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Academic literature on the topic 'Kriging and cokriging models'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Kriging and cokriging models"

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Magno, Melissa, Ingrid Luffman, and Arpita Nandi. "Evaluating Spatial Regression-Informed Cokriging of Metals in Soils near Abandoned Mines in Bumpus Cove, Tennessee, USA." Geosciences 11, no. 11 (October 20, 2021): 434. http://dx.doi.org/10.3390/geosciences11110434.

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Inorganic contaminants, including potentially toxic metals (PTMs), originating from un-reclaimed abandoned mine areas may accumulate in soils and present significant distress to environmental and public health. The ability to generate realistic spatial distribution models of such contamination is important for risk assessment and remedial planning of sites where this has occurred. This study evaluated the prediction accuracy of optimized ordinary kriging compared to spatial regression-informed cokriging for PTMs (Zn, Mn, Cu, Pb, and Cd) in soils near abandoned mines in Bumpus Cove, Tennessee, USA. Cokriging variables and neighborhood sizes were systematically selected from prior statistical analyses based on the association with PTM transport and soil physico-chemical properties (soil texture, moisture content, bulk density, pH, cation exchange capacity (CEC), and total organic carbon (TOC)). A log transform was applied to fit the frequency histograms to a normal distribution. Superior models were chosen based on six diagnostics (ME, RMS, MES, RMSS, ASE, and ASE-RMS), which produced mixed results. Cokriging models were preferred for Mn, Zn, Cu, and Cd, whereas ordinary kriging yielded better model results for Pb. This study determined that the preliminary process of developing spatial regression models, thus enabling the selection of contributing soil properties, can improve the interpolation accuracy of PTMs in abandoned mine sites.
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Baffoe-Twum, Edmund, Eric Asa, and Bright Awuku. "Estimating annual average daily traffic (AADT) data on low-volume roads with the cokriging technique and census/population data." Emerald Open Research 4 (April 22, 2022): 20. http://dx.doi.org/10.35241/emeraldopenres.14632.1.

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Geostatistical methods such as simple, ordinary, and universal kriging are not multivariate models in the usual statistical function. Notwithstanding, simple, ordinary, and universal kriging techniques utilize random function models that include unlimited random variables while modeling one attribute. The cokriging technique is a multivariate estimation method that can simultaneously model two or more attributes, defined with the same domains as coregionalization. For a successful structural analysis, it is necessary to have a minimum amount of each domain's measured attributes. The assumption is that data integration methods such as cokriging may yield more reliable models because their strength is drawn from multiple variables. This study investigates the impact of the population as a variable on traffic volumes. The investigation adopts the annual average daily traffic (AADT) from Montana, Minnesota, and Washington as one attribute and countywide population as a second attribute (or factor controlling traffic volumes). AADT data for this research span from 2009 to 2016. The cross-validation results of the model types explored with the cokriging technique are successfully used to evaluate the interpolation technique's performance and select optimal models for each state. The investigation results based on the cross-validation confirm the model's usefulness. The interpolation surface maps from the Montana and Minnesota models accurately represent the states' traffic and population density. The Washington model had a few exceptions; therefore, it did not necessarily represent the traffic and population density. An indication that other factors may impact the results. Consequently, it is worth exploring the impact of tourism, shopping, recreation centers, and possible transiting patterns throughout the state.
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Carvalho, José Ruy Porto De, Alan Massaru Nakai, and José Eduardo B. A. Monteiro. "Spatio-Temporal Modeling of Data Imputation for Daily Rainfall Series in Homogeneous Zones." Revista Brasileira de Meteorologia 31, no. 2 (June 2016): 196–201. http://dx.doi.org/10.1590/0102-778631220150025.

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Abstract Spatio-temporal modelling is an area of increasing importance in which models and methods have often been developed to deal with specific applications. In this study, a spatio-temporal model was used to estimate daily rainfall data. Rainfall records from several weather stations, obtained from the Agritempo system for two climatic homogeneous zones, were used. Rainfall values obtained for two fixed dates (January 1 and May 1, 2012) using the spatio-temporal model were compared with the geostatisticals techniques of ordinary kriging and ordinary cokriging with altitude as auxiliary variable. The spatio-temporal model was more than 17% better at producing estimates of daily precipitation compared to kriging and cokriging in the first zone and more than 18% in the second zone. The spatio-temporal model proved to be a versatile technique, adapting to different seasons and dates.
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ROGERS, DAVID J., and LUIGI SEDDA. "Statistical models for spatially explicit biological data." Parasitology 139, no. 14 (October 19, 2012): 1852–69. http://dx.doi.org/10.1017/s0031182012001345.

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SUMMARYExisting algorithms for predicting species' distributions sit on a continuum between purely statistical and purely biological approaches. Most of the existing algorithms are aspatial because they do not consider the spatial context, the occurrence of the species or conditions conducive to the species' existence, in neighbouring areas. The geostatistical techniques of kriging and cokriging are presented in an attempt to encourage biologists more frequently to consider them. Unlike deterministic spatial techniques they provide estimates of prediction errors. The assumptions and applications of common geostatistical techniques are presented with worked examples drawn from a dataset of the bluetongue outbreak in northwest Europe in 2006. Emphasis is placed on the importance and interpretation of weights in geostatistical calculations. Covarying environmental data may be used to improve predictions of species’ distributions, but only if their sampling frequency is greater than that of the species’ or disease data. Cokriging techniques are unable to determine the biological significance or importance of such environmental data, because they are not designed to do so.
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Qu, Mingkai, Xu Guang, Hongbo Liu, Yongcun Zhao, and Biao Huang. "Incorporating Auxiliary Data of Different Spatial Scales for Spatial Prediction of Soil Nitrogen Using Robust Residual Cokriging (RRCoK)." Agronomy 11, no. 12 (December 10, 2021): 2516. http://dx.doi.org/10.3390/agronomy11122516.

