Universal Kriging Model Research Articles

Prenatal Exposure to Ambient Air Pollution and Early Childhood Neurodevelopment: A Longitudinal Birth Cohort Study in an Urban Region of the Southeastern U.S.

Background: Animal studies indicate that air pollution may be neurotoxic, but evidence in humans is limited. We analyzed associations between prenatal air pollution and childhood neurodevelopment in a large birth cohort in Shelby County, TN.Methods: We included mother-child dyads who completed a preschool visit in the Conditions Affecting Neurocognitive Development and Early Childhood (CANDLE) study. Primary outcomes were internalizing and externalizing behavior scores (Child Behavior Checklist) and full-scale IQ score as a measure of general cognition. Prenatal exposures to nitrogen dioxide (NO2) and particulate matter less than 10 microns (PM10) at maternal residences were estimated using a national annual average universal kriging model (land-use regression with spatial smoothing). We also measured distance to nearest major roadway as a proxy for traffic-related pollution. In regression models, we adjusted for confounding by individual and neighborhood socioeconomic status, maternal IQ, and other determinants of child neurodevelopment; and tested for effect modification by child sex, maternal race, and prenatal nutrition.Results: The study population (N=1009) was predominantly low-income and 69% African American; mean child age at assessment was 4.4 years. Mean NO2 and PM10 exposures were 12.9 ppb and 20.9 μg/m3, respectively. In fully adjusted models, a 5 ppb increase in prenatal NO2 was associated with 13% higher externalizing behavior score (95% CI: 0.5, 28%) and 2.8 times higher odds (95% CI: 1.0, 7.9) of an externalizing score above the clinical threshold. Full-scale IQ scores averaged 2.5 points (95% CI: 0.1, 4.8) lower per 5 ug/m3 increase in PM10. We found no statistically significant evidence of associations with road proximity or interaction by demographics or nutrition.Conclusions: Our findings support the hypothesis that air pollution impairs neurodevelopment. We observed the most consistent associations between NO2 and externalizing behaviors.

Surrogate model–based optimal feed-forward control for dimensional-variation reduction in composite parts' assembly processes

ABSTRACTDimension control and variation reduction are vital for composite parts' assembly processes. Due to the nonlinear properties of composites, physics-based models cannot accurately and efficiently approximate the assembly processes. In addition, conventional robust parameter design (RPD) and statistical process control (SPC) cannot actively compensate for dimensional errors or prevent defects. This article proposes a surrogate model–based optimal feed-forward control strategy for dimensional-variation reduction and defect prevention in the assembly of composite parts. The objective is accomplished by (i) developing a grouped Latin hypercube sampling approach tailored to the problem; (ii) adopting a universal Kriging model for dimensional prediction and then embedding the model into an optimal feed-forward control algorithm; and (iii) conducting a multiobjective optimization to determine the control actions. A case study reveals that the developed methodology can effectively reduce the mean and standard deviation of dimensional deviations for the assembly of composite parts.

Development of an optimized trend kriging model using regression analysis and selection process for optimal subset of basis functions

Surrogate modeling, or metamodeling, is an efficient way of alleviating the high computational cost and complexity for iterative function evaluation in design optimization. Accuracy is significantly important because optimization algorithms rely heavily on the function response calculated by surrogate model and the optimum solution is directly affected by the quality of surrogate model. In this study, an optimized trend kriging model is proposed to improve the accuracy of the existing kriging models. Within the framework of the proposed model, regression analysis is carried out to approximate the unknown trend of the true function and to determine the order of the universal kriging model, which has a fixed form with a mean structure dependent on the order of model. In addition, the selection of an optimal basis function is conducted to separate the useful basis function terms from the full set of the basis function. The optimal subset of the basis function is selected with the global optimization algorithm; which can accurately represent the trend of true response surface. The mean structure of proposed model has been optimized to maximize the accuracy of kriging model depending on the trend of true function. Two- and three-dimensional analytic functions and a practical engineering problem are chosen to validate the proposed model. The results showed that the OTKG model yield the most accurate responses regardless of the number of initial sample points, and can conversed into well-trained model with few additional sample points.

