Search NASA⌕ Search

SEARCH · Search NASA

Results for “RESEARCH TECHNIQUE, MATHEMATICS”

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.

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

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Full-envelope aerodynamic modeling of the Harrier aircraft

A project to identify a full-envelope model of the YAV-8B Harrier using flight-test and parameter identification techniques is described. As part of the research in advanced control and display concepts for V/STOL aircraft, a full-envelope aerodynamic model of the Harrier is identified, using mathematical model structures and parameter identification methods. A global-polynomial model structure is also used as a basis for the identification of the YAV-8B aerodynamic model. State estimation methods are used to ensure flight data consistency prior to parameter identification.Equation-error methods are used to identify model parameters. A fixed-base simulator is used extensively to develop flight test procedures and to validate parameter identification software. Using simple flight maneuvers, a simulated data set was created covering the YAV-8B flight envelope from about 0.3 to 0.7 Mach and about -5 to 15 deg angle of attack. A singular value decomposition implementation of the equation-error approach produced good parameter estimates based on this simulated data set.

Mcnally, B. David↗
NASA NTRS1990

Recent literature on structural modeling, identification, and analysis

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Craig, Roy R., Jr.↗
NASA NTRS2004

A Formal Methods Approach to the Analysis of Mode Confusion

The goal of the new NASA Aviation Safety Program (AvSP) is to reduce the civil aviation fatal accident rate by 80% in ten years and 90% in twenty years. This program is being driven by the accident data with a focus on the most recent history. Pilot error is the most commonly cited cause for fatal accidents (up to 70%) and obviously must be given major consideration in this program. While the greatest source of pilot error is the loss of situation awareness , mode confusion is increasingly becoming a major contributor as well. The January 30, 1995 issue of Aviation Week lists 184 incidents and accidents involving mode awareness including the Bangalore A320 crash 2/14/90, the Strasbourg A320 crash 1/20/92, the Mulhouse-Habsheim A320 crash 6/26/88, and the Toulouse A330 crash 6/30/94. These incidents and accidents reveal that pilots sometimes become confused about what the cockpit automation is doing. Consequently, human factors research is an obvious investment area. However, even a cursory look at the accident data reveals that the mode confusion problem is much deeper than just training deficiencies and a lack of human-oriented design. This is readily acknowledged by human factors experts. It seems that further progress in human factors must come through a deeper scrutiny of the internals of the automation. It is in this arena that formal methods can contribute. Formal methods refers to the use of techniques from logic and discrete mathematics in the specification, design, and verification of computer systems, both hardware and software. The fundamental goal of formal methods is to capture requirements, designs and implementations in a mathematically based model that can be analyzed in a rigorous manner. Research in formal methods is aimed at automating this analysis as much as possible. By capturing the internal behavior of a flight deck in a rigorous and detailed formal model, the dark corners of a design can be analyzed. This paper will explore how formal models and analyses can be used to help eliminate mode confusion from flight deck designs and at the same time increase our confidence in the safety of the implementation. The paper is based upon interim results from a new project involving NASA Langley and Rockwell Collins in applying formal methods to a realistic business jet Flight Guidance System (FGS).

Butler, Ricky W.↗
NASA NTRS1991

Robust control with structured perturbations

This semi-annual report describes continued progress on the research. Among several approaches in this area of research, our approach to the parametric uncertainties are being matured everyday. This approach deals with real parameter uncertainties which other techniques such as H (sup infinity) optimal control, micron analysis and synthesis, and l(sub 1) optimal control cannot deal. The primary assumption of this approach is that the mathematical models are well obtained so that the most of system uncertainties can be translated into parameter uncertainties of their linear system representations. These uncertainties may be due to modeling, nonlinearity of the physical system, some time-varying parameters, etc. In this report period of research, we are concentrating on implementing a computer aided analysis and design tool based on new results on parametric robust stability. This implementation will help us to reveal further details in this approach.

