A validation metric for model with mixture of random and interval variables

The existing model validation methods under uncertainty based on theory of probability are only applicable to validate model with random variables, but inapplicable to validate model with the mixture of random and interval variables. To address this issue, the validation method for model with the mixture of random and interval variables is studied in this paper. First, the characteristics of the mathematical model with the mixture of random and interval variables are analyzed. Second, a new validation metric is proposed by using interval theory and probability method. This metric provides a comparison between the cumulative distribution functions (CDFs) of the upper and the lower bounds of the model responses and the empirical CDFs of the upper and the lower bounds of the experimental responses to show the disagreement between the quantitative predictions from a model and the physical observations. The mathematical properties of the new metric are discussed, and its estimation method and procedures are presented. Finally, the feasibility and effectiveness of the proposed validation metric are illustrated by a numerical test case and an engineering application with mixture of random and interval variables.