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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.

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NASA NTRSDate not supplied

Formal Verification of the Interaction Between Semi-Algebraic Sets and Real Analytic Functions

Semi-algebraic sets and real analytic functions are fundamental concepts in Real Algebraic Geometry and Real Analysis, respectively. These concepts interact in the study of Differential Equations, where the real analytic solution to a differential equation is known to enter or exit a semi-algebraic set in a predicable way. Motivated to enhance the capability to reason about differential equations in the Prototype Verification System (PVS), a formalization of multivariate polynomials, semi-algebraic sets, and real analytic functions is developed. The favorable way that a real analytic function enters and exits a semi-algebraic set is proven. It is further shown that if the function is assumed to be smooth, a slightly weaker assumption than real analytic, these favorable interactions with semi-algebraic sets may fail.

Real analytic functions↗
NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗
NASA NTRS2014

A Generic Nonlinear Aerodynamic Model for Aircraft

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Grauer, Jared A.↗
NASA NTRS2004

Rapid Chemometric Filtering of Spectral Data

A method of rapid, programmable filtering of spectral transmittance, reflectance, or fluorescence data to measure the concentrations of chemical species has been proposed. By programmable is meant that a variety of spectral analyses can readily be performed and modified in software, firmware, and/or electronic hardware, without need to change optical filters or other optical hardware of the associated spectrometers. The method is intended to enable real-time identification of single or multiple target chemical species in applications that involve high-throughput screening of multiple samples. Examples of such applications include (but are not limited to) combinatorial chemistry, flow cytometry, bead assays, testing drugs, remote sensing, and identification of targets. The basic concept of the proposed method is to perform real-time crosscorrelations of a measured spectrum with one or more analytical function(s) of wavelength that could be, for example, the known spectra of target species. Assuming that measured spectral intensities are proportional to concentrations of target species plus background spectral intensities, then after subtraction of background levels, it should be possible to determine target species concentrations from cross-correlation values. Of course, the problem of determining the concentrations is more complex when spectra of different species overlap, but the problem can be solved by use of multiple analytical functions in combination with computational techniques that have been developed previously for analyses of this type. The method is applicable to the design and operation of a spectrometer in which spectrally dispersed light is measured by means of an active-pixel sensor (APS) array. The row or column dimension of such an array is generally chosen to be aligned along the spectral-dispersion dimension, so that each pixel intercepts light in a narrow spectral band centered on a wavelength that is a known function of the pixel position. The proposed method admits of two hardware implementations for computing cross-correlations in real time.

Beaman, Gregory↗
NASA NTRS2023

From Remotely-Sensed SIF to Ecosystem Structure, Function, and Service: Part I - Harnessing Theory

Solar-induced chlorophyll fluorescence (SIF) is a remotely sensed optical signal emitted during the light reactions of photosynthesis. The past two decades have witnessed an explosion in availability of SIF data at increasingly higher spatial and temporal resolutions, sparking applications in diverse research sectors (e.g., ecology, agriculture, hydrology, climate, and socioeconomics). These applications must deal with complexities caused by tremendous variations in scale and the impacts of interacting and superimposing plant physiology and three-dimensional vegetation structure on the emission and scattering of SIF. At present, these complexities have not been overcome. To advance future research, the two companion reviews aim to (1) develop an analytical framework for inferring terrestrial vegetation structures and function that are tied to SIF emission, (2) synthesize progress and identify challenges in SIF research via the lens of multi-sector applications, and (3) map out actionable solutions to tackle these challenges and offer our vision for research priorities over the next 5–10 years based on the proposed analytical framework. This paper is the first of the two companion reviews, and theory oriented. It introduces a theoretically rigorous yet practically applicable analytical framework. Guided by this framework, we offer theoretical perspectives on three overarching questions: (1) The forward (mechanism) question—How are the dynamics of SIF affected by terrestrial ecosystem structure and function? (2) The inference question: What aspects of terrestrial ecosystem structure, function, and service can be reliably inferred from remotely sensed SIF and how? (3) The innovation question: What innovations are needed to realize the full potential of SIF remote sensing for real-world applications under climate change? The analytical framework elucidates that process complexity must be appreciated in inferring ecosystem structure and function from the observed SIF; this framework can serve as a diagnosis and inference tool for versatile applications across diverse spatial and temporal scales.

carbon fluxes↗
NASA NTRS1989

Theoretical analysis and meteorological interpretation of the role of raindrop shape on microwave attenuation and propagation phase shifts - Implications for the radar measurement of rain

The effects of raindrop shape on the attenuation and propagation phase shift at vertical and horizontal linear polarizations is examined, focusing on the implications of these effects on rain measurements by radars. Analytic expressions for the imaginary and real components of the forward scattering amplitude function are dervied for a wavelength of 2.2 cm. It is shown that the summation attenuation rate and the rate of summation propagation phase shift are both insensitive to the shapes of raindrops.

