Reliability of dynamical systems with combined Gaussian and Poisson white noise via path integral method

Zan, Wanrong; Jia, Wantao; Xu, Yong

doi:10.1016/j.probengmech.2022.103252

Cited by 19 publications

(2 citation statements)

References 43 publications

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“…If the moisture at the -th lattice grid, i.e., for , is of interest, then according to the derivation in Subsect. 2, its transient PDF, denoted as , satisfies the following DR-PDEE, (33) where the intrinsic drift and rate functions are, respectively, (34) In this example, 5 × 5 lattice grid of soil is considered, i.e., , with the periodic boundary conditions, and the four adjacent grids of each grid are regarded as its neighboring grids, i.e., . According to Eq.…”

Section: Example 2: Genetic Toggle Switch With the Sos Pathwaymentioning

confidence: 99%

Probabilistic response determination of high-dimensional nonlinear dynamical systems enforced by parametric multiple Poisson white noises

Chen,

Lyu

2024

Nonlinear Dyn

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Stochastic dynamical systems enforced by Poisson white noise (PWN) are encountered widely in physics, chemistry, biology, and engineering fields, but it is hard to capture the probability density function (PDF) of the quantity of interest of these systems. Recently, the dimension-reduced probability density evolution equation (DR-PDEE) has shown significant advantages in probabilistic response determination of path-continuous processes, especially for systems of high dimensions and strong nonlinearity, but there are still challenges in path-discontinuous processes, such as PWN-driven systems, due to their random jumps. In the present paper, the DR-PDEE governing the PDF of any single component of state vector of interest for a highdimensional system enforced by PWN is established. It is always a one-dimensional partial integro-differential equation regardless of the dimension of the system if merely one single quantity is of interest. The intrinsic drift function and intrinsic rate function (the latter is for parametric excitations) in the DR-PDEE can be identified numerically based on the data from representative deterministic dynamic analyses of the PWNdriven system. Then solving the DR-PDEE numerically yields the solution of transient PDF of the quantity of interest. Numerical examples are illustrated to verify the efficiency and accuracy of the proposed method.

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Section: Example 2: Genetic Toggle Switch With the Sos Pathwaymentioning

confidence: 99%

Probabilistic response determination of high-dimensional nonlinear dynamical systems enforced by parametric multiple Poisson white noises

Chen,

Lyu

2024

Nonlinear Dyn

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“…It is of considerable importance to accurately understand the nonlinear dynamics of the conceptual airfoil models under extreme flight conditions and long-correlation noise to ensure the flight safety of an aircraft. Consequently, we need to further explore the excitation models acting on the aeroelastic airfoil models that can characterize the complex flight conditions of an aircraft, such as Poisson or Lévy noises, [216][217][218] with a large jump describing the extreme flight conditions, fractional Gaussian noise 219 with a long-correlation property, and even other complex cases. (2) High-dimensional nonlinear airfoil models.…”

Section: Future Directions From Past Inspirationmentioning

confidence: 99%

Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview

Liu

Kurths

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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During the past few decades, several significant progresses have been made in exploring complex nonlinear dynamics and vibration suppression of conceptual aeroelastic airfoil models. Additionally, some new challenges have arisen. To the best of the author’s knowledge, most studies are concerned with the deterministic case; however, the effects of stochasticity encountered in practical flight environments on the nonlinear dynamical behaviors of the airfoil systems are neglected. Crucially, coupling interaction of the structure nonlinearities and uncertainty fluctuations can lead to some difficulties on the airfoil models, including accurate modeling, response solving, and vibration suppression. At the same time, most of the existing studies depend mainly on a mathematical model established by physical mechanisms. Unfortunately, it is challenging and even impossible to obtain an accurate physical model of the complex wing structure in engineering practice. The emergence of data science and machine learning provides new opportunities for understanding the aeroelastic airfoil systems from the data-driven point of view, such as data-driven modeling, prediction, and control from the recorded data. Nevertheless, relevant data-driven problems of the aeroelastic airfoil systems are not addressed well up to now. This survey contributes to conducting a comprehensive overview of recent developments toward understanding complex dynamical behaviors and vibration suppression, especially for stochastic dynamics, early warning, and data-driven problems, of the conceptual two-dimensional airfoil models with different structural nonlinearities. The results on the airfoil models are summarized and discussed. Besides, several potential development directions that are worth further exploration are also highlighted.

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亚音速流中二维壁板系统的全局动力学和噪声诱导的跃迁

Yue,

Zhang,

et al. 2024

Acta Mech. Sin.

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Reliability of dynamical systems with combined Gaussian and Poisson white noise via path integral method

Cited by 19 publications

References 43 publications

Probabilistic response determination of high-dimensional nonlinear dynamical systems enforced by parametric multiple Poisson white noises

Probabilistic response determination of high-dimensional nonlinear dynamical systems enforced by parametric multiple Poisson white noises

Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview

亚音速流中二维壁板系统的全局动力学和噪声诱导的跃迁

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