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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Computational methods for the identification of spatially varying stiffness and damping in beams

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Banks, H. T.↗
DOE OSTI2026

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗
DOE OSTI2024

Statistical Behavior of Low-Amplitude Power System Point-on-Wave Measurements

The power grid is undergoing massive changes to ensure resiliency and reliability in a more decentralized world. Distributed energy resources are becoming a prominent source of generation, potentially leading to a lack of centralized generation sources. Due to these new behaviors and system topologies, it is important to install measurement devices that are 1) accurate and 2) self-aware of their measurement quality. In this paper, a residential-scale microgrid is used to generate voltage and current waveforms, captured by Verivolt and National Instruments measurement equipment. A least-squares approach is used to separate the “clean” signals from the noise. Finally, Gaussian mixture modeling is used to approximate noise distributions, and it is shown these higher-order distribution estimates are a better fit to voltage and current noise profiles than single-mode Gaussian estimates.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1984

Light Scattered from Polished Optical Surfaces: Wings of the Point Spread Function

Random figure errors from the polishing process plus particles on the main mirrors in a telescope cause an extended point spread function (PSF) declining approximately as the inverse square of the sine of the angle from a star from about 100 micro-rad to a right angle. The decline in at least one case, and probably in general, proceeds as the inverse cube at smaller angles where the usual focal plane aperture radius is chosen. The photometric error due to misalignment by one Airy ring spacing with an aperture of n rings depends on the net variance in the figure. It is approximately 60/(n+1)(3) when using the data of Kormendy (1973). A typical value is 6 x 10 to the -5th power per ring of misalignment with n = 100 rings. The encircled power may be modulated on a time scale of hours by parts per thousand in a wavelength dependent manner due to relative humidity effects on mirror dust. The scattering according to an inverse power law is due to a random walk in aberration height caused by a multitude of facets and slope errors left by the polishing process. A deviation from such a law at grazing emergence may permit monitoring the dust effects.

Kenknight, C. E.↗
NASA NTRS1972

The lunar conductivity profile and the nonuniqueness of electromagnetic data inversion.

A review of the theory for the electromagnetic functional used to date to determine the lunar conductivity profile from spectral analyses of lunar magnetometer data. The 'hard' boundary condition used by Sonett et al. (1971) and others appears to be a good approximation for the sunlit lunar hemisphere. The use of the spectral data in conjunction with the functional to find a least squares conductivity profile is examined from the point of view of the nonuniqueness of nonlinear estimation. An unsuccessful search was carried out to find models that were both geophysically reasonable and consistent with the data. It is asserted that the failure to find these models is due to the inadequacy of the functional. Of the models generated, those that best fit the data all have a conductivity peak at a depth of 240 km similar to that of the model discussed by Sonett et al. However, all of these models are quite distinct elsewhere in the profile. It is shown how such models are dependent on both the nature of the functional as well as the initial guess in the least squares procedure. A correlation analysis shows that the only resolvable features from this type of model are a low conductivity crust, a high conductivity peak of limited radial extent, and a low conductivity zone beneath the peak.

Phillips, R. J.↗
NASA NTRS1983

Accuracy of measurement of star images on a pixel array

Algorithms are developed for predicting the accuracy with which the brightness of a star can be determined from its image on a digital detector array, as a function of the brightness of the background. The assumption is made that a known profile is being fitted by least squares. The two profiles used correspond to ST images and to ground-based observations. The first result is an approximate rule of thumb for equivalent noise area. More rigorous results are then given in tabular form. The size of the pixels, relative to the image size, is taken into account. Astronometric accuracy is also discussed briefly; the error, relative to image size, is very similar to the photometric error relative to brightness.

