Publication result detail

Polynomial chaos expansion for surrogate modelling: Theory and software

NOVÁK, L.; NOVÁK, D.

Original Title

Polynomial chaos expansion for surrogate modelling: Theory and software

English Title

Polynomial chaos expansion for surrogate modelling: Theory and software

Type

WoS Article

Original Abstract

The paper is focused on the application of a surrogate model to reliability analysis. Despite recent advances in this field, the reliability analysis of complex non-linear finite element models is still highly time-consuming. Thus, the approximation of the nonlinear finite element model by a surrogate meta-model is often the only choice if one wishes to perform a sufficient amount of simulations to enable reliability analysis. First, the basic theory of polynomial chaos expansion (PCE) is described, including the transformation of correlated random variables. The usage of the PCE for the estimation of statistical moments and sensitivity analysis is then presented. It can be done efficiently via the post-processing of the employed surrogate model in explicit form without any additional computational demands. The possibility of utilizing the adaptive algorithm Least Angle Regression is also discussed. The implementation of the discussed theory into a software tool, and its application, are presented in the last part of the paper.

English abstract

The paper is focused on the application of a surrogate model to reliability analysis. Despite recent advances in this field, the reliability analysis of complex non-linear finite element models is still highly time-consuming. Thus, the approximation of the nonlinear finite element model by a surrogate meta-model is often the only choice if one wishes to perform a sufficient amount of simulations to enable reliability analysis. First, the basic theory of polynomial chaos expansion (PCE) is described, including the transformation of correlated random variables. The usage of the PCE for the estimation of statistical moments and sensitivity analysis is then presented. It can be done efficiently via the post-processing of the employed surrogate model in explicit form without any additional computational demands. The possibility of utilizing the adaptive algorithm Least Angle Regression is also discussed. The implementation of the discussed theory into a software tool, and its application, are presented in the last part of the paper.

Keywords

Structural reliability; Polynomial Chaos Expansion; Surrogate model; Software; Sensitivity analysis

Key words in English

Structural reliability; Polynomial Chaos Expansion; Surrogate model; Software; Sensitivity analysis

Authors

NOVÁK, L.; NOVÁK, D.

RIV year

2019

Released

12.09.2018

Publisher

ERNST & SOHN

Location

GERMANY

ISBN

0005-9900

Periodical

Beton- und Stahlbetonbau

Volume

2

Number

113

State

Federal Republic of Germany

Pages from

27

Pages to

32

Pages count

6

URL

https://www.scopus.com/record/display.uri?eid=2-s2.0-85053251446&origin=inward&txGid=b08b733a16ab5e7327284b2473671020

BibTex

@article{BUT150899,
  author="Lukáš {Novák} and Drahomír {Novák}",
  title="Polynomial chaos expansion for surrogate modelling: Theory and software",
  journal="Beton- und Stahlbetonbau",
  year="2018",
  volume="2",
  number="113",
  pages="27--32",
  doi="10.1002/best.201800048",
  issn="0005-9900",
  url="https://www.scopus.com/record/display.uri?eid=2-s2.0-85053251446&origin=inward&txGid=b08b733a16ab5e7327284b2473671020"
}