Model Uncertainty in Finite-Element Analysis: Bayesian Finite Elements

In this paper, probabilistic models for structural analysis are put forward, with particular emphasis on model uncertainty. Context is provided by the finite-element method and the need for probabilistic prediction of structural performance in contemporary engineering. Sources of model uncertainty are identified and modeled. A Bayesian approach is suggested for the assessment of new model parameters within the element formulations. The expressions are formulated by means of numerical "sensors" that influence the model uncertainty, such as element distortion and degree of nonlinearity. An assessment procedure is proposed to identify the sensors that are most suitable to capture model uncertainty. This paper presents the general methodology and specific implementations for a general-purpose structural element. Two numerical examples are presented to demonstrate the methodology and its implications for probabilistic prediction of structural response.