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.     

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.     

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 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.     

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。     

非能动安全系统可靠性评估方法初步研究

非能动安全系统可靠性的分析是广泛采用非能动设计的新一代核电厂概率安全评价(PSA)的重要内容,其量化分析需根据非能动安全系统可靠性评估对象,确定影响系统运行的关键参数,结合事件序列对非能动系统进行研究。本文以AP1000非能动余热排出系统(PRHRS)设计阶段的可靠性研究为例,结合丧失主给水事故,根据燃料包壳完整性以及系统稳定性的功能准则,确定影响PRHRS的关键参数和设计参数。采用拉丁超立方抽样(LHS)确定输入参数组合,运用RELAP5/MOD3程序进行不确定性传递计算,进行关键参数对系统功能敏感性评价与确认,进行系统功能可靠性分析,为AP1000概率安全评价提供PRHRS可靠性估计。     

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.     

功能可靠性分析方法在XAPR堆芯自然循环可靠性评价中的应用

功能失效是导致自然循环系统运行失效的重要因素,需要在其可靠性分析中予以考虑。基于功能可靠性评价流程,通过RELAP5程序模拟自然循环物理过程,对西安脉冲堆（XAPR）池水自然循环冷却堆芯能力的可靠性进行评价。结合中破口失水事故,根据包壳完整性的功能准则,确定影响自然循环的关键参数;采用拉丁超立方抽样确定输入参数组合,进行参数敏感性分析和功能可靠性评价,并将功能可靠性评价结果整合到概率安全评价（PSA）模型中。分析结果表明:在PSA模型中不仅需要考虑硬件可靠性,还应充分考虑功能可靠性,以更好地指导XAPR运行及提高其安全性。      

Validation of the periodicity of checks of nuclear power plant safety systems using the bars system of programs

The application of the BARS program system for choosing the optimal parameters for checking the serviceability of the safety systems of nuclear power plants is described. The types of checks as well as the mathematical models determining the reliability of the components of the system for each type of check are described. Calculations of the failure probability of the safety systems of nuclear power plants which incorporate components with different levels of reliability are presented. The values of the optimal period between serviceability checks for each type of system are determined. An evaluation of the effect of failures of a general type on the reliability of safety systems is presented for two forms of the α-factor model.     

LOCA事故下安全注射系统可靠性的GO-FLOW法分析

反应堆安全注射系统是包含复杂操作时序的动态系统,本文研究了应用GO-FLOW方法对其进行可靠性分析,导出了能将GO-FLOW用于含两种失效模式的可修部件状态概率计算的可靠性参数等效模型,并验证了模型的正确性。给出了实际算例,结果表明,GO-FLOW方法是对含时序问题的动态系统进行可靠性分析的有效工具,本文导出的可靠性参数等效模型提高了GO-FLOW对多状态问题的分析能力。     

Screening of critical parameters influencing thermal-hydraulic reliability of simple passive system

Robust safety nature of passive safety systems (PSSs) accounts for their increasing applications. Critical parameters (CPs) which influence reliability of thermal-hydraulic (t-h) PSSs are considered independent in most cases while considering their effects purposely for simplicity which may not be realistic. Findings affirmed reliability of t-h PSSs to be influenced by CPs that are dependent in most scenarios and thus, effects of CPs dependency which can directly/indirectly influence t-h reliability need to be considered. Reliability assessment methodologies (RAM) can thus be improved upon by considering the dependency of CPs in reliability analysis. In this regard, this paper considers the screening of CPs required to justify their dependency consideration in evaluating t-h reliability. The Pearson’s product moment correlation coefficient and covariance method were applied as illustration for the screening of the possible realistic CPs, which affect natural circulation of a passively water-cooled steam generator. The approach was used to determine the combinations of the CPs that are dependent and screens out those adjudged independent. Based on the results obtained, appropriate considerations (dependency/independency) can be made and further analysis of interest (failure/reliability) can be conducted for the system. Incorporation of this screening approach into the existing t-h RAMs will improve their efficiency.     

Reliability evaluation of a natural circulation system

This paper discusses a reliability study performed with reference to a passive thermohydraulic natural circulation (NC) system, named TTL-1. A methodology based on probabilistic techniques has been applied with the main purpose to optimize the system design. The obtained results have been adopted to estimate the thermal-hydraulic reliability (TH-R) of the same system.A total of 29 relevant parameters (including nominal values and plausible ranges of variations) affecting the design and the NC performance of the TTL-1 loop are identified and a probability of occurrence is assigned for each value based on expert judgment. Following procedures established for the uncertainty evaluation of thermal-hydraulic system codes results, 137 system configurations have been selected and each configuration has been analyzed via the Relap5 best-estimate code. The reference system configuration and the failure criteria derived from the “mission” of the passive system are adopted for the evaluation of the system TH-R.Four different definitions of a less-than-unity “reliability-values” (where unity represents the maximum achievable reliability) are proposed for the performance of the selected passive system. This is normally considered fully reliable, i.e. reliability-value equal one, in typical Probabilistic Safety Assessment (PSA) applications in nuclear reactor safety. The two ‘point’ TH-R values for the considered NC system were found equal to 0.70 and 0.85, i.e. values comparable with the reliability of a pump installed in an “equivalent” forced circulation (active) system having the same “mission.” The design optimization study was completed by a regression analysis addressing the output of the 137 calculations: heat losses, undetected leakage, loop length, riser diameter, and equivalent diameter of the test section have been found as the most important parameters bringing to the optimal system design and affecting the TH-R.As added values for this work, the comparison has been made between results from this study and results from a previous analysis where the same methodology was adopted for the evaluation of the TH-R of a different passive system named Isolation Condenser (IC). The comparison shows that the current single-phase NC system is ‘more reliable’ than the two-phase IC system. This constitutes a proof of qualification and of consistency for the adopted methodology.     

