A tutorial on Bayesian inference to identify material parameters in solid mechanics

Rappel, Hussein; Beex, Lars A A; Hale, Jake S; Noels, Ludovic; Bordas, Stéphane P A

doi:10.1007/s11831-018-09311-x

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A tutorial on Bayesian inference to identify material parameters in solid mechanics

Rappel, Hussein; Beex, Lars A A; Hale, Jake S et al.

2020 • In Archives of Computational Methods in Engineering, 27 (2), p. 361–385

Peer reviewed

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https://hdl.handle.net/2268/230043

DOI
10.1007/s11831-018-09311-x

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This is a pre-print of an article published in Archives of Computational Methods in Engineering. The final authenticated version is available online at: https://doi.org/10.1007/s11831-018-09311-x.

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Keywords :

Bayesian inference; Bayes' theorem; Stochastic identification; statistical identification; parameter identification; Elastoplasticity; Plasticity

Abstract :

[en] The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress-strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress-strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions.

Research center :

A&M - Aérospatiale et Mécanique - ULiège

Disciplines :

Mechanical engineering

Author, co-author :

Rappel, Hussein; Université de Liège - ULiège > A&M > CM3

Beex, Lars A A; University of Luxemburg

Hale, Jake S; University of Luxemburg

Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)

Bordas, Stéphane P A

Language :

English

Title :

A tutorial on Bayesian inference to identify material parameters in solid mechanics

Publication date :

01 April 2020

Journal title :

Archives of Computational Methods in Engineering

ISSN :

1134-3060

Publisher :

International Center for Numerical Methods in Engineering, Spain

Volume :

Issue :

Pages :

361–385

Peer reviewed :

Peer reviewed

European Projects :

FP7 - 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery

Name of the research project :

Hussein Rappel, Lars A.A. Beex and St ephane P.A. Bordas would like to acknowledge the nancial support from the University of Luxembourg. St ephane P.A. Bordas also thanks the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) entitled "Towards real time multiscale simulation of cutting in nonlinear materials with applications to surgical simulation and computer guided surgery". Jack S. Hale is supported by the National Research Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission (FP7-COFUND Grant No. 6693582).

Funders :

UE - Union Européenne [BE]
FNR - Fonds National de la Recherche [LU]
CE - Commission Européenne [BE]

