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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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NASA NTRS1990

Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions

The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.

Schwenke, David W.↗
NASA NTRS2003

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

Raju, I. S.↗
NASA NTRS1975

Solutions to Kuessner's integral equation in unsteady flow using local basis functions

The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

Fromme, J. A.↗
NASA NTRS2022

Structural Shape Sensing from Strain Data Using the Basis Function Method

An aircraft shape must be measured during flight to implement an active trim shape control, such as an active dihedral control for a highly flexible aircraft with a high-aspect-ratio wing, and an active sonic boom control for a supersonic transport aircraft. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration Low Boom Flight Demonstration mission X-59 Quiet Supersonic Technology (QueSST) aircraft (Lockheed Martin, Bethesda, Maryland). A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3-percentprediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data is also demonstrated in this study using the X-59 QueSST aircraft. Predicted structural deformations match reasonably with the target deformations even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.

Chan-gi Pak↗
NASA NTRS2008

New Basis Functions for the Electromagnetic Solution of Arbitrarily-shaped, Three Dimensional Conducting Bodies using Method of Moments

In this work, we present a new set of basis functions, defined over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also defined over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.

Mackenzie, Anne I.↗
NASA NTRS2007

New Basis Functions for the Electromagnetic Solution of Arbitrarily-shaped, Three Dimensional Conducting Bodies Using Method of Moments

In this work, we present a new set of basis functions, de ned over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also de ned over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.

Mackenzie, Anne I.↗
NASA NTRS2008

An Alternate Set of Basis Functions for the Electromagnetic Solution of Arbitrarily-Shaped, Three-Dimensional, Closed, Conducting Bodies Using Method of Moments

In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic cur- rents. However, in the present work, only the conducting body solution is presented and compared with other data.

Mackenzie, Anne I.↗
NASA NTRS2018

Super Resolution of Remote Sensing Images Using Edge-Directed Radial Basis Functions

Edge-Directed Radial Basis Functions (EDRBF) are used to compute super resolution(SR) image from a given set of low resolution (LR) images differing in subpixel shifts. The algorithm is tested on remote sensing images and compared for accuracy with other well-known algorithms such as Iterative Back Projection (IBP), Maximum Likelihood (ML) algorithm, interpolation of scattered points using Nearest Neighbor (NN) and Inversed Distance Weighted (IDW) interpolation, and Radial Basis Functin(RBF) . The accuracy of SR depends on various factors besides the algorithm (i) number of subpixel shifted LR images (ii) accuracy with which the LR shifts are estimated by registration algorithms (iii) and the targeted spatial resolution of SR. In our studies, the accuracy of EDRBF is compared with other algorithms keeping these factors constant. The algorithm has two steps: i) registration of low resolution images and (ii) estimating the pixels in High Resolution (HR) grid using EDRBF. Experiments are conducted by simulating LR images from a input HR image with different sub-pixel shifts. The reconstructed SR image is compared with input HR image to measure the accuracy of the algorithm using sum of squared errors (SSE). The algorithm has outperformed all of the algorithms mentioned above. The algorithm is robust and is not overly sensitive to the registration inaccuracies.

Mareboyana, Manohar M.↗
NASA NTRS2002

A Cubic Radial Basis Function in the MLPG Method for Beam Problems

A non-compactly supported cubic radial basis function implementation of the MLPG method for beam problems is presented. The evaluation of the derivatives of the shape functions obtained from the radial basis function interpolation is much simpler than the evaluation of the moving least squares shape function derivatives. The radial basis MLPG yields results as accurate or better than those obtained by the conventional MLPG method for problems with discontinuous and other complex loading conditions.

