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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Kriging-Based Inverse Uncertainty Quantification of BISON Fission Gas Release Model

Nuclear reactor fuel performance analysis studies the thermo-mechanical behavior of fuel rods and verify their compliance with safety criteria under both normal operation and accidental conditions. One of the major concerns in fuel performance analysis is the behavior of the fission gases xenon and krypton in uranium dioxide fuel, which significantly affect the thermo-mechanical performance of the nuclear fuel rods employed in current LWRs. Previously, the modeling of fission gas release (FGR) in nuclear fuel performance codes have been relying on empirical models which are not applicable beyond their range of calibration. Recently a more efficient and flexible physics-based FGR and swelling model that can describe a wider range of reactor operation conditions have been implemented in fuel performance code BISON. In this work, we performed Bayesian calibration to inversely quantify the uncertainties associated with the 5 tuning parameters in BISON FGR model, based on the time-dependent FGR measurement data from Riso-AN3 benchmark. It takes around 1 hour and 40 minutes for BISON to simulate the Riso-AN3 benchmark with a moderate mesh size using 32 processors. As hundreds of thousands of BISON simulations are needed during Markov Chain Monte Carlo (MCMC) sampling, running BISON directly is not a viable solution. Therefore we propose to use Kriging-based metamodels to replace BISON during MCMC sampling. Surrogate model is an approximation of the input/output relation of a computer code/model. It is also called metamodel, response surface, emulator. Surrogate models usually take much less computational time than the original model (like BISON) while maintaining the input/output relation of the original model to a desirable accuracy. Constructing the metamodels normally requires small number of executions of the original model. Once validated, metamodels can be used to perform uncertainty and sensitivity analysis, Bayesian calibration, optimization, etc.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Cost-Effective Mapping of Benthic Habitats in Inland Reservoirs through Split-Beam Sonar, Indicator Kriging, and Historical Geologic Data

Because bottom substrate composition is an important control on the temporal and spatial location of the aquatic community, accurate maps of benthic habitats of inland lakes and reservoirs provide valuable information to managers, recreational users, and scientists. Therefore, we collected vertical, split-beam sonar data (roughness [E1], hardness [E2], and bathymetry) and sediment samples to make such maps. Statistical calibration between sonar parameters and sediment classes was problematic because the E1:E2 ratios for soft (muck and clay) sediments overlapped a lower and narrower range for hard (gravel) substrates. Thus, we used indicator kriging (IK) to map the probability that unsampled locations did not contain coarse sediments. To overcome the calibration issue we tested proxies for the natural processes and anthropogenic history of the reservoir as potential predictive variables. Of these, a geologic map proved to be the most useful. The central alluvial valley and mudflats contained mainly muck and organic-rich clays. The surrounding glacial till and shale bedrock uplands contained mainly poorly sorted gravels. Anomalies in the sonar data suggested that the organic-rich sediments also contained trapped gases, presenting additional interpretive issues for the mapping. We extended the capability of inexpensive split-beam sonar units through the incorporation of historic geologic maps and other records as well as validation with dredge samples. Through the integration of information from multiple data sets, were able to objectively identify bottom substrate and provide reservoir users with an accurate map of available benthic habitat.

bottom sediment, fisheries, geostatistics, GIS, ha↗
DOE OSTI2018

A Kriging based spatiotemporal approach for traffic volume data imputation

Along with the rapid development of Intelligent Transportation Systems, traffic data collection technologies have progressed fast. The emergence of innovative data collection technologies such as remote traffic microwave sensor, Bluetooth sensor, GPS-based floating car method, and automated license plate recognition, has significantly increased the variety and volume of traffic data. Despite the development of these technologies, the missing data issue is still a problem that poses great challenge for data based applications such as traffic forecasting, real-time incident detection, dynamic route guidance, and massive evacuation optimization. A thorough literature review suggests most current imputation models either focus on the temporal nature of the traffic data and fail to consider the spatial information of neighboring locations or assume the data follow a certain distribution. These two issues reduce the imputation accuracy and limit the use of the corresponding imputation methods respectively. As a result, this paper presents a Kriging based data imputation approach that is able to fully utilize the spatiotemporal correlation in the traffic data and that does not assume the data follow any distribution. A set of scenarios with different missing rates are used to evaluate the performance of the proposed method. The performance of the proposed method was compared with that of two other widely used methods, historical average and K-nearest neighborhood. Comparison results indicate that the proposed method has the highest imputation accuracy and is more flexible compared to other methods.

