Launch period, targeting and error analysis for Mars direct and orbital missions.
Mission capability differences between direct and orbital Mars missions as to launch period selection, targeting capability and error analysis
Marquet, D. W.↗
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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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Gamma Ray Observatory (GRO) OBC attitude error analysis
This analysis involves an in-depth look into the onboard computer (OBC) attitude determination algorithm. A review of TRW error analysis and necessary ground simulations to understand the onboard attitude determination process are performed. In addition, a plan is generated for the in-flight calibration and validation of OBC computed attitudes. Pre-mission expected accuracies are summarized and sensitivity of onboard algorithms to sensor anomalies and filter tuning parameters are addressed.
Harman, R. R.↗
Implementation and (Inverse Modified) Error Analysis for Implicitly Templated ODE-Nets
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. Here, we also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed “gray box” identification.
ODE-nets↗
A Preliminary ZEUS Lightning Location Error Analysis Using a Modified Retrieval Theory
The ZEUS long-range VLF arrival time difference lightning detection network now covers both Europe and Africa, and there are plans for further expansion into the western hemisphere. In order to fully optimize and assess ZEUS lightning location retrieval errors and to determine the best placement of future receivers expected to be added to the network, a software package is being developed jointly between the NASA Marshall Space Flight Center (MSFC) and the University of Nevada Las Vegas (UNLV). The software package, called the ZEUS Error Analysis for Lightning (ZEAL), will be used to obtain global scale lightning location retrieval error maps using both a Monte Carlo approach and chi-squared curvature matrix theory. At the core of ZEAL will be an implementation of an Iterative Oblate (IO) lightning location retrieval method recently developed at MSFC. The IO method will be appropriately modified to account for variable wave propagation speed, and the new retrieval results will be compared with the current ZEUS retrieval algorithm to assess potential improvements. In this preliminary ZEAL work effort, we defined 5000 source locations evenly distributed across the Earth. We then used the existing (as well as potential future ZEUS sites) to simulate arrival time data between source and ZEUS site. A total of 100 sources were considered at each of the 5000 locations, and timing errors were selected from a normal distribution having a mean of 0 seconds and a standard deviation of 20 microseconds. This simulated "noisy" dataset was analyzed using the IO algorithm to estimate source locations. The exact locations were compared with the retrieved locations, and the results are summarized via several color-coded "error maps."
Elander, Valjean↗
Global error analysis of the Chebyshev rational approximation method
The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM’s accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. Finally, we show that the reason for CRAM’s behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.
97 MATHEMATICS AND COMPUTING↗
Geometric error analysis for shuttle imaging spectrometer experiment
The demand of more powerful tools for remote sensing and management of earth resources steadily increased over the last decade. With the recent advancement of area array detectors, high resolution multichannel imaging spectrometers can be realistically constructed. The error analysis study for the Shuttle Imaging Spectrometer Experiment system is documented for the purpose of providing information for design, tradeoff, and performance prediction. Error sources including the Shuttle attitude determination and control system, instrument pointing and misalignment, disturbances, ephemeris, Earth rotation, etc., were investigated. Geometric error mapping functions were developed, characterized, and illustrated extensively with tables and charts. Selected ground patterns and the corresponding image distortions were generated for direct visual inspection of how the various error sources affect the appearance of the ground object images.
Wang, S. J.↗
Reconfigurable G and C computer study for space station use. Volume 7, appendix 5 - D-200 computer family. Appendix 6 - System error analysis. Appendix 7 - Reliability derivation for candidate computers. Appendix 8 - Power converter design data. Appendix 9 - Data transmission medium design Final report, 29 Dec. 1969 - 31 Jan. 1971
D-200 computer family, system error analysis, reliability derivation, and power converter design for reconfigurable guidance and control computer - Vol. 7
Source record↗
Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables
Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.
Fenyes, Peter A.↗
Rounding Error Analysis of Mixed Precision Block Householder QR Algorithms
Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speedups and lower storage cost if applied appropriately. The growing interest in employing mixed precision computations motivates the need for rounding error analysis that properly handles behavior from mixed precision arithmetic. We develop mixed precision variants of existing Householder QR algorithms and show error analyses supported by numerical experiments.
97 MATHEMATICS AND COMPUTING↗
Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems
Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.
Skollermo, G.↗
Orbital and Geodetic Error Analysis
Results that previously required several runs determined in more computer-efficient manner. Multiple runs performed only once with GEODYN and stored on tape. ERODYN then performs matrix partitioning and linear algebra required for each individual error-analysis run.
Felsentreger, T.↗
Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 2: Programmer's manual
The six month effort was responsible for the development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs. The program NOMNAL targets a transfer trajectory from earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty.
Byrnes, D. V.↗
Multiple boundary condition testing error analysis
Techniques for interpreting data from multiple-boundary-condition (MBC) ground tests of large space structures are developed analytically and demonstrated. The use of MBC testing to validate structures too large to stand alone on the ground is explained; the generalized least-squares mass and stiffness curve-fitting methods typically applied to MBC test data are reviewed; and a detailed error analysis is performed. Consideration is given to sensitivity coefficients, covariance-matrix theory, the correspondence between test and analysis modes, constraints and step sizes, convergence criteria, and factor-analysis theory. Numerical results for a simple beam problem are presented in tables and briefly characterized. The improved error-updating capabilities of MBC testing are confirmed, and it is concluded that reasonably accurate results can be obtained using a diagonal covariance matrix.
Glaser, R. J.↗
Scout error analysis, phase 1 Final report
Error sources and their magnitudes in Scout launch vehicle data
Cohen, L. B.↗
Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 1: Analytic and user's manual
Development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system is reported. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs (STEAP). The program NOMNAL targets a transfer trajectory from Earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty. Execution errors at injection, midcourse correction and orbit insertion maneuvers are analyzed along with the navigation uncertainty to determine trajectory control uncertainties and fuel-sizing requirements. The program is also capable of generalized covariance analyses.
Byrnes, D. V.↗
Formulation and error analysis for a generalized image point correspondence algorithm
A Generalized Image Point Correspondence (GIPC) algorithm, which enables the determination of 3-D motion parameters of an object in a configuration where both the object and the camera are moving, is discussed. A detailed error analysis of this algorithm has been carried out. Furthermore, the algorithm was tested on both simulated and video-acquired data, and its accuracy was determined.
Shapiro, Linda↗
Error analysis of numerical methods for thick diffusive neutron transport problems on Shishkin mesh
A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Earth orientation from lunar laser ranging and an error analysis of polar motion services
Lunar laser ranging (LLR) data are obtained on the basis of the timing of laser pulses travelling from observatories on earth to retroreflectors placed on the moon's surface during the Apollo program. The modeling and analysis of the LLR data can provide valuable insights into earth's dynamics. The feasibility to model accurately the lunar orbit over the full 13-year observation span makes it possible to conduct relatively long-term studies of variations in the earth's rotation. A description is provided of general analysis techniques, and the calculation of universal time (UT1) from LLR is discussed. Attention is also given to a summary of intercomparisons with different techniques, polar motion results and intercomparisons, and a polar motion error analysis.
Dickey, J. O.↗