结合定性知识的定量贝叶斯模型外推方法

A Bayesian Inference Method for Model Extrapolation Together with Qualitative Knowledge

针对新设计域中试验数据有限而难以进行模型验证的问题,提出了定性知识与定量贝叶斯推理相结合的模型外推方法.其中,量化方法用于将领域专家意见等定性知识转化为先验概率;贝叶斯网络及限定抽样范围的蒙特卡罗方法用于定量推理,并通过贝叶斯区间假设检验的贝叶斯可信度提供模型外推结果.对Sandia国家实验室某静态力学结构的研究表明,该方法能有效实现新设计域不确定性系统的模型可信度外推.

In order to resolve the problem of model validation with limited test data in the untested domain, this paper presented an extrapolation method together with qualitative knowledge and quantitative Bayesian inference. Qualitative information such as the subject matter experts＇ opinions is transformed to prior probability in the proposed quantification method and applied to Bayesian inference. The Bayesian network with Monte Carlo method which is limited in sampling range is explored for extrapolating quantitatively the inference from the validated domain at the component level to the applied domain at the system level. And Bayesian interval hypothesis testing is performed on the evaluated quantity to assess the model validity. A simplified version of a static frame challenge problem developed by Sandia National Laboratories demon- strates that the method provides a valid approach to facilitate rational decisions in confidence extrapolation.