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Bibliography

Everitt BS, Skrondal A (2010) The Cambridge dictionary of statistics. Cambridge University Press, Cambridge
Walpole RE, Myers RH, Myers SL, Ye K (2013) Probability andstatistics for engineers and scientists. Pearson Custom Library, Pearson, London
Gogu C, Haftka R, Riche RL, Molimard J, Vautrin A (2010) Introduction to the Bayesian approach applied to elastic constants identification. AIAA J 48(5):893–903
Higdon D, Lee H, Bi Z (2002) A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine scale information. IEEE Trans Signal Process 50:388–399
Wang J, Zabaras N (2004) A Bayesian inference approach to the inverse heat conduction problem. Int J Heat Mass Transf 47(17–18):3927–3941
Risholm P, Janoos F, Norton I, Golby AJ, Wells WM (2013) Bayesian characterization of uncertainty in intra-subject non-rigid registration. Med Image Anal 17(5):538–555
Lan S, Bui-Thanh T, Christie M, Girolami M (2016) Emulation of higher-order tensors in manifold Monte Carlo methods for Bayesian inverse problems. J Comput Phys 308:81–101
Beck JL, Katafygiotis LS (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):455–461
Oh CK, Beck JL, Yamada M (2008) Bayesian learning using automatic relevance determination prior with an application to earthquake early warning. J Eng Mech 134(12):1013–1020
Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc Ser B (Stat Methodol) 63(3):425–464
Kaipio J, Somersalo E (2006) Statistical and computational inverse problems, vol 160. Springer, Dordrecht
Isenberg J (1979) Progressing from least squares to Bayesian estimation. In: Proceedings of the 1979 ASME design engineering technical conference, New York, pp 1–11
Alvin KF (1997) Finite element model update via Bayesian estimation and minimization of dynamic residuals. AIAA J 35(5):879–886
Marwala T, Sibusiso S (2005) Finite element model updating using Bayesian framework and modal properties. J Aircr 42(1):275–278
Lai TC, Ip KH (1996) Parameter estimation of orthotropic plates by Bayesian sensitivity analysis. Compos Struct 34(1):29–42
Daghia F, de Miranda S, Ubertini F, Viola E (2007) Estimation of elastic constants of thick laminated plates within a Bayesian framework. Compos Struct 80(3):461–473
Koutsourelakis PS (2012) A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an application to static elastography. Int J Numer Methods Eng 91(3):249–268
Gogu C, Yin W, Haftka R, Ifju P, Molimard J, Le Riche R, Vautrin A (2013) Bayesian identification of elastic constants in multi-directional laminate from moiré interferometry displacement fields. Exp Mech 53(4):635–648
Muto M, Beck JL (2008) Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. J Vib Control 14(1–2):7–34
Liu P, Au SK (2013) Bayesian parameter identification of hysteretic behavior of composite walls. Probab Eng Mech 34:101–109
Fitzenz DD, Jalobeanu A, Hickman SH (2007) Integrating laboratory creep compaction data with numerical fault models: a Bayesian framework. J Geophys Res Solid Earth 112(B8):B08410. 10.1029/2006JB004792
Most T (2010) Identification of the parameters of complex constitutive models: least squares minimization vs. Bayesian updating. In: Straub D (ed) Reliability and optimization of structural systems. CRC Press, New York, pp 119–130
Rosić BV, Kčerová A, Sýkora J, Pajonk O, Litvinenko A, Matthies HG (2013) Parameter identification in a probabilistic setting. Eng Struct 50:179–196
Hernandez WP, Borges FCL, Castello DA, Roitman N, Magluta C (2015) Bayesian inference applied on model calibration of fractional derivative viscoelastic model. In: Steffen Jr V, Rade DA, Bessa WM (eds) DINAME 2015-proceedings of the XVII international symposium on dynamic problems of mechanics, Natal
Rappel H, Beex LAA, Bordas SPA (2018) Bayesian inference to identify parameters in viscoelasticity. Mech Time-Depend Mater 22(2):221–258
Nichols JM, Link WA, Murphy KD, Olson CC (2010) A Bayesian approach to identifying structural nonlinearity using free-decay response: application to damage detection in composites. J Sound Vib 329(15):2995–3007
Abhinav S, Manohar CS (2015) Bayesian parameter identification in dynamic state space models using modified measurement equations. Int J Non-Linear Mech 71:89–103
Madireddy S, Sista B, Vemaganti K (2015) A Bayesian approach to selecting hyperelastic constitutive models of soft tissue. Comput Methods Appl Mech Eng 291:102–122
Oden JT, Prudencio EE, Hawkins-Daarud A (2013) Selection and assesment of phenomenological models of tumor growth. Math Models Methods Appl Sci 23(7):1309–1338
Chiachío J, Chiachío M, Saxena A, Sankararaman S, Rus G, Goebel K (2015) Bayesian model selection and parameter estimation for fatigue damage progression models in composites. Int J Fatigue 70:361–373
Babuška I, Sawlan Z, Scavino M, Szabó B, Tempone R (2016) Bayesian inference and model comparison for metallic fatigue data. Comput Methods Appl Mech Eng 304:171–196
Sarkar S, Kosson DS, Mahadevan S, Meeussen JCL, van der Sloot H, Arnold JR, Brown KG (2012) Bayesian calibration of thermodynamic parameters for geochemical speciation modeling of cementitious materials. Cement Concr Res 42(7):889–902
Cotter SL, Dashti M, Robinson JC, Stuart AM (2009) Bayesian inverse problems for functions and applications to fluid mechanics. Inverse Probl 25(11):115008
Simo JC, Hughes TJR (2000) Computational inelasticity. Springer, New York
Ulrych TJ, Sacchi MD, Woodbury A (2001) A Bayes tour of inversion: a tutorial. Geophysics 66(1):55–69
Gelman A, Carlin JB, Stern HS, Rubin DB (2003) Bayesian data analysis. Chapman & Hall/CRC texts in statistical science. Chapman & Hall/CRC, London
Beck JL, Au SK (2002) Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation. J Eng Mech 128(4):380–391
Marzouk YM, Najm HN, Rahn LA (2007) Stochastic spectral methods for efficient Bayesian solution of inverse problems. J Comput Phys 224(2):560–586
Kristensen J, Zabaras N (2014) Bayesian uncertainty quantification in the evaluation of alloy properties with the cluster expansion method. Comput Phys Commun 185(11):2885–2892
Andrieu C, De Freitas N, Doucet A, Jordan MI (2003) An introduction to MCMC for machine learning. Mach Learn 50(1–2):5–43
Brooks S, Gelman A, Jones G, Meng XL (2011) Handbook of Markov chain Monte Carlo. CRC Press, Boca Raton
Sinharay S (2003) Assessing convergence of the Markov chain Monte Carlo algorithms: ad review. ETS Res Rep Ser 2003(1):i-52
Gelman A, Roberts GO, Gilks WR (1996) Efficient Metropolis jumping rules. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds) Bayesian statistics, vol 5. Oxford Science Publications. Oxford University Press, New York, pp 599–607
Haario H, Saksman E, Tamminen J (1999) Adaptive proposal distribution for random walk Metropolis algorithm. Comput Stat 14(3):375–396
Beck JL (2010) Bayesian system identification based on probability logic. Struct Control Health Monit 17(7):825–847
Prince SJD (2012) Computer vision: models learning and inference. Cambridge University Press, Cambridge
Rappel H, Beex LAA, Noels L, Bordas SPA (2018) Identifying elastoplastic parameters with Bayes’ theorem considering output error, input error and model uncertainty. Probab Eng Mech. 10.1016/j.probengmech.2018.08.004
Ling Y, Mullins J, Mahadevan S (2014) Selection of model discrepancy priors in Bayesian calibration. J Comput Phys 276(Supplement C):665–680
Bishop C (2006) Pattern recognition and machine learning. Information science and statistics. Springer, Berlin
Arhonditsis GB, Papantou D, Zhang W, Perhar G, Massos E, Shi M (2008) Bayesian calibration of mechanistic aquatic biogeochemical models and benefits for environmental management. J Mar Syst 73(1):8–30
Xiong Y, Chen W, Tsui KL, Apley DW (2009) A better understanding of model updating strategies in validating engineering models. Comput Methods Appl Mech Eng 198(15):1327–1337
Arendt PD, Apley DW, Chen W (2012) Quantification of model uncertainty: calibration, model discrepancy, and identifiability. J Mech Des 134(10):100908
Brynjarsdóttir J, O’Hagan A (2014) Learning about physical parameters: the importance of model discrepancy. Inverse Probl 30(11):114007