基于贝叶斯因子和二阶概率方法的圣地亚热传导模型确认挑战问题
收稿日期: 2013-12-02
修回日期: 2014-05-12
网络出版日期: 2014-05-28
基金资助
国防预研项目（426010401）；中国工程物理研究院科学技术发展基金（2012B0403058）
Sandia Model Validation Thermal Challenge Problem Based on Bayes Factor and Second-order Probability Method
Received date: 2013-12-02
Revised date: 2014-05-12
Online published: 2014-05-28
Supported by
National Defense Pre-research Foundation (426010401); Science and Technology Development Foundation of China Academy of Engineering Physics (2012B0403058)
针对美国圣地亚国家实验室为促进模型确认方法的发展所提出的热传导挑战问题，根据现代模型确认思想总结了该挑战问题解答中应包含的核心内容。在确认度量环节采用贝叶斯因子考察了实验数据是否支持所给模型，在此基础上通过二阶概率方法得到了模型预测的分布，以此计算出模型预测结论的置信度。该过程中考虑了模型参数的随机不确定性和认知不确定性，最后通过灵敏度分析辨识了模型参数的不确定性对模型预测的影响。研究表明该挑战问题中的实验数据支持所给模型，模型预测受导热系数的不确定性影响最大，模型预测材料在调控条件下的失效概率不满足调控要求，该结论的置信度为99.97%。
赵亮 , 杨战平 . 基于贝叶斯因子和二阶概率方法的圣地亚热传导模型确认挑战问题[J]. 航空学报, 2014 , 35(9) : 2513 -2521 . DOI: 10.7527/S1000-6893.2014.0097
The objective of the thermal model validation challenge problem presented at American Sandia National Laboratory is to develop methodologies associated with model validation. The article summarizes the key content to answer this problem based on modern model validation idea. Bayes factor is employed as a validation metric to find whether the experimental data supports the model. The distribution of model prediction is obtained by the second-order probability method which propagates both aleatory uncertainty and epistemic uncertainty through the model, and the confidence of the model prediction is calculated from the distribution. Finally the article makes a sensitivity analysis with the model parameters to identify their effects on the prediction. The study indicates that the experimental data supports the given model, the thermal conductivity contributes most to the uncertainty in the model prediction, and with 99.97% confidence we can conclude that the failure probability of the material under regulatory condition predicted by the model doesn't meet the regulatory criterion.
[1] American Institute of Aeronautics and Astronautics. Guide for the verification and validation of computational fluid dynamics simulations, AIAA-1998-G-077[R]. Reston: AIAA, 1998.
[2] American Society of Mechanical Engineers. ASME V&V 20-2008 Standard for verification and validation in computational fluid dynamics and heat transfer[S]. New York: ASME, 2008.
[3] National Aeronautics and Space Administration. NASA-STD-7009 Standard for models and simulations[S]. Washington, D.C.: NASA, 2008.
[4] Trucano T G, Swiler L P, Igusa T, et al. Calibration, validation, and sensitivity analysis: what's what[J]. Reliability Engineering and System Safety, 2006, 91(10-11): 1331-1357.
[5] Roy C J, Oberkampf W L. A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(25-28): 2131-2144.
[6] Hills R G, Pilch M, Dowding K J, et al. Validation challenge workshop[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32): 2375-2380.
[7] Dowding K J, Pilch M, Hills R G. Formulation of the thermal problem[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32): 2385-2389.
[8] McFarland J, Mahadevan S. Multivariate significance testing and model calibration under uncertainty[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32): 2467-2479.
[9] Hills R G, Dowding K J. Multivariate approach to the thermal challenge problem[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32): 2442-2456.
[10] 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.
[11] Liu F, Bayarri M J, Berger J, et al. A Bayesian analysis of the thermal challenge problem[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32): 2457-2466.
[12] Higdon D, Nakhleh C, Gattiker J, et al. A Bayesian calibration approach to the thermal problem[J]. Computer Methods in Applied Mechanics and Engineering, 2008, 197(29-32): 2431-2441.
[13] Zhang B Q, Chen G P, Guo Q T. Solution of model validation thermal challenge problem using a Bayesian method[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(7): 1202-1209. (in Chinese) 张保强, 陈国平, 郭勤涛. 模型确认热传导挑战问题求解的贝叶斯方法[J]. 航空学报, 2011, 32(7): 1202-1209.
[14] Saltelli A, Scott M. The role of sensitivity analysis in the corroboration of models and its link to model structural and parametric uncertainty[J]. Reliability Engineering and System Safety, 1997, 57: 1-4.
[15] Ghosh J K, Delampady M, Samanta T. An introduction to Bayesian analysis[M]. New York: Springer, 2006: 163-185.
[16] Sankararaman S, Mahadevan S. Model validation under epistemic uncertainty[J]. Reliability Engineering and System Safety, 2011, 96(9): 1132-1241.
[17] Swiler L P, Giunta A A. Aleatory and epistemic uncertainty quantification for engineering applications, SAND2007-2670C[R]. Albuquerque: Sandia National Laboratories, 2007: 14-16.
[18] Saltelli A, Ratto M, Tarantola S, et al. Sensitivity analysis practices: Strategies for model-based inference[J]. Reliability Engineering and System Safety, 2006, 91(10-11): 1109-1125.
/
| 〈 |
|
〉 |
CJA