测量不确定度信息约束下的最大熵分布研究

不确定度报告广泛存在于计量工作中,在不确定度报告的有效周期内,如何利用已有的不确定度信息为后续的测量不确定度评定服务是一个重要的问题.文章以被测量已有的不确定度信息为约束条件,提出了一种结合最大信息熵原理和Heaviside阶梯函数的最大熵分布确定方法,实现被测量分布的推导.同时给出遗传算法计算拉格朗日乘子.通过实例分析发现,当被测量为对称性分布时,基于不确定度信息的最大熵分布与理论分布拟合地较好,而当被测量为非对称性分布时,拟合存在一定的偏差.但在仅有测量不确定度信息的情况下,最大熵分布是对被测量真实分布较好的近似,因而可将此分布用于后续的不确定度评定.     

细晶粒钢筋拉伸试验测量不确定度评定

介绍了细晶粒钢筋拉伸试验中测量结果的不确定度评定方法,分析了拉伸试验中屈服强度ReL、抗拉强度Rm、断后伸长率A的影响因素,计算出了各种因素的标准不确定度,得出拉伸试验结果(ReL、Rm、A)的扩展不确定度,并给出最终测量结果的表达式.     

可靠性分析中的模糊信息处理方法

在可靠性分析中,除了常见的随机不确定信息,还普遍存在着模糊不确定信息,因此在传统可靠性的基础上基于模糊理论提出了一种综合处理随机不确定信息与模糊不确定信息的可靠度计算方法。并在应力—强度干涉模型的基础上得出了未被大家重视的可靠度分布曲线,获得了能同时处理概率密度函数与隶属函数的可靠度计算模型,并探索了此模型与模糊可靠性、经典可靠性之间的内在联系。研究结果表明:在随机性与模糊性并存的情况下,此可靠性度量模型能够较好的处理随机信息与模糊信息,所得结果有很高的准确性,并且能够动态的反映可靠度的计算机理。     

基于联系数的钢筋抗拉强度测量不确定度评定新方法

钢筋抗拉强度的不确定度包括:钢筋直径的不确定度分量,拉力的不确定度分量,检测结果重复性引入的不确定度分量,数据修约的不确定度分量等等,因此,测量不确定度是与测量数据相联系的,联系数是处理不确定性问题的一种系统数学理论,可以用联系数来表示测量不确定度,为此,提出一种基于联系数的钢筋抗拉强度测量不确定度评定的新方法.     

马氏调节风险模型下的有限时间破产问题

本文主要研究马氏调节模型中有限时间内的破产变量的分布,给出了有限时间内索赔次数的分布律、总索赔金额的分布函数,且采用了离散近似的方法,显示近似方法的结果与精确的概率密度函数非常接近.此外,使用分解概率密度函数的方法,求出破产时间和破产时赤字的联合分布的具体表达式.     

估计死亡率分布的一个最大熵模型

本文提出了一种估计死亡率分布的新模型一最大熵模型。该模型直接从样本信息出发，不需要对待估分布的概率密度函数或先验分布作任何假定，从而克服了极大似然估计和贝叶斯估计的不足。而且通过两个例子的计算结果，表明该方法与样本数据的拟合效果要好于其它两种方法。     

基于Bayes FFT的螺栓连接结构模型更新方法

提出了一种基于Bayes FFT的螺栓连接结构模型更新方法.该方法中,通过弹簧和薄层单元模拟螺栓连接,借助子结构技术建立了组合结构动力学方程.进一步地,在Bayes理论框架下,由测试时域信号FFT变换系数的统计特征构造模型更新了参数的后验概率密度函数,以其负对数似然函数极值为优化目标进行参数更新,采用最大后验估计得到最优估计值,并通过后验概率分布渐近于Gauss分布的性质进行参数的不确定性量化.在数值算例中,考虑随机载荷作用下组合悬臂梁结构的模型更新问题,针对两种不同连接模型化方式给出了更新参数的不确定量化,并通过测量功率谱和修正功率谱对比,验证了所提出方法的正确性和有效性.     

t分布的概率密度近似于N(0,1)分布的一种证法

<正> 在概率论与数理统计中,t 分布是一种重要的分布。在一些概率论及数理统计的教材中谈到t 分布的性质时部指出“当”充分大时,t 分布的图形类似于标准正态分布的概率密度函数的图形”.“当n 较大时,t 分布的分布函数的Z 处的值近似等于N(0.1)分布函数的值。”事实上.设t(n)分布的概率密度函数为     

SN比及其应用

一、前言 通常,当我们确定产品、零件等的质量水平时,就要进行某种相应的试验、测量或分析.然而,此时总还存在一个问题,那就是关于试验机、量仪或者分析方法的精确度问题. 关于精确度,有的认为灵敏度高的,精确度也高;也有的认为,对某个相应的标准进行测量,共值越接近标准值的,精确度就越高;不一而足. 难道至今就没有一个客观地评定精确度的好方法吗?原来,早在通讯工程学中所使用的被称为SN比(信噪比)的评定方法,可以说是确定接收机等质量优否的重要特性值。 SN比的意义是,就连噪音都被放大的仪器中,信号甚至被噪音所淹没,象这样的接收机共…     

卧式加工中心早期故障间隔时间分布模型研究

运用回归分析和假设检验方法 ,对卧式加工中心早期故障间隔时间进行研究 ,找出早期故障间隔时间分布模型 ,求出卧式加工中心早期故障间隔时间的概率密度函数、分布函数及故障函数。卧式加工中心在早期故障期时 ,故障率曲线为递减型 ,间隔时间服从威布尔分布     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].