Abstract The proper orthogonal decomposition (POD) method has been applied in nuclear reactor physics to extract features of dominant flux or power. In particular, the gappy POD method is used to handle field reconstruction problems based on incomplete data due to limited observations. However, one important question is that the observation data is never noise-free in practice, which might result in blurred property of the gappy POD method, for example, the estimation error might no longer converge or even diverge as the data size increases. To address this issue, a stabilized gappy POD method is proposed within the data assimilation framework, which involves the preknowledge of the manifold structure of the physical states and the L-curve for setting regularization parameter. This method is applied to simulate the power distribution during the control rods movement process for the HPR1000 reactor core. In the numerical experiments, the stabilized gappy POD approach uses some dominant POD basis vectors and a small number of sensor signals, to obtain accurate reconstructed field with low computational cost. In addition, the stabilized gappy POD method has been integrated into the CORCA-3D code package to assimilate the observation data of nuclear reactors, which shows more stable result than the 3D-Var and CC methods used at present.

中文翻译：

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基于稳定间隙适当正交分解方法的反应堆功率分布检测和估计

摘要 适当的正交分解（POD）方法已应用于核反应堆物理中以提取主导通量或功率的特征。特别是，gappy POD 方法用于处理基于有限观察的不完整数据的场重建问题。然而，一个重要的问题是，观测数据在实践中从来都不是无噪声的，这可能会导致间隙 POD 方法的属性模糊，例如，随着数据量的增加，估计误差可能不再收敛甚至发散。为了解决这个问题，在数据同化框架内提出了一种稳定的gappy POD方法，该方法涉及物理状态流形结构的预知和用于设置正则化参数的L曲线。该方法用于模拟HPR1000反应堆堆芯控制棒运动过程中的功率分布。在数值实验中，稳定的间隙 POD 方法使用一些占优势的 POD 基向量和少量传感器信号，以较低的计算成本获得准确的重建场。此外，稳定的gappy POD方法已集成到CORCA-3D代码包中以同化核反应堆的观测数据，显示出比目前使用的3D-Var和CC方法更稳定的结果。