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DOE OSTI2019

A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 1: The 1-D case

In this first part of two papers, we extend the C-method developed in for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities in one space dimension. For gas dynamics, the C-method couples the Euler equations to a scalar reaction-diffusion equation, whose solution C serves as a space-time smooth artificial viscosity indicator. The purpose of this paper is the development of a high-order numerical algorithm for shock-wall collision and bounce-back. Specifically, we generalize the original C-method by adding a new collision indicator, which naturally activates during shock-wall collision. Additionally, we implement a new high-frequency wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We show that our scheme improves the order of accuracy of our WENO algorithm, handles extremely strong discontinuities (ranging up to nine orders of magnitude), allows for shock collision and bounce back, and removes high frequency noise. The causes of the well-known “wall heating” phenomenon are discussed, and we demonstrate that this particular pathology can be effectively treated in the framework of the C-method. This method is generalized to two space dimensions in the second part of this work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A quadratic programming flux correction method for high-order DG discretizations of S transport

In this work, we present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin (DG) discretizations of the S N transport equation, and we demonstrate the compatibility of this approach with the Variable Eddington Factor (VEF) method. The new fixup approach is sweep-compatible: during a transport sweep (block Gauss-Seidel iteration in which the scattering source is lagged), a local quadratic programming (QP) problem is solved in each spatial element to ensure that the solution satisfies certain physical constraints, including local particle balance. In this paper, we describe two choices of physical constraints, resulting in two variants of the method: QP Zero (QPZ) and QP Maximum Principle (QPMP). In QPZ, the finite element coefficients of the solution are constrained to be nonnegative. In QPMP, they are constrained to adhere to an approximate discrete maximum principle. There are two primary takeaways in this paper. First, when the positive Bernstein basis is used for DG discretization, the QPMP method eliminates negativities, preserves high-order accuracy for smooth problems, and significantly dampens unphysical oscillations in the solution. The latter feature – the dampening of unphysical oscillations – is an improvement upon standard, simpler fixup approaches such as the approach described in (denoted as the “zero and rescale” (ZR) method in this paper). This improvement comes at a moderate computational cost, but it is not prohibitive. Our results show that, even in an unrealistic worst-case scenario where 83% of the spatial elements require a fixup, the computational cost of performing a transport sweep with fixup is only ~31% greater than performing one without fixup. The second takeaway is that the VEF method can be used to accelerate the convergence of transport sweeps even when a fixup is applied. When optically thick regions are present, transport sweeps converge slowly, regardless of whether a fixup is applied, and acceleration is needed. However, attempting to apply standard diffusion synthetic acceleration (DSA) to fixed-up transport sweeps results in divergence for optically thick problems. Our results show that the same is not true for VEF. When VEF is combined with fixed-up transport sweeps, the result is a scheme that produces a nonnegative solution, converges independently of the mean free path, and, in the case of the QPMP fixup, adheres to an approximate discrete maximum principle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
DOE OSTI2022

CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multi-material ALE remap with interface sharpening using high-order matrix-free finite element methods

The arbitrary Lagrangian-Eulerian (ALE) technique involves remapping field quantities from a Lagrangian mesh to an optimized mesh in a conservative, accurate and bounds-preserving manner. For methods based on arbitrary order finite elements, as described in a reference, material volume fractions are advected in pseudo-time using flux-corrected transport (FCT) without any form of interface reconstruction. In practice, this can lead to excessive propagation of small volume fractions throughout the domain. In addition, this method requires assembly of a global advection matrix to compute the bounds-preserving low-order FCT solution. In this work, we introduce a new approach for ALE remap using a high-order matrix-free technique which incorporates a flux modification to sharpen material interfaces in a conservative manner. Our approach begins with computing a bounds-preserving low-order solution to the ALE remap equations at the element level. We then compute a sharp interface solution (not guaranteed to be bounds-preserving) which comes from solving an augmented version of the ALE remap equations with a conservative flux modification which acts to sharpen material volume fractions based on their gradients and transport directions. Using the sharp interface solution, we make global corrections to the bounds-preserving solution while maintaining preservation of bounds. By blending with the sharpened solution at the global level we are able to globally conserve mass without hindering the remap pseudo-time step. This new interface-aware ALE remap method is based entirely on partial assembly techniques where globally assembled matrix operators are no longer needed, resulting in a globally matrix-free FCT method for multi-material, multi-field ALE remap with high performance on GPU architectures. We present results of our new remap method on 1D, 2D and 3D benchmarks and describe the algorithmic tailoring for GPU architectures that was developed.

