An adaptive response surface methodology based on active subspaces for mixed random and interval uncertainties

被引：2

作者：

Hu X. ^{[1
]}

Duan Y. ^{[1
]}

Wang R. ^{[2
]}

Liang X. ^{[3
]}

Chen J. ^{[1
]}

机构：

[1] China Aerodynamics Research and Development Center, Mianyang

[2] Institute of Applied Physics and Computational Mathematics, Beijing

[3] School of Math, Shandong University of Science and Technology, Qingdao

来源：

Journal of Verification, Validation and Uncertainty Quantification | 2019年 / 4卷 / 02期

关键词：

Adaptive response surface; Dimension reduction; Interval uncertainty; Random uncertainty; Uncertainty quantification;

D O I：

10.1115/1.4045200

中图分类号：

学科分类号：

摘要：

The popular use of response surface methodology (RSM) accelerates the solutions of parameter identification and response analysis issues. However, accurate RSM models subject to aleatory and epistemic uncertainties are still challenging to construct, especially for multidimensional inputs, which is widely existed in real-world problems. In this study, an adaptive interval response surface methodology (AIRSM) based on extended active subspaces is proposed for mixed random and interval uncertainties. Based on the idea of subspace dimension reduction, extended active subspaces are given for mixed uncertainties, and interval active variable representation is derived for the construction of AIRSM. A weighted response surface strategy is introduced and tested for predicting the accurate boundary. Moreover, an interval dynamic correlation index is defined, and significance check and cross validation are reformulated in active subspaces to evaluate the AIRSM. The effectiveness of AIRSM is demonstrated on two test examples: three-dimensional nonlinear function and speed reducer design. They both possess a dominant one-dimensional active subspace with small estimation error, and the accuracy of AIRSM is verified by comparing with full-dimensional Monte Carlo simulates, thus providing a potential template for tackling high-dimensional problems involving mixed aleatory and interval uncertainties. Copyright © 2019 by ASME

引用

共 41 条

[1]

Lee I., Choi K., Du L., Gorsich D., Dimension Reduction Method for Reliability-Based Robust Design Optimization, Comput. Struct, 86, 13, pp. 1550-1562, (2008)

[2]

Ferson S., Joslyn C. A., Helton J. C., Oberkampf W. L., Sentz K., Summary From the Epistemic Uncertainty Workshop: Consensus Amid Diversity, Reliab. Eng. Syst. Saf, 85, 1–3, pp. 355-369, (2004)

[3]

Swiler L. P., Eldred M. S., Efficient Algorithms for Mixed Aleatory-Epistemic Uncertainty Quantification With Application to Radiation-Hardened Electronics—Part I: Algorithms and Benchmark Results, (2009)

[4]

Roy C. J., Oberkampf W. L., A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing, Comput. Methods Appl. Mech. Eng, 200, 25, pp. 2131-2144, (2011)

[5]

Zang T. A., Hemsch M. J., Hilburger M. W., Kenny S. P., Luckring J. M., Maghami P., Padula S. L., Stroud W. J., National Aeronautics and Space Administration, (2002)

[6]

Mark M., Sankaran M., Uncertainty Quantification and Propagation in Multidisciplinary Analysis and Optimization, (2008)

[7]

Le Maitre O. P., Knio O. M., Introduction: Uncertainty Quantification and Propagation, (2010)

[8]

Yao W., Chen X., Huang Y., van Tooren M., An Enhanced Unified Uncertainty Analysis Approach Based on First Order Reliability Method With Single-Level Optimization, Reliab. Eng. Syst. Saf, 116, pp. 28-37, (2013)

[9]

Steenackers G., Guillaume P., Vanlanduit S., Robust Optimization of an Airplane Component Taking Into Account the Uncertainty of the Design Parameters, Qual. Reliab. Eng. Int, 25, 3, pp. 255-282, (2009)

[10]

Park C., Haftka R. T., Kim N. H., Remarks on Multi-Fidelity Surrogates, Struct. Multidiscip. Optim, 55, 3, pp. 1029-1050, (2017)

← 1 2 3 4 5 →