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Auxiliary data has usually been incorporated into geostatistics for high-accuracy spatial prediction. Due to the different spatial scales, category and point auxiliary data have rarely been incorporated into prediction models together. Moreover, traditionally used geostatistical models are usually sensitive to outliers. This study first quantified the land-use type (LUT) effect on soil total nitrogen (TN) in Hanchuan County, China. Next, the relationship between soil TN and the auxiliary soil organic matter (SOM) was explored. Then, robust residual cokriging (RRCoK) with LUTs was proposed for the spatial prediction of soil TN. Finally, its spatial prediction accuracy was compared with that of ordinary kriging (OK), robust cokriging (RCoK), and robust residual kriging (RRK). Results show that: (i) both LUT and SOM are closely related to soil TN; (ii) by incorporating SOM, the relative improvement accuracy of RCoK over OK was 29.41%; (iii) by incorporating LUTs, the relative improvement accuracy of RRK over OK was 33.33%; (iv) RRCoK obtained the highest spatial prediction accuracy (RI = 43.14%). It is concluded that the recommended method, RRCoK, can effectively incorporate category and point auxiliary data together for the high-accuracy spatial prediction of soil properties.
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Jawak, S. D., and A. J. Luis. "Synergetic merging of Cartosat-1 and RAMP to generate improved digital elevation model of Schirmacher oasis, east Antarctica." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-8 (November 28, 2014): 517–24. http://dx.doi.org/10.5194/isprsarchives-xl-8-517-2014.

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Available digital elevation models (DEMs) of Antarctic region generated by using radar altimetry and the Antarctic digital database (ADD) indicate elevation variations of up to hundreds of meters, which necessitates the generation of local DEM and its validation by using ground reference. An enhanced digital elevation model (eDEM) of the Schirmacher oasis region, east Antarctica, is generated synergistically by using Cartosat-1 stereo pair-derived photogrammetric DEM (CartoDEM)-based point elevation dataset and multitemporal radarsat Antarctic mapping project version 2 (RAMPv2) DEM-based point elevation dataset. In this study, we analyzed suite of interpolation techniques for constructing a DEM from RAMPv2 and CartoDEM-based point elevation datasets, in order to determine the level of confidence with which the interpolation techniques can generate a better interpolated continuous surface, and eventually improves the elevation accuracy of DEM from synergistically fused RAMPv2 and CartoDEM point elevation datasets. RAMPv2 points and CartoDEM points were used as primary data for various interpolation techniques such as ordinary kriging (OK), simple kriging (SK), universal kriging (UK), disjunctive kriging (DK) techniques, inverse distance weighted (IDW), global polynomial (GP) with power 1 and 2, local polynomial (LP) and radial basis functions (RBF). Cokriging of 2 variables with second dataset was used for ordinary cokriging (OCoK), simple cokriging (SCoK), universal cokriging (UCoK) and disjunctive cokriging (DCoK). The IDW, GP, LP, RBF, and kriging methods were applied to one variable, while Cokriging experiments were employed on two variables. The experiment of dataset and its combination produced two types of point elevation map categorized as (1) one variable (RAMPv2 Point maps and CartoDEM Point maps) and (2) two variables (RAMPv2 Point maps + CartoDEM Point maps). Interpolated surfaces were evaluated with the help of differential global positioning system (DGPS) points collected from study area during the Indian Scientific Expedition to Antarctic (ISEA). Accuracy assessment of the RAMPv2 DEM, CartoDEM, and combined eDEM (RAMPv2 + CartoDEM) by using DGPS as ground reference data shows that eDEM achieves much better accuracy (average elevation error 8.44 m) than that of existing DEM constructed by using only CartoDEM (13.57 m) or RAMPv2 (41.44 m) alone. The newly constructed eDEM achieves a vertical accuracy of about 7 times better than RAMPv2 DEM and 1.5 times better than CartoDEM. After using accurate DGPS data for accuracy assessment, the approximation to the actual surface of the eDEM extracted here is much more accurate with least mean root mean square error (RMSE) of 9.22 m than that constructed by using only CartoDEM (RMSE = 14.15 m) point elevation data and RAMPv2 (RMSE = 69.48 m) point elevation data. Our results indicate that, the overall trend of accuracy for the interpolation methods for generating continuous elevation surface from CartoDEM + RAMPv2 point elevation data, based on RMSE, is as follows: GP1 > IDW > GP2 > OK > LP2 > DK > LP1 > RBF > SK > UK. In case of cokriging interpolation methods, OCoK yields more accurate eDEM with the least RMSE of 8.16 m, which can be utilized to generate a highly accurate DEM of the research area.. Based on this work, it is inferred that GP2 and OCok interpolation methods and synergistic use of RAMPv2 and CartoDEM-based point elevation datasets lead to a highly accurate DEM of the study region. This research experiment demonstrates the stability (w.r.t multi-temporal datasets), performance (w.r.t best interpolation technique) and consistency (w.r.t all the experimented interpolation techniques) of synergistically fused eDEM. On the basis of average elevation difference and RMSE mentioned in present research, the newly constructed eDEM may serve as a benchmark for future elevation models such as from the ICESAT-II mission to spatially monitor ice sheet elevation.
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Zhang, Zebin, Martin Buisson, Pascal Ferrand, and Manuel Henner. "Integration of Second-Order Sensitivity Method and CoKriging Surrogate Model." Mathematics 9, no. 4 (February 18, 2021): 401. http://dx.doi.org/10.3390/math9040401.

