A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria

• Published in: Computer methods in applied mechanics and engineering 2008-05, Vol.197 (29), p.2517-2539
• Main Authors: Babuška, I., Nobile, F., Tempone, R.
• Format: Article
• Language: English
• Subjects: Applied mathematics; Bayesian updates; Exact sciences and technology; Failure probability; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); MATEMATIK; MATHEMATICS; Model validation; Physics; Solid mechanics; Structural and continuum mechanics; Tillämpad matematik; Uncertainty quantification
• ISSN: 0045-7825; 1879-2138; 1879-2138
• DOI: 10.1016/j.cma.2007.08.031

This work describes a solution to the validation challenge problem posed at the SANDIA Validation Challenge Workshop, May 21–23, 2006, NM. It presents and applies a general methodology to it. The solution entails several standard steps, namely selecting and fitting several models to the available prior information and then sequentially rejecting those which do not perform satisfactorily in the validation and accreditation experiments. The rejection procedures are based on Bayesian updates, where the prior density is related to the current candidate model and the posterior density is obtained by conditioning on the validation and accreditation experiments. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.