Comptes Rendus
Computational modeling of material forming processes / Simulation numérique des procédés de mise en forme
Comparison of stochastic and interval methods for uncertainty quantification of metal forming processes
Comptes Rendus. Mécanique, Volume 346 (2018) no. 8, pp. 634-646.

Various sources of uncertainty can arise in metal forming processes, or their numerical simulation, or both, such as uncertainty in material behavior, process conditions, and geometry. Methods from the domain of uncertainty quantification can help assess the impact of such uncertainty on metal forming processes and their numerical simulation, and they can thus help improve robustness and predictive accuracy. In this paper, we compare stochastic methods and interval methods, two classes of methods receiving broad attention in the domain of uncertainty quantification, through their application to a numerical simulation of a sheet metal forming process.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2018.06.007
Keywords: Metal forming, Uncertainty quantification, Stochastic methods, Interval methods, Sensitivity analysis, Parameter study

Maarten Arnst 1; Jean-Philippe Ponthot 1; Romain Boman 1

1 Université de Liège, Aérospatiale et Mécanique, Quartier Polytech, 1, allée de la Découverte 9, B-4000 Liège, Belgium
@article{CRMECA_2018__346_8_634_0,
     author = {Maarten Arnst and Jean-Philippe Ponthot and Romain Boman},
     title = {Comparison of stochastic and interval methods for uncertainty quantification of metal forming processes},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {634--646},
     publisher = {Elsevier},
     volume = {346},
     number = {8},
     year = {2018},
     doi = {10.1016/j.crme.2018.06.007},
     language = {en},
}
TY  - JOUR
AU  - Maarten Arnst
AU  - Jean-Philippe Ponthot
AU  - Romain Boman
TI  - Comparison of stochastic and interval methods for uncertainty quantification of metal forming processes
JO  - Comptes Rendus. Mécanique
PY  - 2018
SP  - 634
EP  - 646
VL  - 346
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crme.2018.06.007
LA  - en
ID  - CRMECA_2018__346_8_634_0
ER  - 
%0 Journal Article
%A Maarten Arnst
%A Jean-Philippe Ponthot
%A Romain Boman
%T Comparison of stochastic and interval methods for uncertainty quantification of metal forming processes
%J Comptes Rendus. Mécanique
%D 2018
%P 634-646
%V 346
%N 8
%I Elsevier
%R 10.1016/j.crme.2018.06.007
%G en
%F CRMECA_2018__346_8_634_0
Maarten Arnst; Jean-Philippe Ponthot; Romain Boman. Comparison of stochastic and interval methods for uncertainty quantification of metal forming processes. Comptes Rendus. Mécanique, Volume 346 (2018) no. 8, pp. 634-646. doi : 10.1016/j.crme.2018.06.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.06.007/

[1] Y. Ben-Haim; I. Elishakoff Convex Models of Uncertainty in Applied Mechanics, Elsevier, Amsterdam, The Netherlands, 1990

[2] R. Ghanem; P. Spanos Stochastic Finite Elements: A Spectral Approach, Dover Publications, 2003

[3] D. Moens; D. Vandepitte A survey of non-probabilistic uncertainty treatment in finite element analysis, Comput. Methods Appl. Mech. Eng., Volume 194 (2005), pp. 1527-1555

[4] O. Le Maître; O. Knio Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, Springer, 2010

[5] D. Xiu Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, 2010

[6] D. Moens; M. Hanss Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: recent advances, Finite Elem. Anal. Des., Volume 47 (2011), pp. 4-16 | DOI

[7] M. Grigoriu Stochastic Systems: Uncertainty Quantification and Propagation, Springer-Verlag, 2012

[8] R. Smith Uncertainty Quantification: Theory, Implementation, and Applications, SIAM, 2013

[9] M. Arnst; J.-P. Ponthot An overview of nonintrusive characterization, propagation, and sensitivity analysis of uncertainties in computational mechanics, Int. J. Uncertain. Quantificat., Volume 4 (2014), pp. 387-421

[10] T. Sullivan Introduction to Uncertainty Quantification, Springer, 2015

[11] R. Ghanem; D. Higdon; H. Owhadi Handbook of Uncertainty Quantification, Springer, 2017

[12] C. Soize Uncertainty Quantification, Springer, 2017

[13] M. Arnst; B. Abello Àlvarez; J. Ponthot; R. Boman Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification, J. Comput. Phys., Volume 349 (2017), pp. 59-79

[14] R. Dudley Real Analysis and Probability, Cambridge University Press, Cambridge, United Kingdom, 2002

[15] G. Casella; R. Berger Statistical Inference, 2002 (Duxbury, Pacific Grove, California)

[16] A. Saltelli; M. Ratto; T. Andres; F. Campolongo; J. Cariboni; D. Gatelli; M. Saisana; S. Tarantola Global Sensitivity Analysis: The Primer, Wiley, West Sussex, United Kingdom, 2008

[17] C. Robert; G. Casella Monte Carlo Statistical Methods, Springer, New York, 2010

[18] C. Rasmussen; C. Williams Gaussian Processes for Machine Learning, The MIT Press, 2006

[19] B. Sudret Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Syst. Saf., Volume 93 (2008), pp. 964-979 | DOI

[20] T. Crestaux; O. Le Maître; J.-M. Martinez Polynomial chaos expansion for sensitivity analysis, Reliab. Eng. Syst. Saf., Volume 94 (2009), pp. 1161-1172 | DOI

[21] I. Sobol Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul., Volume 55 (2001), pp. 271-280 | DOI

[22] J. Ponthot Traitement unifié de la mécanique des milieux continus solides en grandes deformations par la méthode des éléments finis, University of Liège, Liège, Belgium, 1995 (Ph.D. thesis)

[23] http://metafor.ltas.ulg.ac.be/ (Metafor, website)

[24] Q. Bui; L. Papeleux; J. Ponthot Numerical simulation of springback using enhanced assumed strain elements, Finite Elem. Anal. Des., Volume 153–154 (2004), pp. 314-318 | DOI

[25] P. Moran Statistical inference with bivariate gamma distributions, Biometrika, Volume 56 (1969), pp. 627-634 http://www.jstor.org/stable/2334670

Cited by Sources:

Comments - Policy