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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗
NASA NTRS2015

Empirical State Error Covariance Matrix for Batch Estimation

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. This empirical error covariance matrix may be calculated as a side computation for each unique batch solution. Results based on the proposed technique will be presented for a simple, two observer and measurement error only problem.

Frisbee, Joe↗
NASA NTRS2016

Simple Test Functions in Meshless Local Petrov-Galerkin Methods

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust.

Raju, Ivatury S.↗
NASA NTRS2015

Operational Challenges In TDRS Post-Maneuver Orbit Determination

The GSFC Flight Dynamics Facility (FDF) is responsible for daily and post maneuver orbit determination for the Tracking and Data Relay Satellite System (TDRSS). The most stringent requirement for this orbit determination is 75 meters total position accuracy (3-sigma) predicted over one day for Terra's onboard navigation system. To maintain an accurate solution onboard Terra, a solution is generated and provided by the FDF Four hours after a TDRS maneuver. A number of factors present challenges to this support, such as maneuver prediction uncertainty and potentially unreliable tracking from User satellities. Reliable support is provided by comparing an extended Kalman Filter (estimated using ODTK) against a Batch Least Squares system (estimated using GTDS).

FDF↗
NASA NTRS1991

Comparison of ERBS orbit determination accuracy using batch least-squares and sequential methods

The Flight Dynamics Div. (FDD) at NASA-Goddard commissioned a study to develop the Real Time Orbit Determination/Enhanced (RTOD/E) system as a prototype system for sequential orbit determination of spacecraft on a DOS based personal computer (PC). An overview is presented of RTOD/E capabilities and the results are presented of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft obtained using RTOS/E on a PC with the accuracy of an established batch least squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. RTOD/E was used to perform sequential orbit determination for the Earth Radiation Budget Satellite (ERBS), and the Goddard Trajectory Determination System (GTDS) was used to perform the batch least squares orbit determination. The estimated ERBS ephemerides were obtained for the Aug. 16 to 22, 1989, timeframe, during which intensive TDRSS tracking data for ERBS were available. Independent assessments were made to examine the consistencies of results obtained by the batch and sequential methods. Comparisons were made between the forward filtered RTOD/E orbit solutions and definitive GTDS orbit solutions for ERBS; the solution differences were less than 40 meters after the filter had reached steady state.

Oza, D. H.↗
NASA NTRS1984

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

Rosen, I. G.↗
NASA NTRS1989

A complete spherical harmonic approach to luni-solar tides

In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni-solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides - for any theory - appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.

Dickman, S. R.↗
NASA NTRS2012

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Orr, Jeb S.↗
NASA NTRS1979

Concerning an application of the method of least squares with a variable weight matrix

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

Sukhanov, A. A.↗
NASA NTRS1980

Mark 3 interactive data analysis system

The interactive data analysis system, a major subset of the total Mark 3 very long baseline interferometry (VLBI) software system is described. The system consists of two major and a number of small programs. These programs provide for the scientific analysis of the observed values of delay and delay rate generated by the VLBI data reduction programs and product the geophysical and astrometric parameters which are among the ultimate products of VLBI. The two major programs are CALC and SOLVE. CALC generates the theoretical values of VLBI delay rate as well as partial derivatives based on apriori values of the geophysical and astronometric parameters. SOLVE is a least squares parameters estimation program which yields the geophysical and astrometric parameters using the observed values by the data processing system and theoretical values and partial derivatives provided by CALC. SOLVE is a highly interactive program in which the user selects the exact form of the recovered parameters and the data to be accepted into the solution.

Ryan, J. W.↗
NASA NTRS1986

Steady surficial core motions - An alternate method

A new method for deriving steady surficial core motions from geomagnetic field models is presented and applied. The original method determines the steady velocity field at the top of a frozen-flux core which best fits, in both the spatial and temporal linear least squares sense, a model of the large scale geomagnetic secular variation (SV) at the base of a source-free mantle (Voorhies, 1986). New method is based upon the same physical assumptions, but fits SV at earth's surface instead of the core-mantle boundary (CMB). The newly derived flow differs somewhat from prior solutions, and shows but slight westward drift; however, other key global properties are virtually unchanged. Over a 15 year interval the new method provides a better fit to the time-varying geomagnetic field at earth's surface than does the old.

