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

doi:10.7527/S1000-6893.2014.0097

Abstract

Abstract:

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.

Key words: model validation challenge problem, Bayes factor, validation metric, second-order probability method, model prediction, sensitivity analysis

CLC Number:

ZHAO Liang, YANG Zhanping. Sandia Model Validation Thermal Challenge Problem Based on Bayes Factor and Second-order Probability Method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(9): 2513-2521.

References

[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.

Sandia Model Validation Thermal Challenge Problem Based on Bayes Factor and Second-order Probability Method

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Le JIANG, Yibiao CHEN, Yanjun LI, Guilin LI, Tao LIU. Flow and separation characteristics of pressurized centrifugal separator for aero⁃engine [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(2): 128675-128675.
[2]	Kailing ZHANG, Siyi LI, Yi DUAN, Chao YAN. Uncertainty quantification of parameters in SST turbulence model for inlet simulation [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729429-729429.
[3]	Zhe LIU, Xige ZHANG, Changzhu WEI, Naigang CUI. High-precision adaptive convex programming for reentry trajectories of suborbital vehicles [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729430-729430.
[4]	Xiaozhe SUN, Dong HOU, Jianzhong YANG. Mechanism and sensitivity of force fight in dual redundant electromechanical actuators [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727661-727661.
[5]	Zhichuang CHEN, Shenghong GE, Zhuolei ZHANG, Yuchuan ZHU. Internal leakage distribution model and parameter sensitivity analysis of spool valve couple at zero position [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(6): 427004-427004.
[6]	Zhikai WANG, Sheng CHEN, Wei FAN. Effect of neural network width on combustor emission prediction [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 126816-126816.
[7]	Bin WANG, Jianjun ZHENG, Wei LIU, Gaoli WANG. Testing load transacting method based on assessment target equivalent [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(17): 228064-228064.
[8]	Zhenkang ZHANG, Wanwu XU, Zhiyan LI, Wei YE. Uncertainty quantification analysis of blunt cone radiation equilibrium temperature [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(15): 528673-528673.
[9]	Bowen SHU, Jiangtao HUANG, Zhenghong GAO, Gang LIU, Chengjun HE, Lu XIA. Sensitivity analysis of vector performance of two⁃dimensional shock vector control nozzle [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(13): 127831-127831.
[10]	Wanying YUN, Zhenzhou LYU. An efficient surrogate method for analyzing parameter global reliability sensitivity [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(12): 227670-227670.
[11]	Muchen WU, Jiangtao CHEN, Tangfan XIAHOU, Wei ZHAO, Yu LIU. Separating sensitivity analysis of aleatory and epistemic uncertainties in non-parametric probability-box [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 226658-226658.
[12]	Haoge LI, Hua YANG, Yuxin YANG, Weifang CHEN. Refinement optimization design for heat reduction on windward surface of hypersonic lifting body [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 124-137.
[13]	WANG Rui, ZHOU Zhou, GUO Ronghua, HUANG Yuechen. Multi-body dynamics simulation and experiment of solar-powered UAV parachute landing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 225721-225721.
[14]	ZHANG Donghui, ZHANG Taihua, CUI Yanxiang, CHEN Chen, WANG Sheng. Sensitivity analysis of aerodynamic parameters of stratospheric tethered balloon [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 125083-125083.
[15]	CAO Fan, ZHANG Meifang, HU Xiao, TANG Zhili. Natural laminar flow optimization and transition sensitivity analysis of axisymmetric nacelle [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 527330-527330.