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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Tal-Ezer, Hillel↗
NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗
DOE OSTI2026

Toward Chemical Accuracy for Chemi- and Physisorption with an Efficient Density Functional

Understanding molecular adsorption on surfaces underpins many problems in chemistry and materials science. Accurately and efficiently describing the adsorption has been a challenging task for first-principles methods as the process can involve both short-range chemical bond formations and long-range physical interactions, e.g., van der Waals (vdW) interaction. Density functional theory presents an appealing choice for modeling adsorption reactions, although calculations with many exchange-correlation density functional approximations struggle to accurately describe both chemical and physical molecular adsorptions. Here, we propose an efficient density functional approximation that is accurate for both chemical and physical adsorption by concurrently optimizing its semilocal component and the long-range vdW correction against the prototypical adsorption CO/Pt(111) and Ar 2 binding energy curve. The resulting function opens the door to accurate and efficient modeling of general molecular adsorption.

adsorption↗
NASA NTRS1980

Design of a recursive vector processor using polynomial splines

The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.

Kim, C. S.↗
NASA NTRS2003

An Approximate Dissipation Function for Large Strain Rubber Thermo-Mechanical Analyses

Mechanically induced viscoelastic dissipation is difficult to compute. When the constitutive model is defined by history integrals, the formula for dissipation is a double convolution integral. Since double convolution integrals are difficult to approximate, coupled thermo-mechanical analyses of highly viscous rubber-like materials cannot be made with most commercial finite element software. In this study, we present a method to approximate the dissipation for history integral constitutive models that represent Maxwell-like materials without approximating the double convolution integral. The method requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. Numerical data is provided to demonstrate the limitations of this approximate method for determining dissipation. Rubber cylinders with imbedded steel disks and with an imbedded steel ball are dynamically loaded, and the nonuniform heating within the cylinders is computed.

Johnson, Arthur R.↗
NASA NTRS2014

Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies

This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio and number of control surfaces. A doublet lattice approach is taken to compute generalized forces. A rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. Although, all parameters can be easily modified if desired.The focus of this paper is on tool presentation, verification and validation. This process is carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool. Therefore the flutter speed and frequency for a clamped plate are computed using V-g and V-f analysis. The computational results are compared to a previously published computational analysis and wind tunnel results for the same structure. Finally a case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to V-g and V-f analysis. This also includes the analysis of the model in response to a 1-cos gust.

Modeling and Simulation↗
NASA NTRS1993

Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams

A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.

Noor, Ahmed K.↗
NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) for matching single-input single-output (SISO) transfer function models to empirical frequency response data is described. The program was written in MATLAB and has a graphical user interface (GUI). It is interactive in that the user manually builds the transfer function model using ``elementary factors'' (gain, delay, differentiators and integrators, and first- and second-order poles and zeros) and adjusts their values with sliders or entry fields. A nonlinear optimization can also be used to determine maximum-likelihood estimates of the transfer function parameters and their associated uncertainties. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and other system identification problems. FRFit is demonstrated using example problems, including the identification of aircraft transfer functions and rational function approximations of Theodorsen's function.

Frequency response↗
NASA NTRS1973

New methods of fragmentary approximation of a function

Certain special methods of fragmentary approximation of a function are examined and the properties of the most widespread elementary functions for such approximation methods are investigated, for the purpose of developing useful characteristics and properties for practical realization, in particular, for their reproduction by analog functional converters, with a significantly smaller number of controlable or adjustable parameters than in known ones.

Kolesnichenko, S. G.↗
DOE OSTI2025

Coherency-Constrained Spectral Clustering for Power Network Reduction

This paper presents a methodology for reducing the complexity of large-scale power network models using spectral clustering, aggregation of electrical components, and cost function approximation. Two approaches are explored using unconstrained and constrained spectral clustering to determine areas for effective system reduction. Once the system areas are determined, both loads and generators by type are aggregated, and their new cost function is approximated through polynomial curve-fitting or statistical methods. The performance of reduced networks is evaluated in terms of their ability to follow the true daily cost of the original system over a 24-hour period considering a set of several days. Two test systems are taken as test beds. Application of the methodology to a modified version of the IEEE 39-bus system reduces it from 17 generators to a 4-bus system and 9 generators with about 93% of accuracy. Similarly, the IEEE 118-bus system is reduced from 19 generators to a 3-bus system with three aggregated units achieving over 99% of accuracy. These findings address scalability challenges and enhance accuracy for high and mid-loading level conditions, and by aggregating thermal units with similar cost functions.