On efficient global optimization via universal Kriging surrogate models

In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomial, a UK with a second-order polynomial, a blind Kriging (BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging (PCK) implementation. The UK-EGO framework with automatic trend function selection derived from the BK and PCK models works by building a UK surrogate model and then performing optimizations via expected improvement criteria on the Kriging model with the lowest leave-one-out cross-validation error. Next, we studied and compared the UK-EGO variants and standard EGO using five synthetic test functions and one aerodynamic problem. Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO. From our results, we found that PCK-EGO was the best variant, as it had more robust performance as compared to the rest of the UK-EGO schemes; however, total-order expansion should be used to generate the candidate trend function set for high-dimensional problems. Note that, for some test functions, the UK with predetermined polynomial trend functions performed better than that of BK and PCK, indicating that the use of automatic trend function selection does not always lead to the best quality solutions. We also found that although some variants of UK are not as globally accurate as the ordinary Kriging (OK), they can still identify better-optimized solutions due to the addition of the trend function, which helps the optimizer locate the global optimum.

Multiobjective optimization for a plasmonic nanoslit array sensor using Kriging models.

We propose an efficient multiobjective optimization approach for a plasmonic nanoslit array sensor using Kriging surrogate models. The universal Kriging models whose regression functions are zeroth-, first-, and second-order polynomials are adopted to estimate objective functions. The multiobjective extension of the genetic algorithm is used for Pareto optimal sensor geometry. The objective functions are the figure of merit defined as a ratio of peak wavelength shift at molecular adsorption and 3 dB bandwidth of transmission spectrum, and peak transmission power, respectively. The optical properties of a plasmonic slit sensor are investigated, such as transmission power, bandwidth, and peak shift, using the finite element method.

National-scale exposure prediction for long-term concentrations of particulate matter and nitrogen dioxide in South Korea

The limited spatial coverage of the air pollution data available from regulatory air quality monitoring networks hampers national-scale epidemiological studies of air pollution. The present study aimed to develop a national-scale exposure prediction model for estimating annual average concentrations of PM10 and NO2 at residences in South Korea using regulatory monitoring data for 2010. Using hourly measurements of PM10 and NO2 at 277 regulatory monitoring sites, we calculated the annual average concentrations at each site. We also computed 322 geographic variables in order to represent plausible local and regional pollution sources. Using these data, we developed universal kriging models, including three summary predictors estimated by partial least squares (PLS). The model performance was evaluated with fivefold cross-validation. In sensitivity analyses, we compared our approach with two alternative approaches, which added regional interactions and replaced the PLS predictors with up to ten selected variables. Finally, we predicted the annual average concentrations of PM10 and NO2 at 83,463 centroids of residential census output areas in South Korea to investigate the population exposure to these pollutants and to compare the exposure levels between monitored and unmonitored areas. The means of the annual average concentrations of PM10 and NO2 for 2010, across regulatory monitoring sites in South Korea, were 51.63 μg/m3 (SD = 8.58) and 25.64 ppb (11.05), respectively. The universal kriging exposure prediction models yielded cross-validated R2s of 0.45 and 0.82 for PM10 and NO2, respectively. Compared to our model, the two alternative approaches gave consistent or worse performances. Population exposure levels in unmonitored areas were lower than in monitored areas. This is the first study that focused on developing a national-scale point wise exposure prediction approach in South Korea, which will allow national exposure assessments and epidemiological research to answer policy-related questions and to draw comparisons among different countries.

