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NASA NTRS1992

Simulation and model reduction for the AFW program

The simulation methodology used in the Active Flexible Wing wind-tunnel test program is described. An overview of the aeroservoelastic modeling used in building the required batch and hot-bench simulations is presented. Successful hot-bench implementation required that the full mathematical model be significantly reduced while assuring that accuracy be maintained for all combinations of 10 inputs and 56 outputs. The reduction was accomplished by using a method based on internally balanced realizations and focussing on the linear, aeroelastic portion of the full mathematical model. The error-bound properties of the internally balanced realization significantly contribute to its utility in the model reduction process. The reduction method and the results achieved are described.

Buttrill, Carey↗

NASA NTRS1991

An integrated research program for TOPEX/Poseidon with emphasis on the Pacific Ocean

There are four distinct but related tasks in this investigation. First, we want to combine estimates of the surface dynamic topography derived independently from altimetry and from hydrography in an optimal way (weighted least squares with a priori estimates) to produce an optimal estimate (with error bounds) of the large-scale circulation. Second, we want to study the large-scale (as opposed to the mesoscale) variability using crossover differences as well as exact repeat tracks. The third task involves the study of mesoscale variability in the Kuroshio Extension, the California Current, and eventually the Pacific Ocean and the whole globe, wherein surface transport estimates are provided for both the Kuroshio Extension and the Gulf Stream. The final task is a study of how altimeter data and other data can be assimilated into numerical models.

Tai, Chang-Kou↗

NASA NTRS1993

Application of artificial neural networks to the design optimization of aerospace structural components

The application of artificial neural networks to capture structural design expertise is demonstrated. The principal advantage of a trained neural network is that it requires trivial computational effort to produce an acceptable new design. For the class of problems addressed, the development of a conventional expert system would be extremely difficult. In the present effort, a structural optimization code with multiple nonlinear programming algorithms and an artificial neural network code NETS were used. A set of optimum designs for a ring and two aircraft wings for static and dynamic constraints were generated by using the optimization codes. The optimum design data were processed to obtain input and output pairs, which were used to develop a trained artificial neural network with the code NETS. Optimum designs for new design conditions were predicted by using the trained network. Neural net prediction of optimum designs was found to be satisfactory for most of the output design parameters. However, results from the present study indicate that caution must be exercised to ensure that all design variables are within selected error bounds.

Berke, Laszlo↗

NASA NTRS1993

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Hagstrom, Thomas↗

NASA NTRS1993

An expert system shell for inferring vegetation characteristics: Changes to the historical cover type database (Task F)

All the options in the NASA VEGetation Workbench (VEG) make use of a database of historical cover types. This database contains results from experiments by scientists on a wide variety of different cover types. The learning system uses the database to provide positive and negative training examples of classes that enable it to learn distinguishing features between classes of vegetation. All the other VEG options use the database to estimate the error bounds involved in the results obtained when various analysis techniques are applied to the sample of cover type data that is being studied. In the previous version of VEG, the historical cover type database was stored as part of the VEG knowledge base. This database was removed from the knowledge base. It is now stored as a series of flat files that are external to VEG. An interface between VEG and these files was provided. The interface allows the user to select which files of historical data to use. The files are then read, and the data are stored in Knowledge Engineering Environment (KEE) units using the same organization of units as in the previous version of VEG. The interface also allows the user to delete some or all of the historical database units from VEG and load new historical data from a file. This report summarizes the use of the historical cover type database in VEG. It then describes the new interface to the files containing the historical data. It describes minor changes that were made to VEG to enable the externally stored database to be used. Test runs to test the operation of the new interface and also to test the operation of VEG using historical data loaded from external files are described. Task F was completed. A Sun cartridge tape containing the KEE and Common Lisp code for the new interface and the modified version of the VEG knowledge base was delivered to the NASA GSFC technical representative.

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NASA NTRS1993

Deduction of emissions of source gases using an objective inversion algorithm and a chemical transport model

An inversion algorithm, constructed to deduce the emissions of a source gas required to produce a specified surface concentration, is applied to the observed surface concentrations of CFC 11, methylchloroform, and methane, using a two-dimensional chemical transport model. The information utilized for this deduction process is limited to the measured atmospheric concentration of the source gas, including the associated standard deviations of these measurements. In this way the amount of objective information available in these measurements is assessed. The algorithm is shown to be capable of producing a latitudinal emissions distribution as well as the error bounds on the deduced emission distribution. The 'ill posed' nature of this inverse problem is discussed as well as the implications this has on the spatial and temporal resolution at which emissions can be resolved. Finally, a methane emission distribution is deduced which has the expected seasonal variations and consistent with results from other, more subjective, deduction studies.

Brown, Margaret↗

NASA NTRS1994

SAGE 2-Umkehr case study of ozone differences and aerosol effects from October 1984 to April 1989

A comparison of 1262 cases of coincident ozone profiles derived from 666 Umkehrs at 17 different stations and 901 SAGE 2 profiles within 1000 km and 12 hours between October 1984 and April 1989 indicates the following layer percentage differences with 2-sigma error bars: layer three 14.6 plus/minus 3.3 percent, layer four 17.6 plus/minus 1.1 percent, layer five -1.3 plus/minus 0.5 percent, layer six -5.7 plus/minus 0.7 percent, layer seven -1.0 plus/minus 0.7 percent, layer eight 4.2 plus/minus 0.7 percent, and layer nine 6.8 plus/minus 1.2 percent. Comparing SAGE 2-Umkehr differences to SAGE 1 version 5.5-Umkehr differences shows SAGE 2 higher than or equal to SAGE 1 relative to Umkehr in all layers except layer three. Adjustment for this bias would produce trends derived from SAGE 2-SAGE 1 differences and Umkehr observations in the 1980s more nearly equal to each other in layers six, seven, and eight. A possible explanation of these differences is a systematic shift in the reference altitude between SAGE 1 and SAGE 2, but there is no independent evidence of this. While the shape of the vertical profile of differences at 17 individual Umkehr stations (mostly in mid-latitudes) is generally consistent at all stations except at Poker Flat, Seoul, and Lauder, significant variation does exists among the stations. The profile of mean difference is similar to previously observed differences between Umkehr and both SAGE 2 and SBUV and also to an eigenvector analysis, but with site-dependent amplitude discrepancies. Because of the close correspondence of stratospheric aerosol optical depth at the SAGE 2-measured 0.525 micron wavelength and the extrapolated 0.32 Umkehr wavelength determined in this study, we use the 0.525 micron data to determine the aerosol effect of Umkehr profiles. The aerosol errors to the Umkehr ozone amounts in percent ozone amount per 0.01 stratospheric aerosol optical depth range from plus 2 percent in layer six to minus 3 percent in layer nine. These results agree with previous theoretical and empirical studies within their respective error bounds in layers nine, eight, and five. The result in layer six differs significantly from previous works. In view of the fact that SAGE 2 and Umkehr produce different ozone retrievals in layers eight and nine and because the intra-layer correlation of SAGE 2 ozone and aerosol in layers eight and nine in non-zero, one must exercise some caution in attributing the entire SAGE 2-Umkehr differences in the upper layers to an aerosol effect.

Newchurch, M. J.↗

NASA NTRS1995

The large discretization step method for time-dependent partial differential equations

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Haras, Zigo↗

NASA NTRS1994

Aerosol effect on Umkehr ozone profiles using Stratospheric Aerosol and Gas Experiment II measurements

This study examines 1211 cases of coincident ozone profiles derived from 1164 Umkehrs and 928 Stratospheric Aerosol and Gas Experiment II (SAGE II) profiles within 1000 km and 12 hours between October 1984 and April 1989 to study the stratospheric-aerosol effect on Umkehr ozone profiles. Because of the close correspondence of stratospheric aerosol optical depth at the SAGE II-measured 0.525-micrometer wavelength and the extrapolated 0.32 Umkehr wavelength determined in this study we use the 0.525-micrometer data to determine the aerosol effect on Umkehr profiles. At the 95% confidence level, we find the following errors to the Umkehr ozone amounts: in Umkehr layer 9 (-2.9 +/- 2.1), layer 8 (-2.3 +/- 1.1), layer 7 (0.1 +/- 1.1), layer 6 (2.2 +/- 1.0), layer 5 (-1.5 +/- 0.8), and layer 4 (-2.4 +/- 1.7) in percent ozone amount per 0.01 stratospheric aerosol optical depth. These results agree with previous theoretical and empirical studies within their respective error bounds in layers 9, 8, and 7. The results in layers 6, 5, and 4 differ significantly from those in previous works. Using only those eight stations with more than 47 coincidences results in mean aerosol effects that are not significantly different from the 14-station results. Because SAGE II and Umkehr produce different ozone retrievals in layer 9 and because the intralayer correlation of SAGE II ozone and aerosol in layer 9 is nonzero, one must exercise some caution in attributing the entire SAGE II-Umkehr difference in this layer to an aerosol effect.

