Variance reduction for generalized likelihood ratio method by conditional Monte Carlo and randomized Quasi-Monte Carlo methods

The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.

Uncertainty and energy-sector equity returns in Iran:a Bayesian and quasi-Monte Carlo time-varying analysis

This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran.The analysis specifically considers the refining,drilling,and petrochemical equity sectors of the Tehran Stock Exchange.The parameter estimation uses the quasi-Monte Carlo and Bayesian optimization methods in the framework of a generalized autoregressive conditional heteroskedasticity model,and a complementary Bayesian network analysis is also conducted.The analysis takes into account geopolitical risk and economic policy uncertainty data as other proxies for uncertainty.This study also aims to detect different price regimes for each equity index in a novel way using homogeneous/non-homogeneous Markov switching autoregressive models.Although these methods provide improvements by restricting the analysis to a specific price-regime period,they produce conflicting results,rendering it impossible to draw general conclusions regarding the contagion effect on returns or the volatility transmission between markets.Nevertheless,the results indicate that the OPEC(historical)price volatility has a stronger effect on the energy sectors than the implied volatility has.These types of oil price shocks are found to have no effect on the drilling sector price pattern,whereas the refining and petrochemical equity sectors do seem to undergo changes in their price patterns nearly concurrently with future demand shocks and oil supply shocks,respectively,gaining dominance in the oil market.

Random vibration analysis of FGM plates subjected to moving load using a refined stochastic finite element method

The article introduces a finite element procedure using the bilinear quadrilateral element or four-node rectangular element(namely Q4 element) based on a refined first-order shear deformation theory(rFSDT) and Monte Carlo simulation(MCS), so-called refined stochastic finite element method to investigate the random vibration of functionally graded material(FGM) plates subjected to the moving load.The advantage of the proposed method is to use r-FSDT to improve the accuracy of classical FSDT, satisfy the stress-free condition at the plate boundaries, and combine with MCS to analyze the vibration of the FGM plate when the parameter inputs are random quantities following a normal distribution. The obtained results show that the distribution characteristics of the vibration response of the FGM plate depend on the standard deviation of the input parameters and the velocity of the moving load.Furthermore, the numerical results in this study are expected to contribute to improving the understanding of FGM plates subjected to moving loads with uncertain input parameters.

Quasi-Monte Carlo Simulation-Based SFEM for Slope Reliability Analysis

Considering the stochastic spatial variation of geotechnical parameters over the slope, a Stochastic Finite Element Method (SFEM) is established based on the combination of the Shear Strength Reduction (SSR) concept and quasi-Monte Carlo simulation. The shear strength reduction FEM is superior to the slice method based on the limit equilibrium theory in many ways, so it will be more powerful to assess the reliability of global slope stability when combined with probability theory. To illustrate the performance of the proposed method, it is applied to an example of simple slope. The results of simulation show that the proposed method is effective to perform the reliability analysis of global slope stability without presupposing a potential slip surface.

Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models

In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.

Random vibration analysis of switching apparatus based on Monte Carlo method

The performance in vibration environment of switching apparatus containing mechanical contact is an important element when judging the apparatus’s reliability. A piecewise linear two-degrees-of-freedom mathematical model considering contact loss was built in this work, and the vibration performance of the model under random external Gaussian white noise excitation was investigated by using Monte Carlo simulation in Matlab/Simulink. Simulation showed that the spectral content and statistical characters of the contact force coincided strongly with reality. The random vibration character of the contact system was solved using time (numerical) domain simulation in this paper. Conclusions reached here are of great importance for reliability design of switching apparatus.

Predicting Surface Urban Heat Island in Meihekou City, China: A Combination Method of Monte Carlo and Random Forest

Given the rapid urbanization worldwide, Urban Heat Island(UHI) effect has been a severe issue limiting urban sustainability in both large and small cities. In order to study the spatial pattern of Surface urban heat island(SUHI) in China’s Meihekou City, a combination method of Monte Carlo and Random Forest Regression(MC-RFR) is developed to construct the relationship between landscape pattern indices and Land Surface Temperature(LST). In this method, Monte Carlo acceptance-rejection sampling was added to the bootstrap layer of RFR to ensure the sensitivity of RFR to outliners of SUHI effect. The SHUI in 2030 was predicted by using this MC-RFR and the modeled future landscape pattern by Cellular Automata and Markov combination model(CA-Markov). Results reveal that forestland can greatly alleviate the impact of SUHI effect, while reasonable construction of urban land can also slow down the rising trend of SUHI. MC-RFR performs better for characterizing the relationship between landscape pattern and LST than single RFR or Linear Regression model. By 2030, the overall SUHI effect of Meihekou will be greatly enhanced, and the center of urban development will gradually shift to the central and western regions of the city. We suggest that urban designer and managers should concentrate vegetation and disperse built-up land to weaken the SUHI in the construction of new urban areas for its sustainability.

