钢坯吊具主连杆可靠性优化设计

应用摄动分析理论,论述了钢坯吊具主连杆结构的可靠性问题.在不确定变量分布形式未知情况下,利用Edgeworth级数,将任意分布的随机变量转化为标准的正态分布形式,建立其分布函数,结合摄动分析方法计算标准化正态变量及结构失效状态函数的均值和方差,得到结构的可靠度指标,可用于描述结构的可靠性程度.以可靠度指标为约束构建优化...     

具连续分布滞量的二阶半线性阻尼微分方程的振动准则

本文研究了一类具连续分布滞量的二阶半线性阻尼微分方程的振动性. 通过利用函数不等式技巧、广义Riccati变换和 函数等方法,给出了此类方程所有解振动新的振动准则,所得结果推广和改进了文献的结果。     

脉动风速过程模拟的正交展开-随机函数方法

在随机过程的正交展开基础上,采用随机函数的思想,提出了脉动风速随机过程模拟的正交展开-随机函数方法。通过将展开式中的一组标准正交随机变量表达为基本随机变量的正交函数形式,实现了用一个基本随机变量来表达原随机过程的目的。应用正交展开-随机函数方法,对脉动风速随机过程进行模拟分析。结果表明,在二阶数值统计意义上,仅需用一个基本随机变量即可对脉动风速随机过程进行精确模拟,进而体现了正交展开-随机函数方法的有效性和优越性。     

带有支座松动故障的转子-轴承系统碰摩的可靠性分析

 针对存在支座松动和碰摩的耦合故障转子-轴承系统,采用短轴承非稳态油膜模型和线性碰摩模型建立转子-轴承系统的动力学方程,应用矩阵微分理论、二阶矩技术、矩阵摄动理论和Kronecker代数方法系统地研究了此耦合故障转子-轴承系统的随机响应问题.应用四阶矩技术和Edgeworth级数展开,对耦合故障转子-轴承系统碰摩的可靠性进行了研究,并求出了数值解,给出了可靠性曲线.     

两端简支输流管道共振可靠度分析

采用基于Galerkin的加权残数法分析输流管道,利用 阶Galerkin截断建立试函数,推导出消除残数方程,得到输流管道的前 阶固有频率,并分析流速对固有频率的影响。建立输流管道共振可靠度的功能函数,利用点估计法计算功能函数的前四阶矩,采用修正Edgeworth级数法求得输流管道的共振可靠度,并讨论了流速对管道共振可靠度的影响。研究结果对于输流管道的防共振设计和共振可靠性评估具有参考价值。     

涡轮盘裂纹萌生扩展数字仿真的故障状态随机函数法

根据某型发动机涡轮盘封严圈裂纹萌生扩展的机理和故障统计资料,把影响封严圈裂纹萌生扩展的四个主要随机变量(裂纹长度、工作寿命、日历寿命和盘件材料的屈服强度)组合构造成为一个综合统计量--故障状态随机函数S.统计分析表明,随机函数S服从威布尔分布,其线性相关系数高于0.9.最后,还根据S函数的分布导出封严圈裂纹长度及其扩展量的分布函数.     

一类L－统计量的a．s．收敛性

本文获得了一类Ｌ－统计量的ａ．ｓ．收敛速度及收敛性。     

基于双变量降维模型和Kriging近似的统计矩点估计法

对复杂随机系统进行统计矩分析时,双变量降维近似模型一定程度上可以缓解“维数灾难”。但当系统维数较高时,双变量分量函数较多,计算量仍然较大。为此,该文将降维近似和Kriging代理模型有机结合起来,提出了一类高效、合理的改进点估计法。充分考虑函数逼近和数值积分中积分点的特点,提出了“米”字形的选点策略,并基于此发展了双变量分量函数的Kriging近似模型;将此近似模型用于原函数和矩函数的双变量降维近似模型中双变量分量函数的近似,分别建立了基于原函数近似和矩函数近似的统计矩改进点估计法;通过多个算例对该文提出方法进行了效率和精度的分析。算例分析结果表明:基于“米”字形选点策略的双变量分量函数的Kriging近似具有较高的精度;相比于已有的基于双变量降维近似模型的统计矩点估计法,建议方法仅需较少的结构分析即可达到与已有方法相当的精度,能更好地体现精度和效率的平衡。     

半线性两点边值问题有限元强超收敛性

通过单元正交展开的余项中添加若干待定的低次项,得到所需的超接近于有限元解的逼近函数,由此导出了一类非线性两点边值问题的强超收敛性。最后给出了一个数例验证了这一结论。     

用(G′/G)展开法求解非线性偏微分方程精确解

本文对(G′/G)展开法中的一类辅助方程—二阶线性常微分方程进行扩展求解,得到了此辅助方程更多形式的新精确解.借助Maple软件,利用此(G′/G)展开法求解了(3+1)-维potential-YTSF方程和(2+1)-维破裂孤子方程,得到了方程大量的新的精确解,包括含参数的双曲函数解和三角函数解.该方法直接简单并能构造出非线性偏微分方程更丰富的精确解,为求解非线性偏微分方程提供了一个更强大的方法.     

Asymptotic expansions for statistics computed from spatial data

Summary The Edgeworth expansions for dependent data are generalized to the context of spatial patterns, with the aim of obtaining asymptotic expansions which approximate the distribution of statistics computed from spatial data, generated by a weakly dependent coverage process. In particular, the case of estimating the expected proportion (its porosity) of a region that is not covered by the process is treated in detail and explicit formulae are given in the context of a Boolean model, assuming that the random sets generating the model are essentially bounded and satisfy a version of Cramér’s condition.     

