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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

A kriging and entropy-based approach to raingauge network design

Highlights: • A kriging and entropy theory-based approach is developed for gauge network design. • The method considers both minimum estimating error andoptimum rainfall information. • The best combination is verified to be effectiveto achieve final goals. Hydrological data, such as precipitation, is fundamental for planning, designing, developing, and managing water resource projects as well as for hydrologic research. An optimal raingauge network leads to more accurate estimates of mean or point precipitation at any site over the watershed. Some studies in the past have suggested increasing gauge network density for reducing the estimation error. However, more stations mean more cost of installation and monitoring. This study proposes an approach on the basis of kriging and entropy theory to determine an optimal network design in the city of Shanghai, China. Unlike the past studies using kriging interpolation and entropy theory for network design, the approach developed in the current study not only used the kriging method as an interpolator to determine rainfall data at ungauged locations but also incorporated the minimum kriging standard error (KSE) and maximum net information (NI) content. The approach would thus lead to an optimal network and would enable the reduction of kriging standard error of precipitation estimates throughout the watershed and achieve an optimum rainfall information. This study also proposed an NI-KSE-based criterion which is dependent on a single-objective optimization. To evaluate the final optimal gauge network, areal average rainfall was estimated and its accuracy was compared with that obtained with the existing rain gauge network.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Quantile Kriging R Package

A re-implementation of Quantile Kriging. Quantile Kriging was described by Matthew Plumlee & Rui Tuo in their 2014 paper "Building Accurate Emulators for Stochastic Simulations via Quantile Kriging." With computational savings when dealing with replication from the recent paper "Practical heteroskedastic Gaussian process modeling for large simulation experiments”, it is now possible to apply Quantile Kriging to a wider class of problems. In addition to fitting the model, other useful tools are provided such as the ability to automatically perform leave-one-out cross validation.

Quinlan, KevinR.↗
DOE OSTI2017

Evaluation of kriging based surrogate models constructed from mesoscale computations of shock interaction with particles

Macro-scale computations of shocked particulate flows require closure laws that model the exchange of momentum/energy between the fluid and particle phases. Closure laws are constructed in this work in the form of surrogate models derived from highly resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the least number of mesoscale simulations. It is shown that if the input data is noise-free, the DKG method converges monotonically; convergence is less robust in the presence of noise. The MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. This work is the first step towards a full multiscale modeling of interaction of shocked particle laden flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Variational multiscale element-free Galerkin method combined with the moving Kriging interpolation for solving some partial differential equations with discontinuous solutions

Solving partial differential equations with discontinuous solutions is an important challenging problem in numerical analysis. To this end, there are some methods such as finite volume method, discontinuous Galerkin approach and particle technique that are able to solve these problems. In the current paper, the moving Kriging element-free Galerkin method has been combined with the variational multiscale algorithm to obtain acceptable and high-resolution solutions. For testing this technique, we select some PDEs with discontinuous solution such as Burgers’, Sod’s shock tube, advection–reaction–diffusion, Kuramoto–Sivashinsky, Boussinesq and shallow water equations. First, we obtain a time-discrete scheme by approximating time derivative via finite difference technique. Then we introduce the moving Kriging interpolation and also obtain their shape functions. We use the element-free Galerkin method for approximating the spatial derivatives. This method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the classical element-free Galerkin method test and trial functions are moving least squares approximation (MLS) shape functions. Since the shape functions of moving least squares (MLS) approximation do not have Kronecker delta property, we cannot implement the essential boundary condition, directly. Thus, we employ the shape functions of moving Kriging interpolation and radial point interpolation technique which have the mentioned property. Also, in the element-free Galekin method, we do not use any triangular, quadrangular or other type of meshes. The element-free Galerkin method is a global method while finite element method is a local one. This technique employs a background mesh for integration which makes it different from the truly mesh procedures. Several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Advances in Kriging-Based Autonomous X-Ray Scattering Experiments

