Uncertainty analysis of system reliability and availability assessment

Uncertainty analysis of system reliability assessments with particular emphasis on commercial nuclear power generation stations have been investigated. Sources of uncertainty in reliability assessments are identified, and methods to account for their treatment are discussed. Available methods for determining uncertainties in system characteristics (such as unavailability) by synthesizing the known or assumed uncertainties in component characteristics (propagation of errors) are presented and compared.New or improved codes developed in this study are compared with previous methods. The use of a data base management system, common cause failure analysis and the influence of noncoherent structures in minimizing uncertainty in reliability assessment are discussed.     

Archaeological analogs and the future of nuclear waste glass

Nuclear energy produces long-lived radioactive waste. Glass containment matrices are used to stabilize such waste and to prevent radionuclide dispersion. Over the past few decades, phenomenological models have been developed to predict the long-term behavior of these materials in anticipation of disposal in a deep geological formation. But considering the geological time scales necessary for radioactive decay validating these models is a challenge. Here we show how the validation of the predictive capacity of a mechanistic model applied to archaeological glass alteration bridges the gap between the short-term laboratory data and the long-term evolution of natural system in complex environment. This model applied to nuclear glass provides reliable uncertainties on long-term alteration rates and demonstrates that present models used in the safety calculations are conservative.     

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.     

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.     

Applying mechanistic models to reliability evaluation of mechanical components – An illustration

The traditional reliability analyses, considers components to be in binary state, either functional or faulty, and does not consider the concept of multi state or intermediate states between these two binary states. However, there are several components, which need to be operated in different states and their failure criterion also depend on these states. Hence, when dealing with these types of components one should use multi state concept. This can be achieved by modeling the components with mechanistic models, which can give a new dimension for reliability analysis for multiple states. The mechanistic model approach is based on the first principles of science and engineering which provides details about the various failure mechanisms and thereby improved understanding of the associated root causes of the failure and driving forces responsible for component failures. In this paper a general methodology for modeling the components with mechanistic models has been explained and is further illustrated with an example component. A case study on feed water system (consisting of control valves and other mechanical components) of a typical nuclear reactor has been presented.     

Reliability analysis of nuclear component cooling water system using semi-Markov process model

A reliability analysis of nuclear component cooling water (NCCW) system is carried out. Semi-Markov process model is used in the analysis because it has potential to solve a reliability block diagram with a mixture of repairable and non-repairable components. With Markov models it is only possible to assume an exponential profile for component failure times. An advantage of the proposed model is the ability to assume Weibull distribution for the failure time of components. In an attempt to reduce the number of states in the model, it is shown that usage of poly-Weibull distribution arises. The objective of the paper is to determine system failure probability under these assumptions. Monte Carlo simulation is used to validate the model result. This result can be utilized as an initiating event probability in probabilistic safety assessment projects.     

Numerical computation of fragility curves for NPP equipment

The seismic probabilistic risk assessment (PRA) methodology is a popular approach for evaluating the risk of failure of engineering structures due to earthquake. In this framework, fragility curves express the conditional probability of failure of a structure or component for a given seismic input motion parameter A, such as peak ground acceleration (PGA) or spectral acceleration. The failure probability due to a seismic event is obtained by convolution of fragility curves with seismic hazard curves. In general, a log-normal model is used in order to estimate fragilities. In nuclear engineering practice, these fragilities are determined using safety factors with respect to design earthquake. This approach allows to determine fragility curves based on design study but largely draws on expert judgement and simplifying assumptions. When a more realistic assessment of seismic fragility is needed, simulation-based statistical estimation of fragility curves is more appropriate. In this paper, we will discuss statistical estimation of parameters of fragility curves and present results obtained for a reactor coolant system of nuclear power plant. We have performed non-linear dynamic response analyses using artificially generated strong motion time histories. Uncertainties due to seismic loads as well as model uncertainties are taken into account and propagated using Monte Carlo simulation.     

