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.

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.

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.

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.

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。

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。

基于MCMC的电网安全稳定控制系统动态可靠性评估方法

现有安全稳定控制系统(简称稳控系统)的可靠性评估方法本质上属于静态建模,由于未能体现系统内各装置老化和检修等动态过程,在一定程度上影响了评估结果的准确性。为此,文中提出一种基于马尔可夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)的稳控系统动态可靠性评估方法。首先针对失效过程,构建四状态非齐次马尔可夫模型来模拟装置老化过程,并给出各状态评判方法;其次针对修复过程,分析不同检修策略对装置状态转移的影响以体现状态检修的差异性;最后考虑稳控装置状态转移过程的时序或条件相关性,对稳控系统可靠性进行动态建模。以实际稳控系统为例,仿真对比不同检修策略下的可靠性,并对模型参数进行灵敏度分析。评估结果表明,该方法可以求解稳控系统的时变可用度,用于指导稳控装置现场合理检修。

基于爬坡方向状态划分的MCMC风电功率序列建模方法

由于电网弃风或者灵活性资源不足往往发生在风电大量发电时,故提高风电时间序列模型对大出力状态的建模-抽样精度,有助于后续的电网灵活性资源相关研究。在传统马尔科夫链蒙特卡洛(MCMC)法和持续与波动蒙特卡罗(PV-MC)法基础上,提出一种考虑爬坡方向状态划分的改进方法,以更准确地描述风电出力连续爬坡至大出力状态的过程。该方法以累积分布概率而不是以功率大小均匀划分状态区间,使各个状态区间的样本分布更均匀,提高了风电时间序列模型对大出力状态的建模-抽样精度。通过算例比较所提方法、MCMC法及PV-MC法生成风电功率序列与历史数据的分布特性和统计特性指标,结果表明,所提方法的拟合度较好,且能够有效解决MCMC法和PV-MC法高出力、样本偏少的问题。

The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian-MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter（RFC） is a complicated nonlinear optimization problem.This paper deals with the RFC problem in a Bayesian framework.It uses the unbiased Markov Chain Monte Carlo（MCMC） sampling technique,which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework.In contrast to the global optimization algorithm,the Bayesian-MCMC can obtain not only the approximate solutions,but also the probability distributions of the solutions,that is,uncertainty analyses of solutions.The Bayesian-MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar seaclutter data.Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter.The inversion algorithm is assessed（i） by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data;（ii） the one-dimensional（1D） and two-dimensional（2D） posterior probability distribution of solutions.

FAST CONVERGENT MONTE CARLO RECEIVER FOR OFDM SYSTEMS

The paper investigates the problem of the design of an optimal Orthogonal Fre- quency Division Multiplexing (OFDM) receiver against unknown frequency selective fading. A fast convergent Monte Carlo receiver is proposed. In the proposed method, the Markov Chain Monte Carlo (MCMC) methods are employed for the blind Bayesian detection without channel es- timation. Meanwhile, with the exploitation of the characteristics of OFDM systems, two methods are employed to improve the convergence rate and enhance the efficiency of MCMC algorithms. One is the integration of the posterior distribution function with respect to the associated channel parameters, which is involved in the derivation of the objective distribution function; the other is the intra-symbol differential coding for the elimination of the bimodality problem resulting from the presence of unknown fading channels. Moreover, no matrix inversion is needed with the use of the orthogonality property of OFDM modulation and hence the computational load is significantly reduced. Computer simulation results show the effectiveness of the fast convergent Monte Carlo receiver.

基于Markov Chain Monte Carlo的幂律过程的Bayesian分析

在多种合理的无信息先验分布下,基于Markov Chain Monte Carlo方法,提出了一种简单且易于抽样的幂律过程的Bayesian分析方法.所提方法将失效、时间截尾数据统一分析,能快捷地获取幂律过程模型参数的Markov Chain Monte Carlo样本,利用该样本不但能直接给出模型参数函数的后验分布,还能给出单样预测和双样预测的分析.一个经典工程数值算例说明了所提方法的可行性、合理性与有效性.该方法具有一定的优越性,可为小子样可靠性增长分析提供一种值得参考的方法.

