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NASA NTRS1993

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Bless, Robert R.↗

NASA NTRS1973

The calculation of efficient high precision orbits by optimum matching of the formulation and numerical integrator

The development of improved computer algorithms is considered for calculating earth satellite orbital trajectories by optimum selection of the analytical method that minimizes the number of perturbative acceleration computations for a given accuracy. A variation of parameter algorithm considering the equation of motion for a satellite proved superior for the geosynchronous orbit.

Velez, C. E.↗

NASA NTRS1992

Possibility expectation and its decision making algorithm

The fuzzy integral has been shown to be an effective tool for the aggregation of evidence in decision making. Of primary importance in the development of a fuzzy integral pattern recognition algorithm is the choice (construction) of the measure which embodies the importance of subsets of sources of evidence. Sugeno fuzzy measures have received the most attention due to the recursive nature of the fabrication of the measure on nested sequences of subsets. Possibility measures exhibit an even simpler generation capability, but usually require that one of the sources of information possess complete credibility. In real applications, such normalization may not be possible, or even desirable. In this report, both the theory and a decision making algorithm for a variation of the fuzzy integral are presented. This integral is based on a possibility measure where it is not required that the measure of the universe be unity. A training algorithm for the possibility densities in a pattern recognition application is also presented with the results demonstrated on the shuttle-earth-space training and testing images.

Keller, James M.↗

NASA NTRS2014

Adaptive Augmenting Control Flight Characterization Experiment on an F/A-18

The NASA Marshall Space Flight Center (MSFC) Flight Mechanics and Analysis Division developed an Adaptive Augmenting Control (AAC) algorithm for launch vehicles that improves robustness and performance by adapting an otherwise welltuned classical control algorithm to unexpected environments or variations in vehicle dynamics. This AAC algorithm is currently part of the baseline design for the SLS Flight Control System (FCS), but prior to this series of research flights it was the only component of the autopilot design that had not been flight tested. The Space Launch System (SLS) flight software prototype, including the adaptive component, was recently tested on a piloted aircraft at Dryden Flight Research Center (DFRC) which has the capability to achieve a high level of dynamic similarity to a launch vehicle. Scenarios for the flight test campaign were designed specifically to evaluate the AAC algorithm to ensure that it is able to achieve the expected performance improvements with no adverse impacts in nominal or nearnominal scenarios. Having completed the recent series of flight characterization experiments on DFRC's F/A-18, the AAC algorithm's capability, robustness, and reproducibility, have been successfully demonstrated. Thus, the entire SLS control architecture has been successfully flight tested in a relevant environment. This has increased NASA's confidence that the autopilot design is ready to fly on the SLS Block I vehicle and will exceed the performance of previous architectures.

VanZwieten, Tannen S.↗

NASA NTRS2008

Signal Analysis Algorithms for Optimized Fitting of Nonresonant Laser Induced Thermal Acoustics Damped Sinusoids

This study seeks a numerical algorithm which optimizes frequency precision for the damped sinusoids generated by the nonresonant LITA technique. It compares computed frequencies, frequency errors, and fit errors obtained using five primary signal analysis methods. Using variations on different algorithms within each primary method, results from 73 fits are presented. Best results are obtained using an AutoRegressive method. Compared to previous results using Prony s method, single shot waveform frequencies are reduced approx.0.4% and frequency errors are reduced by a factor of approx.20 at 303K to approx. 0.1%. We explore the advantages of high waveform sample rates and potential for measurements in low density gases.

Balla, R. Jeffrey↗

NASA NTRS1986

Application of satellite data to the variational analysis of the three dimensional wind field

The use of a hybrid vertical velocity algorithm, composed of the kinematic and adiabatic methods of Pettersen (1956), to analyze three-dimensional wind fields is studied. The basic principles and advantages and disadvantages of the adiabatic and kinematic techniques are discussed. The adiabatic method is useful in the clear regions and above the tropopause and the kinematic method is applicable near the surface and in cloudy regions. The effects of a finite difference scheme and the objective analysis of Barnes (1973) on a wind field are investigated. The variational algorithm is evaluated by applying it to SESAME data collected in April 1979.