Vargas, Arturo [Lawrence Livermore National Labora↗
DOE OSTI2025

Performance evaluation of automated data-driven feature extraction and selection methods for practical and scalable building energy consumption prediction models

Here, this study quantifies the impact of automated feature engineering methods (feature extraction and selection) on the quality and accuracy of machine learning models that predict building energy consumption. The case study compares model performance for three main scenarios: baseline (no feature extraction and selection), feature extraction only, and feature extraction combined with feature selection (filter and/or wrapper methods) for fully trained machine learning models for 200 metered/sub-metered energy measurements across 118 real buildings. For consistency, the same machine learning model architecture (a black box deep learning neural network with probabilistic forecast output) was used for all scenarios. Based on results, all feature engineering methods provided noticeable prediction accuracy improvements (e.g., 29%-68% median prediction improvement) compared to baseline scenarios. However, in this application, feature selection methods provide little practical value due to their limited performance gains and high computational cost. Smarter algorithm development supported by better computational environments will be needed before feature selection methods can reliably and efficiently improve predictive model performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A parallel-in-time algorithm for variable step multistep methods

This paper presents a multigrid reduction in time (MGRIT) algorithm for achieving time parallelism using multistep backward difference formula (BDF) methods on variably-spaced temporal grids. This MGRIT approach transforms the linear multistep methods into single step methods applied to groups of time steps. Stability considerations are addressed through lowering of the order on coarse grids. The methods are presented for fixed and variable time step formulations. Furthermore, numerical results show moderate speedups for the heat equation as well as two IEEE power grid test problems characterized by nonlinear differential algebraic equations (DAE) of index 1. The performance of MGRIT with BDF is compared to MGRIT with Runge-Kutta for both the fixed and variable step methods of the same order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A correlation based fault detection method for short circuits in battery packs

Here this paper presents a fault detection method for short circuits based on the correlation coefficient of voltage curves. The proposed method utilizes the direct voltage measurements from the battery cells, and does not require any additional hardware or effort in modeling during fault detection. Moreover, the inherent mathematical properties of the correlation coefficient ensure the robustness of this method as the battery pack ages or is imbalanced in real applications. In order to apply this method online, the recursive moving window correlation coefficient calculation is adopted to maintain the detection sensitivity to faults during operation. An additive square wave is designed to prevent false positive detections when the batteries are at rest. The fault isolation can be achieved by identifying the overlapped cell in the correlation coefficients with fault flags. Simulation and experimental results validated the feasibility and demonstrated the advantages of this method.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Sample preparation methods for scanning electron microscopy of homogenized Al-Mg-Si billets: A comparative study

Characterization of Mg-Si precipitates is crucial for optimizing the homogenization heat treatment of Al-Mg-Si alloys. Although sample preparation is key for high quality scanning electron microscopy imaging, most common methods lead to dealloying of Mg-Si precipitates. In this article we systematically evaluate different sample preparation methods: mechanical polishing, etching with various reagents, and electropolishing using different electrolytes. We demonstrate that the use of a nitric acid and methanol electrolyte for electropolishing a homogenized Al-Mg-Si alloy prevents the dissolution of Mg-Si precipitates, resulting in micrographs of higher quality. This preparation method is investigated in depth and the obtained scanning electron microscopy images are compared with transmission electron micrographs: the shape and size of Mg-Si precipitates appear very similar in either method. The scanning electron micrographs allow proper identification and measurement of the Mg-Si phases including needles with lengths of roughly 200 nm. These needles are β″ precipitates as confirmed by high resolution transmission electron microscopy. - Highlights: •Secondary precipitation in homogenized 6xxx Al alloys is crucial for extrudability. •Existing sample preparation methods for SEM are improvable. •Electropolishing with nitric acid/methanol yields superior quality in SEM. •The obtained micrographs are compared to TEM micrographs.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Synthesis and photoluminescent properties of Sr{sub (1−x)}Si{sub 2}O{sub 2}N{sub 2}: xEu{sup 2+} phosphor prepared by polymer metal complex method for WLEDs applications

