应用Jeffreys方法计算可靠性参数和始发事件频率的无信息先验

在核电厂概率安全评价（PSA）分析中,有些始发事件频率或设备失效记录在工业界几乎无历史数据。为了计算这些无信息先验的可靠性参数和始发事件频率,可采用Bayesian统计学中的Jeffreys方法。本文阐述了Jeffreys先验和简化的受限无信息先验分布（SCNID）的数学原理,分别导出了Gamma-Poisson模型和Beta-Binomial模型的Jeffreys无信息先验公式和不确定性区间。结合反应堆冷却剂小破口失水事故(SLOCA)实例介绍了如何应用Jeffreys先验计算始发事件频率。结果表明,Jeffreys方法是一种计算无信息先验的有效方法。     

贝叶斯估计方法在Alpha因子模型参数估计中的应用

核电厂的概率安全分析（PSA）结果表明,共因失效（CCF）在系统的不可靠度中占有相当重要的贡献。国内PSA分析中CCF数据一直采用通用数据,难以体现国内核电机组的运行特点。Alpha因子模型由于其参数估计的简单化、计算结果的精确性等特点是PSA中最常用于模化共因失效的模型。但由于共因失效事件的罕见性,使用经典估计算法难以产生合理的统计值,因此,本文给出共因参数的贝叶斯估计方法,该方法能够结合先验信息和样本信息,不需要很大的样本就能得到较好的估计值,有效解决了核电厂共因失效事件少、使用经典估计方法计算结果不合理的问题,适用于核电厂共因失效模型参数估计。      

核动力泵阀截尾无失效数据的多层Bayes处理

针对船用核动力设备无失效数据截尾、小子样的特点,应用多层Bayes估计方法,结合工程实例估算了设备的运行失效率和需求失效概率两类可靠性参数,给出了截尾分布参数的推荐值。结果表明,该方法适用而有效。     

有关正态分布的小样本可靠性评估

当可靠度特征量满足正态分布时,其分布参数(μ,h)的共轭型先验分布为正态伽玛分布。特征量的主观先验信息及其随机自变量的试验信息可被利用以克服小样本统计推断的困难,借助于最大信息熵原理和矩拟合法,将这两类信息转化为分布参数(μ,h)的贝叶斯先验分布,然后利用该先验分布或它与试验信息结合而形成的后验分布进行可靠性评估。介绍了计算方法并给出两个算例。     

IG-110石墨强度分布与失效概率研究

石墨作为一种脆性材料,其强度较为分散。相比较于确定论方法,概率论方法更适合于评价石墨材料的强度。在概率论方法中,失效概率采用的分布函数对结果准确性有较大影响。目前对于石墨材料的强度拟合大都采用威布尔分布,然而对于一些情况,如多轴应力、有残余应力等,威布尔分布并不一定适合。本文以IG-110拉伸、压缩、弯曲大量强度实验数据为基础,首先研究了正态、对数正态以及威布尔分布对实验数据的拟合度,随后采用3种分布计算失效概率,研究不同分布对失效概率方法的影响。     

核电站仪控开关可靠性数据分析与处理

基于仪控开关现场失效数据,分别应用指数分布以及威布尔分布对仪控开关进行可靠性参数估计。对于无失效数据的情况,使用贝叶斯理论进行参数估计。分别得出了不同寿命分布类型开关的失效率。以大亚湾核电站实际使用的3种类型仪控开关为例,对其失效数据进行了可靠性评估,说明了方法的有效性。     

共因失效对平均失效概率计算结果的影响分析

为了评价共因失效(CCF)对平均失效概率(Pavg)计算结果的影响,建立了一个正常激励1oo2双通道系统的需求失效故障树模型。采用β模型,分别计算出不考虑CCF和考虑CCF 2种情况下的Pavg,发现CCF对Pavg的计算结果有较大的影响。相关分析表明,系统越安全(危险失效率越低,危险失效检测率越高),CCF对Pavg的计算结果影响越大。     

