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Results for “variance 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.

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At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Geometric-optical modeling of a conifer forest canopy

A geometric-optical model of a conifer forest canopy was constructed to describe the variance of a remotely-sensed image of a forest stand. The model is driven by interpixel variance generated from three sources: (1) the number of crowns in the pixel; (2) the size of the individual crowns; and (3) the overlapping of crowns and shadows. The illumination of a tree and its shadow is described as a cone using parallel-ray geometry. The model can also be inverted to provide estimates of the size, shape and spacing of the trees using remotely-sensed imagery and a minimum of ground measurements. The results of field tests using 10-meter and 80-meter multispectral imagery of two test conifer stands in northeastern California are presented. It is shown that the model produces reasonable estimates for the geometric parameters of the stand and appears to be sufficiently robust for application to other geometric shapes corresponding to different types of vegetation.

Li, X.↗
NASA NTRS2011

Solar Drivers of 11-yr and Long-Term Cosmic Ray Modulation

In the current paradigm for the modulation of galactic cosmic rays (GCRs), diffusion is taken to be the dominant process during solar maxima while drift dominates at minima. Observations during the recent solar minimum challenge the pre-eminence of drift: at such times. In 2009, the approx.2 GV GCR intensity measured by the Newark neutron monitor increased by approx.5% relative to its maximum value two cycles earlier even though the average tilt angle in 2009 was slightly larger than that in 1986 (approx.20deg vs. approx.14deg), while solar wind B was significantly lower (approx.3.9 nT vs. approx.5.4 nT). A decomposition of the solar wind into high-speed streams, slow solar wind, and coronal mass ejections (CMEs; including postshock flows) reveals that the Sun transmits its message of changing magnetic field (diffusion coefficient) to the heliosphere primarily through CMEs at solar maximum and high-speed streams at solar minimum. Long-term reconstructions of solar wind B are in general agreement for the approx. 1900-present interval and can be used to reliably estimate GCR intensity over this period. For earlier epochs, however, a recent Be-10-based reconstruction covering the past approx. 10(exp 4) years shows nine abrupt and relatively short-lived drops of B to < or approx.= 0 nT, with the first of these corresponding to the Sporer minimum. Such dips are at variance with the recent suggestion that B has a minimum or floor value of approx.2.8 nT. A floor in solar wind B implies a ceiling in the GCR intensity (a permanent modulation of the local interstellar spectrum) at a given energy/rigidity. The 30-40% increase in the intensity of 2.5 GV electrons observed by Ulysses during the recent solar minimum raises an interesting paradox that will need to be resolved.

Cliver, E. W.↗
DOE OSTI2025

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Minimum variance system identification with application to digital adaptive flight control

A new on-line minimum variance filter for the identification of systems with additive and multiplicative noise is described which embodies both accuracy and computational efficiency. The resulting filter is shown to use both the covariance of the parameter vector itself and the covariance of the error in identification. A bias reduction scheme can be used to yield asymptotically unbiased estimates. Experimental results for simulated linearized lateral aircraft motion in a digital closed loop mode are presented, showing the utility of the identification schemes.

Kotob, S.↗
NASA NTRS2018

Observation Error Specification for Near-Surface Soil Moisture Assimilation: Does It Matter?

The observation error variances assumed in the data assimilation (DA) of remotely sensed near-surface soil moisture observations are known to have unrealistic spatial patterns. The temporal variability in the errors is also typically neglected. Soil moisture errors cannot be directly calculated at large scales, and the globally distributed errors are unknown. We apply several approaches to estimating the observation errors (R matrix) for near-surface soil moisture DA experiments, to establish whether the assumed errors are important to the DA performance, and hence whether uncertainty in the observation error specification is a likely source of uncertainty in soil moisture DA output.

Draper, Clara↗
DOE OSTI2017

Mechanical response of 99.999% purity aluminum under dynamic uniaxial strain and near melting temperatures

In this study, a series of reverse geometry normal plate impact experiments are employed to investigate the incipient plastic behavior of commercial purity polycrystalline aluminum under ultra-high strain-rates (~105 /s) and test temperatures up to melt (i.e. 643 °C). The applied stress at the aluminum/target interface, as inferred from the measured normal free-surface particle velocity record, shows progressive weakening with increasing test temperatures ranging from 23–620 °C; at higher temperatures (470–620 °C) this rate of weakening is observed to decrease, and at the highest test temperatures employed in the study, i.e. temperatures approaching the melt point of aluminum (643 °C), a net increase in the longitudinal stress is observed. Additionally, estimates of longitudinal elastic impedance of the sample material, as inferred via impedance matching from the particle velocity states at shock plateau show similar monotonic decrease with temperature, except for the highest test temperature case, in which reversal of this trend is observed. Though slight, these noticeable changes in the impedance, and stress/velocity states likely indicate variances in the strengthening/hardening response of the material, which can be linked to transition in the dominant plastic flow mechanisms as the sample approaches the melting point. Scanning electron microscopy of the impact surface of the post-test samples reveal coarsening of the sample grains due to static recrystallization during the heating phase of the experiment. Additional experiments are performed on annealed specimens to probe the effects of microstructural changes, i.e. grain size, and/or relief of residual strains in the interpretation of the measured response of aluminum. Finally, the results, which show a decrease in the longitudinal acoustic impedance, and decrease in the levels of stress/particle velocity under shock loading, indicate that the effects of annealing may play a role in the observed response by promoting softening of the dynamic strength, and/or lessening of the rate of hardening in a post-yield regime.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Covariance Matrix Evaluations for Independent Mass Fission Yields

