Applications of Mathematics, Vol. 63, No. 6, pp. 713-737, 2018


Polynomial chaos in evaluating failure probability: A comparative study

Eliška Janouchová, Jan Sýkora, Anna Kučerová

Received November 27, 2017.   Published online December 3, 2018.

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
Classification MSC:  41A10, 62P30
DOI:  10.21136/AM.2018.0335-17


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Affiliations:   Eliška Janouchová, Jan Sýkora, Anna Kučerová, Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Praha 6, Czech Republic, e-mail: eliska.janouchova@fsv.cvut.cz, jan.sykora.1@fsv.cvut.cz, Anna.Kucerova@cvut.cz


 
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