基于子集模拟法非能动系统功能故障概率评估

针对非能动系统多维不确定性参数和小功能故障概率问题,提出基于马尔可夫链蒙特卡罗子集模拟的可靠性分析方法。该方法通过引入适当的中间失效事件,将小功能故障概率表达为一系列较大的中间失效事件条件概率乘积的形式,进而利用马尔可夫链模拟的条件样本点来计算条件失效概率。以AP1000非能动余热排出系统为研究对象,考虑热工水力学模型和输入参数的不确定性,对其进行功能故障概率评估。结果表明：与其它概率评估方法相比,子集模拟法具有较高的计算效率,同时又能保证很高的计算精度;对非能动安全系统非线性功能函数有很强的适应性。     

How to effectively compute the reliability of a thermal-hydraulic nuclear passive system

The computation of the reliability of a thermal-hydraulic (T-H) passive system of a nuclear power plant can be obtained by (i) Monte Carlo (MC) sampling the uncertainties of the system model and parameters, (ii) computing, for each sample, the system response by a mechanistic T-H code and (iii) comparing the system response with pre-established safety thresholds, which define the success or failure of the safety function. The computational effort involved can be prohibitive because of the large number of (typically long) T-H code simulations that must be performed (one for each sample) for the statistical estimation of the probability of success or failure. The objective of this work is to provide operative guidelines to effectively handle the computation of the reliability of a nuclear passive system. Two directions of computation efficiency are considered: from one side, efficient Monte Carlo Simulation (MCS) techniques are indicated as a means to performing robust estimations with a limited number of samples: in particular, the Subset Simulation (SS) and Line Sampling (LS) methods are identified as most valuable; from the other side, fast-running, surrogate regression models (also called response surfaces or meta-models) are indicated as a valid replacement of the long-running T-H model codes: in particular, the use of bootstrapped Artificial Neural Networks (ANNs) is shown to have interesting potentials, including for uncertainty propagation. The recommendations drawn are supported by the results obtained in an illustrative application of literature.     

Estimation of the functional failure probability of a thermal-hydraulic passive system by Subset Simulation

In the light of epistemic uncertainties affecting the model of a thermal-hydraulic (T-H) passive system and the numerical values of its parameters, the system may find itself in working conditions which do not allow it to accomplish its function as required. The estimation of the probability of these functional failures can be done by Monte Carlo (MC) sampling of the uncertainties in the model followed by the computation of the system response by a mechanistic T-H code. The procedure requires considerable computational efforts for achieving accurate estimates. Efficient methods for sampling the uncertainties in the model are thus in order.In this paper, the recently developed Subset Simulation (SS) method is considered for improving the efficiency of the random sampling. The method, originally developed to solve structural reliability problems, is founded on the idea that a small failure probability can be expressed as a product of larger conditional probabilities of some intermediate events: with a proper choice of the conditional events, the conditional probabilities can be made sufficiently large to allow accurate estimation with a small number of samples. Markov Chain Monte Carlo (MCMC) simulation, based on the Metropolis algorithm, is used to efficiently generate the conditional samples, which is otherwise a non-trivial task.The method is here developed for efficiently estimating the probability of functional failure of an emergency passive decay heat removal system in a simple steady-state model of a Gas-cooled Fast Reactor (GFR). The efficiency of the method is demonstrated by comparison to the commonly adopted standard Monte Carlo Simulation (MCS).     

Functional reliability analysis of Safety Grade Decay Heat Removal System of Indian 500 MWe PFBR

Passive systems are increasingly deployed in nuclear industry with an objective of increasing reliability and safety of operations with reduced cost. Methods for assessing the reliability of thermal-hydraulic passive systems, that is systems with moving working fluid, address the issues in natural buoyancy-driven flow that could result in a failure to meet the design safety limits under accident scenarios. This is referred as design functional reliability. This paper presents the results of functional reliability analysis carried out for the passive Safety Grade Decay Heat Removal System (SGDHRS) of Indian Prototype Fast Breeder Reactor (PFBR). The analysis is carried out based on the overall approach reported in the Reliability Methods for Passive System (RMPS, European Commission) project. Functional failure probability is calculated using Monte-Carlo method and also with method of moments.     