Newchurch, M. J.↗

NASA NTRS1995

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗

NASA NTRS1996

Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation

An algorithm is presented which solves the multi-dimensional diffusion equation on co mplex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

Abarbanel, Saul↗

NASA NTRS1996

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Phillips, J. R.↗

NASA NTRS1993

Optimum Design of Aerospace Structural Components Using Neural Networks

The application of artificial neural networks to capture structural design expertise is demonstrated. The principal advantage of a trained neural network is that it requires a trivial computational effort to produce an acceptable new design. For the class of problems addressed, the development of a conventional expert system would be extremely difficult. In the present effort, a structural optimization code with multiple nonlinear programming algorithms and an artificial neural network code NETS were used. A set of optimum designs for a ring and two aircraft wings for static and dynamic constraints were generated using the optimization codes. The optimum design data were processed to obtain input and output pairs, which were used to develop a trained artificial neural network using the code NETS. Optimum designs for new design conditions were predicted using the trained network. Neural net prediction of optimum designs was found to be satisfactory for the majority of the output design parameters. However, results from the present study indicate that caution must be exercised to ensure that all design variables are within selected error bounds.

Berke, L.↗

NASA NTRS1998

High Performance, Robust Control of Flexible Space Structures: MSFC Center Director's Discretionary Fund

Many spacecraft systems have ambitious objectives that place stringent requirements on control systems. Achievable performance is often limited because of difficulty of obtaining accurate models for flexible space structures. To achieve sufficiently high performance to accomplish mission objectives may require the ability to refine the control design model based on closed-loop test data and tune the controller based on the refined model. A control system design procedure is developed based on mixed H2/H(infinity) optimization to synthesize a set of controllers explicitly trading between nominal performance and robust stability. A homotopy algorithm is presented which generates a trajectory of gains that may be implemented to determine maximum achievable performance for a given model error bound. Examples show that a better balance between robustness and performance is obtained using the mixed H2/H(infinity) design method than either H2 or mu-synthesis control design. A second contribution is a new procedure for closed-loop system identification which refines parameters of a control design model in a canonical realization. Examples demonstrate convergence of the parameter estimation and improved performance realized by using the refined model for controller redesign. These developments result in an effective mechanism for achieving high-performance control of flexible space structures.

Whorton, M. S.↗

NASA NTRS1998

Assessment Study of the State of the Art in Adaptive Control and its Applications to Aircraft Control

Many papers relevant to reconfigurable flight control have appeared over the past fifteen years. In general these have consisted of theoretical issues, simulation experiments, and in some cases, actual flight tests. Results indicate that reconfiguration of flight controls is certainly feasible for a wide class of failures. However many of the proposed procedures although quite attractive, need further analytical and experimental studies for meaningful validation. Many procedures assume the availability of failure detection and identification logic that will supply adequately fast, the dynamics corresponding to the failed aircraft. This in general implies that the failure detection and fault identification logic must have access to all possible anticipated faults and the corresponding dynamical equations of motion. Unless some sort of explicit on line parameter identification is included, the computational demands could possibly be too excessive. This suggests the need for some form of adaptive control, either by itself as the prime procedure for control reconfiguration or in conjunction with the failure detection logic. If explicit or indirect adaptive control is used, then it is important that the identified models be such that the corresponding computed controls deliver adequate performance to the actual aircraft. Unknown changes in trim should be modelled, and parameter identification needs to be adequately insensitive to noise and at the same time capable of tracking abrupt changes. If however, both failure detection and system parameter identification turn out to be too time consuming in an emergency situation, then the concepts of direct adaptive control should be considered. If direct model reference adaptive control is to be used (on a linear model) with stability assurances, then a positive real or passivity condition needs to be satisfied for all possible configurations. This condition is often satisfied with a feedforward compensator around the plant. This compensator must be robustly designed such that the compensated plant satisfies the required positive real conditions over all expected parameter values. Furthermore, with the feedforward only around the plant, a nonzero (but bounded error) will exist in steady state between the plant and model outputs. This error can be removed by placing the compensator also in the reference model. Design of such a compensator should not be too difficult a problem since for flight control it is generally possible to feedback all the system states.

Kaufman, Howard↗

NASA NTRS2000

An Improved Neutron Transport Algorithm for Space Radiation

A low-energy neutron transport algorithm for use in space radiation protection is developed. The algorithm is based upon a multigroup analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. This analysis is accomplished by solving a realistic but simplified neutron transport test problem. The test problem is analyzed by using numerical and analytical procedures to obtain an accurate solution within specified error bounds. Results from the test problem are then used for determining mean values associated with rescattering terms that are associated with a multigroup solution of the straight-ahead Boltzmann equation. The algorithm is then coupled to the Langley HZETRN code through the evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for a water and an aluminum-water shield-target configuration is then compared with LAHET and MCNPX Monte Carlo code calculations for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. In addition, a two-directional solution of the evaporation source showed even further improvement of the fluence near the front of the water target where diffusion from the front surface is important.

Heinbockel, John H.↗

NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗

NASA NTRS2000

Real-Time Parameter Estimation in the Frequency Domain

A method for real-time estimation of parameters in a linear dynamic state-space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than one cycle of the dominant dynamic mode, using no a priori information, with control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements and could be implemented

Morelli, Eugene A.↗