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Bayesian Treatment of Spatially-Varying Parameter Estimation Problems via Canonical BUS

  • Sadegh RahrovaniEmail author
  • Siu-Kiu Au
  • Thomas Abrahamsson
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

The inverse problem of identifying spatially-varying parameters, based on indirect/incomplete experimental data, is a computationally and conceptually challenging problem. One issue of concern is that the variation of the parameter random field is not known a priori, and therefore, it is typical that inappropriate discretization of the parameter field leads to either poor modelling (due to modelling error) or ill-condition problem (due to the use of over-parameterized models). As a result, classical least square or maximum likelihood estimation typically performs poorly. Even with a proper discretization, these problems are computationally cumbersome since they are usually associated with a large vector of unknown parameters. This paper addresses these issues, through a recently proposed Bayesian method, called Canonical BUS. This algorithm is considered as a revisited formulation of the original BUS (Bayesian Updating using Structural reliability methods), that is, an enhancement of rejection approach that is used in conjunction with Subset Simulation rare-event sampler. Desirable features of CBUS to treat spatially-varying parameter inference problems have been studied and performance of the method to treat real-world applications has been investigated. The studied industrial problem originates from a railway mechanics application, where the spatial variation of ballast bed is of our particular interest.

Keywords

Bayesian methodology Bayesian updating using structural reliability methods (BUS) Subset simulation (SS) Stochastic simulation Rare-event sampler 

References

  1. 1.
    Beck, J.: Bayesian system identification based on probability logic. Struct. Control. Health Monit. 17, 825–847 (2010)CrossRefGoogle Scholar
  2. 2.
    Yuen, K.: Bayesian Methods for Structural Dynamics and Civil Engineering. Wiley, Hoboken (2010)CrossRefGoogle Scholar
  3. 3.
    Muto, M., Beck, J.: Bayesian updating and model class Selection for hysteretic structural models using stochastic simulation. J. Vib. Control. 14(1–2), 7–34 (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Robert, C., Casella, G.: A short history of Markov Chain Monte Carlo subjective recollections from incomplete data. Stat. Sci. 26(1), 102–115 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Spall, J.: Estimation via Markov Chain Monte Carlo. IEEE Control. Syst. 23(2), 34–45 (2003)CrossRefGoogle Scholar
  6. 6.
    Green, P., Worden, K.: Bayesian and MCMC methods for identifying nonlinear systems in the presence of uncertainty. Phil. Trans. R. Soc. A 373 (2015)Google Scholar
  7. 7.
    Au, S.-K., Beck, J.: Estimation of small failure probabilities in high dimensions by subset simulation. Probab. Eng. Mech. 16(4), 263–277 (2001)CrossRefGoogle Scholar
  8. 8.
    Au, S.-K., Wang, Y.: Engineering Risk Assessment with Subset Simulation. Wiley, Singapore (2014)CrossRefGoogle Scholar
  9. 9.
    Webster, C., Zhang, G., Gunzburger, M.: An adaptive sparse-grid iterative ensemble Kalman filter approach for parameter field estimation. Int. J. Comput. Math. 91(4), 798–817 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Koutsourelakis, P.: A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters. J.Comput. Phys. 228, 6184–6211 (2009)CrossRefzbMATHGoogle Scholar
  11. 11.
    Straub, D., Papaioannou, I.: Bayesian updating with structural reliability methods. J. Eng. Mech. 04014134 (2015). doi: 10.1061/(ASCE)EM.1943-7889.0000839
  12. 12.
    Au, S.-K., DiazDelaO, F.A., Yoshida, I.: Bayesian updating and model class selection with subset simulation. Probab. Eng. Mech. 16(4), 263–277 (2016)CrossRefGoogle Scholar
  13. 13.
    Lilja, J., Abrahamsson, T., Nielsen, J.: Experimental investigation of stochastic boundary conditions – planning a railway sleeper test. In: A Conference on Structural Dynamics (IMAC). Springer, Florida (2008)Google Scholar
  14. 14.
    Ching, J., Chen, Y.: Transitional Markov Chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging. J. Eng. Mech. 133(7), 816–832 (2007)CrossRefGoogle Scholar
  15. 15.
    Cheng, Y., Au, F., Cheung, Y.: Vibration of railway bridges under a moving train by using bridge-track-vehicle element. Eng. Struct. 23(12), 1597–1606 (2001)CrossRefGoogle Scholar
  16. 16.
    Zhai, W., Wang, K., Lin, J.: Modelling and experiment of railway ballast vibrations. J. Sound Vib. 270(4–5), 673–683 (2004)CrossRefGoogle Scholar
  17. 17.
    Lam, H., Wong, M., Yang, Y.: A feasibility study on railway ballast damage detection utilizing measured vibration. Eng. Struct. 45, 284–298 (2012)CrossRefGoogle Scholar
  18. 18.
    Lam, H., Hu, Q., Wong, M.: The Bayesian methodology for the detection of railway ballast damage under a concrete sleeper. Eng. Struct. 81, 289–301 (2014)CrossRefGoogle Scholar
  19. 19.
    Kaewunruen, S., Remennikov, A.: Progressive failure of prestressed concrete sleepers under multiple high-intensity impact loads. Eng. Struct. 31(10), 2460–2473 (2009)CrossRefGoogle Scholar
  20. 20.
    Design of mono-bloc concrete sleepers. In: UIC leaflet 713 R, pp. 30 (2004)Google Scholar
  21. 21.
    European standard EN 13230:1:2002: Railway Applications-Track-Concrete Sleepers and Bearers, pp. 36 (2002)Google Scholar
  22. 22.
    Rahrovani, S.: Test data evaluation from field measurements of sleeper-ballast interface. Chalmers University of Technology, Goteborg (2010)Google Scholar
  23. 23.
    Buekett, J.: Concrete sleepers. In: Railway Industry Association, First Track Sector course, Warford, pp. 411–417 (1983)Google Scholar
  24. 24.
    Nielsen, J., Igeland, A.: Vertical dynamic interaction between train and track – influeince of wheel and track imperfections. J. Sound Vib. 187(5), 825–839 (1995)CrossRefGoogle Scholar
  25. 25.
    Bolmsvik, R., Nielsen, J., Singhal, A.: Guideline for design optimization and production of prestressed concrete railway sleepers, Chalmers University, Applied Mechanics, Goteborg, Research report 2011:5 (2011)Google Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Sadegh Rahrovani
    • 1
    Email author
  • Siu-Kiu Au
    • 2
  • Thomas Abrahamsson
    • 1
  1. 1.Department of Applied MechanicsChalmers University of TechnologyGothenburgSweden
  2. 2.School of Engineering, University of LiverpoolLiverpoolUK

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