残差自回归半参数模型的参数估计

研究了残差自回归半参数模型的参数估计,运用广义最小二乘法估计了参数部分．用随机模拟说明了运用广义最小二乘（GLSE）估计出的参数部分优于运用普通最小二乘法（OKSE）得到的估计．     

半参数回归模型的稳健补偿最小二乘估计

本文研究了一类半参数回归模型，利用稳健补偿最小二乘估计法，得到了稳健补偿最小二乘估计量，以及它们的影响函数及渐近方差一协方差，对结果的分析表明了该法优于补偿最小二乘法，而且具有稳定性．     

NA样本半参数回归模型估计的矩相合性

考虑了误差为NA序列的半参数回归模型,利用非参数估计方法给出了模型参数的最小二乘估计和加权最小二乘估计,并在适当条件下得到了它们的矩相合性.     

非线性半参数模型的虚拟观测法

本文首先介绍非线性半参数回归中常用的补偿最小二乘法,然后基于先验信息将其转化成对此问题的虚拟观测,用虚拟观测与原观测联合,按常规的最小二乘方法求解.最后运用的实例计算结果表明,虚拟观测方法计算的结果一般优于常规的补偿最小二乘结果,基本上可达到理论上的最优解.     

果蝇优化最小二乘支持向量机混合预测模型—以我国物流需求量预测为例

为解决最小二乘支持向量机参数设置的盲目性,利用果蝇优化算法对其参数进行优化选择,进而构建了果蝇优化最小二乘支持向量机混合预测模型.以我国物流需求量预测为例,验证了该模型的可行性和有效性.实例验证结果表明:与单一最小二乘支持向量机和模拟退火算法优化最小二乘支持向量机预测模型相比,该模型不仅能够有效选择参数值,而且预测精度更高.     

基于具有LR型模 糊输出回归模型的上证指数预测

以对称二次型模糊回归模型为基础,引入一般二次模糊回归模型,利用模糊最小二乘法估计未知参数．构建评价标准考察两模型的拟合效果,在样本期内和样本期外分别评价模型的实际拟合与预测能力．     

带自由液面粘性流体运动的最小二乘有限元模拟

给出了一种求解带自由液面流体运动的数值方法．流体运动的Navier-Stokes方程应用最小二乘有限元进行离散,有限差分法用来进行时间推进．采用Lagrange方法描述网格．将模型的计算结果与二维矩形和三维圆柱形坝溃的实验结果进行了对比．计算得到的时间历程与实验结果十分吻合,验证了最小二乘有限元在此类问题中应用的可能性．     

三参数Weibull分布的渐近广义最小二乘估计

三参数Ｗｅｉｂｕｌｌ分布是可靠性统计中一个极为重要的分布．本文将利用二步迭代方法给出分布中三个参数的一种渐近广义最小二乘估计,并进一步将结果推广至截尾和缺失数据场合．摸拟表明这种参数估计方法具有既简便又有效的优点．     

基于最小二乘法的空间坐标转换的非迭代算法

利用最小二乘法讨论三维空间的坐标转换问题,先对已知数据进行中心化处理使得坐标转换化为向量形式的最小二乘线性拟合问题,进而化为矩阵形式的最小二乘问题,最后得到法方程以及最小二乘解.如果已知数据量大且维数高,可通过奇异值分解确定相应的转换参数.和现有方法比较,方法的拟合过程不需迭代,简单易行.算例结果表明,拟合结果和原文数据吻合较好.     

门限自回归模型参数最小二乘估计的强收敛速度

本文在给定门限自回归模型阶数、门限和延迟参数的情况下，证明了一般门限自回归模型参数和残差方差的最小二乘估计的强收敛速度为Ｏ（（ｌｏｇｌ９ｏｇｎ／ｎ）１／２），并证明了残差方差的最小二乘估计具有渐近正态性．     

不同先验分布下的后验分布确定土力学参数

岩土工程中各土层参数的取值是根据现场及室内试验数据,采用经典统计学方法进行确定的,但这往往忽略了先验信息的作用。与经典统计学方法不同的是,Bayes法能从考虑先验分布的角度结合样本分布去推导后验分布,为岩土参数的取值提供一种新的分析方法。岩土工程勘察可视为对总体地层的随机抽样,当抽样完成时,样本分布密度函数是确定的,故Bayes法中的后验分布取决于先验分布,因此推导出两套不同的先验分布:利用先验信息确定先验分布及共轭先验分布。通过对先验及后验分布中超参数的计算,当样本总体符合N(μ,σ2)正态分布时,对所要研究的未知参数μ和σ展开分析,综合对比不同先验分布下后验分布的区间长度,给出岩土参数Bayes推断中最佳后验分布所要选择的先验分布。结果表明:共轭情况下的后验分布总是比无信息情况下的后验区间短,概率密度函数分布更集中,取值更方便。在正态总体情形下,根据未知参数μ和σ的联合后验分布求极值方法,确定样本总体中最大概率均值μ_max和方差σ_max作为工程设计采用值,为岩土参数取值方法提供了一条新的路径,有较好的工程意义。     

岩土工程位移时间序列的组合预测研究

将组合预测方法用于岩土工程位移时间序列预测.结合实际观测数据,分别建立位移时间序列预测的GM(1,1)模型、Verhulst模型和趋势曲线模型.采用极小误差法确定各单一模型的权重,建立组合预测模型.应用表明,组合预测的精度高,为岩土工程位移预测提供了一种实用、可靠的方法.     

