渗流弥散的空间变异性及空间插值方法的比较研究

水质模拟与预测是评价和保护地下水工作中不可或缺的重要程序。由于地下水的储藏与运行特性及实际条件的限制,人们在对其进行观测时往往只能得到有限的监测结果,因此需要借助已知点信息来对未知点水质空间分布特性进行估计。现行的空间变异性估计方法很多,使用何种方法可以获得对渗流污染物运移空间变异性的最优估计,成为研究的重要课题。本研究选取反距离加权法、趋势面法、普通克里格法以及方位-分维法作为研究对象,用其对所渗流弥散实验的监测样本在不同的样本密度下进行空间插值,通过各种方法的估值精度的对比,对其在渗流污染物空间估计中的的估计效果做出评价。     

基于Sobol法的复合材料加筋板结构参数灵敏度

复合材料广泛应用于航空航天领域,其可靠性、稳定性及承载能力等对于航空设备尤为重要.以复合材料加筋板作为研究对象,对其材料属性和几何参数进行灵敏度分析.首先,基于ABAQUS软件建立复合材料加筋板的有限元模型,对轴向压缩载荷下的屈曲载荷进行了研究;其次,针对加筋板结构的复杂性,基于Kriging方法的代理模型建立复合材料加筋板屈曲载荷与材料属性和几何参数之间的函数关系;最后,采用Sobol全局灵敏度分析法求解复合材料加筋板材料属性和几何参数的灵敏度.研究结果为复合材料加筋板可靠性设计提供指导.     

安徽皖籍高校大学生体育旅游行为空间分布趋势研究

本文利用ArcGIS9.2软件中的普通克里格插值创建预测图(Prediction Map),根据预测趋势图的结果分析安徽皖籍高校大学生体育旅游行为地理空间分布特征。分析得出皖籍大学生周末加暑假出游分布趋势图为由北边逐渐向南边递减,夏季出游分布趋势为中部向南北两边降低,选择火车作为交通工具分布趋势为东南边缘逐渐向北方递增,和同学朋友出游分布趋势为从东部向西部逐渐递增,通过同学朋友家人的推荐了解体育旅游分布趋势为由南方向西北方逐渐增高等。建议相关部门根据安徽皖籍大学生体育旅游行为地理分布的特点,进行项目开发以及体育旅游活动的组织。     

采煤工作面煤层三维地质建模

为了直观展现采煤工作面煤层地质分布和煤岩体空间赋存状况,增强地质数据的表现力和利用率,提出一种Web端煤层三维建模方案。该方案以某煤矿16402采煤工作面部分采样数据为基础,结合规则格网法和自适应差分进化Kriging空间插值算法构建煤层表面的数字高程模型;之后借助Three.js技术和Catmull-Rom样条曲线实现浏览器端采煤工作面煤层三维可视化模型,并实现煤质指标的动态展示。研究表明,所建模型真实地反映了工作面煤层的形态、产状和矿石品位,为生产方案对比决策提供了可靠依据。     

Mean squared prediction error in the spatial linear model with estimated covariance parameters

The problem considered is that of predicting the value of a linear functional of a random field when the parameter vector of the covariance function (or generalized covariance function) is unknown. The customary predictor when is unknown, which we call the EBLUP, is obtained by substituting an estimator j for in the expression for the best linear unbiased predictor (BLUP). Similarly, the customary estimator of the mean squared prediction error (MSPE) of the EBLUP is obtained by substituting j for in the expression f for the BLUP's MSPE; we call this the EMSPE. In this article, the appropriateness of the EMSPE as an estimator of the EBLUP's MSPE is examined, and alternative estimators of the EBLUP's MSPE for use when the EMSPE is inappropriate are suggested. Several illustrative examples show that the performance of the EMSPE depends on the strength of spatial correlation; the EMSPE is at its best when the spatial correlation is strong.This research was partially supported by a University of Iowa Old Gold Fellowship (Zimmerman) and by the NSF under grant DMS-8703083 (Cressie).     

Screening Effect in Isotropic Gaussian Processes

The screening effect is the phenomenon that optimal linear prediction of a spatial process on an unobserved location mostly depends on nearby observations.That is,the optimal predictor based on just nearby observations yields a good approximation of which based on the whole large dataset.However,the approximation does not always perform well since the screening effect may not hold in all situations.To determine when the screening effect holds is an important issue in spatial statistics.This paper provides some sufficient conditions for ensuring an asymptotic screening effect in Rd based on the spectral density of the underlying isotropic Gaussian process and the geometries of nearby observations.These results apply to isotropic processes with an arbitrary degree of differentiability.Assuming we are predicting at origin,the conditions are(1)the spectral density is nearly a constant in balls of finite radius far from the origin,(2)the positions of nearby observations do not fall on a curve with non-zero intercept whose degree is less or equal to the order of mean square differentiability of the process.These conditions are easy to verify in practice.Convergence rates of the asymptotic screening effect are also obtained.These rates depend on the rate of decrease of the spectral density.Simulation studies on the screening effect for finite samples are also provided.     

对数正态克立格法理论及其应用

本文首先讨论了对数正态分布及三参数对数正态分布理论,然后重点研究了对数正态克立格法。在分析了无偏条件及最小估计方差之后,给出了对数正态克立格法方程组及对数克立格方差。克立格权系数λ_a即为该方程组的解。据此,可以估计矿床中每一块段的克立格估值Z_v,该估值是具最小估计方差的无偏线性估计量。该法已用于一个铁铜矿床的储量计算。     

珠江三角洲网河区水位空间插值的kriging方法

分析了珠江三角洲网河区水位变化特征.基于区域化变量理论,提出珠江三角洲网河区水位空间插值的kriging方法,给出描述该网河区水位空间分布结构的半变异函数,分析了网河区水位的空间分布,以及水位的空间结构性-方向性和相关距离,并给出了丰水期的一个应用实例,为该地区防洪决策提供科学依据.     

Numerical Integration of Harmonic Functions with Restricted Sampling Data

Based on the idea of kriging and the radial basis function approximation, we develop in this paper a numerical scheme to integrate harmonic functions with restricted sampling data. To be more precise, the integration is performed by using the function values which are given as discrete sampling data on only part of the boundary. These problems often arise from non-destructive evaluation techniques in the engineering industry. The existence and uniqueness of the solution and the error estimation for the proposed numerical scheme are also discussed. Several numerical experimental results are presented for the verification on the accuracy and convergence of the method.     

A Taxonomy of Global Optimization Methods Based on Response Surfaces

This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach.