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。     

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。     

Methodology for the reliability evaluation of a passive system and its integration into a Probabilistic Safety Assessment

A methodology has been developed to evaluate the reliability of passive systems characterised by a moving fluid and whose operation is based on thermal–hydraulic (T-H) principles. The methodology includes:

• identification and quantification of the sources of uncertainties and determination of the important variables;

• propagation of the uncertainties through T-H models and assessment of T-H passive system unreliability;

• introduction of passive system unreliability in the accident sequence analysis.

Each step of the methodology is described and commented and a diagram of the methodology is presented. An example of passive system is presented with the aim to illustrate the possibilities of the methodology. This example is the Residual Passive heat Removal system on the Primary circuit (RP2), an innovating system supposed to be implemented on a 900 MWe Pressurized Water Reactor.     

The analytic hierarchy process as a systematic approach to the identification of important parameters for the reliability assessment of passive systems

Passive systems play a crucial role in the development of future solutions for nuclear plant technology. A fundamental issue still to be resolved is the quantification of the reliability of such systems.In this paper, we firstly illustrate a systematic methodology to guide the definition of the failure criteria of a passive system and the evaluation of its probability of occurrence, through the identification of the relevant system parameters and the propagation of their associated uncertainties. Within this methodology, we propose the use of the analytic hierarchy process as a structured and reproducible tool for the decomposition of the problem and the identification of the dominant system parameters. An example of its application to a real passive system is illustrated in details.     

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).     

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.     

Incorporating reliability analysis into the design of passive cooling systems with an application to a gas-cooled reactor

A time-dependent reliability evaluation of a two-loop passive decay heat removal (DHR) system was performed as part of the iterative design process for a helium-cooled fast reactor. The system was modeled using RELAP5-3D. The uncertainties in input parameters were assessed and were propagated through the model using Latin hypercube sampling. An important finding was the discovery that the smaller pressure loss through the DHR heat exchanger than through the core would make the flow to bypass the core through one DHR loop, if two loops operated in parallel. This finding is a warning against modeling only one lumped DHR loop and assuming that n of them will remove n times the decay power. Sensitivity analyses revealed that there are values of some input parameters for which failures are very unlikely. The calculated conditional (i.e., given the LOCA) failure probability was deemed to be too high leading to the identification of several design changes to improve system reliability. This study is an example of the kinds of insights that can be obtained by including a reliability assessment in the design process. It is different from the usual use of PSA in design, which compares different system configurations, because it focuses on the thermal–hydraulic performance of a safety function.     

Reliability assessment of passive containment isolation system using APSRA methodology

In this paper, a methodology known as APSRA (Assessment of Passive System ReliAbility) has been employed for evaluation of the reliability of passive systems. The methodology has been applied to the passive containment isolation system (PCIS) of the Indian advanced heavy water reactor (AHWR). In the APSRA methodology, the passive system reliability evaluation is based on the failure probability of the system to carryout the desired function. The methodology first determines the operational characteristics of the system and the failure conditions by assigning a predetermined failure criterion. The failure surface is predicted using a best estimate code considering deviations of the operating parameters from their nominal states, which affect the PCIS performance. APSRA proposes to compare the code predictions with the test data to generate the uncertainties on the failure parameter prediction, which is later considered in the code for accurate prediction of failure surface of the system. Once the failure surface of the system is predicted, the cause of failure is examined through root diagnosis, which occurs mainly due to failure of mechanical components. The failure probability of these components is evaluated through a classical PSA treatment using the generic data. The reliability of the PCIS is evaluated from the probability of availability of the components for the success of the passive containment isolation system.     

Passive system reliability analysis using Response Conditioning Method with an application to failure frequency estimation of Decay Heat Removal of PFBR

Innovative nuclear reactor designs include passive means to achieve high reliability in accomplishing safety functions. Functional reliability analyses of passive systems include Monte Carlo sampling of system uncertainties, followed by propagation through mechanistic system models. For complex passive safety systems of high reliability, Monte Carlo simulations using mechanistic codes are computationally expensive and often become prohibitive. Passive system reliability analysis using recently proposed Response Conditioning Method, which incorporates the insights obtained from approximate solutions like response surfaces in simulations to obtain computationally efficient and consistent probability estimates, is presented in this paper. The method is applied to evaluate the reliability of passive Decay Heat Removal (DHR) system of Indian Prototype Fast Breeder Reactor (PFBR). The accuracy as well as efficiency of the method is compared with direct Monte Carlo simulation. The variability of the reliability values is estimated using bootstrap technique. The system abilities, to prevent critical structural damage as well as to ensure operational safety, are quantitatively ascertained. The system functional failure probabilities are integrated with hardware failure probabilities and the inclusion of passive system unreliability in Probabilistic Safety Assessment is demonstrated.     

