基于NECP-MCX的蒙特卡罗-确定论耦合及权窗网格粗化方法研究

对于屏蔽计算的深穿透问题,由于仅有少量粒子能够穿透屏蔽层到达计数区,所以计算效率极低。为解决该问题,基于一致性共轭驱动重要性抽样方法研究了蒙特卡罗-确定论耦合方法(简称耦合方法)。本研究实现的耦合方法可以基于蒙特卡罗的组合实体几何建模,自动生成确定论SN计算所需的输入参数,利用SN共轭计算生成一致的源偏倚和权窗参数,提供给蒙特卡罗方法正向计算使用。同时耦合方法使用的基于网格的权窗在大规模问题中会遇到内存瓶颈,本文基于贡献因子理论,研究了自动网格粗化方法。新开发了嵌套网格的结构用于网格粗化,以节省权窗占用的内存,同时不影响权窗的效果。基于NECP-MCX程序实现了耦合方法和网格粗化方法。数值结果表明,对于HBR-2基准题,相比于MCNP程序的权窗自动生成方法,耦合方法的品质因子最高提高了2个数量级。在不影响计算精度和效率的前提下,可以将权窗网格最多减少为原来的1/226。     

Real and virtual sampling in variational processing of stochastic simulation in neutron transport: The one-dimensional rod

We are seeking to combine conventional analogue Monte Carlo simulation that might be used in realistic three-dimensional problems, with variational processing to reduce variance and improve the ratio of accuracy to computing costs. At this stage we investigate a one-dimensional transport problem with left and right scattering, for which exact solutions are available for comparison. We can show that the usual Monte Carlo simulation can be used not only to estimate the forward flux but also the importance or adjoint flux of neutrons sampled, where the importance is to be used in the variational processing. Hence the single simulation potentially holds information to improve the accuracy. The efficiency is improved by the use of virtual rather than fictitious sampling. Virtual sampling is introduced, which consists of marking every location of a neutron as a virtual source, and found to be more efficient than fictitious sampling to determine the importances.     

Efficient reliability estimate of passive thermal hydraulic safety system with automatic differentiation

An approach for efficient estimation of passive safety system functional reliability has been developed and applied to a simplified model of the passive residual heat transport system typical of sodium cooled fast reactors to demonstrate the reduction in computational time. The method is based on generating linear approximations to the best estimate computer code, using the technique of automatic reverse differentiation. This technique enables determination of linear approximation to the code in a few runs independent of the number of input variables for each response variable. The likely error due to linear approximation is reduced by augmented sampling through best estimate code in the neighborhood of the linear failure surface but in a sub domain where linear approximation error is relatively more. The efficiency of this new approach is compared with importance sampling MCS which uses the linear approximation near the failure region and with Direct Monte-Carlo Simulation. In the importance sampling MCS, variants employing random sampling with Box-Muller algorithm and Markov Chain algorithm are inter-compared. The significance of the results with respect to system reliability is also discussed.     

Monte Carlo simulation of Markov unreliability models

A Monte Carlo method is formulated for the evaluation of the unrealibility of complex systems with known component failure and repair rates. The formulation is in terms of a Markov process allowing dependencies between components to be modeled and computational efficiencies to be achieved in the Monte Carlo simulation. Two variance reduction techniques, forced transition and failure biasing, are employed to increase computational efficiency of the random walk procedure. For an example problem these result in improved computational efficiency by more than three orders of magnitudes over analog Monte Carlo. The method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem. A method for separating the variance due to the data uncertainty from that due to the finite number of random walks is presented.     

An easy to implement global variance reduction procedure for MCNP

In this article, an easy to implement global variance reduction procedure is demonstrated. The procedure is capable of flattening the relative error distribution in a global mesh tally covering the geometry of a complex system. The method is fully based on the I/O capabilities of the MCNP Monte Carlo radiation transport code family and requires little additional support code and almost no user judgment to work properly. Increases, with respect to a standard simulation, in a global figure of merit ranging up to a factor 276 for a PWR core configuration have been observed. Also, the relative error distribution was flattened substantially in all studied systems by the application of the procedure and the number of empty mesh tally cells was reduced.     

