SEARCH · Search NASA

Results for “Complete linearization method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Reconstructing cosmological initial conditions from late-time structure with convolutional neural networks

ABSTRACT We present a method to reconstruct the initial linear-regime matter density field from the late-time non-linearly evolved density field in which we channel the output of standard first-order reconstruction to a convolutional neural network (CNN). Our method shows dramatic improvement over the reconstruction of either component alone. We show why CNNs are not well-suited for reconstructing the initial density directly from the late-time density: CNNs are local models, but the relationship between initial and late-time density is not local. Our method leverages standard reconstruction as a preprocessing step, which inverts bulk gravitational flows sourced over very large scales, transforming the residual reconstruction problem from long-range to local and making it ideally suited for a CNN. We develop additional techniques to account for redshift distortions, which warp the density fields measured by galaxy surveys. Our method improves the range of scales of high-fidelity reconstruction by a factor of 2 in wavenumber above standard reconstruction, corresponding to a factor of 8 increase in the number of well-reconstructed modes. In addition, our method almost completely eliminates the anisotropy caused by redshift distortions. As galaxy surveys continue to map the Universe in increasingly greater detail, our results demonstrate the opportunity offered by CNNs to untangle the non-linear clustering at intermediate scales more accurately than ever before.

Astronomy & Astrophysics↗

NASA NTRS2018

An Algorithm for Trajectory Generation in Redundant Manipulators with Joint Transmission Accommodation

Trajectory generation for manipulators involves generating incremental updates of joint variables to achieve a desired end–eﬀector motion. The Jacobian matrix maps incremental joint motion to incremental end–eﬀector motion in a linear fashion and is typically used in manipulator trajectory generation algorithms. In the case of a redundant manipulator, the Jacobian matrix is not square or invertible and therefore algorithms based on pseudoinverses and their variations are commonly used for trajectory generation. These methods either are computationally not eﬃcient or do not utilize all the joints in motion generation and therefore do not completely exploit the redundancy of the manipulator. The method presented in this paper is a simple method that maximizes transmission of all joint variables onto a desired end–eﬀector motion trajectory. The method is based on aligning the null–space of an augmented Jacobian matrix with the path of the desired end–eﬀector motion, from which a linear combination of joints that projects fully onto the desired end–eﬀector trajectory is obtained. In this manner, all joints of the redundant manipulator are used to generate the end–eﬀector trajectory accommodating the ability of each joint in terms of its motion transmission.

Ravani, Bahram↗

NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗

NASA NTRS1973

A review of developments in the theory of elasto-plastic flow

The theory of elasto-plastic flow is developed so that it may accommodate features such as work-hardening, anisotropy, plastic compressibility, non-continuous loading including local or global unloading, and others. A complete theory is given in quasi-linear form; as a result, many useful attributes are accessible. Several integral theorems may be written, finite deformations may be incorporated, and efficient methods for solving problems may be developed; these and other aspects are described in some detail. The theory is reduced to special forms for 2-space, and extensive experience in solving such problems is cited.

Swedlow, J. L.↗

NASA NTRS1979

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

Mitchell, C. E.↗

NASA NTRS2016

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. I. Effects of Line Coupling on Self-Broadened v (sub 1) and Pure Rotational Bands of NH3

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

Trajectory models↗

NASA NTRS2000

Self-Scheduling Parallel Methods for Multiple Serial Codes with Application to WOPWOP

This paper presents a scheme for efficiently running a large number of serial jobs on parallel computers. Two examples are given of computer programs that run relatively quickly, but often they must be run numerous times to obtain all the results needed. It is very common in science and engineering to have codes that are not massive computing challenges in themselves, but due to the number of instances that must be run, they do become large-scale computing problems. The two examples given here represent common problems in aerospace engineering: aerodynamic panel methods and aeroacoustic integral methods. The first example simply solves many systems of linear equations. This is representative of an aerodynamic panel code where someone would like to solve for numerous angles of attack. The complete code for this first example is included in the appendix so that it can be readily used by others as a template. The second example is an aeroacoustics code (WOPWOP) that solves the Ffowcs Williams Hawkings equation to predict the far-field sound due to rotating blades. In this example, one quite often needs to compute the sound at numerous observer locations, hence parallelization is utilized to automate the noise computation for a large number of observers.

Long, Lyle N.↗

NASA NTRS1971

Unsteady flow through compressor stages

The application of the nonsteady Lax-Wendroff technique to problems with asymptotically periodic solution which offers a potentially powerful method for the investigation of the interaction of rotating and stationary blade rows in turbomachinery is reported. A technique for specifying boundary conditions with phase lag was developed to accomplish this. A complete nonlinear analysis is carried out numerically to determine the entire flow field without recourse to the assumption of small disturbances of linear equations which underlie the previous acoustic theories. The result, obtained for the case of equal number of rotor and stator blades shows that transonic flow can be handled without difficulty. In addition, the program is not limited with regard to blade thickness, camber or loading. Extension of this method to incorporate viscous wakes and to analysis of fully three dimensional configuration is feasible, and would greatly expand its utility in practical applications.

