Application of Bayesian Model Selection for Metal Yield Models using ALEGRA and Dakota

This report introduces the concepts of Bayesian model selection, which provides a systematic means of calibrating and selecting an optimal model to represent a phenomenon. This has many potential applications, including for comparing constitutive models. The ideas described herein are applied to a model selection problem between different yield models for hardened steel under extreme loading conditions.

[1]  Otto Eric Strack,et al.  ALEGRA : an arbitrary Lagrangian-Eulerian multimaterial, multiphysics code. , 2008 .

[2]  J. Beck,et al.  Asymptotic Expansions for Reliability and Moments of Uncertain Systems , 1997 .

[3]  R. Armstrong,et al.  Dislocation-mechanics-based constitutive relations for material dynamics calculations , 1987 .

[4]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[5]  Sophia Lefantzi,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. , 2011 .

[6]  Edwin T. Jaynes,et al.  Prior Probabilities , 1968, Encyclopedia of Machine Learning.

[7]  Wasserman,et al.  Bayesian Model Selection and Model Averaging. , 2000, Journal of mathematical psychology.

[8]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[9]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[10]  Laura Painton Swiler,et al.  A user's guide to Sandia's latin hypercube sampling software : LHS UNIX library/standalone version. , 2004 .

[11]  M. Eldred,et al.  Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification , 2009 .

[12]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.

[13]  D. Steinberg,et al.  A constitutive model for metals applicable at high-strain rate , 1980 .

[14]  Todd A. Oliver,et al.  Validating predictions of unobserved quantities , 2014, 1404.7555.

[15]  Ralph C. Smith,et al.  Uncertainty Quantification: Theory, Implementation, and Applications , 2013 .

[16]  D. Xiu.  Numerical Methods for Stochastic Computations: A Spectral Method Approach , 2010 .

[17]  Charles E. Anderson,et al.  TIME-RESOLVED PENETRATION OF LONG RODS INTO STEEL TARGETS , 1995 .

[18]  G. R. Johnson,et al.  A CONSTITUTIVE MODEL AND DATA FOR METALS SUBJECTED TO LARGE STRAINS, HIGH STRAIN RATES AND HIGH TEMPERATURES , 2018 .

[19]  Raphael T. Haftka,et al.  Making the Most Out of Surrogate Models: Tricks of the Trade , 2010, DAC 2010.

[20]  Gaël Varoquaux,et al.  The NumPy Array: A Structure for Efficient Numerical Computation , 2011, Computing in Science & Engineering.

[21]  S. Weinzierl.  Introduction to Monte Carlo methods , 2000, hep-ph/0006269.

[22]  David Richardson,et al.  Markov chain Monte Carlo: an introduction for epidemiologists. , 2013, International journal of epidemiology.

[23]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..