适用于最佳估算事故分析方法的不确定性统计方法比较研究
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摘要
最佳估算加不确定性(BEPU)事故分析方法能定量分析计算结果的不确定性,从而在保证核电厂安全性的前提下,释放出更多的裕量,进一步提高核电站的经济性。BEPU方法需要准确可靠通用的统计分析方法确定容忍区间上限。本文对适用于最佳估算方法的不确定性统计分析方法进行比较研究,使用DAKOTA程序针对标准正态分布函数随机抽样获得的不同容量样本,对比分析不同统计分析方法确定容忍区间上限时的优缺点,为最佳估算方法的开发和应用提供必要的统计分析方法和工具。分析结果表明,欧文因子法获得与理论值最为接近的容忍区间上限均值和最小方差。当样本分布未知且输入不确定性参数数量较大时,可采用非参量高阶WILKS公式计算容忍区间上限。
Best-estimate plus uncertainty(BEPU)accident analyses can quantify the uncertainties in the calculation results,which will help to reduce the margins in the safety analyses and enhance economics in nuclear power station design and operation while maintaining the safety.The BEPU method requires a generic,reliable and accurate statistical analysis method to determine the upper tolerance limit.The objective of this paper is to compare and choose the statistical method and tool suitable for applications to BEPU.The DAKOTA code was used to perform Monte Carlo sampling on the standard normal distribution function to acquire different samples.Several statistical analysis methods were applied to these samples to determine the tolerance limits,which were compared to determine the most suitable one for BEPU.The analysis results show that the mean value and variance of the upper tolerance limits calculated by the Owenfactor method are most close to the analytical solution.When the sample distribution is unknown and there are numbers of input uncertainty variables,the upper tolerance limits can be better calculated by the non-parametric higher order WILKS formula.
Best-estimate plus uncertainty(BEPU)accident analyses can quantify the uncertainties in the calculation results,which will help to reduce the margins in the safety analyses and enhance economics in nuclear power station design and operation while maintaining the safety.The BEPU method requires a generic,reliable and accurate statistical analysis method to determine the upper tolerance limit.The objective of this paper is to compare and choose the statistical method and tool suitable for applications to BEPU.The DAKOTA code was used to perform Monte Carlo sampling on the standard normal distribution function to acquire different samples.Several statistical analysis methods were applied to these samples to determine the tolerance limits,which were compared to determine the most suitable one for BEPU.The analysis results show that the mean value and variance of the upper tolerance limits calculated by the Owenfactor method are most close to the analytical solution.When the sample distribution is unknown and there are numbers of input uncertainty variables,the upper tolerance limits can be better calculated by the non-parametric higher order WILKS formula.
引文
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[3]FREPOLI C.An overview of westinghouse realistic large break loca evaluation model[J].Science and Technology of Nuclear Installations,2008(2008):498737.
[4]USNRC.RG 1.203 Transient and accident analysis methods[S].Washington:Office of Nuclear Regulatory Research,2005.
[5]NEA.Bemuse phaseⅥreport:Status report on the area,classification of the methods,conclusions and recommendations,JT03299065[R].Paris:OECD Nuclear Energy Agency,2011.
[6]MARTIN R P,ODELL L D.Areva’s realistic large break loca analysis methodology[J].Nuclear Engineering and Design,2005,235(16):1 713-1 725.
[7]ROY C J,OBERKAMPF W L.A Complete framework for verification,validation,and uncertainty quantification in scientific computing(invited)[C]∥48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.Orlando,Florida:American Institute of Aeronautics and Astronautics,Inc.,2010.
[8]ATTILA G,MIHA′LY M,LE′NA′RD P.Statistical aspects of best estimate method—Ⅰ[J].Reliability Engineering and System Safety,2003,80(3):217-232.
[9]LIANG T K S,CHOU L Y,ZHANG Z,et al.Development and application of a deterministicrealistic hybrid methodology for loca licensing analysis[J].Nuclear Engineering and Design,2011,241(5):1 857-1 863.
[10]ANL.Uncertainty quantification approaches for advanced reactor analyses,ANL-GenⅣ-110[R].Chicago:Argonne National Laboratory,2008.
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[12]盛骤.概率论与数理统计[M].北京:高等教育出版社,2008.
[13]ADAMS B M,BAUMAN L E,BOHNHOFF W J,et al.Dakota,a multilevel parallel objectoriented framework for design optimization,parameter estimation,uncertainty quantification,and sensitivity analysis:Version 5.3.1 user’s manual,SAND2010-2183[R].Sandia:Sandia National Laboratories,2013.