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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Numerical estimation of phase transformations in solid state during Yb:YAG laser heating of steel sheets

This work concerns the numerical modeling of heat transfer and phase transformations in solid state occurring during the Yb:YAG laser beam heating process. The temperature field is obtained by the numerical solution into transient heat transfer equation with convective term. The laser beam heat source model is developed using the Kriging interpolation method with experimental measurements of Yb:YAG laser beam profile taken into account. Phase transformations are calculated on the basis of Johnson - Mehl - Avrami (JMA) and Koistinen - Marburger (KM) kinetics models as well as continuous heating transformation (CHT) and continuous cooling transformation (CCT) diagrams for S355 steel. On the basis of developed numerical algorithms 3D computer simulations are performed in order to predict temperature history and phase transformations in Yb:YAG laser heating process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dynamic PRA-Based Estimation of PWR Coping Time Using a Surrogate Model for Accident Tolerant Fuel

In this study, we propose an interpolation-based response surface surrogate methodology to manage a large number of scenarios in dynamic probabilistic risk assessment. It adopts the shape Dynamic Time Warping algorithm to cluster the interpolation neighborhood from time series sample data. The interpolation method was adapted from Taylor Kriging to allow a reduced-order model of the Taylor series. In order to demonstrate its applicability to complex issues in risk assessment for nuclear engineering, an example risk response surface to estimate emergency core cooling system (ECCS) criteria for triplex silicon carbide (SiC) accident-tolerant fuel was constructed. The response surface was exploited to estimate the cumulative failure probability of the fuel cladding structure due to the uncertainties in operator actions and safety systems. The functional failures were assessed based on a combination of individual layer failures computed by coupling Risk Analysis Virtual Environment software with a pressurized water reactor 1000-MW(electric) RELAP5 model and the in-house fuel performance assessment module. Results showed that SiC cladding failure probability spiked less than 1 min after a large-break loss-of- coolant accident whenever the current ECCS criteria for Zircaloy-4 (Zr-4) cladding was used. However, it still provides an increased safety margin of three orders of magnitude compared to Zr-4. This positive margin could be utilized to relax active ECCS requirements by allowing deviations of up to 450 s in its actuation time. The proposed surrogate methodology generated a response surface of SiC cladding failure probability reasonably well, with a significant savings of computation time. This methodology is expected to be useful in the analysis of system response with complex uncertainty sources.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis, our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An Approach to Estimate Atmospheric Greenhouse Gas Total Columns Mole Fraction from Partial Column Sampling

This paper presents a new conceptual approach to estimate total column mole fractions of CO 2 and CH 4 using partial column data. It provides a link between airborne in situ and remote sensing observations of greenhouse gases. The method relies on in situ observations, external ancillary sources of information (e.g., atmospheric transport models), and a regression kriging framework. We evaluate our new approach using National Oceanic and Atmospheric Administration's (NOAA's) AirCore program-in situ vertical profiles of CO 2 and CH 4 collected from weather balloons. Our paper shows that under the specific conditions of this study and assumption of unbiasedness, airborne observations up to 6500-9500maltitude are required to achieve comparable total column CO 2 mole fraction uncertainty as the Total Carbon Column Observing Network (TCCON) network provides, given as a precision of the ratio between observed and true total column-integrated mole fraction, assuming 400 ppm XCO 2 (2σ, e.g., 0.8 ppm). If properly calibrated, our approach could be applied to vertical profiles of CO 2 collected from aircraft using a few flask samples, while retaining similar uncertainty level. Our total column CH 4 estimates, by contrast, are less accurate than TCCON's. Aircrafts are not as spatially constrained as TCCON ground stations, so our approach adds value to aircraft-based vertical profiles for evaluating remote sensing platforms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Feedback on Forty-year Long Clean-up Operations of a Contaminated Soil for Environmental Purpose - 20026

