Evaluation of the Reliability of a System: Approach by Monte Carlo Simulation and Application

The objective of this paper is to evaluate the reliability of a system in its different states (absence of failures, partial failure and total failure) and to propose actions to improve this reliability by an approach based on Monte Carlo simulation. It consists of a probabilistic evaluation based on Markov Chains. In order to achieve this goal, the functionalities of Markov Chains and Monte Carlo simulation steps are deployed. The application is made on a production system. .

AN IMPROVED MARKOV CHAIN MONTE CARLO METHOD FOR MIMO ITERATIVE DETECTION AND DECODING

Recently, a new soft-in soft-out detection algorithm based on the Markov Chain Monte Carlo (MCMC) simulation technique for Multiple-Input Multiple-Output (MIMO) systems is proposed, which is shown to perform significantly better than their sphere decoding counterparts with relatively low complexity. However, the MCMC simulator is likely to get trapped in a fixed state when the channel SNR is high, thus lots of repetitive samples are observed and the accuracy of A Posteriori Probability (APP) estimation deteriorates. To solve this problem, an improved version of MCMC simulator, named forced-dispersed MCMC algorithm is proposed. Based on the a posteriori variance of each bit, the Gibbs sampler is monitored. Once the trapped state is detected, the sample is dispersed intentionally according to the a posteriori variance. Extensive simulation shows that, compared with the existing solution, the proposed algorithm enables the markov chain to travel more states, which ensures a near-optimal performance.

Bayesian Markov chain Monte Carlo inversion for anisotropy of PP-and PS-wave in weakly anisotropic and heterogeneous media

A single set of vertically aligned cracks embedded in a purely isotropic background may be con- sidered as a long-wavelength effective transversely iso- tropy （HTI） medium with a horizontal symmetry axis. The crack-induced HTI anisotropy can be characterized by the weakly anisotropic parameters introduced by Thomsen. The seismic scattering theory can be utilized for the inversion for the anisotropic parameters in weakly aniso- tropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derived the linearized PP- and PS-wave reflection coefficients in terms of P- and S-wave impedances, density as well as three anisotropic parameters in HTI media. Then, we proposed a novel Bayesian Mar- kov chain Monte Carlo inversion method of PP- and PS- wave for six elastic and anisotropic parameters directly. Tests on synthetic azimuthal seismic data contaminated by random errors demonstrated that this method appears more accurate, anti-noise and stable owing to the usage of the constrained PS-wave compared with the standards inver- sion scheme taking only the PP-wave into account.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

SEMI-BLIND CHANNEL ESTIMATION OF MULTIPLE-INPUT/MULTIPLE-OUTPUT SYSTEMS BASED ON MARKOV CHAIN MONTE CARLO METHODS

This paper addresses the issues of channel estimation in a Multiple-Input/Multiple-Output (MIMO) system. Markov Chain Monte Carlo (MCMC) method is employed to jointly estimate the Channel State Information (CSI) and the transmitted signals. The deduced algorithms can work well under circumstances of low Signal-to-Noise Ratio (SNR). Simulation results are presented to demonstrate their effectiveness.

多重填补法Markov Chain Monte Carlo模型在有缺失值的妇幼卫生纵向数据中的应用

目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。

基于Markov Chain Monte Carlo模型对医院调查资料中缺失数据的多重估算

目的探讨基于Markov Chain Monte Carlo(MCMC)模型的多重估算法在处理医院调查资料缺失数据中的应用。方法运用SAS9.2编写程序,在分析数据的分布类型和缺失机制的基础上,采用MCMC法对缺失数据进行多次填补和联合统计推断,分析多重估算法的优势。结果数据服从多元正态分布与随机缺失,采用MCMC法填补10次所得的结果最佳。结论多重估算既可反映缺失数据的不确定性,又可充分利用现有资料的信息、提高统计效率、对模型的估计结果更加可信,是处理缺失数据的有效方法。

On Finding the Smallest Generalized Eigenpair Using Markov Chain Monte Carlo Algorithm

This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.

Potential-Decomposition Strategy in Markov Chain Monte Carlo Sampling Algorithms

We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

With increasing complexity of today’s electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace’s equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.

基于Monte Carlo与Markov法参数不确定性条件下SIL评估

为了避免由参数不确定性因素导致较大的Markov法SIL评估偏差,且减少计算工作量和复杂性,采用Monte Carlo(MC)仿真方法处理含不确定性参数的Markov模型,并借助Matlab GUI编程开发MC仿真处理参数不确定性条件下Markov法SIL评估可视化仿真计算软件。在理论研究的基础上,为说明该研究方法与计算软件的可行性,以石油天然气工业高完整性压力保护系统(HIPPS)为算例进行SIL评估。结果表明:MC仿真方法可以有效处理Markov法SIL评估中参数不确定性问题;基于Matlab GUI编程设计出的仿真计算软件在一定程度上可以提高计算效率。

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province,China

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course.Then the paper presents a weighted Markov chain,a method which is used to predict the future incidence state.This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable.It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal.Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province.In summation,this paper proposes ways to improve the accuracy of the weighted Markov chain,specifically in the field of infection epidemiology.