基于响应曲面和重要性抽样方法的热力系统参数失效概率计算

本文研究了将响应曲面与重要性抽样相结合的方法用于复杂热力系统参数失效概率的计算。建立了热力系统物理过程参数失效的数学模型,在此基础上研究了将响应曲面与重要性抽样相结合的算法模型,并给出了热力系统组成设备的性能退化模型和基于重要性抽样的仿真流程,进而对反应堆净化系统工作过程中参数失效问题进行了分析计算。研究表明,对于高维、非线性特性明显并考虑性能退化的复杂热力系统参数失效概率的计算,重要性抽样法较直接抽样能以较高效率获得满意精度的计算结果,而响应曲面法存在局限;响应曲面和重要性抽样相结合的方法是分析热力系统物理过程参数失效的有效方法。     

计算高可靠性系统失效概率的统计估计蒙特卡罗方法

在相似仿真方法的基础上 ,设计了计算系统失效概率的统计估计蒙特卡罗方法 ,包括直接统计估计和加权统计估计蒙特卡罗方法。介绍了统计估计蒙特卡罗可靠性仿真的基本原理 ,给出了统计估计蒙特卡罗计算方法的无偏估计量和具体算法。同时采用直接仿真方法、限制抽样蒙特卡罗方法、强迫转换蒙特卡罗方法、直接统计估计和加权统计估计蒙特卡罗方法计算了一高可靠性系统的失效概率 ,结果表明 ,在高可靠性系统不可靠度计算中加权统计估计蒙特卡罗方法计算结果的方差最小 ,效率最高。     

Improvement of Sliding-Scale Analog-to-Digital Converters through Weighted Averaging

Several figures of merit for characterizing an analog-to-digital converter are considered. It is shown that the sliding scale method of improving through averaging the performance of a converter can be made more effective by introducing variable statistical weights in the averaging procedure. It is found that a parabolic weighting function is the optimum for the differential linearity, if the channel boundaries are independently random distributed with equal variance. Moreover it is shown, through a computer simulation, that this weighting function is more convenient than a rectangular one to improve also a local differential linearity, while it is equivalent as far as correction of channel centroid errors is concerned. A triangular weighing function is found to be slightly worse than the parabolic one as far as overall differential linearity is concerned but somewhat better from the point of view of local behaviour.     

Performance of the improved version of the Monte Carlo A3MCNP code in the design of cask shielding

Abstract

A³MCNP (automatic adjoint accelerated MCNP) is a revised version of the MCNP Monte Carlo code that automatically prepares variance reduction parameters for the CADIS (consistent adjoint driven importance sampling) methodology. Using a deterministic 'importance' (or adjoint) function, CADIS performs source and radiation particle transport biasing within the weight-window technique. The current version of A³MCNP uses the 3-D Sn transport TORT code to determine a 3-D importance function distribution. Based on simulation of several real-life problems, it is demonstrated that A³MCNP provides precise calculation results with a remarkably short computation time by using the proper and objective variance reduction parameters. However, since the first version of A³MCNP provided only a point source configuration option for large-scale shielding problems, such as spent fuel transport casks, a large amount of memory may be necessary to store enough points to properly represent the source. Hence, we have developed an improved version of A³MCNP (referred to as A³MCNPV) which has a volumetric source configuration option. This paper describes the successful use of A³MCNPV in solving the cask neutron and gamma-ray shielding problem.     

Importance Determination Method for Geometry Splitting with Russian Roulette in Monte Carlo Calculations of Thick and Complicated Core Shielding Structure

In case of a shielding analysis of the geometry having thick and complicated structures with a Monte Carlo code, it is a serious problem that it takes too much computer time to obtain results with good statistics. Therefore, it is very important to reduce variances in the calculation. In this study, a method to determine the importance function in 3-dimensional Monte Carlo calculation with geometry splitting with Russian roulette was developed for the shielding analysis of thick and complicated core shielding structures. Only two essential importance ratio curves for one material enable us to determine the importance function easily in the shielding calculation.

The validity of this method was confirmed through a simple benchmark calculation. From the comparison with the result obtained by using weight window (W-W), it was shown that the present method can give an accurate result on the same level with W-W method with less trial and errors. And this method was applied to an actual reactor core shielding analysis to confirm its applicability to a 3-dimensional thick and complicated structure.

Using this method, the variance reduced calculation can be easily realized with the developed importance determination procedure, especially in case that parameter survey calculations are required in order to determine the shield thickness in a design work of a thick and complicated structure. Accordingly, it became easier to use Monte Carlo method as a powerful tool for a reactor core shielding design.     

相关抽样方法在中子、光子输运中的应用

介绍了相关抽样方法在中子、光子输运中的应用，并给出了两个具体例子。相关抽样方法是蒙特卡罗方法中一种有效的方差减小技术，主要适应于计算系统参数发生小改变时输出结果的变化量，并可以在一次计算中同时给出多个相似系统（系统参数差异不大）的结果。     

重要方向抽样在小探测概率问题模拟中的应用

蒙特卡罗方法对于小探测概率问题的模拟计算的效率非常低。介绍了重要方向抽样技术在这类问题中的应用,并给出了此技术对于同时具有小探测概率、深穿透两种特点的问题的解决方法。     