Recent needs for more accurate fission product yields include covariance information to allow improved uncertainty estimations of the parameters used by design codes. The aim of this work is to investigate the possibility to generate more reliable and complete uncertainty information on independent mass fission yields. Mass yields covariances are estimated through a convolution between the multi-Gaussian empirical model based on Brosa's fission modes, which describe the pre-neutron mass yields, and the average prompt neutron multiplicity curve. The covariance generation task has been approached using the Bayesian generalized least squared method through the CONRAD code. Preliminary results on mass yields variance-covariance matrix will be presented and discussed from physical grounds in the case of {sup 235}U(n{sub th}, f) and {sup 239}Pu(n{sub th}, f) reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

The cluster decomposition of the configurational energy of multicomponent alloys

Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.

Chemistry↗
DOE OSTI2019

Evaluation of earthquake stress parameters and its scaling during the 2016-2017 Amatrice-Norcia-Visso sequence -- Part I

The Amatrice–Norcia–Visso sequence is distinguished by complex behaviour that is somewhat atypical of main-shock–aftershock sequences, as there were multiple large main shocks that continued for months. Here, we focus on the Amatrice sequence (main shock 2016 August 24, M w = 5.97) to evaluate the apparent stress values and magnitude-dependent scaling in order to improve our knowledge of processes that control small and large earthquakes within this active region of Italy. Apparent stress is proportional to the ratio of radiated seismic energy and seismic moment, and as such, these stress parameters play an important role in hazard prediction as they have a strong effect on the observed and predicted ground shaking. We analyse 83 events of the sequence from 2016 August 24 to October 16, within a radius of 20 km from the main shock and with an M w ranging between 5.97 and 2.72. Taking advantage of the averaging nature of coda waves, we analyse coda-envelope-based spectral ratios between neighbouring event pairs. We use equations proposed by Walter et al. to consider stable, low-frequency and high-frequency spectral ratio levels which provide measures of the corner frequency and apparent stress ratios of the events within the sequence. The results demonstrate non-self-similar behaviour within the sequence, indicating a change in dynamics between the largest events and the smaller aftershocks. The apparent stress and corner frequency estimates are compared to those obtained by Malagnini and Munafò who utilized hundreds of direct S-wave spectral ratio measurements to obtain their results. Although our analysis is based only on 83 events, our results are in very good agreement, demonstrating once more that the use of coda waves is very stable and provides lower variance measures than those using direct waves. A comparison with recent Central Apennines source scaling models derived from various seismic sequences (1997–1998 Colfiorito, 2002 San Giuliano di Puglia, 2009 L'Aquila) shows that the Amatrice sequence source scaling in this study is well represented by the models proposed by Pacor et al. and Malagnini and Mayeda.

58 GEOSCIENCES↗
NASA NTRS2010

A Framework for Propagation of Uncertainties in the Kepler Data Analysis Pipeline

The Kepler space telescope is designed to detect Earth-like planets around Sun-like stars using transit photometry by simultaneously observing 100,000 stellar targets nearly continuously over a three and a half year period. The 96-megapixel focal plane consists of 42 charge-coupled devices (CCD) each containing two 1024 x 1100 pixel arrays. Cross-correlations between calibrated pixels are introduced by common calibrations performed on each CCD requiring downstream data products access to the calibrated pixel covariance matrix in order to properly estimate uncertainties. The prohibitively large covariance matrices corresponding to the ~75,000 calibrated pixels per CCD preclude calculating and storing the covariance in standard lock-step fashion. We present a novel framework used to implement standard propagation of uncertainties (POU) in the Kepler Science Operations Center (SOC) data processing pipeline. The POU framework captures the variance of the raw pixel data and the kernel of each subsequent calibration transformation allowing the full covariance matrix of any subset of calibrated pixels to be recalled on-the-fly at any step in the calibration process. Singular value decomposition (SVD) is used to compress and low-pass filter the raw uncertainty data as well as any data dependent kernels. The combination of POU framework and SVD compression provide downstream consumers of the calibrated pixel data access to the full covariance matrix of any subset of the calibrated pixels traceable to pixel level measurement uncertainties without having to store, retrieve and operate on prohibitively large covariance matrices. We describe the POU Framework and SVD compression scheme and its implementation in the Kepler SOC pipeline.

