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NASA NTRS1992

A finite-difference approximate-factorization algorithm for solution of the unsteady transonic small-disturbance equation

A time-accurate approximate-factorization (AF) algorithm is described for solution of the three-dimensional unsteady transonic small-disturbance equation. The AF algorithm consists of a time-linearization procedure coupled with a subiteration technique. The algorithm is the basis for the Computational Aeroelasticity Program-Transonic Small Disturbance (CAP-TSD) computer code, which was developed for the analysis of unsteady aerodynamics and aeroelasticity of realistic aircraft configurations. The paper describes details on the governing flow equations and boundary conditions, with an emphasis on documenting the finite-difference formulas of the AF algorithm.

Batina, John T.↗

NASA NTRS1994

A combined algorithm for minimum time slewing of flexible spacecraft

The use of Pontryagin's Maximum Principle for the large-angle slewing of large flexible structures usually results in the so-called two-point boundary-value problem (TPBVP), in which many requirements (e.g., minimum time, small flexible amplitude, and limited control powers, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical computational algorithm. There are many candidate algorithms available for his problem (e.g., quasilinearization, gradient, and shooting, etc.). In this paper, a proposed algorithm, which combines the quasilinearization method with a time shortening technique and a shooting method, is applied to the minimum-time, three-dimensional, and large-angle maneuver of flexible spacecraft, particularly the orbiting Spacecraft Control Laboratory Experiment (SCOLE) configuration. Theoretically, the nonlinear TPBVP can be solved only through the shooting method to find the 'exact' switching times for the bang-bang controls. However, computationally, a suitable guess for the missing initial costates is crucial because the convergence range of the unknown initial costates is usually narrow, especially for systems with high dimensions and when a multi-bang-bang control strategy is needed. On the other hand, the problems of near minimum time attitude maneuver of general rigid spacecraft and fast slewing of flexible spacecraft have been examined by the authors through a numerical approach based on the quasilinearization algorithm with a time shortening technique. Computational results have demonstrated its broad convergence range and insensitivity to initial costate choices. Consequently, a combined approach is naturally suggested here to solve the minimum time slewing problem. That is, in the computational process, the quasilinearization method is used first to obtain a near minimum time solution. Then, the acquired converged initial costates from the quasilinearization approach are transformed (tailored) to and used as the initial costate guess for starting the shooting method. Finally, the shooting method takes over the remaining calculations until the minimum-time solution converges. The nonlinear equations of motion of the SCOLE are formulated by using Lagrange's equations, with the mast modeled as a continuous beam subject to three-dimensional deformations. The numerical results will be presented and some related computational issues will also be discussed.

Bainum, P. M.↗

NASA NTRS1994

A scalable parallel algorithm for multiple objective linear programs

This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.

Wiecek, Malgorzata M.↗

NASA NTRS1993

A fast algorithm for parallel computation of multibody dynamics on MIMD parallel architectures

In this paper the implementation of a parallel O(LogN) algorithm for computation of rigid multibody dynamics on a Hypercube MIMD parallel architecture is presented. To our knowledge, this is the first algorithm that achieves the time lower bound of O(LogN) by using an optimal number of O(N) processors. However, in addition to its theoretical significance, the algorithm is also highly efficient for practical implementation on commercially available MIMD parallel architectures due to its highly coarse grain size and simple communication and synchronization requirements. We present a multilevel parallel computation strategy for implementation of the algorithm on a Hypercube. This strategy allows the exploitation of parallelism at several computational levels as well as maximum overlapping of computation and communication to increase the performance of parallel computation.

Fijany, Amir↗

NASA NTRS1994

Multilevel algorithms for nonlinear optimization

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Alexandrov, Natalia↗

NASA NTRS1994

Strain gage selection in loads equations using a genetic algorithm

Traditionally, structural loads are measured using strain gages. A loads calibration test must be done before loads can be accurately measured. In one measurement method, a series of point loads is applied to the structure, and loads equations are derived via the least squares curve fitting algorithm using the strain gage responses to the applied point loads. However, many research structures are highly instrumented with strain gages, and the number and selection of gages used in a loads equation can be problematic. This paper presents an improved technique using a genetic algorithm to choose the strain gages used in the loads equations. Also presented are a comparison of the genetic algorithm performance with the current T-value technique and a variant known as the Best Step-down technique. Examples are shown using aerospace vehicle wings of high and low aspect ratio. In addition, a significant limitation in the current methods is revealed. The genetic algorithm arrived at a comparable or superior set of gages with significantly less human effort, and could be applied in instances when the current methods could not.

Source record↗

NASA NTRS1992

Efficient geometric rectification techniques for spectral analysis algorithm

The spectral analysis algorithm is a viable technique for processing synthetic aperture radar (SAR) data in near real time throughput rates by trading the image resolution. One major challenge of the spectral analysis algorithm is that the output image, often referred to as the range-Doppler image, is represented in the iso-range and iso-Doppler lines, a curved grid format. This phenomenon is known to be the fanshape effect. Therefore, resampling is required to convert the range-Doppler image into a rectangular grid format before the individual images can be overlaid together to form seamless multi-look strip imagery. An efficient algorithm for geometric rectification of the range-Doppler image is presented. The proposed algorithm, realized in two one-dimensional resampling steps, takes into consideration the fanshape phenomenon of the range-Doppler image as well as the high squint angle and updates of the cross-track and along-track Doppler parameters. No ground reference points are required.

Chang, C. Y.↗

NASA NTRS1995

Separation analysis, a tool for analyzing multigrid algorithms

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Schridubger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to choose performance relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.

Costiner, Sorin↗

NASA NTRS1995

Ice surface temperature retrieval from AVHRR, ATSR, and passive microwave satellite data: Algorithm development and application

During the second phase project year we have made progress in the development and refinement of surface temperature retrieval algorithms and in product generation. More specifically, we have accomplished the following: (1) acquired a new advanced very high resolution radiometer (AVHRR) data set for the Beaufort Sea area spanning an entire year; (2) acquired additional along-track scanning radiometer(ATSR) data for the Arctic and Antarctic now totalling over eight months; (3) refined our AVHRR Arctic and Antarctic ice surface temperature (IST) retrieval algorithm, including work specific to Greenland; (4) developed ATSR retrieval algorithms for the Arctic and Antarctic, including work specific to Greenland; (5) developed cloud masking procedures for both AVHRR and ATSR; (6) generated a two-week bi-polar global area coverage (GAC) set of composite images from which IST is being estimated; (7) investigated the effects of clouds and the atmosphere on passive microwave 'surface' temperature retrieval algorithms; and (8) generated surface temperatures for the Beaufort Sea data set, both from AVHRR and special sensor microwave imager (SSM/I).

Key, Jeff↗

NASA NTRS1995

Application of a new finite difference algorithm for computational aeroacoustics

Acoustic problems have become extremely important in recent years because of research efforts such as the High Speed Civil Transport program. Computational aeroacoustics (CAA) requires a faithful representation of wave propagation over long distances, and needs algorithms that are accurate and boundary conditions that are unobtrusive. This paper applies a new finite difference method and boundary algorithm to the Linearized Euler Equations (LEE). The results demonstrate the ability of a new fourth order propagation algorithm to accurately simulate the genuinely multidimensional wave dynamics of acoustic propagation in two space dimensions with the LEE. The results also show the ability of a new outflow boundary condition and fourth order algorithm to pass the evolving solution from the computational domain with no perceptible degradation of the solution remaining within the domain.

Goodrich, John W.↗

NASA NTRS1995

Validation of space/ground antenna control algorithms using a computer-aided design tool

The validation of the algorithms for controlling the space-to-ground antenna subsystem for Space Station Alpha is an important step in assuring reliable communications. These algorithms have been developed and tested using a simulation environment based on a computer-aided design tool that can provide a time-based execution framework with variable environmental parameters. Our work this summer has involved the exploration of this environment and the documentation of the procedures used to validate these algorithms. We have installed a variety of tools in a laboratory of the Tracking and Communications division for reproducing the simulation experiments carried out on these algorithms to verify that they do meet their requirements for controlling the antenna systems. In this report, we describe the processes used in these simulations and our work in validating the tests used.

Gantenbein, Rex E.↗

NASA NTRS1995

Genetic algorithms as global random search methods

Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that that schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solution and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.

Peck, Charles C.↗

NASA NTRS1995

PSC algorithm description

An overview of the performance seeking control (PSC) algorithm and details of the important components of the algorithm are given. The onboard propulsion system models, the linear programming optimization, and engine control interface are described. The PSC algorithm receives input from various computers on the aircraft including the digital flight computer, digital engine control, and electronic inlet control. The PSC algorithm contains compact models of the propulsion system including the inlet, engine, and nozzle. The models compute propulsion system parameters, such as inlet drag and fan stall margin, which are not directly measurable in flight. The compact models also compute sensitivities of the propulsion system parameters to change in control variables. The engine model consists of a linear steady state variable model (SSVM) and a nonlinear model. The SSVM is updated with efficiency factors calculated in the engine model update logic, or Kalman filter. The efficiency factors are used to adjust the SSVM to match the actual engine. The propulsion system models are mathematically integrated to form an overall propulsion system model. The propulsion system model is then optimized using a linear programming optimization scheme. The goal of the optimization is determined from the selected PSC mode of operation. The resulting trims are used to compute a new operating point about which the optimization process is repeated. This process is continued until an overall (global) optimum is reached before applying the trims to the controllers.

