Search NASA⌕ Search

SEARCH · Search NASA

Results for “Gradient estimation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Transient Interfacial Phenomena in Miscible Polymer Systems (TIPMPS)

Almost one hundred years ago Korteweg published a theory of how stresses could be induced in miscible fluids by concentration gradients, causing phenomena that would appear to be the same as with immiscible fluids. Miscible fluids could manifest a transient or effective interfacial tension (EIT). To this day, there has been no definitive experiment to confirm Korteweg's model but numerous fascinating and suggestive experiments have been reported. The goal of TIPMPS is to answer the question: Can concentration and temperature gradients in miscible materials induce stresses that cause convection? Many polymer processes involving miscible monomer and polymer systems could be affected by fluid flow and so this work could help understand miscible polymer processing, not only in microgravity, but also on earth. Demonstrating the existence of this phenomenon in miscible fluids will open up a new area of study for materials science. The science objectives of TIPMPS are: (1) Determine if convection can be induced by variation of the width of a miscible interface; (2) Determine if convection can be induced by variation of temperature along a miscible interface; (3) Determine if convection can be induced by variation of conversion along a miscible interface An interface between two miscible fluids can best be created via a spatially-selective photopolymerization of dodecyl acrylate with a photoinitiator, which allows the creation of precise and accurate concentration gradients between polymer and monomer. Optical techniques will be used to measure the refractive index variation caused by the resultant temperature and concentration fields. The viscosity of the polymer will be measured from the increase in the fluorescence of pyrene. Because the large concentration and temperature gradients cause buoyancy-driven convection that prevents the observation of the predicted flows, the experiment must be done in microgravity. In this report, we will consider our efforts to estimate the square gradient parameter, k, and our use of the estimates in modeling of the planned TIPMPS experiments. We developed a model consisting of the heat and diffusion equations with convective terms and of the Navier-Stokes equations with an additional volume force written in the form of the Korteweg stresses arising from nonlocal interaction in the fluid. The fluid's viscosity dependence on polymer conversion and temperature was taken from measurements of poly(dodecyl acrylate). Numerical modeling demonstrated that significant flows would arise for conditions corresponding to the planned experiments.

Pojman, John A.↗
DOE OSTI2024

Stochastic Approximation for Multi-period Simulation Optimization with Streaming Input Data

We consider a continuous-valued simulation optimization (SO) problem, where a simulator is built to optimize an expected performance measure of a real-world system while parameters of the simulator are estimated from streaming data collected periodically from the system. At each period, a new batch of data is combined with the cumulative data and the parameters are re-estimated with higher precision. The system requires the decision variable to be selected in all periods. Therefore, it is sensible for the decision-maker to update the decision variable at each period by solving a more precise SO problem with the updated parameter estimate to reduce the performance loss with respect to the target system. We define this decision-making process as the multi-period SO problem and introduce a multi-period stochastic approximation (SA) framework that generates a sequence of solutions. Two algorithms are proposed: Re-start SA (ReSA) reinitializes the stepsize sequence in each period, whereas Warm-start SA (WaSA) carefully tunes the stepsizes, taking both fewer and shorter gradient-descent steps in later periods as parameter estimates become increasingly more precise. We show that under suitable strong convexity and regularity conditions, ReSA and WaSA achieve the best possible convergence rate in expected sub-optimality either when an unbiased or a simultaneous perturbation gradient estimator is employed, while WaSA accrues significantly lower computational cost as the number of periods increases. In addition, we present the regularized ReSA, which obviates the need to know the strong convexity constant and achieves the same convergence rate at the expense of additional computation.

Computer Science↗
NASA NTRS2014

The Uncertainty of Biomass Estimates from LiDAR and SAR Across a Boreal Forest Structure Gradient

