Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ORTHOGONAL FUNCTION”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1993

Nonlinear aerodynamic modeling using multivariate orthogonal functions

The problem to be addressed in this work is that of modeling nondimensional force and moment aerodynamic coefficients over the entire subsonic envelope. The particular application discussed here is the Z force coefficient for the F-18 High Angle of Attack Research Vehicle (HARV).

Morelli, Eugene A.↗
NASA NTRS2022

A Rotation Procedure to Improve Seasonally Varying Empirical Orthogonal Function Bases for MJO Indices

Various indices have been defined to characterize the phase and amplitude of the Madden-Julian oscillation (MJO). One widely used index is the Outgoing Longwave Radiation (OLR) based MJO index (OMI), which is calculated using the spatial pattern of 30-96-day eastward-filtered OLR. The EOFs used to calculate the OMI in observations are prone to degeneracy and exhibit oscillations on the order of 10-20 days, despite initial filtering of the OLR. We propose a simple modification to the OMI that involves aligning the EOFs between neighboring days while retaining the spatial pattern described by the EOFs. This rotation method is implemented as a postprocessing procedure of the current OMI calculation and cleanly removes the spurious oscillations and degeneracy issues seen in the standard method. A similar rotation procedure can be implemented in calculations of other MJO indices.

Sarah Weidman↗
DOE OSTI2015

Fully-Implicit Orthogonal Reconstructed Discontinuous Petrov-Galerkin Method for Multiphysics Problems

This document is focussed on the development of reconstructed discontinuous Galerkin (RDG P n P m ) method, based on orthogonal basis functions. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time discretization. The method is designed for generic partial differential equations, including transient hyperbolic, parabolic and/or elliptic operators, which are attributed to many multiphysics problems. Our driving application of interest is additive manufacturing, which requires simulations of fluid-solid-gas systems, with compressibility effects and phase change (melting/ solidification). Thus, we demonstrate the method capabilities for solving nonlinear heat conduction equation coupled with multi-material Navier-Stokes based compressible fluid (in low Mach number limit) systems. We focus our attention to the method accuracy (in both time and space), as well as solvability of linear algebra involved in linear steps of the Newton-based solver. We demonstrate the accuracy and efficacy of the method, emphasizing the advantages from the orthogonality of basis functions, which makes better conditioning of underlying (approximate) Jacobian matrices, and rapid convergence of Krylov methods. iii

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

Morelli, Eugene A.↗
DOE OSTI2016

An Empirical Orthogonal Function-Based Algorithm for Estimating Terrestrial Latent Heat Flux from Eddy Covariance, Meteorological and Satellite Observations

Accurate estimation of latent heat flux (LE) based on remote sensing data is critical in characterizing terrestrial ecosystems and modeling land surface processes. Many LE products were released during the past few decades, but their quality might not meet the requirements in terms of data consistency and estimation accuracy. Merging multiple algorithms could be an effective way to improve the quality of existing LE products. In this paper, we present a data integration method based on modified empirical orthogonal function (EOF) analysis to integrate the Moderate Resolution Imaging Spectroradiometer (MODIS) LE product (MOD16) and the Priestley-Taylor LE algorithm of Jet Propulsion Laboratory (PT-JPL) estimate. Twenty-two eddy covariance (EC) sites with LE observation were chosen to evaluate our algorithm, showing that the proposed EOF fusion method was capable of integrating the two satellite data sets with improved consistency and reduced uncertainties. Further efforts were needed to evaluate and improve the proposed algorithm at larger spatial scales and time periods, and over different land cover types.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Quantifying the agreement between observed and simulated extratropical modes of interannual variability

Using historical simulations of the Coupled Model Intercomparison Project-5 (CMIP5) and multiple observationally-based datasets, we employ skill metrics to analyze the fidelity of the simulated Northern Annular Mode, the North Atlantic Oscillation, the Pacific North America pattern, the Southern Annular Mode, the Pacific Decadal Oscillation, the North Pacific Oscillation, and the North Pacific Gyre Oscillation. We assess the benefits of a unified approach to evaluate these modes of variability, which we call the common basis function (CBF) approach, based on projecting model anomalies onto observed empirical orthogonal functions (EOFs). The CBF approach circumvents issues with conventional EOF analysis, eliminating, for example, corrections of arbitrarily assigned, but inconsistent, signs of the EOF’s/PC’s being compared. It also avoids the problem that sometimes the first observed EOF is more similar to a higher order model EOF, particularly if the simulated EOFs are not well separated. Compared to conventional EOF analysis of models, the CBF approach indicates that models compare significantly better with observations in terms of pattern correlation and root-mean-squared-error (RMSE) than heretofore suggested. In many cases, models are doing a credible job at capturing the observationally-based estimates of patterns; however, errors in simulated amplitudes can be large and more egregious than pattern errors. In the context of the broad distribution of errors in the CMIP5 ensemble, sensitivity tests demonstrate that our results are relatively insensitive to methodological considerations (CBF vs. conventional approach), observational uncertainties in pattern (as determined by using multiple datasets), and internal variability (when multiple realizations from the same model are compared). The skill metrics proposed in this study can provide a useful summary of the ability of models to reproduce the observed EOF patterns and amplitudes. Additionally, the skill metrics can be used as a tool to objectively highlight where potential model improvements might be made. Finally, we advocate more systematic and objective testing of simulated extratropical variability, especially during the non-dominant seasons of each mode, when many models are performing relatively poorly.

