Mechanical model comparison using Sobol’ indices

Resumo

Models are mathematical representations capable of describing phenomena in different scenarios. Usu-
ally, two or more models are available for the same phenomenon, which leaves the choice of the most suitable

model to the user. In practice, simplified models can be as precise as more refined ones and, simultaneously, less

demanding in terms of computational power. In this work, we present a novel approach for measuring the discrep-
ancy between models when considering the randomness of the variables. We first define a uniformly distributed

random variable that chooses which model is employed to evaluate the response. A global sensitivity analysis
(GSA) is then performed by determining Sobol’ total index of the response with respect to this variable. The result
reveals the importance of choosing between one model or another and indicates the level of discrepancy between
them in the stochastic context. Two numerical examples are presented, indicating the kind of insight the proposed
approach produces.