Monte Carlo Simulations of Density Profiles for Hard-Sphere Chain Fluids Confined Between Surfaces

Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.

Multi-Scale Variation Prediction of PM2.5 Concentration Based on a Monte Carlo Method

Haze concentration prediction,especially PM2.5,has always been a significant focus of air quality research,which is necessary to start a deep study.Aimed at predicting the monthly average concentration of PM2.5 in Beijing,a novel method based on Monte Carlo model is conducted.In order to fully exploit the value of PM2.5 data,we take logarithmic processing of the original PM2.5 data and propose two different scales of the daily concentration and the daily chain development speed of PM2.5 respectively.The results show that these data are both approximately normal distribution.On the basis of the results,a Monte Carlo method can be applied to establish a probability model of normal distribution based on two different variables and random sampling numbers can also be generated by computer.Through a large number of simulation experiments,the average monthly concentration of PM2.5 in Beijing and the general trend of PM2.5 can be obtained.By comparing the errors between the real data and the predicted data,the Monte Carlo method is reliable in predicting the PM2.5 monthly mean concentration in the area.This study also provides a feasible method that may be applied in other studies to predict other pollutants with large scale time series data.

Statistical Inversion Based on Nonlinear Weighted Anisotropic Total Variational Model and Its Application in Electrical Impedance Tomography

Electrical impedance tomography (EIT) aims to reconstruct the conductivity distribution using the boundary measured voltage potential. Traditional regularization based method would suffer from error propagation due to the iteration process. The statistical inverse problem method uses statistical inference to estimate unknown parameters. In this article, we develop a nonlinear weighted anisotropic total variation (NWATV) prior density function based on the recently proposed NWATV regularization method. We calculate the corresponding posterior density function, i.e., the solution of the EIT inverse problem in the statistical sense, via a modified Markov chain Monte Carlo (MCMC) sampling. We do numerical experiment to validate the proposed approach.

利用Monte Carlo技术模拟研究不同缺失值处理方法对完全随机缺失数据的处理效果

目的 以医疗卫生机构年报资料为数据来源,采用成组删除法、极大似然估计法、多重填补法分别对模拟的完全随机缺失数据集缺失值进行处理,比较不同缺失率下三种方法的缺失处理效果。方法 运用SAS9.3,采用Monte Carlo技术模拟完整数据集及不同缺失比例数据集,利用成组删除法、EM算法、MCMC算法对缺失数据进行处理,得到不同处理方法后的参数估计结果,与完整数据集参数估计进行比较。结果 对于完全随机缺失数据,不同缺失率下,成组删除法的准确率均比较好;缺失率小于10%,三种方法处理效果差异不大;缺失率在10%-30%,成组删除法精确度逐渐降低,EM与MCMC准确度与精确度较好,缺失率大于30%,MCMC准确度与精确度相对较好。结论 对于不同缺失率的数据,综合考虑准确度和精确度,采用不同的方法进行处理。

基于Monte Carlo方法的一对二马尔可夫随机格斗模型

讨论了一对二马尔可夫随机格斗双方获胜概率计算问题。提出了一种新颖的一对二马尔可夫随机格斗任意对抗回合双方获胜概率的计算方法,该方法首先基于Monte Carlo仿真计算各个对抗回合中双方发射次序的概率分布,再利用全概率公式确定马尔可夫链的状态转移概率矩阵,从而克服了马尔可夫随机格斗模型往往只能提供无限对抗回合之后格斗双方获胜概率的缺点,为运用马尔可夫随机格斗研究火力运用和弹药分配提供了新途径,并用实例说明了该方法的有效性。

利用Monte Carlo方法求解线性抛物型问题(英文)

提出一种一维线性抛物型偏微分方程的温度分布函数的数值解法,数值算法是基于在空间和时间上采用紧有限差分法(CFD)得到离散化的控制方程进而利用Monte Carlo(MC)随机模拟方法求解所得的方程.通过比较由CFD方法和有限差分法(FD)得到的数值解与精确解的误差的计算结果说明了所提方法的效率和精度.

随机利率影响下信用风险的Monte-Carlo模拟

在前人利用马尔科夫链表示公司信用等级的基础上,将信用等级和随机利率引入离散时间的信用风险模型中,从而提出随机利率影响下的新的信用风险模型。就上述模型,对不同初始信用等级、初始盈余以及不同时刻的破产概率进行Monte-Carlo模拟,并讨论了相同条件下初始盈余与破产概率、初始信用等级与破产概率以及时间长短与破产概率之间的相互关系。

基于网络排队模型的Monte Carlo多线程电梯交通流优化设计

采用Monte Carlo方法对串并联结合的复合电梯系统进行了分析,应用多线程技术模拟电梯交通流模型,并给出相应的算法流程。将该算法应用到电梯配置测评中,通过对多个仿真实例的比较,根据配置结构,给出各实例的相应性能指标。结果表明,以本模型为基础建立的电梯配置测评系统可以平衡乘客候梯时间和电梯负载之间的关系,对电梯系统的结构配置给出合理建议,证明了Monte Carlo方法在电梯群控系统测评和优化中的可行性和优越性。