基于MCMC方法的子通道程序模型参数不确定性量化分析研究  

Uncertainty quantification methodology for model parameters in sub-channel codes using MCMC sampling

作　　者：何鑫[1] 宋美琪 刘晓晶[1,2] HE Xin;SONG Meiqi;LIU Xiaojing(College of Smart Energy,Shanghai Jiao Tong University,Shanghai 200240,China;School of Nuclear Science and Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学智慧能源创新学院,上海200240 [2]上海交通大学核科学与工程学院,上海200240

出　　处：《核技术》2023年第12期120-128,共9页Nuclear Techniques

基　　金：国家自然科学基金(No.U20B2011)资助。

摘　　要：假定模型参数的不确定性服从正态分布,根据贝叶斯原理,其最可能的分布是结合先验信息和观测信息得到的最大后验概率,马尔科夫链蒙特卡罗(Markov Chain Monte Carlo,MCMC)抽样适用于此类反问题求解。鉴于随机论方法的巨大计算量,本研究利用BP(Back Propagation)神经网络及相对熵最小化来自适应加密训练数据,从而建立替代复杂正向程序的代理模型,并利用开发的不确定性分析程序对影响空泡份额的模型参数不确定性进行量化分析,选用的子通道程序为COBRA-IV。结果表明:在求得模型参数不确定性后,通过不确定性正向传递得到结果的95%置信区间对实验值的包络性较好,利用不确定性均值对模型进行标定得到的结果较基准值更接近实验值。因此,本研究建立的不确定性量化分析方法能较好适用于子通道程序的不确定性分析。[Background]Traditional safety analysis methods rely on expert advice and user self-evaluation,lacking the ability to quantify output uncertainty.In contrast,the best estimation plus uncertainty(BEPU)methodology can quantify the uncertainty of the output,thereby avoiding unnecessary conservative assumptions and improving the economic viability of nuclear power.It is now widely used in the design and safety analysis of nuclear reactors.However,owing to the cognitive limitations of science and numerical approximation in programs,most thermalhydraulic programs lack sufficient input uncertainty information related to internal models,often relying on expert advice.[Purpose]This study aims to investigate the uncertainty quantification methodology for model parameters in sub-channel codes using Markov Chain Monte Carlo(MCMC)sampling.[Methods]Firstly,the PSBT void fraction distribution experiments were employed to evaluate the prediction ability of the subchannel program COBRA-IV,and a Python-based uncertainty analysis methodology was developed to quantitatively analyze the model parameter uncertainties that affect the void fraction.Then,the model parameters were assumed to be independent,with their uncertainties following a normal distribution.Based on the Bayesian principle,the most likely maximum a posteriori probability function(PDF)of the model parameters were obtained by combining the prior and observed information,despite the limited actual uncertainty information.Finally,an MCMC sampling methodology was adopted to solve the Bayesian relation,and the statistical uncertainty information of the model parameters were obtained using a stable a posteriori Markov chain,which requires at least 104 magnitudes to achieve convergence and the corresponding forward program runs.Therefore,to reduce the calculation cost and improve the calculation efficiency,a highprecision adaptive BPNN surrogate model was constructed to replace the complex and time-consuming forward program code.Furthermore,a set of uncertainty quantification

关 键 词：马尔科夫链蒙特卡罗抽样 代理模型 不确定性分析 空泡份额 反问题求解 

分 类 号：TL99[核科学技术—核技术及应用]