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Applications of Mathematics

, Volume 63, Issue 6, pp 713–737 | Cite as

Polynomial chaos in evaluating failure probability: A comparative study

  • Eliška JanouchováEmail author
  • Jan Sýkora
  • Anna Kučerová
Article
  • 14 Downloads

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.

Keywords

uncertainty quantification reliability analysis probability of failure safety margin polynomial chaos expansion regression method stochastic collocation method stochastic Galerkin method Monte Carlo method 

MSC 2010

41A10 62P30 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  • Eliška Janouchová
    • 1
    Email author
  • Jan Sýkora
    • 1
  • Anna Kučerová
    • 1
  1. 1.Faculty of Civil Engineering, Department of MechanicsCzech Technical University in PraguePraha 6Czech Republic

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