One of the CEA facilities in France is the place of miscellaneous mapping and clean-up operations since the 1980's. The final purpose of the conducted work deals with the environmental remediation of the building. In France, the absence of a regulatory framework for the management of sites polluted by radioactive substances, especially as the lack of release thresholds, has led to develop different approaches of soil radiological characterization. The geostatistical approach is part of them. Preliminary investigations are an unavoidable step prior to clearance and remediation. First, historical analysis enables to define site perimeters to investigate as well as to precisely locate expected contaminated parts. For radioactive pollutants, the media (water, soil, air) and transfer routes participate in the definition of the investigation perimeter and thus also need to be identified through a geological study. At the same time, functional analysis leads to choose the best measurement means which could provide useful information when combined with visual inspection. An equipment well adapted to easy-to-measure radionuclides as gamma emitters, such as gamma probe or on-site gamma spectrometry, is usually selected as a non-destructive assay. Coupled with spatial positions, processed on-site radiological data can be mapped. Data processing consists in mapping and kriging before a geostatistical analysis in order to identify the zones of interest to be targeted. Selected zones are not only linked to high level count rates but also to low level ones so that a pollution-free reference is known in the area. This data processing also enables to categorize waste types according to their origin and contamination levels. An expected volume of different waste then follows as well as the waste characterization equipments. In-depth investigations, e.g. core drillings and samplings, naturally ensue to aim at remediation optimization through the assessment of environmental impact. After clean-up operations, non-destructive assays as well as destructive samplings enable to check the effective clearance. Following this methodology in the present remediation work, results of the first non-destructive assay campaign highlighted a long-lived transuranic radionuclides contamination in the concrete flagstone. Successive non-destructive assays were then performed in the defined zones of interest. Count rates measured with a surface probe were first mapped. The best localization of destructive assays, i.e. core drillings at a 1 meter depth, came from this surface mapping followed by a geostatistical analysis. The concrete flagstone was totally removed. Then, the depth of soil to remove under the flagstone was optimized from the results of radiological activities measured in core drillings samples. A new surface mapping was then drawn after this partial soil excavation. The sand and demolition rubble samples, homogeneously constituted from the flagstone fragments, were analyzed by gamma spectrometry. Meanwhile, waste drums and other containers were also measured by gamma spectrometry and passive neutron measurement devices. All these results have brought miscellaneous pieces of information. In this context, major issues appear in terms of physical constraints such as the premises tininess as well as of soil sampling techniques and in terms of measurement performances assessment and the representativeness of homogeneous samples. The choice of radiological soil and waste characterization devices is described in the light of enhanced performances by keeping in mind radiation protection requirements and a willing to always optimize waste categories (very low level waste) and volume. The improvement of the characterization methods appears through this forty-year long work while sharing the feedback of encountered difficulties. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2014

A new estimate of the China temperature anomaly series and uncertainty assessment in 1900–2006

While global warming during the last century has been well recognized, the magnitude of the climate warming in regions such as China over the past 100 years still has some uncertainty due to limited observations during the early years. Several series of temperature anomalies for the 20th century in China have been independently developed by different groups. The uncertainty arises mainly from the sparse observations before 1950, where statistics are sensitive to the small and potentially biased sample. In this study, BSHADE–MSN (Biased Sentinel Hospitals Areal Disease Estimation and Means of Stratified Nonhomogeneous Surface), a combination of two novel distinct statistical methods that are applicable with different sample situations to a spatial heterogeneous surface, is applied to estimate annual mean temperature anomalies for China. This method takes into account prior knowledge of geographical spatial autocorrelation and nonhomogeneity of target domains, remedies the biased sample, and maximizes an objective function for the best linear unbiased estimation (BLUE) of the regional mean quantity. For the period 1900–1999, the overall trend estimated by BSHADE–MSN is 0.80°C with a 95% confidential interval between 0.41°C and 1.18°C. This is significantly lower than that calculated by Climate Anomaly Method (CAM) and Block Kriging. The new temperature anomaly series for China exhibits slightly warmer conditions for the period before 1950 than existing studies. All the methods applied so far agree well with each other for the period after 1950, when there are sufficient stations across the country for the estimation of temperature anomaly series. Cross validation shows that the new regional mean temperature anomaly series has smaller estimation error variance and higher accuracy than those based on the other methods assessed in this study.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Special Issue: Geostatistics and Machine Learning

