随机和认知不确定性框架下的CFD模型确认度量综述

doi:10.7527/S1000-6893.2021.25716

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随机和认知不确定性框架下的CFD模型确认度量综述

夏侯唐凡¹, 陈江涛², 邵志栋¹, 吴晓军², 刘宇^1,3

1. 电子科技大学机械与电气工程学院, 成都 611731;
2. 中国空气动力研究与发展中心计算空气动力研究所, 绵阳 621000;
3. 电子科技大学系统可靠性与安全性研究中心, 成都 611731

收稿日期:2021-04-27 修回日期:2021-08-18 出版日期:2022-08-15 发布日期:2021-08-17
通讯作者: 刘宇,E-mail:yuliu@uestc.edu.cn E-mail:yuliu@uestc.edu.cn
基金资助:
国家数值风洞工程(NNW2020ZT7-B32)

Model validation metrics for CFD numerical simulation under aleatory and epistemic uncertainty

XIAHOU Tangfan¹, CHEN Jiangtao², SHAO Zhidong¹, WU Xiaojun², LIU Yu^1,3

1. School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
3. Center for System Reliability and Safety, University of Electronic Science and Technology of China, Chengdu 611731, China

Received:2021-04-27 Revised:2021-08-18 Online:2022-08-15 Published:2021-08-17
Supported by:
National Numerical Wind Tunnel Project (NNW2020ZT7-B32)

摘要/Abstract

摘要： 随着计算机技术迅猛发展,计算流体力学(CFD)数值模拟技术已广泛应用于航空航天、船舶、风力、水利等领域,为装备的复杂流体分析、性能参数评估以及产品气动设计与优化提供重要验证与决策手段。现有的CFD技术都是在确定性的数学模型、物理参数、边界条件下进行数值模拟的。然而,由于物理过程的复杂性及人们的认知偏差,CFD技术中存在着模型参数、数值离散、模型形式等诸多不确定性因素且表征形式各异,给CFD数值模拟的可信度评估带来了极大挑战。文章阐述了CFD技术中面临的不确定性因素,探讨了主流模型确认度量方法的应用条件和适用范围。着重介绍在认知不确定性下的模型确认度量方法,包括几类重要的区间、概率盒下模型确认度量方法。通过NACA0012翼型绕流问题说明了CFD技术中考虑各种不确定性下的模型确认度量方法的有效性。

关键词: 计算流体力学(CFD), 数值模拟, 模型确认, 认知不确定性, 概率盒

Abstract: With the emergence of new computer technologies, Computational Fluid Dynamics (CFD) numerical simulation has been extensively implemented in many areas such as aerospace, national defense, ship hydrodynamics, wind power, and water conservancy. CFD numerical simulation provides effective decision-making and validation methods for complex fluid analysis of equipment, model parameter evaluation, and aerodynamic optimization design. Existing CFD simulations are conducted under the premises of deterministic mathematical models, fixed physical parameters, and fixed boundary conditions. Due to the complexity of physics and cognitive biases of human beings, there are, however, many potential uncertain factors with different representation forms in CFD, such as model parameter uncertainty, numerical dispersion, and model form uncertainty, resulting in a great challenge to the credibility of CFD simulation results. This article elaborates on the uncertain factors encountered in CFD, and provides a comprehensive discussion on the mainstream model validation metrics. We focus on the model validation metrics under epistemic uncertainty, including several metrics under the interval theory and probability-box theory. The NACA0012 airfoil flow problem is leveraged to demonstrate the effectiveness of the model validation metrics under various uncertainties in CFD.

Key words: Computational Fluid Dynamics (CFD), numerical simulation, model validation, epistemic uncertainty, probability-box

中图分类号:

V211
O35

夏侯唐凡, 陈江涛, 邵志栋, 吴晓军, 刘宇. 随机和认知不确定性框架下的CFD模型确认度量综述[J]. 航空学报, 2022, 43(8): 25716-025716.

XIAHOU Tangfan, CHEN Jiangtao, SHAO Zhidong, WU Xiaojun, LIU Yu. Model validation metrics for CFD numerical simulation under aleatory and epistemic uncertainty[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 25716-025716.