Exploring range shifts of contrasting tree species across a bioclimatic transition zone

Bioclimatic transition zones are supposed to encompass sensitive areas to global change effects on forest ecosystems. In this study, we attempt to detect shifts in the ranges of contrasting Iberian tree species in the submediterranean transition zone in Navarra, northern Spain. These shifts are analysed in the context of a significant increase in temperature over recent decades along with moderate land use changes. Data from national forest inventories (1971 and 2010) are compared through universal kriging (UK) and block kriging models to assess the shifts in the ranges of Quercus subpyrenaica, Quercus ilex, Pinus sylvestris and Fagus sylvatica. UK results predicted an increase in the presence probability of the four target species for the whole Navarra region. However, in the submediterranean zone, the presence probability of Q. subpyrenaica, P. sylvestris and F. sylvatica shows a shrinking trend, whereas Q. ilex is expanding its range, supporting a previous hypothesis of a “mediterranization” of this bioclimatic transition region. These trends are concomitant with recent elevational shift patterns towards higher elevations in the case of Q. subpyrenaica, P. sylvestris and F. sylvatica in the transition zone. Moreover, the expected increase in species richness as a consequence of geographical shifts and vegetation recovery is identified. The moderate human influence detected in the study area confirms the major role of climate warming as driver of species range shifts over the period. The results of this study highlight the suitability of bioclimatic transition zones for monitoring the effects of global change on natural ecosystems, providing evidences of the complex mechanisms affecting the distribution of forests.

Individual and Neighborhood Socioeconomic Status and the Association between Air Pollution and Cardiovascular Disease.

Background:Long-term fine particulate matter (PM2.5) exposure is linked with cardiovascular disease, and disadvantaged status may increase susceptibility to air pollution-related health effects. In addition, there are concerns that this association may be partially explained by confounding by socioeconomic status (SES).Objectives:We examined the roles that individual- and neighborhood-level SES (NSES) play in the association between PM2.5 exposure and cardiovascular disease.Methods:The study population comprised 51,754 postmenopausal women from the Women’s Health Initiative Observational Study. PM2.5 concentrations were predicted at participant residences using fine-scale regionalized universal kriging models. We assessed individual-level SES and NSES (Census-tract level) across several SES domains including education, occupation, and income/wealth, as well as through an NSES score, which captures several important dimensions of SES. Cox proportional-hazards regression adjusted for SES factors and other covariates to determine the risk of a first cardiovascular event.Results:A 5 μg/m3 higher exposure to PM2.5 was associated with a 13% increased risk of cardiovascular event [hazard ratio (HR) 1.13; 95% confidence interval (CI): 1.02, 1.26]. Adjustment for SES factors did not meaningfully affect the risk estimate. Higher risk estimates were observed among participants living in low-SES neighborhoods. The most and least disadvantaged quartiles of the NSES score had HRs of 1.39 (95% CI: 1.21, 1.61) and 0.90 (95% CI: 0.72, 1.07), respectively.Conclusions:Women with lower NSES may be more susceptible to air pollution-related health effects. The association between air pollution and cardiovascular disease was not explained by confounding from individual-level SES or NSES.Citation:Chi GC, Hajat A, Bird CE, Cullen MR, Griffin BA, Miller KA, Shih RA, Stefanick ML, Vedal S, Whitsel EA, Kaufman JD. 2016. Individual and neighborhood socioeconomic status and the association between air pollution and cardiovascular disease. Environ Health Perspect 124:1840–1847; http://dx.doi.org/10.1289/EHP199

Spatial Interpolation of Meteorologic Variables in Vietnam using the Kriging Method

This paper presents the applications of Kriging spatial interpolation methods for meteorologic variables, including temperature and relative humidity, in regions of Vietnam. Three types of interpolation methods are used, which are as follows: Ordinary Kriging, Universal Kriging, and Universal Kriging plus Digital Elevation model correction. The input meteorologic data was collected from 98 ground weather stations throughout Vietnam and the outputs were interpolated temperature and relative humidity gridded fields, along with their error maps. The experimental results showed that Universal Kriging plus the digital elevation model correction method outperformed the two other methods when applied to temperature. The interpolation effectiveness of Ordinary Kriging and Universal Kriging were almost the same when applied to both temperature and relative humidity.

