正定Hermite矩阵特征值的相对扰动界

给出了正定Hermite矩阵特征值的一个新扰动界,同以往的结论相比我们的界形式上更简洁而且新的扰动界在合同变换下保持不变。     

On Some Criteria for Estimating the Order of a Markov Chain

Tong (1975) has proposed a procedure for estimating the order of a Markov chain based on Akaike's information criterion (AIC). In this paper, the asymptotic distribution of the AIC estimator is derived and it is shown that the estimator is inconsistent. As an alternative to the AIC procedure, the Bayesian information criterion (BIC) proposed by Schwarz (1978) is shown to be consistent. These two procedures yield different estimated orders when applied to specific samples of meteorological observations. For parameters based on these meteorological examples, the AIC and BIC procedures are compared by means of simulation for finite samples. The results obtained have practical implications concerning whether, in the routine fitting of precipitation data, it is necessary to consider higher than first-order Markov chains.     

On the optimization of free resources using non-homogeneous Markov chain software rejuvenation model

Software rejuvenation is an important way to counteract the phenomenon of software aging and system failures. It is a preventive and proactive technique, which consists of periodically restarting an application at a clean internal state. Starting an application generally means that an amount of memory is captured and closing an application engenders the release of an amount of memory. In general, when an application is initiated an amount of memory is captured and when terminated an amount of memory is released. In this paper a model describing the amount of free memory on a system is presented. The modelling is formulated under a continuous time Markov chain framework. Additionally the cost of performing rejuvenation is also taken into consideration, a cost function for the model is produced and a rejuvenation policy is proposed. The contribution of this paper consists of using a cyclic non-homogeneous Markov chain in order to study the overall behaviour of the system capturing time dependence of the rejuvenation rates and deriving an optimal rejuvenation policy. Finally, a case study is presented in order to illustrate the results of the cost analysis.     

Maximum Likelihood Estimation for a Hidden Semi‐Markov Model with Multivariate Observations

In this paper, a parameter estimation procedure for a condition‐based maintenance model under partial observations is presented. The deterioration process of the partially observable system is modeled as a continuous‐time homogeneous semi‐Markov process. The system can be in a healthy or unhealthy operational state, or in a failure state, and the sojourn time in the operational state follows a phase‐type distribution. Only the failure state is observable, whereas operational states are unobservable. Vector observations that are stochastically related to the system state are collected at equidistant sampling times. The objective is to determine maximum likelihood estimates of the model parameters using the Expectation–Maximization (EM) algorithm. We derive explicit formulae for both the pseudo likelihood function and the parameter updates in each iteration of the EM algorithm. A numerical example is developed to illustrate the efficiency of the estimation procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling of Particle Concentration Distribution in a Fluidized Bed by Means of the Theory of Markov Chains

A one-dimensional mathematical model of particulate solids fluidization based on the theory of Markov chains is proposed. Transition probabilities that form the matrix and control the migration of particles over the bed are subdivided into two types, convection and diffusion. The convection transition probabilities depend on the local particle concentration in cells of the chain and mainly define the bed expansion at certain hydrodynamic conditions. The diffusion transition probabilities form particle concentration distribution over the bed height. On the basis of the model, the heat exchange between gas and particulate solids is described. The batch fluidization model is generalized to the case of continuous fluidization that allows predicting a connection between throughput and hold-up, as well as particle residence time distribution in a bed. Some aspects of the approach are verified experimentally.     

Computing Transition Probability in Markov Chain for Early Prediction of Software Reliability

Early prediction of software reliability provides basis for evaluating potential reliability during early stages of a project. It also assists in evaluating the feasibility of proposed reliability requirements and provides a rational basis for design and allocation decisions. Many researchers have proposed different approaches to predict the software reliability based on a Markov model. The transition probabilities in between the states of the Markov model are input parameters to predict the software reliability. In the existing approaches, these probabilities are either assumed on some knowledge or computed using analytical method, and hence, it does not give accurate predicted reliability figure. Some authors compute them using operational profile data, but that is possible only after the deployment of the software, and this is not early prediction. The work in this paper is devoted to demonstrate the computation of transition probability in the Markov reliability model taking a case study. The proposed approach has been validated on 47 sets of real data. Copyright © 2015 John Wiley & Sons, Ltd.     

基于政府财政干涉的绿色供应链销售渠道模型

以博弈论为基本方法,研究了基于政府财政干涉的绿色供应链销售渠道模型问题。以制造商为市场领导者,构建了单一销售渠道和混合销售渠道的绿色供应链决策模型,通过对决策模型的分析,给出供应链成员的最优绿色度、批发价合同和利润,发现政府的财政干涉能激励供应链成员进行绿色产品的研发工作,且在混合策略下供应链的收益最大。最后通过算例分析验证了以上结论。     

供应链拓扑结构模型研究

供应链是随着全球制造的兴起而出现的新型的管理模式。本文从企业与企业之间关系的角度提出了供应链的拓扑结构模型：链状模型、网状模型和石墨模型，相应地给出了供应链的子网、级、入点、出点等概念。本文针对不同的研究对象和研究阶段而提出的供应链概念和模型有助于对供应链的和认识和研究，对国有企业重组有启示意义。     

