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Results for “method of averaging”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Influence of Averaging Method on the Evaluation of a Coastal Ocean Color Event on the U.S. Northeast Coast

Application of appropriate spatial averaging techniques is crucial to correct evaluation of ocean color radiometric data, due to the common log-normal or mixed log-normal distribution of these data. Averaging method is particularly crucial for data acquired in coastal regions. The effect of averaging method was markedly demonstrated for a precipitation-driven event on the U.S. Northeast coast in October-November 2005, which resulted in export of high concentrations of riverine colored dissolved organic matter (CDOM) to New York and New Jersey coastal waters over a period of several days. Use of the arithmetic mean averaging method created an inaccurate representation of the magnitude of this event in SeaWiFS global mapped chl a data, causing it to be visualized as a very large chl a anomaly. The apparent chl a anomaly was enhanced by the known incomplete discrimination of CDOM and phytoplankton chlorophyll in SeaWiFS data; other data sources enable an improved characterization. Analysis using the geometric mean averaging method did not indicate this event to be statistically anomalous. Our results predicate the necessity of providing the geometric mean averaging method for ocean color radiometric data in the Goddard Earth Sciences DISC Interactive Online Visualization ANd aNalysis Infrastructure (Giovanni).

Acker, James G.↗
NASA NTRS1984

Long-term orbit prediction for the Venus Radar Mapper Mission using an averaging method

A set of singly averaged equations of motion are presented and applied to long-term orbit prediction of an orbiting spacecraft around a slowly rotating planet, using the Venus Radar Mapper Mission as an example. The equations of motion used are valid for all eccentricities less than one. The disturbing potentials used include nonsphericity of the Venus gravity field and third-body effects due to the sun. Recursive relationships are used in the expansion and evaluation of these potentials and their respective partial derivatives. Special care is taken to optimize computational efficiency. The averaging method is compared with high precision Cowell's method using a desktop microcomputer and shows computational saving of about two orders of magnitude.

Kwok, J. H.↗
NASA NTRS2020

Assessing the Impacts of Two Averaging Methods on AIRS Level 3 Monthly Products and Multi-Year Monthly Means

The Atmospheric Infrared Sounder (AIRS) onboard NASA’s Aqua satellite provides more than 16 years of data. Its monthly gridded (Level 3) product has been widely used for climate research and applications. Since counts of successful soundings in a grid cell are used to derive monthly averages, this “Averaged By Observations (ABO)” approach effectively gives equal importance to all participating soundings within a month. It is conceivable, then, that days with more observations due to day-to-day orbit shift and regimes with better retrieval skills, will contribute disproportionately to the monthly average within a cell. Alternatively, the AIRS Level 3 monthly product can be produced through an "Averaged By Days (ABD)” approach, where the monthly mean in a grid cell is a simple average of the daily means. The effects of these averaging methods on the AIRS version 6 monthly product are assessed quantitatively using temperature and water vapor at surface and 500hPa. The ABO method results in a warmer (slightly colder) global mean temperature at surface (500hPa) and a drier global mean water vapor than ABD method. The AIRS multi-year monthly mean temperature and water vapor from both methods are also compared with the Modern-Era Retrospective analysis for Research and Applications – 2 (MERRA-2) product and evaluated with a simulation experiment, indicating the ABD method has less error and is more closely correlated with MERRA-2. In summary, the ABD method is recommended for future versions of the AIRS Level 3 monthly product and more data services supporting Level 3 aggregation are needed.

AIRS↗
NASA NTRS1992

A doubly averaging method for third body perturbations in planet equator coordinates

The first order doubly averaged potential due to third-body gravity is derived in any arbitrary coordinates. The equations of motion are nonsingular at zero eccentricity. The derivation uses a recursive method which allows easy expansion to higher order terms. Instead of using analytical quadrature to obtain the doubly averaged potential, the method presented in this paper simply eliminates the mean anomaly of the perturbed and perturbing bodies by inspection of the recursive formulation. The derivatives of the orbital elements can be numerically integrated rapidly. When a planet equator coordinate system is used, they can be added directly to the derivatives due to gravity harmonics without any coordinate transformation. The method is applied to various high altitude missions. The results are compared with a high precision numerical integration method and are found to provide excellent agreement.