A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representation of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.

Kriging prediction from a circular grid: application to wafer diffusion

In the production process of silicon wafers, which are crystalline slices used as substrate of electronic micro‐circuits, the thickness of the SiO2 deposition on their top is a main characteristic to be controlled during the process. The experimental design that is commonly used to monitor the thickness to the target value consists of a regular array of points lying on concentric circles, the silicon wafer itself being a disk. To speed up the control process, the engineers aim to use just only a limited subset of such points. To reconstruct the values on untried locations of the silicon wafer, the Kriging interpolation has been proposed because of its recognized ability in providing fairly good predictions. In this paper, we consider two methodological issues related to universal Kriging models. First, we discuss the modeling of the covariance structure among the measured points; in fact, spatial data usually show a strong correlation when they come from spatially near observed points. Second, we put forward an algebraic method to assess the identifiability of trend models, based both on the full experimental design and on special fractions of it. Our findings are illustrated by a data set from an industrial application. Copyright © 2013 John Wiley & Sons, Ltd.

A regionalized national universal kriging model using Partial Least Squares regression for estimating annual PM2.5 concentrations in epidemiology

Many cohort studies in environmental epidemiology require accurate modeling and prediction of fine scale spatial variation in ambient air quality across the U.S. This modeling requires the use of small spatial scale geographic or “land use” regression covariates and some degree of spatial smoothing. Furthermore, the details of the prediction of air quality by land use regression and the spatial variation in ambient air quality not explained by this regression should be allowed to vary across the continent due to the large scale heterogeneity in topography, climate, and sources of air pollution. This paper introduces a regionalized national universal kriging model for annual average fine particulate matter (PM2.5) monitoring data across the U.S. To take full advantage of an extensive database of land use covariates we chose to use the method of Partial Least Squares, rather than variable selection, for the regression component of the model (the “universal” in “universal kriging”) with regression coefficients and residual variogram models allowed to vary across three regions defined as West Coast, Mountain West, and East. We demonstrate a very high level of cross-validated accuracy of prediction with an overall R2 of 0.88 and well-calibrated predictive intervals. In accord with the spatially varying characteristics of PM2.5 on a national scale and differing kriging smoothness parameters, the accuracy of the prediction varies by region with predictive intervals being notably wider in the West Coast and Mountain West in contrast to the East.

Gradient-Enhanced Universal Kriging for Uncertainty Propagation

In this work, we investigate the issue of providing a statistical model for the response of a computer model–described nuclear engineering system, for use in uncertainty propagation. The motivation behind our approach is the need for providing an uncertainty assessment even in the circumstances where only a few samples are available. Building on our recent work in using a regression approach with derivative information for approximating the system response, we investigate the ability of a universal gradient-enhanced Kriging model to provide a means for inexpensive uncertainty quantification. The universal Kriging model can be viewed as a hybrid of polynomial regression and Gaussian process regression. For this model, the mean behavior of the surrogate is determined by a polynomial regression, and deviations from this mean are represented as a Gaussian process. Tests with explicit functions and nuclear engineering models show that the universal gradient-enhanced Kriging model provides a more accurate surrogate model than either regression or ordinary Kriging models. In addition, we investigate the ability of the Kriging model to provide error predictions and bounds for regression models.