42 ENGINEERING↗
NASA NTRS1989

Global properties of pseudospectral methods

The present application of polynomial interpolation methods to function-approximation and numerical solutions for hyperbolic and elliptic PDEs allows the explicit construction of the derivative matrix for a general sequence of collocation points. An evaluation of the effect of several factors on the performance of these methods indicates an inability to interpret global methods in terms of local ones; the accuracy of the approximation will differ when the function's large gradients occur near the center of the region or near the boundary, irrespective of the boundary vicinity's collocation-point density.

Solomonoff, A.↗
NASA NTRS1972

Estimation of correlation functions by stochastic approximation.

Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.

Habibi, A.↗
NASA NTRS1987

Performance evaluation of fault tolerant systems represented by Markov models

A method to evaluate the performance of fault tolerant systems whose configuration can be represented by time-invariant, discrete-time, discrete-state Markov models is introduced. Each state is assumed to be associated with a constant qualitative measure of the system's performance. The method first computes the moments of the performance probability mass function (PMF) and then finds an approximating function that has the same moments. The form of this function is a maximum entropy solution of the moment matching problem. A simple algorithm for calculating the necessary moments is derived and a method for finding the approximate performance PMF is suggested. After some modification, the method is applied to an example, the Inertial Upper Stage navigation system.

Missana, Jean-Olivier A. A.↗
NASA NTRS1985

Molecular processes in a high temperature shock layer

The development of techniques for the calculation of electron capture widths, electronic wave functions, cross sections and rates needed for the description of the dissociative recombination (DR) of molecular ions with electrons were described. The cross sections and rates were calculated by using harmonic oscillator wave functions for the ion and a delta function approximation for the continuum vibrational wave function in the repulsive dissociative channel. In order to obtain DR cross sections of quantitative accuracy, a computer program which solves the one dimensional nuclear motion wave equation was revised to calculate the cross sections and rates. The program and the new results are described. Included is a discussion of large windows found in the dissociative recombination cross sections from excited ion vibrational levels. These windows have not been previously reported in the literature. The magnitude of the DR cross sections for several dissociative routes are sensitive to the location of the crossing of the neutral and ion potential curves. Studies of the effects of basis set and CI wave function size on vertical excitation energies are described. Preliminary studies on N2 and O2 using large scale wave functions are also reported.

Guberman, S. L.↗
NASA NTRS1993

Experiment-specific cosmic microwave background calculations made easier - Approximation formula for smoothed delta T/T windows

Simple and easy to implement elementary function approximations are introduced to the spectral window functions needed in calculations of model predictions of the cosmic microwave backgrond (CMB) anisotropy. These approximations allow the investigator to obtain model delta T/T predictions in terms of single integrals over the power spectrum of cosmological perturbations and to avoid the necessity of performing the additional integrations. The high accuracy of these approximations is demonstrated here for the CDM theory-based calculations of the expected delta T/T signal in several experiments searching for the CMB anisotropy.

Gorski, Krzysztof M.↗
NASA NTRS1983

Experimental determination of the particle motions associated with the low order acoustic modes in enclosures

A procedure for experimentally determining, in terms of the particle motions, the shapes of the low order acoustic modes in enclosures is described. The procedure is based on finding differentiable functions which approximate the shape functions of the low order acoustic modes when these modes are defined in terms of the acoustic pressure. The differentiable approximating functions are formed from polynomials which are fitted by a least squares procedure to experimentally determined values which define the shapes of the low order acoustic modes in terms of the acoustic pressure. These experimentally determined values are found by a conventional technique in which the transfer functions, which relate the acoustic pressures at an array of points in the enclosure to the volume velocity of a fixed point source, are measured. The gradient of the function which approximates the shape of a particular mode in terms of the acoustic pressure is evaluated to give the mode shape in terms of the particle motion. The procedure was tested by using it to experimentally determine the shapes of the low order acoustic modes in a small rectangular enclosure.

Byrne, K. P.↗
NASA NTRS1945

Numerical Evaluation by Harmonic Analysis of the (Epsilon)-Function of the Theodorsen Arbitrary-Airfoil Potential Theory

Finite trigonometric series is fitted by harmonic analysis as an approximation function to the psi function of the Theodorsen arbitrary-airfoil potential theory. By harmonic synthesis, the corresponding conjugate trigonometric series is used as an approximation to the epsilon function. A set of coefficients of particularly simple form is obtained algebraically for direct calculation of the epsilon values from the corresponding set of psi values. Complete derivation of this process is presented.

Naiman, Irven↗