Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Early fault diagnosis of rolling bearings is of great significance in the application of mechanical equipment, which makes the extraction of weak fault signals particularly critical by stochastic resonance (SR). Compared with bistable SR, tristable SR has stronger advantages in weak signal extraction, but the classical tristable system (CTSR) was limited by output saturation, which resulted in insufficient signal amplification ability. To solve the above problems, combined with asymmetric system whose output can be improved to a higher degree, a novel piecewise unsaturated asymmetric tristable stochastic resonance (NPUATSR) system is proposed. Through numerical simulation, it is concluded that NPUATSR output amplitude varies proportionally with the amplitude of the input, which overcomes the output saturation of CTSR. Secondly, the stationary probability density and mean first passage time of particles are derived by using adiabatic approximation theory, and the variation law caused by parameters is analyzed in combination with potential function, the internal mechanism of the system is further studied. Through the output signal-to-noise ratio (SNR), it is found that the performance advantage of NPUTASR system is the most obvious, and different parameters affect the output SNR. Finally, the adaptive genetic algorithm is used to optimize the parameters, and the proposed system is applied to early fault diagnosis on different types of bearings. After comparison with different systems, the results show that NPUATSR can effectively detect the fault frequency, and has the most outstanding advantages in spectrum amplification and anti-noise performance, which proves that NPUATSR system has significant value in practical engineering application.

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“…where, A (x) = − dU(x) dt + A cos (2πf 0 t), B (x) = D. The SPD function of the NPUATSR system is written as [31]:…”

Section: The Spd and Mfpt Of Npuatsr Systemmentioning

confidence: 99%

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Zhang

Zhu

zhang

2022

Meas. Sci. Technol.

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“…In addition, under large external impacts, Wang et al investigated the phosphorus dynamics behavior and elaborated the flickering gives early warning information before the catastrophic eutrophic transition [13]. On the other hand, it is worth noting that the dynamic behaviors of nonlinear systems with time-delay and various noises have been recently investigated, which revealed significant results that the time delay can induce rich dynamic behaviors [14][15][16][17]. In the nature, the transmission of information, matter, energy of the nonlinear systems inevitably takes certain time, so it is more reasonable to investigate the time-delayed effect in some actual systems.…”

Section: Introductionmentioning

confidence: 99%

Colored Correlated Noises Induced Regime Shifts in a Time-delayed Lake Eutrophication Ecosystem

Liu¹,

Guo²,

Ding³

et al. 2022

FSD

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The catastrophic regime shifts in the lake eutrophication ecosystems may be usually caused by environmental perturbations, and the lake dynamics exhibit bistability characteristics with oligotrophic and eutrophic states. This paper is devoted to investigate the time delay effect in a time-delayed lake eutrophication ecosystem (TD-LEE), where the dynamics ecosystem is deemed to be disturbed by both multiplicative and additive noises. On the basis of small delay approximation, we derive the expression of the generalized effective potential function in the TD-LEE and discuss the impact of stochastic delay on the regime shifts between oligotrophic and eutrophic states. In the view of dynamical behaviors on the TD-LEE model, we also revealed that the combination with time delay and colored correlated noises can expedite the regime shift from the eutrophication to oligotrophication, thereby inhibiting the development of lake eutrophication and protecting the stability of lake ecosystem.

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“…Time delay is an important factor affecting the dynamical behavior of the systems, and even makes the system unstable. Therefore, the dynamical behavior of time-delayed systems has attracted considerable attention in various fields [26][27][28][29][30]. Time-delayed chaotic systems have more complex and abundant dynamics and are more suitable for some engineering applications, such as secure communication [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Combined projective synchronization for a class of time-delayed hyperchaotic systems via active control

2019

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We investigate combined projective synchronization for a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We overcome some limitations of previous works, where only combined complete synchronization can be achieved. Based on the Lyapunov asymptotical stability theory and active control technology, the effective sufficient conditions derived to ensure the combined projective synchronization for a class of time-delayed hyperchaotic systems can be investigated. The efficiency and effectiveness of the proposed method have been verified with several numerical simulations using well-known time-delayed chaotic systems.

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Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Cited by 19 publications

References 20 publications

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Research and application of a novel piecewise unsaturated asymmetric tristable stochastic resonance system

Colored Correlated Noises Induced Regime Shifts in a Time-delayed Lake Eutrophication Ecosystem

Combined projective synchronization for a class of time-delayed hyperchaotic systems via active control

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