Detail publikace

Polynomial chaos expansion for surrogate modelling: Theory and software

Originální název

Polynomial chaos expansion for surrogate modelling: Theory and software

Anglický název

Polynomial chaos expansion for surrogate modelling: Theory and software

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

BibTex


@article{BUT150899,
  author="Lukáš {Novák} and Drahomír {Novák}",
  title="Polynomial chaos expansion for surrogate modelling: Theory and software",
  annote="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.",
  address="ERNST & SOHN",
  chapter="150899",
  doi="10.1002/best.201800048",
  howpublished="online",
  institution="ERNST & SOHN",
  number="113",
  volume="2",
  year="2018",
  month="september",
  pages="27--32",
  publisher="ERNST & SOHN",
  type="journal article in Web of Science"
}