氢气复合器算例数值模拟结果的不确定性分析和敏感性分析

在安全壳氢气分析中,由于输入参数具有不确定性,因此计算结果也具有不确定性。研究计算结果的变化范围,以及各输入参数对计算结果不确定性的贡献,在安全层面具有重要意义。为了对安全壳氢气复合器算例进行数值模拟,首先向计算流体力学程序HYDRAGON内添加复合器模型,然后选定燃爆转变因子和爆炸总能量及其相关的时刻量作为研究对象。对若干输入参数进行抽样后进行数值模拟。采用非参数统计方法,分析计算结果的不确定性,给出其变化范围。分析计算结果和输入参数之间的敏感性,筛选其不确定性出对计算结果影响较大的输入参数。     

基于HFR的核动力装置非能动系统敏感性分析方法研究

敏感性分析应用于反应堆非能动系统热工水力过程的不确定性分析和可靠性分析，能够定量识别对系统热工水力行为具有重要影响的不确定性输入参数。基于混合随机均衡-傅里叶幅度敏感性测试（HFR）方法，以某型核动力装置非能动余热排出试验系统作为算例进行全局敏感性分析研究，仿真结果证明了HFR方法的可行性与正确性。敏感性分析给出了系统输入参数重要度随时间的变化规律以及系统稳定运行时输入参数的重要度排序，分析结果有助于指导系统的设计优化及运行管理。      

DAKOTA法量化AP1000堆芯物理不确定性

应用DAKOTA程序中的超拉丁立方抽样方法开展AP1000堆芯物理关键参数的不确定性量化分析。分析结果表明:AP1000输入参数的不确定性对堆芯关键参数的不确定性影响较小,均未超过设计限值;全参数不确定性分析和敏感参数不确定性分析具有一定的等价性,可通过敏感性参数不确定性分析来获取AP1000堆芯关键参数的不确定性,提高分析计算效率。     

小破口失水事故最佳估算的不确定性和敏感性分析

本文采用RELAP5最佳估算程序对我国建造的先进热工水力试验（ACME）台架进行了小破口失水事故模拟,并开展了不确定性定量化评估,包括输入不确定性参数的选取、Wilks非参数统计方法的应用以及基于SNAP平台的不确定性传播计算,最后对计算结果进行了不确定性和敏感性分析。计算得到关键参数的95/95不确定性包络带,其中最小堆芯液位的下限仍保持在堆芯活性区以上,表明堆芯有95%的置信度未发生裸露。通过敏感性分析判别出对最小堆芯液位影响较大的输入不确定性参数。     

基于最优化线抽样法的XAPR自然循环功能失效研究与分析

针对多维不确定性参数、小失效概率的功能可靠性分析，提出了一种优化线抽样的可靠性分析方法。该方法采用遗传算法求解约束条件的优化模型来寻求最优化重要方向，进而得到失效概率的高效估计。以西安脉冲堆（XAPR）自然循环冷却堆芯能力的可靠性评价为例，考虑模型与输入参数的不确定性，对中破口失水事故下的自然循环功能失效概率进行了量化分析。结果表明：与其他概率评估方法相比，本文方法具有很高的计算效率，同时又能保证很好的计算精度；对隐式非线性的功能可靠性分析是有效可行的，具有很强的适应性。     

地震载荷下反应堆系统的不确定性量化

反应堆结构力学分析中，由于设计变更、制造安装、计算偏差等因素的影响，会导致力学分析关键输入参数存在一定的不确定性，这种不确定性将直接影响到动力响应、载荷分配与最终的力学评价结果。为量化参数不确定性对载荷计算的影响，本文采用不确定性量化的方法，以反应堆系统为研究对象，开展了地震载荷下系统关键结构参数对系统动力响应与载荷分配的不确定性量化研究。首先依据关键参数的基本特性，利用最大熵原理，建立了描述反应堆系统部件间接触刚度和间隙的概率密度函数。随后，应用马尔科夫链蒙特卡罗采样技术对系统关键参数进行采样，并通过有限元瞬态计算获得了输入输出数据池。最后，以样本数据为基础，考察了不确定性参数对部件动力响应统计分布的影响，开展了名义模型的可靠性与不确定性量化分析。研究发现，结构参数不确定性对系统响应的影响在不同部位、不同频域内呈现不同的分布。在考察名义模型的可靠性时应根据响应具体形式有针对性地进行量化。本文所提出的不确定性量化方法对核动力装置其他系统和设备的动力分析具有推广价值。     