Chance, Barbara A.↗

NASA NTRS2012

A Comparative Study of Interval Management Control Law Capabilities

This paper presents a new tool designed to allow for rapid development and testing of different control algorithms for airborne spacing. This tool, Interval Management Modeling and Spacing Tool (IM MAST), is a fast-time, low-fidelity tool created to model the approach of aircraft to a runway, with a focus on their interactions with each other. Errors can be induced between pairs of aircraft by varying initial positions, winds, speed profiles, and altitude profiles. Results to-date show that only a few of the algorithms tested had poor behavior in the arrival and approach environment. The majority of the algorithms showed only minimal variation in performance under the test conditions. Trajectory-based algorithms showed high susceptibility to wind forecast errors, while performing marginally better than the other algorithms under other conditions. Trajectory-based algorithms have a sizable advantage, however, of being able to perform relative spacing operations between aircraft on different arrival routes and flight profiles without employing ghosting. methods. This comes at the higher cost of substantially increased complexity, however. Additionally, it was shown that earlier initiation of relative spacing operations provided more time for corrections to be made without any significant problems in the spacing operation itself. Initiating spacing farther out, however, would require more of the aircraft to begin spacing before they merge onto a common route.

Barmore, Bryan E.↗

NASA NTRS1995

Imaging spectrometer measurement of water vapor in the 400 to 2500 nm spectral region

The Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) measures the total upwelling spectral radiance from 400 to 2500 nm sampled at 10 nm intervals. The instrument acquires spectral data at an altitude of 20 km above sea level, as images of 11 by up to 100 km at 17x17 meter spatial sampling. We have developed a nonlinear spectral fitting algorithm coupled with a radiative transfer code to derive the total path water vapor from the spectrum, measured for each spatial element in an AVIRIS image. The algorithm compensates for variation in the surface spectral reflectance and atmospheric aerosols. It uses water vapor absorption bands centered at 940 nm, 1040 nm, and 1380 nm. We analyze data sets with water vapor abundances ranging from 1 to 40 perceptible millimeters. In one data set, the total path water vapor varies from 7 to 21 mm over a distance of less than 10 km. We have analyzed a time series of five images acquired at 12 minute intervals; these show spatially heterogeneous changes of advocated water vapor of 25 percent over 1 hour. The algorithm determines water vapor for images with a range of ground covers, including bare rock and soil, sparse to dense vegetation, snow and ice, open water, and clouds. The precision of the water vapor determination approaches one percent. However, the precision is sensitive to the absolute abundance and the absorption strength of the atmospheric water vapor band analyzed. We have evaluated the accuracy of the algorithm by comparing several surface-based determinations of water vapor at the time of the AVIRIS data acquisition. The agreement between the AVIRIS measured water vapor and the in situ surface radiometer and surface interferometer measured water vapor is 5 to 10 percent.

Green, Robert O.↗

NASA NTRSDate not supplied

Investigating seasonal ENSO forecast amplitude calibration for GEOS-S2S-2

The GEOS-S2S-2 is a global coupled model and assimilation system, encompassing many aspects of the Earth climate system. This project looked at seasonal (nine-month) ensemble forecasts, over the period from 1982 through the present. We explored and validated a forecast amplitude correction technique used by the North American Multi-Model Ensemble (NMME), of which GEOS is a member, for Niño3.4 sea-surface temperature (SST) anomaly predictions. The method relies on deriving a set of correction factors based on the standard deviations of hindcast and observed SST anomalies. This algorithm was implemented at the Global Modeling and Assimilation Office (GMAO) and applied to the GEOS-S2S-2 Niño 3.4 hindcasts. In general, the correction reduced the forecast amplitude. This improved the quality of the forecasts when measured by the root mean square error (RMSE) of the ensemble mean forecast. RMSE decreased for most initialization months and forecast leads. The correction had a larger impact on seasons with strong El Niño-Southern Oscillation (ENSO) events than neutral seasons. The effects of the correction on the ensemble characteristics were also examined, and a variation of the algorithm was proposed that preserves the ensemble spread. The outcome of this project is a tool that can be used to calibrate GEOS-S2S-2 ENSO forecasts and potentially improve the precision of multi-model El Niño outlooks.

ENSO↗

NASA NTRS1997

On Approximate Factorization Schemes for Solving the Full Potential Equation

An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.

Holst, Terry L.↗

NASA NTRS2001

Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization

Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.

Wilson, Jeffrey D.↗

NASA NTRS1987

A computational study of the flowfield surrounding the Aeroassist Flight Experiment vehicle

A symmetric total variation diminishing (STVD) algorithm has been applied to the solution of the three-dimensional hypersonic flowfield surrounding the Aeroassist Flight Experiment (AFE) vehicle. Both perfect-gas and chemical nonequilibrium models have been used. The perfect-gas flows were computed at two different Reynolds numbers, including a flight trajectory point at maximum dynamic pressure, and on two different grids. Procedures for coupling the solution of the species continuity equations with the Navier-Stokes equations in the presence of chemical nonequilibrium are reviewed and tested on the forebody of the AFE and on the complete flowfield assuming noncatalytic wall and no species diffusion. Problems with the STVD algorithm unique to flows with variable thermodynamic properties (real gas) are identified and algorithm modifications are suggested. A potential heating problem caused by strong flow impingement on the nozzle lip in the near wake at 0-deg angle of attack has been identified.

