Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
International Journal for Uncertainty Quantification
Factor de Impacto: 4.911 Factor de Impacto de 5 años: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Imprimir: 2152-5080
ISSN En Línea: 2152-5099

Acceso abierto

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003594
pages 371-395

FRAMEWORK FOR CONVERGENCE AND VALIDATION OF STOCHASTIC UNCERTAINTY QUANTIFICATION AND RELATIONSHIP TO DETERMINISTIC VERIFICATION AND VALIDATION

S. Maysam Mousaviraad
IIHR-Hydroscience and Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
Wei He
Visiting scholar from NAOCE, Shanghai Jiao Tong University, Shanghai, China
Matteo Diez
Visiting scholar from CNR-INSEAN, Via di Vallerano 139, 00128 Rome, Italy
Frederick Stern
IIHR-Hydroscience and Engineering, The University of Iowa, Iowa City, Iowa 52242, USA

SINOPSIS

A framework is described for convergence and validation of nonintrusive uncertainty quantification (UQ) methods; the relationship between deterministic verification and validation (V&V) and stochastic UQ is studied, and an example is provided for a unit problem. Convergence procedures are developed for Monte Carlo (MC) without and with metamodels, showing that in addition to the usual user-defined acceptable confidence intervals, convergence studies with systematic refinement ratio are required. A UQ validation procedure is developed using the benchmark UQ results and defining the comparison error and its uncertainty to evaluate validation. A stochastic influence factor is defined to evaluate the effects of input variability on the performance expectation and four possibilities are identified in making design decisions. The unit problem studies a two-dimensional airfoil with variable Re and normal distribution using high-fidelity Reynolds-averaged Navier-Stokes (RANS) simulations. Deterministic V&V studies achieve monotonic grid convergence and validation at the validation uncertainty interval of 2.2% D, averaged between lift and drag, with an average error of 0.25% D. For MC with Latin hypercube sampling the converged results are obtained with 400 computational fluid dynamics (CFD) simulations and are used as validation benchmark in the absence of experimental UQ. The stochastic influence factor is small such that the output expected value is not distinguishable from the deterministic solution. The output uncertainty is one order of magnitude smaller for lift than drag, implying that lift is only weakly dependent on Re. Several metamodels are used with MC, reducing the number of CFD simulations to a minimum of 4. The results are converged and validated at the average intervals of 0.1% for expected value (EV) and 10.7% for standard deviation (SD). The Gauss quadrature and the polynomial chaos (PC) method are validated using 8 and 7 CFD simulations, respectively, at the average intervals of 0.08% for EV and 7.5% for SD. The error values are smallest for the metamodels, followed by the PC method and then the Gauss quadratures.


Articles with similar content:

HIGH DIMENSIONAL SENSITIVITY ANALYSIS USING SURROGATE MODELING AND HIGH DIMENSIONAL MODEL REPRESENTATION
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 5
Edmondo Minisci, Marco Cisternino, Martin Kubicek
RANS modeling of turbulent mixing for a jet in supersonic cross flow: model evaluation and uncertainty quantification
ICHMT DIGITAL LIBRARY ONLINE, Vol.0, 2012, issue
Michael Emory, Gianluca Iaccarino, Catherine Gorle
BAYESIAN MULTISCALE FINITE ELEMENT METHODS. MODELING MISSING SUBGRID INFORMATION PROBABILISTICALLY
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 2
Wing Tat Leung, B. Mallick, Yalchin Efendiev, N. Guha, V. H. Hoang, S. W. Cheung
AN EFFICIENT MONTE CARLO-BASED SOLVER FOR THERMAL RADIATION IN PARTICIPATING MEDIA
4th Thermal and Fluids Engineering Conference, Vol.29, 2019, issue
Somesh P. Roy, Joseph A. Farmer
GOAL-ORIENTED MODEL ADAPTIVITY IN STOCHASTIC ELASTODYNAMICS: SIMULTANEOUS CONTROL OF DISCRETIZATION, SURROGATE MODEL AND SAMPLING ERRORS
International Journal for Uncertainty Quantification, Vol.10, 2020, issue 3
Pedro Bonilla-Villalba, A. Kundu, S. Claus, Pierre Kerfriden