Keel, Leehyun↗
DOE OSTI2022

Research Trends and Applications of PMUs

This work is a survey of current trends in applications of PMUs. PMUs have the potential to solve major problems in the areas of power system estimation, protection, and stability. A variety of methods are being used for these purposes, including statistical techniques, mathematical transformations, probability, and AI. The results produced by the techniques reviewed in this work are promising, but there is work to be performed in the context of implementation and standardization. As the smart grid initiative continues to advance, the number of intelligent devices monitoring the power grid continues to increase. PMUs are at the center of this initiative, and as a result, each year more PMUs are deployed across the grid. Since their introduction, myriad solutions based on PMU-technology have been suggested. The high sampling rates and synchronized measurements provided by PMUs are expected to drive significant advancements across multiple fields, such as the protection, estimation, and control of the power grid. This work offers a review of contemporary research trends and applications of PMU technology. Most solutions presented in this work were published in the last five years, and techniques showing potential for significant impact are highlighted in greater detail. Being a relatively new technology, there are several issues that must be addressed before PMU-based solutions can be successfully implemented. This survey found that key areas where improvements are needed include the establishment of PMU-observability, data processing algorithms, the handling of heterogeneous sampling rates, and the minimization of the investment in infrastructure for PMU communication. Solutions based on Bayesian estimation, as well as those having a distributed architectures, show great promise. The material presented in this document is tailored to both new researchers entering this field and experienced researchers wishing to become acquainted with emerging trends.

42 ENGINEERING↗
DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗
NASA NTRS1984

Atmosphere behavior in gas-closed mouse-algal systems - An experimental and modelling study

A NASA-sponsored research program initiated using mathematical modelling and laboratory experimentation aimed at examining the gas-exchange characteristics of artificial animal/plant systems closed to the ambient atmosphere is studied. The development of control techniques and management strategies for maintaining the atmospheric levels of carbon dioxide and oxygen at physiological levels is considered. A mathematical model simulating the behavior of a gas-closed mouse-algal system under varying environmental conditions is described. To verify and validate the model simulations, an analytical system with which algal growth and gas exchange characteristics can be manipulated and measured is designed, fabricated, and tested. The preliminary results are presented.

Averner, M. M.↗
NASA NTRS1994

A PC program to optimize system configuration for desired reliability at minimum cost

High reliability is desired in all engineered systems. One way to improve system reliability is to use redundant components. When redundant components are used, the problem becomes one of allocating them to achieve the best reliability without exceeding other design constraints such as cost, weight, or volume. Systems with few components can be optimized by simply examining every possible combination but the number of combinations for most systems is prohibitive. A computerized iteration of the process is possible but anything short of a super computer requires too much time to be practical. Many researchers have derived mathematical formulations for calculating the optimum configuration directly. However, most of the derivations are based on continuous functions whereas the real system is composed of discrete entities. Therefore, these techniques are approximations of the true optimum solution. This paper describes a computer program that will determine the optimum configuration of a system of multiple redundancy of both standard and optional components. The algorithm is a pair-wise comparative progression technique which can derive the true optimum by calculating only a small fraction of the total number of combinations. A designer can quickly analyze a system with this program on a personal computer.

Hills, Steven W.↗
NASA NTRS1983

Techniques for studying gravity waves and turbulence

Gravity waves and their associated breaking into turbulence are very important in producing the overall picture of middle atmosphere global dynamics and associated transport. It is shown in this research that MST radars represent a most powerful technique for obtaining the needed parameters for gravity-wave-induced drag and diffusion effects as well as measuring wave accelerations and diffusion directly. A mathematical solution to this problem is that of radiative equilibrium with a balanced thermal wind.

