Study on Quantification of Parameter Uncertainty in Reflooding Model Based on Random Forest Algorithm
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摘要: 为了评估复杂事故现象物理模型参数（输入）的不确定性，提出了基于随机森林算法结合粒子群优化Kriging（PSO-Kriging）代理模型和Sheather-Jones优化核密度估计法（KDE-SJ）非参数统计的反向不确定性量化方法，并应用于大破口事故再淹没现象的模型评估。通过将系统程序的计算结果（输出）与Flooding Experiments with Blocked Arrays（FEBA）实验数据的一致性程度作为随机森林算法的分类标准，得到了模型参数的概率密度分布。验证结果表明在概率密度分布上随机抽样93组计算得到的95%不确定度带可以完全包络实验数据，但利用众数或均值对模型的标定效果可能不如贝叶斯方法得到的最大后验均值。Abstract: In order to assess the uncertainty of physical models (inputs) of complex accidents, an inverse uncertainty quantification method based on Random Forest algorithm combined with PSO-Kriging surrogate model and KDE-SJ nonparametric statistics is proposed, and it is applied to the model assessment of reflooding in large breach accidents. The probability density distributions of the model parameters were obtained through the degree of consistency between the calculation results (output) of the system program and the FEBA experimental data as a classification criterion for the Random Forest algorithm. The validation results show that the 95% uncertainty bands obtained by randomly sampling 93 groups of calculations on the probability density distributions can completely envelope the experimental data, but the calibration effect of the model using mode or mean may not be as good as the maximum posterior mean obtained by Bayesian method.
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图 3 待测参数的概率密度直方图和KDE-SJ估计曲线
Figure 3. Probability Density Histograms and KDE-SJ Estimation Curves for the Parameters to Be Measured
图 4 待评估参数后验分布95%置信区间的RELAP5模拟与FEBA实验数据比较（214工况）
Figure 4. RELAP5 Simulations with 95% Confidence Interval of Posterior Distribution of the Parameters to Be Evaluated Compared with FEBA Experimental Data (Condition 214)
图 5 待评估参数后验分布95%置信区间的RELAP5模拟与FEBA实验数据比较（216工况）
Figure 5. RELAP5 Simulations with 95% Confidence Interval of Posterior Distribution of the Parameters to Be Evaluated Compared with FEBA Experimental Data (Condition 216)
表 1 FEBA选择工况的初始和边界条件
Table 1. Initial and Boundary Conditions for Selected FEBA Operating Conditions
工况编号 进口流速/（cm·s−1） 系统压力/MPa 进口冷却水温度/℃ 棒束功率/kW 0 s 瞬态 223 3.8 0.22 36 200 120% ANS衰变热标准 216 3.8 0.41 37 200 120% ANS衰变热标准 220 3.8 0.62 37 200 120% ANS衰变热标准 214 5.8 0.41 37 200 120% ANS衰变热标准 222 5.8 0.62 36 200 120% ANS衰变热标准 
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表 2 初始选定的输入参数及其先验范围
Table 2. Initially Selected Input Parameters and Their Priori Ranges
编号 参数名称 先验范围 P1 系统压力 0.99~1.01 P2 进口流速 0.98~1.02 P3 进口水温/℃ ±10 P4 初始加热棒壁温/℃ ±10 P5 加热棒功率 0.99~1.01 P6 NiCr 导热率 0.95~1.05 P7 NiCr 体积热容 0.95~1.05 P8 MgO 导热率 0.8~1.2 P9 MgO体积热容 0.8~1.2 P10 过渡沸腾传热系数（壁面对液相） 0.2~ 3.0 P11 过渡沸腾传热系数（壁面对汽相） 0.2~3.0 P12 膜态沸腾传热系数（壁面对液相） 0.2~3.0 P13 膜态沸腾传热系数（壁面对汽相） 0.1~2.5 P14 壁面对液相的摩擦系数（全局） 0.1~4.0 P15 壁面对汽相的摩擦系数（全局） 0.1~4.0 P16 反环状流相间传热系数（相界面对液相） 0.2~2.0 P17 反环状流相间传热系数（相界面对汽相） 0.2~2.0 P18 反塞状流相间传热系数（相界面对液相） 0.2~2.0 P19 反塞状流相间传热系数（相界面对汽相） 0.2~2.0 P20 弥散流相间传热系数（相界面对液相） 0.2~2.0 P21 弥散流相间传热系数（相界面对汽相） 0.2~2.0 P22 弥散流相间摩擦系数 0.2~4.0 P23 最小液滴直径/mm （液滴直径基准值为1.5 mm） 0.5~2.5 P24 润湿前沿判断温度/K（温度基准值为710 K） ±20 P1、P2、P5、P6、P7、P8、P9参数的先验范围均为该参数在系统标准值的系数变化范围
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表 3 构建决策树的自定义特征
Table 3. Customized Features for Building Decision Trees
编号 特征 编号 特征 特征1 包壳3315 mm处最高温度 特征7 包壳3315 mm处润湿时间 特征2 包壳2770 mm处最高温度 特征8 包壳2770 mm处润湿时间 特征3 包壳2225 mm处最高温度 特征9 包壳2225 mm处润湿时间 特征4 包壳1135 mm处最高温度 特征10 包壳1680 mm处润湿时间 特征5 包壳590 mm处最高温度 特征11 包壳1135 mm处润湿时间 特征6 包壳1680 mm处最高温度 特征12 包壳590 mm处润湿时间
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表 4 A类参数的统计均值和标准差
Table 4. Statistical Means and Standard Deviations of Class A Parameters
参数 均值 标准差 过渡沸腾传热系数（壁面对气相） 1.5199 0.77636 膜态沸腾传热系数（壁面对液相） 1.5914 0.60788 弥散流相间传热系数 1.0425 0.65900 弥散流相间摩擦系数 2.3362 1.03410
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