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The global exploring feature of the surrogate model makes it a useful intermedia for design optimization. The accuracy of the surrogate model is closely related with the efficiency of optima-search. The cokriging approach described in present studies can significantly improve the surrogate model accuracy and cut down the turnaround time spent on the modeling process. Compared to the universal Kriging method, the cokriging method interpolates not only the sampling data, but also on their associated derivatives. However, the derivatives, especially high order ones, are too computationally costly to be easily affordable, forming a bottleneck for the application of derivative enhanced methods. Based on the sensitivity analysis of Navier–Stokes equations, current study introduces a low-cost method to compute the high-order derivatives, making high order derivatives enhanced cokriging modeling practically achievable. For a methodological illustration, second-order derivatives of regression model and correlation models are proposed. A second-order derivative enhanced cokriging model-based optimization tool was developed and tested on the optimal design of an automotive engine cooling fan. This approach improves the modern optimal design efficiency and proposes a novel direction for the large scale optimization problems.
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Ma, Liang, and Chang Qing Zuo. "A Comparison of Spatial Interpolation Models for Mapping Rainfall Erosivity on China Mainland." Advanced Materials Research 518-523 (May 2012): 4489–95. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.4489.

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Rainfall erosivity is an essential factor to reveal the response of water erosion to precipitation changes, and its spatial variation reveals erosion regional difference and water conservation regionalization. In this research, average annual rainfall erosivity in 1951 -2008 on China mainland is calculated through daily precipitation data from 711 meteorological stations. Precisions of 29 spatial interpolation models are quantitative compared including inverse distance weighting (IDW), radial basis function (RBF), kriging, cokriging (CK) and thin plate smoothing spline (TPS). Three variables cubic TPS is confirmed the optimum spatial interpolation model to rainfall erosivity on a large scale.
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Akbari, Haghighi, Aghayi, Javadian, Tajrishy, and Kløve. "Assimilation of Satellite-Based Data for Hydrological Mapping of Precipitation and Direct Runoff Coefficient for the Lake Urmia Basin in Iran." Water 11, no. 8 (August 6, 2019): 1624. http://dx.doi.org/10.3390/w11081624.

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Water management in arid basins often lacks sufficient hydro-climatological data because, e.g., rain gauges are typically absent at high elevations and inflow to ungauged areas around large closed lakes is difficult to estimate. We sought to improve precipitation and runoff estimation in an arid basin (Lake Urmia, Iran) using methods involving assimilation of satellite-based data. We estimated precipitation using interpolation of rain gauge data by kriging, downscaling the Tropical Rainfall Measuring Mission (TRMM), and cokriging interpolation of in-situ records with Remote Sensing (RS)-based data. Using RS-based data application in estimations gave more precise results, by compensating for lack of data at high elevations. Cokriging interpolation of rain gauges by TRMM and Digitized Elevation Model (DEM) gave 4–9 mm lower Root Mean Square Error (RMSE) in different years compared with kriging. Downscaling TRMM improved its accuracy by 14 mm. Using the most accurate precipitation result, we modeled annual direct runoff with Kennessey and Soil Conservation Service Curve Number (SCS-CN) models. These models use land use, permeability, and slope data. In runoff modeling, Kennessey gave higher accuracy. Calibrating Kennessey reduced the Normalized RMSE (NRMSE) from 1 in the standard model to 0.44. Direct runoff coefficient map by 1 km spatial resolution was generated by calibrated Kennessey. Validation by the closest gauges to the lake gave a NRMSE of 0.41 which approved the accuracy of modeling.
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Ly, S., C. Charles, and A. Degré. "Spatial interpolation of daily rainfall at catchment scale: a case study of the Ourthe and Ambleve catchments, Belgium." Hydrology and Earth System Sciences Discussions 7, no. 5 (September 27, 2010): 7383–416. http://dx.doi.org/10.5194/hessd-7-7383-2010.

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Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (krigings) are widely used in spatial interpolation from point measurement to continuous surfaces. However, the majority of existing geostatistical algorithms are available only for single-moment data. The first step in kriging computation is the semi-variogram modelling which usually uses only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. In this study, we used daily rainfall data from 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, Cressie's Approximate Weighted Least Squares method was used to fit seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) to daily sample semi-variogram on a daily basis. Seven selected raingages were used to compare the interpolation performance of these algorithms applied to many degenerated-raingage cases. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably interpolation with the Thiessen polygon that is commonly used in various hydrological models. Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) presented the highest Root Mean Square Error (RMSE) between the geostatistical and IDW methods. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases.
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Dissertations / Theses on the topic "Kriging and cokriging models"

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Adu, Agyemang Adela Beauty. "Vulnerability Assessment of Groundwater to NO3 Contamination Using GIS, DRASTIC Model and Geostatistical Analysis." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3264.

