结合Cokriging模型和单目标函数的随机模型修正

将Cokriging代理模型技术和单目标函数进行结合,提出了一种随机模型修正方法。该方法将不确定性模型修正问题转化为较简单的待修正参数统计特征的修正问题,能够在保证模型修正精度的同时,有效缓解模型修正中由于分步修正和多目标修正造成的计算成本高的问题。首先,假设待修正参数和响应均服从高斯分布,采用拉丁超立方抽样获取训练集样本,构造满足精度要求的Cokriging模型替代复杂的有限元模型参与迭代计算。然后,建立有限元模型计算响应统计特征与试验响应统计特征的加权残差目标函数,引入土狼优化算法最小化该单目标函数来得到待修正参数的统计特征。最后,通过二维和三维桁架结构验证了所提方法的可行性。

Obtaining 2D Soil Geotechnical Profiles from Cokriging Interpolation of Sample Data and Electrical Resistivity Tomography (ERT)—Applications in Mass Movements Studies

Brazil annually faces significant challenges with mass movements, particularly in areas with poorly constructed housing, inadequate engineering, and lacking sanitation infrastructure. Campos do Jordão, in São Paulo state, is a city currently grappling with these issues. This paper details a study conducted within a pilot area in Campos do Jordão, where geophysical surveys and geotechnical borehole data were integrated. The geophysical surveys provided 2D profiles, and samples were collected to analyse soil moisture and plasticity. These datasets were combined using a Cokriging-based model to produce an accurate representation of the subsurface conditions. The enhanced modelling of subsurface variability facilitates a deeper understanding of soil behavior, which can be used to improve landslide risk assessments. This approach is innovative, particularly within the international context where similar studies often do not address the complexities associated with urban planning deficits such as those observed in some areas of Brazil. These conditions, including the lack of proper sanitation and irregular housing, significantly influence the geological stability of the region, adding layers of complexity to subsurface assessments. Adapting geotechnical evaluation methods to local challenges offers the potential to increase the efficacy and relevance of geological risk management in regions with similar socio-economic and urban characteristics.

青藏高原东南缘气象要素Anusplin和Cokriging空间插值对比分析

选取地形起伏度巨大的青藏高原东南缘为研究区,利用该研究区96个气象站点,结合高程数据,分别采用Cokriging和Anusplin空间插值方法,获取2010年250 m分辨率的年均温度和年累计降水插值曲面。并采用交叉验证方法对比Anusplin与Cokriging插值精度,分析了误差的空间分布特征,重点对比两种插值曲面差异较大的区域精度优劣,评价两种方法在复杂地区的适用性。结果表明,Anusplin在复杂地表的插值表现优于Cokriging,其中Anusplin气温插值的均方差仅为0.82℃,而Cokriging的均方差为1.45℃;两者的降水插值精度基本一致,但Anusplin在气象要素空间异质性大的区域优于Cokriging。因此,与Cokriging相比,Anusplin更适合青藏高原东南缘复杂地表气象要素空间插值。

一种改进的CoKriging建模方法及其应用

提出了一种改进变可信度代理模型—ICoKriging模型。在CoKriging模型的基础上将CoKriging模型中的高精度样本与低精度样本扩展至高中低三种精度不同的样本,经数值算例及超声速减阻问题验证,该方法比较于Kriging模型和CoKriging模型精度更高,更易于全局寻优。

土壤盐分和含水量的空间变异性及其CoKriging估值——以黄河三角洲地区典型地块为例

以黄河三角洲地区典型地块为研究区,运用经典统计学和地统计学相结合的方法研究了不同深度土层盐分和含水量的空间变异特征。结果表明:研究区土壤盐分和含水量普遍较高,土壤表层积盐作用明显;各层土壤盐分均属于中等变异强度,土壤含水量除表层为中等变异强度外,其余各层为弱变异强度;受结构性因素和随机性因素的共同作用,各土层盐分和含水量均具有中等的空间相关性。对K rig ing插值结果分析表明,研究区各土层盐分和含水量在一定的范围内均存在着空间上的相关性和变异性,表层土壤盐分和含水量的空间分布主要受微地形和气候条件的影响,地下水性质是主导深层土壤盐分及含水量空间分布的主要因素。分别采用表层土壤盐分及相应土层含水量对深层土壤盐分进行CoK rig ing估值,均能提高估值精度,采用表层土壤盐分对深层土壤盐分进行CoK rig ing估值的精度要明显高于采用土壤含水量,其估计方差减少百分数最大达到167.36%。