基于数据挖掘的非能动系统功能可靠性评估方法研究

针对多维不确定性参数及小概率的功能失效问题，提出一种基于数据挖掘的功能可靠性分析方法。该方法将自举抽样响应面拟合模型及最优化线抽样技术相结合，进而高效获得非能动系统的功能可靠性。以西安脉冲堆为例，结合中破口失水事故，考虑输入参数及模型的不确定性，对其进行功能可靠性评价。结果表明，该自举抽样响应面模型具有较高的拟合度；最优化线性抽样技术具有很高的计算效率，同时又能保证很好的计算精度。因此，本研究的评价方法对非能动系统隐式非线性的功能失效分析具有很强的适应性。      

GM计数管的失效规律研究

GM计数管的可靠性应当以失效的工作时间 -寿命 ,以及在寿命期间的失效率来表征。提出并采用了一种 GM管失效规律的新方法 ,该方法的要点是 :测试正在使用的仪器中的 GM管 ;记录测得的性能参数和仪器与计数管的其他信息 ;建立数据库 ,确定失效判据 ,检查计数管是否失效并确定失效模式 ;将相同使用年数的 GM管组成一个子样 ,利用采集到的有关信息 ,将子样样品数恢复成开始投入使用时的样品数 ,统计子样的失效样品数和失效模式分布 ;利用线性拟合法求出威布尔分布函数的参数m、γ、t0 ,进而求出平均寿命、失效率等特征量。利用该方法研究了两种 GM管的失效规律 ,根据它们的失效规律确定其使用寿命为 18～ 2 0 a,在此期间的失效率分别为 5× 10 -6 4× 10 -6 / h。     

针对细颗粒石墨的改进概率评价方法研究

石墨由于其高中子散射截面和低中子吸收截面特性被广泛应用于第4代高温气冷堆中。由于石墨材料强度分散,与常用的确定论评价方法相比,概率论方法评价其失效更为合适。本文通过有限元软件ABAQUS用户子程序开发了石墨构件失效概率分析模型,采用该模型研究了Hindley模型对细颗粒及国产石墨的适用性,在此基础上提出改进的失效概率计算模型,并通过试验数据加以验证。结果表明,Hindley模型过于保守,改进模型则很好地吻合了试验数据,其结果更为合理,为国产石墨在核反应堆中的应用提供参考依据。     

Effect of prior crack growth on cleavage fracture of low toughness precracked Charpy specimens

Cleavage fracture of reactor pressure vessel steels in the upper ductile to brittle transition region generally occurs with prior significant ductile crack growth. For low upper shelf materials and using PreCracked Charpy v-notch (PCCv) specimens that can be obtained from conventional surveillance programs, the effect of prior crack growth could be particularly important. In practice, the shape of the Master Curve and the failure distribution could be affected by ductile crack growth. To quantify the effect in practical applications, the effect of prior ductile on cleavage is evaluated on PCCv specimen.The methodology use finite element calculations to grow a ductile crack and infer the brittle failure probability using the local approach to fracture. It is found that for very low upper shelf toughness materials, ductile crack growth enhances the failure probability, induces a steeper failure distribution and affects the shape of the Master Curve. However, for low toughness materials, the enhanced failure probability due to crack growth is compensated by loss of constraint.     

The estimation of failure rates for low probability events

In many cases the individual components in an engineering system may have suffered no or perhaps only a single failure during their operating history. Such a history may be that of continuous operation over a period of time or it may be over a number of discrete demands. In spite of the apparent lack, or paucity of failure rate data, it is still important to be able to estimate a failure rate or failure probability. In order to do this, it is necessary for the engineer to decide whether there is available some source of information which, while not precisely related to the problem of interest, has some material bearing on it. If this is the case, it may be possible to construct a probability distribution for the failure rate defined by a most probable value and some measure of the variance. If no such information is available then it will be necessary to use a so-called non-informative prior within a Bayesian inference scheme. We describe here the essential results of such a scheme.