Seismic reliability of electrical power transmission systems

The reliability of electric power transmission systems is important for the probabilistic safety assessment of nuclear power plants under a given earthquake loading as it relates to the loss of off site power to the nuclear power plants. Here, a comprehensive model to evaluate the seismic reliability of electric power transmission systems is presented. The model provides probabilistic assessments of structural damage and abnormal power flow that can lead to power interruption in a transmission system under a given earthquake. With the proposed methodology seismic capacities of electrical. equipment are determined on the basis of available test data and simple modeling from which fragility functions of specific substations are developed. Earthquake ground motions are defined as stochastic processes. Probabilities of network disconnectivity and abnormal power flow are assessed through Monte Carlo simulations. The proposed model is applied to the electric power network in San Francisco and vicinity under the 1989 Loma Prieta earthquake, and the probabilities of power interruption are contrasted with the actual power failures observed during that earthquake.     

Quantitative dynamic reliability evaluation of AP1000 passive safety systems by using FMEA and GO-FLOW methodology

The passive safety systems utilized in advanced pressurized water reactor (PWR) design such as AP1000 should be more reliable than that of active safety systems of conventional PWR by less possible opportunities of hardware failures and human errors (less human intervention). The objectives of present study are to evaluate the dynamic reliability of AP1000 plant in order to check the effectiveness of passive safety systems by comparing the reliability-related issues with that of active safety systems in the event of the big accidents. How should the dynamic reliability of passive safety systems properly evaluated? And then what will be the comparison of reliability results of AP1000 passive safety systems with the active safety systems of conventional PWR.

For this purpose, a single loop model of AP1000 passive core cooling system (PXS) and passive containment cooling system (PCCS) are assumed separately for quantitative reliability evaluation. The transient behaviors of these passive safety systems are taken under the large break loss-of-coolant accident in the cold leg. The analysis is made by utilizing the qualitative method failure mode and effect analysis in order to identify the potential failure mode and success-oriented reliability analysis tool called GO-FLOW for quantitative reliability evaluation. The GO-FLOW analysis has been conducted separately for PXS and PCCS systems under the same accident. The analysis results show that reliability of AP1000 passive safety systems (PXS and PCCS) is increased due to redundancies and diversity of passive safety subsystems and components, and four stages automatic depressurization system is the key subsystem for successful actuation of PXS and PCCS system. The reliability results of PCCS system of AP1000 are more reliable than that of the containment spray system of conventional PWR. And also GO-FLOW method can be utilized for reliability evaluation of passive safety systems.     

Quantitative functional failure analysis of a thermal–hydraulic passive system by means of bootstrapped Artificial Neural Networks

The estimation of the functional failure probability of a thermal–hydraulic (T–H) passive system can be done by Monte Carlo (MC) sampling of the epistemic uncertainties affecting the system model and the numerical values of its parameters, followed by the computation of the system response by a mechanistic T–H code, for each sample. The computational effort associated to this approach can be prohibitive because a large number of lengthy T–H code simulations must be performed (one for each sample) for accurate quantification of the functional failure probability and the related statistics.     

CEFR改进型独立热交换器热工水力分析研究

事故余热排出系统是池式钠冷快堆最重要的专设安全设施之一,是实现反应堆相关事故工况下余热排出安全功能的主要手段,如全厂断电工况,而独立热交换器是快堆事故余热排出系统的关键设备之一。本文以ANSYS FLUENT为工具,对中国实验快堆现有的独立热交换器和一种改进的新型独立热交换器布置在快堆热池中的情况进行了瞬态数值模拟,并分析比较其结果,证明了改进型独立热交换器在热工水力上的可行性。本文工作对大型快堆的独立热交换器的设计具有一定的借鉴意义。     

自适应蒙特卡罗方法计算海水淡化堆非能动系统物理过程失效概率

物理过程失效的研究对于非能动系统十分重要。目前,已被广泛应用的重要抽样蒙特卡罗方法需要依赖改进的一次二阶矩法寻找设计点。本文应用自适应蒙特卡罗方法,利用自适应方法确定重要密度函数,避免了改进的一次二阶矩法的不足,提高了抽样效率,而且在相同的模拟条件下,可较好地改善相对误差。以245 MW海水淡化堆非能动系统为研究对象,用自适应蒙特卡罗方法和目前已有的其他方法研究非能动系统的物理失效概率,最后对各方法在非能动系统上的适用性进行比较分析。     

Failure probability evaluation of passive system using fuzzy Monte Carlo simulation

Passive systems have become an inherent feature of the advanced reactors. The main reason being the passive systems are, theoretically, more reliable than the active ones. Nevertheless the passive system may fail to fulfill its mission not only because of a consequence of classical mechanical failure of component (passive or active) of the passive system, but also due to the deviation from expected behavior due to physical phenomena mainly related to thermal hydraulic or due to different boundary or initial conditions. In this paper the methodology used for performing the passive system reliability analysis has been discussed. A case study on passive decay heat removal system (PDHRS) of large sized pressurized heavy water reactor (PHWR) has been discussed. Thermal hydraulic analysis have been carried out by using RELAP5 code to generate the response surface (from various ranges of identified key parameter values), keeping the criterion as clad surface temperature exceeding certain critical value. Some uncertainties, due to incomplete information, cannot be handled satisfactorily in the probability theory and the fuzzy set theory is more appropriate. In this study the random variables are considered as fuzzy numbers and the fuzzy set theory is employed. In addition, the Monte Carlo simulation technique is utilized to evaluate the probability of failure of system.     

