First-order differential sensitivity analysis of a nuclear safety system by Monte Carlo simulation

In this paper we employ a Monte Carlo method to compute the first-order, differential sensitivity indexes of the basic events characterizing the reliability behavior of the containment spray injection system of a nuclear power plant. An exemplification is provided as to how the obtained sensitivity indexes can be used to drive improvements in the system design and operation.     

Monte Carlo simulation for model-based fault diagnosis in dynamic systems

Fault diagnosis requires the accurate estimation of the dynamic state of the system in real time. This can be pursued starting from a model of the system dynamics and on measurements related to the state of the system. In real applications, the nonlinearity of the model and non-Gaussianity of the noise typically affecting the measurement challenge the classical approximate approaches, e.g. the extended-Kalman, Gaussian-sum and grid-based filters, which often turn out to be inaccurate and/or too computationally expensive for real-time applications. On the contrary, Monte Carlo estimation methods, also called particle filters, can be very effective. Based on sequential importance sampling and on a Bayesian formulation of the estimation problem, these methods recursively approximate the relevant probability distributions of the system state by random measures composed of particles (sampled values of the unknown state variables) and associated weights.The present paper aims at demonstrating the power of particle filtering for fault diagnosis. This is done by applying an estimation procedure called sampling importance resampling (SIR) to a case study of literature.     

Probabilistic physics-of-failure models for component reliabilities using Monte Carlo simulation and Weibull analysis: a parametric study

In reliability engineering, component failures are generally classified in one of three ways: (1) early life failures; (2) failures having random onset times; and (3) late life or ‘wear out’ failures. When the time-distribution of failures of a population of components is analysed in terms of a Weibull distribution, these failure types may be associated with shape parameters β having values <1, 1, and >1 respectively. Early life failures are frequently attributed to poor design (e.g. poor materials selection) or problems associated with manufacturing or assembly processes.

We describe a methodology for the implementation of physics-of-failure models of component lifetimes in the presence of parameter and model uncertainties. This treats uncertain parameters as random variables described by some appropriate statistical distribution, which may be sampled using Monte Carlo methods. The number of simulations required depends upon the desired accuracy of the predicted lifetime. Provided that the number of sampled variables is relatively small, an accuracy of 1–2% can be obtained using typically 1000 simulations.

The resulting collection of times-to-failure are then sorted into ascending order and fitted to a Weibull distribution to obtain a shape factor β and a characteristic life-time η.

Examples are given of the results obtained using three different models: (1) the Eyring–Peck (EP) model for corrosion of printed circuit boards; (2) a power-law corrosion growth (PCG) model which represents the progressive deterioration of oil and gas pipelines; and (3) a random shock-loading model of mechanical failure. It is shown that for any specific model the values of the Weibull shape parameters obtained may be strongly dependent on the degree of uncertainty of the underlying input parameters. Both the EP and PCG models can yield a wide range of values of β, from β>1, characteristic of wear-out behaviour, to β<1, characteristic of early-life failure, depending on the degree of dispersion of the uncertain parameters. If there is no uncertainty, a single, sharp value of the component lifetime is predicted, corresponding to the limit β=∞. In contrast, the shock-loading model is inherently random, and its predictions correspond closely to those of a constant hazard rate model, characterized by a value of β close to 1 for all finite degrees of parameter uncertainty.

The results are discussed in the context of traditional methods for reliability analysis and conventional views on the nature of early-life failures.     

Dynamic bounds coupled with Monte Carlo simulations

For the reliability analysis of engineering structures a variety of methods is known, of which Monte Carlo (MC) simulation is widely considered to be among the most robust and most generally applicable. To reduce simulation cost of the MC method, variance reduction methods are applied. This paper describes a method to reduce the simulation cost even further, while retaining the accuracy of Monte Carlo, by taking into account widely present monotonicity. For models exhibiting monotonic (decreasing or increasing) behavior, dynamic bounds (DB) are defined, which in a coupled Monte Carlo simulation are updated dynamically, resulting in a failure probability estimate, as well as a strict (non-probabilistic) upper and lower bounds. Accurate results are obtained at a much lower cost than an equivalent ordinary Monte Carlo simulation. In a two-dimensional and a four-dimensional numerical example, the cost reduction factors are 130 and 9, respectively, where the relative error is smaller than 5%. At higher accuracy levels, this factor increases, though this effect is expected to be smaller with increasing dimension. To show the application of DB method to real world problems, it is applied to a complex finite element model of a flood wall in New Orleans.     

