Polynomial chaos in evaluating failure probability: A comparative study
- 14 Downloads
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.
Keywordsuncertainty quantification reliability analysis probability of failure safety margin polynomial chaos expansion regression method stochastic collocation method stochastic Galerkin method Monte Carlo method
MSC 201041A10 62P30
Unable to display preview. Download preview PDF.
- O. Ditlevsen, H. O. Madsen: Structural Reliability Methods. John Wiley & Sons, Chichester, 1996.Google Scholar
- A. Fülöp, M. Iványi: Safety of a column in a frame. Probabilistic Assessment of Structures Using Monte Carlo Simulation: Background, Exercises and Software (P. Marek et al., eds.). Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, Praha, CD, Chapt. 8. 10, 2003.Google Scholar
- R. G. Ghanem, P. D. Spanos: Stochastic Finite Elements: A Spectral Approach, Revised Edition. Dover Civil and Mechanical Engineering, Dover Publications, 2012.Google Scholar
- M. Gutiérrez, S. Krenk: Stochastic finite element methods. Encyclopedia of Computational Mechanics (E. Stein et al., eds.). John Wiley & Sons, Chichester, 2004.Google Scholar
- S. Hosder, R. W. Walters, M. Balch: Efficient sampling for non–intrusive polynomial chaos applications with multiple uncertain input variables. The 48th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Honolulu. AIAA 2007–1939, 2007, pp. 16.Google Scholar
- E. Janouchová, A. Kučerová, J. Sýkora: Polynomial chaos construction for structural reliability analysis. Proceedings of the Fourth International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering (Y. Tsompanakis et al., eds.). Civil–Comp Press, Stirlingshire, 2015, Paper 9.Google Scholar
- H. G. Matthies: Uncertainty quantification with stochastic finite elements. Encyclopedia of Computational Mechanics (E. Stein et al., eds.). John Wiley & Sons, Chichester, 2007.Google Scholar
- M. P. Pettersson, G. Iaccarino, J. Nordström: Polynomial chaos methods. Polynomial Chaos Methods for Hyperbolic Partial Differential Equations. Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties. Mathematical Engineering, Springer, Cham, 2015, pp. 23–29.zbMATHGoogle Scholar