Jameson, A. R.↗
NASA NTRS1988

High degree interpolation polynomial in Newton form

Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.

Tal-Ezer, Hillel↗
NASA NTRS1983

A baroclinic quasigeostrophic open ocean model

A baroclinic quasigeostrophic open ocean model is presented, calibrated by a series of test problems, and demonstrated to be feasible and efficient for application to realistic mid-oceanic mesoscale eddy flow regimes. Two methods of treating the depth dependence of the flow, a finite difference method and a collocation method, are tested and intercompared. Sample Rossby wave calculations with and without advection are performed with constant stratification and two levels of nonlinearity, one weaker than and one typical of real ocean flows. Using exact analytical solutions for comparison, the accuracy and efficiency of the model is tabulated as a function of the computational parameters and stability limits set; typically, errors were controlled between 1 percent and 10 percent RMS after two wave periods. Further Rossby wave tests with realistic stratification and wave parameters chosen to mimic real ocean conditions were performed to determine computational parameters for use with real and simulated data. Finally, a prototype calculation with quasiturbulent simulated data was performed successfully, which demonstrates the practicality of the model for scientific use.

Miller, R. N.↗
NASA NTRS2014

Airborne Forward-Looking Interferometer for the Detection of Terminal-Area Hazards

The Forward Looking Interferometer (FLI) program was a multi-year cooperative research effort to investigate the use of imaging radiometers with high spectral resolution, using both modeling/simulation and field experiments, along with sophisticated data analysis techniques that were originally developed for analysis of data from space-based radiometers and hyperspectral imagers. This investigation has advanced the state of knowledge in this technical area, and the FLI program developed a greatly improved understanding of the radiometric signal strength of aviation hazards in a wide range of scenarios, in addition to a much better understanding of the real-world functionality requirements for hazard detection instruments. The project conducted field experiments on three hazards (turbulence, runway conditions, and wake vortices) and analytical studies on several others including volcanic ash, reduced visibility conditions, in flight icing conditions, and volcanic ash.

West, Leanne↗
NASA NTRS1998

Scalability Analysis and Use of Compression at the Goddard DAAC and End-to-End MODIS Transfers

The goal of this task is to analyze the performance of single and multiple FTP transfer between SCF's and the Goddard DAAC. We developed an analytic model to compute the performance of FTP sessions as a function of various key parameters, implemented the model as a program called FTP Analyzer, and carried out validations with real data obtained by running single and multiple FTP transfer between GSFC and the Miami SCF. The input parameters to the model include the mix to FTP sessions (scenario), and for each FTP session, the file size. The network parameters include the round trip time, packet loss rate, the limiting bandwidth of the network connecting the SCF to a DAAC, TCP's basic timeout, TCP's Maximum Segment Size, and TCP's Maximum Receiver's Window Size. The modeling approach used consisted of modeling TCP's overall throughput, computing TCP's delay per FTP transfer, and then solving a queuing network model that includes the FTP clients and servers.

Menasce, Daniel A.↗
NASA NTRS1992

Fault detection and diagnosis using neural network approaches

Neural networks can be used to detect and identify abnormalities in real-time process data. Two basic approaches can be used, the first based on training networks using data representing both normal and abnormal modes of process behavior, and the second based on statistical characterization of the normal mode only. Given data representative of process faults, radial basis function networks can effectively identify failures. This approach is often limited by the lack of fault data, but can be facilitated by process simulation. The second approach employs elliptical and radial basis function neural networks and other models to learn the statistical distributions of process observables under normal conditions. Analytical models of failure modes can then be applied in combination with the neural network models to identify faults. Special methods can be applied to compensate for sensor failures, to produce real-time estimation of missing or failed sensors based on the correlations codified in the neural network.

Kramer, Mark A.↗
NASA NTRS1983

The vibration characteristics of a coupled helicopter rotor-fuselage by a finite element analysis

The dynamic coupling between the rotor system and the fuselage of a simplified helicopter model in hover was analytically investigated. Mass, aerodynamic damping, and elastic and centrifugal stiffness matrices are presented for the analytical model; the model is based on a beam finite element, with polynomial mass and stiffness distributions for both the rotor and fuselage representations. For this analytical model, only symmetric fuselage and collective blade degrees of freedom are treated. Real and complex eigen-analyses are carried out to obtain coupled rotor-fuselage natural modes and frequencies as a function of rotor speed. Vibration response results are obtained for the coupled system subjected to a radially uniform, harmonic blade loading. The coupled response results are compared with response results from an uncoupled analysis in which hub loads for an isolated rotor system subjected to the same sinusoidal blade loading as the coupled system are applied to a free-free fuselage.