In some cases, experience with similar systems or elicitation by expert judgement may lead to the construction of a prior which gives some guidance as to the most likely value of a failure rate, even though no failures have actually been observed in the system of interest. The choice of prior is not a ‘mechanical’ process and requires some experience as to the type of data of interest and the amount and form of the information available. Ideally, a complete probability distribution would be desirable, obtained by eliciting information from a large number of experts. This situation is rarely practical for logistical and financial reasons. More commonly, one has a most probable value and a standard deviation, or possibly upper and lower confidence limits. Thus, two pieces of information are available and this restricts the algebraic form of the prior to one which contains two arbitrary parameters. The following functions are therefore suitable candidates and have been used in the past to represent the variability of failure rates in various situations. 1.Gamma distribution, 2.Log-normal distribution, 3.Hat function, 4.Log-uniform distribution. The log-normal distribution is useful to represent data which varies in inverse powers of 10 and is symmetrical about the most probable value on a logarithmic scale. The Gamma distribution, on the other hand, will describe data that is skewed about the most probable value on a logarithmic scale with particular emphasis on the suppression of large values of the failure rate. For cases in which little is known about the data except mean values, standard deviations and confidence limits, then the hat function or log-uniform are appropriate. The log-uniform distribution is particularly useful since it represents probabilities that are of equal likelihood on a logarithmic scale between an upper and lower bound. A new form of prior, based on the Cauchy distribution, is found to be useful to represent situations where information about the system is particularly sparse.

This paper explores these issues by first reviewing some of the seminal work in the area and then applying Bayesian methods to obtain quantitative results of direct use for practicing engineers. In particular, the paper gives results for the zero failure case for continuous and discrete systems. An important conclusion of the work is that the most appropriate failure rate to use in prospective studies, for components that have been operating continuously for a time T with no failures, is 0.55/T.     

包覆燃料颗粒尺寸及其标准偏差对失效概率的影响

三结构同向性型(Tristructural isotropic,TRISO)包覆燃料颗粒是目前高温气冷堆和固态燃料熔盐堆采用的燃料元件。TRISO包覆燃料颗粒破损会导致裂变产物不可接受的释放,由此影响反应堆的安全运行。基于TRISO包覆燃料颗粒压力壳式破损模型,分析了TRISO包覆燃料颗粒核芯和各包覆层的尺寸对失效概率的影响,研究了TRISO包覆燃料颗粒核芯半径、疏松热解碳(Buffer)层厚度和碳化硅(Si C)层厚度的合理设计范围。同时,利用随机抽样统计的方法分析了TRISO包覆燃料颗粒核芯半径分布和各包覆层厚度分布对颗粒失效概率的影响。研究发现,降低Buffer层厚度分布的标准差至16μm可以使TRISO包覆燃料颗粒的失效概率降低一个数量级。     

UN核芯TRISO燃料颗粒破损概率模型研究

TRISO燃料颗粒由核芯和4层包覆层组成,具有良好的裂变产物包容能力。TRISO燃料颗粒破损概率是表征TRISO燃料事故安全特性的关键参数。本文基于修正的PANAMA破损概率计算方法,在考虑UN核芯裂变气体释放导致的气体内压以及内外致密热解炭层辐照蠕变和收缩作用的基础上,开发了UN核芯TRISO燃料颗粒压力壳式破损概率计算方法,并采用IAEA基准题6和基准题9对模型进行了验证;基于开发的UN核芯TRISO颗粒破损概率计算方法,采用随机抽样统计方法分析了事故工况下UN核芯和包覆层设计参数（包括包覆层尺寸及密度）对UN核芯TRISO燃料颗粒破损概率的影响。研究结果显示,疏松热解炭（Buffer）层设计参数是影响TRISO颗粒破损概率的关键因素,可通过降低Buffer层尺寸及密度分布设计标准偏差的方法降低UN核芯TRISO燃料颗粒的破损概率。     