Clarke, Bruce D.↗
DOE OSTI2018

Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields

In this paper, we present a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log-variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. Finally, it is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.

58 GEOSCIENCES↗
DOE OSTI2022

Parametric model-order-reduction development for unsteady convection

A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parameter space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.

leray regularization↗
NASA NTRS2010

Improving Computational Efficiency of Prediction in Model-Based Prognostics Using the Unscented Transform

Model-based prognostics captures system knowledge in the form of physics-based models of components, and how they fail, in order to obtain accurate predictions of end of life (EOL). EOL is predicted based on the estimated current state distribution of a component and expected profiles of future usage. In general, this requires simulations of the component using the underlying models. In this paper, we develop a simulation-based prediction methodology that achieves computational efficiency by performing only the minimal number of simulations needed in order to accurately approximate the mean and variance of the complete EOL distribution. This is performed through the use of the unscented transform, which predicts the means and covariances of a distribution passed through a nonlinear transformation. In this case, the EOL simulation acts as that nonlinear transformation. In this paper, we review the unscented transform, and describe how this concept is applied to efficient EOL prediction. As a case study, we develop a physics-based model of a solenoid valve, and perform simulation experiments to demonstrate improved computational efficiency without sacrificing prediction accuracy.

Daigle, Matthew John↗
NASA NTRS2005

Tools for Basic Statistical Analysis

Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.

Luz, Paul L.↗
DOE OSTI2013

Fission matrix-based Monte Carlo criticality analysis of fuel storage pools

Standard Monte Carlo transport procedures experience difficulties in solving criticality problems in fuel storage pools. Because of the strong neutron absorption between fuel assemblies, source convergence can be very slow, leading to incorrect estimates of the eigenvalue and the eigenfunction. This study examines an alternative fission matrix-based Monte Carlo transport method that takes advantage of the geometry of a storage pool to overcome this difficulty. The method uses Monte Carlo transport to build (essentially) a fission matrix, which is then used to calculate the criticality and the critical flux. This method was tested using a test code on a simple problem containing 8 assemblies in a square pool. The standard Monte Carlo method gave the expected eigenfunction in 5 cases out of 10, while the fission matrix method gave the expected eigenfunction in all 10 cases. In addition, the fission matrix method provides an estimate of the error in the eigenvalue and the eigenfunction, and it allows the user to control this error by running an adequate number of cycles. Because of these advantages, the fission matrix method yields a higher confidence in the results than standard Monte Carlo. We also discuss potential improvements of the method, including the potential for variance reduction techniques. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report

Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

GRAVSAT error analysis by means of global spectral analyses of the marine geoid from SEASAT altimeter data

The geographical variability of short wavelength geoid power spectra (geoid roughness), was mapped for the world's oceans between latitudes 72 deg N and 72 deg S. A spectral analysis of SEASAT altimeter data, reduced to sea surface heights, was performed at 2 minute intervals for 15 consecutive days of the 3-day repeat orbit. The geoid roughness represented by these spectra for wavelengths shorter than about 220 km is separated from the total sea height variance and is displayed in the form of a global contour map. The global average geoid roughness is 32 cm RMS, varying from a high in excess of 2 m RMS near deep ocean trenches to a low of 2 cm RMS in the southeast Pacific near the East Pacific Rise. This average value agrees well with previous estimates based on gravimetry and GEOS-3 altimetry. In general, the smoothest areas in the marine geoid overlie relatively young seafloor adjacent mid-ocean spreading centers, where even short-wavelength topographic variations tend to be isostatically compensated.

Source record↗
NASA NTRS1983

Roughness of the marine geoid from Seasat altimetry

The geographical variability of short wavelength geoid power spectra (geoid roughness) has been mapped for the world's oceans between latitudes 72 deg N and 72 deg S. A spectral analysis of Seasat altimeter data, reduced to sea surface heights, has been performed at 2-min intervals for 15 consecutive days of the 3-day repeat orbit. The geoid roughness represented by these spectra for wavelengths shorter than about 220 km is separated from the total sea height variance and is displayed in the form of a global contour map. The global average geoid roughness is 32 cm RMS, varying from a high in excess of 2 m RMS near deep ocean trenches to a low of 2 cm RMS in the southeast Pacific near the east Pacific rise. This average value agrees well with previous estimates based on gravimetry and GEOS 3 altimetry. In general, the smoothest areas in the marine geoid overlie relatively young sea floor adjacent mid-ocean spreading centers, where even short wavelength topographic variations tend to be isostatically compensated.

Brown, R. D.↗