In this study, a Bayesian framework is outlined for the parameter estimation that arises during the uncertainty quantification in the numerical simulation as well as in the prognosis of the structural performance. In the framework, the parameters are estimated in the form of posterior distribution conditional on the provided data. Several case studies that implement the estimation are presented to illustrate the concept. First one is an inverse estimation, in which the unknown input parameters are inversely estimated based on a finite number of measured response data. 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. Third and fourth one are a prognostics problem, in which the unknown parameters of the degradation model are estimated based on the monitored data. During the numerical implementation, Markov Chain Monte Carlo (MCMC) method is employed, which is a modern computational technique for the efficient and straightforward estimation of parameters. Once the samples are obtained, one can proceed to the posterior predictive inference on the response at the unobserved points or at the future time in the form of confidence interval.
How to Cite
Bayesian framework, inverse estimation, metamodel uncertainty, prognostics and health management (PHM), Markov Chain Monte Carlo (MCMC)
Andrieu, C., Freitas, N. D., Doucet, A. & Jordan, M. (2003). An introduction to MCMC for Machine Learning, Machine Learning, vol. 50, pp. 5-43.
Archard, J. F. (1953). Contact and rubbing of flat surfaces, Journal of Applied Physics, vol. 24, pp. 981-988. Bayes, T. (1763). An Essay towards solving a Problem in the Doctrine of Chances, Philosophical Transactions of the Royal Society of London, vol. 53, pp. 370-418.
Coppe, A., Haftka, R. T. & Kim, N. H. (2010), Least Squares-Filtered Bayesian Updating for Remaining Useful Life Estimation, 51st AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, Florida.
Mauntler, N., Kim, N. H., Sawyer, W. G. & Schmitz, T. L. (2007). An instrumented crank-slider mechanism for validation of a combined finite element and wear model, in Proceedings 22nd Annual Meeting of American Society of Precision Engineering, Dallas, Texas.
O'Hagan, A. (2006). Bayesian Analysis of Computer Code Outputs: A Tutorial, Reliability Engineering and System Safety, vol. 91, pp. 1290-1300.
Paris, P. C., Tada, H. & Donald, J. K. (1999). Service load fatigue damage - a historical perspective, International Journal of fatigue, vol. 21, pp. 35-46.
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.
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.