PDE-Constrained Gaussian Process Model on Material Removal Rate of Wire Saw Slicing Process

Thickness uniformity of wafers is a critical quality measure in a wire saw slicing process. Nonuniformity occurs when the material removal rate (MRR) changes over time during a slicing process, and it poses a significant problem for the downstream processes such as lapping and polishing. Therefore, the MRR should be modeled and controlled to maintain the thickness uniformity. In this paper, a PDE-constrained Gaussian process model is developed based on the global Galerkin discretization of the governing partial differential equations (PDEs). Three features are incorporated into the statistical model: (1) the PDEs governing the wire saw slicing process, which are obtained from engineering knowledge, (2) the systematic errors of the manufacturing process, and (3) the random errors, including both random manufacturing errors and measurement noises. Real experiments are conducted to provide data for the validation of the PDE-constrained Gaussian process model by estimating the model coefficients and further using the model to predict the overall MRR profile. The results of cross-validation indicate that the prediction performance of the PDE-constrained Gaussian process model is better than the widely used universal Kriging model with a mean of second order polynomial functions.

A geostatistical approach to data harmonization – Application to radioactivity exposure data

AbstractEnvironmental issues such as air, groundwater pollution and climate change are frequently studied at spatial scales that cross boundaries between political and administrative regions. It is common for different administrations to employ different data collection methods. If these differences are not taken into account in spatial interpolation procedures then biases may appear and cause unrealistic results. The resulting maps may show misleading patterns and lead to wrong interpretations. Also, errors will propagate when these maps are used as input to environmental process models. In this paper we present and apply a geostatistical model that generalizes the universal kriging model such that it can handle heterogeneous data sources. The associated best linear unbiased estimation and prediction (BLUE and BLUP) equations are presented and it is shown that these lead to harmonized maps from which estimated biases are removed. The methodology is illustrated with an example of country bias removal in a radioactivity exposure assessment for four European countries. The application also addresses multicollinearity problems in data harmonization, which arise when both artificial bias factors and natural drifts are present and cannot easily be distinguished. Solutions for handling multicollinearity are suggested and directions for further investigations proposed.

GIS spatial analysis of population exposure to fine particulate air pollution in Beijing, China

This research diagnoses the exposure of the residential population and the vulnerable groups of children and elderly people to air particle pollution in urban Beijing. We surveyed the air particle pollutant concentrations in the field. We used a universal kriging model in a geographic information system to interpolate the spatial distributions of each pollutant. Spatial patterns of air particle pollution were overlaid to community-level population distributions to identify the community exposures to high air particle pollution. Spatial and statistic modeling reveals that high concentration of ultra-fine air particles of particulate matter (PM) 0.3 m is strongly associated with high-population urban communities in the southwest and central western areas in the winter season. By contrast, all the other particle sizes surveyed (PMs of 0.5, 1.0, 3.0, and 5.0 m) indicate that high concentrations in the summer are associated with high-population communities. Reversed spatial and temporal patterns between PM 0.3 m and other particle sizes suggest that PM 0.3 m may have different sources of origin.

Species dynamics in a montane cloud forest: Identifying factors involved in changes in tree diversity and functional characteristics

Tropical montane cloud forests constitute a rare and fragile ecosystem, which is threatened in many of the areas in which it is found due to the pressure of human-originated disturbances. Cloud forests have been identified as a forest type with high levels of species endemism and biodiversity. The aim of this study, which focuses on a patch of cloud forest located in the Piura region of the Peruvian Andes, is to assess the changes in species composition and to identify the factors involved in the loss of biodiversity using data from a single inventory. Random sampling plots were established throughout the forest area. An index of the difference in species richness between recruitment and older trees (Tree Diversity Change index, TDC index) was calculated for each plot. A Tree Diversity Change Index ( TDC) and an index of species replacement based on the second order properties of the diameter distribution ( RE) were defined to assess changes in species richness and to characterize the change in the functional groups of tree species within the plot. The factors involved in these processes were also identified by means of a Universal Kriging model. The negative correlation between the TDC and the distance to the nearest track indicates that species richness is decreasing close to these tracks and that it is only maintained in the inner areas. The negative correlation of the RE index with altitude and deeper zones indicates that dynamic replacement of humid-condition species by dry-condition species is occurring at lower elevations. A loss in diversity along with a change towards species adapted to dryer conditions was observed throughout the forest. Zones at lower altitudes, on spurs or at the edges of the forest are more prone to these processes. This suggests that a change in the functions of the ecosystem has been taking place and that a minimum extension of cloud forest is required to maintain the ecological processes necessary for the continued existence of the cloud forest.

