Bayesian methods for characterizing unknown parameters of material models

• Published in: Applied mathematical modelling 2016-07, Vol.40 (13-14), p.6395-6411
• Main Authors: Emery, J.M., Grigoriu, M.D., Field Jr, R.V.
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Bayesian method; Computer simulation; Mathematical analysis; Mathematical models; MATHEMATICS AND COMPUTING; Monte Carlo methods; Reduced order models; Stochastic reduced order models; Stochasticity; Transport equations; Uncertain material parameters
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2016.01.046

•A Bayesian method is developed for parameters of material properties.•The method is applied to spatial correlation in a stochastic conductivity field.•The method is also used for material properties of laser welds.•For the laser welds, the method rapidly converges when one variate is assumed.•However, for a bi-variate problem we discover an unexpected non-uniqueness. A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). The Bayesian method is also employed to characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.