Highlights: • SrSi{sub 2}O{sub 2}N{sub 2}: Eu{sup 2+} phosphor was prepared by polymer metal complex (pechini method). • The annealing time was decreased from 6 h in solid state method to 3 h. • The particles are crystalline and dispersed well with average size 6.5 μm. - Abstract: Green emitting Sr{sub (1−x)}Si{sub 2}O{sub 2}N{sub 2}: xEu{sup 2+} (x = 0, 0.02, 0.04, 0.06, 0.08 and 0.1) phosphors were synthesized by polymer metal complex or pechini method. The XRD results confirm the formation of a pure phase at 1400 °C for 3 h. The SEM and particles size results indicate that the prepared phosphor consists of a polyhedral crystalline shape with well dispersed and the average particle size around 6.5 μm. The maximum PL intensity was found at 0.04% Eu{sup 2+} with a wide emission band between 460 and 640 nm and a green emission peak at 531.4 nm. The external quantum efficiency of 0.04% Eu{sup 2+} sample was 43.13%. The results indicate that pechini method is an alternative way and close in efficiency to the solid state method to prepare SrSi{sub 2}O{sub 2}N{sub 2} phosphor with higher homogeneity and more uniform size distribution for near UV and blue region applications for white light emitting diodes WLEDs.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accurately measuring the ionic conductivity of membranes via the direct contact method

Accurately measuring the ionic conductivity of membranes is important both for assessing the performance of new membranes as well as for advancing the fundamental understanding of electric field-driven ion transport in membranes. Yet, despite a considerable number of reports on the topic, there is no standardized method for ionic conductivity measurements. One of the main challenges with ionic conductivity measurements is isolating the membrane resistance from the other resistances in the electrochemical cell. In this study, we present a detailed discussion of factors that affect ionic conductivity measurements with the commonly used direct contact method, in which the membrane contacts the electrodes. Such factors include external resistances due to imperfect contact between the membrane and electrodes, residual impedances due to the sample holder and wiring, and fringe effects. Further, we also present and validate simple methods for isolating the true membrane ionic conductivity in both the through-plane and in-plane orientations. These methods can be implemented with virtually any membrane to obtain accurate and reproducible ionic conductivity values. Finally, we outline recommendations for performing ionic conductivity measurements with the direct contact method and a set of parameters to verify when reporting these results.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Novel method for accurately estimating membrane transport properties and mass transfer coefficients in reverse osmosis

Here, we present a simple and robust method to simultaneously characterize the water and salt permeability (A, B) of reverse osmosis (RO) membranes and mass transfer coefficient (k) in membrane modules. The proposed methodology comprises a set of RO experiments performed at different operating pressures or stages. The measured water and salt fluxes in each stage are simultaneously fitted to the RO transport equations by performing a non-linear regression, using A, B, and k as regression parameters. We first perform a systematic accuracy analysis of the proposed method across the full operational range of RO. The assessment shows that the method accuracy is substantially higher than current methods and increases with number of experimental stages and driving forces. This assessment is used to inform the design of an experimental protocol that minimizes errors in estimated A, B, and k. We then evaluate two commercial RO membranes following the new protocol. For both membranes, A and B parameters decrease by 17% and 15% from the dilute solution to seawater concentrations, whereas the k parameter remains constant. Our study demonstrates that the proposed method, informed by data-driven experimental designs, provides a new approach for accurately characterizing transport phenomenon in membrane processes with feeds of less than 100 g/L total dissolved solids.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Method for system-independent material characterization from spectral X-ray CT

We propose a method for material characterization using Spectral X-ray Computed Tomography (SCT). Our SCT method takes advantage of recently-developed MultiX ME 100 photon counting detectors to simultaneously measure the energy dependence of a material's linear attenuation coefficient (LAC). Relative electron density (ρ e ) and effective atomic number (Z e ) are estimated directly from the energy-dependent LAC measurements. The method employs a spectral correction algorithm and automated selection and weighting of the energy bins for optimized performance. When examining materials with Z e ≤ 23, this method achieves accuracy comparable to traditional dual-energy CT, which is often realized through consecutive data acquisitions, and is compatible with any spectral detector. The method disregards data in photon starved energy channels improving the detection of highly attenuating materials, compared to techniques that use energy integrating detectors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