Autonomous experimentation is an emerging paradigm for scientific discovery, wherein measurement instruments are augmented with decision-making algorithms, allowing them to autonomously explore parameter spaces of interest. We have recently demonstrated a generalized approach to autonomous experimental control, based on generating a surrogate model to interpolate experimental data, and a corresponding uncertainty model, which are computed using a Gaussian process regression known as ordinary Kriging (OK). We demonstrated the successful application of this method to exploring materials science problems using x-ray scattering measurements at a synchrotron beamline. Here, we report several improvements to this methodology that overcome limitations of traditional Kriging methods. The variogram underlying OK is global and thus insensitive to local data variation. We augment the Kriging variance with model-based measures, for instance providing local sensitivity by including the gradient of the surrogate model. As with most statistical regression methods, OK minimizes the number of measurements required to achieve a particular model quality. However, in practice this may not be the most stringent experimental constraint; e.g. the goal may instead be to minimize experiment duration or material usage. We define an adaptive cost function, allowing the autonomous method to balance information gain against measured experimental cost. We provide synthetic and experimental demonstrations, validating that this improved algorithm yields more efficient autonomous data collection.

36 MATERIALS SCIENCE↗
DOE OSTI2019

A Kriging Surrogate Model for Computing Gas Mixture Equations of State

Accurate simulation of the complex flow following the detonation of an explosive material is a challenging problem. In these flows, the detonation products of the explosive must be treated as a real gas while the surrounding air is treated as an ideal gas. As the detonation process unfolds and the blast wave moves into the surrounding ambient air, the products of detonation expand outward and interact with the air creating a mixture region. In this region, both of the state equations for air and the products must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between the equations of state until both pressure and temperature reach an equilibrium inside of a computational cell. Since this mixture region moves and grows over time, this algorithm must be performed millions, or even billions, of times in a typical detonation simulation. As such, these calculations can account for a large percentage of the overall solution time. This work aims to use a kriging surrogate model to replace this process. The iterative method solves a nonlinear system of equations created from the gas mixture density, internal energy, and composition using a Broyden iterative solver to obtain an output pressure and temperature. Kriging is used to produce curve fits which interpolate selected pressures and temperatures from this solver from appropriate ranges of the mixture input quantities. Using a finite volume hydrocode, the performance of the model with respect to the iterative solver is demonstrated in the simulation of a pentaerythritol tetranitrate (PETN) charge detonation. The model's computational speed and accuracy are quantified as a function of the choice of sampling points in order to try optimize the combination as well as to show the benefits of this novel approach.

Engineering↗
DOE OSTI2018

Population parametrization of costly black box models using iterations between SAEM algorithm and kriging

In this article we focus on parametrization of black box models from repeated measurements among several individuals (population parametrization). We introduce a variant of the SAEM algorithm, called KSAEM algorithm, which couples the standard SAEM algorithm with the dynamic construction of an approximate metamodel. The costly evaluation of the genuine black box is replaced by a kriging step, using a basis of precomputed values, basis which is enlarged during SAEM algorithm to improve the accuracy of the metamodel in regions of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

An adaptive Kriging surrogate method for efficient uncertainty quantification with an application to geological carbon sequestration modeling

We present that in numerical modeling of geological carbon sequestration (GCS), uncertainty quantification (UQ) is usually needed to evaluate the impact of uncertain model parameters on model predictions caused by limited measurements and incomplete knowledge of the parameters. However, UQ for GCS is computationally expensive due to the large ensemble of complex and lengthy model simulations. In this study, we propose an adaptive Kriging method to build a fast-to-evaluate surrogate of the GCS model to alleviate the heavy computational burden. The surrogate model is efficiently generated using a Taylor expansion-based adaptive experimental design algorithm that combines a distance-based exploration criterion and an exploitation criterion to adaptively search for informative training samples. In addition, we analyze the uncertainty brought by substituting the surrogate for the actual simulation model and explore its influence on UQ results. Lastly, our method is demonstrated in a synthetic GCS model and its performance is evaluated in comparison with the conventional Monte Carlo sampling. Results indicate that our method can greatly improve the computational efficiency in UQ and provide an effective and reliable UQ solution with the consideration of surrogate uncertainty.

58 GEOSCIENCES↗
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 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↗
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↗
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↗