M/G/1排队系统的性能灵敏度分析

非Markov型排除系统经常被用来作为某些实际工程问题（如通讯网络）的研究模型,对于一般的M／G／1排队系统,本文通过研究其嵌入Markov链,讨论了系统的稳态性能灵敏度分析问题,并给出用嵌入Markov链的势能表示的稳态性能灵敏度公式,由于嵌入Markov链要比描述其系统状态的半Markov过程简单得多,故本文的结果对M／G／1排队系统的性能灵敏度仿真计算及系统的优化,都将带来极大的方便。     

基于参数模型的EVaR风险度量计算方法及实证研究

针对EVaR(Expectile-based Value at Risk)风险度量提出了基于GARCH类和SV波动率模型的EVaR风险度量计算方法,即EVaR计算的参数模型方法.并基于模拟学生t分布时间序列数据,给出EVaR样本外预测的失败率检验方法:Kupiec失败率检验和动态分位数(DQ)检验法.与采用CARE(Conditional Autoregressive Expectile)模型的EVaR计算方法进行了对比研究,结果表明基于GARCH类模型和SV模型相对于基于CARE模型有更优的EVaR预测效果.选取2004年1月5日到2009年12月30日的国内外五个股票市场指数数据,针对日对数收益率进行了EVaR风险度量的实证研究,得出在金融危机期间,基于参数模型的EVaR预测要比基于CARE模型的EVaR预测更接近市场实际风险.     

一类修正Cooper-Frieze网络的稳定性研究

基于Markov链理论,研究了一类修正Cooper-Frieze模型的稳定性.通过将模型中节点度与Markov链建立联系,利用Markov理论中首达概率的思想为稳态度分布的存在性提供了证明,并从数学上推导出度分布的具体表达式.最后,对该模型的度分布和聚集性提供了仿真分析,并与BA模型作了相应的对比.     

根据已知链图找出最大链图的有效的算法

一个有效的处理工具. 代表相同条件独立结构的链图称为Markov等价的. Frydenberg指出在等价的链图中存在一个包含其他所有等价链图的元素, 称为最大链图. 给出了一个根据已知链图找出最大链图的算法, 计算复杂度仅为O(n³) (目前已有算法的复杂度约为O(n!)), 从而给出了直观地判断一个链图是否是与之等价的最大链图的方法.     

血流动力学模型及应用研究

针对现有血流模拟中采用的流体动力学模型计算量大且实时性差的问题,采用不可压缩稳态非牛顿流体模型对血液流动现象进行仿真,提出一种改进的血流模拟数值计算方法.首先根据血液流变性质、仿真的实时性与细节性的要求,选取合适的血流动力学模型;然后根据所选取的动力学模型,对现有的离散方法进行一定的改进,使得离散后方程的计算量符合仿真的实时性要求;最终计算出粒子的运动信息.实验证明,算法能够有效地降低血流数值计算的复杂度,提高血流绘制的效率.     

集值Markov链及其随机集落影性质

提出了一种集值Markov链,该模型是对基于随机变量的Markov链推广,将随机变量提升到随机集上.模型继承了经典Markov链的诸多良好性质,而且可以退化为经典的Markov链模型.为了进一步分析该模型,引入随机集落影理论,提出转移落影、落影分布等概念,并给出了部分结论和性质.最后,给出一个应用实例.     

非正态条件下过程能力指数的仿真研究

研究基于各类计算非正态条件下过程能力指数方法的有效性,采用蒙特卡洛方法,通过建立各方法的仿真模型,模拟仿真并比较各方法的性能优劣.仿真结果显示,Johnson转换法较Box-Cox转换法具有更加广泛的适用范围,并在绝大多数参数取值范围内具有优越性.偏态过程能力指数Cs由于不受数据分布类型的影响,在实际生产中具有较高的应用范围.最后利用研究对焊机关键质量特性进行实证分析,并验证了方法的有效性与可行性.     

