Kriging算法在温度场计算中的应用分析

地质统计学中的Kriging算法是利用空间变异结构进行插值预报的算法，该算法不仅可以获得更好的插值效果，而且能够通过期望方差提供结果的预报误差．文中结合Kriging算法在火烧油层实验模型的温度场计算中的应用，探讨了该算法中相关模型和回归模型等因素对插值结果的影响以及存在的问题．     

基于时空变异函数的Kriging插值及实现

Kriging（克里金）算法通常用于对空间变量进行插值,但不能直接应用于时空变量,它需要进行时空扩展。以月平均气温数据为例,运用时空Kriging方法结合R统计语言进行时空插值研究及其实现。通过时序分解去除气温数据中季节变化项,在分别得到空间变异函数和时间变异函数的基础上构建一类积和式时空变异函数来描述变量的时空相关结构,并给出基于R语言的具体实现步骤。将普通Kriging方法进行时空扩展,应用于气温数据的时空插值中。验证结果表明,基于时空变异函数的Kriging方法能提供较高精度的插值效果,这为时空变量的插值预测提供了有效的途径。     

基于Kriging的三维地质体建模方法研究

对几种三维空间数据模型进行了比较,总结了克里格（Kriging）插值方法在三维地质体建模方面的种种优点。在此基础上,借助于GSTL开源地质统计学库wxWidgets界面库,在Dev-cpp开发环境下开发了一个三维矿体数据的克里格插值系统,为矿体的三维可视化提供了数据支持。该系统实现了Kriging插值、变异函数拟合模型拟合程度的验证一交叉验证以及特定格式的结果输出等功能。     

普通Kriging方法建立宏观地层的验证与评价

空间插值方法对空间变异性和空间相关性的反映程度及其准确性与精度直接影响到三维地质模型的真实性。普通Kriging方法应用于数字地层中,其变异函数模型和参数选择对结果影响很大,利用最值、方差、相关系数、平均误差以及误差分布统计为主要比较指标,采用交叉验证方法结合误差分析,对球状模型、指数模型、线性模型进行比较研究,初步得出线性有块金模型优于其他变异函数模型的结论,对数字地层的工程应用及其真实性评价有一定指导意义。     

改进克里金插值算法的井下无线定位指纹库构建方法

针对煤矿井下巷道中构建一个采集点密集分布的无线定位指纹库,需要逐点采集信号,会耗费大量的人力和时间,为此提出基于模拟退火SA(Simulated Annealing)人工蜂群ABC(Artificial Bee Colony)混合算法优化克里金(Kriging)插值算法的构建井下无线定位指纹库的方法。首先通过无线网络采集井下巷道部分采集点的指纹数据,并建立采集指纹数据库。其次利用采集指纹数据库构建Kriging插值算法模型,再通过SA-ABC算法对变异函数的参数寻优,建立SA-ABC-Kriging插值算法模型。再次用插值算法估算出预测点的信息数据,并建立插值指纹数据库。最后将采集指纹数据库和插值指纹数据库构建井下无线定位指纹库。实验表明,该构建方法比传统Kriging插值算法的定位精度和插值精度更高,而且可减少50%的人工采集指纹数据工作量。     

Kriging空间插值最优估计模型的研究

空间插值对土地价格、降雨量、人口分布,等进行估计是最常用也是最有效的方法。空间插值的理论假设是空间位置上越靠近的点,越可能具有相似的特征值;而距离越远的点,其特征值相似的可能性越小。Kriging插值方法以统计学理论为基础。如果采样点数据比较少的情况下,可设计出对Kriging插值的半变异函数进行拟合的实验方案,并从中选出误差最小的估计模型。     

三维地质体重构中空间数据插值方法的研究

空间插值方法的选择是地质三维可视化当中能真实、准确的再现工程研究对象的关键要素。为此，本文针对建立三维地质体的体数据模型插值算法的特点，对各种常见空间插值方法的特点进行了比较分析。最后结合某矿区的实测勘探数据，采用Kriging方法进行了三维地质体的重构，取得了与工程现场较为一致的效果，证明了该方法在地矿领域的适用性。     

Kriging方法在输电线路气象环境建模中的应用

由于气象测点个数有限、分布不均匀且与线路走廊不一致,无法为研究灾害引发的线路故障及其防御技术提供精确的输电线路气象环境数据模型.为此,本文分析了Kriging空间插值方法的实现原理,应用Kriging插值方法实现对输电线路气象环境数据的网格化建模,并制定插值结果校验方法及评价标准,选取江苏省级电网可获取的996个气象测点2017年某日的温度数据,通过Kriging法进行网格化插值并对结果进行分析比较,验证了适用于该区域输电线路的温度数据网格化插值的Kriging半变异函数模型的选取过程.     

