Abstract
The use of Bayesian techniques in Finite Element Model (FEM) updating has recently increased. These techniques have the ability to quantify and characterize the uncertainties of dynamic structures. In order to update a FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this functions is either difficult (or not available) to solve in an analytical way. In such cases using sampling techniques can provide good approximations of the Bayesian posterior distribution function. The Hybrid Monte Carlo (HMC) method is a powerful sampling method for solving higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) as a global Monte Carlo (MC) move to reach areas of high probability. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate MD trajectory. To overcome this, we propose the use of the Separable Shadow Hybrid Monte Carlo (S2HMC) method. This method generates samples from a separable shadow Hamiltonian. The accuracy and the efficiency of this sampling method is tested on the updating of a GARTEUR SM-AG19 structure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Onãte E (2009) Structural analysis with the finite element method. Linear statics. Volume 1: basis and solids. Springer, Dordrecht
Rao SS (2004) The finite element method in engineering, 4th edn. Elsevier Butterworth Heinemann, Burlington
Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer Academic Publishers, Dordrecht
Marwala T (2010) Finite element model updating using computational intelligence techniques. Springer, London, UK
Bishop CM (2006) Pattern recognition and machine learning. Springer, New York
Yuen KV (2010) Bayesian methods for structural dynamics and civil engineering. Wiley, New York
Cheung SH, Beck JL (2009) Bayesian model updating using Hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters. J Eng Mech 135(4):243–255
Boulkaibet I, Marwala T, Mthembu L, Friswell MI, Adhikari S (2012) Sampling techniques in Bayesian finite element model updating. Proc Soc Exp Mech 29:75–83
Izaguirre JA, Hampton SS, Comput J (2004) Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules. J Comput Phys 200:581–604
Neal RM (2000) Slice sampling. Technical report no. 2005. Department of Statistics, University of Toronto
Hanson KM (2001) Markov Chain Monte Carlo posterior sampling with the Hamiltonian method. Proc SPIE 4322:456–467
Ewins DJ (1984) Modal testing: theory and practice. Research Studies Press, Letchworth
Marwala T, Sibisi S (2005) Finite element model updating using Bayesian approach. In Proceedings of the international modal analysis conference, Orlando, FL, USA, 2005. ISBN: 0-912053-89-5
Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press, Oxford
Ching J, Leu SS (2009) Bayesian updating of reliability of civil infrastructure facilities based on condition-state data and fault-tree model. Reliab Eng Syst Saf 94(12):1962–1974
Boulkaibet I, Mthembu L, Marwala T, Friswell MI, Adhikari S (2013) Finite element model updating using the shadow hybrid Monte Carlo technique. Proc Soc Exp Mech 6:489–498
Sweet CR, Hampton SS, Skeel RD, Izaguirre JA (2009) A separable shadow Hamiltonian hybrid Monte Carlo method. J Chem Phys 131(17):174106
Beskos A, Pillai NS, Roberts GO, Sanz-Serna JM, Stuart AM (2013) Optimal tuning of the hybrid Monte-Carlo algorithm. Bernoulli 19: 1501–1534
Carvallo J, Datta BN, Gupta A, Lagadapati M (2007) A direct method for model updating with incomplete measured data and without spurious modes. Mech Syst Signal Process 21(7):2715–2731
Datta BN (2002) Finite element model updating, eigenstructure assignment and eigenvalue embedding techniques for vibrating systems. Mech Syst Signal Process 16:83–96
Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182
Link M, Friswell MI (2003) Generation of validated structural dynamic models—results of a benchmark study utilizing the GARTEUR SM-AG19 Testbed. Mech Syst Signal Process 17(1):9–20, COST Action Special Issue
Mthembu L (2012) Finite element model updating. Ph.D. thesis, Faculty of Engineering and the Built Environment, University of the Witwatersrand
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Boulkaibet, I., Mthembu, L., Marwala, T., Friswell, M.I., Adhikari, S. (2014). Finite Element Model Updating Using the Separable Shadow Hybrid Monte Carlo Technique. In: Allemang, R. (eds) Topics in Modal Analysis II, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04774-4_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-04774-4_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04773-7
Online ISBN: 978-3-319-04774-4
eBook Packages: EngineeringEngineering (R0)