XAPR中破口失水事故下堆芯自然循环冷却能力的功能可靠性研究

功能失效是导致自然循环系统运行失效的重要因素,需在其可靠性分析中予以考虑。针对多维不确定性参数及小功能失效概率问题,提出了一种将改进响应面法及重要抽样子集模拟法相结合的功能可靠性分析方法。以西安脉冲堆（XAPR）堆池水自然循环冷却为例,结合中破口失水事故,考虑输入参数及模型的不确定性,对其进行了功能可靠性评估和灵敏度分析。结果表明：XAPR堆芯自然循环功能失效概率为3.796×10^-3,需充分考虑系统功能的可靠性。本文方法具有较高的计算效率,同时又能保证很高的计算精度,对XAPR堆芯自然循环非线性功能函数具有很强的适应性。     

Passive system reliability analysis using the APSRA methodology

In this paper, we present a methodology known as APSRA (Assessment of Passive System ReliAbility) for evaluation of reliability of passive systems. The methodology has been applied to the boiling natural circulation system in the Main Heat Transport System of the Indian AHWR concept. In the APSRA methodology, the passive system reliability is evaluated from the evaluation of the failure probability of the system to carryout the desired function. The methodology first determines the operational characteristics of the system and the failure conditions by assigning a predetermined failure criteria. The failure surface is predicted using a best estimate code considering deviations of the operating parameters from their nominal states, which affect the natural circulation performance. Since applicability of the best estimate codes to passive systems are neither proven nor understood enough, APSRA relies more on experimental data for various aspects of natural circulation such as steady-state natural circulation, flow instabilities, CHF under oscillatory condition, etc. APSRA proposes to compare the code predictions with the test data to generate the uncertainties on the failure parameter prediction, which is later considered in the code for accurate prediction of failure surface of the system. Once the failure surface of the system is predicted, the cause of failure is examined through root diagnosis, which occurs mainly due to failure of mechanical components. The failure probability of these components are evaluated through a classical PSA treatment using the generic data. Reliability of the natural circulation system is evaluated from the probability of availability of the components for the success of natural circulation in the system.     

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.     

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.     

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。     

Seismic hazard reassessment of an existing NPP in Slovenia

A seismic hazard reassessment of the site of an existing nuclear power plant in Slovenia was performed. For probabilistic seismic hazard analysis, the extended basic approach laid out by Cornell in 1968 was applied (Cornell, 1968). The study was based on existing data only. To overcome the lack of data and to handle uncertainties in the data, a multiple model approach was applied. Tectonic interpretations, seismic source determinations and estimates of the uncertainty were made by three independent groups of earth-scientists. The delineation of seismic sources and the estimation of their parameters were defined by the distribution of earthquakes, by fault rupture sizes, and by fault slip rates. The Gutenberg–Richter doubly truncated exponential recurrence relationship was used for magnitude distribution. Lower-bound magnitude was set at 5.0 for all seismic sources. Maximum observed earthquakes and assumed fault rupture sizes were used as the main criteria for the estimation of upper-bound magnitudes of area and fault sources respectively. The activity rates were either based on the catalogue or estimated from the assessed average fault slip rates. Subjective weights were assigned to model alternatives and to source parameter alternatives. The results of the study are presented as seismic hazard curves and spectra.     

Evaluation of the dependencies related to passive system failure

A major issue to be addressed in safety and risk studies related to advanced reactors is the reliability of the implemented passive safety features. The passive safety system operation is a quite complex process. This complexity gives rise to unpredictable failure patterns. While there are a number of well-established failure analysis (physics-of-failure) models for individual components, these models do not hold good for complex systems as their failure behaviours may be totally different. Failure analysis of individual components does consider the environmental interactions but is unable to capture the system interaction effects on failure behaviour. These models are based on the assumption of independent failure mechanisms. Dependency relationships and interactions of components in a complex system might give rise to some new types of failures that are not considered during the individual failure analysis of that component.The approach to the passive system reliability assessment based on independent modes of failure begins by identifying critical parameters, as input to basic events, corresponding to the failure modes, arranged in a series system configuration. Within this methodology, the selected system critical parameters are properly modelled through the construction of probability functions. The application of the methodology to a realistic thermal-hydraulic passive system design is illustrated. The analysis reveals that the critical parameters are not suitable to be chosen independently of each other, mainly because of the expected synergism between the different phenomena under investigation, with the potential to jeopardize the system performance. This conclusion allows the implementation of the proposed methodology, by properly capturing the interaction between various failure modes.     

