SEARCH · Search NASA

Results for “Mathematical Methods”

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 721 records · Page 40

All sources NASA NTRS DOE OSTI

NASA NTRS2004

A "Kane's Dynamics" Model for the Active Rack Isolation System Part Two: Nonlinear Model Development, Verification, and Simplification

Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.

Beech, G. S.↗

NASA NTRS2008

Statistical Methodologies to Integrate Experimental and Computational Research

Development of advanced algorithms for simulating engine flow paths requires the integration of fundamental experiments with the validation of enhanced mathematical models. In this paper, we provide an overview of statistical methods to strategically and efficiently conduct experiments and computational model refinement. Moreover, the integration of experimental and computational research efforts is emphasized. With a statistical engineering perspective, scientific and engineering expertise is combined with statistical sciences to gain deeper insights into experimental phenomenon and code development performance; supporting the overall research objectives. The particular statistical methods discussed are design of experiments, response surface methodology, and uncertainty analysis and planning. Their application is illustrated with a coaxial free jet experiment and a turbulence model refinement investigation. Our goal is to provide an overview, focusing on concepts rather than practice, to demonstrate the benefits of using statistical methods in research and development, thereby encouraging their broader and more systematic application.

Parker, P. A.↗

NASA NTRS2009

Uncertainty Management in Remote Sensing of Climate Data. Summary of A Workshop

Great advances have been made in our understanding of the climate system over the past few decades, and remotely sensed data have played a key role in supporting many of these advances. Improvements in satellites and in computational and data-handling techniques have yielded high quality, readily accessible data. However, rapid increases in data volume have also led to large and complex datasets that pose significant challenges in data analysis (NRC, 2007). Uncertainty characterization is needed for every satellite mission and scientists continue to be challenged by the need to reduce the uncertainty in remotely sensed climate records and projections. The approaches currently used to quantify the uncertainty in remotely sensed data, including statistical methods used to calibrate and validate satellite instruments, lack an overall mathematically based framework.

Remote sensing↗

NASA NTRS2010

Ice Sheet Change Detection by Satellite Image Differencing

Differencing of digital satellite image pairs highlights subtle changes in near-identical scenes of Earth surfaces. Using the mathematical relationships relevant to photoclinometry, we examine the effectiveness of this method for the study of localized ice sheet surface topography changes using numerical experiments. We then test these results by differencing images of several regions in West Antarctica, including some where changes have previously been identified in altimeter profiles. The technique works well with coregistered images having low noise, high radiometric sensitivity, and near-identical solar illumination geometry. Clouds and frosts detract from resolving surface features. The ETM(plus) sensor on Landsat-7, ALI sensor on EO-1, and MODIS sensor on the Aqua and Terra satellite platforms all have potential for detecting localized topographic changes such as shifting dunes, surface inflation and deflation features associated with sub-glacial lake fill-drain events, or grounding line changes. Availability and frequency of MODIS images favor this sensor for wide application, and using it, we demonstrate both qualitative identification of changes in topography and quantitative mapping of slope and elevation changes.

Bindschadler, Robert A.↗

NASA NTRS2004

Measurement of Device Parameters Using Image Recovery Techniques in Large-Scale IC Devices

Devices that respond to radiation on a cell level will produce histograms showing the relative frequency of cell damage as a function of damage. The measured distribution is the convolution of distributions from radiation responses, measurement noise, and manufacturing parameters. A method of extracting device characteristics and parameters from measured distributions via mathematical and image subtraction techniques is described.

radiation↗

NASA NTRSDate not supplied

A Microphone Phased Array for Launch Acoustics Application

A new, portable, phased array of microphones is built at NASA Ames Research Center specifically for the harsh environment encountered in launch acoustics applications. It uses 70 rugged, piezo-electric, dynamic pressure sensors optimally distributed on a 10.5ft diameter open frame dome structure. The open frame is light yet robust to sustain the high wind load of typical seaside launch pads, and the blast and acoustic loads from the launch. A 200-ft long cable bundle carries the microphone signals to a weather-protected electronic cabinet containing the data acquisition system, computers, and other equipment. The array is equipped with an infra-red camera and a visible wavelength camera for imaging the launch site. The beamformed noise maps will be superimposed on the video footages collected by the cameras for correct identification of the noise sources. The array is tested with very loud noise sources to determine the beamforming ability. Multiple mathematical models, such as the conventional beamforming, functional beamforming, spectral element method etc. are used to determine the minimum spatial resolution of the sound sources that can be measured at different frequencies. Additionally, the array hardware is being tested for different environmental conditions and electro-magnetic compliance. The immediate goal is to use the array for NASA’s Artemis/SLS vehicle that will be launched from a newly built Mobile Launch platform and a modified launch pad.

