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At least 235 records · Page 13

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NASA NTRS1992

Aperture codes for sensors viewing extended objects from space

The paper describes aperture codes viewing extended objects form space which find application in imaging an extended object which may have relatively low contrast, and whose lateral limits extend beyond the FOV of the sensor. Those elements of an extended object lying near the FOV limits are only partially coded, i.e., flux from those elements cannot cast a shadow of the entire aperture code onto the detector, as can elements near the center of the FOV. This has consequences for the algorithms used to reconstruct the image. The object field is divided into a number of elements which is smaller than the number of detector pixels, and a least squares fit to the data is performed. The methods used for choosing the matrices representing the aperture codes are discussed, and computer simulations of the effects of noise are described.

Curtis, C. C.↗

NASA NTRS1998

Empirical correction for earth sensor horizon radiance variation

A major limitation on the use of infrared horizon sensors for attitude determination is the variability of the height of the infrared Earth horizon. This variation includes a climatological component and a stochastic component of approximately equal importance. The climatological component shows regular variation with season and latitude. Models based on historical measurements have been used to compensate for these systematic changes. The stochastic component is analogous to tropospheric weather. It can cause extreme, localized changes that for a period of days, overwhelm the climatological variation. An algorithm has been developed to compensate partially for the climatological variation of horizon height and at least to mitigate the stochastic variation. This method uses attitude and horizon sensor data from spacecraft to update a horizon height history as a function of latitude. For spacecraft that depend on horizon sensors for their attitudes (such as the Total Ozone Mapping Spectrometer-Earth Probe-TOMS-EP) a batch least squares attitude determination system is used. It is assumed that minimizing the average sensor residual throughout a full orbit of data results in attitudes that are nearly independent of local horizon height variations. The method depends on the additional assumption that the mean horizon height over all latitudes is approximately independent of season. Using these assumptions, the method yields the latitude dependent portion of local horizon height variations. This paper describes the algorithm used to generate an empirical horizon height. Ideally, an international horizon height database could be established that would rapidly merge data from various spacecraft to provide timely corrections that could be used by all.

Hashmall, Joseph A.↗

NASA NTRS1998

Flow Applications of the Least Squares Finite Element Method

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Jiang, Bo-Nan↗

NASA NTRS1995

Fitting Prony Series To Data On Viscoelastic Materials

Improved method of fitting Prony series to data on viscoelastic materials involves use of least-squares optimization techniques. Based on optimization techniques yields closer correlation with data than traditional method. Involves no assumptions regarding the gamma'(sub i)s and higher-order terms, and provides for as many Prony terms as needed to represent higher-order subtleties in data. Curve-fitting problem treated as design-optimization problem and solved by use of partially-constrained-optimization techniques.

Hill, S. A.↗

DOE OSTI2020

Absolute Band Intensity of the Iodine Monochloride Fundamental Mode for Infrared Sensing and Quantitative Analysis

Iodine monochloride (ICl) is a gaseous off-product of molten salt reactors; monitoring this heteronuclear diatomic is of great interest for both environmental and safety purposes. In this paper we investigate the possibility of infrared monitoring of ICl by measuring the far-infrared absorption cross section of its fundamental band near 381 cm -1 . We have performed quantitative studies of the neat gas in a 20 cm cell at 25, 35, 50 and 70 oC at multiple pressures up to ~ 9 Torr and investigated the temperature and pressure dependence of the band’s infrared cross section. Quantitative measurements were problematic due to sample adhesion to the cell walls and windows as well as reactions/possible hydrolysis of ICl to form HCl gas. Effects were mitigated by measuring only the neat gas, using short measurement times and subtracting out the partial pressure of the HCl(g). The integrated band strength is shown to be temperature independent and was found to be equal to 9.1 x 10 -19 (cm 2 /molecule) cm-1. As expected, the temperature dependence of the band profile showed only a small effect over this limited temperature range. Furthermore, we have also investigated using the absorption data along with inverse least squares multivariate methods for the quantitative monitoring of ICl effluent concentrations under different scenarios using infrared (standoff) sensing and compare these results with traditional Beer’s Law (univariate) techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Uncertainty Quantification Enabled by Automatic Differentiation for Hydrodynamic Simulation of Shock‐to‐Detonation Transition in High Explosives

