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International Journal for Uncertainty Quantification
インパクトファクター: 4.911 5年インパクトファクター: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 印刷: 2152-5080
ISSN オンライン: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2020031735
pages 195-223

GOAL-ORIENTED MODEL ADAPTIVITY IN STOCHASTIC ELASTODYNAMICS: SIMULTANEOUS CONTROL OF DISCRETIZATION, SURROGATE MODEL AND SAMPLING ERRORS

Pedro Bonilla-Villalba
Institute of Materials, Mechanics and Advanced Manufacturing, Cardiff University, 5 the Parade, Cardiff, UK
S. Claus
ONERA, 6 Chemin de la Vauve aux Granges, 91120 Palaiseau, France
A. Kundu
Institute of Materials, Mechanics and Advanced Manufacturing, Cardiff University, 5 the Parade, Cardiff, UK
Pierre Kerfriden
Institute of Materials, Mechanics and Advanced Manufacturing, Cardiff University, 5 the Parade, Cardiff, UK; Centre des Matériaux, MINES ParisTech/PSL University, 63-65 rue Henri Auguste Desbruères, Corbeil-essonnes, France

要約

The presented adaptive modeling approach aims to jointly control the level of refinement for each of the building blocks employed in a typical chain of finite element approximations for stochastically parametrized systems, namely: (i) finite error approximation of the spatial fields, (ii) surrogate modeling to interpolate quantities of interest(s) in the parameter domain, and (iii) Monte Carlo sampling of associated probability distribution(s). The control strategy seeks accurate calculation of any statistical measure of the distributions at minimum cost, given an acceptable margin of error as the only tunable parameter. At each stage of the greedy-based algorithm for spatial discretization, the mesh is selectively refined in the subdomains with highest contribution to the error in the desired measure. The strictly incremental complexity of the surrogate model is controlled by enforcing preponderant discretization error integrated across the parameter domain. Finally, the number of Monte Carlo samples is chosen such that either (a) the overall precision of the chain of approximations can be ascertained with sufficient confidence or (b) the fact that the computational model requires further mesh refinement is statistically established. The efficiency of the proposed approach is discussed for a frequency-domain vibration structural dynamics problem with forward uncertainty propagation. Results show that locally adapted finite element solutions converge faster than those obtained using uniformly refined grids.

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