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。     

Reliability analysis of pipe whip impacts

A probability-based approach is presented as the integration of probabilistic methods and deterministic modelling based on the finite element method. An existing finite element software package was linked to an existing probabilistic package to analyse the complex mechanics that occur during the transient non-linear analysis of impact problems. This methodology is applied to a pipe whip analysis of a group-distribution-header, which results from a guillotine break, and subsequent impact with the adjacent building wall; this is a postulated accident for the Ignalina Nuclear Power Plant RBMK-1500 reactors. The uncertainties of material properties, component geometry data and loads were taken into consideration. The probabilities of failure of the impacted header and of the header support-wall were estimated given uncertainties in material properties, geometrical parameters and loading. The software ProFES was used for the probabilistic analysis and the finite element software NEPTUNE for deterministic structural integrity evaluation. The Monte Carlo Simulation, First Order Reliability method and Response Surface method were used in the probabilistic analysis.     

Prediction of residual stress in the welding zone of dissimilar metals using data-based models and uncertainty analysis

Since welding residual stress is one of the major factors in the generation of primary water stress-corrosion cracking (PWSCC), it is essential to examine the welding residual stress to prevent PWSCC. Therefore, several artificial intelligence methods have been developed and studied to predict these residual stresses. In this study, three data-based models, support vector regression (SVR), fuzzy neural network (FNN), and their combined (FNN + SVR) models were used to predict the residual stress for dissimilar metal welding under a variety of welding conditions. By using a subtractive clustering (SC) method, informative data that demonstrate the characteristic behavior of the system were selected to train the models from the numerical data obtained from finite element analysis under a range of welding conditions. The FNN model was optimized using a genetic algorithm. The statistical and analytical uncertainty analysis methods of the models were applied, and their uncertainties were evaluated using 60 sampled training and optimization data sets, as well as a fixed test data set.     

Evaluation of uncertainties related to passive systems performance

A methodological and structured procedure to address the uncertainties related to passive safety functions is presented. The matter is treated with reference to a passive system designed for decay heat removal of advanced light water reactors, relying on natural circulation and provided with a heat exchanger immersed in a cooling pool, acting as heat sink, and connected to the pressure vessel via steam and condensate main lines. Two hazard identification used qualitative methods, as failure mode and effect analysis (FMEA) and hazard and operability study (HAZOP), are utilized and the relative results compared in order to assess the main sources of physical failure. The identification of the sources of uncertainties related to passive system performance, in terms of parameters which drive the failure mechanisms, follows. Finally the uncertainties are evaluated both for their assessment in probabilistic terms and for the determination of most contributors to the system thermal-hydraulic response.     

基于失效物理模型的聚变堆包层管道可靠性数据修正方法研究

由于聚变堆部件特殊的运行环境,部件可靠性数据极度匮乏,通常采用环境因子方法对现有可靠性数据进行修正,但现有可靠性数据修正模型未考虑解决高温模型不能适用的问题。本文提出了高温环境下的失效物理模型修正优化方法,提升了高温失效物理模型在极端环境下的适用范围和部件服役寿命修正精度,并基于失效物理模型修正方法开展了ITER中国氦冷固态包层氚提取系统(TES)管道可靠性数据修正研究,为TES系统可靠性分析提供了数据支持。     

Structured treatment of model uncertainty in complex thermal-hydraulics codes: Technical challenges, prospective and characterization

Code structure uncertainties (model uncertainty) are a crucial source of uncertainty quantification for thermal-hydraulics (TH) system codes, an assembly of models and correlations that simulate physical phenomena and the behavior of system. Technical challenges dealing with the subject are discussed in this paper with the prospective of TH codes model uncertainty characterization. A literature review was conducted on the subject matter to evaluate the state of the art on the topic. A key characteristic of thermal-hydraulics systems codes is complexity. This complexity has its roots in the composite structure of these systems that comprise of many different elements (or sub-systems) whose state inevitably affects the state of the whole system. Its main implication is the dynamic (i.e., many interdependent variables in time) and/or non-linear behavior. Several different situations are met dealing with the TH model uncertainty. In some cases there are alternative sub-models, or several different correlations for calculating a specific phenomenon of interest. There are also “user options” for choosing one of several models, or correlations in performing a specific code computation. Dynamic characteristics of TH add more complexity to the code calculation, meaning, for example, that specific code models and correlations invoked are sequence-dependent, and require certain (dynamic) conditions. This paper discusses the techniques developed in the Integrated Methodology for Thermal-Hydraulics Uncertainty Analysis (IMTHUA), specifically for the treatment of uncertainties due to code structure and models. The methodology comprehensively covers various aspects of complex code uncertainty assessments for important accident transients. It explicitly examines the TH code structural uncertainties by treating internal sub-model uncertainties and by propagating such model uncertainties in the code calculations, including uncertainties about input parameters. Structural uncertainty assessment (model uncertainty) for a single model will be discussed in terms of “correction factor,” “bias,” and Bayesian sub-model output updating with available experimental evidence. In case of multiple alternative models, several techniques, including dynamic model switching, user-controlled model selection, and model mixing, are discussed. Examples from different applications, including Marviken Blowdown, LOFT LBLOCA, and typical PWR LOCA scenario calculations, are provided for greater clarification of the proposed techniques.     