Science & Technology - Other Topics↗
DOE OSTI2019

A Kriging-Based Approach to Autonomous Experimentation with Applications to X-Ray Scattering

Abstract Modern scientific instruments are acquiring data at ever-increasing rates, leading to an exponential increase in the size of data sets. Taking full advantage of these acquisition rates will require corresponding advancements in the speed and efficiency of data analytics and experimental control. A significant step forward would come from automatic decision-making methods that enable scientific instruments to autonomously explore scientific problems—that is, to intelligently explore parameter spaces without human intervention, selecting high-value measurements to perform based on the continually growing experimental data set. Here, we develop such an autonomous decision-making algorithm that is physics-agnostic, generalizable, and operates in an abstract multi-dimensional parameter space. Our approach relies on constructing a surrogate model that fits and interpolates the available experimental data, and is continuously refined as more data is gathered. The distribution and correlation of the data is used to generate a corresponding uncertainty across the surrogate model. By suggesting follow-up measurements in regions of greatest uncertainty, the algorithm maximally increases knowledge with each added measurement. This procedure is applied repeatedly, with the algorithm iteratively reducing model error and thus efficiently sampling the parameter space with each new measurement that it requests. We validate the method using synthetic data, demonstrating that it converges to faithful replica of test functions more rapidly than competing methods, and demonstrate the viability of the approach in an experimental context by using it to direct autonomous small-angle (SAXS) and grazing-incidence small-angle (GISAXS) x-ray scattering experiments.

36 MATERIALS SCIENCE↗
NASA NTRS2005

Analysis of ICESat Data Using Kalman Filter and Kriging to Study Height Changes in East Antarctica

We analyze ICESat derived heights collected between Feb. 03-Nov. 04 using a kriging/Kalman filtering approach to investigate height changes in East Antarctica. The model's parameters are height change to an a priori static digital height model, seasonal signal expressed as an amplitude Beta and phase Theta, and height-change rate dh/dt for each (100 km)(exp 2) block. From the Kalman filter results, dh/dt has a mean of -0.06 m/yr in the flat interior of East Antarctica. Spatially correlated pointing errors in the current data releases give uncertainties in the range 0.06 m/yr, making height change detection unreliable at this time. Our test shows that when using all available data with pointing knowledge equivalent to that of Laser 2a, height change detection with an accuracy level 0.02 m/yr can be achieved over flat terrains in East Antarctica.

Herring, Thomas A.↗
NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Memarsadeghi, Nargess↗
NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Memarsadeghi, Nargess↗
DOE OSTI2022

Reliability estimation of an advanced nuclear fuel using coupled active learning, multifidelity modeling, and subset simulation

Tristructural isotropic (TRISO)-coated particle fuel is a robust nuclear fuel and determining its reliability is critical for the success of advanced nuclear technologies. However, TRISO failure probabilities are small and the associated computational models are expensive. Here we used coupled active learning, multifidelity modeling, and subset simulation to estimate the failure probabilities of TRISO fuels using several 1D and 2D models. With multifidelity modeling, we replaced expensive high-fidelity (HF) model evaluations with information fusion from two low-fidelity (LF) models. For the 1D TRISO models, we considered three multifidelity modeling strategies: only Kriging, Kriging LF prediction plus Kriging correction, and deep neural network (DNN) LF prediction plus Kriging correction. While the results across these multifidelity modeling strategies compared satisfactorily, strategies employing information fusion from two LF models called the HF model least often. Next, for the 2D TRISO model, we considered two multifidelity modeling strategies: DNN LF prediction plus Kriging correction (data-driven) and 1D TRISO LF prediction plus Kriging correction (physics-based). The physics-based strategy, as expected, consistently required the fewest calls to the HF model. However, the data-driven strategy had a lower overall simulation time since the DNN predictions are instantaneous, and the 1D TRISO model requires a non-negligible simulation time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2021