Alzner, E.↗

NASA NTRS1990

The pdf approach to turbulent flow

This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.

Kollmann, W.↗

NASA NTRS1934

The torsional stiffness of thin duralumin shells subjected to large torques

This report gives a simple method of estimating the torsional stiffness of thin shells, such as box beams or stressed-skin wings under large torque loads. A general efficiency chart for shells in torsion is established, based on the assumption that the efficiency of the web sheet in resisting deformation decreases linearly with the average stress. The chart is used to calculate the torsional deflections of eight box beams, a test wing panel, and a complete wing; the results of the calculations are shown in comparison with the test results. The agreement is probably as good as might be expected considering the empirical nature of the method and the well-known dispersion between results of tests on thin sheet-metal structures.

Kuhn, Paul↗

NASA NTRS1976

High angle-of-attack stability-and-control analysis

Methods of linear systems analysis were applied to mathematical models of aircraft flying at high angle of attack and maneuver rate. First order longitudinal and lateral directional coupling is obtained by linearizing the complete nonlinear equations of motion about a generalized (quasi steady) trim point. Open loop stability boundaries are defined using the linear dynamic equations, and pilot in the loop effects are presented. Stability augmentation structures for maneuvering flight conditions are shown to be defined readily using optimal control theory.

Stengel, R. F.↗

NASA NTRS2004

Mid-frequency Band Dynamics of Large Space Structures

High and low intensity dynamic environments experienced by a spacecraft during launch and on-orbit operations, respectively, induce structural loads and motions, which are difficult to reliably predict. Structural dynamics in low- and mid-frequency bands are sensitive to component interface uncertainty and non-linearity as evidenced in laboratory testing and flight operations. Analytical tools for prediction of linear system response are not necessarily adequate for reliable prediction of mid-frequency band dynamics and analysis of measured laboratory and flight data. A new MATLAB toolbox, designed to address the key challenges of mid-frequency band dynamics, is introduced in this paper. Finite-element models of major subassemblies are defined following rational frequency-wavelength guidelines. For computational efficiency, these subassemblies are described as linear, component mode models. The complete structural system model is composed of component mode subassemblies and linear or non-linear joint descriptions. Computation and display of structural dynamic responses are accomplished employing well-established, stable numerical methods, modern signal processing procedures and descriptive graphical tools. Parametric sensitivity and Monte-Carlo based system identification tools are used to reconcile models with experimental data and investigate the effects of uncertainties. Models and dynamic responses are exported for employment in applications, such as detailed structural integrity and mechanical-optical-control performance analyses.

dynamics↗

NASA NTRS1988

Modern wing flutter analysis by computational fluid dynamics methods

The application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter prediction is described. The CAP-TSD code has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Generalized aerodynamic forces and flutter characteristics are calculated and compared with linear theory results and with experimental data for a 45 deg sweptback wing. These results are in good agreement with the experimental flutter data which is the first step toward validating CAP-TSD for general transonic aeroelastic applications. The paper presents these results and comparisons along with general remarks regarding modern wing flutter analysis by computational fluid dynamics methods.

Cunningham, Herbert J.↗

NASA NTRS1987

Modern wing flutter analysis by computational fluid dynamics methods

Cunningham, Herbert J.↗

DOE OSTI2019

HALA: Handy Accelerated Linear Algebra

Accelerated linear algebra libraries often come with C-style of interfaces or even older Fortran77 standards, which makes it difficult to use within generic template programming environment of modern C++. For example, the BLAS and derived standards such as cuBLAS do not accept overloads and a different functions have to be called for each input type, thus it is very challenging to write a single template that handles multiple precision modes and works well with different C++ containers. HALA offers a series of templates that wrap around the BLAS/cuBLAS and other similar methods, automatically infer the relevant types and call the appropriate back-end. The templates work out-of-the-box with all C++ standard vector-like containers and can be easily extended (with template specializations) to handle user-provided containers. The HALA API is also overloaded to handle both GPU and CPU cases with a single "engine" class, thus a single high-level algorithms can utilize both CPU or GPU backends, i.e., the HALA API is unified and handles the variations between cuBLAS and BLAS. In addition to BLAS and cuBLAS, wrapper templates are provided for subset of LAPACK, cuSparse, and Cholmod methods. Work is in progress to complete as many of these standards as possible. HALA also includes a module for low-level extended register vectorization for complex number arithmetic and several simple solvers that build on the basic linear algebra capabilities. A single unified C++ API will benefit fast prototyping and easily writing code that is portable across GPU/CPU platforms as well as precision types and user containers. Note that HALA does not provide any accelerated algorithms, it simply serves as a "handy" front-end to other standards.