Simulation of the small modular reactor severe accident scenario response to SBO using MELCOR code

Advanced small modular reactors (SMRs) use different design in the systems, structures, components from large reactors for achieving a high level of safety and reliability. In present work, the SMRs severe accident caused by the station blackout (SBO) was modeled and analyzed using MELCOR code, and the simulation of the accident scenario response to SBO was conducted. Based on the steady state calculation, which agrees well with designed values, we introduced the SBO accident for transient calculation. First, the case of the SBO accident without the passive core cooling system (PXS) was calculated. The progression and scenario in the reactor pressure vessel (RPV) and the containment were simulated and analyzed, including the transient response, cooling capacity and thermal-hydraulic characteristics and so on. The station black-out transient in the SMR can be simulated accurately, and the main failure model in the accident process can be concluded. Then three other cases of the SBO accident with different passive safety systems (core makeup tank (CMT), accumulator (ACC), passive residual heat removal system heat exchanger (PRHR HX), automatic depressurization system (ADS)) of the PXS were calculated respectively, and the results for different passive safety systems were compared. The passive core cooling system can not only provide water to the primary coolant system, but also take away the reactor decay residual heat. So in a station black-out transient, we can get more time for restoring AC power, and effectively prevent the accidents such as Fukushima.     

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.     

Addressing the challenges posed by advanced reactor passive safety system performance assessment

Passive safety features play an essential role in the development of nuclear technology and within advanced water cooled reactor designs. The assessment of the reliability of such systems in the frame of plant safety and risk studies is still an open issue. This complexity stems from a variety of open points coming out from the efforts conducted so far to address the topic and concern, for instance, the amount of uncertainties affecting the system performance evaluation, including the uncertainties related to the thermal-hydraulic (T-H) codes, as well as the integration within an accident sequence in combination with active systems and human actions. These concerns should be addressed and conveniently worked out, since it is the major goal of the international community (e.g. IAEA) to strive to harmonize the different proposed approaches and to reach a common consensus, in order to add credit to the underlying models and the eventual out coming reliability figures. The main key points that may influence the reliability analysis are presented and discussed and a viable path towards the implementation of the research efforts is delineated, with focus on T-H passive systems.     

Addressing the heavy liquid metal – Water interaction issue in LBE system

The interaction between heavy liquid metal (HLM) and water is a safety concern for the preliminary designs of lead fast reactor (i.e. LFR) and of subcritical transmutation system prototypes (i.e. XT-ADS). Current pool-type configurations have steam generators (SG) inside the reactor vessel. This implies that the primary to secondary leak (e.g. steam generator tube rupture) shall be considered as a postulated initiating event. The issue is addressed for CIRCE facility in ICE (Integral Circulation Experiment) configuration. CIRCE facility is a large pool system aimed at studying key operating principles of Lead Bismuth Eutectic (and Lead) systems. The configuration ICE was carried out to perform integral experiments, simulating the coupling between a high-performance heat source (electrically heated fuel bundle) and the heat exchanger, which was representative of the preliminary design of the XT-ADS heat exchanger. A Failure Mode and Effect Analysis (FMEA) is applied in order to get a complete picture of all the failure modes pertaining to this system, to determine their effects and to classify them according to their severity. The outcome of the analysis has identified as major hazard, relative to the CIRCE facility in the ICE configuration, the risk related to the LBE/water reaction, although with a very low probability, with the potential for a suddenly and dangerous pressurization (beyond the failure threshold) within the main vessel. A SIMMER-III code model of the system has been setup to provide deterministic results of the scenario. The results are supported by means of a LBE/water interaction experiment executed in LIFUS5 facility. LIFUS5 is a separate effect test facility dedicated to the investigation of LBE/water interaction. SIMMER-III code pre-test and post-test analyses are performed to define the boundary conditions of the experiment and to demonstrate the reliability of the code in simulating the phenomena of interest. The activity contributes to solving the safety issue raised for the operation of CIRCE facility and it provides a sample approach for addressing the safety studies needed in the development of the lead fast reactor and of the subcritical transmutation system.