基于改进的GM(1,1)-Markov链组合模型广东省单位GDP能耗预测

本文以灰色系统理论的GM(1,1)模型和随机过程理论的Markov链模型为基础构建了一个动态GM(1,1)-Markov链组合预测模型。该模型同时利用了GM(1,1)模型对序列趋势因素良好的拟合能力和Markov链模型对残差序列信息的提取能力。为进一步提高该模型的预测精度,用泰勒(Taylor)近似方法和新信息优先的思想对该模型进行了改进。最后,以1991-2014年广东省单位GDP能耗数据实证了该模型的预测效果。     

基于有向加权网络的价格传导时滞模型

传统的投入产出价格模型利用矩阵描述并分析价格传导过程.因矩阵表述方式属二维模型,故而无法反映价格随时间变化的动态关系.利用有向加权网络描述各产业部门及部门间的价格传导关系,并将时间维度引入构建了价格传导网络模型,考察价格传导时滞的影响.与现有投入产出价格模型相比,模型具有以下三个优势:一是可计算任意时刻的价格传导波动,而传统投入产出价格模型只是该模型在价格传导时间趋向无穷时的特例;二是模型考虑了各部门不同的价格传导时滞的影响,对价格传导过程描述更加精确;三是该模型不受二维矩阵算法的限制,计算复杂度低,易于仿真模拟.     

基于上凸序列的GM(1,1)模型及其优化

针对GM(1,1)模型对上凸序列建模时会出现误差较大的情况进行了研究.首先分析了GM(1,1)对上凸序列建模时的残差变化规律,然后通过分析得出了残差变化规律的精确描述,同时证明了残差序列的几个性质定理.基于残差序列的性质定理提出了基于上凸序列建模的残差修正GM(1,1)模型.将新模型与多种改进的GM(1,1)模型进行对比,实证结果表明新模型具有很高的模拟预测精度,并且适用于一切上凸序列的建模.     

An efficient algorithm for finding the largest chain graph according to a given chain graph

Chain graph (CG) is a general model of graphical Markov models. Some different chain graphs may describe the same conditional independence structure, then we say that these CGs are Markov equivalent. In 1990 Frydenberg showed that every class of Markov equivalent CGs has a CG which is called the largest chain graph with the greatest number of lines. This paper presents an efficient algorithm for finding the largest chain graph of the corresponding Markov equivalent class of a given CG. The computational complexity of the algorithm is O(n3). It is more efficient than the complexity O(n!) of the present algorithms. Also a more intuitive graphical characterization of the largest chain graph is provided based on the algorithm in this paper.     

A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers

In this work, exact and approximate non-reflecting boundary conditions (NRBCs) are implemented with the Partition of Unity Finite Element Method (PUFEM) to solve short wave scattering problems governed by the Helmholtz equation in two dimensions. By short wave problems, we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer. Various NRBCs are implemented and a comparison of their performance is carried out based on the accuracy of the results, ease of implementation and computational cost. The aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number.     

Rainflow analysis in Coastal Engineering using switching second order Markov models

The paper deals with the use of Markov and switching Markov chain models of turning points to reproduce random sets of sea states. The advantages of these models are emphasized and compared with existing models based on wave height records, indicating that long and short range and period cycles are included, while the wave height records ignore this important information from the point of view of damage accumulation. Existing models for first order Markov processes are extended to the case of second order processes and closed formulas are given to derive the rainflow matrices of these processes. Finally, one illustrative example of application is given.     

Identification of material behavior via a Finite Element Model Updating strategy

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Introduction to the Special Issue on Discrete Event Models of Continuous Systems

Automatic control systems rely on models to predict the near future and identification algorithms to adapt the models to changing process behaviour. The traditionally highly complex models of the activated sludge process developed for scientific purposes cannot be identified from on-line measurements and are not suited for process control purposes in their present form. Model decoupling based on the different time scales of the dynamic processes is one possible way of attacking this problem. It allows the implementation of more simple and realistically applicable controllers in combination with predictions based on simplified models in hierarchical control structure. This paper discusses these concepts and presents a reduced order model describing carbonaceous removal, nitrification, and denitrification in a medium time scale (several hours/days). The model parameters are identifiable from available on-line measurements and the dynamic behaviour is verified against computer simulations of the IAWQ activated sludge model no. 1.     

