Dimension-reduction of FPK equation via equivalent drift coefficient

Jianbing Chen · Peihui Lin

24 citations0/0 files storedTheoretical and Applied Mechanics Letters

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Probabilistic and Robust Engineering Design Model Reduction and Neural Networks stochastic dynamics and bifurcation

Abstract

The Fokker—Planck—Kolmogorov (FPK) equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method (PDEM), in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 24 citations exist upstream.

References

1991Simulation of Stochastic Processes by Spectral Representation 2009Stochastic Dynamics of Structures 2006The principle of preservation of probability and the generalized density evolution equation 2011Random Vibrations: Analysis of Structural and Mechanical Systems 2000Efficient path integration methods for nonlinear dynamic systems 2011Advances of the probability density evolution method for nonlinear stochastic systems 2008A note on the principle of preservation of probability and probability density evolution equation 2013Reliability assessment in structural dynamics

Cited by

2022Physically Driven Exact Dimension Reduction of a Class of Nonlinear Multidimensional Systems Subjected to Additive White Noise 2025Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE 2025DR-PDEE-based probabilistic response analysis for high-dimensional nonlinear dynamical systems under general non-white and non-stationary random excitations via constructing the auxiliary diffusion process 2025Stochastic dynamic response analysis via dimension-reduced probability density evolution equation (DR-PDEE) with enhanced tail-accuracy

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.