A solution to the static frame validation challenge problem using Bayesian model selection

Grigoriu, M. D.; Field, R. V.

doi:10.1016/j.cma.2007.09.023

Title: A solution to the static frame validation challenge problem using Bayesian model selection

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Abstract

Within this paper, we provide a solution to the static frame validation challenge problem (see this issue) in a manner that is consistent with the guidelines provided by the Validation Challenge Workshop tasking document. The static frame problem is constructed such that variability in material properties is known to be the only source of uncertainty in the system description, but there is ignorance on the type of model that best describes this variability. Hence both types of uncertainty, aleatoric and epistemic, are present and must be addressed. Our approach is to consider a collection of competing probabilistic models for the material properties, and calibrate these models to the information provided; models of different levels of complexity and numerical efficiency are included in the analysis. A Bayesian formulation is used to select the optimal model from the collection, which is then used for the regulatory assessment. Lastly, bayesian credible intervals are used to provide a measure of confidence to our regulatory assessment.

Authors:

Grigoriu, M. D. ^[1]; Field, R. V. ^[2]

Cornell Univ., Ithaca, NY (United States). Civil and Environmental Engineering
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Applied Mechanics Development

Publication Date:: Sun Dec 23 00:00:00 EST 2007

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1426977

Report Number(s):: SAND-2007-0885J
Journal ID: ISSN 0045-7825; 524198

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:: Journal Volume: 197; Journal Issue: 29-32; Journal ID: ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Bayesian analysis; Model selection; Model validation; Random fields

Citation Formats


                    Grigoriu, M. D., and Field, R. V. A solution to the static frame validation challenge problem using Bayesian model selection.  United States: N. p., 2007. 
Web.  doi:10.1016/j.cma.2007.09.023.

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                    Grigoriu, M. D., & Field, R. V. A solution to the static frame validation challenge problem using Bayesian model selection.  United States.  https://doi.org/10.1016/j.cma.2007.09.023

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                    Grigoriu, M. D., and Field, R. V. Sun .  
"A solution to the static frame validation challenge problem using Bayesian model selection".  United States.  https://doi.org/10.1016/j.cma.2007.09.023.  https://www.osti.gov/servlets/purl/1426977.

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@article{osti_1426977,

  title        = {A solution to the static frame validation challenge problem using Bayesian model selection},

  author       = {Grigoriu, M. D. and Field, R. V.},

  abstractNote = {Within this paper, we provide a solution to the static frame validation challenge problem (see this issue) in a manner that is consistent with the guidelines provided by the Validation Challenge Workshop tasking document. The static frame problem is constructed such that variability in material properties is known to be the only source of uncertainty in the system description, but there is ignorance on the type of model that best describes this variability. Hence both types of uncertainty, aleatoric and epistemic, are present and must be addressed. Our approach is to consider a collection of competing probabilistic models for the material properties, and calibrate these models to the information provided; models of different levels of complexity and numerical efficiency are included in the analysis. A Bayesian formulation is used to select the optimal model from the collection, which is then used for the regulatory assessment. Lastly, bayesian credible intervals are used to provide a measure of confidence to our regulatory assessment.},

  doi          = {10.1016/j.cma.2007.09.023},

  journal      = {Computer Methods in Applied Mechanics and Engineering},

  number       = 29-32,

  volume       = 197,

  place        = {United States},

  year         = {Sun Dec 23 00:00:00 EST 2007},

  month        = {Sun Dec 23 00:00:00 EST 2007}

}

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