MCMC Approach for Parameter Estimation in the Structural Analysis and Prognosis

  • Received : 2010.10.29
  • Accepted : 2010.12.06
  • Published : 2010.12.31


Estimation of uncertain parameters is required in many engineering problems which involve probabilistic structural analysis as well as prognosis of existing structures. In this case, Bayesian framework is often employed, which is to represent the uncertainty of parameters in terms of probability distributions conditional on the provided data. The resulting form of distribution, however, is not amenable to the practical application due to its complex nature making the standard probability functions useless. In this study, Markov chain Monte Carlo (MCMC) method is proposed to overcome this difficulty, which is a modern computational technique for the efficient and straightforward estimation of parameters. Three case studies that implement the estimation are presented to illustrate the concept. The first one is an inverse estimation, in which the unknown input parameters are inversely estimated based on a finite number of measured response data. The next one is a metamodel uncertainty problem that arises when the original response function is approximated by a metamodel using a finite set of response values. The last one is a prognostics problem, in which the unknown parameters of the degradation model are estimated based on the monitored data.


Supported by : National Research Foundation of Korea (NRF)


  1. Anand, L. (1985) Constitutive Equations for Hot-Working of Metals, International Journal of Plasticity, 1, pp.213-231.
  2. Andrieu, C., Freitas, N.D., Doucet, A., Jordan, M. (2003) An Introduction to MCMC for Machine Learning, Machine Learning, 50, pp.5-43.
  3. Bayes, T. (1763) An Essay Towards Solving a Problem in the Doctrine of Chances, Philosophical Transactions of the Royal Society of London, 53, pp.370-418.
  4. Coppe, A., Haftka, R., Kim, N. (2010) Least Squarebased Bayesian Updating to Reduce Uncertainty in Damage Growth Properties, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA, AIAA 2010-2593.
  5. Luo, J., Pattipati, K.R., Qiao, L., Chigusa, S. (2008) Model-based Prognostic Techniques Applied to a Suspension System, IEEE Transactions on System, Man and Cybernetics, 38(5), pp.1156-1168.
  6. O'Hagan, A. (2006) Bayesian Analysis of Computer Code Outputs: A Tutorial, Reliability Engineering and System Safety, 91, pp.1290-1300.
  7. Paris, P.C., Tada, H., Donald, J.K. (1999) Service Load Fatigue Damage-a Historical Perspective, International Journal of Fatigue, 21, pp.35-46.
  8. Pollack, D. (2003) Validity of Constitutive Properties of ANAND Model as Applied to Thermo-Mechanical Deformation Analysis of Eutectic Solder, Master of Science Thesis, University of Maryland.
  9. Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P. (1989) Design and Analysis of Computer Experiments, Statistical Science, 4(4), pp.409-423.