Randomized Objective Function Linear Programming in Risk Management

The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.

海浪谱法模拟海面场景仿真参数选取准则

为提升海面场景模拟的物理真实感,本文探讨了仿真参数对海洋粗糙面模拟精确性的影响,并建立了海表模拟中仿真参数的选取准则。依据海浪谱和随机过程统计理论,采用自相关函数研究了海面相关长度随风速变化规律。通过建立海浪蒙特卡罗仿真模型,结合随机粗糙面误差分析,提出了不同风速条件下海面场景仿真参数的选取准则。研究表明:将海表模拟的采样间隔限定在顺风向相关长度的0.1~0.5倍,可显著提高海面场景模拟的精确度;而当海面仿真参数超出上述范围时,可能导致海面场景模拟失真,进而影响其视觉真实感。本文所提出的仿真参数选取标准可为开发航海模拟器提供技术支撑。

考虑土性参数空间变异性的珠三角软土地区土钉支护结构可靠度分析

如何定量定性描述软土土性参数空间变异性对准确确定软土土性参数和合理评价软土地区土钉支护结构稳定性至关重要。采用既有统计分析方法定量描述空间变异性通常需要大量数据,难以满足。本文基于随机场理论模拟软土土性参数空间变异性,建立了一套考虑土性空间变异性的软土地区土钉支护结构可靠度设计方法,最后以MATLAB软件包为平台进行计算程序的开发与工程实例研究。分析结果表明,本文采用随机场方法模拟软土土体固有空间变异性及其在土钉支护结构可靠度分析中的应用具有合理性与普适性。

随机微裂纹对岩石宏观裂纹扩展的影响规律研究

岩石微裂纹控制着岩石的宏观力学特性和破裂行为,其分布具有不确定性。现有关于岩石裂纹扩展的研究侧重于确定性裂纹扩展规律研究,而随机微裂纹的影响研究不足。该文基于键型近场动力学(Peridynamics,PD)理论,引入随机分布函数预设微裂纹的几何、位置随机参数,对预设有宏观裂纹和随机微裂纹的岩石构件拉伸破坏过程进行大规模蒙特卡洛模拟,提出了物质点断裂失效概率因子(PFP)来描述物质点的破坏概率,揭示了随机微裂纹对岩石拉伸宏观裂纹扩展的影响规律。通过分析两个经典算例,分别与FEM和XFEM对比,其结果有较强的一致性。另外,该文引入了含宏观裂纹与微裂纹的岩石构件,根据微裂纹的位置、角度和长度随机分布,首次绘制不同情况下随机裂纹的PFP云图,获得了各参数对裂纹扩展的影响规律。该文首创了物质点断裂失效概率因子,定量描述微裂纹对宏观裂纹扩展的影响规律,为预测含随机微裂纹的岩石裂纹扩展研究提供了一种新思路新方法。

基于Neumann展开Monte-Carlo有限元法的随机温度场分析

利用Neumann展开Monte-Carlo随机有限元法,对导热系数、换热系数、热流密度、环境温度以及内热源等物理参数同时具有随机性的温度场问题进行了分析,给出了节点温度响应的均值、变异系数和节点温度落在某一区间内的概率计算公式.通过算例考察了各随机变量的变异性大小对节点温度响应的影响,并表明随着结构的自由度数目增大,文中方法呈现出计算效率高的优点.