A method to measure prompt fission neutron spectrum using gamma multiplicity tagging

In order to improve on current prompt fission neutron spectrum measurements, a gamma multiplicity tagging method was developed at the Rensselaer Polytechnic Institute Gearttner Linear Accelerator Center. This method involves using a coincidence requirement on an array of BaF 2 gamma detectors to determine the timing of a fission event. This allows for much larger fission samples to be used due to the higher penetrability of gammas compared to fission fragments. Additionally, since the method relies on gammas as opposed to fission fragments, the effects of the low level discriminator, used in fission chambers to eliminate alpha events, are not seen. A 252 Cf fission chamber was constructed in order to determine the viability of this method as well as the efficiency when compared to a fission chamber. The implemented multiple gamma tagging method was found to accurately reproduce the prompt fission neutron spectrum for the spontaneous fission of 252 Cf and to detect 30% of fission events.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

New method for level-lifetime measurements with thick scintillators

Level lifetimes provide key insight into the structure of atomic nuclei and serve as stringent tests of theoretical descriptions. Though several methods for determining level lifetimes exist for both reaction measurements and decay studies, here the focus is on techniques involving the direct measurement of time differences between population and subsequent depopulation of excited states. The techniques presented herein are broadly applicable across multiple timing ranges, but the approach is specifically described for the βγ timing method. A multi-step, amplitude-dependent time walk correction was employed to address the data analysis complications that arise from using thick scintillators for electron detection. Further, additional corrections for the depth of the interaction must also be performed when the parent isotope has been implanted into the detector. Techniques are presented for performing these time walk and depth of interaction corrections. Subsequently, a new Monte Carlo method utilizing measured detector responses obtained from the data, coupled with chi-square minimization, is presented for extracting excited state lifetimes ≳ 100 picoseconds. The framework of this Monte Carlo method is developed for the decay of a state in 68 Zn with a known 1.6 ps half life, which is considered prompt given the detection sensitivity of the technique, and then benchmarked using two other excited states in neutron-rich Ni isotopes with 120(34) ps and 1.05(3) ns half lives. Using this new method which takes into account the thick scintillator used, these same half lives were measured to be 135(10) ps and 1.04(24) ns, respectively. The overall good agreement demonstrates the validity of the technique.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Diagnosing nuclear power plant pipe wall thinning due to flow accelerated corrosion using a passive, thermal non-destructive evaluation method: Feasibility assessment via numerical experiments

Flow accelerated corrosion (FAC) in nuclear power plant pipes is one of the leading causes of accidents, fatalities, damage and outages. Current FAC identification methods employ expensive sensing technology and are “active” methods, where the response of the piping system to an externally-generated thermal, mechanical or optical excitation must be measured. As a result, these techniques require a disruptive and time-consuming setup. Here we propose a method that utilizes pipe surface temperature measurements to passively monitor for FAC-induced pipe wall thinning without the need for expensive equipment or post-installation setup time. This diagnostic method utilizes a simulation data-driven diagnostic model to estimate the amount of thickness reduction in a pipe based on changes in measured steady-state pipe temperatures. In order to reduce the computational burden of generating large, simulation-based datasets, the behavior of the insulation of the pipe was modeled using a suitably calibrated heat transfer boundary parameter. Additionally, global sensitivity analysis was performed to determine system parameter(s), such as the temperature of water flowing inside the pipe, which significantly affect the steady state pipe wall temperature and could cause errors in diagnosis. Two diagnostic models, one using only the change in steady-state temperature as an indicator for FAC-induced pipe wall thinning and the other using water temperature as an additional diagnostic model input were evaluated for their ability to estimate thickness reductions in a pipe using simulated pipe wall temperature data. For the numerical experiments conducted in this work, both models estimated wall thickness with errors within 0.5 mm, indicating that the proposed technique can potentially be used as a low-cost, first-pass method for FAC monitoring.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