多种参数不确定性分析方法在AP1000 LBLOCA中的适用性研究

参数不确定性分析是利用合理的方法来建立输入参数不确定性和输出结果不确定性之间的响应关系,以能更真实地模拟电厂状态,在兼顾安全性的前提下,提高电厂的经济性。本文通过对AP1000 LBLOCA分析,发现随机取样统计方法、敏感性分析数值方法、传统误差传递分析方法均能提供较大的燃料包壳峰值温度（PCT）安全裕度,对核电厂经济性提高过程中参数不确定性量化方法的选择具有参考意义。此外,随机取样统计方法利用数理统计理论分析,减少了分析过程中的保守性,故在3种方法之中可提供最大的安全裕度。相较传统的参数包络分析方法,随机取样统计方法可额外提供的PCT裕度约100 K,而敏感性分析数值方法和传统误差传递分析方法额外提供的PCT裕度则约50～60 K。     

基于方差分解的堆芯下封头熔池模型敏感性分析

下封头熔池模型是熔融物堆内滞留(IVR)有效性评价的重要模型，具有关系式复杂、输入参数多且具有较大不确定性的特点，传统的局部敏感性分析方法在进行复杂模型敏感性分析时具有计算量大、效率低的缺点。本文基于方差分解的全局敏感性分析方法，采用中国核动力研究设计院自主研发的敏感性分析工具SALib和熔融物堆内滞留软件CISER，针对下封头壁面热流密度比等5个关键结果参数开展了输入参数敏感性分析，得到了输入参数对关键结果的敏感性系数及影响趋势，可为下封头熔池模型和严重事故策略的优化提供参考。     

静默式热管反应堆热工水力特性不确定性分析

基于不确定性分析软件DAKOTA和自编程热管反应堆单通道热工分析程序HEART,对静默式热管反应堆(NUSTER)稳态热工水力特性进行了不确定性分析。根据热管反应堆相关实验数据，选取运行功率、燃料热导率、气隙宽度、包壳厚度、热管蒸发段长度和基体厚度6个关键热工参数并确定其基准值与概率密度分布，通过大量重复性计算，获得了95%置信水平下热管蒸发段温度、热管冷凝段温度、燃料峰值温度、包壳峰值温度及基体温度的统计分布，并对各参数的不确定性对热管反应堆安全性的影响进行了分析。分析结果表明：热管蒸发段及冷凝段温度有0.67%的概率超过热管温度限值；由于热管反应堆堆芯为固态堆芯，传热以纯导热为主，输入变量的不确定性对不同目标参数的影响相同，燃料热导率的不确定性对5个目标参数的影响最为显著，且为负相关。本研究获得的结果可为热管反应堆的优化及其后续发展提供方向指引。     

灵敏度分析方法在非能动系统可靠性研究中的应用

在研究核电站安全时,热工水力非能动系统的可靠性研究基于所建立的热工水力学数值模型。模型通常极其复杂,具有多个输入参数,且输入参数具有不确定性,对模型输出的不确定性的影响又各不相同。灵敏度分析的目的是将各参数对模型输出的不确定性的影响进行排序,找出显著的影响参数。本文首先描述灵敏度分析的方法,然后应用秩转换回归分析方法计算HTR-10余热排出系统模型各参数的灵敏度,找出关键影响因素,将模型简化,并对简化模型应用响应面方法计算了失效概率。简化模型算得的失效概率与原模型的很接近。     