A Monte Carlo simulation approach to the availability assessment of multi-state systems with operational dependencies

This paper deals with multi-state systems (MSS), whose performance can settle on different levels, e.g. 100%, 80%, 50% of the nominal capacity, depending on the operative conditions of the constitutive multi-state elements. Examples are manufacturing, production, power generation and gas and oil transportation systems. Often in practice, MSS are such that operational dependencies exist between the system state and the state of its components. For example, in a production line of nodal series structure, with no buffers between the nodes, if one of the nodes throughput changes (e.g. switches from 100% to 50% due to a deterministic or stochastic transition of one of its components), the other nodes must be reconfigured (i.e. their components must deterministically change their states) so as to provide the same throughput.In this paper, we present a Monte Carlo simulation technique which allows modelling the complex dynamics of multi-state components subject to operational dependencies with the system overall state. A correlation method is tailored to model the automatic change of state of the relevant components following a change in one of the system nodes. The proposed technique is verified on a simple case study of literature.     

Analysis of truncation limit in probabilistic safety assessment

A truncation limit defines the boundaries of what is considered in the probabilistic safety assessment and what is neglected. The truncation limit that is the focus here is the truncation limit on the size of the minimal cut set contribution at which to cut off. A new method was developed, which defines truncation limit in probabilistic safety assessment. The method specifies truncation limits with more stringency than presenting existing documents dealing with truncation criteria in probabilistic safety assessment do. The results of this paper indicate that the truncation limits for more complex probabilistic safety assessments, which consist of larger number of basic events, should be more severe than presently recommended in existing documents if more accuracy is desired. The truncation limits defined by the new method reduce the relative errors of importance measures and produce more accurate results for probabilistic safety assessment applications. The reduced relative errors of importance measures can prevent situations, where the acceptability of change of equipment under investigation according to RG 1.174 would be shifted from region, where changes can be accepted, to region, where changes cannot be accepted, if the results would be calculated with smaller truncation limit.     

Prediction of micro-channel flows using direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) method is a particle-based numerical modeling technique. It is recently used for simulating gaseous flow in micro-electro-mechanical-systems (MEMS) where micron-scale features become important. In this paper, numerical simulations of fluid flow in micro-channels are carried out using the DSMC method. The details in determining the parameters critical for DSMC applications in micro-channels are provided. Streamwise velocity distributions in the slip-flow regime are compared with the analytical solution based on the Navier–Stokes equations with slip velocity boundary condition. Satisfactory agreements have been achieved. Effects of the entrance and exit regions on simulation results are discussed. Simulations are then extended to transition flow regime (Kn>0.1) and compared with the analytical solution. It is shown that the results are distinguished with the analytical solutions, which fail to predict the flow due to the break down of continuum assumption. It is indicated that the gradient of the pressure along the channel direction dominates the motion of the fluid flow.     

Identification of missing scenarios in ESDs using probabilistic dynamics

The event sequence diagram (ESD) framework can be used to qualitatively represent dynamic scenarios. The solution of ESDs can be performed in an analytical manner. Since the construction of ESDs has some inherent analyst dependence, there is scope for omitting scenarios due to certain simplifying assumptions. This is one of the prime drawbacks of the ESD framework. This paper presents an approach for identifying missing scenarios by combining ESDs with probabilistic dynamics. The approach also helps in reducing the variance of a Monte Carlo simulation procedures.     

