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.

Modified sequential importance resampling filter

In order to deal with the particle degeneracy and impov- erishment problems existed in particle filters, a modified sequential importance resampling （MSIR） filter is proposed. In this filter, the resampling is translated into an evolutional process just like the biological evolution. A particle generator is constructed, which introduces the current measurement information （CMI） into the resampled particles. In the evolution, new particles are first pro- duced through the particle generator, each of which is essentially an unbiased estimation of the current true state. Then, new and old particles are recombined for the sake of raising the diversity among the particles. Finally, those particles who have low quality are eliminated. Through the evolution, all the particles retained are regarded as the optimal ones, and these particles are utilized to update the current state. By using the proposed resampling approach, not only the CMI is incorporated into each resampled particle, but also the particle degeneracy and the loss of diver- sity among the particles are mitigated, resulting in the improved estimation accuracy. Simulation results show the superiorities of the proposed filter over the standard sequential importance re- sampling （SIR） filter, auxiliary particle filter and unscented Kalman particle filter.

Particle filter based on iterated importance density function and parallel resampling

The design, analysis and parallel implementation of particle filter(PF) were investigated. Firstly, to tackle the particle degeneracy problem in the PF, an iterated importance density function(IIDF) was proposed, where a new term associating with the current measurement information(CMI) was introduced into the expression of the sampled particles. Through the repeated use of the least squares estimate, the CMI can be integrated into the sampling stage in an iterative manner, conducing to the greatly improved sampling quality. By running the IIDF, an iterated PF(IPF) can be obtained. Subsequently, a parallel resampling(PR) was proposed for the purpose of parallel implementation of IPF, whose main idea was the same as systematic resampling(SR) but performed differently. The PR directly used the integral part of the product of the particle weight and particle number as the number of times that a particle was replicated, and it simultaneously eliminated the particles with the smallest weights, which are the two key differences from the SR. The detailed implementation procedures on the graphics processing unit of IPF based on the PR were presented at last. The performance of the IPF, PR and their parallel implementations are illustrated via one-dimensional numerical simulation and practical application of passive radar target tracking.

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.

Comparison of uniform resampling and nonuniform sampling direct-reconstruction methods in k-space for FD-OCT

The nonuniform distribution of interference spectrum in wavenumber k-space is a key issue to limit the imaging quality of Fourier-domain optical coherence tomography(FD-OCT).At present,the reconstruction quality at different depths among a variety of processing methods in k-space is still uncertain.Using simulated and experimental interference spectra at different depths,the effects of common six processing methods including uniform resampling(linear interpolation(LI),cubic spline interpolation(CSI),time-domain interpolation(TDI),and K-B window convolution)and nonuniform sampling direct-reconstruction(Lomb periodogram(LP)and nonuniform discrete Fourier transform(NDFT))on the reconstruction quality of FD-OCT were quantitatively analyzed and compared in this work.The results obtained by using simulated and experimental data were coincident.From the experimental results,the averaged peak intensity,axial resolution,and signal-to-noise ratio(SNR)of NDFT at depth from 0.5 to 3.0mm were improved by about 1.9 dB,1.4 times,and 11.8 dB,respectively,compared to the averaged indices of all the uniform resampling methods at all depths.Similarly,the improvements of the above three indices of LP were 2.0 dB,1.4 times,and 11.7 dB,respectively.The analysis method and the results obtained in this work are helpful to select an appropriate processing method in k-space,so as to improve the imaging quality of FD-OCT.

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.

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.

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.

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

我们调查自发的对称为 4 由使用潜在的重要性采样方法在参数空格在一个方形的格子上建模的φ ~ 碎的现象，它被 Milchev， Heermann，和文件夹建议[J。Stat。Phys。44 (1986 ) 749 ] 。参数的批评价值允许我们决定模型的阶段图。同时，象危险性那样的一些相关数量和特定的热也被获得。

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.

On the Impact of Bootstrap in Stratified Random Sampling

In general the accuracy of mean estimator can be improved by stratified random sampling. In this paper, we provide an idea different from empirical methods that the accuracy can be more improved through bootstrap resampling method under some conditions. The determination of sample size by bootstrap method is also discussed, and a simulation is made to verify the accuracy of the proposed method. The simulation results show that the sample size based on bootstrapping is smaller than that based on central limit theorem.

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.

ANNEALED IMPORTANCE SAMPLING FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS

This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually.The numerical results show that the variance of the sample weights is relatively small.

A K-Means Clustering-Based Multiple Importance Sampling Algorithm for Integral Global Optimization

In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.

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。