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Polynomial chaos in evaluating failure probability: A comparative study

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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.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Department of Mechanics, Czech Technical University in Prague, Thákurova 7, 166 29, Praha 6, Czech Republic

    Eliška Janouchová, Jan Sýkora & Anna Kučerová

Authors
  1. Eliška Janouchová
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  2. Jan Sýkora
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  3. Anna Kučerová
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Correspondence to Eliška Janouchová.

Additional information

The research has been financially supported by the Czech Science Foundation, project No. 15-07299S.

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Janouchová, E., Sýkora, J. & Kučerová, A. Polynomial chaos in evaluating failure probability: A comparative study. Appl Math 63, 713–737 (2018). https://doi.org/10.21136/AM.2018.0335-17

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  • DOI: https://doi.org/10.21136/AM.2018.0335-17

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