随机-区间混合不确定性多输出模型确认指标

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.