Quantifying the effects of uncertainty in a reactive burn model on the run-to-detonation time in high explosives (HEs) provides a robust methodology for assessing the probability of an HE failing the IHE qualification standard. Moreover, uncertainty quantification helps evaluate whether the model calibration accurately represents data outside the calibration set. This study uses a specialized hydrodynamic simulation code for modeling detonation to determine the run-to-detonation time of the HE PBX 9502 for various impact velocities. To quickly approximate uncertainties in the model, a surrogate was constructed using a Taylor series expansion centered at the mean of the input parameters. To obtain the sensitivities required for constructing the Taylor series, HYP-percomplex Automatic Differentiation (HYPAD) was implemented. HYPAD is a methodology for infusing existing codes with automatic differentiation capabilities by augmenting variables with one or more imaginary units to compute step-size independent partial derivatives. These derivatives are accurate to machine precision with respect to the implemented numerical algorithm, meaning their accuracy reflects that of the underlying method (e.g., integration or discretization schemes). Using reduced order modeling techniques, the mean and standard deviation of the run-to-detonation time of a shock within PBX 9502 were computed for a number of initial impact velocities. A weighted least squares regression was then performed to obtain a best fit curve and prediction interval for the computed statistics. Historical data points from explosively driven wedge tests were utilized to validate the prediction interval, ensuring its reliability in predicting future outcomes. With this prediction interval and a known safety constraint curve, the most probable point of failure and the probability of failure for the HE PBX 9502 were determined.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗

NASA NTRS1986

Static shape control for flexible structures

An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.

Rodriguez, G.↗

DOE OSTI2026

Transient Catalytic Reaction Analysis Through Signal Defragmentation

The Temporal Analysis of Products (TAP) pulse response technique provides valuable insights into catalytic function and reaction kinetics. However, complex fragmentation patterns in the TAP mass spectrometry signals can complicate precise quantification, particularly when analyzing transient gas flux data typical of TAP experiments. This work demonstrates a standard defragmentation method that deconvolves transient TAP signals while maintaining the temporal resolution of the experiment. First, the integrals of calibration gas fluxes are used to determine the fingerprint fragmentation pattern and construct a fragmentation matrix. This matrix is then used to defragment experimental flux data at each recorded time point via a non-negative least squares regression. The effectiveness of this method is demonstrated using virtual data and control experiments with a TAP reactor system. The defragmentation is then applied to the more complex propane dehydrogenation reaction on a chromia/alumina catalyst, which can contain up to ten significant gas species in the reactor outlet. Initial propane pulsing reveals an induction period during which propane is fully oxidized to CO2, followed by partial reduction to CO. Afterwards, there is a transition in chemistries towards coking and propylene production. Our example illustrates a practical method for the accurate determination of the time-dependent reactant/product concentrations and rates for a thorough analysis of the propane dehydrogenation kinetics. This approach can be broadly applied to any transient mass spectrometry experiment for a better understanding of catalyst-reaction dynamics.

36 - MATERIALS SCIENCE↗

NASA NTRS1987

Studies of outer planet satellites, Mercury and Uranus

Arguments were made, based on geometry, for both an impact and an internal origin for the ancient, partially preserved furrow system of Ganymede. It was concluded that furrows were not concentric, but could be impact related if multiringed structures on icy satellites are initially noncircular. The geometry of the Valhalla ring structure on Callisto was examined in order to assess the circularity of an unmodified ring system. The Ganymede furrow system was remapped to make use of improvements in coordinate control. The least-squares center of curvature for all furrows in the Marius and Galileao Regio is -20.7, and 179.2 degrees. Furrows in Marius and Galileo Regio are reasonably concentric, and are much more circular than previously estimated. The perceived present nonalignment of the assumed originally concentric furrows were used to argue for large-scale lateral motion of dark terrain blocks in Ganymede's crust, presumably in association with bright terrain formation., The overall alignment of furrows as well as the inherent scatter in centers of curvature from subregions of Galileo and Marius do not support this hypothesis.

