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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 NTRS2021

Nonlinear Unsteady Aerodynamic Modeling Using Empirical Orthogonal Functions

Empirical orthogonal function modeling is explained and applied to identify compact discrete-time nonlinear unsteady aerodynamic models from data generated by an unsteady three-dimensional compressible Navier-Stokes flow solver for an airfoil undergoing various pitching motions. Model structures, model parameter estimates, and model parameter uncertainty estimates for nondimensional lift, drag, and pitching moment coefficient models were determined autonomously and directly from the data. Prediction tests using data that were not used in the modeling process showed that the identified models exhibited excellent prediction capability, which is a strong indicator of an accurate model.

empirical↗
NASA NTRS1982

Sampling errors in the estimation of empirical orthogonal functions

Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is 'close' to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

North, G. R.↗
NASA NTRS1993

Nonlinear aerodynamic modeling using multivariate orthogonal functions

A technique was developed for global modeling of nonlinear aerodynamic coefficients using multivariate orthogonal functions based on the data. Each orthogonal function retained in the model was decomposed into an expansion of ordinary polynomials in the independent variables, so that the final model could be interpreted as selectively retained terms from a multivariable power series expansion. A predicted squared-error metric was used to determine the orthogonal functions to be retained in the model; analytical derivatives were easily computed. The approach was demonstrated on the Z-body axis aerodynamic force coefficient (Cz) wind tunnel data for an F-18 research vehicle which came from a tabular wind tunnel and covered the entire subsonic flight envelope. For a realistic case, the analytical model predicted experimental values of Cz very well. The modeling technique is shown to be capable of generating a compact, global analytical representation of nonlinear aerodynamics. The polynomial model has good predictive capability, global validity, and analytical differentiability.

Morelli, Eugene A.↗
DOE OSTI2026

Challenges and alternatives to empirical orthogonal functions for earth system data

Empirical orthogonal functions (EOFs) applied to gridded Earth system data enables users to diagnose modes of variability with relative ease. Yet, many challenges to interpretation exist such that they must be used with awareness and intention when applied to gridded climate data, especially with large ensembles. Utilizing data from two different Earth system modelling large ensemble frameworks, the Energy Exoscale Earth System Model and the Community Earth System Model, as well as reanalysis data, common EOF pitfalls are summarized and discussed. Challenges include erroneous mode swapping, sign flipping, and the temporal variability of the centers of action. For modes of variability with similar contribution to variance, mode swapping is not uncommon. Sign flipping can occur with almost any mode where the pattern is correct, but the sign is arbitrary. Although the variability of the center of action is not necessarily problematic, it potentially complicates interpretation over multi-century timescales. A wide variety of alternative methods to EOFs exist, but fitness-for-purpose must be evaluated. Additionally, illustrations of alternative methods and examples of proper use are provided. Alternative methods fit into three categories: EOF variants, linear methods, and multilinear methods.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2003

Wind Tunnel Database Development using Modern Experiment Design and Multivariate Orthogonal Functions

A wind tunnel experiment for characterizing the aerodynamic and propulsion forces and moments acting on a research model airplane is described. The model airplane called the Free-flying Airplane for Sub-scale Experimental Research (FASER), is a modified off-the-shelf radio-controlled model airplane, with 7 ft wingspan, a tractor propeller driven by an electric motor, and aerobatic capability. FASER was tested in the NASA Langley 12-foot Low-Speed Wind Tunnel, using a combination of traditional sweeps and modern experiment design. Power level was included as an independent variable in the wind tunnel test, to allow characterization of power effects on aerodynamic forces and moments. A modeling technique that employs multivariate orthogonal functions was used to develop accurate analytic models for the aerodynamic and propulsion force and moment coefficient dependencies from the wind tunnel data. Efficient methods for generating orthogonal modeling functions, expanding the orthogonal modeling functions in terms of ordinary polynomial functions, and analytical orthogonal blocking were developed and discussed. The resulting models comprise a set of smooth, differentiable functions for the non-dimensional aerodynamic force and moment coefficients in terms of ordinary polynomials in the independent variables, suitable for nonlinear aircraft simulation.

Morelli, Eugene A.↗
NASA NTRS1984

Empirical orthogonal functions and normal modes

An attempt to provide physical insight into the empirical orthogonal function (EOF) representation of data fields by the study of fields generated by linear stochastic models is presented in this paper. In a large class of these models, the EOFs at individual Fourier frequencies coincide with the orthogonal mechanical modes of the system - provided they exist. The precise mathematical criteria for this coincidence are derived and a physical interpretation is provided. A scheme possibly useful in forecasting is formally constructed for representing any stochastic field by a linear Hermitian model forced by noise.

North, G. R.↗
NASA NTRS1989

Empirical orthogonal functions and multiple flow regimes in the Southern Hemisphere winter

A new empirical orthogonal function (EOF) analysis of winter 500 mb geopotential height anomalies in the Southern Hemisphere is presented. An earlier EOF analysis prefiltered the anomalies to exclude wavenumbers 5 and higher; the present analysis does not. The different preprocessing of data affects the results. All three distinct planetary flow regimes identified in the winter circulation of the Southern Hemisphere by a pattern correlation method are captured by the new set of EOFs; only two of those regimes were captured by the earlier set. The new results, therefore, lend further support to the idea that EOFs point to distinct planetary flow regimes.

