Abonnement à la biblothèque: Guest
Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections
International Journal for Uncertainty Quantification
Facteur d'impact: 3.259 Facteur d'impact sur 5 ans: 2.547 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

Ouvrir l'accès

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015008446
pages 275-295

AN OPTIMAL SAMPLING RULE FOR NONINTRUSIVE POLYNOMIAL CHAOS EXPANSIONS OF EXPENSIVE MODELS

Michael Sinsbeck
Institute for Modeling Hydraulic and Environmental Systems (LS3)/SimTech, University of Stuttgart, Stuttgart, Germany
Wolfgang Nowak
Institute for Modeling Hydraulic and Environmental Systems (LS3)/SimTech, University of Stuttgart, Stuttgart, Germany

RÉSUMÉ

In this work we present the optimized stochastic collocation method (OSC). OSC is a new sampling rule that can be applied to polynomial chaos expansions (PCE) for uncertainty quantification. Given a model function, the goal of PCE is to find the polynomial from a given polynomial space that is closest to the model function with respect to the L2-norm induced by a given probability measure. Many PCE methods approximate the involved projection integral by discretization with a finite set of integration points. Our key idea is to choose these integration points through numerical optimization based on an operator norm derived from the discretized projection operator. OSC is a generalization of Gaussian quadrature: both methods coincide for one-dimensional integration and under appropriate problem settings in multidimensional problems. As opposed to many established integration rules, OSC does not generally lead to tensor grids in multidimensional problems. With OSC, the user can specify the number of integration points independently of the problem dimension and PCE expansion order. This allows one to reduce the number of model evaluations and still achieve a high accuracy. The input parameters can follow any kind of probability distribution, as long as the statistical moments up to a certain order are available. Even statistically dependent parameters can be handled in a straightforward and natural fashion. Moreover, OSC allows reusing integration points, if results from earlier model evaluations are available. Gauss-Kronrod and Stroud integration rules can be reproduced with OSC for the respective special cases.


Articles with similar content:

STOCHASTIC GALERKIN METHODS AND MODEL ORDER REDUCTION FOR LINEAR DYNAMICAL SYSTEMS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 3
E. Jan W. ter Maten, Roland Pulch
A GENERAL FRAMEWORK FOR ENHANCING SPARSITY OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Xiaoliang Wan, Huan Lei, Xiu Yang, Lin Lin
ADAPTIVE SELECTION OF SAMPLING POINTS FOR UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.7, 2017, issue 4
Casper Rutjes, Enrico Camporeale, Ashutosh Agnihotri
A NEW CRACK TIP ENRICHMENT FUNCTION IN THE EXTENDED FINITE ELEMENT METHOD FOR GENERAL INELASTIC MATERIALS
International Journal for Multiscale Computational Engineering, Vol.10, 2012, issue 4
Haim Waisman, Xia Liu, Jacob Fish
A NUMERICAL METHOD FOR THREE-DIMENSIONAL PARABOLIC FLOW AND HEAT TRANSFER IN STRAIGHT DUCTS OF IRREGULAR CROSS SECTION
Computational Thermal Sciences: An International Journal, Vol.1, 2009, issue 3
Nirmalakanth Jesuthasan, Bantwal Rabi Baliga