Abstract Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different origins, machine learning and geostatistics share concepts and methods. For example, the kriging formalism can be cast in the machine learning framework of Gaussian process regression. Machine learning, with its focus on algorithms and ability to seek, identify, and exploit hidden structures in big data sets, is providing new tools for exploration and prediction in the earth sciences. Geostatistics, on the other hand, offers interpretable models of spatial (and spatiotemporal) dependence. This special issue on Geostatistics and Machine Learning aims to investigate applications of machine learning methods as well as hybrid approaches combining machine learning and geostatistics which advance our understanding and predictive ability of spatial processes.

58 GEOSCIENCES↗
DOE OSTI2019

Machine learning-based surrogate modeling for data-driven optimization: a comparison of subset selection for regression techniques

Optimization of simulation-based or data-driven systems is a challenging task, which has attracted significant attention in the recent literature. A very efficient approach for optimizing systems without analytical expressions is through fitting surrogate models. Due to their increased flexibility, nonlinear interpolating functions, such as radial basis functions and Kriging, have been predominantly used as surrogates for data-driven optimization; however, these methods lead to complex nonconvex formulations. Alternatively, commonly used regression-based surrogates lead to simpler formulations, but they are less flexible and inaccurate if the form is not known a priori. In this work, we investigate the efficiency of subset selection regression techniques for developing surrogate functions that balance both accuracy and complexity. Subset selection creates sparse regression models by selecting only a subset of original features, which are linearly combined to generate a diverse set of surrogate models. Five different subset selection techniques are compared with commonly used nonlinear interpolating surrogate functions with respect to optimization solution accuracy, computation time, sampling requirements, and model sparsity. Furthermore, our results indicate that subset selection-based regression functions exhibit promising performance when the dimensionality is low, while interpolation performs better for higher dimensional problems.

42 ENGINEERING↗
DOE OSTI2020

Accelerating geostatistical modeling using geostatistics-informed machine Learning

Ordinary Kriging (OK) is a popular geostatistical algorithm for spatial interpolation and estimation. The computational complexity of OK changes quadratically and cubically for memory and speed, respectively, given the number of data. Therefore, it is computationally intensive and also challenging to process a large set of data, especially in three-dimensional (3D) cases. This paper develops a geostatistics-informed machine learning (GIML) model to improve the efficiency of OK by reducing the number of points required to be estimated using OK. Specifically, only a very few of the unknown points are estimated by OK to get the weights and estimations, which are used as the training dataset. Moreover, the governing equations of OK are used to guide our proposed machine learning to better reproduce the spatial distributions. Our results show that the proposed GIML can reduce the computational time of OK by at least one order of magnitude. The effectiveness of the GIML is evaluated and compared using a 2D case. Furthermore, we demonstrate its efficiency and robustness by considering a different number of training samples on various 3D simulation grids.

