Center for Computing Research (CCR)
Center for Computing Research (CCR)

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A comparison of methods for representing sparsely sampled random quantities

Romero, Vicente J.; Swiler, Laura P.; Urbina, Angel U.

This report discusses the treatment of uncertainties stemming from relatively few samples of random quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse data samples it is not practical to have a goal of accurately estimating the underlying probability density function (PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a specified percentile range of the actual PDF, say the range between 0.025 and .975 percentiles, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the desired percentile range of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem interesting and difficult. In this report, five uncertainty representation techniques are characterized for their performance on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods, statistical Tolerance Intervals and a kernel density approach specifically developed for handling sparse data, exhibit significantly better overall performance than the others.

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TYPE SAND Report YEAR 2013
DOIOSTI

Nonlinear kinematics for piezoelectricity in ALEGRA-EMMA

Mitchell, John A.; Fuller, Timothy J.

This report develops and documents nonlinear kinematic relations needed to implement piezoelectric constitutive models in ALEGRA-EMMA [5], where calculations involving large displacements and rotations are routine. Kinematic relationships are established using Gausss law and Faradays law; this presentation on kinematics goes beyond piezoelectric materials and is applicable to all dielectric materials. The report then turns to practical details of implementing piezoelectric models in an application code where material principal axes are rarely aligned with user defined problem coordinate axes. This portion of the report is somewhat pedagogical but is necessary in order to establish documentation for the piezoelectric implementation in ALEGRA-EMMA. This involves transforming elastic, piezoelectric, and permittivity moduli from material principal axes to problem coordinate axes. The report concludes with an overview of the piezoelectric implementation in ALEGRA-EMMA and small verification examples.

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TYPE SAND Report YEAR 2013
DOIOSTI

Kalman-filtered compressive sensing for high resolution estimation of anthropogenic greenhouse gas emissions from sparse measurements

Ray, Jaideep; Lee, Jina; Lefantzi, Sophia; Van Bloemen Waanders, Bart

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. The limited nature of the measured data leads to a severely-underdetermined estimation problem. If the estimation is performed at fine spatial resolutions, it can also be computationally expensive. In order to enable such estimations, advances are needed in the spatial representation of ffCO2 emissions, scalable inversion algorithms and the identification of observables to measure. To that end, we investigate parsimonious spatial parameterizations of ffCO2 emissions which can be used in atmospheric inversions. We devise and test three random field models, based on wavelets, Gaussian kernels and covariance structures derived from easily-observed proxies of human activity. In doing so, we constructed a novel inversion algorithm, based on compressive sensing and sparse reconstruction, to perform the estimation. We also address scalable ensemble Kalman filters as an inversion mechanism and quantify the impact of Gaussian assumptions inherent in them. We find that the assumption does not impact the estimates of mean ffCO2 source strengths appreciably, but a comparison with Markov chain Monte Carlo estimates show significant differences in the variance of the source strengths. Finally, we study if the very different spatial natures of biogenic and ffCO2 emissions can be used to estimate them, in a disaggregated fashion, solely from CO2 concentration measurements, without extra information from products of incomplete combustion e.g., CO. We find that this is possible during the winter months, though the errors can be as large as 50%.

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TYPE SAND Report YEAR 2013
DOIOSTI

LDRD project 151362 : low energy electron-photon transport

Kensek, Ronald P.; Hjalmarson, Harold P.; Magyar, Rudolph J.; Bondi, Robert J.

At sufficiently high energies, the wavelengths of electrons and photons are short enough to only interact with one atom at time, leading to the popular %E2%80%9Cindependent-atom approximation%E2%80%9D. We attempted to incorporate atomic structure in the generation of cross sections (which embody the modeled physics) to improve transport at lower energies. We document our successes and failures. This was a three-year LDRD project. The core team consisted of a radiation-transport expert, a solid-state physicist, and two DFT experts.

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TYPE SAND Report YEAR 2013
DOIOSTI

A margin based approach to determining sample sizes via tolerance bounds

Newcomer, Justin T.; Rodriguez, Katherine E.

This paper proposes a tolerance bound approach for determining sample sizes. With this new methodology we begin to think of sample size in the context of uncertainty exceeding margin. As the sample size decreases the uncertainty in the estimate of margin increases. This can be problematic when the margin is small and only a few units are available for testing. In this case there may be a true underlying positive margin to requirements but the uncertainty may be too large to conclude we have sufficient margin to those requirements with a high level of statistical confidence. Therefore, we provide a methodology for choosing a sample size large enough such that an estimated QMU uncertainty based on the tolerance bound approach will be smaller than the estimated margin (assuming there is positive margin). This ensures that the estimated tolerance bound will be within performance requirements and the tolerance ratio will be greater than one, supporting a conclusion that we have sufficient margin to the performance requirements. In addition, this paper explores the relationship between margin, uncertainty, and sample size and provides an approach and recommendations for quantifying risk when sample sizes are limited.

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TYPE SAND Report YEAR 2013
DOIOSTI
Results 8601–8650 of 12,511
Results 8601–8650 of 12,511
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