一类改进的GOM(1,1)模型及其应用

本文考虑非负递减序列的建模预测问题.考虑到灰作用量会随着时间和空间的变化而发展变化,将灰作用量近似看作为时间的线性函数从而构建了灰作用量优化的GOM(1,1)模型.结合灰色预测模型数据序列的非齐次指数特性,利用积分推导出GOM(1,1)模型的最优化背景值.以原始序列和模拟序列的平均相对误差平方和最小为原则,确定最优的时...     

基于非等间距GM(1,1)的校准周期预测方法研究

为科学合理地确定计量器具的校准周期,提出了基于非等间距GM(1,1)的计量器具校准周期预测方法.该方法以灰色系统理论为依据,首先将已知的非等间距序列进行累加生成处理,对生成序列建立白化微分方程,通过最小二乘法求待辩识参数,进而得出非等间距GM(1,1);并通过Matlab7.5.5实现了非等间距GM(1,1)模型的快速...     

非等间距GM(1,1)幂模型及其工程应用

针对工程中大量存在的非等间距序列的建模问题,提出了非等间距GM(1,1)幂模型。以平均相对误差绝对值最小化为目标,以模型参数之间的关系为约束,构建了一个非线性优化模型实现非等间距GM(1,1)幂模型的参数估计。结果表明,非等间距GM(1,1)幂模型的形式较为灵活,非等间距GM(1,1)模型和灰色Verhulst模型均是非等间距GM(1,1)幂模型的特殊情形,幂指数的优化有利于提高建模精度。最后通过一个工程实例验证了非等间距GM(1,1)幂模型的有效性与实用性。     

改进灰色沉降预测模型及其应用

根据GM(1,1)灰色模型的指数特性,首先对原始数据取λ次幂以降低原始数据的分散性,再通过在区间上求积分计算模型的背景值,并采用最小二乘法求解最优的模型初始值由此建立改进灰色预测模型,将其应用到某高速公路沉降预测计算,结果表明,改进模型较之原GM(1,1)模型模拟和预测精度要高.     

汨罗市城市路基沉降的GM(2,1)模型预测

针对汨罗地裂缝沉降观测资料,运用灰色理论建立地面沉降的GM(2,1)模型,其中非等时距位移序列采用拉格朗日插值函数转变为等时距序列。为了减少对外界因素干扰的敏感性,方便求解,采用非等时距GM(2,1)和GM(1,1)模型对西安市地面沉降观测点进行安全预测。预测结果和实际吻合较好。本文提出的GM(2,1)地面沉降变形预测模型,计算简单,与原始数据的升降凹凸性保持一致。非等时距GM(2,1)模型预测地面沉降精度总体较GM(1,1)模型高,较好的反映了地面沉降的变形趋势,具有很好的实用价值。     

非齐次马氏链样本相对熵率存在定理

样本相对熵率是信息论中一个重要的内容,在统计假设检验及编码理论中起着非常重要的作用.本文的目的是要研究在有限状态空间中取值的非齐次马氏链样本相对熵率的存在性.首先将数列绝对平均收敛的定义推广到平面上,并得到平面点列绝对平均收敛的定义及相关引理,然后利用非齐次马氏链二元函数的一类平均极限定理及强大数定律,给出非齐次马氏链样本相对熵率存在的条件.本文将信息论中关于独立同分布随机变量序列的假设检验问题做了更为广泛的推广.     

基于UKF的非齐次泊松跳跃市场微结构模型研究

本文针对不确定性因素引起资产价格的巨大波动,构建了一个由非齐次泊松过程驱动的跳跃市场微结构模型.在模型参数未知的情况下,我们使用非参数化方法检测出时变跳跃强度,由此再利用无迹卡尔曼滤波和极大似然法来估计跳跃市场微结构模型参数的值.模拟仿真与实证分析验证了该方法的有效性,并利用AIC准则对两类跳跃波动率模型进行了优劣比较.研究结果表明,跳跃市场微结构模型在拟合股指数据方面要优于跳跃随机波动模型.     

