Model validation based on random set theory

This paper considers the model validation under epistemic uncertainty in model inputs. The random set theory is used to quantify the uncertainty of model prediction. With the probability box obtained by the random set theory, a pignistic probability transformation is applied to construct a single probability distribution to be the prior distribution for the model prediction. Then a posterior probability distribution is updated based on the experimental observations in Bayesian principle. The Bayes factor derived from the ratio between the posterior and the prior probability distributions is used as the validation metric to quantify the extent to which the experimental observations support the model. A thermal conduction example and an aerospace bolted joint example are presented to illustrate the proposed method. It is shown that the method presented in this paper provides a convenient mechanism to consider different types of uncertainty during the model validation.