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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

New methods of fragmentary approximation of a function

Certain special methods of fragmentary approximation of a function are examined and the properties of the most widespread elementary functions for such approximation methods are investigated, for the purpose of developing useful characteristics and properties for practical realization, in particular, for their reproduction by analog functional converters, with a significantly smaller number of controlable or adjustable parameters than in known ones.

Kolesnichenko, S. G.↗
DOE OSTI2025

Coherency-Constrained Spectral Clustering for Power Network Reduction

This paper presents a methodology for reducing the complexity of large-scale power network models using spectral clustering, aggregation of electrical components, and cost function approximation. Two approaches are explored using unconstrained and constrained spectral clustering to determine areas for effective system reduction. Once the system areas are determined, both loads and generators by type are aggregated, and their new cost function is approximated through polynomial curve-fitting or statistical methods. The performance of reduced networks is evaluated in terms of their ability to follow the true daily cost of the original system over a 24-hour period considering a set of several days. Two test systems are taken as test beds. Application of the methodology to a modified version of the IEEE 39-bus system reduces it from 17 generators to a 4-bus system and 9 generators with about 93% of accuracy. Similarly, the IEEE 118-bus system is reduced from 19 generators to a 3-bus system with three aggregated units achieving over 99% of accuracy. These findings address scalability challenges and enhance accuracy for high and mid-loading level conditions, and by aggregating thermal units with similar cost functions.

42 ENGINEERING↗
DOE OSTI2023

DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories

This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1989

Global properties of pseudospectral methods

The present application of polynomial interpolation methods to function-approximation and numerical solutions for hyperbolic and elliptic PDEs allows the explicit construction of the derivative matrix for a general sequence of collocation points. An evaluation of the effect of several factors on the performance of these methods indicates an inability to interpret global methods in terms of local ones; the accuracy of the approximation will differ when the function's large gradients occur near the center of the region or near the boundary, irrespective of the boundary vicinity's collocation-point density.

Solomonoff, A.↗
DOE OSTI2021

Confronting Domain Shift in Trained Neural Networks

Neural networks (NNs) are known as universal function approximators and can interpolate nonlinear functions between observed data points. However, when the target domain for deployment shifts from the training domain and NNs must extrapolate, the results are notoriously poor. Prior work Martinez et al. (2019) has shown that NN uncertainty estimates can be used to correct binary predictions in shifted domains without retraining the model. We hypothesize that this approach can be extended to correct real-valued time series predictions. As an exemplar, we consider two mechanical systems with nonlinear dynamics. The first system consists of a spring-mass system where the stiffness changes abruptly, and the second is a real experimental system with a frictional joint that is an open challenge for structural dynamicists to model efficiently. Our experiments will test whether 1) NN uncertainty estimates can identify when the input domain has shifted from the training domain and 2) whether the information used to calculate uncertainty estimates can be used to correct the NN’s time series predictions. While the method as proposed did not significantly improve predictions, our results did show potential for modifications that could improve models’ predictions and play a role in structural health monitoring systems that directly impact public safety.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Estimation of correlation functions by stochastic approximation.

Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.

Habibi, A.↗
NASA NTRS1987

Performance evaluation of fault tolerant systems represented by Markov models

A method to evaluate the performance of fault tolerant systems whose configuration can be represented by time-invariant, discrete-time, discrete-state Markov models is introduced. Each state is assumed to be associated with a constant qualitative measure of the system's performance. The method first computes the moments of the performance probability mass function (PMF) and then finds an approximating function that has the same moments. The form of this function is a maximum entropy solution of the moment matching problem. A simple algorithm for calculating the necessary moments is derived and a method for finding the approximate performance PMF is suggested. After some modification, the method is applied to an example, the Inertial Upper Stage navigation system.

