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

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

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%。

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.