物性参数对氟盐球床堆传热模型不确定性和敏感性的影响分析

为了确保氟盐球床堆堆芯传热模型的预测能力满足安全限制，研究了氟盐冷却剂的物性参数对堆芯传热模型不确定度和敏感性的影响。采用统计学不确定性评估方法，将氟盐冷却剂物性参数（包括动力粘度、密度、比热容、导热系数）作为输入参数，选取经典传热关联式作为计算模型，分析了努赛尔数（Nu）的不确定性及其对物性参数的敏感性程度。结果表明，无论氟盐物性参数的概率分布为正态分布或均匀分布，计算得到的Nu的平均值非常接近，其分布形式都接近正态分布；同时发现，动力粘度是物性参数中对Nu影响最大的参数，并且呈负相关；导热系数对Nu的影响为负相关，密度和比热容对Nu的影响较小且均为正相关。      

Void fraction and flow regime in adiabatic upward two-phase flow in large diameter vertical pipes

In pipes with very large diameters, slug bubbles cannot exist. For this reason, the characteristics of two-phase flow in large pipes are much different than those in small pipes. Knowledge of these characteristics is essential for the prediction of the flow in new nuclear reactor designs which include a large chimney to promote natural circulation. Two of the key parameters in the prediction of the flow are the void fraction and flow regime. Void fraction measurements were made in a vertical tube with diameter of 0.15 m and length of 4.4 m. Superficial gas and liquid velocities ranged from 0.1 to 5.1 m/s and from 0.01 to 2.0 m/s, respectively. The measured void fractions ranged from 0.02 to 0.83. Electrical impedance void meters at four axial locations were used to measure the void fraction. This data was verified through comparison with previous data sets and models. The temporal variation in the void fraction signal was used to characterize the flow regime through use of the Cumulative Probability Density Function (CPDF). The CPDF of the signal was used with a Kohonen Self-Organized Map (SOM) to classify the flow regimes at each measurement port. The three flow regimes used were termed bubbly, cap-bubbly, and churn flow. The resulting flow regime maps matched well with the maps developed previously through other methods. Further, the flow regime maps matched well with the criteria which were proposed based on Mishima and Ishii's (1984) criteria.     

The fluctuating mechanical forces on a pipe-bend in a PWR system

Digitized fluctuation signals from an ex-core ion-chamber of a PWR were analysed to produce a Power Spectral Density, (PSD), curve by two means: (1) by digital filter techniques and (2) by a Fast Fourier Transform program. For both these methods, the effects of the precision of the input data were investigated and it is shown that reasonably good PSD curves may be obtained using very poor input precision.     

Critical heat flux function approximation using genetic algorithms

Function approximation is the problem of finding a system that best explains the relationship between input variables and an output variable. We propose two hybrid genetic algorithms (GAs) of parametric and nonparametric models for function approximation. The former GA is a genetic nonlinear Levenberg-Marquardt algorithm of parametric model. We designed the chromosomes in a way that geographically exploits the relationships between parameters. The latter one is another GA of nonparametric model that is combined with a feedforward neural network. The neuro-genetic hybrid here differs from others in that it evolves diverse input features instead of connection weights. We tested the two GAs with the problem of finding a better critical heat flux (CHF) function of nuclear fuel bundle which is directly related to the nuclear-reactor thermal margin and operation. The experimental result improved the existing CHF function originated from the KRB-1 CHF correlation at the Korea Atomic Energy Research Institute (KAERI) and achieved the correlation uncertainty reduction of 15.4% that would notably contribute to increasing the thermal margin of the nuclear power plants.     

基于抽样方法的燃耗计算核素积存量不确定度分析

基于抽样基本原理研究了应用于燃耗计算的不确定度分析方法,并开发了燃耗计算不确定度分析程序。基于评价核数据库ENDF/B-Ⅷ.0的裂变产额标准差和衰变常量标准差计算得到了衰变常量协方差矩阵和带相关性的裂变产额协方差矩阵,并结合SCALE6.2程序包的56群反应截面协方差数据库,对Takahama-3压水堆组件基准题中SF95-4样品进行不确定度分析。计算了反应截面、衰变常量和裂变产额不确定度引起的核素积存量的不确定度。计算结果表明,反应截面的不确定度是锕系核素积存量不确定度的主要来源,裂变产额和衰变常量的不确定度对部分裂变产物的积存量会引入较大的不确定度。但考虑裂变产额相关性后,裂变产额引起的不确定度显著降低。     