基于耦合CFD-FEM方法的严重事故下RPV蠕变失效风险评估

核电站严重事故发生后，反应堆压力容器（RPV）的剩余固壁在高温差、内压、熔池重量等的作用下可能发生蠕变失效。本文以CPR1000 RPV为研究对象，基于FLUENT软件二次开发求解反应堆压力容器下封头烧蚀温度场，然后基于ANSYS Workbench开展耦合CFD-FEM力学分析，求解严重事故下RPV烧蚀温度场稳定后72 h内的等效应力、等效塑性应变和等效蠕变应变，并评估了RPV的蠕变失效风险。结果表明：当堆坑注水等措施投运后，RPV剩余固壁在72 h内不会发生蠕变失效和塑性变形失效，有效卸压可明显提升RPV结构完整性的安全裕度。     

全厂断电时安全壳直接加热的概率研究

安全壳直接加热(DCH)是导致安全壳早期失效的潜在因素,本文应用基于风险导向的事故分析方法(ROAAM),对堆芯碎片中UO_2的质量和Zr的氧化份额的概率密度分布抽样,对安全壳直接加热模型TCE(Two-cell Equilibrium)编程,将抽样结果带人TCE模型中计算,得到安全壳压力峰值的累积概率分布和安全壳失效概率,研究压水堆全厂断电始发事故下轴封破口面积不同的情况对下封头失效后安全壳压力峰值的影响。其中TCE模型的输入数据由严重事故分析程序计算给出。     

Risk Assessment of Creep Failure for RPV under Severe Accident Condition Based on Coupled CFD-FEM Method

After a reactor core melt accident, creep failure may occur in the residual solid wall of the reactor pressure vessel (RPV) under the influence of high temperature difference, internal pressure and the weight of the molten pool. In this work, the CPR1000 RPV was used as a research object. The ablation temperature field of the lower head of RPV was solved through the secondary development of the FLUENT software. And then, a CFD-FEM coupling analysis was carried out based on ANSYS Workbench software. The equivalent stress, the equivalent plastic strain and the equivalent creep strain of the RPV within 72 h under severe accident after the wall ablation and temperature field distribution formed stably were calculated. The risk of creep failure of the RPV was evaluated. The results show that when the reactor pit water injection measure puts into operation, the residual solid wall of the RPV will not experience creep failure and plastic deformation failure within 72 h, and besides, the pressure relief can significantly increase the safety margin of the structural integrity of the RPV.     

基于自适应重要抽样法非能动系统功能故障概率评估

针对非能动系统功能故障概率评估,提出一种新的自适应重要抽样方法。这种方法先对失效域进行预抽样,然后拟合出失效域中样本分布的密度函数,以之作为重要抽样密度函数。以1000 MW非能动先进压水堆(AP1000)非能动余热排出系统为研究对象,考虑模型和输入参数的不确定性,将响应面法和自适应重要抽样法相结合,对其进行功能故障概率评估。结果表明:与传统的概率评估方法相比,自适应重要抽样法具有较高的计算效率,同时又能保证很高的计算精度。     

基于主观推断的可靠性评估方法

通过主观推断得到的可靠性信息一般是不完全先验信息 ,这些信息通常以可靠度均值或可信区间的形式存在。以贝塔分布作为先验信息的分布类型 ,介绍了用最大熵原理将不完全信息转化为完全型先验信息的计算方法 ,并用贝叶斯方法进行了成败型产品的可靠性评估 ,最后给出了算例     

蒸汽发生器传热管破损叠加全船断电事故放射性分析

以严重事故分析程序MELCOR为计算工具,研究了某型船用堆发生蒸汽发生器传热管破损叠加全船断电事故,针对传热管破损所导致的放射性物质向其他舱室的泄漏,着重分析了惰性气体和CsI的释放、迁移、滞留特点及其在舱室内的分布。计算结果表明:二回路蒸汽管道会发生超压失效,氢燃导致堆舱邻舱的超压失效。至计算结束,约占累积总量99.61%的Xe和49.96%的CsI从堆芯释放出来。舱室Ⅰ和Ⅱ内Xe的分布份额分别为38%和18%,CsI的分布份额分别为22.2%和2.7%,CsI主要存在于舱底水池中,且泄漏至舱室Ⅱ的份额微少。本文分析结果可为进一步的源项剂量分析及船内外应急提供依据。