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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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17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

A game theoretic approach to a finite-time disturbance attenuation problem

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.

Rhee, Ihnseok↗
NASA NTRS2003

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Knuth, Kevin H.↗
NASA NTRS1993

System identification and model reduction using modulating function techniques

Weighted least squares (WLS) and adaptive weighted least squares (AWLS) algorithms are initiated for continuous-time system identification using Fourier type modulating function techniques. Two stochastic signal models are examined using the mean square properties of the stochastic calculus: an equation error signal model with white noise residuals, and a more realistic white measurement noise signal model. The covariance matrices in each model are shown to be banded and sparse, and a joint likelihood cost function is developed which links the real and imaginary parts of the modulated quantities. The superior performance of above algorithms is demonstrated by comparing them with the LS/MFT and popular predicting error method (PEM) through 200 Monte Carlo simulations. A model reduction problem is formulated with the AWLS/MFT algorithm, and comparisons are made via six examples with a variety of model reduction techniques, including the well-known balanced realization method. Here the AWLS/MFT algorithm manifests higher accuracy in almost all cases, and exhibits its unique flexibility and versatility. Armed with this model reduction, the AWLS/MFT algorithm is extended into MIMO transfer function system identification problems. The impact due to the discrepancy in bandwidths and gains among subsystem is explored through five examples. Finally, as a comprehensive application, the stability derivatives of the longitudinal and lateral dynamics of an F-18 aircraft are identified using physical flight data provided by NASA. A pole-constrained SIMO and MIMO AWLS/MFT algorithm is devised and analyzed. Monte Carlo simulations illustrate its high-noise rejecting properties. Utilizing the flight data, comparisons among different MFT algorithms are tabulated and the AWLS is found to be strongly favored in almost all facets.

Shen, Yan↗
NASA NTRS1998

Formal Modeling of Multi-Agent Systems using the Pi-Calculus and Epistemic Logic

Multi-agent systems have become important recently in computer science, especially in artificial intelligence (AI). We allow a broad sense of agent, but require at least that an agent has some measure of autonomy and interacts with other agents via some kind of agent communication language. We are concerned in this paper with formal modeling of multi-agent systems, with emphasis on communication. We propose for this purpose to use the pi-calculus, an extension of the process algebra CCS. Although the literature on the pi-calculus refers to agents, the term is used there in the sense of a process in general. It is our contention, however, that viewing agents in the AI sense as agents in the pi-calculus sense affords significant formal insight. One formalism that has been applied to agents in the AI sense is epistemic logic, the logic of knowledge. The success of epistemic logic in computer science in general has come in large part from its ability to handle concepts of knowledge that apply to groups. We maintain that the pi-calculus affords a natural yet rigorous means by which groups that are significant to epistemic logic may be identified, encapsulated, structured into hierarchies, and restructured in a principled way. This paper is organized as follows: Section 2 introduces the pi-calculus; Section 3 takes a scenario from the classical paper on agent-oriented programming [Sh93] and translates it into a very simple subset of the n-calculus; Section 4 then shows how more sophisticated features of the pi-calculus may bc brought into play; Section 5 discusses how the pi-calculus may be used to define groups for epistemic logic; and Section 6 is the conclusion.

Rorie, Toinette↗
NASA NTRS1985

Space Mathematics: A Resource for Secondary School Teachers

A collection of mathematical problems related to NASA space science projects is presented. In developing the examples and problems, attention was given to preserving the authenticity and significance of the original setting while keeping the level of mathematics within the secondary school curriculum. Computation and measurement, algebra, geometry, probability and statistics, exponential and logarithmic functions, trigonometry, matrix algebra, conic sections, and calculus are among the areas addressed.

Kastner, Bernice↗
NASA NTRS1987

Polarization effects on hard target calibration of lidar systems

The theory of hard target calibration of lidar backscatter data, including laboratory measurements of the pertinent target reflectance parameters, is extended to include the effects of polarization of the transmitted and received laser radiation. The bidirectional reflectance-distribution function model of reflectance is expanded to a 4 x 4 matrix allowing Mueller matrix and Stokes vector calculus to be employed. Target reflectance parameters for calibration of lidar backscatter data are derived for various lidar system polarization configurations from integrating sphere and monostatic reflectometer measurements. It is found that correct modeling of polarization effects is mandatory for accurate calibration of hard target reflectance parameters and, therefore, for accurate calibration of lidar backscatter data.