microphone phased-array↗

NASA NTRS2021

System Identification for Propellers at High Incidence Angles

Propellers used for electric vertical takeoff and landing (eVTOL) aircraft propulsion systems experience a wide range of aerodynamic conditions, including large incidence angles relative to oncoming airflow. In oblique flow, propellers exhibit deviations in thrust and torque oriented along the propeller axis of rotation, as well as significant off-axis forces and moments. Although important for modeling eVTOL aircraft aerodynamics, sparse experimental data or mathematical models exist for propellers at incidence. This paper describes a propulsion system modeling methodology for the LA-8 tandem tilt-wing, eVTOL aircraft. System identification methods are applied to isolated propeller wind tunnel data gathered across the vehicle's flight envelope to develop a mathematical model of the propulsion system, including a static motor model, dynamic motor model, and propeller aerodynamic model. Modeling results validated against data withheld from the modeling process indicate good predictive capability and agree with theoretical expectations. The results are followed by a discussion of model implementation strategies into high-fidelity eVTOL aircraft simulations.

system identification↗

NASA NTRS1978

Mathematical simulation of power conditioning systems. Volume 1: Simulation of elementary units. Report on simulation methodology

Methods and algorithms used for the simulation of elementary power conditioning units buck, boost, and buck-boost, as well as shunt PWM are described. Definitions are given of similar converters and reduced parameters. The various parts of the simulation to be carried out are dealt with; local stability, corrective network, measurements of input-output impedance and global stability. A simulation example is given.

Prajous, R.↗

NASA NTRS1989

Advanced methods for 3-D inelastic structural analysis for hot engine structures

Three-dimensional Inelastic Analysis Methods are described. These methods were incorporated into a series of new computer codes embodying a progression of mathematical models (mechanics of materials, specialty finite element, boundary element) for streamlined analysis of hot engine structures such as: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (displacements, frequencies, amplitudes, buckling) structural behavior of the three respective components. The methods and the three computer codes, referred to as MOMM (Mechanics Of Materials Model), MHOST (MARC-Hot Section Technology), and BEST3D (Boundary Element Stress Technology), have been developed and are briefly described.

Chamis, C. C.↗

NASA NTRS1987

Image reconstruction from multiple 1-D scans using filtered localized projection

The spatial resolution that can be attained using scanning linear arrays (consisting of discrete IR solid-state detectors) for image acquisition is considered, and a filtered local projection (FLP) method is described which efficiently combines all available scan information into one rectangular grid without the need for explicit interpolation. Mathematically, the FLP algorithm consists of a localized summation followed by an inverse-filter operation, and it has application to nonlinear restoring techniques. The present method is applied, using a linear array, to simulated data for staggered parallel scans and to multiple scan directions. Noise effects and limitations of the technique are also considered.

Frieden, B. Roy↗

NASA NTRS2003

Flux-Based Deadbeat Control of Induction-Motor Torque

An improved method and prior methods of deadbeat direct torque control involve the use of pulse-width modulation (PWM) of applied voltages. The prior methods are based on the use of stator flux and stator current as state variables, leading to mathematical solutions of control equations in forms that do not lend themselves to clear visualization of solution spaces. In contrast, the use of rotor and stator fluxes as the state variables in the present improved method lends itself to graphical representations that aid in understanding possible solutions under various operating conditions. In addition, the present improved method incorporates the superposition of high-frequency carrier signals for use in a motor-self-sensing technique for estimating the rotor shaft angle at any speed (including low or even zero speed) without need for additional shaft-angle-measuring sensors.

Kenny, Barbara H.↗

NASA NTRS1981

Pitfalls and guidelines for the numerical evaluation of moderate-order system frequency response

The design and evaluation of a feedback control system via frequency response methods relies heavily upon numerical methods. In application, one can usually develop low order simulation models which for the most part are devoid of numerical problems. However, when complex feedback interactions, for example, between instrument control systems and their flexible mounting structure, must be evaluated, simulation models become moderate to large order and numerical problems become common. A large body of relevant numerical error analysis literature is summarized in a large language understandable to nonspecialists. The intent is to provide engineers using simulation models with an engineering feel for potential numerical problems without getting intertwined in the complexities of the associated mathematical theory. Guidelines are also provided by suggesting alternate state of the art methods which have good numerical evaluation characteristics.