基于改进多层交叉熵方法的核动力装置非能动系统可靠性评估

针对非能动系统可靠性评估问题中重要抽样分布构造困难以及实际工程应用中标准多层交叉熵方法存在的缺陷,进行了算法结构改进并引入均匀性更好的“Halton序列”抽样方法,提出一种改进多层交叉熵方法,并以某型核动力装置非能动余热排出试验系统为例,给出改进多层交叉熵方法的性能验证分析和实例分析。计算结果表明,改进方法失效率估计结果的相对误差分布更集中、变异系数分布相近,在节省运算量的情况下具有更好的估计精度和稳健性;改进方法不需要额外设置平滑参数、可根据系统特征和采样情况提前结束评估过程,在实际工程应用中具有更强的适用性。      

用于厚屏蔽小探测器的蒙特卡罗模拟减方差方法研究

反应堆屏蔽计算中经常出现厚屏蔽、小探测器问题，常规蒙特卡罗方法难以有效解决。基于自动重要抽样（AIS）方法，本文提出了小探测器自动重要抽样(SDAIS)方法，并针对小探测器问题，优化了AIS方法的虚粒子赌分裂算法。该方法在自主开发的蒙特卡罗屏蔽程序MCShield上进行了实现。使用NUREG/CR-6115 PWR基准题验证该方法的正确性和计算效率。结果表明，SDAIS方法可有效地解决厚屏蔽小探测器问题，相比AIS方法及传统的重要性方法，计算效率提升1~2个量级。     

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).     

Biased Selection of Particle Flight Directions as a Variance Reduction Technique in Monte Carlo Calculations

As a practical variance reduction technique applicable to Monte Carlo shielding calculations, the present article shows a new simple biased sampling technique on particle flight directions. Scattered particles not directed towards the detector positions are killed if they are not so important, that is, if the particle weights are sufficiently small compared to the source weight. In this way, we can reduce the sample size required for obtaining an accurate estimate for the detector response.

The present technique was incorporated into the multigroup neutron and γ-ray transport code MORSE, and sample calculations were performed on spherical fast neutron systems. The results have shown that this biased technique is effective for dealing with neutron multiplication as well as neutron transmission problems. The neutron flux or the effective multiplication factor of a nuclear reactor is estimated more accurately than from the method of path-length stretching with about the same computation time. In addition, it is shown that the flight-direction biasing can further effectively be used by combining it with other variance reduction techniques.     

Application of On-Line Digital Noise Analysis to Reactor Diagnosis in JMTR

The reactor noise analysis technique is particularly useful in reactor diagnosis for on-line monitoring if the raw noise signals can be processed in almost real time.

An on-line reactor noise analysis system has been developed with use made of the mini-computer HITAC-10. This system utilizes functions for calculating the power spectral density in almost real time, plots the output by digital incremental plotter, and displays the results by means of color graphic display equipment, in order to detect anomalous reactor conditions with the statistical technique.

Using this system, reactor noise signals have been measured and analyzed under various operational conditions in the JMTR. The variance of the power spectral density is found to fit a logarithmic probability density function. This function is independent of the frequency, but is dependent on the number of sampling functions.

A logical procedure for anomaly detection based on statistical characteristics has been developed. It is applied to a case where it is supposed that the PWR operating mode in the OWL-1 is the normal process and that the BWR mode is the anomalous. It is demonstrated as a result, that this procedure can successfully detect anomalous processes.     

Direct simulation Monte Carlo aerosol dynamics: Collisional sampling algorithms

The computation of nuclear aerosol evolution is complicated, and a study of the direct simulation Monte Carlo (DSMC) technique to elucidate the role of various physical phenomena that influence the evolution has been undertaken. In our previous works, we explored important new directions by including most coagulation mechanisms like Brownian, gravitational, turbulence, and reduced the computation time using the Metropolis sampling algorithm for collisional sampling. In this paper, we further explore other sampling algorithms – the no time counter (NTC) and modified direct sampling algorithms. A comparison study on the four sampling algorithms – direct, the Metropolis, the NTC and modified direct sampling algorithms has been made and the results are discussed in this work. From the results, we are able to conclude that the Metropolis sampling algorithm can be used for the simulations as it provides more accurate results and is also time efficient in comparison to the NTC and modified direct sampling algorithms.     

反应堆乏燃料组件的破损检测

为了解决某反应堆101盒乏燃料组件外运送贮,对乏燃料组件破损检测方法进行了研究,在已有技术的基础上,根据自身的需求设计、加工了新的采样系统,设计了工作流程,并给出了测量数据的判断依据。该采样系统可以在水下实现一次对一批乏燃料组件进行逐个取样,每个样品对应一个确定的组件,检测效率高。测量破损检测样品101个,根据测量结果判断出1个样品含有85Kr,其余样品不含85Kr或是85Kr的含量低于该条件下仪器的探测限,表明101盒乏燃料组件中有1盒组件包壳存在破损情况,其余组件包壳未破损。     

自适应蒙特卡罗方法计算海水淡化堆非能动系统物理过程失效概率

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