Missana, Jean-Olivier A. A.↗
DOE OSTI2023

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange–correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew–Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn–Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional and barrier heights of the BH6 database better than some of the most widely used hybrid functionals. The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). Furthermore, this work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials (CCDM) August 1, 2014 - July 31, 2018; Center for Complex Materials from First Principles (CCM) August 1, 2018 - July 31, 2021 (Final Report)

The mission of the DOE Energy Frontier Research Centers CCDM (2014-2018) and CCM (2018-2021) was to theoretically develop, computationally apply, and experimentally validate electronic structure methods for all materials, with a focus on the complex materials, especially layered and two-dimensional materials, strongly-correlated materials, and liquid water. This was achieved by over 200 published journal articles authored by about 17 senior investigators from physics and chemistry and from theory, computation, and experiment, plus their collaborators. In particular, the Centers confirmed the predictive power of the SCAN (strongly constrained and appropriately normed) density functional, which was constructed to satisfy 17 known exact constraints and several appropriate norms. Without being fitted to real bonded systems, and at a modest computational cost, SCAN correctly predicted covalent, ionic, metallic, hydrogen, and van der Waals bonds in many challenging materials. SCAN gave an improved description of defects in semiconductors, surface properties of metals, seven phases of ice, liquid water, liquid and supercooled silicon, subtle structural distortions in ferroelectrics, formation energies and structural predictions for solids, and critical pressures for structural phase transitions. Perhaps most remarkably, SCAN correctly described some strongly-correlated materials that were previously believed to be beyond the reach of density-functional approximations. SCAN is the only density functional that correctly predicts the band gap closing under chemical doping of the cuprate high-temperature superconducting materials. SCAN also predicts a landscape of competing stripe and magnetic phases in the cuprates. For some materials with some codes, SCAN has convergence problems that are greatly reduced by the CCM-developed r 2 SCAN, without loss of accuracy or rigor. SCAN and r 2 SCAN still make some self-interaction error, which is greatly reduced by the CCDM/ CCM-developed local orbital scaling correction (LOSC). These Centers further proved that the fundamental energy gaps of a solid from an orbital energy difference and from total energy differences are the same for a large class of generalized Kohn-Sham (GKS) functionals, including SCAN and standard hybrid functionals, and that symmetry breaking arises when a dynamic density fluctuation drops to zero frequency. The Centers identified new mechanisms for catalysis in layered materials with ions intercalated between the layers, investigated charge density waves both in model systems and in real layered materials, studied changes of band gap with the number of layers, and explored topological ultrathin films, bent nanoribbons, and defects.

08 HYDROGEN↗
NASA NTRS1985

Molecular processes in a high temperature shock layer

The development of techniques for the calculation of electron capture widths, electronic wave functions, cross sections and rates needed for the description of the dissociative recombination (DR) of molecular ions with electrons were described. The cross sections and rates were calculated by using harmonic oscillator wave functions for the ion and a delta function approximation for the continuum vibrational wave function in the repulsive dissociative channel. In order to obtain DR cross sections of quantitative accuracy, a computer program which solves the one dimensional nuclear motion wave equation was revised to calculate the cross sections and rates. The program and the new results are described. Included is a discussion of large windows found in the dissociative recombination cross sections from excited ion vibrational levels. These windows have not been previously reported in the literature. The magnitude of the DR cross sections for several dissociative routes are sensitive to the location of the crossing of the neutral and ion potential curves. Studies of the effects of basis set and CI wave function size on vertical excitation energies are described. Preliminary studies on N2 and O2 using large scale wave functions are also reported.

Guberman, S. L.↗
NASA NTRS1993

Experiment-specific cosmic microwave background calculations made easier - Approximation formula for smoothed delta T/T windows

Simple and easy to implement elementary function approximations are introduced to the spectral window functions needed in calculations of model predictions of the cosmic microwave backgrond (CMB) anisotropy. These approximations allow the investigator to obtain model delta T/T predictions in terms of single integrals over the power spectrum of cosmological perturbations and to avoid the necessity of performing the additional integrations. The high accuracy of these approximations is demonstrated here for the CDM theory-based calculations of the expected delta T/T signal in several experiments searching for the CMB anisotropy.

