Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Online Input and State Estimation in Structural Dynamics Read chapter Read first chapter

2016 | OriginalPaper | Chapter

6. An Adaptive Markov Chain Monte Carlo Method for Bayesian Finite Element Model Updating

Authors : I. Boulkaibet, T. Marwala, M. I. Friswell, S. Adhikari

Published in: Special Topics in Structural Dynamics, Volume 6

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, an adaptive Markov Chain Monte Carlo (MCMC) approach for Bayesian finite element model updating is presented. This approach is known as the Adaptive Hamiltonian Monte Carlo (AHMC) approach. The convergence rate of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm is high due to its trajectory which is guided by the derivative of the posterior probability distribution function. This can lead towards high probability areas in a reasonable period of time. However, the HMC performance decreases when sampling from posterior functions of high dimension and when there are strong correlations between the uncertain parameters. The AHMC approach, a locally adaptive version of the HMC approach, allows efficient sampling from complex posterior distribution functions and in high dimensions. The efficiency and accuracy of the AHMC method are investigated by updating a real structure.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Detection and Identification of Firearms Upon Discharge Using Floor-Based Accelerometers
next chapter Modal Parameters of Multiple-Disk Shaft System from Multiple Reference Impact Test
Literature
1.
Bhatti, M.A.: Fundamental Finite Element Analysis and Applications. Wiley, New York (2005)
2.
Onãte, E.: Structural Analysis with the Finite Element Method. Linear Statics, vol. 1: Basis and Solids. Springer, Dordrecht (2009)
3.
Rao, S.S.: The Finite Element Method in Engineering, 4th edn. Elsevier Butterworth Heinemann, Burlington (2004)
4.
Friswell, M.I., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics. Kluwer, Academic Publishers, Dordrecht (1995)
5.
Marwala, T.: Finite Element Model Updating Using Computational Intelligence Techniques. Springer, London, UK (2010)CrossRefMATH
6.
Boulkaibet, I., Mthembu, L., De Lima Neto, F., Marwala, T.: Finite element model updating using fish school search optimization method. In: 1st BRICS & 11th CBIC Brazilian Congress on Computational Intelligence, Brazil, 2013
7.
Boulkaibet, I., Mthembu, L., De Lima Neto, F., Marwala, T.: Finite element model updating using fish school search and volitive particle swarm optimization. Integr. Comput. Aid. Eng. 22(4), 361–376 (2015)CrossRef
8.
Yuen, K.V.: Bayesian Methods for Structural Dynamics and Civil Engineering. Wiley, New York (2010)CrossRef
9.
Haddad Khodaparast, H.: Stochastic Finite Element Model Updating and its Application in Aero-Elasticity. Ph.D. Thesis, University of Liverpool (2010)
10.
Marwala, T., Sibisi, S.: Finite element model updating using Bayesian approach. In: Proceedings of the International Modal Analysis Conference, Orlando, Florida, USA, 2005. ISBN: 0-912053-89-5
11.
Moens, D., Vandepitte, D.: Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis. Arch. Comput. Meth. Eng. 13(3), 389–464 (2006)MathSciNetCrossRefMATH
12.
Hanss, M., Willner, K.: A fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters. Mech. Res. Commun. 27(3), 257–272 (2000)CrossRefMATH
13.
Boulkaibet, I., Mthembu, L., Marwala, T., Friswell, M.I., Adhikari, S.: Finite element model updating using the shadow hybrid Monte Carlo technique. Mech. Syst. Sig. Process. 52, 115–132 (2015)CrossRef
14.
Boulkaibet, I., Marwala, T., Mthembu, L., Friswell, M.I., Adhikari, S.: Finite element model updating using an evolutionary Markov Chain Monte Carlo algorithm. Dyn. Civil Struct. 2, 245–253 (2015)
15.
Boulkaibet, I., Mthembu, L., Marwala, T., Friswell, M.I., Adhikari, S.: Finite element model updating using the separable shadow hybrid Monte Carlo technique. Top. Modal Anal. II 8, 267–275 (2014)
16.
Boulkaibet, I., Marwala, T., Mthembu, L., Friswell, M.I., Adhikari, S.: Sampling techniques in bayesian finite element model updating. Top. Model Validat. Uncertain. Quantif. 4, 75–83 (2012)CrossRef
17.
Boulkaibet, I.: Finite element model updating using Markov Chain Monte Carlo techniques. Ph.D. Thesis, University of Johannesburg (2015)
18.
Mares, C., Mottershead, J.E., Friswell, M.I.: Stochastic model updating: part 1—theory and simulated example. Mech. Syst. Sig Process. 20(7), 1674–1695 (2006)CrossRef
19.
Nichols, J., Link, W., Murphy, K., Olson, 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 (2001)CrossRef
20.
Ching, J., Muto, M., Beck, J.L.: Structural model updating and health monitoring with incomplete modal data using Gibbs Sampler. Comput. Aid. Civil Infrast. Eng. 21(4), 242–257 (2006)CrossRef
21.
Ching, J., Chen, Y.J.: Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133(7), 816–832 (2007)CrossRef
22.
Muto, M., Beck, J.L.: Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. J. Vib. Control 14, 7–3 (2008)CrossRefMATH
23.
Cheung, S.H., Beck, J.L.: 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 (2009)CrossRef
24.
Duane, S., Kennedy, A.D., Pendleton, B.J., Roweth, D.: Hybrid Monte Carlo. Phys. Lett. B 195(2), 216–222 (1987)CrossRef
25.
Kennedy, A.D., Pendleton, B.: Acceptances and autocorrelations in hybrid Monte Carlo. Nucl. Phys. B Proc. Suppl. 20, 118–121 (1991)CrossRef
26.
Beskos, A., Pillai, N.S., Roberts, G.O., Sanz-Serna, J.M., Stuart, A.M.: Optimal tuning of the hybrid Monte-Carlo algorithm. Bernoulli, 319(5A), 1501–1534 (2011)
27.
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)MATH
28.
Neal, R.M., MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, volume 2, pp. 113–162. Chapman & Hall/CRC Press, Boca Raton, FL (2011)
29.
30.
Metadata
Title
An Adaptive Markov Chain Monte Carlo Method for Bayesian Finite Element Model Updating
Authors
I. Boulkaibet
T. Marwala
M. I. Friswell
S. Adhikari
Copyright Year
2016
Book
Special Topics in Structural Dynamics, Volume 6

Print ISBN: 978-3-319-29909-9

Electronic ISBN: 978-3-319-29910-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-29910-5_6

Premium Partners

    Image Credits