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At least 541 records · Page 30

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NASA NTRS2002

On Accuracy of Adaptive Grid Methods for Captured Shocks

The accuracy of two grid adaptation strategies, grid redistribution and local grid refinement, is examined by solving the 2-D Euler equations for the supersonic steady flow around a cylinder. Second- and fourth-order linear finite difference shock-capturing schemes, based on the Lax-Friedrichs flux splitting, are used to discretize the governing equations. The grid refinement study shows that for the second-order scheme, neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points. For the fourth-order scheme, the dominant first-order error component is reduced by the grid adaptation, while the design-order error component drastically increases because of the grid nonuniformity. As a result, both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved. Similar error behavior has been obtained for the pressure integral across the shock. A simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy. Based on these results, a new grid adaptation criterion for captured shocks is proposed.

Yamaleev, Nail K.↗

NASA NTRS2021

Performance Assessment of a Western Range 915-MHz Doppler Radar Wind Profiler

Please find enclosed the performance assessment for a Western Range 915-MHz Doppler Radar Wind Profiler (DRWP). This assessment was conducted following the installation of the new DRWP systems at the Western and Eastern Ranges. DRWP profiles were compared to Automated Meteorological Profiling System balloons launched from Vandenberg Space Force Base. Balloon data was collected from both normal synoptic and launch operations as well as some releases at the DRWP site. These results will include errors due to the spatial separation of winds. Root Mean Square wind speed deltas between the balloons and DRWP system mainly ranged between 1.0 and 2.3 m/s. Mean wind direction deltas mainly ranged between 10 and 28 degrees for wind speeds greater than or equal to 4 m/s. Data availability at discrete altitudes ranged from 20% to 94% with the least amount of available profiles being in the lower altitude ranges between 100 m and 500 m. The effective vertical resolution was determined to be approximately 250 m. The results from this analysis were requested by the United States Space Force for use of the acceptance of the DRWP system and for internal EV44 reference.

B J Barbre↗

NASA NTRS1994

Data compression of discrete sequence: A tree based approach using dynamic programming

A dynamic programming based approach for data compression of a ID sequence is presented. The compression of an input sequence of size N to that of a smaller size k is achieved by dividing the input sequence into k subsequences and replacing the subsequences by their respective average values. The partitioning of the input sequence is carried with the intention of reducing the mean squared error in the reconstructed sequence. The complexity involved in finding the partitions which would result in such an optimal compressed sequence is reduced by using the dynamic programming approach, which is presented.

Shivaram, Gurusrasad↗

NASA NTRS1975

Shuttle propellant loading instrumenation development

A continuous capacitance sensor was developed and an analog signal conditioner was evaluated to demonstrate the acceptability of these items for use in the space shuttle propellant loading system. An existing basic sensor concept was redesigned to provide capability for cryogenic operation, to improve performance, and to minimize production costs. Sensor development verification consisted of evaluation of sensor linearity, cryogenic performance, and stability during vibration. The signal conditioner evaluation consisted mainly of establishing the effects of the variations in temperature and cable parameters and evaluating the stability. A sensor linearity of 0.04 in. was achieved over most of the sensor length. The sensor instability caused by vibration was 0.04 percent. The cryogenic performance data show a maximum instability of 0.19 percent at liquid hydrogen temperature; a theoretical calibration can be computed a within 1 percent. The signal conditioner evaluation showed that, with temperature compensation, all error sources typically contribute much less than 1 percent. An estimate of the accuracy achievable with the sensor and signal conditioner shows an rss estimate of 0.75 in. for liquid oxygen and 1.02 in. for liquid hydrogen. These are approximately four times better than the shuttle requirements. Comparison of continuous sensor and discrete sensor performance show the continuous sensor to be significantly better when there is surface activity due to sloshing, boiling, or other disturbances.

Hamlet, J.↗

NASA NTRS1977

Algorithms for adaptive stochastic control for a class of linear systems

Control of linear, discrete time, stochastic systems with unknown control gain parameters is discussed. Two suboptimal adaptive control schemes are derived: one is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single input, third order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known.

Toda, M.↗

NASA NTRS1984

Maneuvering of large flexible space antennas using optimal discrete-time controllers

The problem of maneuvering large space structures is formulated as a discrete-time, finite-duration optimal regulator problem. Two methods are considered for minimizing the elastic motion during the maneuver. The methods are applied to retargetting maneuver of a large space antenna, and the results are compared with those obtained using bang-bang control. The optimal regulator designed using the model error sensitivity supression method gives the best performance.

Joshi, S. M.↗

NASA NTRS1993

Euler solutions for blunt bodies using triangular meshes - Artificial viscosity forms and numerical boundary conditions

A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.

Winterstein, R.↗

NASA NTRS2018

Discrete Assemblers Utilizing Conventional Motion Systems

An alternative to additive manufacturing is disclosed, introducing an end-to-end workflow in which discrete building blocks are reversibly joined to produce assemblies called digital materials. Described is the design of the bulk-material building blocks and the devices that are assembled from them. Detailed is the design and implementation of an automated assembler, which takes advantage of the digital material structure to avoid positioning errors within a large tolerance. To generate assembly sequences, a novel CAD/CAM workflow is described for designing, simulating, and assembling digital materials. The structures assembled using this process have been evaluated, showing that the joints perform well under varying conditions and that the assembled structures are functionally precise.