Geller, M. A.↗
NASA NTRSDate not supplied

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of A Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗
NASA NTRSDate not supplied

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of a Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗
NASA NTRS2017

Determining the Products of Inertia for Small Scale UAVs

Moments of inertia and products of inertia often need to be determined for aircraft. As complex bodies, their mass properties need to be determined experimentally for best accuracy. While several moment of inertia experimental techniques have been developed, there are few to determine the products of inertia. Products of inertia can be easily determined mathematically if the angle between the aircraft x body axis and principal x axis is known. This method finds the principal inclination angle by mathematically correlating the measured moments of inertia about a range of axes of the aircraft. This correlation uses a least squares error minimization of a mathematical model that describes the ellipse of inertia in the aircraft's x-z axes plane. Results from a test conducted on a small scale UAV (Unmanned Aerial Vehicle) at NASA Armstrong Flight Research Center is also presented, which is an example of the intended application of this technique.

mass properties↗
NASA NTRS1980

Low order equivalent models of highly augmented aircraft determined from flight data using maximum likelihood estimation

This paper presents the results of a study of the feasibility of using low order equivalent mathematical models of a highly augmented aircraft, the F-8 digital fly-by-wire (DFBW), for flying qualities research. Increasingly complex models were formulated and evaluated using flight data and maximum likelihood estimation techniques. The aircraft actuator was modeled alone first. Next the equivalent derivatives were used to model the longitudinal unaugmented F-8 DFBW aircraft dynamics. The most complex model incorporated a pure time shift of the pilot input, a first order lag, and the basic longitudinal airframe model. This same model was then implemented for the F-8 DFBW aircraft in a highly augmented mode. Excellent matching of the dynamics resulted for this model, indicating that low order equivalent models which are good representations of the highly augmented F-8 DFBW aircraft can be formulated with these methods.

Shafer, M. F.↗
NASA NTRS1987

Anticipation of the landing shock phenomenon in flight simulation

An aircraft landing may be described as a controlled crash because a runway surface is intercepted. In a simulation model the transition from aerodynamic flight to weight on wheels involves a single computational cycle during which stiff differential equations are activated; with a significant probability these initial conditions are unrealistic. This occurs because of the finite cycle time, during which large restorative forces will accompany unrealistic initial oleo compressions. This problem was recognized a few years ago at Ames Research Center during simulation studies of a supersonic transport. The mathematical model of this vehicle severely taxed computational resources, and required a large cycle time. The ground strike problem was solved by a described technique called anticipation equations. This extensively used technique has not been previously reported. The technique of anticipating a significant event is a useful tool in the general field of discrete flight simulation. For the differential equations representing a landing gear model stiffness, rate of interception and cycle time may combine to produce an unrealistic simulation of the continuum.

Mcfarland, Richard E.↗
NASA NTRS2001

Deriving the Coronal Magnetic Field Using Parametric Transformation Analysis

When plasma-beta greater than 1 then the gas pressure dominates over the magnetic pressure. This ratio as a function along the coronal magnetic field lines varies from beta greater than 1 in the photosphere at the base of the field lines, to beta much less than 1 in the mid-corona, to beta greater than 1 in the upper corona. Almost all magnetic field extrapolations do not or cannot take into account the full range of beta. They essentially assume beta much less than 1, since the full boundary conditions do not exist in the beta greater than 1 regions. We use a basic parametric representation of the magnetic field lines such that the field lines can be manipulated to match linear features in the EUV and SXR coronal images in a least squares sense. This research employs free-form deformation mathematics to generate the associated coronal magnetic field. In our research program, the complex magnetic field topology uses Parametric Transformation Analysis (PTA) which is a new and innovative method to describe the coronal fields that we are developing. In this technique the field lines can be viewed as being embedded in a plastic medium, the frozen-in-field-line concept. As the medium is deformed the field lines are similarly deformed. However the advantage of the PTA method is that the field line movement represents a transformation of one magnetic field solution into another magnetic field solution. When fully implemented, this method will allow the resulting magnetic field solution to fully match the magnetic field lines with EUV/SXR coronal loops by minimizing the differences in direction and dispersion of a collection of PTA magnetic field lines and observed field lines. The derived magnetic field will then allow beta greater than 1 regions to be included, the electric currents to be calculated, and the Lorentz force to be determined. The advantage of this technique is that the solution is: (1) independent of the upper and side boundary conditions, (2) allows non-vanishing magnetic forces, and (3) provides a global magnetic field solution, which contains high- and low-beta regimes and maximizes the similarity between the field lines structure and all the coronal images of the region. The coronal image analysis is crucial to the investigation and for the first time these images can be exploited to derive the coronal magnetic field in a well-posed mathematical formulation. This program is an outgrowth of an investigation in which an extrapolated potential field was required to be "inflated" in order to have the field lines match the Yohkoh/SXT images. The field lines were radially stretched resulting in a better match to the coronal loops of an active region. The PTA method of radial and non-radial deformations of field lines to provide a match to the EUV/SXR images will be presented.