In this study, weexamined the uncertainty of aboveground live biomass (AGB) estimates based on light detection and ranging (LiDAR) and synthetic aperture radar (SAR) measurements distributed across a low-biomass vegetation structure gradient fromforest to non-forest in boreal-like ecosystems. The conifer-dominant structure gradient was compiled from ground data amassed from multiple field expeditions in central Maine (USA), Aurskog (Norway), and across central Siberia (Russia). Single variable empirical models were built tomodel AGB fromremote sensingmetrics. Using thesemodels, we calculated a rootmean square error (RMSE) and a 95% confidence interval (CI) of the RMSE fromthe difference between the remote sensing AGB predictions and the ground reference AGB estimates within AGB intervals across a 0-100 Mg ha(exp.−1) boreal forest structure gradient. The results show that the error in AGB predictions (RMSE) and the error uncertainty (the CI) from LiDAR and SAR change across a forest gradient. The errors of airborne LiDAR and SAR metrics and spaceborne LiDAR platforms show a general trend of reduced relative errors as AGBmagnitudes increase, particularly from0 to 60 Mg ha (exp.−1). Empirical models relating spaceborne metrics to AGB and estimates of spaceborne LiDAR error uncertainty demonstrate the difficulty of characterizing differences in AGB at the site-level with current spaceborne sensors, particularly below 80 Mg ha (exp.−1) with less than 50-100% error.

Taiga↗
DOE OSTI2022

Temperature distribution in a laser-heated diamond anvil cell as described by finite element analysis

Finite element analysis (FEA) is a powerful tool for numerically solving partial differential equations over complex geometries and is thus useful for analyzing heat transport in laser-heated diamond anvil cell (LHDAC) experiments. Our models expand on previously published simulations by calculating the volume-averaged temperatures of both the sample and insulation/pressure media under steady-state heating to determine the thermal pressure of the hot sample. Our goal is to produce an accurate relationship between the measured surface temperature of the absorbing sample and the temperature of the transparent insulating media, which is used to determine thermal pressure but susceptible to steep temperature gradients. We find that in doing so, our FEA models of temperature within the pressure/insulation media can differ from simplified estimates of temperature gradients by more than a factor of 2. We also explore temperature-dependent and temperature-independent thermal conductivity models and find that the volume-averaged temperatures differ by up to a factor of 1.3, forcing the predicted thermal pressures determined to also differ by up to a factor of 1.5 at a temperature of 2000 K at 50 GPa for neon. Higher temperatures exacerbate this difference. We also find that unintentional asymmetric sample insertion and sample heating, which are common in LHDAC experiments, do not have a first-order effect on volume-averaged temperatures. The FEA models, available in both Python and FlexPDE, are versatile across different sample geometries, materials, and heat source laser shapes.

Farah, Frederick↗
DOE OSTI2022

Statistical Modeling of Peak Accelerating Gradients in LCLS-II and LCLS-II-HE

In this report, we study the vertical test gradient performance and the gradient degradation between vertical test and cryomodule test for the 1.3 GHz LCLS-II cavities. We develop a model of peak gradient statistics, and use our understanding of the LCLS-II results and the changes implemented for LCLS-II-HE to estimate the expected gradient statistics for the new machine. Finally, we lay out a plan to ensure that the LCLS-II-HE cryomodule gradient specifications are met while minimizing cavity disqualification by introducing a variable acceptance threshold for the accelerating gradient.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Stochastic gradient descent for optimization for nuclear systems

The use of gradient descent methods for optimizing k-eigenvalue nuclear systems has been shown to be useful in the past, but the use of k-eigenvalue gradients have proved computationally challenging due to their stochastic nature. ADAM is a gradient descent method that accounts for gradients with a stochastic nature. This analysis uses challenge problems constructed to verify if ADAM is a suitable tool to optimize k-eigenvalue nuclear systems. ADAM is able to successfully optimize nuclear systems using the gradients of k-eigenvalue problems despite their stochastic nature and uncertainty. Furthermore, it is clearly demonstrated that low-compute time, high-variance estimates of the gradient lead to better performance in the optimization challenge problems tested here.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

The tonotopic map in the embryonic chicken cochlea

The purpose of the present study was to determine the tonotopic map in the chicken cochlea at 19 days of incubation (E19) by obtaining characteristic frequencies (CFs) for primary afferents, labeling the characterized neurons, and documenting their projections to the papilla. The lowest and highest CFs recorded were 188 and 1623 Hz respectively. The embryonic tonotopic map coincided with maps reported for post-hatch chicks. There were no evidence that neurons selective to low frequencies project inappropriately to more basal locations of the embryonic papilla. Linear regression was used to estimate the frequency gradient (b = 0.037 +/- 0.012 In Hz/% [b +/- SEb]) and intercept (In C, where C = 111 Hz) of the semilog plot of frequency versus cochlear position (in % distance from apex). From these estimates the octave distribution was calculated to be 18.7%/octave or 0.58 mm/octave. These quantities were not significantly different from those found in post hatch chickens. We conclude that the tonotopic map of the avian cochlea for CFs between 100 and 1700 Hz is stable and relatively mature from age E19 to post-hatch day 21 (P21). The most striking sign of immaturity in the E19 embryo is the limited range of high CFs. We offer the hypothesis that, between the ages of E19 and P21, improvements in middle ear admittance alone or in combination with functional maturation of the cochlear base may be the principal factors responsible for the appearance of adult-like high CF limits and not an apically shifting tonotopic map.