Kavaya, Michael J.↗
NASA NTRS2020

Shape Validation and RF Performance of Inflatable Antennas

Inflatable aperture antennas are an emerging technology that is being investigated for potential use in science and exploration missions. In particular, for missions to Mars and beyond, large deployable aperture antennas can provide the antenna gain required for high data rate communications, where the necessary antenna diameter exceeds the available volume of typical launch vehicle platforms. As inflatable aperture antennas have not been proven fully qualified for space missions, the author's Master's Thesis assessed the Ruze equation in characterizing this antenna technology. Inflatable aperture antennas do not follow a parabolic shape, and so the Ruze equation is not applicable due to the macroscopic shape errors of this technology. Therefore, geometric evaluations of the surface profile cannot simply correlate antenna gain degradation with the root-mean-square shape error with a parabolic surface. Consequently, the focus of this work was to derive an accurate mathematical model of an inflatable aperture antenna in order to characterize its Radio Frequency (RF) performance. Calculus of Variations methodologies were used to derive the surface profile shape of the inflatable aperture antenna. Physical Optics techniques were used to generate the antenna pattern profile. Validation testing of the predicted inflatable antenna shape model was performed through use of Laser Radar metrology measurements on an inflatable test article. Assessments of the RF performance of the inflatable aperture antenna, compared with nominally shaped paraboloidal antennas, were obtained through simulations of both technologies using a common diameter, depth, and arc length. Assessments of the RF performance of the inflatable aperture antenna was also performed against itself for changes in distance of the antenna feed location in the axial direction. Whereas the Ruze equation is limited to assessing gain reduction, this effort will also assess beam spreading and first side lobe angle and magnitude. The ability to characterize the RF response of this antenna will provide for an improved understanding of this technology. The accurate representation of the shape of this type of antenna technology will help to identify the most appropriate ways in which this technology could be utilized in planning future communication architectures for NASA missions to Mars and beyond.

Welch, Bryan W.↗
NASA NTRS2020

Shape Validation and RF Performance of Inflatable Antennas

Inflatable aperture antennas are an emerging technology that is being investigated for potential use in science and exploration missions. In particular, for missions to Mars and beyond, large deployable aperture antennas can provide the antenna gain required for high data rate communications, where the necessary antenna diameter exceeds the available volume of typical launch vehicle platforms. As inflatable aperture antennas have not been proven fully qualified for space missions, the author's Master's Thesis assessed the Ruze equation in characterizing this antenna technology. Inflatable aperture antennas do not follow a parabolic shape, and so the Ruze equation is not applicable due to the macroscopic shape errors of this technology. Therefore, geometric evaluations of the surface profile cannot simply correlate antenna gain degradation with the root-mean square shape error with a parabolic surface. Consequently, the focus of this work was to derive an accurate mathematical model of an inflatable aperture antenna to in order to characterize its Radio Frequency (RF) performance. Calculus of Variations methodologies were used to derive the surface profile shape of the inflatable aperture antenna. Physical Optics techniques were used to generate the antenna pattern profile. Validation testing of the predicted inflatable antenna shape model was performed through use of Laser Radar metrology measurements on an inflatable test article. Assessments of the RF performance of the inflatable aperture antenna, compared with nominally shaped paraboloidal antennas, were obtained through simulations of both technologies using a common diameter, depth, and arc length. Assessments of the RF performance of the inflatable aperture antenna was also performed against itself for changes in distance of the antenna feed location in the axial direction. Whereas the Ruze equation is limited to assessing gain reduction, this effort will also assess beam spreading and first side lobe angle and magnitude. The ability to characterize the RF response of this antenna will provide for an improved understanding of this technology. The accurate representation of the shape of this type of antenna technology will help to identify the most appropriate ways in which this technology could be utilized in planning future communication architectures for NASA missions to Mars and beyond.

Welch, Bryan↗
NASA NTRS2004

Measuring Questions: Relevance and its Relation to Entropy

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Acz6l, I show that this is indeed the case; and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective of the Principle of Maximum Entropy.

Knuth, Kevin H.↗
NASA NTRS2004

Deriving Laws from Ordering Relations

The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.

Knuth, Kevin H.↗
NASA NTRS2003

NASA Tech Briefs, November 2003

Topics covered include: Computer Program Recognizes Patterns in Time-Series Data; Program for User-Friendly Management of Input and Output Data Sets; Noncoherent Tracking of a Source of a Data-Modulated Signal; Software for Acquiring Image Data for PIV; Detecting Edges in Images by Use of Fuzzy Reasoning; A Timer for Synchronous Digital Systems; Prototype Parts of a Digital Beam-Forming Wide-Band Receiver; High-Voltage Droplet Dispenser; Network Extender for MIL-STD-1553 Bus; MMIC HEMT Power Amplifier for 140 to 170 GHz; Piezoelectric Diffraction-Based Optical Switches; Numerical Modeling of Nanoelectronic Devices; Organizing Diverse, Distributed Project Information; Eigensolver for a Sparse, Large Hermitian Matrix; Modified Polar-Format Software for Processing SAR Data; e-Stars Template Builder; Software for Acoustic Rendering; Functionally Graded Nanophase Beryllium/Carbon Composites; Thin Thermal-Insulation Blankets for Very High Temperatures; Prolonging Microgravity on Parabolic Airplane Flights; Device for Locking a Control Knob; Cable-Dispensing Cart; Foam Sensor Structures Would be Self-Deployable and Survive Hard Landings; Real-Gas Effects on Binary Mixing Layers; Earth-Space Link Attenuation Estimation via Ground Radar Kdp; Wedge Heat-Flux Indicators for Flash Thermography; Measuring Diffusion of Liquids by Common-Path Interferometry; Zero-Shear, Low-Disturbance Optical Delay Line; Whispering-Gallery Mode-Locked Lasers; Spatial Light Modulators as Optical Crossbar Switches; Update on EMD and Hilbert-Spectra Analysis of Time Series; Quad-Tree Visual-Calculus Analysis of Satellite Coverage; Dyakonov-Perel Effect on Spin Dephasing in n-Type GaAs; Update on Area Production in Mixing of Supercritical Fluids; and Quasi-Sun-Pointing of Spacecraft Using Radiation Pressure.