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The study employed Geographical Information System (GIS) technology to investigate the vulnerability of groundwater to NO3 content in Buncombe County, North Carolina in two different approaches. In the first study, the spatial distribution of NO3 contamination was analyzed in a GIS environment using Kriging Interpolation. Cokriging interpolation was used to establish how NO3 relates to land cover types and depth to water table of wells in the county. The second study used DRASTIC model to assess the vulnerability of groundwater in Buncombe County to NO3 contamination. To get an accurate vulnerability index, the DRASTIC parameters were modified to fit the hydrogeological settings of the county. A final vulnerability map was created using regression based DRASTIC, a statistic method to measure how NO3 relates to each of the DRASTIC variables. Although the NO3 concentration in the county didn’t exceed the USEPA standard limit (10mg/L), some areas had NO3 as high as 8.5mg/L.
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YATES, SCOTT RAYMOND. "GEOSTATISTICAL METHODS FOR ESTIMATING SOIL PROPERTIES (KRIGING, COKRIGING, DISJUNCTIVE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187990.

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Geostatistical methods were investigated in order to find efficient and accurate means for estimating a regionalized random variable in space based on limited sampling. The random variables investigated were (1) the bare soil temperature (BST) and crop canopy temperature (CCT) which were collected from a field located at the University of Arizona's Maricopa Agricultural Center, (2) the bare soil temperature and gravimetric moisture content (GMC) collected from a field located at the Campus Agricultural Center and (3) the electrical conductivity (EC) data collected by Al-Sanabani (1982). The BST was found to exhibit strong spatial auto-correlation (typically greater than 0.65 at 0⁺ lagged distance). The CCT generally showed a weaker spatial correlation (values varied from 0.15 to 0.84) which may be due to the length of time required to obtain an "instantaneous" sample as well as wet soil conditions. The GMC was found to be strongly spatially dependent and at least 71 samples were necessary in order to obtain reasonably well behaved covariance functions. Two linear estimators, the ordinary kriging and cokriging estimators, were investigated and compared in terms of the average kriging variance and the sum of squares error between the actual and estimated values. The estimate was obtained using the jackknifing technique. The results indicate that a significant improvement in the average kriging variance and the sum of squares could be expected by using cokriging for GMC and including 119 BST values in the analysis. A nonlinear estimator in one variable, the disjunctive kriging estimator, was also investigated and was found to offer improvements over the ordinary kriging estimator in terms of the average kriging variance and the sum of squares error. It was found that additional information at the estimation site is a more important consideration than whether the estimator is linear or nonlinear. Disjunctive kriging produces an estimator of the conditional probability that the value at an unsampled location is greater than an arbitrary cutoff level. This latter feature of disjunctive kriging is explored and has implications in aiding management decisions.
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Long, Andrew Edmund. "Cokriging, kernels, and the SVD: Toward better geostatistical analysis." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186892.

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Three forms of multivariate analysis, one very classical and the other two relatively new and little-known, are showcased and enhanced: the first is the Singular Value Decomposition (SVD), which is at the heart of many statistical, and now geostatistical, techniques; the second is the method of Variogram Analysis, which is one way of investigating spatial correlation in one or several variables; and the third is the process of interpolation known as cokriging, a method for optimizing the estimation of multivariate data based on the information provided through variogram analysis. The SVD is described in detail, and it is shown that the SVD can be generalized from its familiar matrix (two-dimensional) case to three, and possibly n, dimensions. This generalization we call the "Tensor SVD" (or TSVD), and we demonstrate useful applications in the field of geostatistics (and indicate ways in which it will be useful in other areas). Applications of the SVD to the tools of geostatistics are described: in particular, applications dependent on the TSVD, including variogram modelling in coregionalization. Variogram analysis in general is explored, and we propose broader use of an old tool (which we call the "corhogram ", based on the variogram) which proves useful in helping one choose variables for multivariate interpolation. The reasoning behind kriging and cokriging is discussed, and a better algorithm for solving the cokriging equations is developed, which results in simultaneous kriging estimates for comparison with those obtained from cokriging. Links from kriging systems to kernel systems are made; discovering kerneIs equivalent to kriging systems will be useful in the case where data are plentiful. Finally, some results of the application of geostatistical techniques to a data set concerning nitrate pollution in the West Salt River Valley of Arizona are described.
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Johnson, Crystal. "Using Kriging, Cokriging, and GIS to Visualize Fe and Mn in Groundwater." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2498.

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For aesthetic, economic, and health-related reasons, allowable concentrations of iron (Fe) and manganese (Mn) found present in drinking water are 0.3 mg/L and 0.05 mg/L, respectively. Water samples taken from private drinking wells in the rural communities within Buncombe County, North Carolina contain amounts of these metals in concentrations higher than the suggested limits. This study focused on bedrock geology, elevation, saprolite thickness, and well depth to determine factors affecting Fe and Mn. Using ArcGIS 10.2, spatial trends in Fe and Mn concentrations ranges were visualized, and estimates of the metal concentrations were interpolated to unmonitored areas. Results from this analysis were used to create a map that delineates the actual spatial distribution of Fe and Mn. The study also established a statistically significant correlation between Fe and Mn concentrations, which can be attributed to bedrock geology. Additionally, higher Fe in groundwater was concentrated in shallower wells and valley areas.
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Hemmati, Sahar. "Steady-State Co-Kriging Models." Thesis, West Virginia University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10614907.