组合方法改进Monte Carlo计算中的伪随机数发生器

针对随机数产生基本方法的局限性,提出了一种高品质的组合随机数产生方法。使用此方法改进MCNP程序中的随机数发生器,能大大增加随机数周期的长度,显著改善伪随机数的品质,并使随机数的产生速度有明显提高,能有效地满足各种问题的计算要求。

大规模非线性系统随机振动显式迭代Monte Carlo模拟法

探讨了非平稳随机激励下大规模非线性系统随机振动Monte Carlo模拟法。引入等效激励的概念,把非线性系统动力方程写成状态方程的形式,并采用精细积分法对状态方程进行数值求解,导出非线性系统振动分析的显式迭代法。基于所导出的显式迭代公式,可以有效提高单次确定性非线性振动分析的计算效率,从而可以通过Monte Carlo模拟获得非平稳随机激励下非线性系统随机响应的统计信息,同时还可以获取非线性系统随机响应的演化概率密度函数。数值算例表明,所提出的方法迭代收敛速度快,计算精度高,适用于求解大规模非线性系统随机振动问题。

基于MATLAB的PN结形成过程蒙特卡罗程序研发

本文基于蒙特卡罗随机行走的思想,用概率和随机抽样模拟PN结形成过程中载流子的运动以及动态分布,解决平衡态PN结电势所满足的泊松方程过于复杂、难以计算以及模拟的问题.利用MATLAB软件将演化过程中的载流子的运动过程可视化,并且将平衡态PN结的电势分布可视化.该方法可通过模拟载流子的运动规律及分布了解PN结的形成过程,进而及时对物理模型进行修正.该程序实现手段简便,物理图像清晰,可以用于半导体物理等相关课程的课堂教学.

液压支架随机载荷历程及Monte Carlo法的应用

为较准确地预测液压支架的使用寿命,利用支架与围岩的相互作用关系,通过围岩的运动规律,分析出了液压支架外载荷的来源及特征.应用Monte Carlo法进行随机抽样获取载荷谱,统计得到其载荷幅值服从形状参数为1.31,尺度参数为216.96的威布尔分布,而载荷均值服从均值为1 200 N·m,标准差为51.96N·m的正态分布,进而模拟出了液压支架在井下真实的载荷历程.为进一步研究和编制程序载荷谱,进行实验室模拟试验和疲劳寿命预测做好准备.

用Monte Carlo方法模拟砂土的自然堆积过程

用MonteCarlo随机模拟方法模拟砂土颗粒在重力作用下,在圆柱与长方体容器中的自然堆积过程。首先用参考网格法生成一个砂土颗粒的松散结构,松散结构中粒子与粒子、粒子与边界间不存在任何接触;然后启动MonteCarlo随机模拟算法,即给处于松散结构中的每个粒子施加随机位移,得到新构形,如果新构形中粒子间或粒子与边界间发生重叠,则放弃这个构形;如果没有重叠存在,则判别粒子体系的势能变化,运用Metropolis准则来判别这个构形是否被接受,重复这个过程可以得到砂土的密集堆积结构。采用Schinner建议的接触发现算法判别粒子间是否存在重叠,同时详细介绍了粒子与边界间的接触发现算法。模拟结果表明,用MonteCarlo方法模拟砂土的自然堆积结构是非常有效的,可以为砂土的流动、压实等的数值模拟工作提供初始构形。

基于人工神经网络和Monte-Carlo法的混凝土配合比优化设计研究

结合BP人工神经网络和Monte Carlo随机试验法 ,建立混凝土配合比的直接优化设计模型 ,并开发出实用软件。该设计过程包括 :( 1 )首先建立配合比试验样本数据库 ,然后根据不同混凝土的设计要求 ,检索该数据库并动态建立网络模型 ;( 2 )以混凝土原材料和制作工艺作为输入单元 ,混凝土最终性能指标作为输出单元 ,训练、测试BP神经网络 ,并检验其可靠性 ;( 3)以建立的BP神经网络模型和其它配合比限制条件作为约束条件 ,混凝土单位成本作为优化目标建立Monte Carlo直接优化模型 ,设计出混凝土初步配合比 ;( 4 )按《普通混凝土配合比设计规程》对上述设计出的配合比进行试拌、调整 ,得到实际可使用配合比。

Monte Carlo方法在岩体裂隙结构面模拟中的应用

介绍了Monte Carlo方法的基本思想、随机数的产生方法和随机分布数的产生方法。对野外工程岩体观察数据采集的原则做了简要说明,并介绍了对采集数据的分析过程和分析目的,建立了岩体裂隙结构面模拟的基本假设,并在基本假设与随机变量产生方法的基础上给出了程序框图和应用实例。