Thermal–hydraulics system codes uncertainty assessment: A review of the methodologies

By revising the ECCS licensing rules in 1989, the USNRC has allowed the use of “best estimate” thermal–hydraulics computer codes (such as RELAP5, TRAC, and TRACE), with the requirement that uncertainty analysis accompany the results. Several methodologies have been developed for the quantification of the uncertainties of such codes. These methodologies are either input-driven or output-driven. They disagree in definition for the uncertainty range, qualification and quantification steps, types of uncertainty sources considered, methods of assignment of uncertainty distribution or range to various parameters, approach to propagation of uncertainty, and the way the dynamic characteristics of TH codes are handled. The IMTHUA methodology, developed by the author, is a hybrid approach where an input-driven “white box” method is augmented with output correction based on experimental results relevant to code output. This paper offers a comparative assessment of uncertainty analysis methodologies for thermal–hydraulics transient calculations. The methods will be compared based on their approaches for treatment of input, propagation, and code models and correlations, as well as output. Comprehensiveness, approach to data treatment, and interpretation of results are among the criteria for comparison. Several examples are provided to clarify the differences.     

Uncertainty analysis of system fragility for seismic safety evaluation of NPP

In this study, a Seismic Probabilistic Safety Assessment (SPSA) methodology considering the uncertainty of fragilities was studied. A system fragility curve is estimated by combining component fragilities expressed by two variance sources, inherent randomness and modeling uncertainty. The sampling based methods, Monte Carlo Simulation (MCS) and Latin Hypercube Sampling (LHS), were used to quantify the uncertainties of the system fragility. The SPSA of an existing nuclear power plant (NPP) was performed to compare the two uncertainty analysis methods. Convergence of the uncertainty analysis for the system fragility was estimated by calculating High Confidence Low Probability of Failure (HCLPF) capacity. Alternate HCLPF capacity by composite standard deviation was also verified. The annual failure frequency of the NPP was estimated and the result was discussed with that from the other researches. As a result, the criteria of the uncertainty analysis and its effect was investigated.     

A proposal on accuracy estimation method for the sampling-based uncertainty analysis with Monte Carlo simulation technique

The sampling-based uncertainty analysis method is a stochastic approach to estimate response uncertainties caused by the uncertainty in the input parameters. Conventionally, to minimize the effects caused by the Monte Carlo stochastic uncertainty, lots of particle histories have been used for the uncertainty analysis. However, this can cause inefficiencies in the uncertainty analysis. To optimize the calculation efficiency, how the Monte Carlo stochastic uncertainty influences the response uncertainty should be clearly verified. In this study, a method to estimate the accuracy of the response uncertainty is proposed by introducing a standard error and an error propagation theory. Using the proposed method, response uncertainties and standard errors of the multiplication factors for three benchmark problems are evaluated by the Monte Carlo method. Our results show that the proposed method can accurately estimate the accuracy of the response uncertainty caused by the input uncertainty in using the Monte Carlo simulation method. The proposed method can be directly utilized to estimate the accuracy of the sampling-based uncertainty analysis using the Monte Carlo simulation method. Also, it is expected that the proposed method will contribute to an increase in the calculation efficiency in the sampling-based sensitivity and uncertainty analysis.     

最佳估算方法中不确定度评估关键问题分析

应用最佳估算+不确定度（BEPU）分析方法对核电厂进行事故分析或安全评审已成为国际发展趋势。本文对最佳估算分析中基于输入传递的统计类不确定度评估的流程进行了总结,并对其关键步骤进行了分析和研究。分析认为,评估流程可分为确定目标参数、确定重要输入参数及其分布、抽样、模型分析和目标参数分析5步,其中现象识别和重要度排序表（PIRT）是一种适用的重要输入参数确定方法,输入参数的分布需根据试验数据或专家判断确定;抽样方法上,可采用参数抽样或非参数抽样,后者可大幅减小抽样数量;不确定度评估所用模型须经过充分试验或分析证明其适用性;通过对目标参数进行统计,可获得不确定度范围及输入参数的敏感性。