Study on a Data-Enabled Physics-Informed Reactor Physics Operational Digital Twin
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摘要: 为了快速精准地在线计算和预测核反应堆运行行为，提出一种基于物理指引和数据增强的反应堆物理运行数字孪生，以实现堆芯快、热群中子通量分布、功率分布等物理场的快速和精确计算。基于模型降阶技术和机器学习构建中子物理快速计算模型，实现物理指引；基于快速计算模型构建反问题模型，实现数据驱动。通过“华龙一号”反应堆设计运行数据测试表明：数字孪生在时间和精度方面均满足工程要求，具备在线监测工程应用的潜力。
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关键词:
- 数字孪生 /
- 模型降阶 /
- 机器学习 /
- 本征正交分解（POD） /
- 核反应堆物理
Abstract: To realize the fast and accurate online calculation and to predict the operation behavior of nuclear reactors, a physics-informed data-enabled reactor physics operational digital twin is proposed, to achieve rapid and accurate calculation of physical fields such as fast and thermal neutron flux and power distribution in the core. The physics-informed property is achieved through a fast calculation model of neutronics based on model order reduction technology and machine learning; the data enabled property is realized through an inverse model based on the fast calculation model. The test of the design and operation data of HPR1000 reactor shows that the digital twin meets the engineering requirements in terms of time and accuracy, and has the potential for online monitoring applications in real engineering. -
图 1 KNN与DT机器学习预测的第1、2、3和40维POD系数与真实值的比较
Figure 1. Comparison of 1st, 2nd, 3rd and 40th Dimensional POD Coefficients Predicted by KNN and DT Machine Learning with Real Values
图 2 KNN与DT机器学习预测的物理场在测试集上的均方误差随POD基函数维数的变化
Figure 2. The Variation of the Mean Square Error of the Physical Field predicted by KNN and DT Machine Learning on the Test Set with the Dimension of POD Basis Function
表 1 KNN、DT及POD在3组输入参数样本上的物理场重构精度比较
Table 1. Comparison of Physical Field Reconstruction Accuracy of KNN, DT and POD on Three Groups of Input Parameter Samples
输入参数
样本序号参数向量 均方误差/% Bu/
[MW·d/t(U)]St/步 Pw /%FP Tin/℃ POD KNN DT 1 344 100 79.6 292.0 0.55 2.1 2.2 2 107 150 84.6 298.9 0.59 2.4 2.7 3 473 50 89.3 293.2 0.65 1.8 1.8 
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表 2 6组真实输入参数与初始估计输入参数设置
Table 2. 6 Groups of Real Input Parameters and Initial Estimated Input Parameter Settings
样本序号 真实输入参数 初始估计输入参数 Bu/ [MW·d/t(U)] St/步 Pw /%FP Tin/℃ Bu/[MW·d/t(U)] St/步 Pw /%FP Tin/℃ 1 0 0 61.11 291.76 20 100 61.11 291.76 2 200 500 73.51 290.54 210 600 71.51 293.54 3 400 1000 28.03 298.74 400 1000 18.00 293.54 4 500 1000 52.96 291.51 500 1000 35.00 297.54 5 130 1500 52.15 291.01 120 1700 52.15 300.00 6 130 1500 52.15 291.01 130 1480 52.15 300.00
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表 3 根据KNN和DT求解器求解反问题获得的最佳估计输入参数
Table 3. Best Estimated Input Parameters Obtained by Solving the Inverse Problem Based on KNN and DT Solvers
样本序号 μKNN μDT Bu/[MW·d/t(U)] St/步 Pw /%FP Tin/℃ Bu/[MW·d/t(U)] St/步 Pw /%FP Tin/℃ 1 0 17.7 58.30 287.40 196.1 545.3 72.86 288.01 2 198.8 679.1 70.76 288.21 394.4 917.5 28.77 297.34 3 400.7 998.7 31.65 290.13 502.7 1046.3 54.61 289.71 4 501.6 1035.3 51.07 295.52 133.4 1523.7 41.74 305.07 5 128.9 1607.9 48.34 295.93 129.9 1484.1 51.40 296.37 6 133.1 1506.1 49.24 292.63 13.4 4.5 56.64 285.93
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表 4 利用初始参数根据KNN和DT求解器求解正问题及利用观测值求解反问题获得的物理场与真实物理场的均方误差 %
Table 4. The Mean Square Error between the Physical Field and the Real Physical Field Obtained by Using the Initial Parameters to Solve the Forward Problem Based on KNN and DT Solvers and the Inverse Problem Using the Observed Value
样本序号 POD KNN 正问题 KNN 反问题 DT 正问题 DT 反问题 1 0.47 8.41 0.63 9.98 0.57 2 0.64 2.92 0.93 2.14 0.64 3 0.74 3.21 1.01 5.41 0.72 4 0.62 3.74 0.72 2.80 1.31 5 0.61 2.73 0.91 4.50 1.02 6 0.61 2.71 0.85 4.55 1.33
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