核电厂安全系统冗余度研究

本文对核电厂安全系统冗余度的概念进行了澄清,认为不能简单地将安全系列的数量机械地等效于冗余度。N+1的冗余度满足单一故障准则的强制性要求,N+2的冗余度是实现在线维修的可选项。进而介绍了国际上主要核电机型的安全系统配置和冗余度,说明了冗余度与运行灵活性的具体关系。在冗余度研究的基础上,对三环路压水堆的两种安全系统配置方案(两个系列带母管和三个独立系列)进行了分析比较。两种方案均为N+1冗余度,但是对非能动部件(母管)单一故障的考虑有所差异。通过对我国和国际核安全法规、用户要求文件及相关标准的研究发现,非能动部件的单一故障问题不应成为这两个方案选择的决定因素。综合考虑安全性利益及经济性代价,两个系列带母管的方案是更加优化更平衡的设计。     

Validation of CATHARE V2.5 thermal-hydraulic code against full-scale PERSEO tests for decay heat removal in LWRs

The PERSEO experimental program was performed in the framework of a domestic research program on innovative safety systems with the purpose to increase the reliability of passive decay heat removal systems implementing in-pool heat exchangers. The conceived system was tested at SIET laboratories by modifying the existing PANTHERS IC-PCC facility utilized in the past for testing a full scale module of the GE-SBWR in-pool heat exchanger. Integral tests and stability tests were conducted to verify the operating principles, the steadiness and the effectiveness of the system. Two of the more representative tests have been analyzed with CATHARE V2.5 for code validation purposes. The paper deals with the comparison of code results against experimental data. The capabilities and the limits of the code in simulating such kind of tests are highlighted. An improvement in the modeling of the large water reserve pool is suggested trying to reduce the discrepancies observed between code results and test measurements.     

Probabilistic simulation of cable performance and water based protection in cable tunnel fires

Nuclear power plants contain a significant amount of fire load in form of electrical cables. The performance of the cables is interesting both from the fire development and system failure viewpoints. In this work, cable tunnel fires are studied using numerical simulations, focusing on the fire spreading along power cables and the efficiency of the water suppression in preventing the cable failures. Probabilistic simulations are performed using Monte Carlo technique and the Fire Dynamics Simulator (FDS) as the deterministic fire model. The primary fire load, i.e. the power cables are modelled using the one-dimensional pyrolysis model, for which the material parameters are estimated from the experimental data. Two different water suppression systems are studied. The simulation results indicate that using either suppression system decreased the heat release rate in the tunnel to less than 10% of the non-suppressed case. Without water suppression, the cables of the second sub-system were damaged in almost all fires, but when either of the studied water suppression systems was used, the probability of the cable failures was decreased to less than 1%. This result indicates that in current scenario, the probability of losing both sub-systems is determined directly by the suppression system unavailability.     

重要厂用水系统地震情况下可靠性分析

重要厂用水系统是核电厂重要的安全系统之一,其失效概率通常由系统可靠性分析获得。而地震情况下设备的失效概率是地震动峰值加速度的函数,且地震的发生又具有随机性,目前概率安全评价中传统的故障树分析方法对此种情况缺乏足够的处理能力。本文采用蒙特卡罗模拟方法解决条件概率的问题,针对地震情况系统可靠性分析,提出了评价模型,并对核电厂重要厂用水系统进行了分析计算,得到地震情况下重要厂用水系统的年失效概率为1.46×10^-4。计算结果与设备抗震性能数据符合,验证了分析模型的合理性。     

Fuzzy uncertainty modeling applied to AP1000 nuclear power plant LOCA

This article presents an uncertainty modeling study using a fuzzy approach applied to the Westinghouse advanced nuclear reactor. The AP1000 Westinghouse Nuclear Power Plant (NPP) is provided of passive safety systems, based on thermo physics phenomenon, that require no operating actions, soon after an incident has been detected. The use of advanced passive safety systems in NPP has limited operational experience. As it occurs in any reliability study, statistically non-significant events report introduces a significant uncertainty level about the failure rates and basic events probabilities used on the fault tree analysis (FTA). In order to model this uncertainty, a fuzzy approach was employed to reliability analysis of the AP1000 large break Loss of Coolant Accident (LOCA). The final results have revealed that the proposed approach may be successfully applied to modeling of uncertainties in safety studies.     

