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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Effective constitutive relations for the microstructure of periodic frames

Effective micro-structure properties of two-dimensional large repetitive frame-like structures are derived using straightforward combinations of energy methods of linear transformations. Once the actual structure is identified symmetry considerations are used in order to identify its independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified, (2) effective continuum properties are derived for each of these planar basic grids using energy methods, and (3) orthogonal transformations are finally used to determine the contribution of each basic set to the overall effective continuum properties of the structure.

Nayfeh, A. H.↗
NASA NTRS1976

A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study

An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.

Thornton, C. L.↗
NASA NTRS1980

Continuum modeling of the mechanical and thermal behavior of discrete large structures

In the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss-like repetitive structures. Once the actual structure is specified, the construction procedure can be outlined by the following three steps: (a) all sets of parallel members are identified, (b) unidirectional 'effective continuum' properties are derived for each of these sets and (c) orthogonal transformations are finally used to determine the contribution of each set to the 'overall effective continuum' properties of the structure. Here the properties includes mechanical (stiffnesses), thermal (coefficients of thermal expansions) and material densities. Once expanded descriptions of the steps (b) and (c) are done, the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods.

Nayfeh, A. H.↗
NASA NTRS1983

Discrete model improvement by eigenvector updating

An eigenvector updating method is proposed to fit modal test data. The calculated eigenvectors are updated by coinciding some of them with the corresponding measured eigenvectors as a result of an orthogonal transformation. The advantage of the method is the applicability to large complex structures without necessity of recomputation of the eigendata.

Zak, M.↗
NASA NTRS1987

Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversion

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Backus, George↗
NASA NTRS1987

Isotropic probability measures in infinite-dimensional spaces

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub in :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity) (P sub n to the -1 (B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Backus, George↗
NASA NTRS1989

Grids for DSMC computation of two and three-dimensional flows

Contemporary grid schemes for use in Direct Simulation Monte Carlo (DSMC) method of computing two- and three-dimensional flows are briefly surveyed. The grids described include: (1) simple, constant area cells defined by a rectangular grid; (2) multilevel rectangular grids; (3) adaptive rectangular cells; (4) 'point reference' scheme; (5) body-fitted 'analytical' cells; (6) 'general' schemes; (7) 'general' schemes with subcells; (8) orthogonal transformation to rectangular grid; (9) structural tetrahedral grids; (10) rectangular multilevel subcells with adaptive body-fitted cells.

Bird, G. A.↗
NASA NTRS1990

Converting gravity bins to spherical harmonic coefficients

The gravity bin technique as originally formulated recovers the local gravity field from the bin parameters by finite differencing. The spherical harmonic coefficients of the gravity field are then computed by an orthogonal transformation of the local gravity field. The result differs from that of the traditional method. This paper discusses the difference and proposes a new algorithm to convert the bin parameters to spherical harmonic coefficients. It is shown that the new method produces the same gravity field as the traditional method and maintains the high computational efficiency of the basic gravity bin technique.

Wu, J. T.↗
NASA NTRS2000

Evaluation of the Use of Second Generation Wavelets in the Coherent Vortex Simulation Approach

The objective of this study is to investigate the use of the second generation bi-orthogonal wavelet transform for the field decomposition in the Coherent Vortex Simulation of turbulent flows. The performances of the bi-orthogonal second generation wavelet transform and the orthogonal wavelet transform using Daubechies wavelets with the same number of vanishing moments are compared in a priori tests using a spectral direct numerical simulation (DNS) database of isotropic turbulence fields: 256(exp 3) and 512(exp 3) DNS of forced homogeneous turbulence (Re(sub lambda) = 168) and 256(exp 3) and 512(exp 3) DNS of decaying homogeneous turbulence (Re(sub lambda) = 55). It is found that bi-orthogonal second generation wavelets can be used for coherent vortex extraction. The results of a priori tests indicate that second generation wavelets have better compression and the residual field is closer to Gaussian. However, it was found that the use of second generation wavelets results in an integral length scale for the incoherent part that is larger than that derived from orthogonal wavelets. A way of dealing with this difficulty is suggested.

Goldstein, D. E.↗
NASA NTRS1975

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Howard, J. C.↗
NASA NTRS1994

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Brozenec, Thomas F.↗
NASA NTRS2011

Hyperspectral Remote Sensing of Atmosphere and Surface Properties

Atmospheric Infrared Sounder (AIRS), Infrared Atmospheric Sounding Interferometer (IASI), and Cross-track Infrared Sounder (CrIS) are all hyper-spectral satellite sensors with thousands of spectral channels. Top of atmospheric radiance spectra measured by these sensors contain high information content on atmospheric, cloud, and surface properties. Exploring high information content contained in these high spectral resolution spectra is a challenging task due to computation e ort involved in modeling thousands of spectral channels. Usually, only very small fractions (4{10 percent) of the available channels are included in physical retrieval systems or numerical weather forecast (NWP) satellite data assimilations. We will describe a method of simultaneously retrieving atmospheric temperature, moisture, cloud, and surface properties using all available spectral channels without sacrificing computational speed. The essence of the method is to convert channel radiance spectra into super-channels by an Empirical Orthogonal Function (EOF) transformation. Because the EOFs are orthogonal to each other, about 100 super-channels are adequate to capture the information content of the radiance spectra. A Principal Component-based Radiative Transfer Model (PCRTM) developed at NASA Langley Research Center is used to calculate both the super-channel magnitudes and derivatives with respect to atmospheric profiles and other properties. There is no need to perform EOF transformations to convert super channels back to spectral space at each iteration step for a one-dimensional variational retrieval or a NWP data assimilation system. The PCRTM forward model is also capable of calculating radiative contributions due to multiple-layer clouds. The multiple scattering effects of the clouds are efficiently parameterized. A physical retrieval algorithm then performs an inversion of atmospheric, cloud, and surface properties in super channel domain directly therefore both reducing the computational need and preserving the information content of the IASI measurements. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance matrices and a priori information as constraints. One advantage of this approach is that it uses all information content from the hyper-spectral data so that the retrieval is less sensitive to instrument noise and eliminates the need for selecting a sub-set of the channels.

Liu, Xu↗
NASA NTRS1978

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Gnoffo, P. A.↗
NASA NTRS1999

Substructure Synthesis: A Controls Approach

Substructure synthesis from a controls perspective is considered. An efficient and computationally robust method for synthesis of substructures is developed. The method considers the interface forces/moments as control inputs and redefines the synthesis problem in terms of obtaining a constant gain compensator which would ensure the connectivity requirements of the combined structure. Orthogonal similarity transformations are used to provide simplified synthesized dynamics of the combined system. The simplicity of form in transformed coordinates are exploited to effectively deal with modeling parametric and non-parametric uncertainties at substructure level. Uncertainty models of reasonable size and complexity are derived for the combined structure from those in the substructure models.

Maghami, Peiman G.↗