HTR-10应急电力系统设计及其调试

在充分利用高温气冷堆所具有的良好固有安全性这一特点的基础上，以安全级不间断电源装置组成了静止式新型应急电源系统，从而大大地减化了系统，降低了投资，并显著地提高了系统的安全性和可靠性，本文全成介绍了10MW高温气冷实验堆（HTR－10）应急电力系统的系统功能，主要设计原则，系统组成以及应急电力系统的核心设备－安全级不间断电源装置的运行方式和安全特性，并系统地总结了应急电力系统的调试工作。     

Response of proposed passive safety injection system for an intermediate size break LOCA on CHASNUPP-1

A passive safety injection system (PSIS) is proposed for Chashma nuclear power plant-1 (CHASNUPP-1) type nuclear power plants, for the simplification of their safety systems. This system is based upon passive components and is proposed in place of the existing safety injection system, for safety enhancement. The functionality of the proposed system is analyzed using reactor simulation. For this purpose an intermediate size break LOCA is simulated using the simulation software APROS. For this transient, different thermal-hydraulic parameters of the proposed and other safety related systems are presented and discussed. The results obtained show that the proposed system works properly by performing its role in the transient, leading to cold shutdown conditions.     

A comparative method for improving the reliability of brittle components

Calculating the absolute reliability built in a product is often an extremely difficult task because of the complexity of the physical processes and physical mechanisms underlying the failure modes, the complex influence of the environment and the operational loads, the variability associated with reliability-critical design parameters and the non-robustness of the prediction models. Predicting the probability of failure of loaded components with complex shape for example is associated with uncertainty related to: the type of existing flaws initiating fracture, the size distributions of the flaws, the locations and the orientations of the flaws and the microstructure and its local properties. Capturing these types of uncertainty, necessary for a correct prediction of the reliability of components is a formidable task which does not need to be addressed if a comparative reliability method is employed, especially if the focus is on reliability improvement. The new comparative method for improving the resistance to failure initiated by flaws proposed here is based on an assumed failure criterion, an equation linking the probability that a flaw will be critical with the probability of failure associated with the component and a finite element solution for the distribution of the principal stresses in the loaded component. The probability that a flaw will be critical is determined directly, after a finite number of steps equal to the number of finite elements into which the component is divided. An advantage of the proposed comparative method for improving the resistance to failure initiated by flaws is that it does not rely on a Monte Carlo simulation and does not depend on knowledge of the size distribution of the flaws and the material properties. This essentially eliminates uncertainty associated with the material properties and the population of flaws.On the basis of a theoretical analysis we also show that, contrary to the common belief, in general, for non-interacting flaws randomly located in a stressed volume, the distribution of the minimum failure stress is not necessarily described by a Weibull distribution. For the simple case of a single group of flaws all of which become critical beyond a particular threshold value for example, the Weibull distribution fails to predict correctly the probability of failure. If in a particular load range, no new critical flaws are created by increasing the applied stress, the Weibull distribution also fails to predict correctly the probability of failure of the component. In these cases however, the probability of failure is correctly predicted by the suggested alternative equation. The suggested equation is the correct mathematical formulation of the weakest-link concept related to random flaws in a stressed volume. The equation does not require any assumption concerning the physical nature of the flaws and the physical mechanism of failure and can be applied in any situation of locally initiated failure by non-interacting entities.     

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.     

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.     

Structural analysis of W7-X: Overview

The Wendelstein 7-X (W7-X) modular stellarator is in the assembly phase at the Max-Planck-Institut für Plasmaphysik (IPP) in Greifswald, Germany. The goal of the project is to demonstrate that this type of machine is a viable option for a fusion power-plant. The “pentagonal” magnet system of the machine encompasses 50 non-planar and 20 planar superconducting coils with sophisticated support structure. Structural reliability of components as well as resulting deformations and displacements during various modes of operation have to be considered not only for the magnet system but also throughout the whole cryostat whose main components are the plasma vessel, outer vessel, ports, and thermal insulation.A reliable prediction of the W7-X structural behaviour is only possible by employing complex finite element (FE) simulations with a hierarchical set of FE models. A special strategy has been developed and implemented for the task.The design is basically completed, main parameters are defined, and most of the W7-X components are manufactured. Therefore, the focus in the analysis is being shifted to the creation of parametric FE models which allow performing fast analyses of possible non-conformities, changes in the assembly procedure, and future exploration of operational limits.This paper gives an overview of the implemented analysis strategy, the applied safety margins, and focuses on the most remarkable results.     

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。     

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。