Asymptotic Expansions of the Distribution of the Estimator for the Generalized Partial Correlation Under Nonnormality

The generalized partial correlation is denned as a correlation between two variables, where the linear effects of common and unique third variables are partialed out from the two variables. The generalized partial correlation includes simple, partial, part/semipartial and bipartial correlations as special cases. The Edgeworth expansion of the distribution of the standardized sample coefficient for the generalized partial correlation is obtained up to order O(1/n) under nonnormality. Also asymptotic expansions of the distribution of the Studentized estimator are obtained using the Edgeworth expansion, Cornish-Fisher expansion and Hall’s method with variable transformation. As extensions, the results of multivariate cases or generalized partial set-correlations are given.

     

Higher-order approximations to the quantile of the distribution for a class of statistics in the first-order autoregression

Higher-order approximations for quantiles can be derived upon inversions of the Edgeworth and saddlepoint approximations to the distribution function of a statistic. The inversion of the Edgeworth expansion leads to the well known Cornish–Fisher expansion. This paper deals with the inversions of Esscher’s, Lugannani–Rice and r* saddlepoint approximations for a class of statistics in the first-order autoregression. Such inversions provide analytically explicit approximations to the quantile, alternative to the Cornish–Fisher expansion. We assess the accuracy of the new approximations both theoretically and numerically and compare them with the normal approximation and the second and third-order Cornish–Fisher expansions.     

单自由度非线性随机参数系统的可靠性分析

阐述了具有随机参数的单自由度非线性振动系统的可靠性方法，使用四阶矩技术确定了系统响应和状态函数的前四阶矩，应用Ｅｄｇｗｏｒｔｈ级数把未知响应和状态函数的概率分布展开成标准正态分布的表达式，从而获得了系统的可靠度。     

Approximations to the Distribution of the Sample Coefficient Alpha Under Nonnormality

Approximate distributions of the sample coefficient alpha under nonnormality as well as normality are derived by using the single- and two-term Edgeworth expansions up to the term of order 1/n. The case of the standardized coefficient alpha including the weights for the components of a test is also considered. From the numerical illustration with simulation using the normal and typical nonnormal distributions with different types/degrees of nonnormality, it is shown that the variances of the sample coefficient alpha under nonnormality can be grossly different from those under normality. The corresponding biases and skewnesses are shown to be negative under various conditions. The method of developing confidence intervals of the population coefficient alpha using the Cornish-Fisher expansion with sample cumulants is presented.

     

From Fourier Expansions to Arithmetic-Haar Expressions on Quaternion Groups

Arithmetic expressions for switching functions are introduced through the replacement of Boolean operations with arithmetic equivalents. In this setting, they can be regarded as the integer counterpart of Reed-Muller expressions for switching functions. However, arithmetic expressions can be interpreted as series expansions in the space of complex valued functions on finite dyadic groups in terms of a particular set of basic functions. In this case, arithmetic expressions can be derived from the Walsh series expansions, which are the Fourier expansions on finite dyadic groups. In this paper, we extend the arithmetic expressions to non-Abelian groups by the example of quaternion groups. Similar to the case of finite dyadic groups, the arithmetic expressions on quaternion groups are derived from the Fourier expansions. Attempts are done to get the related transform matrices with a structure similar to that of the Haar transform matrices, which ensures efficiency of computation of arithmetic coefficients. Received: October 5, 1999; revised version: June 14, 2000     

Travelling and evanescent parts of the optical near field

Abstract

The optical near field of a localized source has been studied by means of the angular spectrum representation of the electromagnetic Green's tensor. This Green's tensor can be expressed in terms of four auxiliary functions, which depend on the field point through the dimensionless radial distance q to the source, or origin of coordinates, and the polar angle ρ with the z axis. Each function separates into a part containing travelling (radiative) waves and a part which is a superposition of evanescent (decaying) waves. We have derived series expansions in q of the four functions, both for the travelling and for the evanescent parts. It is shown that the travelling waves are finite at the origin of coordinates, and that all singular behaviour of the radiation field is governed by the evanescent waves. It is illustrated numerically that the series expansions are applicable up to about five wavelengths from the origin. In order to extend the range to also cover larger values of q, we have derived series expansions of the auxiliary functions which converge rapidly near the x-y plane, and a full asymptotic expansion with the z coordinate as the large variable. Finally, from the properties of the Taylor coefficients we have derived simple new integral representations for the auxiliary functions.     

Solution to the practical problem of moments using non-classical orthogonal polynomials, with applications for probabilistic analysis

A method is presented for solving the “practical” problem of moments to produce probability density functions (PDFs) using non-classical orthogonal polynomials. PDFs are determined from given sets of moments by applying the Gram–Schmidt process with the aid of computer algebra. By selecting weighting functions of similar shape to desired PDFs, orthogonal polynomial series are obtained that are stable at high order and allow accurate approximation of tail probabilities.

The method is first demonstrated by approximating a χ² PDF with an orthogonal series based on a lognormal weighting function. More general orthogonal expansions, based on Pearson type I and Johnson transform distributions, are then demonstrated. These expansions are used to produce PDFs for maximum daily river discharge, concrete strength, and maximum seasonal snow depths, using limited data sets. In all three cases the moments of the high order series are found to closely match those of the data.     

Eigenmode expansions using biorthogonal functions: complex-valued Hermite-Gaussians: comment

In this communication, certain comments are made on the paper by Kostenbauder et al., "Eigenmode expansions using biorthogonal functions: complex-valued Hermite-Gaussians,"J. Opt. Soc. Am. A 14, 1780 (1997).