Premium
Polynomial chaos expansion for surrogate modelling: Theory and software
Author(s) -
Novak Lukas,
Novak Drahomir
Publication year - 2018
Publication title -
beton‐ und stahlbetonbau
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.486
H-Index - 25
eISSN - 1437-1006
pISSN - 0005-9900
DOI - 10.1002/best.201800048
Subject(s) - polynomial chaos , reliability (semiconductor) , surrogate model , computer science , finite element method , transformation (genetics) , polynomial , mathematical optimization , mathematics , software , sensitivity (control systems) , algorithm , monte carlo method , statistics , engineering , mathematical analysis , power (physics) , physics , biochemistry , chemistry , structural engineering , quantum mechanics , electronic engineering , gene , programming language
The paper is focused on the application of a surrogate model to reliability analysis. Despite recent advances in this field, the reliability analysis of complex non‐linear finite element models is still highly time‐consuming. Thus, the approximation of the non‐linear finite element model by a surrogate meta‐model is often the only choice if one wishes to perform a sufficient amount of simulations to enable reliability analysis. First, the basic theory of polynomial chaos expansion (PCE) is described, including the transformation of correlated random variables. The usage of the PCE for the estimation of statistical moments and sensitivity analysis is then presented. It can be done efficiently via the post‐processing of the employed surrogate model in explicit form without any additional computational demands. The possibility of utilizing the adaptive algorithm Least Angle Regression is also discussed. The implementation of the discussed theory into a software tool, and its application, are presented in the last part of the paper.