TY - JOUR
T1 - Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components
AU - Bianchini, Ilaria
AU - Argiento, Raffaele
AU - Auricchio, Ferdinando
AU - Lanzarone, Ettore
PY - 2015
Y1 - 2015
N2 - The great influence of uncertainties on the behavior of physical systems has always drawn attention to the
importance of a stochastic approach to engineering prob-
lems. Accordingly, in this paper, we address the problem of
solving a Finite Element analysis in the presence of uncer-
tain parameters. We consider an approach in which several
solutions of the problem are obtained in correspondence
of parameters samples, and propose a novel non-intrusive
method, which exploits the functional principal component
analysis, to get acceptable computational efforts. Indeed, the
proposed approach allows constructing an optimal basis of
the solutions space and projecting the full Finite Element
problem into a smaller space spanned by this basis. Even if
solving the problem in this reduced space is computationally
convenient, very good approximations are obtained by upper
bounding the error between the full Finite Element solution
and the reduced one. Finally, we assess the applicability of
the proposed approach through different test cases, obtaining
satisfactory results.
AB - The great influence of uncertainties on the behavior of physical systems has always drawn attention to the
importance of a stochastic approach to engineering prob-
lems. Accordingly, in this paper, we address the problem of
solving a Finite Element analysis in the presence of uncer-
tain parameters. We consider an approach in which several
solutions of the problem are obtained in correspondence
of parameters samples, and propose a novel non-intrusive
method, which exploits the functional principal component
analysis, to get acceptable computational efforts. Indeed, the
proposed approach allows constructing an optimal basis of
the solutions space and projecting the full Finite Element
problem into a smaller space spanned by this basis. Even if
solving the problem in this reduced space is computationally
convenient, very good approximations are obtained by upper
bounding the error between the full Finite Element solution
and the reduced one. Finally, we assess the applicability of
the proposed approach through different test cases, obtaining
satisfactory results.
KW - Finite element analysis, Stochastic input parameters, Output uncertainty quantification, Functional, principal component analysis, Reduced basis
KW - Finite element analysis, Stochastic input parameters, Output uncertainty quantification, Functional, principal component analysis, Reduced basis
UR - http://hdl.handle.net/10807/148070
U2 - 10.1007/s00466-015-1185-7
DO - 10.1007/s00466-015-1185-7
M3 - Article
SN - 0178-7675
VL - 56
SP - 533
EP - 549
JO - Computational Mechanics
JF - Computational Mechanics
ER -