Bayesian inference to identify parameters in viscoelasticity

Bayesian inference; Bayes’ theorem; Parameter identification; Statistical identification; Viscoelasticity; Bayesian networks; Identification (control systems); Inference engines; Strain rate; Uncertainty analysis; Constant strain rate tests; Identified parameter; Input parameter; Relaxation test; Standard linear solid models; Parameter estimation

Abstract :

[en] This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are: (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned issues, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity. © 2017 Springer Science+Business Media B.V.

Disciplines :

Mechanical engineering
Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Rappel, Hussein ; Université de Liège - ULiège > Form. doct. sc. ingé. & techno. (aéro. & mécan. - Paysage)

Beex, L. A. A.; Faculty of Science, Technology and Communication, University of Luxembourg, Maison du Nombre, 6, Avenue de la Fonte, Esch-sur-Alzette, Luxembourg

Bordas, S. P. A.; Faculty of Science, Technology and Communication, University of Luxembourg, Maison du Nombre, 6, Avenue de la Fonte, Esch-sur-Alzette, Luxembourg, School of Engineering, Cardiff University, Queens Buildings, The Parade, Cardiff, Wales, United Kingdom, Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, 35 Stirling Highway, Crawley/Perth, WA, Australia

Language :

English

Title :

Bayesian inference to identify parameters in viscoelasticity

Publication date :

2018

Journal title :

Mechanics of Time-Dependent Materials

ISSN :

1385-2000

eISSN :

1573-2738

Publisher :

Springer Netherlands

Pages :

1-38

Peer reviewed :

Peer reviewed

Available on ORBi :

since 06 May 2018

Statistics

Number of views

113 (10 by ULiège)

