Probability density evolution method: background, significance and recent developments
J Li - Probabilistic Engineering Mechanics, 2016 - Elsevier
Investigation of a stochastic system from a viewpoint of studying the randomness
propagation process in a physical system starts to play an important role in understanding …
propagation process in a physical system starts to play an important role in understanding …
Sparse representations and compressive sampling approaches in engineering mechanics: A review of theoretical concepts and diverse applications
IA Kougioumtzoglou, I Petromichelakis… - Probabilistic Engineering …, 2020 - Elsevier
A review of theoretical concepts and diverse applications of sparse representations and
compressive sampling (CS) approaches in engineering mechanics problems is provided …
compressive sampling (CS) approaches in engineering mechanics problems is provided …
A decoupled approach for determination of the joint probability density function of a high-dimensional nonlinear stochastic dynamical system via the probability density …
The joint probability density function (PDF) of multiple response processes of a system is a
crucial topic in the fields of science and engineering. It is adopted to describe the dependent …
crucial topic in the fields of science and engineering. It is adopted to describe the dependent …
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations
It has long been one of the main challenges in science and engineering to capture the
probabilistic response of high-dimensional nonlinear stochastic dynamic systems involving …
probabilistic response of high-dimensional nonlinear stochastic dynamic systems involving …
Addressing the curse of dimensionality in stochastic dynamics: A Wiener path integral variational formulation with free boundaries
I Petromichelakis… - Proceedings of the …, 2020 - royalsocietypublishing.org
A Wiener path integral variational formulation with free boundaries is developed for
determining the stochastic response of high-dimensional nonlinear dynamical systems in a …
determining the stochastic response of high-dimensional nonlinear dynamical systems in a …
Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral
A novel approximate analytical technique for determining the non-stationary response
probability density function (PDF) of randomly excited linear and nonlinear oscillators …
probability density function (PDF) of randomly excited linear and nonlinear oscillators …
Multi-output multi-physics-informed neural network for learning dimension-reduced probability density evolution equation with unknown spatio-temporal-dependent …
Abstract The Dimension-Reduced Probability Density Evolution Equation (DR-PDEE) offers
a promising approach for evaluating probability density evolution in stochastic dynamical …
a promising approach for evaluating probability density evolution in stochastic dynamical …
A Wiener path integral technique for determining the stochastic response of nonlinear oscillators with fractional derivative elements: A constrained variational …
Y Zhang, IA Kougioumtzoglou, F Kong - Probabilistic Engineering …, 2023 - Elsevier
A technique based on the concept of Wiener path integral (WPI) is developed for
determining approximately the joint response probability density function (PDF) of nonlinear …
determining approximately the joint response probability density function (PDF) of nonlinear …
An extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems
IG Mavromatis, IA Kougioumtzoglou… - International Journal of …, 2024 - Elsevier
An extrapolation approach within the Wiener path integral (WPI) technique is developed for
determining the stochastic response of diverse nonlinear dynamical systems. Specifically …
determining the stochastic response of diverse nonlinear dynamical systems. Specifically …
Reliability of dynamical systems with combined Gaussian and Poisson white noise via path integral method
Analyzing the reliability of a stochastic dynamical system represents one of the most
challenging problems in stochastic dynamics. In this paper, the reliability of dynamical …
challenging problems in stochastic dynamics. In this paper, the reliability of dynamical …