参考文献

[1] 余瑾, 王松, 刘勇, 等. 基于CFD/CSD松耦合的直升机配平分析方法[J]. 北京航空航天大学学报, 2020, 46(5): 941-951. YU J, WANG S, LIU Y, et al. Trim analysis method of helicopter based on CFD/CSD loose coupling[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 941-951 (in Chinese).
[2] 王友进, 郑咏岚, 张庆兵, 等. 基于CFD方法的典型防空导弹气动反设计研究[J]. 现代防御技术, 2011, 39(2): 1-6, 21. WANG Y J, ZHENG Y L, ZHANG Q B, et al. Aerodynamic inverse design of typical air defense missiles based on CFD method[J]. Modern Defence Technology, 2011, 39(2): 1-6, 21 (in Chinese).
[3] 倪崇本. 基于CFD的船舶阻力性能综合研究[D]. 上海: 上海交通大学, 2011. NI C B. A comprehensive investigation of ship resistance prediction based on CFD theory[D]. Shanghai: Shanghai Jiao Tong University, 2011 (in Chinese).
[4] 庄智, 余元波, 叶海, 等. 建筑室外风环境CFD模拟技术研究现状[J]. 建筑科学, 2014, 30(2): 108-114. ZHUANG Z, YU Y B, YE H, et al. Review on CFD simulation technology of wind environment around buildings[J]. Building Science, 2014, 30(2): 108-114 (in Chinese).
[5] 王志清. 基于CFD的水泵水轮机流场计算与分析[D]. 郑州: 华北水利水电大学, 2019. WANG Z Q. Calculation and analysis of flow field in pump turbine based on CFD[D]. Zhengzhou: North China University of Water Resources and Electric Power, 2019 (in Chinese).
[6] 唐钊. 发动机冷却风扇叶片参数的研究和优化[D]. 广州: 华南理工大学, 2012. TANG Z. A research on parameters of engine cooling fan blade and optimization[D]. Guangzhou: South China University of Technology, 2012 (in Chinese).
[7] 王一伟, 钟星立, 杜特专. 翼型多目标气动优化设计方法[J]. 计算力学学报, 2007, 24(1): 98-102. WANG Y W, ZHONG X L, DU T Z. Multi-objective optimization of airfoils[J]. Chinese Journal of Computational Mechanics, 2007, 24(1): 98-102 (in Chinese).
[8] 燕振国. 高精度数值风洞在飞行器设计中的作用[J]. 航空科学技术, 2013, 24(5): 11-14. YAN Z G. The role of TH-HiNWT in flight vehicle design[J]. Aeronautical Science & Technology, 2013, 24(5): 11-14 (in Chinese).
[9] JAMESON A. Computational fluid dynamics and airplane design: Its current and future impact[R]. Lecture in University of Cincinnati, 2008.
[10] 刘智益. 不确定性CFD模拟方法及其应用研究[D]. 北京: 华北电力大学, 2014. LIU Z Y. Investigation on non-deterministic methodologies and applications in CFD simulations[D]. Beijing: North China Electric Power University, 2014 (in Chinese).
[11] CHOI S K, GRANDHI R, CANFIELD R A. Reliability-based structural design[M].Berlin: Springer Science & Business Media, 2006.
[12] 熊芬芬, 杨树兴, 刘宇. 工程概率不确定性分析方法[M]. 北京: 科学出版社, 2015. XIONG F F, YANG S X, LIU Y. Uncertainty analysis method of engineering probability [M]. Beijing: Science Press, 2015 (in Chinese).
[13] MAHADEVAN S. Uncertainty quantification for decision-making in engineered systems[C]//Proceedings of the International Symposium on Engineering Under Uncertainty: Safety Assessment and Management (ISEUSAM-2012), 2013: 97-117.
[14] 邱志平, 王晓军, 许孟辉. 工程结构不确定优化设计技术[M]. 北京: 科学出版社, 2013. QIU Z P, WANG X J, XU M H. Uncertainty optimization technology of engineering structure [M]. Beijing: Science Press, 2013 (in Chinese).
[15] LE MAÎTRE O P, KNIO O M, NAJM H N, et al. A stochastic projection method for fluid flow: I. basic formulation[J]. Journal of Computational Physics, 2001, 173(2): 481-511.
[16] LE MAÎTRE O P, REAGAN M T, DEBUSSCHERE B, et al. Natural convection in a closed cavity under stochastic non-boussinesq conditions[J]. SIAM Journal on Scientific Computing, 2004, 26(2): 375-394.
[17] MATHELIN L, HUSSAINI M Y, ZANG T A, et al. Uncertainty propagation for a turbulent, compressible nozzle flow using stochastic methods[J]. AIAA Journal, 2004, 42(8): 1669-1676.