基于Bayesian-MCMC方法的深受弯构件受剪概率模型研究

考虑主观、客观不确定性因素的影响,以深受弯构件受剪分析模型为研究对象,基于引入马尔科夫链-蒙特卡洛(MCMC)高效采样方法,通过R语言对深受弯构件概率模型参数进行MCMC随机模拟,给出参数的最优估计值及其对应的可信度,在先验模型基础上建立钢筋混凝土深受弯构件受剪承载力概率模型,完成模型前后的对比分析,并根据不同置信水平确定了深受弯构件受剪承载力的特征值。结果表明:基于MCMC方法得到的受剪承载力概率模型是在50000次迭代分析后产生的结果,能合理地解释影响参数的不确定性,可信度较高;后验概率模型计算结果与试验结果吻合良好,较先验模型更接近试验值,且离散性小。

基于MCMC填补的SSA-SVM煤与瓦斯突出预测模型

为提升煤与瓦斯突出预测准确度,减小数据缺失对煤与瓦斯突出预测的不利影响,提出1种基于链式多重填补马尔科夫链蒙特卡罗(MCMC)的麻雀搜索算法(SSA)优化支持向量机(SVM)预测模型。根据突出影响因素选取模型参数,运用MCMC对突出事故缺失值进行数据填补,采用SSA优化SVM,建立MCMC-SSA-SVM模型对填补后数据集进行预测,验证MCMC填补有效性和SSA优化性能;分别构建SVM、SSA-SVM、PSO-SVM、GAM-SVM、CMC-SVM、MCMC-PSO-SVM和MCMC-GA-SVM这7种模型进行突出预测,对比预测准确度,分析MCMC-SSA-SVM、MCMC-PSO-SVM和MCMC-GA-SVM的适应度。研究结果表明:MCMC填补后准确度均提升7.89个百分点以上,SSA的优化性能强于PSO和GA,MCMC-SSA-SVM预测准确度最高,为97.37%,泛化能力优于对比模型。研究结果可为煤与瓦斯突出预测研究提供借鉴和参考。

基于LIM-MCMC模型研究江苏近海北部海域食物网能量流动特征

食物网结构特征和能量流动的研究,对于维持海洋生态系统结构和功能的稳定具有重要意义,有助于深入理解海洋生态系统的复杂过程。本研究基于2019-2021年在江苏近海北部海域开展的季节性渔业资源底拖网调查数据,通过构建基于蒙特卡罗马尔科夫链算法的逆线性模型(Linear Inverse Models using a Monte Carlo Method Coupled with Markov Chain, LIM-MCMC),结合生态网络分析(Ecological Network Analysis,ENA)的方法,分析了该海域生态系统状态和食物网能量流动特征,旨在为江苏近海北部海域食物网营养动力学研究提供参考依据。结果表明,该海域生态系统共包含299条能量流动路径,能量流动分布整体呈典型的金字塔结构,各功能群呼吸消耗和流入有机碎屑的能量保持同步性。通过与其他海域比较发现,江苏近海北部海域生态系统的连接指数(Connectance,C)和系统杂食指数(System Omnivory Index,SOI)分别为0.40和0.22,处于较高水平,表明该生态系统不同营养级间的营养联系较为紧密,食物网结构相对复杂,能够在较大程度上抵御外界扰动。总初级生产力/总呼吸(Total Primary Production/Total Respiration,TPP/TR)和Finn’s循环指数(Finn’s Cycling Index,FCI)分别为1.05和5.76%,表明该生态系统对能量利用效率较高。此外,约束效率(Constraint Efficiency,CE)、发展程度(Extent of Development,AC)、协同效应指数(Synergism Index,b/c)和主导间接效应(Dominance Indirect Effects,i/d)也表明该生态系统具有较高的系统发展程度、再生潜力和系统发展空间。本研究将有助于为江苏近海北部海域生态系统的修复和渔业资源的可持续利用提供理论基础,为实施基于生态系统的渔业管理提供科学依据。

