Quantification of model-form and parametric uncertainty using evidence theory

It is common that two or more models can be created to predict responses of a physical system. Given a set of physical models, the response predictions might be significantly influenced by model-form uncertainty, which occurs due to the lack of certainty in selecting the true (or at least the best) one from the model set. In this paper, a mathematical methodology is developed to quantify both model-form and parametric uncertainty using expert evidence within evidence theory. Using the belief structure associated with evidence theory, degrees of belief are numerically specified for subsets of a model set. Response predictions supported by the subsets of a model set are integrated into a composite prediction using the disjunctive rule of combination. A nonlinear spring–mass system is utilized to demonstrate the process for implementing the proposed approach. Finally, the applicability of the approach to large-scale engineering problems is investigated through a problem of simulating a laser peening process depending on different material model theories.

▸ A new approach is developed to quantify both model-form and parametric uncertainty using expert evidence within evidence theory. ▸ The constraint that probability theory demands regarding assigning model probability is loosen to effectively represent imprecise expert judgments. ▸ Predictions of a model set which involve parametric uncertainty are combined using the disjunctive rule of combination. ▸ The applicability of the proposed approach to engineering problems is investigated by addressing a large-scale simulation problem.