[18] XIU D B, KARNIADAKIS G E. Modeling uncertainty in flow simulations via generalized polynomial chaos[J]. Journal of Computational Physics, 2003, 187(1): 137-167.
[19] KNIO O M, LE MAÎTRE O P. Uncertainty propagation in CFD using polynomial chaos decomposition[J]. Fluid Dynamics Research, 2006, 38(9): 616-640.
[20] 王晓东, 康顺. 多项式混沌方法在随机方腔流动模拟中的应用[J]. 中国科学: 技术科学, 2011, 41(6): 790-798. WANG X D, KANG S. Application of polynomial chaos on numerical simulation of stochastic cavity flow[J]. Scientia Sinica (Technologica), 2011, 41(6): 790-798 (in Chinese).
[21] LING Y, MAHADEVAN S. Quantitative model validation techniques: New insights[J]. Reliability Engineering & System Safety, 2013, 111: 217-231.
[22] LIU Y, CHEN W, ARENDT P, et al. Towards a better understanding of model validation metrics[C]//13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference. Reston: AIAA, 2010: 9240.
[23] MAUPIN K A, SWILER L P, PORTER N W. Validation metrics for deterministic and probabilistic data[J]. Journal of Verification, Validation and Uncertainty Quantification, 2018, 3(3): 031002.
[24] OBERKAMPF W L, ROY C J. Verification and validation in scientific computing[M]. Cambridge: Cambridge University Press, 2010.
[25] 李文华, 苏明军. 常用湍流模型及其在FLUENT软件中的应用[J]. 水泵技术, 2006(4): 39-40, 31. LI W H, SU M J. Common turbulence models and its application in FLUENT software[J]. Pump Technology, 2006(4): 39-40, 31 (in Chinese).
[26] EDELING W N, CINNELLA P, DWIGHT R P. Predictive RANS simulations via Bayesian model-scenario averaging[J]. Journal of Computational Physics, 2014, 275: 65-91.
[27] 赵辉, 胡星志, 张健, 等. 湍流模型系数不确定度对翼型绕流模拟的影响[J]. 航空学报, 2019, 40(6): 122581. ZHAO H, HU X Z, ZHANG J, et al. Effects of uncertainty in turbulence model coefficients on flow over airfoil simulation[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(6): 122581 (in Chinese).
[28] 陈江涛, 章超, 刘骁, 等. 基于稀疏多项式混沌方法的不确定性量化分析[J]. 航空学报, 2020, 41(3): 123382. CHEN J T, ZHANG C, LIU X, et al. Uncertainty quantification analysis with sparse polynomial chaos method[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(3): 123382 (in Chinese).
[29] 钱炜祺, 周宇, 陈江涛. SA一方程湍流模型参数影响分析与辨识[J]. 航空工程进展, 2015, 6(1): 46-51. QIAN W Q, ZHOU Y, CHEN J T. Parameter influence analysis and identification of SA one-equation turbulence model[J]. Advances in Aeronautical Science and Engineering, 2015, 6(1): 46-51 (in Chinese).
[30] ERB A J, HOSDER S. Uncertainty analysis of turbulence model closure coefficients for shock wave-boundary layer interaction simulations[C]//2018 AIAA Aerospace Sciences Meeting. Reston: AIAA, 2018: 2077.
[31] ROACHE P J. Quantification of uncertainty in computational fluid dynamics[J]. Annual Review of Fluid Mechanics, 1997, 29: 123-160.
[32] EINARSSON B. Use of Richardson extrapolation for the numerical calculation of Fourier transforms[J]. Journal of Computational Physics, 1976, 21(3): 365-370.
[33] ROACHE P J. Perspective: A method for uniform reporting of grid refinement studies[J]. Journal of Fluids Engineering, 1994, 116(3): 405-413.
[34] 赵训友, 林景松, 童晓艳. 基于Richardson外推法的CFD中离散不确定度估计[J]. 系统仿真学报, 2014, 26(10): 2315-2320. ZHAO X Y, LIN J S, TONG X Y. Discretization uncertainty estimation in CFD based on Richardson extrapolation method[J]. Journal of System Simulation, 2014, 26(10): 2315-2320 (in Chinese).
[35] XING T, STERN F. Factors of safety for Richardson extrapolation[J]. Journal of Fluids Engineering, 2010, 132(6): 061403.
[36] EÇA L, HOEKSTRA M. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies[J]. Journal of Computational Physics, 2014, 262: 104-130.
