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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An Iterative Response-Surface-Based Approach for Chance-Constrained AC Optimal Power Flow Considering Dependent Uncertainty

A modern power system is characterized by a stochastic variation of the loads and an increasing penetration of renewable energy generation, which results in large uncertainties in its states. These uncertainties bring formidable challenges to the power system planning and operation process. To address these challenges, we propose a cost-effective, iterative response-surface-based approach for the chance-constrained AC optimal power-flow problem that aims to ensure the secure operation of the power systems considering dependent uncertainties. Starting from a stochastic-sampling-based framework, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose, instead of using the original complicated power-system model, to rely on a polynomial-chaos-based response surface. This response surface allows us to efficiently evaluate the time-consuming power-system model at arbitrary distributed sampled values with a negligible computational cost. This further enables us to efficiently conduct an online stochastic testing for the system states that not only screens out the statistical active constraints, but also assists in a better design of the tightened bounds without using any Gaussian or symmetric assumption. Finally, an iterative procedure is executed to fine-tune the optimal solution that better satisfies a predefined probability. The simulations conducted in multiple test systems demonstrate the excellent performance of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Learning Distribution Grid Topologies: A Tutorial

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. Here this tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Surrogate Model for Distribution Networks Influenced by Weather

Here, we propose a method for generating reduced representations of time series and for constructing low dimensional surrogate models for time dependent calculations of power and voltage in distribution networks. We employ Fourier polynomials. The surrogate model strategy is aimed at reducing the computational cost of time dependent simulations, albeit, at the expense of fidelity. The reduced representation is achieved by identifying a small and most consequential subset of degrees of freedom. In power and voltage distribution networks dynamics that are heavily influenced by strong cyclic weather events, e.g., the hourly, diurnal and seasonal cycles, the weather/climate time series spectrum exposes these most energetic components. Once the degrees of freedom are identified their amplitudes are optimized using training data. The key challenge in using spectral methods in power network surrogates is addressing the computation of quotients. For this we propose a numerically-stable deconvolution strategy.

Weather events↗
DOE OSTI2020

In Situ Oxygen Isotope Determination in Serpentine Minerals by SIMS: Addressing Matrix Effects and Providing New Insights on Serpentinisation at Hole BA1B (Samail ophiolite, Oman)

The ability to constrain the petrogenesis of multiple serpentine generations recorded at the microscale is crucial for estimating the extent and conditions of modern versus fossil serpentinisation in ophiolites. To address matrix bias effects during oxygen isotope analysis by SIMS, we present the first investigation analysing antigorite in the compositional range Mg# = 77.5–99.5 mole %, using a CAMECA IMS–1280 secondary ion mass spectrometer. Spot–to–spot homogeneity is ≤ 0.5‰ (2s) for the new antigorite reference materials. The relative bias between antigorite reference materials with different Mg/Fe ratios is described by a second order polynomial, and a maximum difference in bias of ~ 1.8‰ was measured for Mg# ~ 78 to 100. We observed a bias up to ~ 1.0‰ between lizardite and antigorite attributed to their different crystal structure. Orientation effects up to ~ 1‰ were observed in chrysotile. The new analytical protocol allowed the identification of oxygen isotope zoning up to ~ 7‰ in serpentine minerals from two serpentinites recovered from an area of active serpentinisation in the Samail ophiolite. Furthermore in situ analysis is capable of resolving isotopic heterogeneity that may directly reflect changes in the physical and chemical conditions of multiple serpentinisation events in the Samail ophiolite.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Processing Aleatory and Epistemic Uncertainties in Experimental Data From Sparse Replicate Tests of Stochastic Systems for Real-Space Model Validation

This paper presents a practical methodology for propagating and processing uncertainties associated with random measurement and estimation errors (that vary from test-to-test) and systematic measurement and estimation errors (uncertain but similar from test-to-test) in inputs and outputs of replicate tests to characterize response variability of stochastically varying test units. Also treated are test condition control variability from test-to-test and sampling uncertainty due to limited numbers of replicate tests. These aleatory variabilities and epistemic uncertainties result in uncertainty on computed statistics of output response quantities. The methodology was developed in the context of processing experimental data for “real-space” (RS) model validation comparisons against model-predicted statistics and uncertainty thereof. The methodology is flexible and sufficient for many types of experimental and data uncertainty, offering the most extensive data uncertainty quantification (UQ) treatment of any model validation method the authors are aware of. It handles both interval and probabilistic uncertainty descriptions and can be performed with relatively little computational cost through use of simple and effective dimension- and order-adaptive polynomial response surfaces in a Monte Carlo (MC) uncertainty propagation approach. A key feature of the progressively upgraded response surfaces is that they enable estimation of propagation error contributed by the surrogate model. Sensitivity analysis of the relative contributions of the various uncertainty sources to the total uncertainty of statistical estimates is also presented. Finally, the methodologies are demonstrated on real experimental validation data involving all the mentioned sources and types of error and uncertainty in five replicate tests of pressure vessels heated and pressurized to failure. Simple spreadsheet procedures are used for all processing operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Prediction and Validation of Flow Properties in Porous Lattice Structures