58 GEOSCIENCES↗
DOE OSTI2016

Exploring the spatial variability of soil properties in an Alfisol Catena

Detailed digital soil maps showing the spatial heterogeneity of soil properties consistent with the landscape are required for site-specific management of plant nutrients, land use planning and process-based environmental modeling. We characterized the short-scale spatial heterogeneity of soil properties in an Alfisol catena in a tropical landscape of Sri Lanka. The impact of different land-uses (paddy, vegetable and un-cultivated) was examined to assess the impact of anthropogenic activities on the variability of soil properties at the catenary level. Conditioned Latin hypercube sampling was used to collect 58 geo-referenced topsoil samples (0–30 cm) from the study area. Soil samples were analyzed for pH, electrical conductivity (EC), organic carbon (OC), cation exchange capacity (CEC) and texture. The spatial correlation between soil properties was analyzed by computing crossvariograms and subsequent fitting of theoretical model. Spatial distribution maps were developed using ordinary kriging. The range of soil properties, pH: 4.3–7.9; EC: 0.01–0.18 dS m –1 ; OC: 0.1–1.37%; CEC: 0.44– 11.51 cmol (+) kg –1 ; clay: 1.5–25% and sand: 59.1–84.4% and their coefficient of variations indicated a large variability in the study area. Electrical conductivity and pH showed a strong spatial correlation which was reflected by the cross-variogram close to the hull of the perfect correlation. Moreover, cross-variograms calculated for EC and Clay, CEC and OC, CEC and clay and CEC and pH indicated weak positive spatial correlation between these properties. Relative nugget effect (RNE) calculated from variograms showed strongly structured spatial variability for pH, EC and sand content (RNE < 25%) while CEC, organic carbon and clay content showed moderately structured spatial variability (25% < RNE < 75%). Spatial dependencies for examined soil properties ranged from 48 to 984 m. The mixed effects model fitting followed by Tukey's post-hoc test showed significant effect of land use on the spatial variability of EC. Our study revealed a structured variability of topsoil properties in the selected tropical Alfisol catena. Except for EC, observed variability was not modified by the land uses. Investigated soil properties showed distinct spatial structures at different scales and magnitudes of strength. Our results will be useful for digital soil mapping, site specific management of soil properties, developing appropriate land use plans and quantifying anthropogenic impacts on the soil system.

Geo-statistical analysis↗
DOE OSTI2021

Gaussian process regression constrained by boundary value problems

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

42 ENGINEERING↗
DOE OSTI2016

Multi-fidelity machine learning models for accurate bandgap predictions of solids

Here, we present a multi-fidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. Additionally, the adopted Gaussian process regression formulation allows us to predict the underlying uncertainties as a measure of our confidence in the predictions. In using a set of 600 elpasolite compounds as an example dataset and using semi-local and hybrid exchange correlation functionals within density functional theory as two levels of fidelities, we demonstrate the excellent learning performance of the method against actual high fidelity quantum mechanical calculations of the bandgaps. The presented statistical learning method is not restricted to bandgaps or electronic structure methods and extends the utility of high throughput property predictions in a significant way.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Nested polynomial trends for the improvement of Gaussian process-based predictors

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence

In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and highfidelity data using a parameterized GP with hyperparameters identified via optimization. Our approach reduces the cost of optimization for inferring hyperparameters by incorporating partial physical knowledge. We prove that the physical constraints in the form of deterministic linear operators are satisfied up to an error bound. Furthermore, we combine CoPhIK with a greedy active learning algorithm for guiding the selection of additional observation locations. The eciency and accuracy of CoPhIK are demonstrated for reconstructing the partially observed modified Branin function, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.

Yang, Xiu↗
DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A unified approach to evaluating precipitation frequency estimates with uncertainty quantification: Application to Florida and California watersheds

Although a variety of climate datasets are now available, including observational and model products, there remains a pressing need for the development of a unified, automated and application-focused approach for evaluating and comparing climate extremes within and across these datasets. Precipitation frequency (PF) es- timates for extreme precipitation events are useful decision-relevant quantities among water managers. Our objective and quantitative framework for computing PF estimates of any duration uses known techniques in a novel combination. Our framework consists of three steps: (1) use of a regionalization-based statistical method for precipitation frequency estimation at observed sites; this involves hierarchical clustering (here we used Ward’s method) for delineating homogeneous regions, and regional frequency analysis using L-moments; (2) use of kriging for spatial mapping because of its advantages over other conventional interpolation methods; (3) use of z-scores accounts for estimation uncertainties when comparing PF estimates between datasets. The 24-h PF estimates in the Kissimmee-Southern Florida watershed (flat topography) and the Sacramento-San Joaquin watershed (complex topography) demonstrate the applicability of this approach in regions of any geographical complexity. Our results are shown to be reasonably calibrated using the probability integral transform (PIT) histogram of the best fitted distribution. Our results are compared with that of the NOAA Atlas 14 reports and show that for most of the stations the two estimates are statistically indistinguishable; and, the confidence intervals of our estimates are narrower than those of the NOAA estimates. Our approach is applicable to a variety of datasets and provides a baseline for assessing performance of climate models in historical simulations – a necessary first step towards analyzing future projections.