Uncertainty Quantification for Multivariate Eco-Hydrological Risk in the Xiangxi River within the Three Gorges Reservoir Area in China

This study develops a multivariate eco-hydrological risk-assessment framework based on the multivariate copula method in order to evaluate the occurrence of extreme eco-hydrological events for the Xiangxi River within the Three Gorges Reservoir (TGR) area in China. Parameter uncertainties in marginal distributions and dependence structure are quantified by a Markov chain Monte Carlo (MCMC) algorithm. Uncertainties in the joint return periods are evaluated based on the posterior distributions. The probabilistic features of bivariate and multivariate hydrological risk are also characterized. The results show that the obtained predictive intervals bracketed the observations well, especially for flood duration. The uncertainty for the joint return period in “AND” case increases with an increase in the return period for univariate flood variables. Furthermore, a low design discharge and high service time may lead to high bivariate hydrological risk with great uncertainty.     

灰色马尔可夫链在道路交通事故预测中的应用

将灰色系统理论与马尔可夫链相结合,建立道路交通事故灰色马尔可夫链预测模型研究证明．这种模型的预测精度高于GM（1,1）模型,可用于道路交通事故预测。     

On Generating Optimal Sparse Probabilistic Boolean Networks with Maximum Entropy from a Positive Stationary Distribution

To understand a genetic regulatory network, two popular mathematical models, Boolean Networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been proposed. Here we address the problem of constructing a sparse Probabilistic Boolean Network (PBN) from a prescribed positive stationary distribution. A sparse matrix is more preferable, as it is easier to study and identify the major components and extract the crucial information hidden in a biological network. The captured network construction problem is both ill-posed and computationally challenging. We present a novel method to construct a sparse transition probability matrix from a given stationary distribution. A series of sparse transition probability matrices can be determined once the stationary distribution is given. By controlling the number of nonzero entries in each column of the transition probability matrix, a desirable sparse transition probability matrix in the sense of maximum entropy can be uniquely constructed as a linear combination of the selected sparse transition probability matrices (a set of sparse irreducible matrices). Numerical examples are given to demonstrate both the efficiency and effectiveness of the proposed method.     

基于公铁联运的多温蓄冷箱全程冷链集配优化

目的 针对多品种、高频次、小批量、高时效及高附加值等特点的消费者订单需求,借助自主研发设计的多温蓄冷箱,提出基于公铁联运的多温蓄冷箱全程冷链集配模式,并展开实证研究。方法 以总成本最小化为目标,构建基于公铁联运的多温蓄冷箱全程运输及配送优化模型,对比全程机械式冷藏汽车多温共配模式,采用遗传算法优化求解,并对配送时效和高铁运价进行灵敏性分析。结果 基于公铁联运的多温蓄冷箱全程冷链集配相较于全程机械式冷藏汽车多温共配的总成本减少了38%,其中,制冷成本、碳排放成本及时间惩罚成本明显减少;以正常配送时间约束为参照,延长或缩短时间窗,基于公铁联运的多温蓄冷箱全程冷链集配的时间惩罚成本比全程机械式冷藏汽车多温共配的减少了61%~83%。与铁路整车货运价格相比,高铁货运价格在上浮不超过220%的情况下,基于公铁联运的多温蓄冷箱全程冷链集配模式相较于全程机械式冷藏汽车多温共配模式在经济效益和社会效益两方面更具优势。结论 公铁联运的多温蓄冷箱全程冷链集配能为企业降本增效、节能减排,为运输主体提供新思路,为整合闲置运力提供一种新型的运营模式。     

基于离散元方法的沥青混合料力链演化及分布量化分析

为了研究沥青混合料内部颗粒间力链的演化及分布规律,以AC-13沥青混合料作为研究对象,利用离散元方法重构沥青混合料数字试件,模拟简单性能试验,提取试件内部颗粒间的力链信息进行力链演化、概率分布和角度分布分析。结果表明,通过比较预测结果和实测结果,基于离散元方法重构的AC-13沥青混合料细观模型用于模拟其细观力学特性是可行的。试件内部力链空间分布具有各向异性,以垂直方向的压力力链为主,承受大部分的半正弦荷载。法向力链概率分布随加载时间的变化规律基本一致,法向接触力与平均法向接触力比值f最小时,概率分布出现最大值,f=1.75时,概率分布再次达到峰值,然后逐渐减小并趋于稳定。法向力链角度分布主要位于90°和270°附近,第一、二象限的角度分布比例远大于第三、四象限,60~120°、30~150°中法向力链角度分布比例均大于70%,最小为72.733%。     

On the design of nonparametric runs-rules schemes using the Markov chain approach

The aim of this paper is to highlight some concerns about the partly inaccurate manner in which the currently available 2-of-2 and 2-of-3 simple and improved runs-rules charts based on the sign and the signed-rank statistics were designed using Markov chain matrix. Because of the memory-less property of the Markov chains, the empirical average run-length (ARL) values were not affected; but the design structure of the matrix makes it difficult to formulate the general expressions of the ARL explicitly. Also, the dimension (and consequently, the simplicity) of the transition probability matrices (TPMs) and the false alarm rates expressions were affected negatively. Thus, we present some zero- and steady-state formulae that make it easier to construct some key elements of the run-length distribution (including the TPMs) of the simple and improved 2-of-(H + 1) runs-rules charts based on the sign and the signed-rank statistics, for any positive integer value H > 0, not just H = 1 and 2, as currently available for these monitoring schemes, so that any interested reader may use these formulae to obtain the corresponding empirical study.     

