面向协方差矩阵抽样的快堆不确定性分析方法研究

基于传统统计学抽样的不确定性分析方法由于算法简单、程序容易实现及同时考虑高阶效应受到国内外广泛关注，但上述方法通常需要大量样本才能保证响应量计算精度。研究发现，产生以上现象的原因是抽样样本质量不高。通过改进抽样方法，面向协方差矩阵抽样时小样本量可以保证较高的计算精度。文中首先从理论上证明了面向协方差矩阵抽样方法的可行性，用简单测试题对其进行验证。在此基础上，使用自主开发的快能谱反应堆敏感性和不确定性分析程序SUFR，选取国际快堆基准装置ZPR-6/7，计算多个核素不同反应类型的核截面引起的有效增殖因子（k_eff）的不确定度，并与使用确定论方法计算的不确定度进行对比。结果表明，使用面向协方差矩阵抽样的情况下，样本量为50时，2种方法计算的不确定度偏差均低于1.3%。由此说明，面向协方差矩阵抽样方法可以很好地解决传统抽样方法计算不确定度时存在的问题，且SUFR程序面向协方差矩阵抽样功能的开发是正确的，该方法是对传统抽样方法的进一步发展。 

Study on Uncertainty Analysis Method of Fast Reactor Based on Covariance Matrix Sampling

The uncertainty analysis methods based on traditional statistical sampling have received widespread attention in China and other countries due to their simple algorithms, easy realization of codes, and consideration of high-order effects. However, these methods usually require a large number of samples to ensure the calculation accuracy of response variables. As found in the study, this phenomenon occurs because of the poor quality of the samples. After a covariance matrix sampling is used instead of the traditional sampling method, a small sample size can also ensure a high calculation accuracy. This paper firstly demonstrates theoretically the feasibility of the covariance matrix sampling method, and verifies it with simple tests. On this basis, this paper, using the self-developed fast spectrum reactor sensitivity and uncertainty analysis code - SUFR and the international reference configuration for fast reactor ZPR-6/7, calculates the uncertainty of effective multiplication factor (k_eff) caused by the nuclear cross sections of different reaction types of multiple nuclides, and compares the calculation results with the uncertainty calculated using the deterministic method. As demonstrated by the results, if the covariance matrix sampling is used, with a sample size of 50, the uncertainty deviation calculated in the two methods each is below 1.3%. This indicates that the use of the covariance matrix sampling method can solve the problems present in the use of the traditional sampling method to calculate uncertainty, and that it is appropriate to develop the SUFR code function against the covariance matrix sampling. This method represents a further development of the traditional sampling method.