基于Bayesian-MCMC估计的隐身飞机RCS模型优化

对隐身飞机的雷达散射截面（RCS）统计建模时,传统方法通过直接计算RCS样本的统计特征估计模型参数,可能会产生较大的拟合误差。本文提出采用贝叶斯-蒙特卡罗（Bayesian-MCMC）方法提高起伏模型的参数估计精度,从而减小模型的拟合误差。首先将卡方分布模型和对数正态分布模型进行贝叶斯推导,得到其特征参数的后验估计表达式。然后采用MCMC算法构造后验分布的马尔可夫链,从而计算特征参数的估计值。最后通过比较2种方法的拟合曲线及其误差可知,本文方法适用于2种起伏模型,模型参数的估计误差比收敛误差门限值低1~2个数量级,2种分布模型的拟合精度均提高50%以上。

Hierarchical Bayesian Calibration and On-line Updating Method for Influence Coefficient of Automatic Dynamic Balancing Machine

Measurement error of unbalance＇s vibration response plays a crucial role in calibration and on-line updating of influence coefficient（IC）. Focusing on the two problems that the moment estimator of data used in calibration process cannot fulfill the accuracy requirement under small sample and the disturbance of measurement error cannot be effectively suppressed in updating process, an IC calibration and on-line updating method based on hierarchical Bayesian method for automatic dynamic balancing machine was proposed. During calibration process, for the repeatedly-measured data obtained from experiments with different trial weights, according to the fact that measurement error of each sensor had the same statistical characteristics, the joint posterior distribution model for the true values of the vibration response under all trial weights and measurement error was established. During the updating process, information obtained from calibration was regarded as prior information, which was utilized to update the posterior distribution of IC combined with the real-time reference information to implement online updating. Moreover, Gibbs sampling method of Markov Chain Monte Carlo（MCMC） was adopted to obtain the maximum posterior estimation of parameters to be estimated. On the independent developed dynamic balancing testbed, prediction was carried out for multiple groups of data through the proposed method and the traditional method respectively, the result indicated that estimator of influence coefficient obtained through the proposed method had higher accuracy; the proposed updating method more effectively guaranteed the measurement accuracy during the whole producing process, and meantime more reasonably compromised between the sensitivity of IC change and suppression of randomness of vibration response.

Bayesian zero-failure reliability modeling and assessment method for multiple numerical control(NC) machine tools

A new problem that classical statistical methods are incapable of solving is reliability modeling and assessment when multiple numerical control machine tools(NCMTs) reveal zero failures after a reliability test. Thus, the zero-failure data form and corresponding Bayesian model are developed to solve the zero-failure problem of NCMTs, for which no previous suitable statistical model has been developed. An expert-judgment process that incorporates prior information is presented to solve the difficulty in obtaining reliable prior distributions of Weibull parameters. The equations for the posterior distribution of the parameter vector and the Markov chain Monte Carlo(MCMC) algorithm are derived to solve the difficulty of calculating high-dimensional integration and to obtain parameter estimators. The proposed method is applied to a real case; a corresponding programming code and trick are developed to implement an MCMC simulation in Win BUGS, and a mean time between failures(MTBF) of 1057.9 h is obtained. Given its ability to combine expert judgment, prior information, and data, the proposed reliability modeling and assessment method under the zero failure of NCMTs is validated.

Bayesian Study Using MCMC of Three-Parameter Frechet Distribution Based on Type-I Censored Data

Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.

Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models

When modeling a stealth aircraft with low RCS（Radar Cross Section）, conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian–Markov Chain Monte Carlo（Bayesian-MCMC） method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models.