Some new advance on the research of stochastic non-smooth systems

Xu, Wei; Wang, Liang; Feng, Jinqian; Qiao, Yan; Han, Ping

doi:10.1088/1674-1056/27/11/110503

Cited by 17 publications

(7 citation statements)

References 111 publications

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“…Due to the discontinuities, the systems display some distinctive features that are quite different from the smooth cases. In recent years, this interesting topic [6][7][8][9][10][11][12][13] has been paid considerable attentions. In this work, we focus on some specific systems that are modelled by stochastic differential equations (SDEs) with piecewisesmooth drifts.…”

Section: Introductionmentioning

confidence: 99%

Flux Reconstruction Schemes for Fokker-Planck Equations with Drift-Admitting Jumps

Lin

Chen

Deng

2023

J. Phys.: Conf. Ser.

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We develop in this work flux reconstruction (FR) schemes for one-dimensional Fokker-Planck equations with drift-admitting jumps, which have applications in describing the propagators of piecewise-smooth stochastic differential equations. Since the propagators are nonsmooth at the jumps of the drift, difficulties arise in finding the corresponding solutions not only theoretically but also numerically. To be more specific, the main difficulties lie in the fact that two matching conditions have to be imposed simultaneously at each jump, i.e., where the the propagator and the probability current are continuous. In this work, we show that the FR method is an ideal choice for designing numerical schemes for solving this problem. The corresponding FR schemes are given in details. Some benchmark examples are also employed to validate the proposed schemes numerically.

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Section: Introductionmentioning

confidence: 99%

Flux Reconstruction Schemes for Fokker-Planck Equations with Drift-Admitting Jumps

Lin

Chen

Deng

2023

J. Phys.: Conf. Ser.

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“…Through the study of actual mechanical engineering problems, it is found that the treatment of non-smooth systems under noise disturbance is often a big hassle [1][2][3]. Different types of mechanical systems, such as hydraulic safety valves, aircraft wings, energy harvesting, flexible manipulator with clearance, rotor-stator interactions in turbines and so on, will inevitably produce non-smooth dynamics [4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Solving Response of Stochastic Vibro-impact Systems with Two-sided Barriers

Ma¹,

Ning

Wang

et al. 2022

Preprint

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The research of stochastic steady-state response of vibration systems including bilateral impacts and gaps has important theoretical and practical significance. At present, conventional analytical methods destroy the inherent non-smooth of the systems because of many approximate transformations when solving response. In order to deal with this problem, we propose a new method to preserve the velocity jump under the bilateral impact without nonsmooth transformation in this paper. A complete process is regarded as the one-step transition probability that the stochastic trajectories start from one barrier, and return to the original barrier after impacting with another barrier. Then, the intervals of response are established based on the initial barrier to ensure of the continuity of the state space. We analyzed the steady-state response of a bilateral Rayleigh vibro-impact oscillator and a piezoelectric energy harvesting device with two symmetric barriers by utilizing the proposed method, respectively. Comparing with Monte Carlo simulations, it is fully demonstrated the effectiveness of this method. At the same time, it is found that the cases using our proposed method have wide applicability under different position of barriers, restitution coefficient, noise excitation and system parameters.

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“…However, friction produces strong and non-smooth nonlinearity, which signiﬁcantly changes the performance of the original system. 8…”

Section: Introductionmentioning

confidence: 99%

“…However, friction produces strong and non-smooth nonlinearity, which significantly changes the performance of the original system. 8 Quite a few models have been established for friction, such as the Coulomb friction model, the Stribeck friction model, 9 and the LuGre model. 10 The Coulomb friction model is the simplest and has been extensively employed, especially for dry friction.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective optimization of vehicle seat suspension with friction under random excitation

Luo

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part D:

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A seat suspension contributes greatly to vehicle ride comfort as a result of direct contact with the human body. Friction in a seat suspension produces strong non-smooth nonlinearity in seat dynamics, which makes the simulation-based optimization on the seat suspension’s performance time-consuming. This study tries to address parameter optimization on a vehicle seat suspension with the friction force in an analytical approach. A two degrees of freedom model is firstly established for the human body-seat system with friction and subjected to bandlimited random excitation. The nonlinear model is converted into an equivalent linear model by using Gaussian linearization. The dynamic responses of the linear model have then derived analytically and validated by Monte Carlo simulations. Based on the analytical solution, a multi-objective optimization strategy is proposed for the seat suspension. The acceleration of the human body and the suspension travel are chosen as the objective indexes to evaluate seat performance. Simulation results show that the proposed optimization strategy is efficient, where a global optimum is guaranteed owing to the analytical expression of the objective function. The optimization approach taking advantage of model linearization can be applied to similar mechanical systems with friction.

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Some new advance on the research of stochastic non-smooth systems

Cited by 17 publications

References 111 publications

Flux Reconstruction Schemes for Fokker-Planck Equations with Drift-Admitting Jumps

Flux Reconstruction Schemes for Fokker-Planck Equations with Drift-Admitting Jumps

A Novel Method for Solving Response of Stochastic Vibro-impact Systems with Two-sided Barriers

Multi-objective optimization of vehicle seat suspension with friction under random excitation

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