Frisch, H. P.↗

NASA NTRS1991

Model correlation and damage location for large space truss structures: Secant method development and evaluation

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

Smith, Suzanne Weaver↗

NASA NTRS1989

Image gathering and restoration - Information and visual quality

A method is investigated for optimizing the end-to-end performance of image gathering and restoration for visual quality. To achieve this objective, one must inevitably confront the problems that the visual quality of restored images depends on perceptual rather than mathematical considerations and that these considerations vary with the target, the application, and the observer. The method adopted in this paper is to optimize image gathering informationally and to restore images interactively to obtain the visually preferred trade-off among fidelity resolution, sharpness, and clarity. The results demonstrate that this method leads to significant improvements in the visual quality obtained by the traditional digital processing methods. These traditional methods allow a significant loss of visual quality to occur because they treat the design of the image-gathering system and the formulation of the image-restoration algorithm as two separate tasks and fail to account for the transformations between the continuous and the discrete representations in image gathering and reconstruction.

Mccormick, Judith A.↗

NASA NTRS1987

An approximate semi-analytical method for prediction of interlaminar shear stresses in an arbitrarily laminated thick plate

An approximate semianalytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate has been presented. The method is based on the assumptions of transverse inextensibility and layerwise constant shear angle theory (LCST) and utilizes an assumed quadratic displacement potential energy based finite element method (FEM). Centroid of the triangular surface has been proved from a rigorous mathematical point of view (Aubin-Nitsche theory), to be the point of exceptional accuracy for the interlaminar shear stresses. Numerical results indicate close agreement with the available three-dimensional elasticity theory solutions. A comparison between the present theory and that due to an assumed stress hybrid FEM suggest that the (normal) traction-free-edge condition is not satisfied in the latter approach. Furthermore, the present paper is the first to present the results for interlaminar shear stresses in a two-layer thick square plate of balanced unsymmetric angle-ply construction. A comparison with the recently proposed Equilibrium Method (EM) indicates the superiority of the present method, because the latter assures faster convergence as well as simultaneous vanishing of the transverse shear stresses on both of the exposed surfaces of the laminate. Superiority of the present method over the EM, in the case of a symmetric laminate, is limited to faster convergence alone. It has also been demonstrated that the combination of the present method and the reduced (quadratic order) numerical integration scheme yields convergence of the interlaminar shear stresses almost as rapidly as that of the nodal displacements, in the case of a thin plate.

Chaudhuri, Reaz A.↗

NASA NTRS2016

Numerical Simulation of Bolide Entry with Ground Footprint Prediction

As they decelerate through the atmosphere, meteors deposit mass, momentum and energy into the surrounding air at tremendous rates. Trauma from the entry of such bolides produces strong blast waves that can propagate hundreds of kilometers and cause substantial terrestrial damage even when no ground impact occurs. We present a new simulation technique for airburst blast prediction using a fully-conservative, Cartesian mesh, finite-volume solver and investigate the ability of this method to model far- field propagation over hundreds of kilometers. The work develops mathematical models for the deposition of mass, momentum and energy into the atmosphere and presents verification and validation through canonical problems and the comparison of surface overpressures, and blast arrival times with actual results in the literature for known bolides. The discussion also examines the effects of various approximations to the physics of bolide entry that can substantially decrease the computational expense of these simulations. We present parametric studies to quantify the influence of entry-angle, burst-height and other parameters on the ground footprint of the airburst, and these values are related to predictions from analytic and handbook-methods.

Simulation↗

NASA NTRSDate not supplied

System Identification for Propellers at High Incidence Angles

Propellers used for electric vertical takeoff and landing (eVTOL) aircraft propulsion systems experience a wide range of aerodynamic conditions, including large incidence angles relative to oncoming airflow. In oblique flow, propellers exhibit deviations in thrust and torque oriented along the propeller axis of rotation, as well as significant off-axis forces and moments. Although important for modeling eVTOL aircraft aerodynamics, sparse experimental data or mathematical models exist for propellers at incidence. This paper describes a propulsion system modeling methodology for the Langley Aerodrome No. 8 (LA-8) tandem tilt-wing, eVTOL aircraft. System identification methods are applied to isolated propeller wind tunnel data gathered across the vehicle's flight envelope to develop a mathematical model of the propulsion system, including a static motor model, dynamic motor model, and propeller aerodynamic model. Modeling results validated against data withheld from the modeling process indicate good predictive capability and agree with theoretical expectations. The results are followed by a discussion of model implementation strategies into high-fidelity eVTOL aircraft simulations.

system identification↗

NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