Weak signal detection based on Mathieu-Duffing oscillator with time-delay feedback and multiplicative noise

Wang, Qiubao; Yang, Yuejuan; Zhang, Xing

doi:10.1016/j.chaos.2020.109832

Cited by 35 publications

(15 citation statements)

References 27 publications

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“…When

, let

(

) be the root of the equation

. Through the work [32] , we can obtain that

satisfies the following equation:

where

. Set

, then

…”

Section: The Analysis Of the Modelmentioning

confidence: 99%

“…Next, we use the stochastic center manifold theorem to reduce the delay differential equation (3) to an ordinary equation [32] , [34] . we should notice that

and

, the space

is spanned by the two-dimensional subspace

, which is driven by the eigenvalues

of the equation

at Hopf bifurcation, plus the infinite-dimensional subspace

associated with all the other eigenvalues of

, namely

.…”

Section: The Reduction and Stochastic Stability And Bifurcation Of Th...mentioning

confidence: 99%

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There exists the “smartest” movement rate to control the epidemic rather than “city lockdown”

Wang

2022

Applied Mathematical Modelling

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“…When

, let

(

) be the root of the equation

. Through the work [32] , we can obtain that

satisfies the following equation:

where

. Set

, then

…”

Section: The Analysis Of the Modelmentioning

confidence: 99%

“…Next, we use the stochastic center manifold theorem to reduce the delay differential equation (3) to an ordinary equation [32] , [34] . we should notice that

and

, the space

is spanned by the two-dimensional subspace

, which is driven by the eigenvalues

of the equation

at Hopf bifurcation, plus the infinite-dimensional subspace

associated with all the other eigenvalues of

, namely

.…”

Section: The Reduction and Stochastic Stability And Bifurcation Of Th...mentioning

confidence: 99%

There exists the “smartest” movement rate to control the epidemic rather than “city lockdown”

Wang

2022

Applied Mathematical Modelling

Self Cite

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“…For signal detection using the dynamical behaviours transfer, these papers [9][10][11] make a preliminary discussion with duffing oscillator. This paper is based on the methods of TVICM and TV that proposed by us [12,13] Furthermore, we obtain a whole set of procedures for signal detection and feature extraction.…”

Section: Introductionmentioning

confidence: 99%

The effect of fractional damping and time-delayed feedback on the stochastic resonance of asymmetric SD oscillator

Wang

Yang

2022

Nonlinear Dyn

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This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillators under time-delay feedback control with a fractional damping. With the effect of displacement and velocity feedback, the oscillator can be adjusted to the desired vibration state and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delay feedback to SR, especially which induced by fractional damping. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.

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“…There are many research results on the identification of these parameters. At present, weak signal identification systems adopt continuous systems, such as Duffing system [1][2][3], the variable scale Duffing system [4,5], the Vanderpol-Duffing system [6], the dual coupling Duffing system [7], L-Y system [8][9][10], the time-delay Mathieu-Duffing system [11], Lorenz system [12], etc. But there are many shortcomings: (1) The calculation process of the Melnikov function of the continuous system is more complicated; (2) The calculation of the chaotic threshold often adopts necessary conditions, and the result is not accurate enough.…”

Section: Introductionmentioning

confidence: 99%

Frequency and Amplitude Identification of Weak Signal Based on the Limit System of Smooth and Discontinuous Oscillator

Tian

Zhang

et al. 2022

J Nonlinear Math Phys

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In this paper, a new method is proposed to identify the frequency and amplitude of weak signals by using a non-smooth system. The variable scale limit system of smooth and discontinuous (SD) oscillator without considering the phase is adopted as the identification system. By using the non-smooth stochastic subharmonic-like Melnikov method, an analytical expression of chaotic threshold under Gaussian white noise is given. Based on the phase diagram and Poincaré section diagram, the influence of noise intensity on the recognition system is studied. According to the non-smooth variable scale-convex-peak frequency identification method, the frequency of the signal to be detected can be accurately identified. Using the numerical simulation, the amplitude of the signal to be measured is identified according to the amplitude bifurcation diagram of the reference signal. The optimal value range of the parameters of the identification system is determined. Through an example of early fault of wheelset bearing of high-speed train, the frequency and amplitude of the early weak fault signal can be identified and the fault location can be determined, which verifies the effectiveness of the above method. The results show that the non-smooth system can identify the frequency and amplitude of the weak signal submerged in strong noise, and it has a wider application and higher accuracy than the continuous system.

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Weak signal detection based on Mathieu-Duffing oscillator with time-delay feedback and multiplicative noise

Cited by 35 publications

References 27 publications

There exists the “smartest” movement rate to control the epidemic rather than “city lockdown”

There exists the “smartest” movement rate to control the epidemic rather than “city lockdown”

The effect of fractional damping and time-delayed feedback on the stochastic resonance of asymmetric SD oscillator

Frequency and Amplitude Identification of Weak Signal Based on the Limit System of Smooth and Discontinuous Oscillator

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