Comparing sampling patterns for kriging the spatial mean temporal trend

In monitoring the environment one often wishes to detect the temporal trend in a variable that varies across a region. A useful executive summary is then the temporal trend in the spatial mean. In this article, the best linear unbiased predictor of the spatial mean temporal trend and its variance are derived under a universal kriging model. Five different, spatially explicit sampling patterns are compared in terms of this variance. For small spatial ranges, the time-separation pattern is optimal, regardless of the temporal range. For larger spatial ranges, the best pattern depends on the temporal range. If the temporal range is small (less than ca. 1/20 of the spatial range), then the always-revisit pattern is best. For larger temporal ranges (between ca. 1/20 and ca. 1/4 of the spatial range) the serially alternating pattern is best, whereas the time-separation pattern is best for larger temporal ranges. The gain in using the serially alternating pattern or time-separation pattern instead of the always-revisit pattern can be substantial. The potential loss with respect to the always-revisit pattern is only minor for the serially alternating pattern, but can be substantial for the time-separation pattern. Unless one has good knowledge of the spatial and temporal range, the serially alternating pattern is thus a good choice. This work extends that by Urquhart and Kincaid and gives further support to their plea for the serially alternating pattern.

An automatic moving window approach for mapping meteorological data

Two distinctive characteristics of meteorological data are their global extent and their replication in time. Examples of such variables are rainfall, atmospheric pressure, temperature and humidity. Mapping these variables requires an initial interpolation of values on a regular grid. In Earth sciences, geostatistics is a widely used approach for this type of interpolation; generally, however, the variables have a local character, only one data set is available and the data are usually time independent. In this paper we show how these techniques can be adapted to take account of the global character and high spatial and temporal variability of meteorological data, by using a moving window approach to model selection and parameter inference within the framework of the universal kriging model. The universal kriging model is general because it includes the constant mean case as well as cases in which the mean is variable (in the terminology of geostatistics, a variable mean is known as drift). The latter is not unusual in meteorological variables such as rainfall, where topography, latitude or wind directions may produce definite patterns. The minimum Akaike information criterion is used for selecting a model for which the parameters are estimated by maximum likelihood. Finally, once a model has been selected (i.e. a value for the order of the drift and parameters of the semi-variogram or covariance function), universal kriging provides unbiased estimates and an assessment of the estimation variance. The implementation of this methodology is discussed and the methodology is illustrated by an application to mapping monthly rainfall over a large area of the west of the African continent. Copyright © 2005 Royal Meteorological Society.

Geostatistical Mapping with Continuous Moving Neighborhood

An issue that often arises in such GIS applications as digital elevation modeling (DEM) is how to create a continuous surface using a limited number of point observations. In hydrological applications, such as estimating drainage areas, direction of water flow is easier to detect from a smooth DEM than from a grid created using standard interpolation programs. Another reason for continuous mapping is esthetic; like a picture, a map should be visually appealing, and for some GIS users this is more important than map accuracy. There are many methods for local smoothing. Spline algorithms are usually used to create a continuous map, because they minimize curvature of the surface. Geostatistical models are commonly used approaches to spatial prediction and mapping in many scientific disciplines, but classical kriging models produce noncontinuous surfaces when local neighborhood is used. This motivated us to develop a continuous version of kriging. We propose a modification of kriging that produces continuous prediction and prediction standard error surfaces. The idea is to modify kriging systems so that data outside a specified distance from the prediction location have zero weights. We discuss simple kriging and conditional geostatistical simulation, models that essentially use information about mean value or trend surface. We also discuss how to modify ordinary and universal kriging models to produce continuous predictions, and limitations using the proposed models.