Model-form uncertainty in structural reliability: a variety of modellings

For a long time, deterministic approaches have been taking account of model uncertainty (also called model-form uncertainty) through model coefficients. However, the model coefficient is not rigorously defined in the deterministic approach. Following Ditlevsen's approach, this paper reminds that it is acceptable to propose a probabilistic representation of model uncertainty. A variety of probabilistic modellings for model uncertainty appear in the literature. Some common issues can be pointed out. All modellings include unknown parameters as well as a residual error term. These parameters, likely to be calibrated to improve the predictability of the model, are incorporated either to the base model, or, in the most common representation, to a corrective term representing the systematic bias of the base model. The paper presents these two main modellings, as well as a proposal of more general representation and an overview of some common simplifications. This work was an input to the SICODYN funded research project aiming at a better predictivity of structural dynamics models. Some indications about the three main uncertainty treatment methodologies applied in this project are given