Loading [MathJax]/extensions/tex2jax.js

Stochastic response determination of multi-dimensional nonlinear systems endowed with fractional derivative elements by the GE-GDEE

Research output: Contribution to journalReview articleResearchpeer review

Authors

  • Yi Luo
  • Pol D. Spanos
  • Jianbing Chen

External Research Organisations

  • Rice University
  • Tongji University

Details

Original languageEnglish
Article number104247
JournalInternational Journal of Non-Linear Mechanics
Volume147
Early online date23 Sept 2022
Publication statusPublished - Dec 2022
Externally publishedYes

Abstract

In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.

Keywords

    Fractional derivative, Globally-evolving-based generalized density evolution equation (GE-GDEE), Multi-dimensional, Nonlinear, Stochastic dynamic analysis

ASJC Scopus subject areas

Cite this

Stochastic response determination of multi-dimensional nonlinear systems endowed with fractional derivative elements by the GE-GDEE. / Luo, Yi; Spanos, Pol D.; Chen, Jianbing.
In: International Journal of Non-Linear Mechanics, Vol. 147, 104247, 12.2022.

Research output: Contribution to journalReview articleResearchpeer review

Download
@article{1de0dbca29084093a660003f224fb7ad,
title = "Stochastic response determination of multi-dimensional nonlinear systems endowed with fractional derivative elements by the GE-GDEE",
abstract = "In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.",
keywords = "Fractional derivative, Globally-evolving-based generalized density evolution equation (GE-GDEE), Multi-dimensional, Nonlinear, Stochastic dynamic analysis",
author = "Yi Luo and Spanos, {Pol D.} and Jianbing Chen",
note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Ltd",
year = "2022",
month = dec,
doi = "10.1016/j.ijnonlinmec.2022.104247",
language = "English",
volume = "147",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Ltd.",

}

Download

TY - JOUR

T1 - Stochastic response determination of multi-dimensional nonlinear systems endowed with fractional derivative elements by the GE-GDEE

AU - Luo, Yi

AU - Spanos, Pol D.

AU - Chen, Jianbing

N1 - Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/12

Y1 - 2022/12

N2 - In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.

AB - In this paper a recently developed technique relying on the globally-evolving-based generalized density evolution equation (GE-GDEE) is extended. It is applied to determining the response statistics of multi-dimensional nonlinear systems with fractional derivative elements subject to Gaussian white noise. In particular, the GE-GDEE is derived by a new approach, which enhances its applicability to general continuous processes. Thus, non-Markovian system responses can be treated directly and efficiently. Specifically, for a high-dimensional nonlinear system with fractional derivative elements, of which the responses are non-Markovian, a one- or two-dimensional GE-GDEE, in terms of the response quantity of interest, is obtained. Note that the associated effective drift coefficients involve no fractional terms, and are estimated numerically from data derived from a fairly small number of deterministic analyses. Then, the GE-GDEE is solved by path integration. The accuracy and efficiency of the proposed technique are assessed by applying it for specific nonlinear system and juxtaposing the derived results with pertinent Monte Carlo Simulation data.

KW - Fractional derivative

KW - Globally-evolving-based generalized density evolution equation (GE-GDEE)

KW - Multi-dimensional

KW - Nonlinear

KW - Stochastic dynamic analysis

UR - http://www.scopus.com/inward/record.url?scp=85139826873&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2022.104247

DO - 10.1016/j.ijnonlinmec.2022.104247

M3 - Review article

AN - SCOPUS:85139826873

VL - 147

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

M1 - 104247

ER -