Numerical simulation of point-to-plane corona discharge using a Monte Carlo method

Monte Carlo simulation techniques are used to study the dynamical properties of charged particles in point-to-plane corona discharge. The numerical model includes the release of electron-ion pairs by photoionization and secondary electron emission from cathode as well as the first Townsend ionization. The simulation results of negative corona discharge in nitrogen show that electron avalanche takes place in the region of high electric field near pin electrode and the photoionization is the essential mechanism to sustain the discharge as well as electron impact ionization.     

磁性多层膜系统自旋重取向行为的Monte Carlo模拟

依据Heisenberg模型,利用Monte　Carlo方法模拟了磁性多层膜系统的自旋重取向行为,研究了各向异性、偶极相互作用以及外磁场对系统自旋取向的影响。通过模拟计算,获得了系统组态、磁分量等随偶极相互作用、外加磁场和温度的变化规律,重点研究了磁性多层膜系统在外磁场作用下的磁滞现象。     

Monte Carlo simulation analysis of the effects of different system performance levels on the importance of multi-state components

In the present paper, we consider some frequently used importance measures, in their generalized form proposed by the authors for application to multi-state systems constituted by multi-state components. To catch the dynamics of multi-state systems, Monte Carlo simulation has been utilized. A simulation approach has been presented which allows estimating of all the importance measures of the components at a given performance level in a single simulation, provided that the components are independent. The effects of different performance demands made on the system on the importance of its multi-state components have been examined with respect to a simple multi-state series–parallel system. The results have shown that a performance level of a component may be more critical for the achievement of a system performance and less critical for another.     

Quantitative Analysis of Dynamic Fault Trees Based on the Coupling of Structure Functions and Monte Carlo Simulation

This paper focuses on the quantitative analysis of Dynamic Fault Trees (DFTs) by means of Monte Carlo simulation. In a previous article, we defined an algebraic framework allowing to determine the structure function of DFTs. We exploit this structure function and the minimal cut sequences that it allows to determine, to know the failure mode configuration of the system, which is an input of Monte Carlo simulation. We show that the results obtained are in good accordance with theoretical results and that some results, such as importance measures and sensitivity indexes, are not provided by common quantitative analysis and yet interesting. We finally illustrate our approach on a DFT example from the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Monte Carlo estimation of the differential importance measure: application to the protection system of a nuclear reactor

In this paper, we perform a reliability/availability analysis by means of the Monte Carlo simulation method and illustrate a perturbation method, inherited from the particle transport field, which allows to compute first-order, differential sensitivity indexes with little additional computational effort. The proposed method is illustrated first on a simple case study and, successively, on a nuclear safety system, the reactor protection system. In these applications, the sensitivity indexes are used to compute the differential importance measure, recently introduced to respond to the need of the analyst/decision maker to get information about the importance of changes in the stochastic properties of system components.     

Production rate of synchronous transfer lines using Monte Carlo simulation

In this paper, we consider unpaced synchronous transfer lines producing a single product. The transfer line stations are arranged in a series con?guration, have no buffers, and are subject to operation-dependent failures. Throughput is an important performance measure for transfer lines, and we have adopted that measure. Analytical methods for determining capacity of such transfer lines are available only for the simplest systems, but we show Monte Carlo simulation to be a fast, flexible, easy, and accurate method of estimating throughput in lines of any length and having a wide range of operating characteristics.     

Biased Monte Carlo unavailability analysis for systems with time-dependent failure rates

In this paper we consider systems made of components with time-dependent failure rates. A proper analysis of the time-dependent failure behaviour is very important for considerations of life-extension of safety critical systems such as nuclear power plants. This problem is tackled by Monte Carlo simulation which does not suffer from the additional complexity introduced by the model parameters' time inhomogeneity.The high reliability of the systems typically encountered in practice entails resorting to biasing techniques for favouring the events of interest. In this work, we investigate the possibility of biasing the system failures to be distributed in time according to exponential laws. The drawbacks encountered in such procedure have driven us towards the adoption of biasing schemes relying on uniform distributions which distribute failures over the system life more evenly.     

