Bayesian methods for characterizing unknown parameters of material models

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

doi:10.1016/j.apm.2016.01.046

Title: Bayesian methods for characterizing unknown parameters of material models

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Abstract

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed to characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.

Authors:

; Grigoriu, M. D.;

Publication Date:: Fri Jul 01 00:00:00 EDT 2016

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

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

OSTI Identifier:: 1635552

Alternate Identifier(s):: OSTI ID: 1237654; OSTI ID: 1425692

Report Number(s):: SAND-2015-3898J
Journal ID: ISSN 0307-904X; S0307904X16300427; PII: S0307904X16300427

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Published Article

Journal Name:: Applied Mathematical Modelling

Additional Journal Information:: Journal Name: Applied Mathematical Modelling Journal Volume: 40 Journal Issue: 13-14; Journal ID: ISSN 0307-904X

Publisher:: Elsevier

Country of Publication:: United Kingdom

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Emery, J. M., Grigoriu, M. D., and Field Jr., R. V. Bayesian methods for characterizing unknown parameters of material models.  United Kingdom: N. p., 2016. 
Web.  doi:10.1016/j.apm.2016.01.046.

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                    Emery, J. M., Grigoriu, M. D., & Field Jr., R. V. Bayesian methods for characterizing unknown parameters of material models.  United Kingdom.  https://doi.org/10.1016/j.apm.2016.01.046

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                    Emery, J. M., Grigoriu, M. D., and Field Jr., R. V. Fri .  
"Bayesian methods for characterizing unknown parameters of material models".  United Kingdom.  https://doi.org/10.1016/j.apm.2016.01.046.

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@article{osti_1635552,

  title        = {Bayesian methods for characterizing unknown parameters of material models},

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

  abstractNote = {A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed to characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.},

  doi          = {10.1016/j.apm.2016.01.046},

  journal      = {Applied Mathematical Modelling},

  number       = 13-14,

  volume       = 40,

  place        = {United Kingdom},

  year         = {Fri Jul 01 00:00:00 EDT 2016},

  month        = {Fri Jul 01 00:00:00 EDT 2016}

}

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