NASA Discipline Neuroscience↗
NASA NTRS1993

Systematic chemical variations in large 3AB iron meteorites: Clues to core crystallization

Analysis of numerous individual iron meteorites have shown that fractional crystallization of iron cores result in variations in chemical concentration of the solid core which span several orders of magnitude. The magnitude and direction of the resulting spatial gradients in the core can provide clues to the physical nature of the core crystallization process. We have analyzed suites of samples from three large 3AB irons (Cape York, 58t; Chupaderos, 24t; Morito, 10t) in order to estimate local chemical gradients. Initial results for the concentrations of Ge, Pd, Pt (Massey group), Ir, Au, As, Co, Os, and Rh (Dalhouse group), and P (Arizona group) show significant ranges among the Cape York and Chupaderos samples and marginally significant ranges among the Morito samples. Measurements of Au, Ir, Co, Ni, Cu, Ga, As, W, Re (from UCLA) and Ni and Co (Arizona group) are in progress. We find a spatial Ir gradient in Chupaderos with a magnitude similar to the one reported for Agpalilik (Cape York iron) by Esbensen et al.

Haack, H.↗
NASA NTRS2011

Sensitivity of Seawater Oxygen Isotopes to Climatic and Tectonic Boundary Conditions in an Early Paleogene Simulation with GISS ModelE-R

An isotope-enabled ocean-atmosphere general circulation model (GISS ModelE -R) is used to estimate the spatial gradients of the oxygen isotopic composition of seawater (delta O-18(sub sw), where delta is the deviation from a known reference material in per mil) during the early Paleogene (45.65 Ma). Understanding the response of delta O-18(sub sw) to changes in climatic and tectonic boundary conditions is important because records of carbonate delta O-18 document changes in hydrology, as well as changes in temperature and global ice -volume. We present results from an early Paleogene configuration of ModelE -R which indicate that spatial gradients of surface ocean delta O-18(sub sw) during this period could have been significantly different to those in the modern ocean. The differences inferred from ModelE -R are sufficient to change early Paleogene sea surface temperature estimates derived from primary carbonate delta O-18 signatures by more than +/-2 C in large areas of the ocean. In the North Atlantic, Indian, and Southern Oceans, the differences in d18Osw inferred from our simulation with ModelE -R are in direct contrast with those from another d18O ]tracing model study which used different, but equally plausible, early Paleogene boundary conditions. The large differences in delta O-18(sub sw) between preindustrial and early Paleogene simulations, and between models, emphasizes the sensitivity of d18Osw to climatic and tectonic boundary conditions. For this reason, absolute estimates of Eocene/ Paleocene temperature derived from carbonate delta O-18 alone are likely to have larger uncertainties than are usually assumed.

Roberts, Christopher D.↗
NASA NTRS1980

Tropical cyclone outer surface winds derived from satellite microwave sounder data

Upper tropospheric temperature anomalies are detected in brightness temperature data from the Nimbus 6 Scanning Microwave Spectrometer (SCAMS). Brightness temperature anomalies are related to surface pressure anomalies through the radiative transfer and hydrostatic equation. Surface wind speeds at outer radii are then estimated using the gradient wind equation and a shearing parameter. The method is first tested using simulated satellite data constructed from temperature, pressure and height data recorded by aircraft reconnaissance of four hurricanes. Wind speeds in the 80-95 kPa region are estimated with 2-3 m/sec accuracy. Next, 55.45 GHz SCAMS data over eight typhoons during 1975 are used to estimate the radii of 15.4 m/sec (30 kt) and 27.5 m/sec (50 kt) winds. Accuracies of about + or - 80 and + or - 70 km, respectively, are found. It is suggested that the technique be further tested using data from the Microwave Sounding Unit on board the TIROS-N and NOAA 6 satellites.