基于水稻冠层光谱信息的稻田土壤速效N的Cokriging插值研究

该文以嘉善县陶庄农场内一块3.34 hm2农田为试验区,研究样点土壤养分(土壤全N、全P、有机质、速效N、速效K)与水稻各生长期水稻冠层光谱的关系,并将光谱指数作为协因子,进行土壤养分的Cokriging插值研究。结果表明,正常施肥区各生长期根据TM、SPOT波段组合计算的某些冠层光谱指数,特别是比值光谱指数RSI、归一化光谱指数NDSI,与土壤速效N、有机质等土壤养分具有显著的相关性,可以作为协因子参与这些土壤养分的估算;选择正常施肥区分蘖期TM、SPOT组合中与速效N相关性最高的比值光谱指数TM4/TM3、B3/B2作为协因子,参与土壤速效N的Cokriging插值,与普通Kriging相比,插值精度有一定程度的提高,并且,当采样点越少,或土壤养分与协因子的相关性越高时,插值精度提高更明显。

土壤含水量的Kriging和Cokriging估值研究

分析了田间同深度土壤含水量的半方差和不同深度土壤含水量的交互半方差特征 ,探讨了土壤含水量的Kriging和Cokriging估值方法。研究表明 ,同深度土壤含水量与不同深度的土壤含水量之间均具有显著的空间相关性 ,用Kriging方法进行土壤含水量的估值精度较传统方法高。加入浅层土壤含水量用Cokriging方法来估测深层土壤含水量 。

预测孔隙率的Cokriging方法及其应用

本文讨论了用地震资料预测储层孔隙率的Cokriging方法的基本原理。然后用该方法对模拟储层作了孔隙率预测，以检验此法的精度和编程的正确性。最后预测了泌阳凹陷核三段地层中含油砂组的孔隙率平面分布情况，均取得了满意的效果。储层模拟技术是根据结定井的孔隙率与地震慢度的空间依赖关系，构造具有特定相关结构的双变量随机过程。在利用Cokriging法预测空隙率时，使用奇异值分解法（SVD）求解加权向量，用动态压缩修正法修正权系数，再用统一量钢的数据变换方法对应用资料进行数据变换，从而提高了预测精度，拓宽了资料的应用范围。

基于CoKriging模型的单室火灾温度预测

高保真数值模拟和单保真机器学习替代模型均需大量时间才能对火场温度做出准确预测,无法满足消防管理的应急需求.为解决上述问题,引入了CoKriging模型,并从建模时间成本、预测时间成本及预测结果准确性这3方面讨论了该模型在单室火灾温度预测中的适用性与特点.该模型利用CFAST和FDS模拟产生的154组混合数据进行训练.交叉验证的结果表明,当高、低保真度数据占比为10∶1时,该模型就能得到有效训练.进一步对不同方法、模型展开对比分析,结果表明,CoKriging模型的预测结果与高保真模拟FDS的计算结果十分接近,且模型一旦构建成功,其做出一次新的预测所需时间远少于FDS.除此之外,在将建模时间成本缩短至1/10的情况下,CoKriging模型仍能达到与单保真替代模型ANN、Kriging一致的预测准确度.实验还发现,高、低保真数据占比不会对CoKriging模型预测结果产生显著影响,即使只有少量FDS数据参与训练,仍能保证CoKriging模型的预测准确性.因此,CoKriging模型可作为一种快速而有效的回归分析方法,应用在单室火灾的温度预测中.

Comparison of Artificial Neural Networks,Geographically Weighted Regression and Cokriging Methods for Predicting the Spatial Distribution of Soil Macronutrients(N,P,and K)

Soil macronutrients(i.e. nitrogen(N), phosphorus(P), and potassium(K)) are important soils components and knowing the spatial distribution of these parameters are necessary at precision agriculture. The purpose of this study was to evaluate the feasibility of different methods such as artificial neural networks(ANN) and two geostatistical methods(geographically weighted regression(GWR) and cokriging(CK)) to estimate N, P and K contents. For this purpose, soil samples were taken from topsoil(0–30 cm) at 106 points and analyzed for their chemical and physical parameters. These data were divided into calibration(n = 84) and validation(n = 22). Chemical and physical variables including clay, p H and organic carbon(OC) were used as auxiliary soil variables to estimate the N, P and K contents. Results showed that the ANN model(with coefficient of determination R^2 = 0.922 and root mean square error RMSE = 0.0079%) was more accurate compared to the CK model(with R^2 = 0.612 and RMSE = 0.0094%), and the GWR model(with R^2 = 0.872 and RMSE = 0.0089%) to estimate the N variable. The ANN model estimated the P with the RMSE of 3.630 ppm, which was respectively 28.93% and 20.00% less than the RMSE of 4.680 ppm and 4.357 ppm from the CK and GWR models. The estimated K by CK, GWR and ANN models have the RMSE of 76.794 ppm, 75.790 ppm and 52.484 ppm. Results indicated that the performance of the CK model for estimation of macro nutrients(N, P and K) was slightly lower than the GWR model. Also, the accuracy of the ANN model was higher than CK and GWR models, which proved to be more effective and reliable methods for estimating macro nutrients.

