模型确认热传导挑战问题求解的贝叶斯方法

doi:CNKI:11-1929/V.20110402.1751.002

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模型确认热传导挑战问题求解的贝叶斯方法

张保强¹, 陈国平¹, 郭勤涛²

1. 南京航空航天大学机械结构力学与控制国家重点实验室, 江苏南京 210016;
2. 南京航空航天大学机电学院, 江苏南京 210016

收稿日期:2010-11-02 修回日期:2010-12-03 出版日期:2011-07-25 发布日期:2011-07-23
作者简介:张保强(1981- ) 男,博士研究生。主要研究方向:复杂结构动力学有限元建模、模型修正和模型确认。 Tel: 025-84892197 E-mail: zbq0533@126.com 陈国平(1956- ) 男,博士,教授,博士生导师。主要研究方向:复杂结构动力学与控制,结构减振和振动控制,飞行器结构抗坠撞仿真。 Tel: 025-84895983 E-mail: gpchen@nuaa.edu.cn 郭勤涛(1970- ) 男,博士,副教授,硕士生导师。主要研究方向:机械结构动态设计和优化,计算/试验联合建模,大型复杂结构有限元建模、模型修正、模型确认,机械振动工程。 Tel: 025-84892905 E-mail: guo_qintao@nuaa.edu.cn
基金资助:
国家"863"计划 (2008AA12A205); 南京航空航天大学基本科研业务费专项科研项目(NJ2010009,NS2010006,NS20100124)

Solution of Model Validation Thermal Challenge Problem Using a Bayesian Method

ZHANG Baoqiang¹, CHEN Guoping¹, GUO Qintao²

1. The State Key Laboratory of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2010-11-02 Revised:2010-12-03 Online:2011-07-25 Published:2011-07-23

摘要/Abstract

摘要： 为了进一步推动模型确认方法的发展并明确其具体实施步骤,以圣地亚国家实验室提出的模型确认热传导挑战问题为例,建立了模型确认的贝叶斯框架,并阐述模型确认的思想以及实现的一般过程。模型确认不仅是一个评定仿真模型准确度的过程,而且是一个通过确认结果提高模型预测精度的过程。首先介绍了贝叶斯及不确定性量化的基本理论,强调了模型修正在模型确认中的作用,然后比较了各种模型修正方法的优缺点,最后将贝叶斯模型修正用于热传导问题的模型确认中,得到了比初始模型更准确的预测结果。研究表明贝叶斯模型修正方法用于模型确认能显著提高预测精度。

关键词: 模型确认, 不确定性分析, 不确定性量化, 热传导挑战问题, 贝叶斯模型修正, 预测

Abstract: To further promote the development of model validation and understand the specific implementation steps of model validation, the framework, ideas and general process for model validation utilizing Bayesian method are achieved by the example of model validation thermal challenge problem presented in Sandia National Laboratories. Model validation is not merely a process of assessing the accuracy of a simulation model, but also a process to improve the predictive precision through the model validation results. The basic theories of Bayesian analysis and uncertainty quantification are introduced and several model updating methods are emphasized and compared in model validation. Finally, the Bayesian model updating method is applied to model validation thermal challenge problem, and more accurate prediction results are obtained than those from the initial model. The results demonstrate that the model predictive precision can be significantly improved when utilizing Bayesian model updating method in model validation.

Key words: model validation, uncertainty analysis, uncertainty quantification, thermal challenge problem, Bayesian model updating, prediction

中图分类号:

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.

ZHANG Baoqiang, CHEN Guoping, GUO Qintao. Solution of Model Validation Thermal Challenge Problem Using a Bayesian Method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(7): 1202-1209.

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[12] 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.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

模型确认热传导挑战问题求解的贝叶斯方法

Solution of Model Validation Thermal Challenge Problem Using a Bayesian Method

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