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

Files


Full Text
revised_manuscript.pdf
Author postprint (1.27 MB)
Request a copy

All documents in ORBilu are protected by a user license.

Send to



Details



Keywords :
Bayesian inference; Bayes' theorem; copula; 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 fi elds (which vary from one realization of the fi eld 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 fi elds 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 fi elds are therefore described using the copula theorem and Gaussian fi elds, which allow di fferent 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 fi elds and transform them into the new random fields. The bene fit 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 fi eld). Bayesian inference regards the parameters that are to be identi fied as random variables and requires a user-defi ned 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 su ciffient to accurately recover the distribution parameter values.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Aerospace & aeronautics engineering
Civil engineering
Materials science & engineering
Mechanical engineering
Author, co-author :
RAPPEL, Hussein ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Wu, Ling;  University of Liege > Aerospace and Mechanical Engineering
Noels, Ludovic;  University of Liege > Aerospace and Mechanical Engineering
BEEX, Lars ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
yes
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 :
In press
Journal title :
Journal of Applied Mechanics
ISSN :
0021-8936
eISSN :
1528-9036
Publisher :
ASME
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
FnR Project :
FNR11501927 - A Virtual Lab For Ni/Pu Hybrid Foams: Stochastic Micromechanical Identification And Efficient Numerical Simulations, 2016 (01/03/2018-28/02/2021) - Lars Beex
Name of the research project :
FNR11501927 > Lars Beex > Open-cell metal foams > A virtual lab for Ni/PU hybrid foams: stochastic micromechanical identification and efficient numerical simulations > 01/03/2018 > 28/02/2021 > 2017
Funders :
FNR - Fonds National de la Recherche
Available on ORBilu :
since 28 August 2019

Statistics


Number of views
229 (16 by Unilu)
Number of downloads
1 (0 by Unilu)

Scopus citations®
 
13
Scopus citations®
without self-citations
8
OpenCitations
 
10
OpenAlex citations
 
14
WoS citations
 
11

Bibliography


Similar publications



Contact ORBilu