| Citation: | ZHAO Lufeng, LYU Zhenzhou, KAN Lijuanet al. A validation metric for model with mixture of random and interval variables[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(5): 967-974. doi: 10.13700/j.bh.1001-5965.2017.0345(in Chinese)
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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.
| [1] |
OBERKAMPF W L, ROY C J.Verification and validation in scientific computing[M].New York:Cambridge University Press, 2010:21-25.
|
| [2] |
OBERKAMPF W L, BARONE M F.Measures of agreement between computation and experiment:Validation metrics[J].Journal of Computational Physics, 2006, 217:5-36. doi: 10.1016/j.jcp.2006.03.037
|
| [3] |
OBERKAMPF W L, SINDIR M, CONLISK A.Guide for the verification and validation of computational fluid dynamics simulations[M].Reston:AIAA, 1998:2-4.
|
| [4] |
XIONG Y, CHEN W, TSUI K L, et al.A better understanding of model updating strategies in validating engineering models[J].Compute Methods in Applied Mechanics and Engineering, 2009, 189(15-16):1327-1337.
|
| [5] |
MESSER M, PANCHAL J H, KRISHNAMURTHY V, et al.Model selection under limited information using a value of information based indicator[J].Journal of Mechanical Design, 2010, 132(12):121008. doi: 10.1115/1.4002751
|
| [6] |
KENNEDY M C, O'HAGAN A.Bayesian calibration of computer models[J].Journal of the Royal Statistical Society, 2001, 63(3):425-464. doi: 10.1111/rssb.2001.63.issue-3
|
| [7] |
BAYARRI M J, BERGER J O, PAULO R, et al.A framework for validation of computer models[J].Technometrics, 2007, 49(2):138-154. doi: 10.1198/004017007000000092
|
| [8] |
ARENDT P D, APLEY D W, CHEN W, et al.Improving identifiability in model calibration using multiple responses[J].Journal of Mechanical Design, 2012, 134(10):100909. doi: 10.1115/1.4007573
|
| [9] |
ARENDT P D, APLEY D W, CHEN W.Quantification of model uncertainty:Calibration, model discrepancy, and identifiability[J].Journal of Mechanical Design, 2012, 134(10):100908. doi: 10.1115/1.4007390
|
| [10] |
LIU Y, CHEN W, ARENDT P, et al.Toward a better understanding of model validation metrics[J].Journal of Mechanical Design, 2011, 133(7):071005. doi: 10.1115/1.4004223
|
| [11] |
REBBA R, MAHADEVAN S.Validation of models with multivariate output[J].Reliability Engineering and System Safety, 2006, 91(8):861-871. doi: 10.1016/j.ress.2005.09.004
|
| [12] |
FERSON S, OBERKAMPF W L.Validation of imprecise probability models[J].International Journal of Reliability and Safety, 2009, 3:3-22. doi: 10.1504/IJRS.2009.026832
|
| [13] |
FERSON S, OBERKAMPF W L, GINZBURG L.Model validation and predictive capability for the thermal challenge problem[J].Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32):2408-2430. doi: 10.1016/j.cma.2007.07.030
|
| [14] |
赵录峰, 吕震宙, 张磊刚, 等.多输出模型确认中的混合矩指标[J].国防科技大学学报, 2015, 37(6):61-68. doi: 10.11887/j.cn.201506013
ZHAO L F, LYU Z Z, ZHANG L G, et al.Mixed moment validation metric for models with multivariate output[J].Journal of National University of Defense Technology, 2015, 37(6):61-68(in Chinese). doi: 10.11887/j.cn.201506013
|
| [15] |
LI W, CHEN W, JIANG Z, et al.New validation metrics for models with multiple correlated responses[J].Reliability Engineering and System Safety, 2014, 127:1-11. doi: 10.1016/j.ress.2014.02.002
|
| [16] |
ZHAO L F, LU Z Z, YUN W Y, et al.Validation metric based on Mahalanobis distance for models with multiple correlated responses[J].Reliability Engineering and System Safety, 2017, 159:80-89. doi: 10.1016/j.ress.2016.10.016
|
| [17] |
胡嘉蕊, 吕震宙.基于核主成分分析的多输出模型确认方法[J].北京航空航天大学学报, 2017, 43(7):1470-1480. http://bhxb.buaa.edu.cn/CN/abstract/abstract14108.shtml
HU J R, LYU Z Z.Model validation model with multivariate output based on kernel principal component analysis[J].Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7):1470-1480(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract14108.shtml
|
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