Spatial Interpolation and Sample Size Optimization for Soil Copper(Cu) Investigation in Cropland Soil at County Scale Using Cokriging

Knowledge on spatial distribution and sampling size optimization of soil copper （Cu） could lay solid foundations for environmetal quality survey of agricultural soils at county scale. In this investigation, cokriging method was used to conduct the interpolation of Cu concentraiton in cropland soil in Shuangliu County, Sichuan Province, China. Based on the original 623 physicochmically measured soil samples, 560, 498, and 432 sub-samples were randomly selected as target variable and soil organic matter （SOM） of the whole original samples as auxiliary variable. Interpolation results using Cokriging under different sampling numbers were evaluated for their applicability in estimating the spatial distribution of soil Cu at county sacle. The results showed that the root mean square error （RMSE） produced by Cokriging decreased from 0.9 to 7.77%, correlation coefficient between the predicted values and the measured increased from 1.76 to 9.76% in comparison with the ordinary Kriging under the corresponding sample sizes. The prediction accuracy using Cokriging was still higher than original 623 data using ordinary Kriging even as sample size reduced 10%, and their interpolation maps were highly in agreement. Therefore, Cokriging was proven to be a more accurate and economic method which could provide more information and benefit for the studies on spatial distribution of soil pollutants at county scale.

Spatial prediction and modeling of soil salinity using simple cokriging, artificial neural networks, and support vector machines in El Outaya plain, Biskra, southeastern Algeria

Soil salinization is one of the most predominant environmental hazards responsible for agricultural land degradation,especially in the arid and semi-arid regions.An accurate spatial prediction and modeling of soil salinity in agricultural land are so important for farmers and decision-makers to develop the appropriate mechanisms to prevent the loss of fertile soil and increase crop production.El Outaya plain is marked by soil salinity increases due to the excessive use of poor groundwater quality for irrigation.This study aims to compare the performance of simple kriging,cokriging(SCOK),multilayer perceptron neural networks(MLP-NN),and support vector machines(SVM)in the prediction of topsoil and subsoil salinity.The field covariates including geochemical properties of irrigation groundwater and physical properties of soil and environmental covariates including digital elevation model and remote sensing derivatives were used as input candidates to SCOK,MLP-NN,and SVM.The optimal input combination was determined using multiple linear stepwise regression(MLSR).The results revealed that the SCOK using field covariates including water electrical conductivity(ECw)and sand percentage(sand%),and environmental covariates including land surface temperature(LST),topographic wetness index(TWI),and elevation could significantly increase the accuracy of soil salinity spatial prediction.The comparison of the prediction accuracy of the different modeling techniques using the Taylor diagram indicated that MLP-NN using LST,TWI,and elevation as inputs were more accurate in predicting the topsoil salinity[ECs(TS)]with a mean absolute error(MAE)of 0.43,root mean square error(RMSE)of 0.6 and correlation coefficient of 0.946.MLP-NN using ECw and sand%as inputs were more accurate in predicting the subsoil salinity[ECs(SS)]with MAE of 0.38,RMSE of0.6,and R of 0.968.

基于GIS土壤酸碱度的Kriging和Cokriging估值研究

应用地统计学的半方差函数和克立格法,在仪征地区利用高程这一辅助变量把土壤pH和成土母质联系起来,分析了土壤pH的半方差和不同高程土壤pH的交互半方差特征,比较了土壤pH的Kriging和Cokriging估值。研究表明,预测值与实测值之间的相关系数协同克立格法比普通克立格法提高了39.00%,使估值的结果进一步精确。

3D Property Modeling of Void Ratio by Cokriging

Void ratio measures compactness of ground soil in geotechnical engineering. When samples are collected in certain area for mapping void ratios, other relevant types of properties such as water content may be also analyzed. To map the spatial distribution of void ratio in the area based on these types of point, observation data interpolation is often needed. Owing to the variance of sampling density along the horizontal and vertical directions, special consideration is required to handle anisotropy of estimator. 3D property modeling aims at predicting the overall distribution of property values from limited samples, and geostatistical method can be employed naturally here because they help to minimize the mean square error of estimation. To construct 3D property model of void ratio, cokriging was used considering its mutual correlation with water content, which is another important soil parameter. Moreover, K-D tree was adopted to organize the samples to accelerate neighbor query in 3D space during the above modeling process. At last, spatial configuration of void ratio distribution in an engineering body was modeled through 3D visualization, which provides important information for civil engineering purpose.