58 GEOSCIENCES↗
DOE OSTI2021

Comparison of fiber-optic distributed temperature sensing and high-sensitivity sensor spatial surveying of stream temperature

Measuring surface water temperature spatial variability is needed to estimate the interaction between surface water and groundwater, evaluate fish habitat and thermal inertia, and to estimate streamflow frequency and duration. Fiber optic distributed temperature sensing (FO-DTS) has been used in rivers and lakes, providing high-resolution and sensitive temperature monitoring over large temporal and spatial scales. However, in streams with cobbly or bedrock-lined streambeds and variable bathymetry, use of FO-DTS to measure temperature close to the surface water and groundwater interface can be challenging if even feasible. FO-DTS can also be costly, involve difficult installations, and require an advanced understanding of the technology, calibration, and data processing. In this study, we compared FO-DTS stream temperature survey results to an alternative temperature survey method employing a towed transect of high-resolution temperature loggers spaced at 1-m and transported in the stream along the study reach, to measure the spatial distribution of stream-water temperature in East Fork Poplar Creek near Oak Ridge, Tennessee, USA. We assessed the applicability and limitations of the two methods, and quantitatively compared in-situ temperature survey results measured simultaneously with each method. Regression results showed strong temporal and spatial correlation between the two methods. Differences were only elevated near the stream banks in areas that were coincident with correlation slope deviations from unity, which was attributed to shallower water and lower data density. Kriging standard errors were also low at channel center with minor increases near the stream banks. Furthermore, the results suggested that the array of the individual temperature sensors can provide a practical alternative to FO-DTS for thermal characterization of surface water, providing slightly lower spatial and temporal resolution, but with higher accuracy of temperature measurement, with greater simplicity, and with a broader range of conditions where it may be applied.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Deep-learning-based workflow for boundary and small target segmentation in digital rock images using UNet++ and IK-EBM

We report three-dimensional (3D) X-ray micro-computed tomography (μCT) has been widely used in petroleum engineering because it can provide detailed pore structural information for a reservoir rock, which can be imported into a pore-scale numerical model to simulate the transport and distribution of multiple fluids in the pore space. The partial volume blurring (PVB) problem is a major challenge in segmenting raw μCT images of rock samples, which impacts boundaries and small targets near the resolution limit. We developed a deep-learning (DL)-based workflow for accurate and fast partial volume segmentation. The DL model's performance depends primarily on the training data quality and model architecture. This study employed the entropy-based-masking indicator kriging (IK-EBM) to segment 3D Berea sandstone images as training datasets. The comparison between IK-EBM and manual segmentation using a 3D synthetic sphere pack, which had a known ground truth, showed that IK-EBM had higher accuracy on partial volume segmentation. We then trained and tested the UNet++ model, a state-of-the-art supervised encoder-decoder model, for binary (i.e., void and solid) and four-class segmentation. We compared the UNet++ with the commonly used U-Net and wide U-Net models and showed that the UNet++ had the best performance in terms of pixel-wise and physics-based evaluation metrics. Specifically, boundary-scaled accuracy demonstrated that the UNet++ architecture outperformed the regular U-Net architecture in the segmentation of pixels near boundaries and small targets, which were subjected to the PVB effect. Feature map visualization illustrated that the UNet++ bridged the semantic gaps between the feature maps extracted at different depths of the network, thereby enabling faster convergence and more accurate extraction of fine-scale features. The developed workflow significantly enhances the performance of supervised encoder-decoder models in partial volume segmentation, which has extensive applications in fundamental studies of subsurface energy, water, and environmental systems.

02 PETROLEUM↗