Research on a Monte Carlo global variance reduction method based on an automatic importance sampling method

Global variance reduction is a bottleneck in Monte Carlo shielding calculations.The global variance reduction problem requires that the statistical error of the entire space is uniform.This study proposed a grid-AIS method for the global variance reduction problem based on the AIS method,which was implemented in the Monte Carlo program MCShield.The proposed method was validated using the VENUS-Ⅲ international benchmark problem and a self-shielding calculation example.The results from the VENUS-Ⅲ benchmark problem showed that the grid-AIS method achieved a significant reduction in the variance of the statistical errors of the MESH grids,decreasing from 1.08×10^(-2) to 3.84×10^(-3),representing a 64.00% reduction.This demonstrates that the grid-AIS method is effective in addressing global issues.The results of the selfshielding calculation demonstrate that the grid-AIS method produced accurate computational results.Moreover,the grid-AIS method exhibited a computational efficiency approximately one order of magnitude higher than that of the AIS method and approximately two orders of magnitude higher than that of the conventional Monte Carlo method.

Face tracking algorithm based on particle filter with mean shift importance sampling

The condensation tracking algorithm uses a prior transition probability as the proposal distribution, which does not make full use of the current observation. In order to overcome this shortcoming, a new face tracking algorithm based on particle filter with mean shift importance sampling is proposed. First, the coarse location of the face target is attained by the efficient mean shift tracker, and then the result is used to construct the proposal distribution for particle propagation. Because the particles obtained with this method can cluster around the true state region, particle efficiency is improved greatly. The experimental results show that the performance of the proposed algorithm is better than that of the standard condensation tracking algorithm.

Importance Sampling Method in V-Space

Based on the observation of importance sampling and second order information about the failure surface of a structure, an importance sampling region is defined in V-space which is obtained by rotating a U-space at the point of maximum likelihood. The sampling region is a hyper-ellipsoid that consists of the sampling ellipse on each plane of main curvature in V-space. Thus, the sampling probability density function can be constructed by the sampling region center and ellipsoid axes. Several examples have shown the efficiency and generality of this method.

Active Kriging-Based Adaptive Importance Sampling for Reliability and Sensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like highnonlinearity,multi-failure regions,and small failure probability,which brings in unacceptable computing efficiency and accuracy of the current analysismethods.In this case,by fitting the implicit limit state function(LSF)with active Kriging(AK)model and reducing candidate sample poolwith adaptive importance sampling(AIS),a novel AK-AIS method is proposed.Herein,theAKmodel andMarkov chainMonte Carlo(MCMC)are first established to identify the most probable failure region(s)(MPFRs),and the adaptive kernel density estimation(AKDE)importance sampling function is constructed to select the candidate samples.With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF,the failure probability and sensitivity indices are acquired at a lower cost.The proposed method is verified by twomulti-failure numerical examples,and then applied to the reliability and sensitivity analyses of a typical stator blade regulator.Withmethods comparison,the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.

Importance-Weighted Transfer Learning for Fault Classification under Covariate Shift

In the process of fault detection and classification,the operation mode usually drifts over time,which brings great challenges to the algorithms.Because traditional machine learning based fault classification cannot dynamically update the trained model according to the probability distribution of the testing dataset,the accuracy of these traditional methods usually drops significantly in the case of covariate shift.In this paper,an importance-weighted transfer learning method is proposed for fault classification in the nonlinear multi-mode industrial process.It effectively alters the drift between the training and testing dataset.Firstly,the mutual information method is utilized to perform feature selection on the original data,and a number of characteristic parameters associated with fault classification are selected according to their mutual information.Then,the importance-weighted least-squares probabilistic classifier(IWLSPC)is utilized for binary fault detection and multi-fault classification in covariate shift.Finally,the Tennessee Eastman(TE)benchmark is carried out to confirm the effectiveness of the proposed method.The experimental result shows that the covariate shift adaptation based on importance-weight sampling is superior to the traditional machine learning fault classification algorithms.Moreover,IWLSPC can not only be used for binary fault classification,but also can be applied to the multi-classification target in the process of fault diagnosis.

DOA estimation of incoherently distributed sources using importance sampling maximum likelihood

In this paper, an importance sampling maximum likelihood(ISML) estimator for direction-of-arrival(DOA) of incoherently distributed(ID) sources is proposed. Starting from the maximum likelihood estimation description of the uniform linear array(ULA), a decoupled concentrated likelihood function(CLF) is presented. A new objective function based on CLF which can obtain a closed-form solution of global maximum is constructed according to Pincus theorem. To obtain the optimal value of the objective function which is a complex high-dimensional integral,we propose an importance sampling approach based on Monte Carlo random calculation. Next, an importance function is derived, which can simplify the problem of generating random vector from a high-dimensional probability density function(PDF) to generate random variable from a one-dimensional PDF. Compared with the existing maximum likelihood(ML) algorithms for DOA estimation of ID sources, the proposed algorithm does not require initial estimates, and its performance is closer to CramerRao lower bound(CRLB). The proposed algorithm performs better than the existing methods when the interval between sources to be estimated is small and in low signal to noise ratio(SNR)scenarios.