非整形圆弧样板测量数据的最小二乘处理

用最小二乘法处理坐标法测量园孤样板所得到的测量值，在此数学模型基础上可实现编程处理原始数据．该方法特别适用于非整形圆弧样板。     

区域物流需求预测方法比较分析

用组合预测法对区域物流需求进行预测,各单项预测方法组合前需进行有效性分析.定性分析后选择回归分析、灰色预测、指数平滑法,定量计算验证时以1991～2004年综合货运量的预测为例,求出三种单项预测方法的预测精度序列值及相对误差值,依据组合预测的有效性对计算结果进行比较分析,经计算本文最终选定回归分析、指数平滑和灰色模型作为非线性组合预测模型的输入方法.     

二叉树上非齐次分支马氏链一类强极限定理

近年来树图或者树形网络等诸多复杂系统的结构性质与极限性质逐渐成为研究的热点问题,特别是在树指标马尔可夫链领域的研究中,国内外学者们取得了丰富的研究成果.二叉树上非齐次分支马尔可夫链作为一类特殊的树指标马尔可夫链,该模型的极限性质被国内外学者的广泛研讨并应用于生物动力学、信息论等诸多领域.本文致力于研究在有限状态空间空间取值的二叉树上非齐次分支马尔可夫链转移概率调和平均的极限性质以及该性质与树指标马尔可夫链模型之间的联系.首先在新的条件下,本文给出了在有限状态空间中取值的二叉树上非齐次分支马氏链的强极限定理,并进一步得到了其随机转移概率调和平均的强极限定理,最后借助于两类模型之间的等价关系以及平均值不等式,推广了树指标非齐次马氏链随机转移概率的极限定理。     

Empirical approach for estimating the pavement transition probabilities used in non-homogenous Markov chains

An empirical approach is proposed to estimate the transition probabilities associated with non-homogenous Markov chains typically used in developing stochastic-based pavement performance prediction models. A reliable pavement performance prediction model is a key component of any advanced pavement management system. The proposed empirical approach is designed to account for two major factors that cause the transition probabilities (i.e. deterioration rates) to increase over time. The first major factor is the progressive increase in traffic loading as represented by the equivalent single axle load applications. The second major factor is the gradual decline in the pavement structural capacity which can be represented by an appropriate pavement strength indicator such as the structural number. The proposed empirical model can recursively estimate the non-homogenous transition probabilities for an analysis period of (n) transitions by simply multiplying the first-year (i.e. present) transition probabilities by two adjustment factors, namely the load and strength factors. Once the empirical model is calibrated, these two factors can capture the impact of traffic load increases and gradual pavement structural losses on the transition probabilities over time. The calibration process requires the estimation of the model two exponents to be obtained from the minimisation of sum of squared errors wherein the error is defined as the difference between the observed and predicted pavement distress ratings (DRs). The predicted DRs are mainly estimated based on the state probabilities, which are recursively derived from the non-homogenous Markov model. A sample empirical model is presented with results indicating its effectiveness in estimating the pavement non-homogenous transition probabilities.     

软化特征可控的双参指数型约束混凝土本构及其应用

约束混凝土本构模型的下降段影响着钢管混凝土的力学性能预测,结合6组方钢管混凝土短柱轴压破坏试验结果,提出一种软化特征可控的双参指数型约束混凝土本构。双参指数型本构考虑了方钢管宽厚比、混凝土强度、钢管截面含钢率等因素的影响,能够很好地模拟在不同约束条件下混凝土的软化行为。基于双参指数型本构,对6组方钢管混凝土试验结果进行了轴压破坏的受力全过程模拟,计算结果和试验结果吻合良好。     