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).     

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.     

防御共因失效对策有效性估计方法

共因失效严重低系统可靠性，增加事故序列发生频率，影响安全运行。故近１０多年来，国际上广泛地开展对它的研究，提出了许多分析模型。但至今的研究工作都集中于对共因失效问题的讨论和定量估计，对防御共因失效对策及其有效性的研究工作却很少。本文以部件失效数据收集和工程判断为基础，运用降低矩阵和模糊集并运算原理，建立防御共因失效对策有效性估计模型，并例示其应用方法。     

Probabilistic seismic safety study of an existing nuclear power plant

This study was conducted as part of an overall safety study of the Oyster Creek nuclear power plant. The earthquake hazard was considered as an initiating event that could result in radioactive release from the site as a result of core melt. The probability of earthquake initiated releases were compared with the probability of releases due to other initiating events.Three steps are necessary to evaluate the probability of earthquake initiated core melt.

1. (1) estimate the ground motion (peak ground acceleration) and uncertainty in this estimate as functions of annual probability of occurrence;

2. (2) estimate the conditional probability of failure and its uncertainty for structures, equipment, piping, controls, etc., as functions of ground acceleration; and

3. (3) combine these estimates to obtain probabilities of earthquake induced failure and uncertainties in such estimates to be used in event trees, system models, and fault trees for evaluating the probability of earthquake induced core melt.

This paper concentrates on the first two steps with emphasis on step 2. The major difference between the work presented and previous papers is the development and use of uncertainty estimates for both the ground motion probability estimates and the conditional probability of failure estimates.The ground motion capacity of a structure, component, etc., is treated for simplicity and clarity as a product random variable A given by , where is the best estimate of the median ground acceleration capacity, _R and _U are lognormal random variables with unit median and logarithmic standard deviation β_R and β_U, respectively. β_R expresses the dispersion in the ground acceleration capacity due to underlying randomness from such sources as (1) the variability of an earthquake time-history and thus of structural response when the earthquake is only defined in terms of the peak ground acceleration; and (2) the variability of structural material properties associated with strength, inelastic energy absorption and damping. Essentially, β_R represents those sources of dispersion which cannot be reduced by more detailed evaluation or more data. Uncertainty concerning the ground motion capacity is expressed by β_U which results from such things as (1) lack of complete knowledge of structural material properties; and (2) errors in calculating response due to approximate modelling. This paper presents a methodology (with examples) for estimating , β_R, and β_U for structures and components. These estimates are then used to estimate conditional probabilities of failure with confidence bounds on these estimates.The conclusion is that a rational approach exists for estimating earthquake induced probabilities of failure. Confidence bounds on such estimates can be developed to express uncertainty in the parameters used. Such an approach is preferable over one in which dispersion due to underlying randomness, and due to uncertainty in the data are combined into a single probability of failure estimate with no estimate of the uncertainty in this probability.     

Failure pressure evaluation of the containment building of a large dry nuclear power plant

The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described in this paper. The proposed method considers fully three-dimensional finite element models in order to take into account the effect of the most significant structural characteristics (presence of three buttresses, penetrations, additional reinforcement around the penetrations, etc.), the lack of symmetry of the forces generated by the prestressing system, as well as the nonlinear behaviour of the materials and the sensitivity of the results to uncertainties associated with several parameters. The computational model is completely described, including the constitutive equations for the concrete, the reinforcing steel and prestressing tendons, the spatial discretization—isoparametric elements including the reinforcement are used. The structural models and the analyses performed for their calibration are also described. The influence on the failure pressure of incorporating the foundation slab in the structural model, and the influence of the thermal effects, are discussed. One of the conclusions of the numerical study is that the failure process can be appropriately simulated by means of a structural model which does not include either the foundation slab or the thermal effects. Finally, results of a probabilistic simulation of the failure pressure are given.