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

In oceanography, there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling. In particular, there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them. Such changes are associated with autocovariance changes. This article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application. More specifically, the framework considers time series under the locally stationary wavelet (LSW) framework, deriving a joint density for scale processes in the raw wavelet periodogram. By embedding this density within a hidden Markov model (HMM) framework, we consider changepoint characteristics under this multiscale setting. Such a methodology allows us to model changepoints and their uncertainty for a wide range of models, including piecewise second-order stationary processes, for example, piecewise moving average processes.     

The State of the Art of Hidden Markov Models for Predictive Maintenance of Diesel Engines

The maintenance of diesel Engines is usually scheduled according to the maintenance procedures defined by manufacturers. However, the state of the art shows that the condition monitoring maintenance associated with adequate prediction algorithms allows performance improvement both by increasing the intervals between interventions and by helping to maintain reliability levels. There are many types of variables that can be used to measure equipment condition, as is the case of several types of pollutant emissions such as NO_x, CO2, HC, PM, and NOISE, among others. This is a typical problem that can be solved through a hidden Markov model, taking into account the specificity of this type of equipment. The paper describes two algorithms that can help to increase the quality of assessment of engine states and the efficiency of maintenance planning. Those are the Viterbi and Baum–Welch algorithms. The importance of how to calculate the performance index of the model by the use of the perplexity algorithm is also emphasized. In this paper, a new paradigm is proposed, designated as ecological predictive maintenance. Copyright © 2017 John Wiley & Sons, Ltd.     

A general formulation for transition probabilities of Markov model and the application to fracture of composite materials

A generalized method for formulating unit-jump Markov chain model is presented. This method uses geometric series to determine the transition probabilities instead of using a moment generation function. Recursive equation for the transition probabilities has been derived in terms of the mean values. Present method is also compared by other method for robustness. Application of the unit-jump Markov chain model for characterizing fracture process of composites is described. By introducing a proper scaling factor, the entire probability history of the crack propagation at any loading states can be evaluated by the present model.     

考虑道路坡度影响的多约束冷链配送问题研究

目的 为改进传统冷链VRP将配送区域默认为二维平面,使得实际调度与理想状态产生差异而造成配送成本增加的问题,本文对相关问题进行深入研究,旨在合理规划资源配置,提升企业经济效益。方法 通过引入坡度函数对油耗成本和碳排放成本进行计算,综合考虑三维空间位置、多车型、载质量变化、客户取送货需求和时间窗要求等多种现实约束,并提出一种基于K–means多维时空聚类的改进遗传算法进行求解。结果 求解结果表明,若最初将道路坡度考虑在成本计算内,可有效降低9.58%的配送成本。同时,应避免大型车辆在重载时突然发生海拔变化。当发生海拔变化时,大型车辆可在卸载一部分货物后改变至更高的高度。结论 本文研究的模型更加贴近实际路网,具有更高的适用性,特别是对有明显道路坡度城市的冷链品的配送具有现实的借鉴意义。     

考虑级配颗粒物质间接触力力链的分布概率分析

为了揭示颗粒物质间接触力力链的分布规律,选取10 mm、13 mm、16 mm、19 mm和20 mm五组粒径的刚性颗粒进行复写纸压痕试验,利用概率分析方法研究了单一粒径和考虑级配不同粒径颗粒体内部接触力力链的分布概率。研究结果表明:两种单一粒径的法向力与平均法向力比值f的分布概率呈先增大达到峰值后减小的趋势,分布概率达到峰值处所对应的f值接近1;10 mm颗粒的分布概率曲线所产生的误差较小,20 mm颗粒的分布概率曲线产生的误差相对较大;考虑级配的颗粒体,其分布概率均呈指数形式单调衰减,未出现分布概率峰值,并且强力链比例基本小于10 mm和20 mm的单一粒径颗粒体。     

An Equation of State for the Hard-Sphere Chain Fluid Based on the Thermodynamic Perturbation Theory of Sequential Polymerization

New equations of state for freely jointed hard-sphere chain fluids are developed. The equations of state are based on the thermodynamic perturbation theory. The new equations of state use the contact values of the radial distribution function (RDF) for monomer–dimer mixtures, which is derived from the multidensity Ornstein–Zernike theory. These RDFs are composed of a monomer reference term, the Carnahan–Starling or the Percus–Yevick expression, and an additional bond contribution. These equations of state are then extended to real fluids. To calculate the phase equilibrium properties of nonassociating chain fluids, a dispersion contribution is added to the repulsive hard-chain reference term. With the new equations of state of chain fluids supplemented with the dispersion term, the vapor pressures and the coexisting densities of several real fluids are calculated.