The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass

Tian, Yuan; Yu, Tao; He, Guiqin; Zhong, Linfeng; Stanley, H. Eugene

doi:10.1016/j.physa.2019.123731

Cited by 15 publications

(5 citation statements)

References 57 publications

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“…Herein, we can analyze the system stationary state response under the framework of the classical method proposed in [24,[29][30][31].…”

Section: Ffamentioning

confidence: 99%

A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

Zhang¹,

Chen²,

Wang³

2023

Meas. Sci. Technol.

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Stochastic resonance (SR) has been widely used in bearing fault diagnosis due to the enhancement principle of energy conversion from noise to weak signal. However, the diagnosis efficiency and robustness is still challenging.Under the mechanism of generalized stochastic resonance (GSR), in the paper we propose a scale-transformed linear oscillator (SLO), and obtain the analytical expression of fault feature amplification (FFA) to replace the numerical implementation of output signal-to-noise ratio (SNR) in the multi-parameter optimization.It brings the substantial benefit to the reduction of time complexity in fast fault diagnosis, which is verified in both theory and simulations.In the experimental diagnosis for some typical cases, the results show that the proposed method is valid and exhibits the superiority in diagnosis performance, efficiency, and robustness, which demonstrates that the FFA-guided GSR-SLO method has great potential in the engineering applications, especially the real-time fault diagnosis in complex operating environments.

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“…Herein, we can analyze the system stationary state response under the framework of the classical method proposed in [24,[29][30][31].…”

Section: Ffamentioning

confidence: 99%

A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

Zhang¹,

Chen²,

Wang³

2023

Meas. Sci. Technol.

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“…Herein, we can analyze the system stationary state response within the framework of the classical method proposed in [31,[37][38][39]. First, we average equation (11) with respect to the noise term η(t) to obtain…”

Section: System Stationary State Responsementioning

confidence: 99%

The adaptive bearing fault diagnosis based on generalized stochastic resonance in a scale-transformed fractional oscillator driven by unilateral attenuated impulse signal

Zhang

Chen²,

Wang³

2022

Meas. Sci. Technol.

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Bearing fault diagnosis is vital to guarantee the safety operation of rotating machines. Due to the enhancement principle of energy conversion from noise to weak signal, noise-assisted stochastic resonance (SR) methods have been widely applied. In this paper, to utilize the memory-dependent property of mechanical degradation process, we develop a scale-transformed fractional oscillator (SFO) driven by unilateral attenuated impulse signal, and reveal the active effect of generalized stochastic resonance (GSR) on the energy conversion from internal multiplicative noise to signal. By applying quantum particle swarm optimization (QPSO) algorithm in the multi-parameter regulation, we propose the adaptive GSR-SFO diagnosis method to realize the enhancement of weak fault characteristics. The experimental results demonstrate that the proposed method is valid and exhibits the superiority in diagnosis performance, especially in several typical difficult cases, such as smeared bearing fault caused by mechanical looseness, smeared bearing fault disturbed by strong random pulses, and corrupted bearing fault disturbed by patches of electrical noise.

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“…In addition, fractional models [32][33][34] are more suitable for describing memory effects and non-local behavior, and some numerical methods [35][36][37] have been proposed for solving fractional integro-differential equations. Therefore, generalized SR in time-delay fractional oscillators with random masses [38,39], random damping [40,41], and random frequencies [42] has been recently investigated through theoretical analysis and numerical calculations.…”

Section: Introductionmentioning

confidence: 99%

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

He,

Wang,

Lin

2024

Fractal Fract

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In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.

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The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass

Cited by 15 publications

References 57 publications

A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

A robust index-guided GSR approach to improve the efficiency of bearing fault diagnosis

The adaptive bearing fault diagnosis based on generalized stochastic resonance in a scale-transformed fractional oscillator driven by unilateral attenuated impulse signal

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

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