Farrara, John D.↗
NASA NTRS1989

Empirical orthogonal function analysis of cloud-containing coastal zone color scanner images of northeastern North American coastal waters

Empirical-orthogonal-function (EOF) analyses were carried out on 36 images of the Mid-Atlantic Bight and the Gulf of Maine, obtained by the CZCS aboard Nimbus 7 for the time period from February 28 through July 9, 1979, with the purpose of determining pigment concentrations in coastal waters. The EOF procedure was modified so as to include images with significant portions of data missing due to cloud obstruction, making it possible to estimate pigment values in areas beneath clouds. The results of image analyses explained observed variances in pigment concentrations and showed a south-to-north pattern corresponding to an April Mid-Atlantic Bight bloom and a June bloom over Nantucket Shoals and Platts Bank.

Eslinger, David L.↗
NASA NTRS1986

Investigation of seasonal variability of the wind stress curl over the North Atlantic Ocean by means of empirical orthogonal function analysis

The seasonal variability of the wind stress curl over the North Atlantic is investigated by means of empirical orthogonal function (EOF) analysis. The curl field is calculated from 1 year of First Global GARP Experiment wind data. It was found that 44 percent of the variability is contained in four significant eigenvectors. Their spatial patterns are characterized by basin-sized oscillations with larger amplitude to the north of 40 deg N. Their associated time series coefficients have the highest amplitude during the winter and show a tendency toward a white frequency spectrum which nevertheless exhibits noticeable peaks or gaps at certain frequencies. Physically, the first EOF is seen as the seasonal fluctuations of the mean wind stress curl pattern. Five other eigenvectors are also found to be above the noise level, but they account for only a smaller percentage of variability (19 percent). They are characterized by smaller spatial scales than the basin size. Their time series coefficients show a whiter frequency spectrum.

Barnier, B.↗
NASA NTRS2012

A High-resolution Model of Field-aligned Currents Through Empirical Orthogonal Functions Analysis (MFACE)

Ten years of CHAMP magnetic field measurements are integrated into MFACE, a model of field-aligned currents (FACs) using empirical orthogonal functions (EOFs). EOF1 gives the basic Region-1/Region-2 pattern varying mainly with the interplanetary magnetic field Bz component. EOF2 captures separately the cusp current signature and By-related variability. Compared to existing models, MFACE yields significantly better spatial resolution, reproduces typically observed FAC thickness and intensity, improves on the magnetic local time (MLT) distribution, and gives the seasonal dependence of FAC latitudes and the NBZ current signature. MFACE further reveals systematic dependences on By, including 1) Region-1/Region-2 topology modifications around noon; 2) imbalance between upward and downward maximum current density; 3) MLT location of the Harang discontinuity. Furthermore, our procedure allows quantifying response times of FACs to solar wind driving at the bow shock nose: we obtain 20 minutes and 35-40 minutes lags for the FAC density and latitude, respectively.

CHAMP↗
NASA NTRS1999

Modeling the High Speed Research Cycle 2B Longitudinal Aerodynamic Database Using Multivariate Orthogonal Functions

The data for longitudinal non-dimensional, aerodynamic coefficients in the High Speed Research Cycle 2B aerodynamic database were modeled using polynomial expressions identified with an orthogonal function modeling technique. The discrepancy between the tabular aerodynamic data and the polynomial models was tested and shown to be less than 15 percent for drag, lift, and pitching moment coefficients over the entire flight envelope. Most of this discrepancy was traced to smoothing local measurement noise and to the omission of mass case 5 data in the modeling process. A simulation check case showed that the polynomial models provided a compact and accurate representation of the nonlinear aerodynamic dependencies contained in the HSR Cycle 2B tabular aerodynamic database.

Morelli, E. A.↗
NASA NTRS2001

Response Surface Modeling Using Multivariate Orthogonal Functions

A nonlinear modeling technique was used to characterize response surfaces for non-dimensional longitudinal aerodynamic force and moment coefficients, based on wind tunnel data from a commercial jet transport model. Data were collected using two experimental procedures - one based on modem design of experiments (MDOE), and one using a classical one factor at a time (OFAT) approach. The nonlinear modeling technique used multivariate orthogonal functions generated from the independent variable data as modeling functions in a least squares context to characterize the response surfaces. Model terms were selected automatically using a prediction error metric. Prediction error bounds computed from the modeling data alone were found to be- a good measure of actual prediction error for prediction points within the inference space. Root-mean-square model fit error and prediction error were less than 4 percent of the mean response value in all cases. Efficacy and prediction performance of the response surface models identified from both MDOE and OFAT experiments were investigated.

Morelli, Eugene A.↗
NASA NTRS1984

Description of sunspot cycles by orthogonal functions

Based on the principal component analysis technique and evidence for a 22-yr double-sunspot cycle periodicity. The time series of sunspot numbers is represented as a sum of mutually orthogonal eigenvectors in the time domain. It is shown that the first two eigenvectors account for about 90 percent of the cumulative 'signal power,' and that this is sufficient for reconstruction of the raw data curve. It is also noted that the second eigenvector behaves as the time derivative of the first, and that a phase-plane plot of these eigenvectors (i.e. a plot of a variable vs. its rate of change) suggests that the sun's sunspot cycle is driven by an oscillator; the implication is that, embedded within the sun, a chronometer is at work (e.g. Dicke, 1979).

Teuber, D. L.↗
NASA NTRS1984

Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform

A technique for applying discrete Fourier series to infinite domains is presented. The technique uses mappings designed to minimize truncation error and can be applied to solve mixed initial boundary value problems among others. The method is alias-free and yields consistent differentiation and integration operators. The mapping-induced truncation error is explicitly expressible and small in nearly all cases of interest. The method is illustrated for three problems involving convection, diffusion, and vortex interaction.

Cain, A. B.↗