Application of Importance Sampling Method in Sliding Failure Simulation of Caisson Breakwaters

It is assumed that the storm wave takes place once a year during the design period, and Nhistories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.

Dropping Rate Simulation for a Handover Scheme Using Importance Sampling

The process of changing the channel associated with the current connection while a call is in progress is under consideration. The estimation of dropping rate in handover process of a one dimensional traffic system is discussed. To reduce the sample size of simulation, dropping calls at base station is considered as rare event and simulated with importance sampling - one of rare event simulation approaches. The simulation results suggest the sample size can be tremendously reduced by using importance sampling.

Numerical Study of φ^4 Model by Potential Importance Sampling Method

We investigate the phenomena of spontaneous symmetry breaking for φ^4 model on a square lattice in the parameter space by using the potential importance samplingmethod, which was proposed by Milchev, Heermann, and Binder [J. Star. Phys. 44 （1986） 749]. The critical values of the parameters allow us to determine the phase diagram of the model. At the same time, some relevant quantifies such as susceptibility and specific heat are also obtained.

A Hybrid Importance Sampling Algorithm for Estimating VaR under the Jump Diffusion Model

Value at Risk (VaR) is an important tool for estimating the risk of a financial portfolio under significant loss. Although Monte Carlo simulation is a powerful tool for estimating VaR, it is quite inefficient since the event of significant loss is usually rare. Previous studies suggest that the performance of the Monte Carlo simulation can be improved by impor-tance sampling if the market returns follow the normality or the distributions. The first contribution of our paper is to extend the importance sampling method for dealing with jump-diffusion market returns, which can more precisely model the phenomenon of high peaks, heavy tails, and jumps of market returns mentioned in numerous empirical study papers. This paper also points out that for portfolios of which the huge loss is triggered by significantly distinct events, naively applying importance sampling method can result in poor performance. The second contribution of our paper is to develop the hybrid importance sampling method for the aforementioned problem. Our method decomposes a Monte Carlo simulation into sub simulations, and each sub simulation focuses only on one huge loss event. Thus the perform-ance for each sub simulation is improved by importance sampling method, and overall performance is optimized by determining the allotment of samples to each sub simulation by Lagrange’s multiplier. Numerical experiments are given to verify the superiority of our method.

Importance Sampling Strategy for Oscillatory Stochastic Processes

This paper contributes to the structural reliability problem by presenting a novel approach that enables for identification of stochastic oscillatory processes as a critical input for given mechanical models. Identification development follows a transparent image processing paradigm completely independent of state-of-the-art structural dynamics, aiming at delivering a simple and wide purpose method. Validation of the proposed importance sampling strategy is based on multi-scale clusters of realizations of digitally generated non-stationary stochastic processes. Good agreement with the reference pure Monte Carlo results indicates a significant potential in reducing the computational task of first passage probabilities estimation, an important feature in the field of e.g., probabilistic seismic design or risk assessment generally.

Particle filter with importance density function generated by updated system equation

The current measurement was exploited in a more efficient way. Firstly, the system equation was updated by introducing a correction term, which depends on the current measurement and can be obtained by running a suboptimal filter. Then, a new importance density function(IDF) was defined by the updated system equation. Particles drawn from the new IDF are more likely to be in the significant region of state space and the estimation accuracy can be improved. By using different suboptimal filter, different particle filters(PFs) can be developed in this framework. Extensions of this idea were also proposed by iteratively updating the system equation using particle filter itself, resulting in the iterated particle filter. Simulation results demonstrate the effectiveness of the proposed IDF.

Sensitivity of Sample for Simulation-Based Reliability Analysis Methods

In structural reliability analysis,simulation methods are widely used.The statistical characteristics of failure probability estimate of these methods have been well investigated.In this study,the sensitivities of the failure probability estimate and its statistical characteristics with regard to sample,called‘contribution indexes’,are proposed to measure the contribution of sample.The contribution indexes in four widely simulation methods,i.e.,Monte Carlo simulation(MCS),importance sampling(IS),line sampling(LS)and subset simulation(SS)are derived and analyzed.The proposed contribution indexes of sample can provide valuable information understanding the methods deeply,and enlighten potential improvement of methods.It is found that the main differences between these investigated methods lie in the contribution indexes of the safety samples,which are the main factors to the efficiency of the methods.Moreover,numerical examples are used to validate these findings.

传统村落木结构灭火失效概率分析

为研究传统村落木结构灭火失效概率,结合消防队介入模型和Benichou模型提出传统村落失效功能函数。在此基础上,利用JC法计算验算点值,采用蒙特卡洛重要性抽样模拟分析灭火失效概率,并使用提出的功能函数对云南丽江传统村落木结构进行灭火失效概率分析。结果表明,该村落的失效概率达到53.3%,且随着门窗开启率的增加,灭火失效概率逐步降低;行车时间的不确定性对失效概率影响最大,门窗开启率的不确定性对失效概率影响最小;随着救援距离的减少,灭火失效概率呈降低趋势,可通过减少救援距离、增加门窗开启率等改进措施降低灭火失效概率。

B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration

The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N^-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.