基于时空Kriging方法的时空数据插值研究

在对气象数据进行插值的过程中, 如果只考虑数据的空间信息而忽视数据在时间上的关联, 必然影响插值的精度.针对具有时空特性的气象数据, 提出一种将时空Kriging方法与弹性网方法相结合的新方法.该方法主要利用弹性网算法解决时空Kriging算法中的时空变异函数矩阵为病态矩阵而无法求逆的问题, 通过弹性网算法获得变异函数矩阵方程的稀疏解, 从而提高时空插值的精度.在实际观测的气温数据和AQI数据上的仿真实验验证了该方法对气象时空数据插值的准确性.     

基于Kriging插值与VRML的桥梁监测数据可视化方法

就目前桥梁监测系统可视化的现状,从数据插值和VRML两个方面总结了现有研究工作,针对目前桥梁健康监测需求提出了一种基于Kriging插值和VRML的桥梁监测系统数据可视化方法。首先使用修改过的Kriging算法对由桥梁健康监测传感器网络得到的数据进行插值,并为数据点赋予相应颜色,最后将结果加载到三维模型中。实验结果表明,该方法简单快捷,实现了较高的插值精度和可视化效果,在桥梁健康监测数据可视化实现方面具有广泛用途。     

基于地统计方法的二氧化碳浓度空间插值研究

克里格法（Kriging）是地质统计学的主要内容之一,从统计意义上说,是从变量关系和变异性出发,在有限区域内对区域化变量的取值进行无偏、最优估计的一种方法：从插值角度讲是对空间分布的数据求线性最优、无偏内插估计的一种方法。克里格法的适用条件是区域化变量存在空间相关性。将临安市内的二氧化碳作为区域化变量．根据不同的半变异函数理论模型,采用普通Kriging法,通过对比分析得到：基于地统计的插值方法。根据半变异函数云图和试验方差最小的原理．选择合适的半变异函数理论模型进行变量的空间插值．能够较好地模拟区域化变量的空间连续分布格局．并取得较好效果。     

Performance study of gradient-enhanced Kriging

The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Kriging-based surrogate models are popular for approximating deterministic computer models. In this work, the performance of Kriging is investigated when gradient information is introduced for the approximation of computationally expensive black-box simulations. This approach, known as gradient-enhanced Kriging, is applied to various benchmark functions of varying dimensionality (2D-20D). As expected, results from the benchmark problems show that additional gradient information can significantly enhance the accuracy of Kriging. Gradient-enhanced Kriging provides a better approximation even when gradient information is only partially available. Further comparison between gradient-enhanced Kriging and an alternative formulation of gradient-enhanced Kriging, called indirect gradient-enhanced Kriging, highlights various advantages of directly employing gradient information, such as improved surrogate model accuracy, better conditioning of the correlation matrix, etc. Finally, gradient-enhanced Kriging is used to model 6- and 10-variable fluid–structure interaction problems from bio-mechanics to identify the arterial wall’s stiffness.     

分形布朗运动在水下地形模拟中的应用

由于水下地形的高程数据获取困难,如何运用少量的数据生成真实感强、精度高的地形模型是值得研究的问题。运用分形布朗运动（fBm）模型得到水下地形的分形特征参数,结合随机中点位移内插算法,通过Matlab编程实现了三维水下地形的模拟。以长江口深水航道为例,讨论了其运用fBm的可行性,模拟生成了三维航道地形,并与 ArcGIS自带的插值方法进行比较,采用等深线重构法对插值结果进行精度分析。比较结果显示,基于fBm模型模拟得到的地形具有丰富的地表细节,反映了地形的复杂性和不规则性,具有很好的可视化效果,同时能保证较好的精度。     

A Critical Assessment of Kriging Model Variants for High-Fidelity Uncertainty Quantification in Dynamics of composite Shells