58 GEOSCIENCES↗
NASA NTRS1987

The structure and evolution of seasonal wind anomalies over the near-equatorial eastern Indian and western Pacific Oceans

The longitude-height-time structure and evolution of near-equatorial wind variability over the eastern Indian and western Pacific Oceans are studied using data obtained from a network of eight radiosonde stations extending from southern India to the central Pacific Ocean. The seasonal zonal wind anomalies observed at the cross section beween Trivandrum and Majuro stations are analyzed using an empirical orthogonal function. The Walker Circulation fluctuations are described in terms of standing oscillations in the longitude-height plane, and it is determined that Southern Oscillation propagation anomaly best represents the wind fluctuations. A complex empirical orthogonal function (CEOF) analysis and an El Nino compositing methodology are applied to the seasonal zonal wind anomalies. It is determined that the composite El Nino anomalies correspond to the spatial structure and temporal evolution of anomalies implied by the CEOF analysis.

Gutzler, David S.↗
NASA NTRS2007

Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular Apertures

For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.

Aronstein, David L.↗
DOE OSTI2023

Evaluation of global teleconnections in CMIP6 climate projections using complex networks

In climatological research, the evaluation of climate models is one of the central research subjects. As an expression of large-scale dynamical processes, global teleconnections play a major role in interannual to decadal climate variability. Their realistic representation is an indispensable requirement for the simulation of climate change, both natural and anthropogenic. Therefore, the evaluation of global teleconnections is of utmost importance when assessing the physical plausibility of climate projections. We present an application of the graph-theoretical analysis tool δ-MAPS, which constructs complex networks on the basis of spatio-temporal gridded data sets, here sea surface temperature and geopotential height at 500 hPa. Complex networks complement more traditional methods in the analysis of climate variability, like the classification of circulation regimes or empirical orthogonal functions, assuming a new non-linear perspective. While doing so, a number of technical tools and metrics, borrowed from different fields of data science, are implemented into the δ-MAPS framework in order to overcome specific challenges posed by our target problem. Those are trend empirical orthogonal functions (EOFs), distance correlation and distance multicorrelation, and the structural similarity index. δ-MAPS is a two-stage algorithm. In the first place, it assembles grid cells with highly coherent temporal evolution into so-called domains. In a second step, the teleconnections between the domains are inferred by means of the non-linear distance correlation. We construct 2 unipartite and 1 bipartite network for 22 historical CMIP6 climate projections and 2 century-long coupled reanalyses (CERA-20C and 20CRv3). Potential non-stationarity is taken into account by the use of moving time windows. The networks derived from projection data are compared to those from reanalyses. Our results indicate that no single climate projection outperforms all others in every aspect of the evaluation. But there are indeed models which tend to perform better/worse in many aspects. Differences in model performance are generally low within the geopotential height unipartite networks but higher in sea surface temperature and most pronounced in the bipartite network representing the interaction between ocean and atmosphere.

58 GEOSCIENCES↗
DOE OSTI2014

Periodicity and patterns of ocean wind and wave climate

Winds and waves play a significant role in the global climate that can be examined through the proven Climate Forecast System Reanalysis (CFSR). A standard empirical orthogonal function method extracts dominant spatial patterns from time series of the reanalysis data. The results show strong zonal structures in the winds and saturation of swells across the ocean basins, but these dominant features obscure the periodicity of the climate cycles. Implementation of the Fourier transform removes non-oscillatory signals in the wind and waves for elucidation of cyclic features through the empirical orthogonal function method. A systematic analysis illustrates the dominant modes and their periodicity in the three major ocean basins. The North Atlantic dominates the variability in the entire ocean basin with a broad range of intra-seasonal signals. The Indian and Pacific are strongly influenced by inter-annual cycles of the El Niño Southern Oscillation and the Antarctica Oscillation. Here, these two oceans have strong components in the period of 50-90 days that have similar spatial structure to those of 2-5 years period suggesting linkage between the two frequency components.

13 HYDRO ENERGY↗
DOE OSTI2022

A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theory

The technique of surrogate optimisation is to use a simpler function to approximate a complex function that is time-consuming to evaluate. Here we show that the maximum of a special type of surrogate function f(U)=Tr(AU),UϵO(n) is at A T (AA T ) 1/2 , and that there is one and only one local maximum both in SO(n) and O(n)–SO(n). This function f(U) has been found to be useful in various aspects of electronic structure theory, including proving the Carlson-Keller theorem, and localising orbitals. As one other example, we apply it here to optimise the ground state of molecules using the Generalised Valence Bond wavefunction.

74 ATOMIC AND MOLECULAR PHYSICS↗