Spatiotemporal interpolation of precipitation across Xinjiang, China using space-time CoKriging

In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.

Geoid undulation modeling through the Cokriging methode——A case study of Guayaquil, Ecuador

The determination of vertical component plays a fundamental role in the initial phase of engineering applications. However, its acquisition is technically and economically demanding, mainly due to the precise heights relative to a reference surface, such as the mean sea level. The Cokriging technique is a necessary input for the calculation of the vertical component of the geodetic control points measured by GNSS, and it requires less auxiliary data and uses complementary available variables for the calculation.Therefore, the main goal is to use Cokriging to establish a geoid undulation prediction model for the rural area of the canton of Guayaquil, Ecuador. Ordinary, Residual and Universal Cokriging and Kriging techniques were used to compare their results and select the best for achieving accuracy. The validation of the application techniques yielded that Universal Cokriging was the most accurate with an RMSE of 8 cm and RSR of 2 cm, obtained just with 66 samples(20% of the dataset). Furthermore, considering the comparison with other regional geoid undulation models, the proposed model increased the accuracy of the results by a ratio of 9.68 and 6.96 in relation to EGM96 and EGM08, respectively.

3D inversion of borehole gravity data using cokriging

Borehole gravity has been used in mineral exploration recently with the advent of slim-hole gravimeters. It is logical to perform inversion to utilize the information in the newly acquired data. The inversions were carried out by using cokriging,which is a geostatistical method of estimation that minimizes the error variance by applying cross-correlation between several variables. In this study the estimated densities are derived by using boreholes gravity and known densities along the borehole. This method does not need iterative process and computes efficiently. The selection of examples demonstrates that this method has the ability to include physical property from borehole measurements in the inversion. The synthetic examples demonstrate the density variation along a borehole can be well determined without depth constraints in the inversion. The resolution of the recovered model can be further improved by including the densities along the borehole for inversion. However,this capability decreases dramatically with the increasing of distance between the anomalous body and the borehole.

The Effect of Using Cokriging against Ordinary Kriging When Estimating Phosphate Deposits at Elsebaiya Area, Egypt

Application of geostatistical techniques when evaluating mineral deposits could reflect some geological characteristics which help through the stage of planning and production. In the present study, an attempt has been done on two phosphate deposits at Elsebaiya area on both sides of the River Nile namely: Um Tondoba mine at Elsebaiya East area and Western River Nile mine in Elsebaiya West area. Depending on the available data, statistical analysis illustrated differences in the distribution of P2O5 % and ore thickness within the studied areas. Geostatistics used to start with constructing variograms for P2O5 % and thickness for the two phosphate deposits to be used with ordinary kriging models, also constructing cross variograms between P2O5 % and thickness to be used with cokriging models where the difference in the variogram parameters reflected a specific variation for each deposit horizontally and vertically. The ordinary kriging models and cokriging models illustrated different distribution behavior through both the two kriging techniques.

应用Cokriging空间插值技术协同生成弱透水层流场

夹在潜水层和承压层之间弱透水层的水头是与潜水、承压含水层水头同时区域化的 ;以松辽盆地大庆市典型复合含水层为例 ,采用协同Cokriging方法生成了弱透水层流场。该方法计算简单 ,与传统方法相比具有较高的精度 ,可用于弱透水层流场分析和评价。

基于Cokriging的住房价格空间格局分析——以长沙市为例

以长沙市为研究对象,在空间自相关分析的基础上分别采用Kriging和Cokriging方法构建空间插值地图,并通过对比分析探讨住房价格空间格局特征。结果表明:1与Kriging方法相比,考虑多区域因素的Cokriging方法其空间插值预测精度更高,结果更佳;2长沙市住房价格的空间自相关性显著,南北向和东西向都呈二阶形态由中心向边缘递减,住房价格变化的空间变异表现为各向异性;3长沙市住房价格的空间格局整体表现为同心椭圆分布,核心圈层为传统的五一商圈,南北向扩散态势明显;4长沙市住房价格变化幅度区域性差异显著,二环内等值线分布密集,河西相较河东,等值线分布较为稀疏,价格衰减较慢。