基于统计抽样的敏感性系数计算方法

分析核系统的不确定性和敏感性，对于减小核设计的设计余量、提高核系统的经济性具有重要意义。基于统计抽样的不确定度分析方法，由于算法简单、可考虑高阶效应且对响应量没有特殊要求等，越来越受到重视。但之前认为基于统计抽样法很难进行敏感性系数分析，其原因主要是响应量的变化是由多变量同时变化引起，很难把单独一个变量的变化导致的响应量的变化确定出来。本文首先推导了利用统计抽样法进行敏感性系数分析的理论公式，然后利用裸堆双群近似的临界公式和复杂的压水堆单栅元问题进行了验证，验证了统计抽样法的可行性。针对实际问题协方差矩阵求逆困难的问题，本文提出了两种替代解决方法，即采用简化协方差矩阵或统一微扰量的方法，利用²³⁵U裂变截面对上述方法进行了验证分析，证明了方法的可行性和正确性；同时分析了不同敏感性系数对不确定度计算的影响。

Calculation Method of Sensitivity Coefficient Based on Statistical Sampling

Uncertainty and sensitivity analysis of the nuclear system is of great significance for reducing the design margin of nuclear design and improving the economics of the nuclear system. The sampling method for the uncertainty and sensitivity analysis is becoming more and more important because of its simple algorithm, taking into account high-order effects, and no special requirement for response parameters. However, it was previously considered that it was difficult to analyze the sensitivity coefficient based on the statistical sampling method. The main reason was that the change of the response was caused by the simultaneous change of the multivariate, and it was difficult to determine the change of the response caused by the change of a single variable. In this paper, the theoretical formula of sensitivity coefficient analysis using statistical sampling method was deduced firstly. Then the critical formula of bare reactor with two groups approximation and the PWR cell TMI benchmark were verified, and the feasibility of the method was verified. In order to deal with the difficulty of inversion of the covariance matrix of the actual problem, the simplified covariance matrix and the unified perturbation method were proposed in this study, and the two alternative solutions were verified by using the ²³⁵U fission cross section. The analysis proves the feasibility of the method. At the same time, the influence of different sensitivity coefficients on the TMI infinite multiplication factor uncertainty was also analyzed.