A Method for Treating Discretization Error in Nondeterministic Analysis

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A response surface methodology-based technique is presented for treating discretization error in non-deterministic analysis. The response surface, or metamodel, is estimated from computer experiments which vary both uncertain physical parameters and the fidelity of the computational mesh. The resultant metamodel is then used to propagate the variabilities in the continuous input parameters, while the mesh size is taken to zero, its asymptotic limit. With respect to mesh size, the metamodel is equivalent to Richardson extrapolation, in which solutions on coarser and finer meshes are used to estimate discretization error. The method is demonstrated on a one dimensional prismatic bar, in ... continued below

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Alvin, K.F. January 27, 1999.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 13 times . More information about this article can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Laboratories, Albuquerque, NM, and Livermore, CA
    Place of Publication: Albuquerque, New Mexico

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Description

A response surface methodology-based technique is presented for treating discretization error in non-deterministic analysis. The response surface, or metamodel, is estimated from computer experiments which vary both uncertain physical parameters and the fidelity of the computational mesh. The resultant metamodel is then used to propagate the variabilities in the continuous input parameters, while the mesh size is taken to zero, its asymptotic limit. With respect to mesh size, the metamodel is equivalent to Richardson extrapolation, in which solutions on coarser and finer meshes are used to estimate discretization error. The method is demonstrated on a one dimensional prismatic bar, in which uncertainty in the third vibration frequency is estimated by propagating variations in material modulus, density, and bar length. The results demonstrate the efficiency of the method for combining non-deterministic analysis with error estimation to obtain estimates of total simulation uncertainty. The results also show the relative sensitivity of failure estimates to solution bias errors in a reliability analysis, particularly when the physical variability of the system is low.

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  • 1999 AIAA/ASME Forum on Non-Deferministic Appoaches; St.Louis, MO; 04/12-15/1999

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  • Other: DE00003300
  • Report No.: SAND99-0224C
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 3300
  • Archival Resource Key: ark:/67531/metadc684559

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  • January 27, 1999

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  • July 25, 2015, 2:20 a.m.

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  • Nov. 29, 2016, 8:03 p.m.

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Alvin, K.F. A Method for Treating Discretization Error in Nondeterministic Analysis, article, January 27, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc684559/: accessed July 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.