Application of meshless EFG method in fluid flow problems

This paper deals with the solution of two-dimensional fluid flow problems using the meshless element-free Galerkin method. The unknown function of velocity u(x) is approximated by moving least square approximants u^h(x). These approximants are constructed by using a weight function, a monomial basis function and a set of non-constant coefficients. The variational method is used for the development of discrete equations. The Lagrange multiplier technique has been used to enforce the essential boundary conditions. A new exponential weight function has been proposed. The results are obtained for a two-dimensional model problem using different EFG weight functions and compared with the results of finite element and exact methods. The results obtained using proposed weight functions (exponential) are more promising as compared to those obtained using existing weight functions (quartic spline and Gaussian)     

Dual approach to local mean square error criterion for stochastic equivalent linearization

Based on the dual conception, the paper suggests a consideration at global level to the local mean square error criterion of the stochastic equivalent linearization method. It results in new values of linearization coefficients that are obtained as global averaged values of all local linearization coefficients. The numerical analysis of some typical nonlinear systems under white noise excitation shows that the accuracy of the proposed criterion is significantly improved in comparison with the one of the classical mean square error criterion.     

基于改进最小二乘步骤的NARMA模型辨识非线性时变结构系统

基于时变非线性自回归滑动平均模型利用改进的递推最小二乘算法提出一种用于非线性时变结构系统辨识的方法。利用线性变换将非线性时不变结构系统的动力学模型转化为非线性自回归滑动平均模型,然后将非线性项展开为系统输出数据的多项式的形式。利用短时时不变假设,通过改变模型的参数跟踪系统参数的变化,将非线性时变系统的辨识问题转化为线性时变系统的辨识问题,再利用改进的递推最小二乘算法实现对非线性时变结构系统的辨识。最后通过一个具有非线性时变刚度的三自由度结构系统的仿真算例表明,该方法可以有效地辨识非线性时变结构系统。     

Computer-aided roll pass design for continuous billet mill

A mathematical model has been developed for computing the geometrical dimensions of square-diamond square pass sequence for a continuous billet mill. The model is based on derivation of shape and size factor from the geometry of the pass taking into account pass filling, pass rounding etc. Using these factors and a basic equation of spread for flat rolling, a governing equation incorporating angle of diamond and reduction in consecutive passes has been formulated. Newton’s substitution method has been used to solve the equation. With known reduction between consecutive passes, geometrical dimension of square and diamond passes are computed. A model has been used to calculate pass design of a finishing train of a continuous billet mill producing 60 mm square billet from 120 mm square bloom. The elongation values have been optimized by varying the apex angle of diamond. A close agreement between computed and actual values shows the validity of the model.     

基于Kriging模型和无迹卡尔曼滤波的转向架构架模型修正

为提高转向架构架模型的修正效率和实时性,提出了一种基于Kriging模型和无迹卡尔曼滤波的模型修正方法.首先,对构架进行模态分析,引入信息熵确定模态阶数来优选频响函数频率区间.其次,构造Kriging模型,将频响函数经过小波变换并提取第4层低频系数作为Kriging模型输出,并通过改进的灰狼算法(grey wolf o...     

Three-dimensional fundamental solution of wave propagation and transient heat transfer in non-homogenous media

The main purpose of this paper is developing fundamental solutions of three-dimensional wave and transient heat conduction in non-homogenous media. A variable transformation method is used to change the basic equations into a simple standard Helmholtz form. First, two different ways, i.e. harmonic excitation method and Laplace transform are used to eliminate time expression, and final solutions are expressed in the time-space domain. In addition, FE approach is applied to solve transient heat conduction in functionally graded material (FGM) domain. Different numerical examples are used to validate the proposed methodology by comparing the results with others and FE method. Fundamental solutions are found for both homogenous and non-homogenous media separately. For each example, appropriate graphs are provided to show the differences between the results of homogenous and non-homogenous media.     

Modelling traffic congestion using queuing networks

Traffic studies have been carried out predominantly using simulation models which are both time and capital intensive. In this paper, an analytical model of uninterrupted single-lane traffic is proposed using queuing analysis. Well-known Traffic Flow-Density diagrams are obtained using simple Jackson queuing network analysis. Such simple analytical models can be used to capture the effect of non-homogenous traffic.