This paper presents a critical comparative assessment of Kriging model variants for surrogate based uncertainty propagation considering stochastic natural frequencies of composite doubly curved shells. The five Kriging model variants studied here are: Ordinary Kriging, Universal Kriging based on pseudo-likelihood estimator, Blind Kriging, Co-Kriging and Universal Kriging based on marginal likelihood estimator. First three stochastic natural frequencies of the composite shell are analysed by using a finite element model that includes the effects of transverse shear deformation based on Mindlin’s theory in conjunction with a layer-wise random variable approach. The comparative assessment is carried out to address the accuracy and computational efficiency of five Kriging model variants. Comparative performance of different covariance functions is also studied. Subsequently the effect of noise in uncertainty propagation is addressed by using the Stochastic Kriging. Representative results are presented for both individual and combined stochasticity in layer-wise input parameters to address performance of various Kriging variants for low dimensional and relatively higher dimensional input parameter spaces. The error estimation and convergence studies are conducted with respect to original Monte Carlo Simulation to justify merit of the present investigation. The study reveals that Universal Kriging coupled with marginal likelihood estimate yields the most accurate results, followed by Co-Kriging and Blind Kriging. As far as computational efficiency of the Kriging models is concerned, it is observed that for high-dimensional problems, CPU time required for building the Co-Kriging model is significantly less as compared to other Kriging variants.     

Permeability prediction and construction of 3D geological model: application of neural networks and stochastic approaches in an Iranian gas reservoir

Determination of petrophysical parameters by using available data has a specific importance in exploration and production studies for oil and gas industries. Modeling of corrected permeability as a petrophysical parameter can help in decision making processes. The objective of this study is to construct a comprehensive and quantitative characterization of a carbonate gas reservoir in marine gas field. Artificial neural network is applied for prediction of permeability in accordance with other petrophysical parameters at well location. Correlation coefficient for this method is 84 %. In the study, the geological reservoir model is developed in two steps: First, the structure skeleton of the field is constructed, and then, reservoir property is distributed within it by applying new stochastic methods. Permeability is modeled by three techniques: kriging, sequential Gaussian simulation (SGS) and collocated co-simulation using modeled effective porosity as 3D secondary variable. This paper enhances the characterization of the reservoir by improving the modeling of permeability through a new algorithm called collocated co-simulation. Kriging is very simple in modeling the reservoir permeability, and also, original distribution of the data changes considerably in this model. In addition, the SGS model is noisy and heterogeneous, but it retains the original distribution of the data. However, the addition of a 3D secondary variable in third method resulted in a much more reliable model of permeability.     

三维油藏彩色模型原理和算法

三维油藏彩色模型可真实直观地反三维地质构造的特点、渗透率和孔隙度等物性参数的分布规律。文中讨论了在ＳＵＮ工作站的Ｘ－Ｗｉｎｄｏｗｓ／Ｍｏｔｉｆ平台上建立２５６色三维油藏几何模型的基本方法,研究了如何建立三维网络化数据体,追踪可视面,对模型进行旋转和切割,以及着色、消隐等可视化技术的实现。     

Effects of the correlation model,the trend model,and the number of training points on the accuracy of Kriging metamodels

This paper explores the effects of the correlation model, the trend model, and the number of training points on the accuracy of Kriging metamodels. Gaussian correlation models are found to be superior to exponential and linear correlation models. No particular trend model is found to be better than the other models. The number of training points used in constructing the Kriging metamodels is observed to change the relative performances of the trend and the correlation functions. The leave‐one‐out cross‐validation error is found to become a better surrogate for the actual error, as the number of training points is increased. Finally, the use of an ensemble of metamodels is discussed and it is found that using an ensemble may improve the accuracy.     

基于Kriging和Marching cube算法的地学3维形态模拟

地质构造的复杂性和勘查数据的不完备性,决定了对地质要素(地质体和场)的空间形态进行3维模拟是一个面临众多技术难题的艰巨任务。针对此问题,探讨了一种利用空间插值和等值面勾绘来建立地质要素的接近真实的3维可视化模型的方法。Kriging算法,由于其在揭示空间数据非均匀、各向异性分布规律方面具有良好表现,因而被用于对不完备地学数据进行空间插值,即先将分散的不规则分布的数据转换成规则分布的网格数据;再通过Marching cube算法实现由网格离散点构建光滑3维等值曲面;最后通过OpenGL接口实现等值曲面的计算机3维重绘。整个过程采用VC .net结合OpenGL编程完成。应用这种方法,可实现有限钻孔取样分析数据的矿体品位3维等值面模拟和电磁测深2维反演数据的电阻率3维等值面模拟,其模拟结果接近于传统勘探方法解释的结果,而且其效率高得多,也更加直观,证明此方法是有效的和实用的。