Number of downloads

482 (8 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Abhinav, S., Manohar, C.: Bayesian parameter identification in dynamic state space models using modified measurement equations. Int. J. Non-Linear Mech. 71, 89–103 (2015)
Alvin, K.: Finite element model update via Bayesian estimation and minimization of dynamic residuals. AIAA J. 35(5), 879–886 (1997)
Andrieu, C., De Freitas, N., Doucet, A., Jordan, M.I.: An introduction to MCMC for machine learning. Mach. Learn. 50(1–2), 5–43 (2003)
Babuška, I., Sawlan, Z., Scavino, M., Szabó, B., Tempone, R.: Bayesian inference and model comparison for metallic fatigue data. Comput. Methods Appl. Math. 304, 171–196 (2016)
Banks, H.T., Hu, S., Kenz, Z.R.: A brief review of elasticity and viscoelasticity for solids. Adv. Appl. Math. Mech. 3(1), 1–51 (2011)
Beck, J.L., Au, S.K.: Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation. J. Eng. Mech. 128(4), 380–391 (2002)
Beck, J.L., Katafygiotis, L.S.: Updating models and their uncertainties, I: Bayesian statistical framework. J. Eng. Mech. 124(4), 455–461 (1998)
Beex, L.A.A., Verberne, C.W., Peerlings, R.H.J.: Experimental identification of a lattice model for woven fabrics: application to electronic textile. Composites, Part A, Appl. Sci. Manuf. 48, 82–92 (2013)
Brooks, S., Gelman, A., Jones, G., Meng, X.L.: Handbook of Markov Chain Monte Carlo. CRC Press, Boca Raton (2011)
Calvetti, D., Somersalo, E.: An Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing, vol. 2. Springer, New York (2007)
Chaparro, B.M., Thuillier, S., Menezes, L.F., Manach, P.Y., Fernandes, J.V.: Material parameters identification: gradient-based, genetic and hybrid optimization algorithms. Compos. Mater. Sci. 44(2), 339–346 (2008)
Chiachío, J., Chiachío, M., Saxena, A., Sankararaman, S., Rus, G., Goebel, K.: Bayesian model selection and parameter estimation for fatigue damage progression models in composites. Int. J. Fatigue 70, 361–373 (2015)
Daghia, F., de Miranda, S., Ubertini, F., Viola, E.: Estimation of elastic constants of thick laminated plates within a Bayesian framework. Compos. Struct. 80(3), 461–473 (2007)
Elster, C., Wübbeler, G.: Bayesian regression versus application of least squares an example. Metrologia 53(1), S10–S16 (2016)
Fitzenz, D.D., Jalobeanu, A., Hickman, S.H.: Integrating laboratory creep compaction data with numerical fault models: a Bayesian framework. J. Geophys. Res., Solid Earth 112, B08410 (2007)
Gelman, A., Roberts, G.O., Gilks, W.R.: Efficient Metropolis jumping rules. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (eds.) Bayesian Statistics, vol. 5, pp. 599–607. Oxford Univ. Press, New York (1996)
Genovese, K., Lamberti, L., Pappalettere, C.: Improved global-local simulated annealing formulation for solving non-smooth engineering optimization problems. Int. J. Solids Struct. 42(1), 203–237 (2005)
Gogu, C., Haftka, R., Molimard, J., Vautrin, A.: Introduction to the Bayesian approach applied to elastic constants identification. AIAA J. 48(5), 893–903 (2010)
Gogu, C., Yin, W., Haftka, R., Ifju, P., Molimard, J., Le Riche, R., Vautrin, A.: Bayesian identification of elastic constants in multi-directional laminate from Moiré interferometry displacement fields. Exp. Mech. 53(4), 635–648 (2013)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison–Wesley, Reading (1989)
Haario, H., Saksman, E., Tamminen, J.: Adaptive proposal distribution for random walk Metropolis algorithm. Comput. Stat. 14(3), 375–396 (1999)
Hernandez, W.P., Borges, F.C.L., Castello, D.A., Roitman, N., Magluta, C.: Bayesian inference applied on model calibration of fractional derivative viscoelastic model. In: Steffen, V. Jr, Rade, D.A., Bessa, W.M. (eds.) Proceedings of the XVII International Symposium on Dynamic Problems of Mechanics, DINAME 2015, Natal (2015)
Higdon, D., Lee, H., Bi, Z.: A Bayesian approach to characterizing uncertainty in inverse problems using. coarse and fine scale information. IEEE Trans. Signal Process. 50, 388–399 (2002)
Isenberg, J.: Progressing from least squares to Bayesian estimation. In: Proceedings of the 1979 ASME Design Engineering Technical Conference, pp. 1–11 (1979)
Kaipio, J., Somersalo, E.: Statistical and Computational Inverse Problems, vol. 160. Springer, New York (2007)
Kenz, Z.R., Banks, H.T., Smith, R.C.: Comparison of frequentist and Bayesian confidence analysis methods on a viscoelastic stenosis model. SIAM/ASA J. Uncertain. Quantificat. 1(1), 348–369 (2013)
Koutsourelakis, P.S.: 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 (2012)
Kristensen, J., Zabaras, N.: Bayesian uncertainty quantification in the evaluation of alloy properties with the cluster expansion method. Comput. Phys. Commun. 185(11), 2885–2892 (2014)
Lai, T.C., Ip, K.H.: Parameter estimation of orthotropic plates by Bayesian sensitivity analysis. Compos. Struct. 34(1), 29–42 (1996)
Liu, P., Au, S.K.: Bayesian parameter identification of hysteretic behavior of composite walls. Probab. Eng. Mech. 34, 101–109 (2013)
Liu, X.Y., Chen, X.F., Ren, Y.H., Zhan, Q.Y., Wang, C., Yang, C.: Alveolar type II cells escape stress failure caused by tonic stretch through transient focal adhesion disassembly. Int. J. Biol. Sci. 7(5), 588–599 (2011)
Madireddy, S., Sista, B., Vemaganti, K.: A Bayesian approach to selecting hyperelastic constitutive models of soft tissue. Comput. Methods Appl. Math. 291, 102–122 (2015)
Magorou, L.L., Bos, F., Rouger, F.: Identification of constitutive laws for wood-based panels by means of an inverse method. Compos. Sci. Technol. 62(4), 591–596 (2002)
Marwala, T., Sibusiso, S.: Finite element model updating using Bayesian framework and modal properties. J. Aircr. 42(1), 275–278 (2005)
Marzouk, Y.M., Najm, H.N., Rahn, L.A.: Stochastic spectral methods for efficient Bayesian solution of inverse problems. J. Comput. Phys. 224(2), 560–586 (2007)
Mehrez, L., Kassem, E., Masad, E., Little, D.: Stochastic identification of linear-viscoelastic models of aged and unaged asphalt mixtures. J. Mater. Civ. Eng. 27(4), 04014149 (2015)
Miles, P., Hays, M., Smith, R., Oates, W.: Bayesian uncertainty analysis of finite deformation viscoelasticity. Mech. Mater. 91, 35–49 (2015)
Most, T.: Identification of the parameters of complex constitutive models: least squares minimization vs. Bayesian updating. In: Straub, D. (ed.) Reliability and Optimization of Structural Systems, pp. 119–130. CRC Press, Boca Raton (2010)
Muto, M., Beck, J.L.: Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. J. Vib. Control 14(1–2), 7–34 (2008)
Nichols, J.M., Link, W.A., Murphy, K.D., Olson, C.C.: A Bayesian approach to identifying structural nonlinearity using free-decay response: application to damage detection in composites. J. Sound Vib. 329(15), 2995–3007 (2010)
Oden, J.T., Prudencio, E.E., Hawkins-Daarud, A.: Selection and assessment of phenomenological models of tumor growth. Math. Models Methods Appl. Sci. 23(7), 1309–1338 (2013)
Oh, C.K., Beck, J.L., Yamada, M.: Bayesian learning using automatic relevance determination prior with an application to earthquake early warning. J. Eng. Mech. 134(12), 1013–1020 (2008)
Orosz, M., Molnarka, G., Monos, E.: Curve fitting methods and mechanical models for identification of viscoelastic parameters of vascular wall—a comparative study. Med. Sci. Monit. 3(4), MT599–MT604 (1997)
Rappel, H., Beex, L.A.A., Hale, J.S., Bordas, S.P.A.: Bayesian inference for the stochastic identification of elastoplastic material parameters: introduction, misconceptions and additional insight. arXiv:1606.02422 (2016)
Rosić, B.V., Kčerová, A., Sýkora, J., Pajonk, O., Litvinenko, A., Matthies, H.G.: Parameter identification in a probabilistic setting. Eng. Struct. 50, 179–196 (2013)
Sarkar, S., Kosson, D.S., Mahadevan, S., Meeussen, J.C.L., van der Sloot, H., Arnold, J.R., Brown, K.G.: Bayesian calibration of thermodynamic parameters for geochemical speciation modeling of cementitious materials. Cem. Concr. Res. 42(7), 889–902 (2012)
Ulrych, T.J., Sacchi, M.D., Woodbury, A.: A Bayes tour of inversion: a tutorial. Geophysics 66(1), 55–69 (2001)
Wang, J., Zabaras, N.: A Bayesian inference approach to the inverse heat conduction problem. Int. J. Heat Mass Transf. 47(17–18), 3927–3941 (2004)
Zhang, E., Chazot, J.D., Antoni, J., Hamdi, M.: Bayesian characterization of Young’s modulus of viscoelastic materials in laminated structures. J. Sound Vib. 332(16), 3654–3666 (2013)
Zhao, X., Pelegri, A.A.: A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging. Int. J. Numer. Methods Biomed. Eng. 32(4), e02741 (2016)