King, I. R.↗
DOE OSTI2024

Anderson acceleration with approximate calculations: Applications to scientific computing

Here we provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗
DOE OSTI2021

Calculation of permanent magnet arrangements for stellarators: a linear least-squares method

A problem arising in several engineering areas is to design magnets outside a volume that produce a desired magnetic field inside it. One instance of this problem is stellarator design, where it has recently been shown that permanent magnets can provide the required shaping of the magnetic field. Here we demonstrate a robust and efficient algorithm REGCOIL_PM to calculate the spatial distribution of these permanent magnets. The procedure involves a small number of fixed-point iterations, with a linear least-squares problem solved at each step. Furthermore, the method exploits the Biot–Savart Law's exact linearity in magnetization density and approximate linearity in magnet size, for magnets far from the target region. No constraint is placed on the direction of magnetization, so Halbach solutions are found naturally, and the magnitude of the magnetization can be made uniformly equal to a target value.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

Intensity changes in the UV spectrum of Beta Cephei

Fifty eight short wavelength International Ultraviolet Explorer spectra were taken over a 152 day period. Variations in the absorption lines of C IV (1550 A), Si IV (1393 and 1404 A) and N V (1239 and 1243 A) and a Cr III feature (1208 to 1211 A) were observed. A data reduction technique was developed in order to compare the changes in the equivalent widths of these absorption lines. Periods were determined by least squares fit to a sinusoid using several combinations of the data. In one case eighteen spectra for each ion taken at approximately one day intervals were used; in another, all 58 measurements of each were used; and in a third all measurements from all the ions wee combined. Using both variable metric and interactive algorithms it was determined that for all combinations mentioned a period of 6.10 + or - .06 days is the best fit to the vector of equivalent widths versus time. No other period, with or without the 6.10 day period removed from the data, was found. Analysis of the Cr III feature near 1210 A gives the same period as the others, but in antiphase.

Fahey, R. P.↗
NASA NTRS1984

Absolute intensities of spectral lines in carbon dioxide bands near 2050/cm

The absolute intensities of individual lines of eleven relatively weak bands of (C-12)(O-16)2, (C-13)(O-16)2, (O-16)(C-12)(O-18), and (O-16)(C-12)(O-17) near 2050/cm were measured and recorded at room temperature and 0.01/cm resolution with the Fourier transform spectrometer located in the McMath solar telescope complex located at the National Solar Observatory on Kitt Peak. Each spectrum was obtained with an integration time of one hour, the temperature and pressure were monitored during this time, and the signal-to-rms noise in the 5 micron region was approximately 4000 for all scans. The intensities were determined from analysis of 1-2/cm segments of spectra using nonlinear least-squares spectral curve fitting, and analyzed to determine the vibrational band intensity and F-factor coefficients for each of the bands. The results are pertinent to a wide variety of problems in atmospheric physics and for the analysis of remote-sensing data.

Rinsland, C. P.↗
NASA NTRS1996

(abstract) An All Sky Cirrus Confusion Noise Map for WIRE

The Wide Field Infrared Explorer (WIRE) is a Small Explorer (SMEX) satellite scheduled for launch in 1998 which will carry out a sky survey of at least 100 square degrees in the wavelength regions of 9-15(micro)m and 21-27(micro)m with spatial resolution of approximately 20 arcsec and sensitivity exceeding 0.6mJy. At this sensitivity level WIRE observations can be seriously affected by the confusion noise contribution from the infrared cirrus emission, so the WIRE survey must be planned with some knowledge of the expected level of cirrus confusion. Production of a cirrus confusion noise map with 0.5 degree resolution based on the spatial power spectral density of the cirrus emission in the IRAS ISSA data is in progess using the method described by Gauthier, et al. Spectrally resolved power spectra density data is obtained from the ISSA maps with a wavelet transform technique.

Wide Field Infrared Explorer WIRE infrared sky sur↗
NASA NTRS1993

Improving the chi-squared approximation for bivariate normal tolerance regions

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation.

