Maximum entropy-based uncertainty modeling at the elemental level in linear structural and thermal problems

Pengchao Song, Marc Mignolet

Research output: Contribution to journalArticle

Abstract

A novel approach is proposed for the modeling of uncertainties in finite element models of linear structural or thermal problems. This uncertainty is introduced at the level of each finite element by randomizing the corresponding elemental matrices (e.g., mass, stiffness, conductance) using the maximum entropy concept. The approach is characterized by only two parameters, one expressing the overall level of uncertainty while the other is the correlation length underlying the random elemental matrices. As it proceeds from the finite element mean model matrices, the modeling can be performed from finite element models constructed in commercial software. In fact, the approach is exemplified on a structural example developed within Nastran with the assembly of the random elemental matrices performed outside of this software.

Original languageEnglish (US)
JournalComputational Mechanics
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Fingerprint

Heat problems
Uncertainty Modeling
Maximum Entropy
Entropy
Random Matrices
Uncertainty
Finite Element Model
Finite Element
Software
Matrix Models
Correlation Length
Conductance
Modeling
Two Parameters
Stiffness

Keywords

  • Linear finite element
  • Maximum entropy
  • Uncertainty modeling

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{ecf3125693ad4bdfa0ca8ffcc54d65c2,
title = "Maximum entropy-based uncertainty modeling at the elemental level in linear structural and thermal problems",
abstract = "A novel approach is proposed for the modeling of uncertainties in finite element models of linear structural or thermal problems. This uncertainty is introduced at the level of each finite element by randomizing the corresponding elemental matrices (e.g., mass, stiffness, conductance) using the maximum entropy concept. The approach is characterized by only two parameters, one expressing the overall level of uncertainty while the other is the correlation length underlying the random elemental matrices. As it proceeds from the finite element mean model matrices, the modeling can be performed from finite element models constructed in commercial software. In fact, the approach is exemplified on a structural example developed within Nastran with the assembly of the random elemental matrices performed outside of this software.",
keywords = "Linear finite element, Maximum entropy, Uncertainty modeling",
author = "Pengchao Song and Marc Mignolet",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s00466-019-01734-y",
language = "English (US)",
journal = "Computational Mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",

}

TY - JOUR

T1 - Maximum entropy-based uncertainty modeling at the elemental level in linear structural and thermal problems

AU - Song, Pengchao

AU - Mignolet, Marc

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A novel approach is proposed for the modeling of uncertainties in finite element models of linear structural or thermal problems. This uncertainty is introduced at the level of each finite element by randomizing the corresponding elemental matrices (e.g., mass, stiffness, conductance) using the maximum entropy concept. The approach is characterized by only two parameters, one expressing the overall level of uncertainty while the other is the correlation length underlying the random elemental matrices. As it proceeds from the finite element mean model matrices, the modeling can be performed from finite element models constructed in commercial software. In fact, the approach is exemplified on a structural example developed within Nastran with the assembly of the random elemental matrices performed outside of this software.

AB - A novel approach is proposed for the modeling of uncertainties in finite element models of linear structural or thermal problems. This uncertainty is introduced at the level of each finite element by randomizing the corresponding elemental matrices (e.g., mass, stiffness, conductance) using the maximum entropy concept. The approach is characterized by only two parameters, one expressing the overall level of uncertainty while the other is the correlation length underlying the random elemental matrices. As it proceeds from the finite element mean model matrices, the modeling can be performed from finite element models constructed in commercial software. In fact, the approach is exemplified on a structural example developed within Nastran with the assembly of the random elemental matrices performed outside of this software.

KW - Linear finite element

KW - Maximum entropy

KW - Uncertainty modeling

UR - http://www.scopus.com/inward/record.url?scp=85067676685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067676685&partnerID=8YFLogxK

U2 - 10.1007/s00466-019-01734-y

DO - 10.1007/s00466-019-01734-y

M3 - Article

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

ER -