基于自动重要抽样方法的减方差技巧体系构建与验证

屏蔽计算问题根据求解目标不同一般可分为源-探测器问题、区域问题和全局问题。MCShield研究团队针对3类问题中存在的深穿透问题提出了相应的减方差技巧,本文以此为基础构建了基于自动重要抽样(AIS)方法的减方差技巧体系,并开展了验证工作。针对源-探测器问题,采用NUREG/CR-6115 PWR压力容器计算基准题对小探测器自动重要抽样(SDAIS)方法进行验证。结果表明,SDAIS方法的计算效率约为AIS方法的7倍。此外还提出并验证了基于AIS伴随蒙特卡罗的耦合减方差(AIS-CADIS)方法,将AIS方法引入到蒙特卡罗伴随计算中,取得了良好的效果。针对全局问题,提出网格化-AIS方法并使用简化反应堆屏蔽计算算例进行验证,结果表明,网格化-AIS方法的计算效率是AIS方法的12倍左右,是直接蒙特卡罗方法的290倍左右。

深穿透跨尺度辐射场分析软件NECP-MCX研发及应用

西安交通大学核工程计算物理实验室自主研发了深穿透跨尺度辐射场分析软件NECP-MCX。针对大空间伽马射线辐射输运模拟、聚变堆停堆剂量模拟和点源屏蔽问题等新应用场景下的新问题与新挑战,在NECP-MCX中研发了对应的新方法与新功能。针对km尺度的伽马射线辐射输运问题,提出一致性共轭驱动重要性抽样(CADIS)-下次事件估计器(NEE)耦合方法,该方法能够精确高效地获得km尺度距离处的光子通量密度,计算效率比传统的NEE高6.8倍;针对聚变堆停堆剂量问题,采用粒子输运-燃耗-活化-源项耦合分析方法,获得PF线圈、TF线圈、真空室和偏滤器处停堆剂量随停堆时间的变化;对于点源屏蔽问题,提出首次碰撞源(FCS)-CADIS方法,解决CADIS方法对点源进行源偏倚的局限性,FCS-CADIS方法的计算效率比CADIS方法高2倍。

基于重要性采样的超图网络高效表示方法

现有的超图网络表示方法需要分析全批量节点和超边以实现跨层递归扩展邻域,这会带来巨大的计算开销,且因过度扩展导致更低的泛化精度.为解决这一问题,提出一种基于重要性采样的超图表示方法.首先,它将节点和超边看作是两组符合特定概率测度的独立同分布样本,用积分形式解释超图的结构特征交互;其次,设计带可学习参数的邻域重要性采样规则,根据节点和超边的物理关系和特征计算采样概率,逐层递归采集固定数目的对象,构造一个更小的采样邻接矩阵;最终,利用蒙特卡洛方法近似估计整个超图的空间特征.此外,借鉴PINN的优势,将需要缩减的方差作为物理约束加入到超图神经网络中,以获取更具泛化能力的采样规则.多个数据集上的广泛实验表明,所提出的方法能够获得更准确的超图表示结果,同时具有更快的收敛速度.

基于集成重要性采样的随机梯度下降算法

许多机器学习和深度学习问题都可以使用随机梯度优化算法求解,目前流行的算法大多通过均匀采样从样本集中抽取样本计算梯度估计。然而,随机采样的梯度估计会带来较大的方差,这个方差会随着优化的进行而累积,降低算法收敛速度。为缓解这一现象,可以为每个样本赋予不同的采样概率。该文基于集成学习的思想,提出了一种新的选取非均匀采样分布的算法。算法的主要目的是选取一个采样器权重,使梯度估计的方差尽可能小。所提算法由多个简单采样器组成,采样权重为每个简单采样器分配贡献权重,从而得到最终的采样分布。集成重要性采样算法可以和以往的随机梯度优化方法任意结合,该文给出了使用集成重要性采样的随机梯度下降算法。在试验中,可以直观地看到算法起效的原因。在真实数据集中,展示了所提算法减小方差的效果,与其他算法相比具有一定优势。

基于电子加速器的核共振荧光无损探测模拟计算

核共振荧光(nuclear resonance fluorescence,NRF)是一种新兴的无损探测技术,通过分析伽马能谱中的特征能量来识别特定同位素,在含未知爆炸物小型箱体的扫描检查中发挥重要作用。本研究利用电子加速器韧致辐射产生的X射线为射线源,通过蒙特卡罗模拟程序Geant4优化设计NRF背散射探测方案。结果表明,优化后的X射线泄漏率降低了386倍,束流不对称度低于2%,束流均匀度高于70%。基于HPGe探测器获得石墨样品、硝酸铵样品的NRF特征能谱验证了设计方案的可行性,利用重要性抽样法将石墨样品模拟计算效率提高了72.23倍。该设计方案和计算结果可为基于NRF的无损核探测系统研发提供技术支撑。