Polynomial chaos in evaluating failure probability: A comparative study

Eliška Janouchová; Jan Sýkora; Anna Kučerová

Applications of Mathematics (2018)

  • Volume: 63, Issue: 6, page 713-737
  • ISSN: 0862-7940

Abstract

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Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial chaos and its use in computing failure probability. In particular, we compare results for the stochastic Galerkin method, stochastic collocation, and the regression method based on Latin hypercube sampling with predictions obtained by crude Monte Carlo sampling. As an illustrative engineering example, we consider a simple frame structure with uncertain parameters in loading and geometry with prescribed distributions defined by realistic histograms.

How to cite

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Janouchová, Eliška, Sýkora, Jan, and Kučerová, Anna. "Polynomial chaos in evaluating failure probability: A comparative study." Applications of Mathematics 63.6 (2018): 713-737. <http://eudml.org/doc/294272>.

@article{Janouchová2018,
abstract = {Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial chaos and its use in computing failure probability. In particular, we compare results for the stochastic Galerkin method, stochastic collocation, and the regression method based on Latin hypercube sampling with predictions obtained by crude Monte Carlo sampling. As an illustrative engineering example, we consider a simple frame structure with uncertain parameters in loading and geometry with prescribed distributions defined by realistic histograms.},
author = {Janouchová, Eliška, Sýkora, Jan, Kučerová, Anna},
journal = {Applications of Mathematics},
keywords = {uncertainty quantification; reliability analysis; probability of failure; safety margin; polynomial chaos expansion; regression method; stochastic collocation method; stochastic Galerkin method; Monte Carlo method},
language = {eng},
number = {6},
pages = {713-737},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Polynomial chaos in evaluating failure probability: A comparative study},
url = {http://eudml.org/doc/294272},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Janouchová, Eliška
AU - Sýkora, Jan
AU - Kučerová, Anna
TI - Polynomial chaos in evaluating failure probability: A comparative study
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 6
SP - 713
EP - 737
AB - Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction of polynomial chaos and its use in computing failure probability. In particular, we compare results for the stochastic Galerkin method, stochastic collocation, and the regression method based on Latin hypercube sampling with predictions obtained by crude Monte Carlo sampling. As an illustrative engineering example, we consider a simple frame structure with uncertain parameters in loading and geometry with prescribed distributions defined by realistic histograms.
LA - eng
KW - uncertainty quantification; reliability analysis; probability of failure; safety margin; polynomial chaos expansion; regression method; stochastic collocation method; stochastic Galerkin method; Monte Carlo method
UR - http://eudml.org/doc/294272
ER -

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