Nobbs, Steven G.↗

NASA NTRS1995

Spectral identification of minerals using imaging spectrometry data: Evaluating the effects of signal to noise and spectral resolution using the tricorder algorithm

The rapid development of sophisticated imaging spectrometers and resulting flood of imaging spectrometry data has prompted a rapid parallel development of spectral-information extraction technology. Even though these extraction techniques have evolved along different lines (band-shape fitting, endmember unmixing, near-infrared analysis, neural-network fitting, and expert systems to name a few), all are limited by the spectrometer's signal to noise (S/N) and spectral resolution in producing useful information. This study grew from a need to quantitatively determine what effects these parameters have on our ability to differentiate between mineral absorption features using a band-shape fitting algorithm. We chose to evaluate the AVIRIS, HYDICE, MIVIS, GERIS, VIMS, NIMS, and ASTER instruments because they collect data over wide S/N and spectral-resolution ranges. The study evaluates the performance of the Tricorder algorithm, in differentiating between mineral spectra in the 0.4-2.5 micrometer spectral region. The strength of the Tricorder algorithm is in its ability to produce an easily understood comparison of band shape that can concentrate on small relevant portions of the spectra, giving it an advantage over most unmixing schemes, and in that it need not spend large amounts of time reoptimizing each time a new mineral component is added to its reference library, as is the case with neural-network schemes. We believe the flexibility of the Tricorder algorithm is unparalleled among spectral-extraction techniques and that the results from this study, although dealing with minerals, will have direct applications to spectral identification in other disciplines.

Swayze, Gregg A.↗

NASA NTRS1993

A spectral algorithm for envelope reduction of sparse matrices

A new algorithm for reducing the envelope of a sparse matrix is presented. This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix. A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix. Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK's reverse Cuthill-McKee (RCM).

Barnard, Stephen T.↗

NASA NTRS1994

Development of practical multiband algorithms for estimating land-surface temperature from EOS/MODIS data

A practical multiband, hierarchical algorithm for estimating land-surface temperature from NASA's future Earth Observing System (EOS) instruments Moderate Resolution Imaging Spectroradiometer (MODIS) and Advance Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is developed through comprehensive, accurate, radiative transfer simulations at moderate spectral steps of 1-5/cm for wide ranges of atmospheric and surface conditions. The algorithm will accept empirical or estimated information about the surface emissivity and reflectivity and the atmospheric temperature and water-vapor profiles. Ground-based and aircraft measurements are necessary to validate and improve the algorithm and to establish its quality. Its accuracy depends on the calibration accuracy of thermal infrared data, uncertainties in surface heterogeneity, and temperature-dependent atmospheric absorption coefficients. Better knowledge of land-surface spectral emissivities and more accurate coefficients for atmospheric molecular band absorption and water vapor continuum absorption are needed to develop global land-surface temperature algorithms accurate to 1-2 K.

Dozier, J.↗

NASA NTRS1994

Coagulation algorithms with size binning

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.

Statton, David M.↗

NASA NTRS1994

A passive microwave technique for estimating rainfall and vertical structure information from space. Part 1: Algorithm description

This paper describes a multichannel physical approach for retrieving rainfall and vertical structure information from satellite-based passive microwave observations. The algorithm makes use of statistical inversion techniques based upon theoretically calculated relations between rainfall rates and brightness temperatures. Potential errors introduced into the theoretical calculations by the unknown vertical distribution of hydrometeors are overcome by explicity accounting for diverse hydrometeor profiles. This is accomplished by allowing for a number of different vertical distributions in the theoretical brightness temperature calculations and requiring consistency between the observed and calculated brightness temperatures. This paper will focus primarily on the theoretical aspects of the retrieval algorithm, which includes a procedure used to account for inhomogeneities of the rainfall within the satellite field of view as well as a detailed description of the algorithm as it is applied over both ocean and land surfaces. The residual error between observed and calculated brightness temperatures is found to be an important quantity in assessing the uniqueness of the solution. It is further found that the residual error is a meaningful quantity that can be used to derive expected accuracies from this retrieval technique. Examples comparing the retrieved results as well as the detailed analysis of the algorithm performance under various circumstances are the subject of a companion paper.

Kummerow, Christian↗