A Discrete Element Approach for Wave Propagation in Thin Rods

Wave propagation and evoked side effects, such as material failure, are important parts of analysis of dynamically exposed structures like buildings or machinery. One of the numerical analysis tools for wave propagation is the well-known Finite Element Method (FEM) with its impressive performance but also with the drawback of not being able to model easily material failure, discontinuities and contacts. In contrast, the Discrete Element Method (DEM) is capable to describe these effects on a meso-scale more easily. The here selected concept is based on a DEM particle which is considered as deformable, and can establish and remove lasting bonds with other particles. The simulation example used is a thin rod that has been an extensive numerical and experimental research subject since the last century. A longitudinal wave is excited within the thin rod by simulating an impact on one end of the rod in a free-free configuration. It is found, that the simulation data, the velocity profile and the resulting displacement at the end of the rod, are in good agreement with experimental obtained data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulations of collision of ice particles

The objective of this paper is to develop a realistic model for ice–structure interaction. To this end, the experiments made by Bridges et al. [Bridges FG, Hatzes A, Liu DNC. Structure, stability and evolution of Saturn’s rings. Nature 1984;309:333–5] in order to measure the coefficient of restitution for ice particles are thoroughly analyzed. One particularly troublesome aspect of the aforementioned experiments is fracture of the ice particles during a collision. In the present effort, the collisional properties of the ice particles are investigated using a Finite Element approach. It is found that a major challenge in modeling collision of the ice balls is the prediction of the onset of fracture and crack propagation in them. In simulations of a block of ice collision to a structure, it is crucial that fracture is determined correctly, as it will influence the collisional properties of the ice particles. The results of the simulation, considering fracture criterion implemented into the Finite Element Model [Zamankhan P, Bordbar M-H. Complex flow dynamics in dense granular flows. Part I: experimentation. J Appl Mech (T-ASME) 2006;73:648–57; Zamankhan P, Huang J. Complex flow dynamics in dense granular flows. Part II: simulations. J Appl Mech (T-ASME) 2007;74:691–702] together with a material model for the ice, imply that most of the kinetic energy dissipation occurs as a result of fracturing at the contact surface of the ice particles. The results obtained in the present study suggest that constitutive models such as those proposed by Brilliantov et al. [Brilliantov NV, Spahn F, Hertzsch JM, Poschel T. Model for collisions in granular gases. Phys Rev E;1996;53:5382–92] for collisions of ice particles are highly questionable.     

Stochastic modeling of phytoplankton allelopathy

The study of dynamic interactions between two competing phytoplankton species in the presence of toxic substances is an active field of research due to the global increase of harmful phytoplankton blooms. Ordinary differential equation models for two competing phytoplankton species, when one or both the species liberate toxic substances, are unable to capture the oscillatory and highly variable growth of phytoplankton populations. The deterministic formulation never predicts the sudden localized extinction of certain species. These obstacles of mathematical modeling can be overcome if we include stochastic variability in our modeling approach. In this investigation, we construct stochastic models of allelopathic interactions between two competing phytoplankton species as a continuous time Markov chain model as well as an Itô stochastic differential equation model. Approximate extinction probabilities for both species are obtained analytically for the continuous time Markov chain model. Analytical estimates are validated with the help of numerical simulations.     

Switching diffusion logistic models involving singularly perturbed Markov chains: Weak convergence and stochastic permanence

Focusing on stochastic dynamics involve continuous states as well as discrete events, this article investigates stochastic logistic model with regime switching modulated by a singular Markov chain involving a small parameter. This Markov chain undergoes weak and strong interactions, where the small parameter is used to reflect rapid rate of regime switching among each state class. Two-time-scale formulation is used to reduce the complexity. We obtain weak convergence of the underlying system so that the limit has much simpler structure. Then we utilize the structure of limit system as a bridge, to invest stochastic permanence of original system driving by a singular Markov chain with a large number of states. Sufficient conditions for stochastic permanence are obtained. A couple of examples and numerical simulations are given to illustrate our results.