概率盒框架下多响应模型确认度量方法
作者:
作者单位:

(1. 厦门大学航空航天学院,福建厦门361005;2. 南京航空航天大学机电学院,南京210016)

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E-mail: bqzhang@xmu.edu.cn.

中图分类号:

TP273

基金项目:

国家自然科学基金项目(51505398);国家自然科学基金委员会与中国工程物理研究院联合基金项目(U1530122);航空科学基金项目(20150968003);中央高校基本科研业务费专项资金项目(20720170044);江苏省高校自然科学基金项目(16KJD110007).


Model validation metrics with multiple correlated responses under the frame of probability box
Author:
Affiliation:

(1. School of Aerospace Engineering,Xiamen University,Xiamen361005,China;2. College of Mechanical and Electrical Engineering,Nanjing University of Aeronautics & Astronautics,Nanjing210016,China)

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    摘要:

    在随机和认知混合不确定性表征的概率盒框架下,提出一种多响应模型确认度量方法.概率盒框架下的模型确认度量主要采用面积方法量化仿真与实验结果的一致程度,但传统面积度量方法并不适用于多个相关响应量的多输出确认度量问题.不确定性条件下多响应量模型确认度量问题,实质上是量化计算模型的多个响应量的联合概率分布与实验观测数据所服从的联合概率分布之间的差异程度.对此,引入马氏距离的概念对多响应量模型确认度量问题进行降维,以马氏距离作为转换的统计量,将多响应量的多指标确认度量问题转化为马氏距离的综合指标度量问题.数值仿真算例验证了所提出方法的正确性和稳定性,并将该方法应用于“2014年圣地亚验证与确认挑战问题”的研究.研究表明,基于概率盒和马氏距离的确认度量方法可以有效解决多相关响应量多输出模型确认度量问题.

    Abstract:

    A model validation metric for multiple response is presented under the framework of probability box that characterized by mixed aleatory and epistemic uncertainties. Area metric is mainly used to quantify the measurement of agreement between the simulation results and experimental observations under the framework of the probability box. However, the traditional area metric is not suitable for validation activities with multiple outputs when the responses are related with each other. Multi-response model validation metric considering uncertainty conditions, actually returns the quantification of the difference between joint probability distribution functions of simulation results and experimental observations. The Mahalanobis distance is introduced to convert the multi-dimensional samples into Mahalanobis distance values. Then, the cumulative probability distribution function of Mahalanobis distance is defined, and probability box of the simulation and experimental observations is obtained by double-deck Monte Carlo sampling. As a result, the validation metric for multiple responses is converted into the calculation of the area of the Mahalanobis distance. A simulation example verifies the effectiveness and stability of the proposed method, and it is applied to study the “2014 Sandia Verification and Validation Challenge” engineering problem. The research demonstrates that the proposed validation metric for multiple related responses based on the Mahalanobis distance and probability box is feasible and effective.

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张保强,苏国强,展铭,等.概率盒框架下多响应模型确认度量方法[J].控制与决策,2019,34(12):2642-2648

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  • 在线发布日期: 2019-12-04
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