Gorski, Krzysztof M.↗
DOE OSTI2018

Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number

Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps, and excitation energies. Here, we present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C 12 H 14 polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge-based data point could therefore permit fitting/tuning of functionals with lower delocalization error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

Experimental determination of the particle motions associated with the low order acoustic modes in enclosures

A procedure for experimentally determining, in terms of the particle motions, the shapes of the low order acoustic modes in enclosures is described. The procedure is based on finding differentiable functions which approximate the shape functions of the low order acoustic modes when these modes are defined in terms of the acoustic pressure. The differentiable approximating functions are formed from polynomials which are fitted by a least squares procedure to experimentally determined values which define the shapes of the low order acoustic modes in terms of the acoustic pressure. These experimentally determined values are found by a conventional technique in which the transfer functions, which relate the acoustic pressures at an array of points in the enclosure to the volume velocity of a fixed point source, are measured. The gradient of the function which approximates the shape of a particular mode in terms of the acoustic pressure is evaluated to give the mode shape in terms of the particle motion. The procedure was tested by using it to experimentally determine the shapes of the low order acoustic modes in a small rectangular enclosure.

Byrne, K. P.↗
NASA NTRS1945

Numerical Evaluation by Harmonic Analysis of the (Epsilon)-Function of the Theodorsen Arbitrary-Airfoil Potential Theory

Finite trigonometric series is fitted by harmonic analysis as an approximation function to the psi function of the Theodorsen arbitrary-airfoil potential theory. By harmonic synthesis, the corresponding conjugate trigonometric series is used as an approximation to the epsilon function. A set of coefficients of particularly simple form is obtained algebraically for direct calculation of the epsilon values from the corresponding set of psi values. Complete derivation of this process is presented.

Naiman, Irven↗
DOE OSTI2022

Scaling patch analysis of planar turbulent wakes

In this work, a scaling patch approach is used to investigate the proper scales in planar turbulent wakes. A proper scale for the mean axial flow is the well-known maximum velocity deficit U ref = U ∞ –U ctr , where U ∞ is the free stream velocity and U ctr is the mean axial velocity at the wake centerline. From an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is found as V ref = (dδ/dx)U ref , where dδ/dx is the growth rate of the wake width. From an admissible scaling of the mean momentum equation, a proper scale for the kinematic Reynolds shear stress is found as R uv,ref = U ∞ V ref , which is a mixed scale of the free stream velocity and the mean transverse flow scale. Expressions are derived for the scaled mean transverse velocity and Reynolds shear stress in the far field of planar turbulent wakes. Using a Gaussian function for the mean axial velocity deficit, approximate functions for the scaled mean transverse velocity and Reynolds shear stress are developed and found to agree well with experimental and simulation data. This work reveals that the mean transverse flow, despite its small magnitude, plays an important role in the scaling and understanding of the planar turbulent wake.

42 ENGINEERING↗
DOE OSTI2021

Learning Optimal Power Flow Solutions using Linearized Models in Power Distribution Systems

Solving nonlinear optimal power flow (OPF) problem is computationally expensive, and poses scalability challenges for power distribution networks. An alternative to solving the original nonlinear OPF is the linear approximated OPF models. Although, these linear approximated OPF models are fast, the resulting solutions may result in significant optimality gap. Lately, the application of machine learning (ML) methods in successfully solving the nonlinear OPF has been reported. These methods learn and estimate the nonlinear control policies using a purely data-driven approach. In this paper, we propose an approach to complements the ML based approach to solving OPF using solutions from known linearized OPF model. Specifically, we use supervised learning to map the solutions of linear OPF to nonlinear control variables. Unlike, the traditional ML based methods for OPF that approximate the full distribution feeder model using function approximation, our approach uses a two-node approximation of radial networks. The proposed approach is validated using IEEE 123 bus test system for OPF solutions obtained using the nonlinear OPF models.

optimal power flow, power distribution systems, su↗
NASA NTRS1989

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

The theoretical basis of flexible-aircraft modeling techniques encompassing aerodynamic, control, and elastic-structure effects is investigated analytically, with a focus on methods which employ minimum-state approximations for the unsteady aerodynamics. Rational-function approximations to generalized aerodynamic forces are reviewed; constraints and lag-coefficient optimization are explained; the problem of physical weighting in the minimum-state equations of motion is examined; and results of typical analyses from the NASA Active Flexible Wing project (Perry et al., 1988) are presented in extensive tables and graphs and discussed in detail. The minimum-state approach is shown to produce accurate models at significantly reduced computation costs.

Tiffany, Sherwood H.↗