Stoyanov, MiroslavK.↗

NASA NTRS2001

Assessment of Stirling Technology Has Provided Critical Data Leading Toward Flight Readiness of the Stirling Converter

The NASA Glenn Research Center is supporting the development of a Stirling converter with the Department of Energy (DOE, Germantown, Maryland) for an advanced Stirling Radioisotope Power System (SRPS) to provide spacecraft onboard electric power for NASA space science missions. A key technology assessment completed by Glenn and DOE has led to the SRPS being identified as a high-efficiency power source for such deep space missions as the Europa Orbiter and the Solar Probe. In addition, the Stirling system is now being considered for unmanned Mars rovers, especially where mission profiles may exclude the use of photovoltaic power systems, such as exploration at high Martian latitudes or for missions of long duration. The SRPS efficiency of over 20 percent will reduce the required amount of radioisotope by more than a factor of 3 in comparison to current radioisotope thermoelectric generators. This significantly reduces radioisotope cost, radiological inventory, and system cost, and it provides efficient use of scarce radioisotope resources. In support of this technology assessment, Glenn conducted a series of independent evaluations and tests to determine the technology readiness of a 55-We Stirling converter developed by Stirling Technology Company (Kennewick, Washington) and DOE. Key areas evaluated by Glenn included: 1) Radiation tolerance of materials; 2) Random vibration testing of the Stirling converter in Glenn's Structural Dynamics Lab to simulate operation in the launch environment; 3) Electromagnetic interference and compatibility (EMI/EMC) of the converter operating in Glenn's EMI lab; Independent failure modes, effects, and criticality analysis, and life and reliability 4. Independent failure modes, effects, and criticality analysis, and life and reliability assessment; and 5) SRPS cost estimate. The data from these evaluations were presented to NASA Headquarters and the Jet Propulsion Laboratory mission office by a joint industry/Government team consisting of DOE, Glenn, and Lockheed Martin Astronautics. This team concluded that there are no technical reasons that would rule out using the Stirling converter for deep space missions. As a direct result of the successful testing at Glenn, the DOE/Stirling Technology Company 55-We Stirling converter has been baselined for the SRPS. Glenn is now continuing an in-house project to assist in developing the Stirling converter for readiness for space qualification and mission implementation. As part of this effort, the Stirling converter will be further characterized under launch environment random vibration testing, methods to reduce converter EMI will be developed, and an independent performance verification will be completed. Converter life assessment and permanent magnet aging characterization tasks are also underway. Substitute organic materials for the linear alternator and piston bearing coatings for use in a high-radiation environment have been identified and have now been incorporated in Stirling converters built by Stirling Technology Company for Glenn. Electromagnetic and thermal finite element analyses for the alternator are also being conducted.

Thieme, Lanny G.↗

NASA NTRS1983

Subsonic panel method for designing wing surfaces from pressure distribution

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Bristow, D. R.↗

NASA NTRS2018

Scattering and Radiative Properties of Morphologically Complex Carbonaceous Aerosols: A Systematic Modeling Study

This paper provides a thorough modeling-based overview of the scattering and radiative properties of a wide variety of morphologically complex carbonaceous aerosols. Using the numerically-exact superposition T-matrix method, we examine the absorption enhancement, absorption Angstroem exponent (AAE), backscattering linear depolarization ratio (LDR), and scattering matrix elements of black-carbon aerosols with 11 different model morphologies ranging from bare soot to completely embedded soot-sulfate and soot-brown carbon mixtures. Our size-averaged results show that fluffy soot particles absorb more light than compact bare-soot clusters. For the same amount of absorbing material, the absorption cross section of internally mixed soot can be more than twice that of bare soot. Absorption increases as soot accumulates more coating material and can become saturated. The absorption enhancement is affected by particle size, morphology, wavelength, and the amount of coating. We refute the conventional belief that all carbonaceous aerosols have AAEs close to 1.0. Although LDRs caused by bare soot and certain carbonaceous particles are rather weak, LDRs generated by other soot-containing aerosols can reproduce strong depolarization measured by Burton et al. for aged smoke. We demonstrate that multi-wavelength LDR measurements can be used to identify the presence of morphologically complex carbonaceous particles, although additional observations can be needed for full characterization. Our results show that optical constants of the host/coating material can significantly influence the scattering and absorption properties of soot-containing aerosols to the extent of changing the sign of linear polarization. We conclude that for an accurate estimate of black-carbon radiative forcing, one must take into account the complex morphologies of carbonaceous aerosols in remote sensing studies as well as in atmospheric radiation computations.

carbonaceous aerosols; scattering matrix; polariza↗