Raju, I. S.↗
NASA NTRS1991

Determination of a natural basis function set on thick, structured slabs using Prony's method

The calculation of currents on a thick, structured slab such as a thick slab of honeycomb is discussed. Unfortunately, for certain applications, the slab can be on the order of several wavelengths, so that the straightforward application of the method of moments using subdomain basis functions is too expensive. The authors discuss how to apply Prony's method to the currents calculated for a thin, structured slab to obtain a natural set of basis functions to represent the currents in the interior of a thick slab. Prony's method represents the currents as a series of complex exponential functions. The thick slab problem is then solved by the method of moments using subdomain basis functions near the slab interfaces and one or two of the complex exponentials as basis functions within the slab.

Jorgenson, Roy E.↗
NASA NTRS1975

The use of local basis functions in unsteady aerodynamics

This paper reports a successful demonstration of using local basis functions to solve Kussner's integral equation for unsteady airloads. Pressure basis functions are defined over relatively small subsets of the aerodynamic surface and are zero elsewhere. This formulation combines the accuracy and smoothness of distribution methods with the simplicity and versatility of panel methods. Application is made to subsonic compressible flow about oscillating planar surfaces with controls. Numerical results are presented. Convergence with respect to panel size, extensions to more general classes of solutions, and areas needing additional investigation are discussed.

Fromme, J.↗
NASA NTRS1992

A radial basis function neurocomputer implemented with analog VLSI circuits

An electronic neurocomputer which implements a radial basis function neural network (RBFNN) is described. The RBFNN is a network that utilizes a radial basis function as the transfer function. The key advantages of RBFNNs over existing neural network architectures include reduced learning time and the ease of VLSI implementation. This neurocomputer is based on an analog/digital hybrid design and has been constructed with both custom analog VLSI circuits and a commercially available digital signal processor. The hybrid architecture is selected because it offers high computational performance while compensating for analog inaccuracies, and it features the ability to model large problems.

Watkins, Steven S.↗
NASA NTRS1993

Radial basis function neural networks applied to NASA SSME data

This paper presents a brief report on the application of Radial Basis Function Neural Networks (RBFNN) to the prediction of sensor values for fault detection and diagnosis of the Space Shuttle's Main Engines (SSME). The location of the Radial Basis Function (RBF) node centers was determined with a K-means clustering algorithm. A neighborhood operation about these center points was used to determine the variances of the individual processing notes.

Wheeler, Kevin R.↗
NASA NTRS2007

Paired Pulse Basis Functions for the Method of Moments EFIE Solution of Electromagnetic Problems Involving Arbitrarily-shaped, Three-dimensional Dielectric Scatterers

A pair of basis functions is presented for the surface integral, method of moment solution of scattering by arbitrarily-shaped, three-dimensional dielectric bodies. Equivalent surface currents are represented by orthogonal unit pulse vectors in conjunction with triangular patch modeling. The electric field integral equation is employed with closed geometries for dielectric bodies; the method may also be applied to conductors. Radar cross section results are shown for dielectric bodies having canonical spherical, cylindrical, and cubic shapes. Pulse basis function results are compared to results by other methods.

MacKenzie, Anne I.↗
NASA NTRS2012

A Cross-Validation Approach to Approximate Basis Function Selection of the Stall Flutter Response of a Rectangular Wing in a Wind Tunnel

The stall flutter response of a rectangular wing in a low speed wind tunnel is modelled using a nonlinear difference equation description. Static and dynamic tests are used to select a suitable model structure and basis function. Bifurcation criteria such as the Hopf condition and vibration amplitude variation with airspeed were used to ensure the model was representative of experimentally measured stall flutter phenomena. Dynamic test data were used to estimate model parameters and estimate an approximate basis function.

Kukreja, Sunil L.↗
NASA NTRS2003

Precision of a radial basis function neural network tracking method

The precision of a radial basis function (RBF) neural network based tracking method has been assessed against real targets. Precision was assessed against traditionally measured frame-by-frame measurements from the recorded data set. The results show the potential limit for the technique and reveal intricacies associated with empirical data not necessarily observed in simulations.

autonomous tracking neural network target recognit↗