[37] OBERKAMPF W L, TRUCANO T G. Verification and validation in computational fluid dynamics[J]. Progress in Aerospace Sciences, 2002, 38(3): 209-272.
[38] FERSON S, OBERKAMPF W L. Validation of imprecise probability models[J]. International Journal of Reliability and Safety, 2009, 3(1/2/3): 3.
[39] JIANG X M, MAHADEVAN S. Bayesian risk-based decision method for model validation under uncertainty[J]. Reliability Engineering & System Safety, 2007, 92(6): 707-718.
[40] LI W, CHEN W, JIANG Z, et al. New validation metrics for models with multiple correlated responses[J]. Reliability Engineering & System Safety, 2014, 127: 1-11.
[41] 赵亮, 杨战平. 基于概率分布距离的多响应模型确认度量[J]. 控制与决策, 2015, 30(6): 1014-1020. ZHAO L, YANG Z P. Multiple response model validation metric based on distance of probability distribution[J]. Control and Decision, 2015, 30(6): 1014-1020 (in Chinese).
[42] 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. 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).
[43] 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. HU J R, LYU Z Z. Model validation method 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).
[44] 张保强, 苏国强, 展铭, 等. 概率盒框架下多响应模型确认度量方法[J]. 控制与决策, 2019, 34(12): 2642-2648. ZHANG B Q, SU G Q, ZHAN M, et al. Model validation metrics with multiple correlated responses under the frame of probability box[J]. Control and Decision, 2019, 34(12): 2642-2648 (in Chinese).
[45] REBBA R, MAHADEVAN S. Validation of models with multivariate output[J]. Reliability Engineering & System Safety, 2006, 91(8): 861-871.
[46] 肖钊, 韩旭, 杨刚. 基于区间技术的模型确认方法及应用[J]. 机械工程学报, 2014, 50(14): 177-184. XIAO Z, HAN X, YANG G. Model validation method and its application based on the interval techniques[J]. Journal of Mechanical Engineering, 2014, 50(14): 177-184 (in Chinese).
[47] 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.
[48] WANG N, YAO W, ZHAO Y, et al. A new interval area metric for model validation with limited experimental data[J]. Journal of Mechanical Design, 2018, 140(6): 061403.
[49] DVORETZKY A, KIEFER J, WOLFOWITZ J. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator[J]. The Annals of Mathematical Statistics, 1956, 27(3): 642-669.
[50] FERSON S, KREINOVICK V, GINZBURG L, et al. Constructing probability boxes and dempster-shafer structures[R]. Office of Scientific and Technical Information (OSTI), 2003.
[51] HE Q S. Model validation based on probability boxes under mixed uncertainties[J]. Advances in Mechanical Engineering, 2019, 11(5): 168781401984741.
[52] 赵录峰, 吕震宙, 阚丽娟. 随机和区间变量共存条件下的模型确认指标[J]. 北京航空航天大学学报, 2018, 44(5): 967-974. ZHAO L F, LYU Z Z, KAN L J. 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 (in Chinese).
[53] MCKEAND A M, GORGULUARSLAN R M, CHOI S K. Stochastic analysis and validation under aleatory and epistemic uncertainties[J]. Reliability Engineering & System Safety, 2021, 205: 107258.
[54] BI S F, BROGGI M, BEER M. The role of the Bhattacharyya distance in stochastic model updating[J]. Mechanical Systems and Signal Processing, 2019, 117: 437-452.
[55] KENNEDY M C, O’HAGAN A. Bayesian calibration of computer models[J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2001, 63(3): 425-464.

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随机和认知不确定性框架下的CFD模型确认度量综述

Model validation metrics for CFD numerical simulation under aleatory and epistemic uncertainty

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