Fatigue crack growth prediction in nuclear piping using Markov chain Monte Carlo simulation

In this paper, we present and demonstrate a methodology to improve probabilistic fatigue crack growth (FCG) predictions by using the concept of Bayesian updating using Markov chain Monte Carlo simulations. The methodology is demonstrated on a cracked pipe undergoing fatigue loading. Initial estimates of the FCG rate are made using the Paris law. The prior probability distributions of the Paris law parameters are taken from the tests on specimen made of the same material as that of pipe. Measured data on crack depth over number of loading cycles are used to update the prior distribution using the Markov chain Monte Carlo. The confidence interval on the predicted FCG rate is also estimated. In actual piping placed in a plant, the measured data can be considered equivalent to the data received from in-service inspection. It is shown that the proposed methodology improves the fatigue life prediction. The number of observations used for updating is found to leave a significant effect on the accuracy of the updated prediction.     

光子在闪烁晶体中传输的蒙特卡罗模拟

为了找到构筑闪烁晶体探测器的优化方法，使用蒙特卡罗方法对闪烁晶体BGO（Bi4Ge3O12，锗酸铋）的光收集效率进行了模拟研究。模拟结果表明：入射面为粗糙面，其余为抛光面，同时外层包装上高反射率的材料，可得到最大的光输出（约59．1％的光子被收集）；耦合剂的折射率的得到高的光输出也起着非常重要的作用。     

Challenges in using a probabilistic safety assessment in a risk informed process (illustrated using risk informed inservice inspection)

Many of the ongoing and expected uses of Probabilistic Safety Assessment (PSA)¹ create new challenges to ensuring that the resulting conclusions are valid. This paper provides a summary of some of these challenges. Work conducted by the authors on Risk-Informed Inservice Inspection (RI-ISI) is used to illustrate these challenges. Means to address all of the challenges are not provided in detail in this paper. Several earlier papers discuss how these challenges can be addressed. References are provided for the interested reader (Chapman JR et al. In: PSA '95, vol. 1, Seoul, 1995: 177–80; Chapman JR et al. In: ICONE-IV, New Orleans, 1996; Dimitrijevic VB et al. In: Croatian Nuclear Society International Conference, Opatija, 1996: 245–54; Dimitrijevic VB et al. In: Croatian Nuclear Society International Conference, Opatija, 1996: 255–62; Dimitrijevic VB. In: Yugoslav Nuclear Society Conference, Belgrade, 1996: 53–61; O'Regan PJ et al. In: PSA '95, Seoul, vol. 1, 1995: 403–5; O'Regan PJ. In: ICONE-IV, vol. 5, New Orleans, 1996: 277–80).     

Modeling uncertainty in risk assessment: An integrated approach with fuzzy set theory and Monte Carlo simulation

Modeling uncertainty during risk assessment is a vital component for effective decision making. Unfortunately, most of the risk assessment studies suffer from uncertainty analysis. The development of tools and techniques for capturing uncertainty in risk assessment is ongoing and there has been a substantial growth in this respect in health risk assessment. In this study, the cross-disciplinary approaches for uncertainty analyses are identified and a modified approach suitable for industrial safety risk assessment is proposed using fuzzy set theory and Monte Carlo simulation. The proposed method is applied to a benzene extraction unit (BEU) of a chemical plant. The case study results show that the proposed method provides better measure of uncertainty than the existing methods as unlike traditional risk analysis method this approach takes into account both variability and uncertainty of information into risk calculation, and instead of a single risk value this approach provides interval value of risk values for a given percentile of risk. The implications of these results in terms of risk control and regulatory compliances are also discussed.     

Multiobjective spare part allocation by means of genetic algorithms and Monte Carlo simulation

The management of spare parts is a major concern for several industrial organizations, due to the significant amount of resources invested every year for holding spares inventories.In this paper, we explore the possibility of using genetic algorithms for the task of optimizing the number of spare parts required by a multi-component system. To address the question of how many spares should be kept in inventory for each component kind, the analyst is required to define objective functions with respect to which the optimization is sought. In our work we will look at multiple objectives such as, for example, the maximization of system revenues and the minimization of the total spares volume. The modeling of the system failure, repair and replacement stochastic processes is done by means of Monte Carlo simulation, whose flexibility allows a closer adherence to reality.