First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method

Han, Qun; Xu, Wei; Yue, Xiaole; Zhang, Ying

doi:10.1016/j.cnsns.2014.11.009

Cited by 28 publications

(3 citation statements)

References 32 publications

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“…Generally, the analytical methods solve the FPK equation of the systems by various means, then the steady-state PDFs of the systems can be obtained [30,31]. However, for the stochastic non-smooth impact systems under harmonic excitation, the FPK equations are non-homogeneous, and it is difficult to solve the stationary FPK response of the systems [32]. Specially, as an efficient numerical method, the generalized cell mapping (GCM) method has been applied in stochastic smooth systems [33][34][35].…”

Section: The Non-smooth R-d Oscillator and The Response Calculation M...mentioning

confidence: 99%

P-bifurcation phenomena of the non-smooth modified rayleigh-duffing oscillator under the combined action of harmonic excitation and noise perturbation

Ma¹,

Wang

Zhang³

et al. 2023

Phys. Scr.

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In this paper, the stochastic dynamics of a modified Rayleigh-Duffing oscillator with Coulomb frictional damping and elastic impact is investigated under combined harmonic and noise excitations. On the premise of retaining the non-smooth properties, a non-smooth steady-state probability density response numerical calculation method is introduced by taking advantage of Markov process. Utilizing this method, the stochastic P-bifurcation phenomena of oscillators without and with externally excitation are discussed in detail by inscribing changes in the topology of the steady-state probability density function. It is displayed that certain nonlinear damping coefficient and external excitation amplitude change the structure of the response, and that both the friction coefficient and the elastic coefficient of the contact surface induce stochastic P-bifurcation phenomena in systems without and with harmonic excitation, respectively. This study reveals the effect of non-smooth factors on the stability of the Rayleigh-Duffing oscillator.

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Section: The Non-smooth R-d Oscillator and The Response Calculation M...mentioning

confidence: 99%

P-bifurcation phenomena of the non-smooth modified rayleigh-duffing oscillator under the combined action of harmonic excitation and noise perturbation

Ma¹,

Wang

Zhang³

et al. 2023

Phys. Scr.

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“…One of the most common models for non-Gaussian random loadings is Poisson white noise. Responses of smooth systems subjected to Poisson white noise have been intensively investigated by using equivalent linearization [29,30], cell mapping and path integration [31,32], moment equations [33], stochastic averaging method [34][35][36], etc. For vibroimpact systems with elastic impacts under Poisson white noise, analytical study is relatively little [37], let alone that with inelastic impacts for inherent difficulties due to additional finite relations at the impact instants.…”

Section: Introductionmentioning

confidence: 99%

Random vibrations of Rayleigh vibroimpact oscillator under Parametric Poisson white noise

Yang

Jia

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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“…Despite the enormous interest, the first-passage problem is still a challenging problem in stochastic theory, and analytical solutions are limited even for one-dimensional case. Many useful methods, such as Monte Carlo (MC) simulation, finite element method (Bergman and Heinrich, 1982), generalized cell mapping method (Han et al, 2015; Sun and Hsu, 1990), and other methods (Xu et al, 2017), have been developed so far for solving the first-passage problem. However, for a multi-degree-of-freedom system, the associated backward Kolmogorov equation (BKE), which normally governs the reliability function of a random system, is often a high-dimensional partial differential equation which is usually very difficult to be solved.…”

Section: Introductionmentioning

confidence: 99%

Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators

Sun

Lei

Ying

et al. 2021

Journal of Vibration and Control

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A closed-loop controlled system usually consists of the main structure, sensors, and actuators. The dynamics of sensors and actuators may influence the motion of the main structure. This article presents an analytical study on the first-passage reliability of a nonlinear stochastic controlled system under the consideration of the dynamics of sensors and actuators. The coupled dynamic equations of the controlled systems with sensors and actuators are first given, which are further integrated into a controlled, randomly excited, dissipated Hamiltonian system. By applying the stochastic averaging method for quasi-Hamiltonian systems, a one-dimensional averaged differential equation for the Hamiltonian function is obtained. The backward Kolmogorov equation associated with the averaged equation is then derived for the first-passage reliability analysis, from which the approximate reliability function and probability density of first-passage time are obtained. The accuracy of the proposed procedure is demonstrated by an example. A comparative analysis of the reliability of the system with/without sensors and actuators is carried out, which indicates that ignoring sensors and actuators will make underestimation of the reliability of the closed-loop system with small time. However, when time increases, there appears the opposite trend. Our findings provide a reference for control strategy design.

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First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method

Cited by 28 publications

References 32 publications

P-bifurcation phenomena of the non-smooth modified rayleigh-duffing oscillator under the combined action of harmonic excitation and noise perturbation

P-bifurcation phenomena of the non-smooth modified rayleigh-duffing oscillator under the combined action of harmonic excitation and noise perturbation

Random vibrations of Rayleigh vibroimpact oscillator under Parametric Poisson white noise

Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators

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