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In deterministic computer experiments, a computer code can often be run at different levels of complexity/fidelity and a hierarchy of levels of code can be obtained. The higher the fidelity and hence the computational cost, the more accurate output data can be obtained. Methods based on the co-kriging methodology Cressie (2015) for predicting the output of a high-fidelity computer code by combining data generated to varying levels of fidelity have become popular over the last two decades. For instance, Kennedy and O’Hagan (2000) first propose to build a metamodel for multi-level computer codes by using an auto-regressive model structure. Forrester et al. (2007) provide details on estimation of the model parameters and further investigate the use of co-kriging for multi-fidelity optimization based on the efficient global optimization algorithm Jones et al. (1998). Qian and Wu (2008) propose a Bayesian hierarchical modeling approach for combining low-accuracy and high-accuracy experiments. More recently, Gratiet and Cannamela (2015) propose sequential design strategies using fast cross-validation techniques for multi-fidelity computer codes.

This research intends to extend the co-kriging metamodeling methodology to study steady-state simulation experiments. First, the mathematical structure of co-kriging is extended to take into account heterogeneous simulation output variances. Next, efficient steady-state simulation experimental designs are investigated for co-kriging to achieve a high prediction accuracy for estimation of steady-state parameters. Specifically, designs consisting of replicated longer simulation runs at a few design points and replicated shorter simulation runs at a larger set of design points will be considered. Also, design with no replicated simulation runs at long simulation is studied, along with different methods for calculating the output variance in absence of replicated outputs.

Stochastic co-kriging (SCK) method is applied to an M/M/1, as well as an M/M/5 queueing system. In both examples, the prediction performance of the SCK model is promising. It is also shown that the SCK method provides better response surfaces compared to the SK method.

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Watanabe, Jorge. "Métodos geoestatísticos de co-estimativas: estudo do efeito da correlação entre variáveis na precisão dos resultados." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/44/44137/tde-14082008-165227/.

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Esta dissertação de mestrado apresenta os resultados de uma investigação sobre os métodos de co-estimativa comumente utilizados em geoestatística. Estes métodos são: cokrigagem ordinária; cokrigagem colocalizada e krigagem com deriva externa. Além disso, a krigagem ordinária foi considerada apenas a título de ilustração como esse método trabalha quando a variável primária estiver pobremente amostrada. Como sabemos, os métodos de co-estimativa dependem de uma variável secundária amostrada sobre o domínio a ser estimado. Adicionalmente, esta variável deveria apresentar correlação linear com a variável principal ou variável primária. Geralmente, a variável primária é pobremente amostrada enquanto a variável secundária é conhecida sobre todo o domínio a ser estimado. Por exemplo, em exploração petrolífera, a variável primária é a porosidade medida em amostras de rocha retiradas de testemunhos e a variável secundária é a amplitude sísmica derivada de processamento de dados de reflexão sísmica. É importante mencionar que a variável primária e a variável secundária devem apresentar algum grau de correlação. Contudo, nós não sabemos como eles funcionam dependendo do grau de correlação. Esta é a questão. Assim, testamos os métodos de co-estimativa para vários conjuntos de dados apresentando diferentes graus de correlação. Na verdade, esses conjuntos de dados foram gerados em computador baseado em algoritmos de transformação de dados. Cinco valores de correlação foram considerados neste estudo: 0,993, 0,870, 0,752, 0,588 e 0,461. A cokrigagem colocalizada foi o melhor método entre todos testados. Este método tem um filtro interno que é aplicado no cálculo do peso da variável secundária, que por sua vez depende do coeficiente de correlação. De fato, quanto maior o coeficiente de correlação, maior é o peso da variável secundária. Então isso significa que este método funciona mesmo quando o coeficiente de correlação entre a variável primária e a variável secundária é baixo. Este é o resultado mais impressionante desta pesquisa.
This master dissertation presents the results of a survey into co-estimation methods commonly used in geostatistics. These methods are ordinary cokriging, collocated cokriging and kriging with an external drift. Besides that ordinary kriging was considered just to illustrate how it does work when the primary variable is poorly sampled. As we know co-estimation methods depend on a secondary variable sampled over the estimation domain. Moreover, this secondary variable should present linear correlation with the main variable or primary variable. Usually the primary variable is poorly sampled whereas the secondary variable is known over the estimation domain. For instance in oil exploration the primary variable is porosity as measured on rock samples gathered from drill holes and the secondary variable is seismic amplitude derived from processing seismic reflection data. It is important to mention that primary and secondary variables must present some degree of correlation. However, we do not know how they work depending on the correlation coefficient. That is the question. Thus, we have tested co-estimation methods for several data sets presenting different degrees of correlation. Actually, these data sets were generated in computer based on some data transform algorithms. Five correlation values have been considered in this study: 0.993; 0.870; 0.752; 0.588 and 0.461. Collocated simple cokriging was the best method among all tested. This method has an internal filter applied to compute the weight for the secondary variable, which in its turn depends on the correlation coefficient. In fact, the greater the correlation coefficient the greater the weight of secondary variable is. Then it means this method works even when the correlation coefficient between primary and secondary variables is low. This is the most impressive result that came out from this research.
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Araújo, Cristina da Paixão. "Uso de informação secundária imprecisa e inacurada no planejamento de curto prazo." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/127891.

