Article (Scientific journals)
A Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials
Hussein, Rappel; Wu, Ling; Noels, Ludovic et al.
2019In Journal of Applied Mechanics, 86 (12), p. 121009
Peer Reviewed verified by ORBi
 

Files


Full Text
2020_JAM_BAYES.pdf
Author preprint (1.26 MB) Creative Commons License - Attribution, Non-Commercial, No Derivative
(c) JOURNAL OF APPLIED MECHANICS.
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
Bayesian inference; Bayes’ theorem; Gaussian fields; Gaussian processes; Gaussian copula; copula processes; Gaussian copula processes
Abstract :
[en] For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application approaches the length scale of the micro-structure however, spatially fluctuating parameter fields (which vary from one realization of the field to another) can be incorporated to make the model capture the stochasticity of the underlying micro-structure. Randomly fluctuating parameter fields are often described as Gaussian fields. Gaussian fields however assume that the probability density function of a material parameter at a given location is a univariate Gaussian distribution. This entails for instance that negative parameter values can be realized, whereas most material parameters have physical bounds (e.g. the Young’s modulus cannot be negative). In this contribution, randomly fluctuating parameter fields are therefore described using the copula theorem and Gaussian fields, which allow different types of univariate marginal distributions to be incorporated, but with the same correlation structure as Gaussian fields. It is convenient to keep the Gaussian correlation structure, as it allows us to draw samples from Gaussian fields and transform them into the new random fields. The benefit of this approach is that any type of univariate marginal distribution can be incorporated. If the selected univariate marginal distribution has bounds, unphysical material parameter values will never be realized. We then use Bayesian inference to identify the distribution parameters (which govern the random field). Bayesian inference regards the parameters that are to be identified as random variables and requires a user- defined prior distribution of the parameters to which the observations are inferred. For the homogenized Young’s modulus of a columnar polycrystalline material of interest in this study, the results show that with a relatively wide prior (i.e. a prior distribution without strong assumptions), a single specimen is sufficient to accurately recover the distribution parameter values.
Research center :
A&M - Aérospatiale et Mécanique - ULiège
Disciplines :
Materials science & engineering
Mechanical engineering
Author, co-author :
Hussein, Rappel;  Université du Luxembourg - UniLu
Wu, Ling ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Noels, Ludovic  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Beex, Lars A. A.;  Université du Luxembourg - UniLu
Language :
English
Title :
A Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials
Publication date :
December 2019
Journal title :
Journal of Applied Mechanics
ISSN :
0021-8936
eISSN :
1528-9036
Publisher :
American Society of Mechanical Engineers (ASME), New-York, United States - New York
Volume :
86
Issue :
12
Pages :
121009
Peer reviewed :
Peer Reviewed verified by ORBi
Name of the research project :
Hussein Rappel and Lars Beex gratefully acknowledge the financial support of the Fonds National de la Recherche Luxembourg under grant number INTER/DFG/16/11501927.
Funders :
FNR - Fonds National de la Recherche [LU]
Available on ORBi :
since 27 August 2019

Statistics


Number of views
120 (20 by ULiège)
Number of downloads
23 (8 by ULiège)

Scopus citations®
 
12
Scopus citations®
without self-citations
7
OpenCitations
 
9

Bibliography


Similar publications



Contact ORBi