Weekly Mapping of Sea Ice Freeboard in the Ross Sea from ICESat-2

NASA’s ICESat-2 has been providing sea ice freeboard measurements across the polar regions since October 2018. In spite of the outstanding spatial resolution and precision of ICESat-2, the spatial sparsity of the data can be a critical issue for sea ice monitoring. This study employs a geostatistical approach (i.e., ordinary kriging) to characterize the spatial autocorrelation of the ICESat-2 freeboard measurements (ATL10) to estimate weekly freeboard variations in 2019 for the entire Ross Sea area, including where ICESat-2 tracks are not directly available. Three variogram models (exponential, Gaussian, and spherical) are compared in this study. According to the cross-validation results, the kriging-estimated freeboards show correlation coefficients of 0.56–0.57, root mean square error (RMSE) of ~0.12 m, and mean absolute error (MAE) of ~0.07 m with the actual ATL10 freeboard measurements. In addition, the estimated errors of the kriging interpolation are low in autumn and high in winter to spring, and low in southern regions and high in northern regions of the Ross Sea. The effective ranges of the variograms are 5–10 km and the results from the three variogram models do not show significant differences with each other. The southwest (SW) sector of the Ross Sea shows low and consistent freeboard over the entire year because of the frequent opening of wide polynya areas generating new ice in this sector. However, the southeast (SE) sector shows large variations in freeboard, which demonstrates the advection of thick multiyear ice from the Amundsen Sea into the Ross Sea. Thus, this kriging-based interpolation of ICESat-2 freeboard can be used in the future to estimate accurate sea ice production over the Ross Sea by incorporating other remote sensing data.

Satellite altimeter↗
DOE OSTI2019

Physics-Informed Machine Learning with Application to Solid Oxide Fuel Cell System Modeling and Optimization

Traditional data-driven machine learning (ML) techniques were combined with the physics-based SOFC-MP model toward improving SOFC system-level performance prediction. Four different physics-informed ML methods were proposed to demonstrate better prediction accuracy compared with traditional ML methods. First, it was preferred that the existing Kriging-based surrogate model not be entirely abandoned, so errors between Kriging regression prediction and true solution are learned using ML. The goal was to find the pattern of the error distribution as a function of model input so discrepancies between the Kriging prediction and true solution could be reduced by adding the additional ML-trained error term to the existing prediction. Second, deep neural networks (DNN) coupled with the mass balance model (MBM) have been developed to significantly decrease the reduced order model (ROM) prediction error with fewer training data compared to the traditional Kriging-based ROM and traditional DNN regression approaches. Third, DNN regression coupled with a neural networks (NN) classifier and MBM was developed. It provides superior performance on classifying the physically operational conditions for natural gas fuel cell (NGFC) than traditional classification approaches. Finally, two kinds of DNN transferring were studied and tested. One was transferring DNN for low-fidelity model data to a high-fidelity model. The second one was transferring DNN from state-of-the-art NGFC to advanced NGFC. These physic-informed ML frameworks can serve as a solid foundation for estimating U.S. Department of Energy-targeted fuel cell performance and exhibit great potential to be employed to other engineering applications.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2023

Physics-Informed Deep Learning for Reconstruction of Spatial Missing Climate Information in the Antarctic

Understanding the influence of the Antarctic on the global climate is crucial for the prediction of global warming. However, due to very few observation sites, it is difficult to reconstruct the rational spatial pattern by filling in the missing values from the limited site observations. To tackle this challenge, regional spatial gap-filling methods, such as Kriging and inverse distance weighted (IDW), are regularly used in geoscience. Nevertheless, the reconstructing credibility of these methods is undesirable when the spatial structure has massive missing pieces. Inspired by image inpainting, we propose a novel deep learning method that demonstrates a good effect by embedding the physics-aware initialization of deep learning methods for rapid learning and capturing the spatial dependence for the high-fidelity imputation of missing areas. We create the benchmark dataset that artificially masks the Antarctic region with ratios of 30%, 50% and 70%. The reconstructing monthly mean surface temperature using the deep learning image inpainting method RFR (Recurrent Feature Reasoning) exhibits an average of 63% and 71% improvement of accuracy over Kriging and IDW under different missing rates. With regard to wind speed, there are still 36% and 50% improvements. In particular, the achieved improvement is even better for the larger missing ratio, such as under the 70% missing rate, where the accuracy of RFR is 68% and 74% higher than Kriging and IDW for temperature and also 38% and 46% higher for wind speed. In addition, the PI-RFR (Physics-Informed Recurrent Feature Reasoning) method we proposed is initialized using the spatial pattern data simulated by the numerical climate model instead of the unified average. Compared with RFR, PI-RFR has an average accuracy improvement of 10% for temperature and 9% for wind speed. When applied to reconstruct the spatial pattern based on the Antarctic site observations, where the missing rate is over 90%, the proposed method exhibits more spatial characteristics than Kriging and IDW.

54 ENVIRONMENTAL SCIENCES↗