考虑已知不确定性的随机Kriging建模方法

系统仿真学报 ›› 2016, Vol. 28 ›› Issue (6): 1261-1272.

考虑已知不确定性的随机Kriging建模方法

王波^{1, 2}, HaechangGea², 白俊强³, 张玉东¹, 宫建¹, 张卫民¹

1.中国航天空气动力技术研究院研发中心,北京 100074;
2.新泽西州立大学机械宇航学院,新泽西,Piscataway 08854;
3.西北工业大学航空学院,西安 710072

收稿日期:2015-07-08 修回日期:2015-11-17 出版日期:2016-06-08 发布日期:2020-06-08

Stochastic Kriging for Random Simulation Metamodeling with Known Uncertainty

Wang Bo^{1, 2}, Gea Haechang², Bai Junqiang³, Zhang Yudong¹, Gong Jian¹, Zhang Weimin¹

1. Research and Development Center, China Academy of Aerospace Aerodynamics, Beijing 100074, China;
2. Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA;
3. School of Aeronautics, Northwestern Polytechnical University of China, Xi’an 710072, China;

Received:2015-07-08 Revised:2015-11-17 Online:2016-06-08 Published:2020-06-08
About author:Wang Bo(1984-), Gender: Male, Born in Neihuang, China, Han nationality, Degree: Doctor, Interest: Metamodeling, Aircraft Design, CFD. Haechang Gea, Gender: Male, Degree: Doctor, Interest: Optimization, Uncertainty.
Supported by:
National Natural Science Foundation of China (11302213)

摘要/Abstract

摘要： 近年来考虑不确定性的设计引起了各领域越来越多的关注。为了解决不确定性研究中计算量大的问题,构建了针对已知不确定性问题的随机Kriging模型,所建立模型通过将固有不确定性假设引入随机Kriging模型最初问题的构建和固有不确定性相关性的推导,以充分考虑输入变量的随机性因素。三个基础算例被用来测试所构建模型相对于已有随机Kriging建模方法的优势,结果显示本文所构建随机Kriging模型是相比确定性的Kriging理论更具通用性的方法,适用于对各非均等已知不确定性问题的预测,解决了已有模型无法得到可信估计方差的问题。

关键词: 随机问题, 不确定性估计, 代理模型, Kriging方法

Abstract: Uncertainty-based design has been widely carried out these years. In order to deal with the problems with large amount of calculation, a stochastic kriging for random simulation metamodeling with known uncertainty was derived, which firstly included intrinsic uncertainty in metamodel initial formulation to fully account for inputs uncertainty, and then incorporated the correlationships of intrinsic uncertainty among all observed points. Several examples with known uncertainty were also conducted, in which the proposed method shows much better variance predictions than other similar methods. Simulation results show the proposed method is a more general form of kriging, which can also widely deal with the uncertainty-based problems with heterogeneous variances as a stochastic metamodel.

Key words: stochastic problems, uncertainty estimation, metamodeling, kriging method

中图分类号:

TP391.9

王波, HaechangGea, 白俊强, 张玉东, 宫建, 张卫民. 考虑已知不确定性的随机Kriging建模方法[J]. 系统仿真学报, 2016, 28(6): 1261-1272.

Wang Bo, Gea Haechang, Bai Junqiang, Zhang Yudong, Gong Jian, Zhang Weimin. Stochastic Kriging for Random Simulation Metamodeling with Known Uncertainty[J]. Journal of System Simulation, 2016, 28(6): 1261-1272.

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