Advertisement

Sampling Techniques in Bayesian Finite Element Model Updating

  • I. BoulkaibetEmail author
  • T. Marwala
  • L. Mthembu
  • M. I. Friswell
  • S. Adhikari
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main problem in the development and updating of FEMs. This paper highlights the complexities and challenges of implementing any Bayesian method when the analysis involves a complicated structural dynamic model. In such systems an analytical Bayesian formulation might not be available in an analytic form; therefore this leads to the use of numerical methods, i.e. sampling methods. The main challenge then is to determine an efficient sampling of the model parameter space. In this paper, three sampling techniques, the Metropolis-Hastings (MH) algorithm, Slice Sampling and the Hybrid Monte Carlo (HMC) technique, are tested by updating a structural beam model. The efficiency and limitations of each technique is investigated when the FEM updating problem is implemented using the Bayesian Approach. Both MH and HMC techniques are found to perform better than the Slice sampling when Young’s modulus is chosen as the updating parameter. The HMC method gives better results than MH and Slice sampling techniques, when the area moment of inertias and section areas are updated.

Keywords

Bayesian Finite element model updating Hybrid monte carlo method Markov chain monte carlo Metropolis- hastings method Sampling Slice sampling method 

References

  1. 1.
    Onãte E (2009) Structural analysis with the finite element method. Linear statics, vol 1, Basis and solids. Springer, Dordrecht/LondonzbMATHCrossRefGoogle Scholar
  2. 2.
    Rao SS (2004) The finite element method in engineering, 4th edn. Elsevier Butterworth Heinemann, BurlingtonGoogle Scholar
  3. 3.
    Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer, Dordrecht/BostonzbMATHCrossRefGoogle Scholar
  4. 4.
    Marwala T (2010) Finite element model updating using computational intelligence techniques. Springer, LondonzbMATHCrossRefGoogle Scholar
  5. 5.
    Yuen KV (2010) Bayesian methods for structural dynamics and civil engineering. Wiley, New YorkCrossRefGoogle Scholar
  6. 6.
    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):243–255CrossRefGoogle Scholar
  7. 7.
    Ewins DJ (1984) Modal testing: theory and practice. Research Studies, LetchworthGoogle Scholar
  8. 8.
    Guyan RJ (1965) Reduction of stiffness and mass matrices. Am Inst Aeronaut Astronaut 11(5):380–388Google Scholar
  9. 9.
    Bishop CM (2006) Pattern recognition and machine learning. Springer, New YorkzbMATHGoogle Scholar
  10. 10.
    Marwala T, Sibisi S (2005) Finite element model updating using Bayesian approach. In: Proceedings of the international modal analysis conference, Orlando, ISBN: 0-912053-89-5Google Scholar
  11. 11.
    Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press, Oxford, UKGoogle Scholar
  12. 12.
    Vapnik VN (1995) The nature of statistical learning theory. Springer, New YorkzbMATHCrossRefGoogle Scholar
  13. 13.
    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):1962–1974CrossRefGoogle Scholar
  14. 14.
    Neal RM (2000) Slice sampling. Technical Report, No. 2005, Department of Statistics, University of TorontoGoogle Scholar
  15. 15.
    Hanson KM (2001) Markov Chain Monte Carlo posterior sampling with the Hamiltonian method. Proc SPIE 4322:456–467CrossRefGoogle Scholar
  16. 16.
    Kraaij CS (2007) Model updating of a ‘clamped’-free beam system using FEMTOOLS. Technische Universiteit EindhovenGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2012 2012

Authors and Affiliations

  • I. Boulkaibet
    • 1
    Email author
  • T. Marwala
    • 1
  • L. Mthembu
    • 1
  • M. I. Friswell
    • 2
  • S. Adhikari
    • 3
  1. 1.The Centre For Intelligent System Modelling (CIMS), Electrical and Electronics Engineering DepartmentUniversity of JohannesburgAuckland ParkSouth Africa
  2. 2.Aerospace Structures, College of EngineeringSwansea UniversitySwanseaUK
  3. 3.Aerospace Engineering, College of EngineeringSwansea UniversitySwanseaUK

Personalised recommendations