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No setor de mineração, a amostragem está presente no empreendimento mineral desde a fase da exploração até a lavra. Para diminuir a incerteza na previsão de teores, o planejamento de lavra requer adensamento da amostragem para garantir previsões acuradas e precisas. Acredita-se, que quanto maior a quantidade de amostras, maior a confiabilidade nas estimativa de teores. Na fase exploração, geralmente, a amostragem é realizada por furos de sondagem com coroas diamantadas, que é uma técnica com alto custo de execução e produz amostras com acuracidade e precisão. Nesta fase, existem poucos dados com alta qualidade. Já na fase operacional, a amostragem é realizada por outras técnicas devido a restrições orçamentárias e ao alto custo de execução da sondagem diamantada. Em geral, estas amostras possuem baixa qualidade (imprecisas e inacuradas) e não são submetidas a protocolos de controle que qualidade. Logo, nesta fase existem muitos dados com baixa qualidade com erro de vies e precisao. Esta dissertação avalia o impacto do uso de dados imprecisos no planejamento de curto prazo. Para isto, foram analisados dois bancos de dados distintos. O primeiro estudo utiliza o banco de dados exaustivo Walker Lake, que foi usado e considerado como o teor real do depósito. Inicialmente, as amostras foram obtidas a partir do conjunto de dados com espaçamento regular de 20×20 m e 5×5 m, a partir do banco de dados exaustivo. Um erro relativo de ±25% (imprecisão) e 10% de viés foram adicionados aos dados espaçados a 5×5 m (dados geológicos curto prazo) em diferentes cenários. Depois foram estudadas diferentes metodologias para incorporar a informação imprecisa nas estimativas. O segundo estudo é realizado em uma mina de ouro, com dois tipos de dados diferentes, a furos de sondagem (dados primários) e circulação reversa (dados secundários). Nestes estudos foram investigadas duas metodologias: cokrigagem e krigagem ordinária, e os dados foram utilizados para estimar blocos. As curvas teor tonelagem, análise de deriva e a classificação errônea dos blocos foram avaliadas para cada estudo. Para o banco de dados, Walker Lake, os resultados mostraram que o uso da cokrigagem ordinária estandardizada é a melhor metodologia em situações que existem dados imprecisos e enviesados, com boa correlação entre as variáveis primárias e secundárias. As estimativas produzidas são mais próximas da distribuição real dos blocos, reduzindo o erro de classificação dos blocos. Já para o banco de dados de Ouro, as amostras possuem moderada correlaçao e continuidade espacial curta para pequenas distâncias do depósito. Nesta situação, a correção da imprecisão da variável secundária utilizando a krigagem ordinária produziram melhores resultados com estimativas menos enviesadas e melhor classificação dos blocos como minério e estéril.
Decisions starting at mineral exploration through mining are based on grade block models obtained from samples. To decrease the uncertainty in the estimates, the short term mining planning requires additional sampling to ensure accurate and precise predictions. As more samples are made available, there is trend towards more reliable estimates. In the exploration stage, usually, sampling is performed by diamond drill holes (DDH), which are expensive but produces accurate and precise samples. In this stage there are few data with high quality. In the production stage, sampling is obtained by other techniques due to the high costs of DDHs. In general, these samples have low quality and are not controlled by QA / QC protocols. This study evaluates the impact of using imprecise data in short-term mineplanning. For this, it was analyzed two different data sets. The first case used the exhaustive Walker Lake dataset as the source to obtain the true and sampled grades. Initially, samples were obtained from the exhaustive dataset at regularly spaced grids at 20 × 20 m and 5 × 5 meters. A relative error (imprecision) of ± 25% and a 10% bias were added to the data spaced at 5 × 5 m (short-term geological data) in different scenarios. The second study is in a gold mine with two different types of data obtained from diamond drilling holes (DDH_Hard data) and reverse circulation (RC_Soft data).To combine these different types of data, two methodologies were investigated: cokriging and ordinary kriging. Both types of data were used to estimate a block model using the two methodologies. The grade tonnage curves and swath plots were used to compare the results against the true block grades at the same block support. In addition, the block misclassification was evaluated. In the Walker Lake the results show that standardized ordinary cokriging is a better methodology for imprecise and biased data and produces estimates closer to the true grade block distribution, reducing block misclassification. For the data set at the underground mine gold, the samples had moderate correlation and short spatial continuity for small distances at this deposit. In this situation, the estimates using ordinary kriging with hard and soft data (standardized and re-escaled) produced better results with less bias and better blocks classification of ore and waste.
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Wang, Xiang. "Two kriging models, and the expanded readsold package." Ohio University / OhioLINK, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1183382153.

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Muré, Joseph. "Objective Bayesian analysis of Kriging models with anisotropic correlation kernel." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC069/document.

