• 论文 •

### 随机和区间变量共存条件下的模型确认指标

1. 1. 西北工业大学 航空学院, 西安 71007;
2. 空军工程大学 装备管理与安全工程学院, 西安 710051
• 收稿日期:2017-05-22 出版日期:2018-05-20 发布日期:2017-09-18
• 通讯作者: 吕震宙 E-mail:zhenzhoulu@nwpu.edu.cn
• 作者简介:赵录峰,男,博士研究生。主要研究方向:可靠性工程、模型确认;吕震宙,女,教授,博士生导师。主要研究方向:可靠性工程、灵敏度分析、模型确认和多学科优化;阚丽娟,女,博士研究生。主要研究方向:安全性工程。
• 基金资助:
国家自然科学基金（51475370）；中央高校基本科研业务费专项资金（3102015BJ（Ⅱ）CG009）

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

ZHAO Lufeng1, LYU Zhenzhou1, KAN Lijuan2

1. 1. School of Aeronautics, Northwestern Polytechnical University, Xi'an 71007;
2. Equipment Management and Safety Engineering College, Air Force Engineering University, Xi'an 710051, China
• Received:2017-05-22 Online:2018-05-20 Published:2017-09-18

Abstract: 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.