Source record↗
NASA NTRS2019

Approach for Propagating Radiometric Data Uncertainties Through NASA Ocean Color Algorithms

Spectroradiometric satellite observations of the ocean are commonly referred to as “ocean color” remote sensing. NASA has continuously collected, processed, and distributed ocean color datasets since the launch of the Sea-viewing Wide-field-of-view Sensor (SeaWiFS) in 1997. While numerous ocean color algorithms have been developed in the past two decades that derive geophysical data products from sensor-observed radiometry, few papers have clearly demonstrated how to estimate measurement uncertainty in derived data products. As the uptake of ocean color data products continues to grow with the launch of new and advanced sensors, it is critical that pixel-by-pixel data product uncertainties are estimated during routine data processing. Knowledge of uncertainties can be used when studying long-term climate records, or to assist in the development and performance appraisal of bio-optical algorithms. In this method paper we provide a comprehensive overview of how to formulate first-order first-moment (FOFM) calculus for propagating radiometric uncertainties through a selection of bio-optical models. We demonstrate FOFM uncertainty formulations for the following NASA ocean color data products: chlorophyll-a pigment concentration (Chl), the diffuse attenuation coefficient at 490 nm (K(sub d,490)), particulate organic carbon (POC), normalized fluorescent line height (nflh), and inherent optical properties (IOPs). Using a quality-controlled in situ hyperspectral remote sensing reflectance (R(sub rs,i)) dataset, we show how computationally inexpensive, yet algebraically complex, FOFM calculations may be evaluated for correctness using the more computationally expensive Monte Carlo approach. We compare bio-optical product uncertainties derived using our test R(sub rs) dataset assuming spectrally-flat, uncorrelated relative uncertainties of 1, 5, and 10%. We also consider spectrally dependent, uncorrelated relative uncertainties in R(sub rs). The importance of considering spectral covariances in R(sub rs), where practicable, in the FOFM methodology is highlighted with an example SeaWiFS image. We also present a brief case study of two POC algorithms to illustrate how FOFM formulations may be used to construct measurement uncertainty budgets for ecologically-relevant data products. Such knowledge, even if rudimentary, may provide useful information to end-users when selecting data products or when developing their own algorithms.

Bio-optics↗
NASA NTRS1981

An algorithm to generate input data from meteorological and space shuttle observations to validate a CH4-CO model

Objective procedures to analyze data from meteorological and space shuttle observations to validate a three dimensional model were investigated. The transport and chemistry of carbon monoxide and methane in the troposphere were studied. Four aspects were examined: (1) detailed evaluation of the variational calculus procedure, with the equation of continuity as a strong constraint, for adjustment of global tropospheric wind fields; (2) reduction of the National Meteorological Center (NMC) data tapes for data input to the OSTA-1/MAPS Experiment; (3) interpolation of the NMC Data for input to the CH4-CO model; and (4) temporal and spatial interpolation procedures of the CO measurements from the OSTA-1/MAPS Experiment to generate usable contours of the data.

Peters, L. K.↗
NASA NTRS2003

Deriving Laws from Ordering Relations

It took much effort in the early days of non-Euclidean geometry to break away from the mindset that all spaces are flat and that two distinct parallel lines do not cross. Up to that point, all that was known was Euclidean geometry, and it was difficult to imagine anything else. We have suffered a similar handicap brought on by the enormous relevance of Boolean algebra to the problems of our age-logic and set theory. Previously, I demonstrated that the algebra of questions is not Boolean, but rather is described by the free distributive algebra. To get to this stage took much effort, as many obstacles-most self-placed-had to be overcome. As Boolean algebras were all I had ever known, it was almost impossible for me to imagine working with an algebra where elements do not have complements. With this realization, it became very clear that the sum and product rules of probability theory at the most basic level had absolutely nothing to do with the Boolean algebra of logical statements. Instead, a measure of degree of inclusion can be invented for many different partially ordered sets, and the sum and product rules fall out of the associativity and distributivity of the algebra. To reinforce this very important idea, this paper will go over how these constructions are made, while focusing on the underlying assumptions. I will derive the sum and product rules for a distributive lattice in general and demonstrate how this leads to probability theory on the Boolean lattice and is related to the calculus of quantum mechanical amplitudes on the partially ordered set of experimental setups. I will also discuss the rules that can be derived from modular lattices and their relevance to the cross-ratio of projective geometry.

Knuth, Kevin H.↗
NASA NTRS2002

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