High-porosity metal foams have been extensively studied as an attractive candidate for efficient and compact heat exchanger design. With the advancements in additive manufacturing, such foams can be manufactured with controlled topology to yield highly tailorable mechanical and transport properties. In this study, a lattice Boltzmann method (LBM)-based pore-scale model is implemented to simulate the fluid flow in additively manufactured (AM) metal foams with unit cell topologies of Cube, Face Diagonal (FD)-Cube, Tetrakaidecahedron (TKD), and Octet lattices. The pressure gradient versus average velocity profiles predicted by the LBM model were validated against in-house measurements on the AM lattice samples with the same unit cell topologies. Based on the simulation results, a novel hybrid model is proposed to accurately predict the volume averaged flow properties (permeability and inertial coefficients) of the four structures. Specifically, the linear LBM (neglecting inertial forces) is first implemented to obtain the intrinsic permeability, and then the standard LBM is applied to obtain the inertial coefficient. Convenient correlations for those flow properties as a function of porosity and fiber diameter are constructed. The effects of the AM print qualities on the flow properties are also discussed. The advantages of the hybrid model compared to the polynomial fitting approach for determining flow properties are discussed and compared quantitatively. The hybrid model and presented results are valuable for flow and thermal transport evaluation when designing new metal foams for specific applications and with different materials and topologies. Finally, the presented correlations based on pore-scale simulations can also be conveniently used in volume-averaged models to predict the macroscale flow behavior in such complex structures.

42 ENGINEERING↗
DOE OSTI2024

Material Model Parameters Optimization in Liquid Mercury Target Dynamics Simulation With Machine Learning Surrogates

A pulsed spallation target is subjected to very short (∼0.7μs) but intense loads (23.3 kJ) from repeated proton pulses, which knock away neutrons from the mercury atoms’ nuclei for a wide range application in physics, engineering, medicine, petroleum exploration, biology, chemistry, etc. The effect of this pulsed loading on the stainless-steel target module which contains the flowing mercury target material is difficult to predict not only due to its short but intense explosive-like physical reaction, but also the nonlinear material behavior of the liquid mercury in the structure. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at high power level stage. However, prediction of the resultant loading on the target is more difficult when helium gas is intentionally injected into the mercury. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. A parameter sensitivity study was firstly employed to understand their impact on the simulation strains. The investigated parameters included E, μ, γ, σ, n, VFgas, and gas cumulative volume curve control parameters a and b. Verification and validation results from sparse polynomial expansions (SPE) method and directional Gaussian smoothing (DGS) optimization show that the surrogate model had training error of ∼7% and validation error of ∼15%, indicating that machine learning methods and surrogate models can help optimize the uncertain parameters in the complex 2-phase material model. This approach is expected to fill the knowledge gap between unknown liquid-gas mixture material model and measured vessel strain responses.

Lin, Lianshan↗
DOE OSTI2020

Analytical expressions of the surface shape of ‘diaboloid’ mirrors

Modern deterministic polishing processes allow fabrication of x-ray optics with almost any arbitrary aspherical surface shape. Among these optics, the so called "diaboloid"mirror is of special interest. The diaboloid mirror that converts a cylindrical wave to a spherical wave would improve focusing in x-ray beamlines implementing a diffraction element between a parabolic cylinder and a toroidal mirror. The replacement of the toroidal mirror in existing beamlines by the diaboloid mirror would mitigate aberrations. The shape of the diaboloid mirror is usually calculated numerically based on a truncated polynomial solution of the optical path problem. Here, we present an exact analytical solution for the shape of a diaboloid mirror as a function of the conjugate parameters of the mirror placed in a beamline. The derived analytical expressions for the diaboloid mirror in both the canonical and mirror-based coordinate systems are implemented in ray-tracing simulations to verify the beamline performances.

Yashchuk, Valeriy V.↗
DOE OSTI2020

Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis

An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies, revealing a rich dataset consisting of up to 19 measurements of the third-order complex modulus at distinct three-frequency coordinates. We discuss how the choice of input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and reducing variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting dataset is indeed large and feature-rich, while still acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represent measurements of an intrinsic material function by studying its internal consistency, compatibility with low-frequency predictions for Coleman–Noll simple fluids, and agreement with data obtained via MAOS amplitude sweeps. Finally, the data are compared to predictions from the corotational Maxwell model to demonstrate the power of MAPS rheology in determining whether a constitutive model is consistent with a material’s time-dependent response.

Lennon, Kyle R. (ORCID:0000000212515461)↗
DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on finite element method--spectral element method (FEM-SEM) equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order (p = 1) finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in the polynomial degree of the high-order operator, requiring specialized solvers to treat the anisotropy. We make use of an element-structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in h and p. The method is extended to interior penalty and Bassi and Rebay (BR2) discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Finally, numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods

In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-Driven Learning of Nonautonomous Systems

In this work, we present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Adaptive Time Step Control for Multirate Infinitesimal Methods

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Projective Integral Updates for High-Dimensional Variational Inference

Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. Furthermore, this integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.

Gaussian mean-field↗