Gary, G. Allen↗
NASA NTRS2016

Engaging Students, Teachers, and the Public with NASA Astromaterials Research and Exploration Science (ARES) Assets

Engaging students, teachers, and the public with NASA Astromaterials Research and Exploration Science (ARES) assets, including Science, Technology, Engineering and Mathematics (STEM) experts and NASA curation astromaterial samples, provides an extraordinary opportunity to connect citizens with authentic aspects unique to our nation's space program. Effective engagement can occur through both virtual connections such as webcasts and in-person connections at educator workshops and public outreach events. Access to NASA ARES assets combined with adaptable resources and techniques that engage and promote scientific thinking helps translate the science and research being facilitated through NASA exploration, elicits a curiosity that aims to carry over even after a given engagement, and prepares our next generation of scientific explorers.

Graff, P. V.↗
NASA NTRS1992

Correction techniques for depth errors with stereo three-dimensional graphic displays

Three-dimensional (3-D), 'real-world' pictorial displays that incorporate 'true' depth cues via stereopsis techniques have proved effective for displaying complex information in a natural way to enhance situational awareness and to improve pilot/vehicle performance. In such displays, the display designer must map the depths in the real world to the depths available with the stereo display system. However, empirical data have shown that the human subject does not perceive the information at exactly the depth at which it is mathematically placed. Head movements can also seriously distort the depth information that is embedded in stereo 3-D displays because the transformations used in mapping the visual scene to the depth-viewing volume (DVV) depend intrinsically on the viewer location. The goal of this research was to provide two correction techniques; the first technique corrects the original visual scene to the DVV mapping based on human perception errors, and the second (which is based on head-positioning sensor input data) corrects for errors induced by head movements. Empirical data are presented to validate both correction techniques. A combination of the two correction techniques effectively eliminates the distortions of depth information embedded in stereo 3-D displays.

Parrish, Russell V.↗
NASA NTRS2008

Long-Range Transhorizon Lunar Surface Radio Wave Propagation in the Presence of a Regolith and a Sparse Exospheric Plasma

Long-range, over-the-horizon (transhorizon) radio wave propagation is considered for the case of the Moon. In the event that relay satellites are not available or otherwise unwarranted for use, transhorizon communication provides for a contingency or backup option for non line-of-sight lunar surface exploration scenarios. Two potential low-frequency propagation mechanisms characteristic of the lunar landscape are the lunar regolith and the photoelectron induced plasma exosphere enveloping the Moon. Although it was hoped that the regolith would provide for a spherical waveguide which could support a trapped surface wave phenomena, it is found that, in most cases, the regolith is deleterious to long range radio wave propagation. However, the presence of the plasma of the lunar exosphere supports wave propagation and, in fact, surpasses the attenuation of the regolith. Given the models of the regolith and exosphere adopted here, it is recommended that a frequency of 1 MHz be considered for low rate data transmission along the lunar surface. It is also recommended that further research be done to capture the descriptive physics of the regolith and the exospheric plasma so that a more complete model can be obtained. This comprehensive theoretical study is based entirely on first principles and the mathematical techniques needed are developed as required; it is self-contained and should not require the use of outside resources for its understanding.

Manning, Robert M.↗