Critical parameter study of PWR primary coolant pipe leak failure using probabilistic fracture mechanics

This paper discusses the critical parameters which influence the failure probabilities of a PWR primary coolant loop. Probabilistic fracture mechanics (PFM) is applied for the parametric study, using the Monte Carlo program PRAISE to predict the failure probabilities of a PWR primary coolant loop from various distributions of input parameters. Parameters such as nondetection probability of preservice and inservice inspection, vibratory stress, residual stresses, and their correlations are extensively studied. Critical crack depth which causes immediate failure are calculated in the presence of various vibratory stresses with and without residual stresses. Crack growth schemes are determined with various initial defect depth and depth-length ratio as a function of plant operation time. The results show quantitatively how PWR primary coolant loop reliability can be greatly improved by increasing the sensitivity and decreasing the uncertainty of preservice nondestructive inspection.     

基于自适应MCMC和子集模拟的非能动系统热工水力可靠性评估

基于修正Metropolis-Hastings（MMH）算法的子集模拟（SS）方法在较低失效率水平下候选样本接受率降低、失效率估计误差增大、稳健性较差。为进一步提高SS用于反应堆非能动系统热工水力可靠性评估的精度、效率和稳健性，引入一种基于自适应条件采样（aCS）的马尔可夫链蒙特卡罗（MCMC）方法，提出了一种基于自适应MCMC和SS的非能动系统热工水力可靠性评估方法。以某型核动力装置二次侧非能动余热排出试验系统为例，给出了基于aCS的子集模拟（aCS-SS）与基于MMH的子集模拟（MMH-SS）在不同失效率水平下的性能比较。计算结果表明：较低失效率水平下aCS-SS能更好地使候选样本接受率在目标值附近保持稳定，失效率估计的精度和稳健性均高于MMH-SS。     

The fake of reliability measures as absolutes

It is claimed that any reliability measure defined in connection with a limit state theory of a high reliability technological system is a purely formal comparative measure of safety. It only makes sense to make comparisons within classes of “similar” technological systems which are all accessible to the same theory. Interpretation of calculated formal failure probabilities as predictions of real failure rates are generally not justified.     

Integration of functional reliability analysis with hardware reliability: An application to safety grade decay heat removal system of Indian 500 MWe PFBR

A passive system can fail either due to classical mechanical failure of components, referred to as hardware failure, or due to the failure of physical phenomena to fulfill the intended function, referred to as functional failure. In this paper a methodology is discussed for the integration of these two kinds of unreliability and applied to evaluate the integrated failure probability of the passive decay heat removal system of Indian 500 MWe prototype fast breeder reactor (PFBR). The probability of occurrence of various system hardware configurations is evaluated using the fault tree method and functional failure probabilities on the corresponding configurations are determined based on the overall approach reported in the reliability methods for passive system (RMPS) project. The variation of functional reliability with time, which is coupled to the probability of occurrence of various hardware system configurations is studied and incorporated in the integrated reliability analysis. It is observed that this consideration of the dependence of functional reliability on time will give significant advantages on system reliability. The integrated reliability analysis is also explained using an event tree. The impact of the provision for forced circulation in the primary circuit on functional reliability is also studied with this procedure and it is found that the forced circulation capability helps to bring down the total decay heat removal failure probability by lowering the peak temperatures after the reactor shut down.     

Application of first and second order reliability methods in the safety assessment of cracked steam generator tubing

The First- and Second Order Reliability Methods (FORM and SORM) have been applied in the safety assessment of steam generator tubes with through-wall axial stress corrosion cracks. The underlying probabilistic fracture mechanics model takes into account the scatter in tube geometry, material properties and stable crack propagation. Also, the effect of the maintenance strategy has been considered. A realistic numerical example has been given to compare the failure probabilities calculated by FORM and SORM to those obtained by different versions of Monte Carlo simulations. The relative errors of the numerical methods employed have been analysed, which has shown that FORM performs in an acceptable and SORM in an excellent manner. Some changes in failure surface properties, caused by different maintenance strategies, are indicated and a sensitivity analysis of influencing parameters is made. The results obtained demonstrate the applicability of FORM and SORM in the safety assessment of stress corrosion cracked steam generator tubing.