Gnoffo, Peter A.↗

NASA NTRS1988

Viscous hypersonic shock-on-shock interaction on blunt cowl lips

The effects of impinging ramp shocks on a two-dimensional viscous inlet cowl of the National Aerospace Plane (NASP) or blunt body flow fields for various impingement locations are numerically simulated by a recently developed second-order implicit total variation diminishing (TVD) algorithm. The results demonstrate that accurate computation of heat transfer rate is crucially dependent on adequate normal grid resolution at the wall. The various numerical results are compared with recent experimental data. Due to the complex flow patterns that occur for the shock-on-shock flows, adaptive grid procedures are utilized.

Klopfer, G. H.↗

NASA NTRS1987

A prototype 4800 bps voice terminal for the mobile satellite experiment

The authors report the final stage of a research project for the NASA mobile satellite experiment (MSAT-X). The work has resulted in two alternative coding techniques which have achieved good communications quality at 4.8 kb/s while tolerating vehicle noise, fading, and a fairly high-error-rate, bursty channel. The authors have constructed a circuit board based on three AT&T 32-bit floating-point DSP32 digital signal processors (DSP) and providing both excess processing power and considerable flexibility for handling different variations of the algorithms. A Motorola 68HC11 microcomputer chip serves as the board controller and interface handler. Mounted on a wirewrapped card, the prototype's circuit footprint amounts to only 225 cm2 and consumes about 13 W of power. A description is given of the architecture, signal processing and communication functions, circuitry, and firmware of the prototype. Issues such as synchronization, framing, error control, and modem interface are also addressed.

Chan, Wai-Yip↗

NASA NTRS1991

High-Resolution Computations Of Hypersonic Flows

Report discusses extension, to hypersonic flows, of class of implicit, total-variation-diminishing (TVD) algorithms suitable for numerical simulation of transonic and supersonic flows obeying Euler and Navier-Stokes equations. Stabilities and rates of convergence, relative to those of other algorithms discussed. Study complemented by variety of compuations of steady and unsteady viscous and inviscid hypersonic flows about blunt bodies.

Yee, H. C.↗

NASA NTRS1996

A Fast parallel tridiagonal algorithm for a class of CFD applications

The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz tridiagonal (STT) systems. Implementation results on Langley's Intel Paragon and IBM SP2 show that both the PDD and reduced PDD algorithms are efficient and scalable.

Moitra, Stuti↗

NASA NTRS2004

Application of SeaWinds Scatterometer and TMI-SSM/I Rain Rates to Hurricane Analysis and Forecasting

Results provided by two different assimilation methodologies involving data from passive and active space-borne microwave instruments are presented. The impact of the precipitation estimates produced by the TRMM Microwave Imager (TMI) and Special Sensor Microwave/Imager (SSM/I) in a previously developed 1D variational continuous assimilation algorithm for assimilating tropical rainfall is shown on two hurricane cases. Results on the impact of the SeaWinds scatterometer on the intensity and track forecast of a mid-Atlantic hurricane are also presented. This work is the outcome of a collaborative effort between NASA and NOAA and indicates the substantial improvement in tropical cyclone forecasting that can result from the assimilation of space-based data in global atmospheric models.

Atlas, Robert↗

NASA NTRS2004

Computational Aerothermodynamic Simulation Issues on Unstructured Grids

The synthesis of physical models for gas chemistry and turbulence from the structured grid codes LAURA and VULCAN into the unstructured grid code FUN3D is described. A directionally Symmetric, Total Variation Diminishing (STVD) algorithm and an entropy fix (eigenvalue limiter) keyed to local cell Reynolds number are introduced to improve solution quality for hypersonic aeroheating applications. A simple grid-adaptation procedure is incorporated within the flow solver. Simulations of flow over an ellipsoid (perfect gas, inviscid), Shuttle Orbiter (viscous, chemical nonequilibrium) and comparisons to the structured grid solvers LAURA (cylinder, Shuttle Orbiter) and VULCAN (flat plate) are presented to show current capabilities. The quality of heating in 3D stagnation regions is very sensitive to algorithm options in general, high aspect ratio tetrahedral elements complicate the simulation of high Reynolds number, viscous flow as compared to locally structured meshes aligned with the flow.

Gnoffo, Peter A.↗