Aiming at dealing with the model validation issue for multi-output model with the mixture of random and interval inputs

a new model validation metric is proposed. Based on the probability method and interval theory

characteristics of multi-output model involving both random and interval inputs under the fixed random variables are analyzed. The new multi-output model validation metric is defined by extending the multi-output model validation method based on Mahalanobis distance (MD) under random inputs to multi-output model with the mixture of random and interval inputs. This metric provides a comparison between the MD cumulative distribution function (CDF) curves of the upper and lower bounds from model responses to which from experimental one

and meanwhile shows disagreement with model predictions and corresponding physical observations. Finally

estimation procedures are presented with a discussion of new metric properties and the correctness and effectiveness of the proposed metric are demonstrated by a numerical and an engineering case

respectively. Results show that: the new metric

on one hand

is able to measure the difference between system responses with experimental results under sufficient physical observations; and

on the other hand

can correctly differentiate models in worse or better accuracy.