Langford, William Kai↗

NASA NTRS1972

On higher order discrete phase-locked loops.

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.

Gill, G. S.↗

NASA NTRS1977

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗

NASA NTRS1981

Influence of boundary approximations and conditions on finite difference solutions

Numerical representations of boundary approximations and conditions for three problems are investigated to determine the resulting global accuracy of the steady state solution. Numerical accuracy with various boundary approximations is determined for quasi-one-dimensional inviscid flow in a duct with the interior grid points evaluated using the MacCormack scheme. When an extrapolation approximation with first order local truncation error is used, the global second order accuracy of the difference scheme can be destroyed. For one dimensional flow in a porous medium, an implicit midpoint difference scheme which is consistent with the boundary conditions is developed without the need of boundary approximations. A dissipative model problem is solved with the boundary conditions discretized with first and second order accuracy. The overall second order accuracy of the difference scheme is destroyed if first order numerical representation of one of the boundary conditions is used. With a boundary approximation, the second order global accuracy of the model problem is retained if either second order extrapolation or first order representation of the governing equation is used.

Blottner, F. G.↗

NASA NTRS1988

An analysis of the Kalman filter in the Gamma Ray Observatory (GRO) onboard attitude determination subsystem

The Gamma Ray Observatory (GRO) spacecraft needs a highly accurate attitude knowledge to achieve its mission objectives. Utilizing the fixed-head star trackers (FHSTs) for observations and gyroscopes for attitude propagation, the discrete Kalman Filter processes the attitude data to obtain an onboard accuracy of 86 arc seconds (3 sigma). A combination of linear analysis and simulations using the GRO Software Simulator (GROSS) are employed to investigate the Kalman filter for stability and the effects of corrupted observations (misalignment, noise), incomplete dynamic modeling, and nonlinear errors on Kalman filter. In the simulations, on-board attitude is compared with true attitude, the sensitivity of attitude error to model errors is graphed, and a statistical analysis is performed on the residuals of the Kalman Filter. In this paper, the modeling and sensor errors that degrade the Kalman filter solution beyond mission requirements are studied, and methods are offered to identify the source of these errors.

Snow, Frank↗

NASA NTRS1999

Variable Structure PID Control to Prevent Integrator Windup

PID controllers are frequently used to control systems requiring zero steady-state error while maintaining requirements for settling time and robustness (gain/phase margins). PID controllers suffer significant loss of performance due to short-term integrator wind-up when used in systems with actuator saturation. We examine several existing and proposed methods for the prevention of integrator wind-up in both continuous and discrete time implementations.

Hall, C. E.↗

NASA NTRS2003

Unstructured Adaptive Meshes: Bad for Your Memory?

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Biswas, Rupak↗

NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

NASA NTRS1993

Use of switched capacitor filters to implement the discrete wavelet transform

This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.

Kaiser, Kraig E.↗

NASA NTRS1994

Parallelized direct execution simulation of message-passing parallel programs

As massively parallel computers proliferate, there is growing interest in findings ways by which performance of massively parallel codes can be efficiently predicted. This problem arises in diverse contexts such as parallelizing computers, parallel performance monitoring, and parallel algorithm development. In this paper we describe one solution where one directly executes the application code, but uses a discrete-event simulator to model details of the presumed parallel machine such as operating system and communication network behavior. Because this approach is computationally expensive, we are interested in its own parallelization specifically the parallelization of the discrete-event simulator. We describe methods suitable for parallelized direct execution simulation of message-passing parallel programs, and report on the performance of such a system, Large Application Parallel Simulation Environment (LAPSE), we have built on the Intel Paragon. On all codes measured to date, LAPSE predicts performance well typically within 10 percent relative error. Depending on the nature of the application code, we have observed low slowdowns (relative to natively executing code) and high relative speedups using up to 64 processors.

Dickens, Phillip M.↗

NASA NTRS2002

Formation Flying Satellite Control Around the L2 Sun-Earth Libration Point

A growing interest in formation flying satellites demands development and analysis of control and estimation algorithms for station-keeping and formation maneuvering. This paper discusses the development of a discrete linear-quadratic-regulator control algorithm for formations in the vicinity of the L2 sun-earth libration point. The development of an appropriate Kalman filter is included as well. Simulations are created for the analysis of the station-keeping and various formation maneuvers of the Stellar Imager mission. The simulations provide tracking error, estimation error, and control effort results. From the control effort, useful design parameters such as delta V and propellant mass are determined. For formation maneuvering, the formation spacecraft track to within 4 meters of their desired position and within 1.5 millimeters per second of their desired zero velocity. The filter, with few exceptions, keeps the estimation errors within their three-sigma values. Without noise, the controller performs extremely well, with the formation spacecraft tracking to within several micrometers. Each spacecraft uses around 1 to 2 grams of propellant per maneuver, depending on the circumstances.

Hamilton, Nicholas H.↗