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. .

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.

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.

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。

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。

Effective-field and Monte Carlo studies of mixed spin-2 and spin-1/2 Ising diamond chain

The magnetic properties of a mixed spin-2 and spin-1/2 ferromagnetic diamond chain are studied by effective-field theory and Monte Carlo（MC） simulation based on the Ising model.The temperature dependences of magnetization,magnetic susceptibility,internal energy,and specific heat are studied,respectively.The exchange interaction dependences of magnetization and the critical temperature are calculated by MC simulation.The changes of magnetization depending on the field increasing and then the field decreasing under steady-static conditions are also given.

STUDY ON THE SEQUENCE STRUCTURE OF SBR BY ^(13)C-NMR METHOD Ⅵ MONTE CARLO SIMULATION OF THE SEQUENCE OF SBR

A program of Monte Carlo simulation of binary copolymerization for E-SBR (emulsion polymn. SB rubber) was made according to the terminal model. The simulation results obtained by this program were in good agreement with those experimental ones. A detail microstructure information of E-SBR molecular chain has been provided.

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.

Monte Carlo Study on Spontaneous Recoil of Confined DNA Chain

A part of a long DNA chain was driven into a confined environment by an electric field, while the rest remains in the higher-entropy region. Upon removal of the field, the chain recoils to the higher-entropy region spontaneously. This dynamical process was investigated by Monte Carlo simulations. The simulation reproduces the experimentally-observed phenomenon that the recoil of the DNA chain is initially slow and gradually increases in speed due to the presence of the confinement-entropic force. The results show that with increasing the dimension or decreasing the spacing of the nanopillars the recoil velocity of the DNA chain will increase. Further analysis suggests that the characteristic entropy per monomer in the confinement is proportional to the area fraction of the free part in the confinement.

Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain

The configurational properties of tail-like polymer chains with one end attached to a flat surface are studied by using dynamic Monte Carlo technique. We find that the probability distribution of the free end in z direction P（Rz） and the density profile p（z） can be scaled approximately by a factor β to be a length independent function for both random walking （RW） and self-avoiding walking （SAW） tail-like chains, where the factor β is related to the mean square end-to-end distance 〈RE〉. The scaled P（Rz） of the SAW chain roughly overlaps that of the RW chain, but the scaled p（z） of the SAW chain locates at smaller βz than that of the RW chain.

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.

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.

Monte Carlo Simulation of Band Texture Formation in Macroscopically Oriented Semirigid Polymer System

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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。

基于Monte Carlo模拟法和Markov过程理论效果评估研究

在扫雷作业过程中会出现许多复杂的随机性问题,用确定性方法对扫雷效果进行评估给出其近似解是很困难的,甚至是不可能的;而在水雷工作制度、扫雷概率以及水雷最大定次未知的情况下,对非接触扫雷雷区的状态进行评估,是实用上最常遇到的问题.针对上述情况,设计实现了基于Monte Carlo模拟法和Markov过程理论的扫雷作业模拟和评估模型,并对模型进行了仿真计算,验证了模型的正确性.

应用Markov-Monte Carlo模型评价ACS患者应用抗血小板药物致出血不良事件的经济负担

目的:为急性冠脉综合征(ACS)患者抗血小板治疗提供决策依据。方法:收集PLATO和TREAT研究中的相关数据建立Markov模型,计算ACS患者应用替格瑞洛或氯吡格雷的总出血风险、主要出血风险、次要出血风险及致命出血风险等,依据既往文献收集、计算各状态间的转移概率、各状态的成本及效用值,运用TreeAge Pro 2011软件计算不同方案的医疗费用、质量调整生命年(QALYs)以及增量-成本效果比(ICER),并对模型进行单因素敏感性分析及概率敏感性分析。结果:替格瑞洛组平均总成本是66449.38元,获得7.34 QALYs;氯吡格雷组平均总成本是53846.03元,获得6.68 QALYs。替格瑞洛组与氯吡格雷组相比的ICER为19095.98元/QALYs,即每多获得1个QALYs,替格瑞洛组患者需多花19095.98元,低于意愿支付阈值(64644元)。敏感性分析结果与上述结果一致。结论:相较于氯吡格雷,替格瑞洛对ACS患者尤其是发生出血不良事件的ACS患者具有更小的经济负担。

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.

应用Markov-Monte Carlo模型评价抗血小板药物CYP2C19基因检测的药物经济学分析

目的应用Markov-Monte Carlo模型评价抗血小板药物CYP2C19基因检测指导抗血小板药物应用的可行性。方法回顾性分析2017年9月-2019年8月广东省人民医院南海医院心血管内科收治的213例拟接受经皮冠状动脉介入术ACS患者资料,根据治疗策略分为氯吡格雷组(n=52)、替格瑞洛组(n=83)和基因检测组(n=78)。建立Markov模型,比较3种治疗策略用于中国ACS患者抗血小板治疗的有效性和经济学优势。结果与氯吡格雷比较,替格瑞洛和基因检测治疗1年质量调整寿命年(QALYs)增加,但成本相应增加且增量成本-效果比(ICER)>中国社会意愿支付阈值(WTP);对ICER影响最显著的不确定因素为替格瑞洛无事件状态成本、氯吡格雷无事件状态成本;当WTP为59 660元/QALY时,净收益占比从高到低依次为替格瑞洛、氯吡格雷、基因检测;替格瑞洛具有成本-效果性概率随WTP增加呈上升趋势;当WTP阈值为59 660元/QALY时,替格瑞洛显示出最具成本效果优势,本研究模型评价结果稳定。结论相对氯吡格雷而言,替格瑞洛和CYP2C19基因检测指导的个性化治疗方案对中国ACS患者均具有一定药物经济学优势,根据中国人均国内生产总值水平,替格瑞洛显示出更显著的药物经济学优势。