Mckinnon, William B.↗

DOE OSTI2021

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Prototype partial one-third octave band spectrum analyzer for acoustic, vibration and other wideband data for flight applications

The design refinement of a compact frequency analyzer for measurement and analysis on board flight vehicles is discussed. The analyzer has been constructed in a partial one-third octave band configuration with six filters and detectors spaced by the square root of 10 from 316 Hz to 100,000 Hz and a broadband detector channel. The analyzer has been tested over a temperature range of 40 to 120 F at a pressure of one atmosphere, and at a temperature of 75 F at an absolute pressure of 0.000001 torr, and has demonstrated at least 60 db of dynamic range.

Source record↗

NASA NTRS1989

On damping mechanisms in beams

A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.

Banks, H. T.↗

NASA NTRS1991

On damping mechanisms in beams

Banks, H. T.↗

DOE OSTI2024

Rapid subsurface analysis of frequency-domain thermoreflectance images with K-means clustering

K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μm of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K = 3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μm length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.

36 MATERIALS SCIENCE↗

NASA NTRS1993

A least-squares finite element method for 3D incompressible Navier-Stokes equations

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Jiang, Bo-Nan↗

NASA NTRS1999

Comparative Studies for the Sodium and Potassium Atmospheres of the Moon and Mercury

A summary discussion of recent sodium and potassium observations for the atmospheres of the Moon and Mercury is presented with primary emphasis on new full-disk images that have become available for sodium. For the sodium atmosphere, image observations for both the Moon and Mercury are fitted with model calculations (1) that have the same source speed distribution, one recently measured for electron-stimulated desorption and thought to apply equally well to photon-stimulated desorption, (2) that have similar average surface sodium fluxes, about 2.8 x 10(exp 5) to 8.9 x 10(exp 5) atoms cm(exp -2)s(exp -1) for the Moon and approximately 3.5 x 10(exp 5) to 1.4 x 10(exp 6) atoms cm(exp -2)s(exp -1) for Mercury, but (3) that have very different distributions for the source surface area. For the Moon, a sunlit hemispherical surface source of between approximately 5.3 x 10(exp 22) to 1.2 x 10(exp 23) atoms/s is required with a spatial dependence at least as sharp as the square of the cosine of the solar zenith angle. For Mercury, a time dependent source that varies from 1.5 x 10(exp 22) to 5.8 x l0(exp 22) atoms/s is required which is confined to a small surface area located at, but asymmetrically distributed about, the subsolar point. The nature of the Mercury source suggest that the planetary magnetopause near the subsolar point acts as a time varying and partially protective shield through which charged particles may pass to interact with and liberate gas from the planetary surface. Suggested directions for future research activities are discussed.

Smyth, William H.↗

NASA NTRS1984

A linear aerodynamic analysis for unsteady transonic cascades

A potential flow analysis to predict unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers is presented. The unsteady aerodynamic model includes the effects of blade geometry, finite mean pressure variation across the blade row, high frequency blade motion, and shock motion within the framework of a linearized, frequency domain formulation. The unsteady equations are solved implicit, least squares, finite difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady field is determined by matching a solution determined on a rectilinear type cascade mesh, which covers an extended blade passage region, to a solution determined on a detailed polar type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Cascades of double circular arc and flat plate blades demonstrate the unsteady analysis, and partially illustrate the effects of blade geometry, inlet Mach number, blade vibration frequency and shock motion on unsteady response.

Verdon, J. M.↗