Voorhies, Coerte V.↗
NASA NTRSDate not supplied

Navigation Performance of the BioSentinel Deep Space CubeSat Mission

The BioSentinel mission was recently launched aboard the SLS launch vehicle (LV) as part of the Artemis- 1 campaign. The BioSentinel navigation team successfully tracked and guided the spacecraft through a lunar gravity assist to its destination Earth-trailing heliocentric orbit. This 6U CubeSat carries live yeast cells to analyze the effects of radiation at large distances from Earth, becoming the first biological payload in Deep Space. Prelaunch activities included mission design updates, orbit determination rehearsals and the development of a tracking schedule in coordination with the Artemis-1 payload office and the Deep Space Network (DSN). An important influence on the trajectories of Artemis I secondaries was the uncertainty associated with deployment from the Interim Cryogenic Propulsion System (ICPS), the upper stage of the SLS LV. The ICPS was rotating at a rate of 1 rpm; there was also an uncertainty in the spin axis attitude, which translated into an unknown clock angle of deployment. The variability in this angle and magnitude of deployment implied the existence of a non-negligible risk of a lunar impact, which was evaluated for various potential launch dates. We present the results of Monte Carlo analyses and compute the pertinent maneuvers to avoid it. In addition, we present a comparison with the actual deployment once the mission launched by reconstructing our trajectory with tracking data. On November 16th 2022 BioSentinel successfully deployed from ICPS and the navigation team started to receive 2-way Doppler and Sequential Ranging data from the DSN. We processed early data to try to obtain a first ephemeris using Initial Orbit Determination (IOD) methods such as the least squares. Soon after deployment, the spacecraft was tumbling and entered safe mode, creating a period where the tracking data were sparse. The mission team recovered the spacecraft and after four tracking passes, we solved for a first ephemeris that was sent to the DSN for better tracking of the spacecraft. After propagating this first ephemeris solution, we determined that we avoided impact with a margin of a few hundred km from the lunar surface. More tracking data over the next few days (from DSN as well as ESA antennas) allowed for a more refined orbit solution predicting a periselene altitude of 406 km and a lunar eclipse lasting 36.5 minutes. Therefore, BioSentinel operators aborted any correction maneuvers. This periselene altitude also gave us the necessary energy to achieve a heliocentric orbit. The next challenge was due to the necessary adjustments in our orbit determination method due to the large energy boost resulting from the lunar flyby. After a series of tracking passes we were able to get a nominal solution that resulted into a stable trajectory. This paper discusses in detail the navigation performance using the X-band IRIS transponder, as well as the challenges and lessons learned prior to and during this deep space, CubeSat mission.

Andres Dono Perez↗
NASA NTRS1996

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.

Wu, Jie↗
NASA NTRS1998

A Novel Four-Node Quadrilateral Smoothing Element for Stress Enhancement and Error Estimation

A four-node, quadrilateral smoothing element is developed based upon a penalized-discrete-least-squares variational formulation. The smoothing methodology recovers C1-continuous stresses, thus enabling effective a posteriori error estimation and automatic adaptive mesh refinement. The element formulation is originated with a five-node macro-element configuration consisting of four triangular anisoparametric smoothing elements in a cross-diagonal pattern. This element pattern enables a convenient closed-form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge-wise penalty constraints. The degree-of-freedom reduction scheme leads to a very efficient formulation of a four-node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh refinement solutions for an elasticity problem and an aerospace structural component.

Tessler, A.↗
NASA NTRS2021

Deriving Mercury Geodetic Parameters with Altimetric Crossovers from the Mercury Laser Altimeter (MLA)

Based on the previous applications of laser altimetry to planetary geodesy at GSFC, we use the recently developed PyXover software package to analyze altimetric crossovers from the Mercury Laser Altimeter (MLA). Using PyXover, we place new constraints on Mercury's geodetic parameters via least squares minimization of crossover discrepancies. We simultaneously solve for orbital corrections for each MLA ground track, for the geodetic parameters of the International Astronomical Union-recommended orientation model for Mercury (pole right-ascension and declination coordinates, prime meridian rotation rate, and librations), and for the Mercury's Love number h2. We calibrate the formal errors of our solution based on closed-loop simulations and on the level of robustness against a priori values, data selection, and parametrization. Our solution of the Mercury's rotational parameters is consistent with published values. In particular, our new estimate for the orientation of the pole places Mercury in a Cassini state, with an obliquity ϵ = 2.031 ± 0.03 arcmin compatible with previous “surface” related measurements. Moreover, we provide a first data-based estimate of the Love number h_(2) = 1.55 ± 0.65. The latter is consistent with expectations from models of Mercury's interior, although its precision does not enable their refinement.

S. Bertone↗
NASA NTRS2010

Improving Global Mass Flux Solutions from Gravity Recovery and Climate Experiment (GRACE) Through Forward Modeling and Continuous Time Correlation

We describe Earth's mass flux from April 2003 through November 2008 by deriving a time series of mas cons on a global 2deg x 2deg equal-area grid at 10 day intervals. We estimate the mass flux directly from K band range rate (KBRR) data provided by the Gravity Recovery and Climate Experiment (GRACE) mission. Using regularized least squares, we take into account the underlying process dynamics through continuous space and time-correlated constraints. In addition, we place the mascon approach in the context of other filtering techniques, showing its equivalence to anisotropic, nonsymmetric filtering, least squares collocation, and Kalman smoothing. We produce mascon time series from KBRR data that have and have not been corrected (forward modeled) for hydrological processes and fmd that the former produce superior results in oceanic areas by minimizing signal leakage from strong sources on land. By exploiting the structure of the spatiotemporal constraints, we are able to use a much more efficient (in storage and computation) inversion algorithm based upon the conjugate gradient method. This allows us to apply continuous rather than piecewise continuous time-correlated constraints, which we show via global maps and comparisons with ocean-bottom pressure gauges, to produce time series with reduced random variance and full systematic signal. Finally, we present a preferred global model, a hybrid whose oceanic portions are derived using forward modeling of hydrology but whose land portions are not, and thus represent a pure GRACE-derived signal.

Sabaka, T. J.↗
NASA NTRS1971

A method for nonlinear exponential regression analysis

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Junkin, B. G.↗
NASA NTRS1986

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.

Smith, R. L.↗