An a posteriori error estimator for plane-strain geotechnical analyses

In this paper, an a posteriori error estimator suitable for use in geotechnical engineering has been developed. This error criterion is based on the superconvergent patch recovery method with equilibrium and boundary conditions method, taking into account Biot's coupled consolidation theory. After testing on several problems, the introduction of pore pressures and other parameters into the error estimator was found to improve results significantly, providing a convergence rate of approximately two orders higher than the global rate.     

Decoupled reliability-based geotechnical design of deep excavations of soil with spatial variability

This paper presents a general decoupled method for reliability-based geotechnical design that takes into account the spatial variability of soil properties. In this method, reliability analyses that require a lot of computational resources are decoupled from the optimization procedure by approximating the failure probability function globally. Failure samples are iteratively generated over the entire design space so that their global distribution information can be extracted to construct the failure probability function. The method is computationally efficient, is flexible to implement, and is well suited for geotechnical problems that may involve sophisticated models. A design example of two-dimensional deep excavation against basal heave is discussed for Singapore marine clay where the density and normalized undrained shear strength of soil mass are modeled as random fields. Results demonstrate that the proposed method works well in practice and is advantageous over the coupled or locally decoupled reliability-based geotechnical design methods.     

Bayesian decision analysis of dam safety

Inspections and safety assessments are germane elements of proper dam maintenance programs. To aid geotechnical engineers and/or dam owners in developing such programs, a Bayesian methodology is presented. It offers four main features: (1) the engineer can formally combine his judgment based on expertise with factual information obtained from geotechnical tests, (2) uncertainty about the state of the dam can be quantified explicitly, (3) the owner can specify the desired risk preference, and (4) an optimal geotechnical test plan and remedial action can be determined so as to take account of uncertainty, risk preference, and economic losses. The methodology is illustrated by a case study of an earth dam.     

基于粒子群优化Kriging模型的边坡可靠度分析

采用传统极限平衡法进行边坡可靠度分析时,不可避免会遇到一个问题,即边坡功能函数形式的高度非线性以及隐含性.对于隐式功能函数,传统的求解方法是通过对功能函数进行多次迭代,从而得到安全系数值.但是由于功能函数的形式较为复杂,导致迭代计算的过程变得尤为繁琐且效率低下.鉴于传统边坡可靠度分析中存在的安全系数计算繁琐耗时的问题,...     

Modelling internal erosion of cohesionless soils using a microstructural parameter

Internal erosion processes are of vital importance for the risk management of geotechnical structures as well as for the understanding of the macroscopic mechanical and hydraulic properties of the subsoil in various man-made constructions. Here, a 4-phase continuum model is presented and numerically applied to illustrative applications. The role of interfacial area and related microstructural parameters is addressed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

饱和粘土非线性渗流规律与径向固结

以多孔介质等效渗流概念得出粘土平均孔隙微尺度数量级范围在0.01 μm至0.1μm,与测试结果一致．实验结果表明饱和粘土微尺度孔隙渗流为非线性流．理论推导表明固液界面作用与渗透率平方根或孔隙半径成反比,固液界面相互作用是导致饱和粘土非线性渗流的重要原因．提出了精确描述饱和粘土微尺度孔隙非线性渗流基本规律的数学模型,其参数量纲明确,物理意义清楚．建立了饱和粘土非线性渗流新定律,统一描述了从较低到较高水力梯度全过程渗流曲线特征,达西定律是其特例．基于新定律,建立了饱和粘土非线性渗流定流量径向固结数学模型．以粘性边界层思想与稳态依序替换法及积分方程法,导出了粘土非线性渗流平均质量守恒方程及活动边界运动方程,给出了饱和粘土非线性渗流超孔隙水压力分布公式与平均固结度计算公式,获得了粘土层压力分布规律和平均固结度随时间变化规律．结果表明:饱和粘土非线性渗流使活动边界运动速度减小．研究结果为粘土地质工程与岩土工程应用提供了新的科学依据．达西渗流径向固结计算是新的非线性渗流固结计算的特例．     

Stepwise covariance matrix decomposition for efficient simulation of multivariate large-scale three-dimensional random fields

The spatial variability of geomaterials affects the failure mechanism and reliability of geotechnical structures significantly, and can be modeled rigorously as a three-dimensional (3-D) random field. However, the simulation of multivariate, large-scale and high-resolution 3-D random fields is a challenging task due to extraordinary demands in computational resources. This paper proposes a stepwise covariance matrix decomposition method (CMD) with the aid of separable correlation functions, in which the 3-D random field is generated sequentially along each single dimension with small one-dimensional correlation matrices. The method not only inherits the simplicity of the widely-used general CMD, but also significantly reduces the computational time and required memory space. It only takes a few seconds to construct large-scale and high-resolution 3-D random fields, with the requirement on memory space reduced by more than ten orders of magnitude. The maximum random field resolution is significantly improved from approximately 21 × 21 × 41 using the general CMD to over 501 × 501 × 1001 using the stepwise CMD, which suffices in most engineering applications. The stepwise CMD facilitates 3-D spatial variability modeling in probabilistic site characterization and routine geotechnical reliability analysis.     

集中力作用于剪切模量沿深度线性变化的半空间的公式

根据一个引理和一个假设,本文绘出集中力作用于泊桑比v为常数和剪切模量G沿深度线性变化的半空间的公式.当用积分方程法分析桩和其它地学工程问题时,这些公式可以用作一近似的基本解.