Search NASA⌕ Search

SEARCH · Search NASA

Results for “VECTOR ANALYSIS”

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 91 records · Page 5

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Storaasli, Olaf O.↗

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.

Storaasli, O. O.↗

Data Analysis for the SOLIS Vector Spectromagnetograph

The National Solar Observatory's SOLIS Vector Spectromagnetograph (VSM), which will produce three or more full-disk maps of the Sun's photospheric vector magnetic field every day for at least one solar magnetic cycle, is in the final stages of assembly. Initial observations, including cross-calibration with the current NASA/NSO spectromagnetograph (SPM) will soon be carried out at a test site in Tucson. This paper discusses data analysis techniques for reducing the raw data, calculation of line-of-sight magnetograms and both quick-look and high-precision inference of vector fields from Stokes spectral profiles. Existing SPM algorithms, suitably modified to accomodate the cameras, scanning pattern, and polarization calibration optics for the VSM, will be used to "clean" the raw data and to process line-of-sight, magnetograms. A recent. version of the High Altitude Observatory Milne-Eddington (HAO-ME) inversion code (Skumanich and Lites; 1987, 11)J 322, p. 473) will he used for high-precision vector fields since the algorithm has been extensively tested, is well understood, and is fast enough to complete data analysis within 24 hours of data acquisition. The simplified inversion algorithm of Auer, Heasley. arid House (1977, Sol. Phys. 55, p. 47) forms the initial guess for this version of the HAO-ME code and will be used for quick-look vector analysis of VSM data since its performance on simulated Stokes profiles is better than other candidate methods. Improvements (e.g., principal components analysis or neural networks) are under consideration and will be straightforward to implement. However, current resources are sufficient to store the original Stokes profiles only long enough for high-precision analysis. Retrospective reduction of Stokes data with improved methods will not be possible, and modifications will only be introduced when the advantages of doing so are compelling enough to justify discontinuity in the long-term data stream.

Jones, Harrison P.↗

Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures

An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.

Mangalgiri, P. D.↗

Simulation-Based Analysis and Prediction of Thrust Vector Servoelastic Coupling

A method of analysis and prediction of servoelastic coupling in launch vehicles is presented, surveying the discovery and subsequent resolution of a predicted servoelastic resonance phenomenon affecting the NASA Space Launch System launch vehicle at specific flight conditions. A physics-based linearized multibody mechanization of the governing equations is combined with first principles analysis to demonstrate that antisymmetric bending of the solid rocket motors leads to a reduction of equivalent viscous modal damping through coupling with the thrust vector control actuators. The sensitivity to parameters and the effects of the resonance phenomenon on flight control performance and stability are confirmed through extensive simulation verification in the time and frequency domain. A novel enhancement in model fidelity that accounts for Coriolis effects of fluid flow on bending within the solid rocket motor case and nozzle is shown to add sufficient damping to reduce the risk of adverse control-structure interaction.

Jeb S Orr↗

Discrete Fourier Transform Analysis in a Complex Vector Space

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Dean, Bruce H.↗

Development of load-dependent Ritz vector method for structural dynamic analysis of large space structures

The development and preliminary assessment of a method for dynamic structural analysis based on load-dependent Ritz vectors are presented. The vector basis is orthogonalized with respect to the mass and structural stiffness in order that the equations of motion can be uncoupled and efficient analysis of large space structure performed. A series of computer programs was developed based on the algorithm for generating the orthogonal load-dependent Ritz vectors. Transient dynamic analysis performed on the Space Station Freedom using the software was found to provide solutions that require a smaller number of vectors than the modal analysis method. Error norm based on the participation of the mass distribution of the structure and spatial distribution of structural loading, respectively, were developed in order to provide an indication of vector truncation. These norms are computed before the transient analysis is performed. An assessment of these norms through a convergence study of the structural response was performed. The results from this assessment indicate that the error norms can provide a means of judging the quality of the vector basis and accuracy of the transient dynamic solution.

Ricles, James M.↗

An analysis of satellite state vector observability using SST tracking data

Observability of satellite state vectors, using only SST tracking data was investigated by covariance analysis under a variety of satellite and station configurations. These results indicate very precarious observability in most short arc cases. The consequences of this are large variances on many state components, such as the downrange component of the relay satellite position. To illustrate the impact of observability problems, an example is given of two distinct satellite orbit pairs generating essentially the same data arc. The physical bases for unobservability are outlined and related to proposed TDRSS configurations. Results are relevant to any mission depending upon TDRSS to determine satellite state. The required mathematical analysis and the software used is described.

Englar, T. S., Jr.↗

Uncertainty Analysis of the Single-Vector Force Balance Calibration System

This paper presents an uncertainty analysis of the Single-Vector Force Balance Calibration System (SVS). This study is focused on the uncertainty involved in setting the independent variables during the calibration experiment. By knowing the uncertainty in the calibration system, the fundamental limits of the calibration accuracy of a particular balance can be determined. A brief description of the SVS mechanical system is provided. A mathematical model is developed to describe the mechanical system elements. A sensitivity analysis of these parameters is carried out through numerical simulations to assess the sensitivity of the total uncertainty to the elemental error sources. These sensitivity coefficients provide valuable information regarding the relative significance of the elemental sources of error. An example calculation of the total uncertainty for a specific balance is provided. Results from this uncertainty analysis are specific to the Single-Vector System, but the approach is broad in nature and therefore applicable to other measurement and calibration systems.

Parker, Peter A.↗

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Nguyen, D. T.↗

Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers

Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.

Baddourah, Majdi A.↗

A hybrid state vector approach to aeroelastic analysis with application to composite lifting surfaces

A computational technique has been developed for performing preliminary design aeroelastic analyses of large aspect ratio lifting surfaces. This technique, applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. An integrating matrix is employed to solve these equations for divergence and flutter eigenvalues and steady aeroelastic deformation. Results are presented for simple examples which verify the technique and demonstrate how it can be applied to analyze lifting surfaces, including those constructed from composite materials.

Lehman, L. L.↗

Statistical Analysis of Fading Power Vectors for Real-Time Atmospheric Channel Emulation

The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model for the fading channel suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode- limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.

free-space optical communication↗

Statistical Analysis of Fading Power Vectors for Real-Time Atmospheric Channel Emulation

The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model for the fading channel suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.

free-space optical communication↗

Vector space methods of photometric analysis - Applications to O stars and interstellar reddening

A multivariate vector-space formulation of photometry is developed which accounts for error propagation. An analysis of uvby and H-beta photometry of O stars is presented, with attention given to observational errors, reddening, general uvby photometry, early stars, and models of O stars. The number of observable parameters in O-star continua is investigated, the way these quantities compare with model-atmosphere predictions is considered, and an interstellar reddening law is derived. It is suggested that photospheric expansion affects the formation of the continuum in at least some O stars.

Massa, D.↗