Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Capture Cross Sections
Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Capture Cross Sections
复制标题
应用于亚临界实验反应堆物理基准的综合二阶伴随灵敏度分析方法 (2nd-ASAM)：I. 不精确已知的微观总截面和俘获截面的影响
作者：
D. Cacuci;R. Fang;J. Favorite
包括在核能机构(NEA)国际临界安全基准评估项目(ICSBEP)手册中的亚临界聚乙烯反射钚(PerP)金属基础物理基准已被选为一个范例说明性反应堆物理系统，用于应用CACCI开发的二阶伴随灵敏度分析方法(Second-ASAM)。2-ASAM允许对系统响应的一阶和二阶灵敏度的精确值进行详尽的确定性计算。本文利用空间和角度独立变量离散的确定性多群中子输运方程对PEP基准进行了数值模拟。因此，PERP基准的数值模型包括以下不精确的已知不确定参数：180个群平均总微观截面，21,600个群平均散射微观截面，120个裂变过程参数，60个裂变谱参数，10个描述实验核源的参数，以及6个同位素数密度。因此，PERP基准的数值模拟模型包含21,976个不确定参数，这意味着，对于任何感兴趣的响应，对模型参数总共有21,976个一阶灵敏度和482,944,576个二阶灵敏度。计算这些灵敏度正好代表了反应堆物理领域有史以来最大的灵敏度分析努力。只有241,483,276个相互不同，其中一些被证明是零，因为二阶灵敏度的对称性。所有这些敏感性的数值结果，以及对其主要影响的讨论，将在《能源》特刊《核能系统的敏感性分析、不确定性量化和预测建模》的系列出版物中发表。这是这一系列中的第一项工作，给出了中子输运问题的通用公式，以及由这些公式产生的关于中子输运模型的群平均同位素总截面的PEP泄漏响应的180个一阶和32,400个二阶灵敏度的数值结果。为了便于比较，本工作还给出了关于中子输运模型的群平均同位素俘获截面的PEP泄漏响应的180个一阶和32,400个二阶灵敏度的通用公式和数值结果。到目前为止，人们普遍认为，对于用中子输运或扩散方程模拟的反应堆物理系统，二阶灵敏度都比一阶灵敏度小得多。然而，与这种普遍的看法相反，这项工作中得到的数值结果第一次证明了许多二阶灵敏度比相应的一阶灵敏度大得多，因此它们的影响可以变得比一阶灵敏度的相应效应大得多。例如，PERP泄漏响应的二阶灵敏度导致该响应的期望值明显大于相应的计算值。二阶灵敏度的重要性随着横截面相对标准偏差的增大而增大。例如，对于完全相关截面的极端情况，忽略二阶灵敏度将导致泄漏响应的期望值误差高达2000%，泄漏响应的方差误差高达6000%。混合二阶灵敏度的显著影响强调了对可能存在于总横截面之间的相关性的可靠取值的需要，这些值目前还无法获得。相对于总横截面的二阶灵敏度也会导致响应分布相对于期望值偏向正值。因此，忽略二阶灵敏度可能会通过少报响应方差和期望值而潜在地导致非常大的非保守误差。
The subcritical polyethylene-reflected plutonium (PERP) metal fundamental physics benchmark, which is included in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook, has been selected to serve as a paradigm illustrative reactor physics system for the application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) that was developed by Cacuci. The 2nd-ASAM enables the exhaustive deterministic computation of the exact values of the 1st-order and 2nd-order sensitivities of a system response to the parameters underlying the respective system. The PERP benchmark is numerically modeled in this work by using the deterministic multigroup neutron transport equation discretized in the spatial and angular independent variables. Thus, the numerical model of the PERP benchmark developed includes the following imprecisely known uncertain parameters: 180 group-averaged total microscopic cross sections, 21,600 group-averaged scattering microscopic cross sections, 120 fission process parameters, 60 fission spectrum parameters, 10 parameters describing the experiment’s nuclear sources, and six isotopic number densities. Thus, the numerical simulation model for the PERP benchmark comprises 21,976 uncertain parameters, which implies that, for any response of interest, there are a total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to the model parameters. Computing these sensitivities exactly represents the largest sensitivity analysis endeavor ever carried out in the field of reactor physics. Only 241,483,276 are distinct from each other, and some of these turned out to be zero due to the symmetry of the 2nd-order sensitivities. The numerical results for all of these sensitivities, together with discussions of their major impacts, will be presented in a sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”. This work is the first in this sequence, presenting formulas of general use for neutron transport problems, along with the numerical results that were produced by these formulas for the 180 first-order and 32,400 second-order sensitivities of the PERP leakage response with respect to the neutron transport model’s group-averaged isotopic total cross sections. For comparison, this work also presents formulas of general use and numerical results for the 180 first-order and 32,400 second-order sensitivities of the PERP leakage response with respect to the neutron transport model’s group-averaged isotopic capture cross sections. It has been widely believed hitherto that, for reactor physics systems modeled by the neutron transport or diffusion equations, the second-order sensitivities are all much smaller than the first-order ones. However, contrary to this widely held belief, the numerical results that were obtained in this work prove, for the first time ever, that many of the 2nd-order sensitivities are much larger than the corresponding 1st-order ones, so their effects can become much larger than the corresponding effects stemming from the 1st-order sensitivities. For example, the 2nd-order sensitivities of the PERP leakage response cause the expected value of this response to be significantly larger than the corresponding computed value. The importance of the 2nd-order sensitivities increases as the relative standard deviations for the cross sections increase. For the extreme case of fully correlated cross sections, for example, neglecting the 2nd-order sensitivities would cause an error as large as 2000% in the expected value of the leakage response and up to 6000% in the variance of the leakage response. The significant effects of the mixed 2nd-order sensitivities underscore the need for reliable values for the correlations that might exist among the total cross sections, which are unavailable at this time. The 2nd-order sensitivities with respect to the total cross sections also cause the response distribution to be skewed towards positive values relative to the expected value. Hence, neglecting the 2nd-order sensitivities could potentially cause very large non-conservative errors by under-reporting of the response variance and expected value.