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Les métamodèles statistiques sont régulièrement confrontés au manque de données qui engendre des difficultés à estimer les paramètres. Le paradigme bayésien fournit un moyen élégant de contourner le problème en décrivant la connaissance que nous avons des paramètres par une loi de probabilité a posteriori au lieu de la résumer par une estimation ponctuelle. Cependant, ce paradigme nécessite de définir une loi a priori adéquate, ce qui est un exercice difficile en l'absence de jugement d'expert. L'école bayésienne objective propose des priors par défaut dans ce genre de situation telle que le prior de référence de Berger-Bernardo. Un tel prior a été calculé par Berger, De Oliveira and Sansó [2001] pour le modèle de krigeage avec noyau de covariance isotrope. Une extension directe au cas des noyaux anisotropes poserait des problèmes théoriques aussi bien que pratiques car la théorie de Berger-Bernardo ne peut s'appliquer qu'à un jeu de paramètres ordonnés. Or dans ce cas de figure, tout ordre serait nécessairement arbitraire. Nous y substituons une solution bayésienne objective fondée sur les posteriors de référence conditionnels. Cette solution est rendue possible par une théorie du compromis entre lois conditionnelles incompatibles. Nous montrons en outre qu'elle est compatible avec le krigeage trans-gaussien. Elle est appliquée à un cas industriel avec des données non-stationnaires afin de calculer des Probabilités de Détection de défauts (POD de l'anglais Probability Of Detection) par tests non-destructifs dans les tubes de générateur de vapeur de centrales nucléaires
A recurring problem in surrogate modelling is the scarcity of available data which hinders efforts to estimate model parameters. The Bayesian paradigm offers an elegant way to circumvent the problem by describing knowledge of the parameters by a posterior probability distribution instead of a pointwise estimate. However, it involves defining a prior distribution on the parameter. In the absence of expert opinion, finding an adequate prior can be a trying exercise. The Objective Bayesian school proposes default priors for such can be a trying exercise. The Objective Bayesian school proposes default priors for such situations, like the Berger-Bernardo reference prior. Such a prior was derived by Berger, De Oliveira and Sansó [2001] for the Kriging surrogate model with isotropic covariance kernel. Directly extending it to anisotropic kernels poses theoretical as well as practical problems because the reference prior framework requires ordering the parameters. Any ordering would in this case be arbitrary. Instead, we propose an Objective Bayesian solution for Kriging models with anisotropic covariance kernels based on conditional reference posterior distributions. This solution is made possible by a theory of compromise between incompatible conditional distributions. The work is then shown to be compatible with Trans-Gaussian Kriging. It is applied to an industrial case with nonstationary data in order to derive Probability Of defect Detection (POD) by non-destructive tests in steam generator tubes of nuclear power plants
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Asritha, Kotha Sri Lakshmi Kamakshi. "Comparing Random forest and Kriging Methods for Surrogate Modeling." Thesis, Blekinge Tekniska Högskola, Fakulteten för datavetenskaper, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-20230.

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The issue with conducting real experiments in design engineering is the cost factor to find an optimal design that fulfills all design requirements and constraints. An alternate method of a real experiment that is performed by engineers is computer-aided design modeling and computer-simulated experiments. These simulations are conducted to understand functional behavior and to predict possible failure modes in design concepts. However, these simulations may take minutes, hours, days to finish. In order to reduce the time consumption and simulations required for design space exploration, surrogate modeling is used. \par Replacing the original system is the motive of surrogate modeling by finding an approximation function of simulations that is quickly computed. The process of surrogate model generation includes sample selection, model generation, and model evaluation. Using surrogate models in design engineering can help reduce design cycle times and cost by enabling rapid analysis of alternative designs.\par Selecting a suitable surrogate modeling method for a given function with specific requirements is possible by comparing different surrogate modeling methods. These methods can be compared using different application problems and evaluation metrics. In this thesis, we are comparing the random forest model and kriging model based on prediction accuracy. The comparison is performed using mathematical test functions. This thesis conducted quantitative experiments to investigate the performance of methods. After experimental analysis, it is found that the kriging models have higher accuracy compared to random forests. Furthermore, the random forest models have less execution time compared to kriging for studied mathematical test problems.
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Books on the topic "Kriging and cokriging models"

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Design Optimization with Kriging Models (WBBM Report Series 47). Delft Univ Pr, 2000.

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National Aeronautics and Space Administration (NASA) Staff. Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle. Independently Published, 2018.

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Comparison of response surface and kriging models in the multidisciplinary design of an aerospike nozzle. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Sheehan, Daniel Dean. Interpolating a regular grid of elevations from random points using three algorithms: Kriging, splines, and polynomial surfaces. 1987.

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Book chapters on the topic "Kriging and cokriging models"

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Christensen, Ronald. "Linear Models for Spatial Data: Kriging." In Springer Texts in Statistics, 269–311. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3847-6_6.

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Christensen, Ronald. "Linear Models for Spatial Data: Kriging." In Springer Texts in Statistics, 262–99. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4757-4103-2_6.

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Christensen, Ronald. "Linear Models for Spatial Data: Kriging." In Springer Texts in Statistics, 321–55. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29164-8_8.

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Wackernagel, Hans. "Kriging with Discrete Point-Bloc Models." In Multivariate Geostatistics, 273–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05294-5_36.

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Schafmeister, Maria-Th. "Parameter Estimation for Groundwater Models by Indicator Kriging." In geoENV I — Geostatistics for Environmental Applications, 165–76. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-1675-8_14.

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Conde, R. P., and J. K. Yamamoto. "Evaluation of Kriging and Cokriging for Asbestos Ore Reserve Estimation at the Cana Brava Mine, Goiás, Brazil." In Geostatistics Rio 2000, 191–203. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-1701-4_14.

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Bernardes, T., I. Gontijo, H. Andrade, T. G. C. Vieira, and H. M. R. Alves. "Digital Terrain Models Derived from SRTM Data and Kriging." In Lecture Notes in Geoinformation and Cartography, 673–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-36998-1_51.

