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Title: Efficient Computation of Info-Gap Robustness for Finite Element Models

Abstract

A recent research effort at LANL proposed info-gap decision theory as a framework by which to measure the predictive maturity of numerical models. Info-gap theory explores the trade-offs between accuracy, that is, the extent to which predictions reproduce the physical measurements, and robustness, that is, the extent to which predictions are insensitive to modeling assumptions. Both accuracy and robustness are necessary to demonstrate predictive maturity. However, conducting an info-gap analysis can present a formidable challenge, from the standpoint of the required computational resources. This is because a robustness function requires the resolution of multiple optimization problems. This report offers an alternative, adjoint methodology to assess the info-gap robustness of Ax = b-like numerical models solved for a solution x. Two situations that can arise in structural analysis and design are briefly described and contextualized within the info-gap decision theory framework. The treatments of the info-gap problems, using the adjoint methodology are outlined in detail, and the latter problem is solved for four separate finite element models. As compared to statistical sampling, the proposed methodology offers highly accurate approximations of info-gap robustness functions for the finite element models considered in the report, at a small fraction of the computational cost. Itmore » is noted that this report considers only linear systems; a natural follow-on study would extend the methodologies described herein to include nonlinear systems.« less

Authors:
 [1];  [1];  [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
DOE/LANL
OSTI Identifier:
1045402
Report Number(s):
LA-UR-12-22695
TRN: US1203660
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; 42 ENGINEERING; 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; APPROXIMATIONS; DESIGN; LANL; NONLINEAR PROBLEMS; OPTIMIZATION; RESOLUTION; SAMPLING; SIMULATION

Citation Formats

Stull, Christopher J., Hemez, Francois M., and Williams, Brian J. Efficient Computation of Info-Gap Robustness for Finite Element Models. United States: N. p., 2012. Web. doi:10.2172/1045402.
Stull, Christopher J., Hemez, Francois M., & Williams, Brian J. Efficient Computation of Info-Gap Robustness for Finite Element Models. United States. https://doi.org/10.2172/1045402
Stull, Christopher J., Hemez, Francois M., and Williams, Brian J. 2012. "Efficient Computation of Info-Gap Robustness for Finite Element Models". United States. https://doi.org/10.2172/1045402. https://www.osti.gov/servlets/purl/1045402.
@article{osti_1045402,
title = {Efficient Computation of Info-Gap Robustness for Finite Element Models},
author = {Stull, Christopher J. and Hemez, Francois M. and Williams, Brian J.},
abstractNote = {A recent research effort at LANL proposed info-gap decision theory as a framework by which to measure the predictive maturity of numerical models. Info-gap theory explores the trade-offs between accuracy, that is, the extent to which predictions reproduce the physical measurements, and robustness, that is, the extent to which predictions are insensitive to modeling assumptions. Both accuracy and robustness are necessary to demonstrate predictive maturity. However, conducting an info-gap analysis can present a formidable challenge, from the standpoint of the required computational resources. This is because a robustness function requires the resolution of multiple optimization problems. This report offers an alternative, adjoint methodology to assess the info-gap robustness of Ax = b-like numerical models solved for a solution x. Two situations that can arise in structural analysis and design are briefly described and contextualized within the info-gap decision theory framework. The treatments of the info-gap problems, using the adjoint methodology are outlined in detail, and the latter problem is solved for four separate finite element models. As compared to statistical sampling, the proposed methodology offers highly accurate approximations of info-gap robustness functions for the finite element models considered in the report, at a small fraction of the computational cost. It is noted that this report considers only linear systems; a natural follow-on study would extend the methodologies described herein to include nonlinear systems.},
doi = {10.2172/1045402},
url = {https://www.osti.gov/biblio/1045402}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {7}
}