Feiveson, Alan H.↗
DOE OSTI2021

Potential energy surfaces for high-energy N + O 2 collisions

Potential energy surfaces for high-energy collisions between an oxygen molecule and a nitrogen atom are useful for modeling chemical dynamics in shock waves. In the present work, we present doublet, quartet, and sextet potential energy surfaces that are suitable for studying collisions of O 2 ( 3 Σ$^{–}_{g}$) with N( 4 S) in the electronically adiabatic approximation. Two sets of surfaces are developed, one using neural networks (NNs) with permutationally invariant polynomials (PIPs) and one with the least-squares many-body (MB) method, where a two-body part is an accurate diatomic potential and the three-body part is expressed with connected PIPs in mixed-exponential-Gaussian bond order variables (MEGs). We find, using the same dataset for both fits, that the fitting performance of the PIP-NN method is significantly better than that of the MB-PIP-MEG method, even though the MB-PIP-MEG fit uses a higher-order PIP than those used in previous MB-PIP-MEG fits of related systems (such as N 4 and N 2 O 2 ). However, the evaluation of the PIP-NN fit in trajectory calculations requires about 5 times more computer time than is required for the MB-PIP-MEG fit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Hierarchical approach to reconstruct surfaces by using iteratively rectified imagery

A new approach to reconstruct the 3D surface of the object space from digital images is described. All the object points obtained by an automatic orientation procedure lead to a first approximation of the surface. Edges are computed for one image and matched to the other image by grey level correlation or least-squares matching through the scale space. To every discrete step in the scale space there exists the digital stereopair (image pyramid), the corresponding surface digital elevation model (DEM), and the warped images. The warped images in this discrete scale space representation correspond to digital orthophotos obtained from the DEMs that result from matching the image pyramid. The warped images will be used on every successive level in the image pyramid in order to reduce the foreshortening problems associated with any area-based matching method.

Schenk, Toni↗
NASA NTRS1993

Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.

Everitt, C. W. F.↗
DOE OSTI2023

Aggregation of Leslie matrix models with application to ten diverse animal species

Some grouping is necessary when constructing a Leslie matrix model because it involves discretizing a continuous process of births and deaths. Here, the level of grouping is determined by the number of age classes and frequency of sampling. It is largely unknown what is lost or gained by using fewer age classes, and I address this question using aggregation theory. I derive an aggregator for a Leslie matrix model using weighted least squares, determine what properties an aggregated matrix inherits from the original matrix, evaluate aggregation error, and measure the influence of aggregation on asymptotic and transient behaviors. To gauge transient dynamics, I employ reactivity of the standardized Leslie matrix. I apply the aggregator to 10 Leslie models developed for animal populations drawn from a diverse set of species. Several properties are inherited by the aggregated matrix: (a) it is a Leslie matrix; (b) it is irreducible whenever the original matrix is irreducible; (c) it is primitive whenever the original matrix is primitive; and (d) its stable population growth rate and stable age distribution are consistent with those of the original matrix if the least squares weights are equal to the original stable age distribution. In the application, depending on the population modeled, when the least squares weights do not follow the stable age distribution, the stable population growth rate of the aggregated matrix may or may not be approximately consistent with that of the original matrix. Transient behavior is lost with high aggregation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies

An approximation scheme is developed for the identification of hybrid systems describing the transverse vibrations of flexible beams with attached tip bodies. In particular, problems involving the estimation of functional parameters are considered. The identification problem is formulated as a least squares fit to data subject to the coupled system of partial and ordinary differential equations describing the transverse displacement of the beam and the motion of the tip bodies respectively. A cubic spline-based Galerkin method applied to the state equations in weak form and the discretization of the admissible parameter space yield a sequence of approximating finite dimensional identification problems. It is shown that each of the approximating problems admits a solution and that from the resulting sequence of optimal solutions a convergent subsequence can be extracted, the limit of which is a solution to the original identification problem. The approximating identification problems can be solved using standard techniques and readily available software.

Banks, H. T.↗