Stochastic Model Calibration Based on Measurements from Different Experiments

Abstract:

The calibration of a heterogeneous material model can be formulated as a search for probabilistic description of its parameters providing the distribution of the model response corresponding to the distribution of the observed data. This contribution is focused on developing a method for identification of parameters along with their variations based on combining measurements from different types of destructive experiments.

• Periodical: Applied Mechanics and Materials (Volume 825)
• Pages: 135-140
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.825.135
• Online since: February 2016
• Authors: Eliška Janouchová*, Anna Kučerová, Jan Sýkora
• Keywords: Heterogeneous Materials, Markov Chain Monte Carlo Sampling, Principal Component Analysis, Stochastic Inversion Problem, Uncertain Parameter Identification, Uncertainty Quantification

References

[1] X. Frank Xu, A multiscale stochastic finite element method on elliptic problems involving uncertainties, Computer Methods in Applied Mechanics and Engineering 196(2007), pp.2723-2736.

DOI: 10.1016/j.cma.2007.02.002

[2] I. Babuška, M. Motamed and R. Tempone, A stochastic multiscale method for the elastodynamic wave equation arising from fiber composites, Computer Methods in Applied Mechanics and Engineering 276(2014), pp.190-211.

DOI: 10.1016/j.cma.2014.02.018

[3] X. Guan et al., A stochastic multiscale model for predicting mechanical properties of fiber reinforced concrete, International Journal of Solids and Structures 56-57(2015), pp.280-289.

DOI: 10.1016/j.ijsolstr.2014.10.008

[4] W. L. Oberkampf et al., Error and uncertainty in modeling and simulation, Reliability Engineering and System Safety 75(2002), pp.333-357.

DOI: 10.1016/s0951-8320(01)00120-x

[5] P. Mantovan and E. Todini, Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology, Journal of Hydrology 330(2006), pp.368-381.

DOI: 10.1016/j.jhydrol.2006.04.046

[6] K. Beven, P. Smith and J. Freer, Comment on Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology, by Pietro Mantovan and Ezio Todini, Journal of Hydrology 338(2007), pp.315-318.

DOI: 10.1016/j.jhydrol.2007.02.023

[7] J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, New York: Springer-Verlag, 2005. 339 p. Applied mathematical sciences. ISBN 03-872-2073-9.

DOI: 10.1007/b138659

[8] Y. M. Marzouk, H. N. Najm and L. A. Rahn, Stochastic spectral methods for efficient Bayesian solution of inverse problems, Journal of Computational Physics 224(2007), pp.560-586.

DOI: 10.1016/j.jcp.2006.10.010

[9] B. V. Rosić et al., Parameter Identification in a Probabilistic Setting, Engineering Structures 50(2013), pp.179-196.

[10] Y. M. Marzouk and H. N. Najm, Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems, Journal of Computational Physics 228(2009), p.1862-(1902).

DOI: 10.1016/j.jcp.2008.11.024

[11] J. R. Fonseca et al., Uncertainty identification by the maximum likelihood method, Journal of Sound and Vibration 288(2005), pp.587-599.

DOI: 10.1016/j.jsv.2005.07.006

[12] S. Fang, Q. Zhang and W. Ren, Parameter variability estimation using stochastic response surface model updating, Mechanical Systems and Signal Processing 49(2014), pp.249-263.

DOI: 10.1016/j.ymssp.2014.04.017

[13] K. Sepahvand and S. Marburg, Identification of composite uncertain material parameters from experimental modal data, Probabilistic Engineering Mechanics 37(2014), pp.148-153.

DOI: 10.1016/j.probengmech.2014.06.008

[14] M. Arnst, R. Ghanem and C. Soize, Identification of Bayesian posteriors for coefficients of chaos expansions, Journal of Computational Physics 229(2010), pp.3134-3154.

DOI: 10.1016/j.jcp.2009.12.033

[15] C. Soize, Stochastic modeling of uncertainties in computational structural dynamics - Recent theoretical advances, Journal of Sound and Vibration 332(2013), pp.2379-2395.

DOI: 10.1016/j.jsv.2011.10.010

[16] C. J. Geyer, Handbook of Markov Chain Monte Carlo, In: Introduction to Markov Chain Monte Carlo, Boca Raton, Fla.: Chapman & Hall/CRC, 2011, pp.3-48. ISBN 978-1-4200-7942-5.

DOI: 10.1201/b10905-2

[17] I. Jolliffe, Principal component analysis, 2nd ed. New York: Springer, 2002. 487 p. ISBN 03- 879-5442-2.

[18] D. Xiu and G. E. Karniadakis, The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing 24(2002), pp.619-644.

DOI: 10.1137/s1064827501387826