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At least 1,153 records · Page 64

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NASA NTRS1999

Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Toomarian, Nikzad↗

NASA NTRSDate not supplied

Spacesuit Sizing by Multivariate Simulation: Case Study for Liquid Cooling and Ventilation Garment

A technique was developed to assess the fit of spacesuit garment liquid cooling and ventilation garment (LCVG). A fit scoring scheme was built from the spacesuit sizing requirements and guidelines, and the accommodated proportion of the wearer population was estimated from statistically synthesized pseudo population data. The method evaluated different scenarios of LCVG sizing systems including 1) baseline 7-size system, 2) 7-sizes with target body dimensions iteratively adjusted for maximum fit, and 3) 9-sizes with iterative adjustments. Overall, the baseline sizing system showed 81% accommodation rate, while the hypothetical new systems in-tegrating iterative adjustments for 7- and 9-sizes predictively indicated that accommodation could improve up to 92 and 97%. The proposed method provided a structured metric to quantify fit performance of a garment sizing system, which can be further applied to different spacesuit component, PPE and garment designs.

Han Kim↗

NASA NTRS1979

Improvements in surface singularity analysis and design methods

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Bristow, D. R.↗

NASA NTRS1977

Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics

Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.

Martin, E. D.↗

NASA NTRS1982

Calculation of vortex flows on complex configurations

The calculation of aerodynamic characteristics of complex configurations having strongly coupled vortex flows is a non-linear problem requiring iterative solution techniques. This paper discusses the use of a low-order panel method as a means of obtaining practical solutions to such problems. The panel method is based on piecewise constant source and doublet quadrilateral panels and uses the internal Dirichlet boundary condition of zero perturbation potential. The problems of predicting vortex/surface interaction and vortex separation are discussed. Some example calculations are included but further test cases have yet to be carried out, in particular for comparisons with experimental data. The problem of convergence on the iterative calculation for the shape of the free vortex sheet is addressed and a preprocessor routine, based on an unsteady, two-dimensional version of the panel method, is put forward as a cost-effective way of generating an initial vortex structure for use as a starting solution for general configurations.

Maskew, B.↗

NASA NTRS1969

Determination of the temperature profile in an atmosphere from its outgoing radiation

A highly convergent relaxation method for the inversion of the full radiative transfer equation was developed. The results of the iterative solution indicate that convergence can be achieved over a wide range of initial guesses, enabling the temperature profile of a relatively unknown atmosphere to be unambiguously determined. The method is illustrated by examples for the outgoing radiance in the earth's atmosphere for the region of the 4.3 microns CO2 band, but can be similarly applied in other frequency ranges.

Chahine, M. T.↗

NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗

NASA NTRS1989

Direct method for solution of three-dimensional unsteady incompressible Navier-Stokes equations

A three-dimensional, unsteady analysis for the velocity-vorticity formulation of the Navier-Stokes (NS) equations is described. This formulation highlights the natural separation of the spin dynamics of a fluid particle from its translational kinematics. This separation is exploited to produce a single pass direct inversion of the full unsteady NS operator without the need to iterate either the future wall vorticity or the nonlinear vorticity convection terms. The method has uniform second-order accuracy in time and space. As an example, it is applied to the problem of the three-dimensional flow within a shear-driven cubical box. Results are obtained for Re = 100, 400, and 1000 using a preliminary (25, 25, 25) mesh.

Osswald, G. A.↗

NASA NTRS2012

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test.

He, Yuning↗

NASA NTRS1988

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗

NASA NTRS1990

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Sidi, Avram↗

NASA NTRS2016

Observations of the Geometry of Horizon-Based Optical Navigation

NASA's Orion Project has sparked a renewed interest in horizon-based optical navigation(OPNAV) techniques for spacecraft in the Earth-Moon system. Some approaches have begun to explore the geometry of horizon-based OPNAV and exploit the fact that it is a conic section problem. Therefore, the present paper focuses more deeply on understanding and leveraging the various geometric interpretations of horizon-based OPNAV. These results provide valuable insight into the fundamental workings of OPNAV solution methods, their convergence properties, and associated estimate covariance. Most importantly, the geometry and transformations uncovered in this paper lead to a simple and non-iterative solution to the generic horizon-based OPNAV problem. This represents a significant theoretical advancement over existing methods. Thus, we find that a clear understanding of geometric relationships is central to the prudent design, use, and operation of horizon-based OPNAV techniques.

Christian, John↗

NASA NTRS1986

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Murphy, P. C.↗

NASA NTRS2016

Effects of Liner Length and Attenuation on NASA Langley Impedance Eduction

This study explores the effects of liner length and attenuation on the CHE (convected Helmholtz equation) impedance eduction method, in which the surface impedance of an acoustic liner is inferred through an iterative process based on repeated solutions to the convected Helmholtz equation. Wire mesh-over-honeycomb and perforate-over-honeycomb acoustic liners are tested in the NASA Langley Grazing Flow Impedance Tube, and the resultant data are processed using two impedance eduction methods. The first is the CHE method, and the second is a direct method (labeled the KT method) that uses the Kumaresan and Tufts algorithm to compute the impedance directly. The CHE method has been extensively used for acoustic liner evaluation, but experiences anomalous behavior under some test conditions. It is postulated that the anomalies are related to the liner length and/or attenuation. Since the KT method only employs data measured over the length of the liner, it is expected to be unaffected by liner length. A comparison of results achieved with the two impedance eduction methods is used to explore the interactive effects of liner length and attenuation on the CHE impedance eduction method.

Jones, M. G.↗

NASA NTRS1984

Conjugate gradient coupled with multigrid for an indefinite problem

An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

Gozani, J.↗

NASA NTRS1989

Fourier transform methods in local gravity modeling

New algorithms were derived for computing terrain corrections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algoriithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface were developed to avoid the very large transforms necessary when making computations at high resolution over a wide area. A new method for the numerical solution of Molodensky's problem was developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations. Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.

Harrison, J. C.↗

NASA NTRS1981

An iterative finite element-integral technique for predicting sound radiation from turbofan inlets

A new iterative solution technique for predicting the sound field radiated from a turbofan inlet is presented. The sound field is divided into two regions; the sound field within the inlet which is computed using the finite element method and the radiation field outside the inlet which is calculated using an integral solution technique. A 'unified' solution is obtained by matching the finite element and integral solutions at the interface between the interior and exterior regions. The applicability of the iterative technique is demonstrated by considering several simple cases for which exact or 'classical' solutions for the sound field are available. These examples show that the proper solution is obtained within five iterations. The overall accuracy of the method is demonstrated by comparison with experimental data.

Horowitz, S. J.↗

NASA NTRS1980

Spacecraft loads methodology - Transient vs. shock spectra method

The methodology for the establishment of spacecraft loads is strongly influenced by project constraints which include the cost, schedule and allowable weight. The most rigorous approach is the transient loads analysis which requires a composite mathematical model of the spacecraft and launch vehicle. The structural member loads for the entire composite structure are computed by applying the forcing functions, which represent various dynamic environments during the mission, to the composite model. Although this method ideally leads to a lightweight design, it is costly and time consuming due to complex interfaces involving many organizations. To reduce complexity and cost a shock spectra method has been used to design spacecraft structures. This method utilizes envelopes of shock spectra of launch vehicle accelerations obtained from analysis and/or flight measurements. Since only limited information on the launch vehicle model is involved in this process the design loads iteration cycle can be rapidly performed within the payload organization. In the present paper, these two methods will be evaluated by comparing the loads for several spacecraft. Flight measured loads will also be used in the evaluation.

Chen, J. C.↗