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Hardtke, William, and Celeste Wilson. "Fixing Panel Artifacts in Localized Indicator Kriging (LIK) Block Models." In Geostatistics Valencia 2016, 213–23. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-46819-8_14.

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Morató, A., and S. Sriramula. "Reliability analysis of offshore wind turbine support structures using Kriging models." In Risk, Reliability and Safety: Innovating Theory and Practice, 1425–31. Taylor & Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742: CRC Press, 2016. http://dx.doi.org/10.1201/9781315374987-214.

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Pereira, Paulo Elias C., Daniel R. Gonçalves, Stanley W. F. Rezende, Jose dos Reis V. Moura, and Roberto M. Finzi. "On Kriging Techniques & Impedance-based SHM as Applied to Damage Detection in 2D Structures." In Uncertainty Modeling: Fundamental Concepts and Models, 427–58. Brasilia, DF, Brazil: Biblioteca Central da Universidade de Brasilia, 2022. http://dx.doi.org/10.4322/978-65-86503-88-3.c13.

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Conference papers on the topic "Kriging and cokriging models"

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Nagawkar, Jethro, and Leifur Leifsson. "Applications of Polynomial Chaos-Based Cokriging to Simulation-Based Analysis and Design Under Uncertainty." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22369.

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Abstract This paper demonstrates the use of the polynomial chaos-based Cokriging (PC-Cokriging) on various simulation-based problems, namely an analytical borehole function, an ultrasonic testing (UT) case and a robust design optimization of an airfoil case. This metamodel is compared to Kriging, polynomial chaos expansion (PCE), polynomial chaos-based Kriging (PC-Kriging) and Cokriging. The PC-Cokriging model is a multi-variate variant of PC-Kriging and its construction is similar to Cokriging. For the borehole function, the PC-Cokriging requires only three high-fidelity samples to accurately capture the global accuracy of the function. For the UT case, it requires 20 points. Sensitivity analysis is performed for the UT case showing that the F-number has negligible effect on the output response. For the robust design case, a 75 and 31 drag count reduction is reported on the mean and standard deviation of the drag coefficient, respectively, when compared to the baseline shape.
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Rumpfkeil, Markus, Wataru Yamazaki, and Mavriplis Dimitri. "A Dynamic Sampling Method for Kriging and Cokriging Surrogate Models." In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-883.

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Kontoudis, George P., and Daniel J. Stilwell. "A Comparison of Kriging and Cokriging for Estimation of Underwater Acoustic Communication Performance." In WUWNET'19: International Conference on Underwater Networks & Systems. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3366486.3366515.

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Martin, Jay. "Robust Kriging Models." In 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
18th AIAA/ASME/AHS Adaptive Structures Conference
12th. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-2854.

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Leszczynska, Natalia, Selvakumar Ulaganathan, Adam Lamecki, Tom Dhaene, and Michal Mrozowski. "Kriging models for microwave filters." In 2016 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO). IEEE, 2016. http://dx.doi.org/10.1109/nemo.2016.7561660.

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Martin, Jay D., and Timothy W. Simpson. "On the Use of Kriging Models to Approximate Deterministic Computer Models." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57300.

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The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.
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Martin, Jay D., and Timothy W. Simpson. "On Using Kriging Models as Probabilistic Models in Design." In SAE 2004 World Congress & Exhibition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2004. http://dx.doi.org/10.4271/2004-01-0430.

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Martin, Jay D., and Timothy W. Simpson. "A Study on the Use of Kriging Models to Approximate Deterministic Computer Models." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dac-48762.

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The use of kriging models for approximation and global optimization has been steadily on the rise in the past decade. The standard approach used in the Design and Analysis of Computer Experiments (DACE) is to use an Ordinary kriging model to approximate a deterministic computer model. Universal and Detrended kriging are two alternative types of kriging models. In this paper, a description on the basics of kriging is given, highlighting the similarities and differences between these three different types of kriging models and the underlying assumptions behind each. A comparative study on the use of three different types of kriging models is then presented using six test problems. The methods of Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) for model parameter estimation are compared for the three kriging model types. A one-dimension problem is first used to visualize the differences between the different models. In order to show applications in higher dimensions, four two-dimension and a 5-dimension problem are also given.
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Martin, Jay D. "On Using Kriging Models for Complex Design." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48579.

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The design of most modern systems requires the tight integration of multiple disciplines. In practice, these multiple disciplines are often optimized independently, given only fixed values or targets for their interactions with other disciplines. The result is a system that may not represent the optimal system-level design. It may also not be a robust design in the sense that small changes in each subsystem’s performance may have a large impact on the system-level performance. The use of kriging models to represent the response surfaces of subsystems that are then combined to estimate system-level performance can be used as a method to provide collaboration between design teams. The difficulty with this method is the creation of the models given potentially large number of dimensions or observations. This paper presents a method to reduce the dimensionality of the input space for kriging models used for designing of complex systems. The input dimensionality of the kriging model is reduced to only includes the most important factors needed for the prediction of the observed output. A result of using these reduced dimensionality models is the need to no longer force interpolation of all of the observations used to create the models.
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Krishnamurty, Sundar, and Gregory Wilmes. "Preference-Based Updating of Kriging Surrogate Models." In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-4484.

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