Rutkowski, M. J.↗
NASA NTRS1978

Reliable dual-redundant sensor failure detection and identification for the NASA F-8 DFBW aircraft

A technique was developed which provides reliable failure detection and identification (FDI) for a dual redundant subset of the flight control sensors onboard the NASA F-8 digital fly by wire (DFBW) aircraft. The technique was successfully applied to simulated sensor failures on the real time F-8 digital simulator and to sensor failures injected on telemetry data from a test flight of the F-8 DFBW aircraft. For failure identification the technique utilized the analytic redundancy which exists as functional and kinematic relationships among the various quantities being measured by the different control sensor types. The technique can be used not only in a dual redundant sensor system, but also in a more highly redundant system after FDI by conventional voting techniques reduced to two the number of unfailed sensors of a particular type. In addition the technique can be easily extended to the case in which only one sensor of a particular type is available.

Deckert, J. C.↗
NASA NTRS2010

Atmospheric Delay Reduction Using KARAT for GPS Analysis and Implications for VLBI

We have been developing a state-of-the-art tool to estimate the atmospheric path delays by raytracing through mesoscale analysis (MANAL) data, which is operationally used for numerical weather prediction by the Japan Meteorological Agency (JMA). The tools, which we have named KAshima RAytracing Tools (KARAT)', are capable of calculating total slant delays and ray-bending angles considering real atmospheric phenomena. The KARAT can estimate atmospheric slant delays by an analytical 2-D ray-propagation model by Thayer and a 3-D Eikonal solver. We compared PPP solutions using KARAT with that using the Global Mapping Function (GMF) and Vienna Mapping Function 1 (VMF1) for GPS sites of the GEONET (GPS Earth Observation Network System) operated by Geographical Survey Institute (GSI). In our comparison 57 stations of GEONET during the year of 2008 were processed. The KARAT solutions are slightly better than the solutions using VMF1 and GMF with linear gradient model for horizontal and height positions. Our results imply that KARAT is a useful tool for an efficient reduction of atmospheric path delays in radio-based space geodetic techniques such as GNSS and VLBI.

Ichikawa, Ryuichi↗
NASA NTRS1995

Optimal guidance law development for an advanced launch system

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

Calise, Anthony J.↗
NASA NTRS2022

Low-Earth Orbit Trajectory Optimization in the Presence of Atmospheric Uncertainty

The previous 20 to 25 years have seen a tremendous increase in space exploration, and with that an increase in the level of logistics planning needed to ensure mission success. For spacecraft that are designed to be periodically re-supplied, a key logistics consumable is propellant, as it constitutes the greatest up-mass on re-supply vehicles. A trajectory design strategy is therefore desired that minimizes propellant usage in order to ease the demand for propellant re-supply missions. This thesis develops such a strategy in three stages, and uses the International Space Station (ISS) as its testbed, as no other LEO spacecraft is more challenging from a space logistics standpoint. First, the ISS trajectory planning problem is formulated as a constrained burn optimization problem assuming a deterministic atmosphere. The cost function is total ∆v, with constraints imposed on longitude of ascending viii node (LAN) and semi-major axis (SMA) altitude. Analytic derivatives are constructed for both the cost and constraints, which are necessary given the 6-week to 2-year time frames being considered. A gradient-based optimizer is then utilized to find locally-optimal solutions to real-world ISS trajectory planning problems. Second, atmospheric uncertainty is addressed by constructing a probabilistic model of space weather data using Gaussian Processes (GPs). Bayesian inference is performed using the GP model to generate mean and covariance estimates for space weather predictions, whose pedigree is assessed against test data. The predictions are then mapped into atmospheric density via the analytic Jacchia-Roberts density model, and the effect of space weather uncertainty on orbital lifetime is examined. Third, an ISS burn execution uncertainty model is developed. This model, along with the space weather uncertainty model, are deployed in a linear covariance analysis to ascertain their combined effect on LAN and SMA altitude dispersions. The deterministic constraints from the original problem are re-formulated as stochastic constraints, where now the constraint uncertainty interval is required to fall within specified bounds. An updated optimization framework is constructed using the original ∆v cost function along with the stochastic constraints to solve the trajectory optimization problem under atmospheric uncertainty. Finally, the complete architecture is summarized for deployment in an operational setting.

Trajectory Optimization↗
NASA NTRS1978

Multispectral data acquisition and classification - Statistical models for system design

In this paper we relate the statistical processes that are involved in multispectral data acquisition and classification to a simple radiometric model of the earth surface and atmosphere. If generalized, these formulations could provide an analytical link between the steadily improving models of our environment and the performance characteristics of rapidly advancing device technology. This link is needed to bring system analysis tools to the task of optimizing remote sensing and (real-time) signal processing systems as a function of target and atmospheric properties, remote sensor spectral bands and system topology (e.g., image-plane processing), radiometric sensitivity and calibration accuracy, compensation for imaging conditions (e.g., atmospheric effects), and classification rates and errors.

Huck, F. O.↗