Kidder, S. Q.↗
DOE OSTI2021

Temperature Homogeneity under Selective and Localized Microwave Heating in Structured Flow Reactors

Selective heating of different phases of multiphase systems via microwaves can result in energy savings and suppression of side reactions. However, materials properties and operating conditions that maximize temperature gradients are poorly understood. Here we utilize computational fluid dynamics (CFD) computations and temperature measurements in structured flow reactors (monoliths) in a monomodal microwave cavity to assess the temperature difference between the walls and the fluid and develop a simple lumped model to estimate when temperature gradients exist. We also explore the material’s thermal and electrical properties of structured reactors for isothermal catalyst conditions. We propose that CFD simulations can be used as a nonintrusive, predictive tool of temperature homogeneity. Importantly, we demonstrate that localized heating in the bed under several conditions rather than selective heating is responsible for the selectivity enhancement. Furthermore, our results indicate that structured beds made of high thermal conductivity materials avoid arcing and enable temperature homogeneity and low electrical conductivity materials allow microwaves to penetrate the domain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems

This work is an improvement of the previous note (Bradji in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) which dealt with the convergence analysis of a finite volume scheme for the Poisson’s equation with a linear oblique derivative boundary condition. The formulation of the finite volume scheme given in Bradji (in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) involves the discrete gradient introduced recently in Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010). In this paper, we consider the convergence analysis of finite volume schemes involving the discrete gradient of Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010) for elliptic and parabolic equations with linear oblique derivative boundary conditions. Linear oblique derivative boundary conditions arise for instance in the study of the motion of water in a canal, cf. Lesnic (Commun Numer Methods Eng 23(12):1071–1080, 2007). We derive error estimates in several norms which allow us to get error estimates for the approximations of the exact solutions and its first derivatives. In particular, we provide an error estimate between the gradient of the exact solutions and the discrete gradient of the approximate solutions. Convergence of the family of finite volume approximate solutions towards the exact solution under weak regularity assumption is also investigated. In the case of parabolic equations with oblique derivative boundary conditions, we develop a new discrete a priori estimate result. The proof of this result is based on the use of a discrete mean Poincaré–Wirtinger inequality. Thanks to the stated a priori estimate and to a comparison with an appropriately chosen auxiliary finite volume scheme, we derive the convergence results. This work can be viewed as a continuation of the previous work (Bradji and Gallouët in Int J Finite Vol 3(2):1–35, 2006) where a convergence analysis for a finite volume scheme, based on the admissible mesh of Eymard et al. (In: Ciarlet and Lions, Handbook of numerical analysis, North-Holland, Amsterdam, 2000), for the Poisson’s equation with a linear oblique derivative boundary conditions is given. The obtained convergence results do not require any relation between the mesh sizes of the spatial and time discretizations. Some numerical tests are presented for both elliptic and parabolic equations. In particular, we present three methods to compute the discrete solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Automated extraction of interfacial dislocations and disconnections from atomistic data

Here we introduce Interfacial Line Defect Analysis (ILDA), a method for identifying and extracting interfacial dislocations and disconnections with little-to-no input from the user on the nature of the interface. By simply providing the orientations and coherency strains for the crystals in a coherent reference state of the interface, ILDA provides exact Burgers vectors. Alternatively, these orientations and strains can be estimated using local atomic deformation gradients, making ILDA fully automated and providing estimated Burgers vectors. ILDA also determines the step height associated with each defect line segment, in case the associated defect is a disconnection. The heart of the method is the identification of atoms residing at co-incidence sites between the two crystals and the construction of a surface mesh connecting these sites that is used to compose Burgers circuits and insert defect line segments. We demonstrate the performance of ILDA in two test cases: a twist grain boundary and a phase boundary.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Gradient-Based Multi-Area Distribution System State Estimation

The increasing distributed and renewable energy resources and controllable devices in distribution systems make fast distribution system state estimation (DSSE) crucial in system monitoring and control. We consider a large multi-phase distribution system and formulate DSSE as a weighted least squares (WLS) problem. We divide the large distribution system into smaller areas of subtree structure, and by jointly exploring the linearized power flow model and the network topology, we propose a gradient-based multi-area algorithm to exactly and efficiently solve the WLS problem. The proposed algorithm enables distributed and parallel computation of the state estimation problem without compromising any performance. Numerical results on a 4,521-node test feeder show that the designed algorithm features fast convergence and accurate estimation results. Comparison with traditional Gauss-Newton method shows that the proposed method has much better performance in distribution systems with a limited amount of reliable measurement. The real-time implementation of the algorithm tracks time-varying system states with high accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