A Bayesian Framework to Identify Random Parameter Fields Based on the Copula Theorem and Gaussian Fields: Application to Polycrystalline Materials

[1]  André Jalobeanu,et al.  Integrating laboratory creep compaction data with numerical fault models: A Bayesian framework , 2007 .

[2]  R. Nelsen.  An Introduction to Copulas , 1998 .

[3]  Andrew Gelman,et al.  Handbook of Markov Chain Monte Carlo , 2011 .

[4]  Francesco Ubertini,et al.  Estimation of elastic constants of thick laminated plates within a Bayesian framework , 2007 .

[5]  Heikki Haario,et al.  Adaptive proposal distribution for random walk Metropolis algorithm , 1999, Comput. Stat..

[6]  K. D. Murphy,et al.  A Bayesian Approach to Identifying Structural Nonlinearity using Free-Decay Response: Application to Damage Detection in Composites , 2010 .

[7]  James L. Beck,et al.  Bayesian Updating and Model Class Selection for Hysteretic Structural Models Using Stochastic Simulation , 2008 .

[8]  Andrew Gordon Wilson,et al.  Copula Processes , 2010, NIPS.

[9]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .

[10]  Phaedon-Stelios Koutsourelakis,et al.  A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters , 2008, J. Comput. Phys..

[11]  Simon Rogers,et al.  A First Course in Machine Learning , 2011, Chapman and Hall / CRC machine learning and pattern recognition series.

[12]  Raphael T. Haftka,et al.  Introduction to the Bayesian Approach Applied to Elastic Constants Identification , 2010 .

[13]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[14]  J. Beck,et al.  Updating Models and Their Uncertainties. I: Bayesian Statistical Framework , 1998 .

[15]  J. Beck.  Bayesian system identification based on probability logic , 2010 .

[16]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[17]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[18]  P. X. Song,et al.  Multivariate Dispersion Models Generated From Gaussian Copula , 2000 .

[19]  Hussein Rappel,et al.  Estimating fibres’ material parameter distributions from limited data with the help of Bayesian inference , 2019, European Journal of Mechanics - A/Solids.

[20]  Andrea Vigliotti,et al.  Bayesian inference of the spatial distributions of material properties , 2018, Journal of the Mechanics and Physics of Solids.

[21]  P. S. Koutsourelakis,et al.  A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an application to static elastography , 2012, 1512.05913.

[22]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[23]  Stéphane Bordas,et al.  Bayesian inference to identify parameters in viscoelasticity , 2018 .

[24]  H. Rappel,et al.  Identifying elastoplastic parameters with Bayes’ theorem considering output error, input error and model uncertainty , 2019, Probabilistic Engineering Mechanics.

[25]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[26]  Hedibert Freitas Lopes,et al.  Copula, marginal distributions and model selection: a Bayesian note , 2008, Stat. Comput..

[27]  Peter A. Flach,et al.  Evaluation Measures for Multi-class Subgroup Discovery , 2009, ECML/PKDD.

[28]  Paul D. Arendt,et al.  Quantification of model uncertainty: Calibration, model discrepancy, and identifiability , 2012 .

[29]  J. Golinval,et al.  A stochastic multi-scale approach for the modeling of thermo-elastic damping in micro-resonators , 2016 .

[30]  K. F. Alvin,et al.  Finite Element Model Update via Bayesian Estimation and Minimization of Dynamic Residuals , 1996 .

[31]  Ludovic Noels,et al.  Bayesian identification of Mean-Field Homogenization model parameters and uncertain matrix behavior in non-aligned short fiber composites , 2019, Composite Structures.

[32]  K. Ip,et al.  Parameter estimation of orthotropic plates by Bayesian sensitivity analysis , 1996 .

[33]  Daniel Straub,et al.  Reliability and Optimization of Structural Systems , 2010 .

[34]  Kyung K. Choi,et al.  Identification of marginal and joint CDFs using Bayesian method for RBDO , 2009 .

[35]  Siu-Kui Au,et al.  Bayesian parameter identification of hysteretic behavior of composite walls , 2013 .

[36]  Sebastian Jaimungal,et al.  Kernel-Based Copula Processes , 2009, ECML/PKDD.

[37]  James O. Berger,et al.  A Framework for Validation of Computer Models , 2007, Technometrics.

[38]  A. Vautrin,et al.  Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields , 2012, Experimental Mechanics.

[39]  Stéphane Bordas,et al.  A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics , 2019, Archives of Computational Methods in Engineering.

[40]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[41]  Thomas Most,et al.  Identification of the parameters of complex constitutive models: Least squares minimization vs. Bayesian updating , 2010 .

[42]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[43]  Tshilidzi Marwala,et al.  Finite Element Model Updating Using Bayesian Framework and Modal Properties , 2005 .

[44]  Ludovic Noels,et al.  A stochastic computational multiscale approach; Application to MEMS resonators , 2015 .