随机和区间变量共存条件下的模型确认指标

现有的不确定性模型确认方法建立在概率理论基础之上，仅仅适用于随机不确定性因素影响下的模型确认，而不适合随机和区间变量共存条件下的模型确认问题。针对这一问题，研究了随机和区间变量共存条件下的模型确认方法。首先，分析了随机和区间变量共存条件下数学模型的特点；然后，运用概率方法和区间理论，提出了一种新的模型确认指标，通过模型响应量的上下界分布函数（CDF）与实验响应量的上下界经验CDF之间差异，来度量随机和区间输入变量共存条件下模型预测与实际物理实验结果之间的不一致性；讨论了所提指标的数学性质，给出了指标的计算方法和步骤；最后，采用一个数字算例和一个工程算例验证了所提指标在随机和区间输入变量共存条件下进行模型确认的可行性和有效性。

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 ran-dom 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 dis-cussed,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 mix-ture of random and interval variables.