erasometry based on Duffing oscillator

“…At present, for weak signal detection, conventional methods generally divide time domain processing and frequency domain processing [1] . Although the time-domain method has certain detection and processing capabilities for weak signals, it generally has low input signal-to-noise ratio and high computational intensity [2] [3] . Frequency domain analysis method has a high frequency resolution, but it will produce leakage effect when detecting non-stationary signals [4] .…”

Automated weak signal frequency estimation method based on Duffing oscillator and particle swarm optimization

“…Li et al [26] utilized the weighted-permutation entropy (WPE) method to distinguish the chaotic state and the large-scale periodic state and combined it with the complete ensemble empirical mode decomposition (CEEMD) method to estimate the frequencies of a complex weak underwater acoustic signal. Akilli et al [4,27] used the wavelet scale index to determine the phase state of the Duffing oscillator and applied it to the characteristic extraction of EEG signals from epileptic patients. Yang et al [28] proposed a Duffing phase state identification method based on the Kalman gain.…”