Hwok, Johnny H.↗
NASA NTRS1978

A note on the averaging method

A simple problem of a two-body system perturbed by the disturbing function epsilon/r-squared is considered to show that the time-averaged equations of the true and mean anomaly are not necessarily equal. Secular effects due to perturbations in the mean and true anomalies are different not only in value but also in sign. A more general case where the disturbing function is periodic with respect to the mean anomaly is also considered. Here a discrepancy in the time-averaged solutions is due to the fact that the mean anomaly is an action-angle variable conjugate to the action variable L, while the true anomaly is not. When the action-angle variables are chosen as dependent variables, the Hamiltonian is a function only of action variables. One must first derive first-order solutions, substitute them into the right-hand side of the equations of motion, and then take time averages.

Kinoshita, H.↗
NASA NTRS1977

A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume 1: The generalized method of averaging applied to the artificial satellite problem

A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.

Mcclain, W. D.↗
NASA NTRS1990

Cell averaging Chebyshev methods for hyperbolic problems

A cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form is described. Formulas are presented for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in spectral methods. The cell averaging methods presented are proven stable for linear scalar hyperbolic equations and present numerical simulations of shock-density wave interaction using the new cell averaging Chebyshev methods.

Wei, Cai↗
DOE OSTI2025

The Method of Finite Averages

The Method of Finite Averages (MoFA) is a rigorous multiscale modeling methodology for efficiently modeling multi-physical phenomena in heterogeneous porous media. The code developed in this project aims to perform the numerical calculations required to formulate, implement, and verify MoFA models for Earth and Energy systems (i.e., model verification refers to performing fully-resolved simulations of the systems and comparing their results to those of the models). In general, MoFA transforms partial differential equations (PDEs) describing the fine-scale physics of a system into coupled ordinary differential equations (ODEs)---in time---that describe the coarse-scale---or "average"---physical behaviors of the system. This transformation significantly expedites system simulation, as the coarse-scale ODEs involve vastly fewer degrees of freedom than the fine-scale PDEs. The code developed under this project will allow users to 1.) generate system geometries and numerical meshes, 2.) solve the PDE and ODE systems required for MoFA model formulation and implementation, 3.) solve the PDE systems required to obtain fully-resolved simulation results for model verification, and 4.) compare and plot results (e.g., the model and fully-resolved simulation solutions, the error between the solutions, etc.).

Pietrzyk, KyleM [Lawrence Livermore National Labor↗
DOE OSTI2026

Evaluation of methods and improvement of predictions for specification properties of petroleum-based and alternative aviation fuels

To support our research and process modeling for liquid fuels, including blends, from petroleum and synthetic sources such as from biomass intermediates, we evaluated composition-based prediction methods and improved predictions for five key specification properties of petroleum-based and alternative aviation fuels, namely distillation temperatures (10 % distilled, t 10 , and final boiling point, t FBP ), density, flash point, net heat of combustion, and freezing point. The types of fuels included were petroleum-based jet fuels, jet-fuel surrogate mixtures, synthetic blending components obtained from different sources, and blends of Jet A with many synthetic blending components. Expanded datasets to update associated parameters allowed significant improvements for one of the prediction methods used in earlier work, namely the Modified Weighted Average method published initially by Shi et al. By considering the importance of lighter compounds for flash points and heavier compounds for freezing points, the revised Modified Weighted Average method was further improved. For liquid density, the revised Modified Weighted Average method gave the best overall results. The revised Modified Weighted Average method, the American Society for Testing and Materials D7215 method, and the D7215 method modified by another group gave comparable results for flash point, while the revised Modified Weighted Average and D3338 methods gave the best results for net heat of combustion. Freezing point was well predicted using the revised Modified Weighted Average method and showed the most significant improvements over current predictions. Distillation temperature t 10 was not well predicted, while t FBP was predicted with a mean absolute error comparable to experimental reproducibility.

09 BIOMASS FUELS↗
NASA NTRS1982

Equivalence of the generalized Lie-Hori method and the method of averaging

In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence both Duffing's equation and the van der Pol equation are solved using each method.

Ahmed, A.↗
NASA NTRS1984

Equivalence of the generalized Lie-Hori method and the method of averaging

In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence Duffing's equation, the van der Pol equation and the oscillator with quadratic damping problem are solved using each method.

Ahmed, A. H.↗
DOE OSTI2024

Stochastic average model methods

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

97 MATHEMATICS AND COMPUTING↗