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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.

Maddalon, Jeffrey M.↗
NASA NTRS2016

Enhanced Engine Performance During Emergency Operation Using a Model-Based Engine Control Architecture

This paper discusses the design and application of model-based engine control (MBEC) for use during emergency operation of the aircraft. The MBEC methodology is applied to the Commercial Modular Aero-Propulsion System Simulation 40k (CMAPSS40k) and features an optimal tuner Kalman Filter (OTKF) to estimate unmeasured engine parameters, which can then be used for control. During an emergency scenario, normally-conservative engine operating limits may be relaxed to increase the performance of the engine and overall survivability of the aircraft; this comes at the cost of additional risk of an engine failure. The MBEC architecture offers the advantage of estimating key engine parameters that are not directly measureable. Estimating the unknown parameters allows for tighter control over these parameters, and on the level of risk the engine will operate at. This will allow the engine to achieve better performance than possible when operating to more conservative limits on a related, measurable parameter.

engine control↗
NASA NTRS1987

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.

Sather, Duane P.↗
NASA NTRS2022

Molecular information theory meets protein folding

We propose an application of molecular information theory to analyze the folding of single domain proteins. We analyze results from various areas of protein science, such as sequence-based potentials, reduced amino acid alphabets, backbone configurational entropy, secondary structure content, residue burial layers, and mutational studies of protein stability changes. We found that the average information contained in the sequences of evolved proteins is very close to the average information needed to specify a fold ~2.2 ± 0.3 bits/(site operation). The effective alphabet size in evolved proteins equals the effective number of conformations of a residue in the compact unfolded state at around 5. We calculated an energy-to-information conversion efficiency upon folding of around 50%, lower than the theoretical limit of 70%, but much higher than human built macroscopic machines. We propose a simple mapping between molecular information theory and energy landscape theory and explore the connections between sequence evolution, configurational entropy and the energetics of protein folding.

Ignacio E. Sánchez↗
NASA NTRS1961

A Threshold Theory for Phase-Locked Loops

A model of a phase-locked loop has been developed which is valid for all signal-to-noise ratios. The model is in the form of a nonlinear feedback system with randomly time-varying parameters. The analysis considers two operating regions. In low signal-to-noise ratio regions, the important consideration is stability. We want to study the asymptotic stability in the mean of a nonlinear system. It follows directly that a necessary condition for asymptotic stability of any nonlinear system is that a linearized model about some equilibrium point be asymptotically stable. By considering all possible equilibrium points, we can find an upper bound on the value of noise density which makes the system unstable. This upper bound represents a threshold value for system operation. In high signal-to-noise ratio regions, our results provide an exact statistical. description of system behavior. Therefore, knowledge of the spectrum of the signal and noise may be used to optimize the system configuration.

Van Trees, H. L.↗
NASA NTRS1975

The NATA code; theory and analysis. Volume 3: Programmer's manual

The present, third volume of the final report is a programmer's manual for the code. It provides a listing of the FORTRAN 4 source program; a complete glossary of FORTRAN symbols; a discussion of the purpose and method of operation of each subroutine (including mathematical analyses of special algorithms); and a discussion of the operation of the code on IBM/360 and UNIVAC 1108 systems, including required control cards and the overlay structure used to accommodate the code to the limited core size of the 1108. In addition, similar information is provided to document the programming of the NOZFIT code, which is employed to set up nozzle profile curvefits for use in NATA.

Bade, W. L.↗
NASA NTRS1972

The application of elastohydrodynamic lubrication in gear tooth contacts

An analytical method is presented for determining elastohydrodynamic film thickness in gears from theory and how the film affects gear failure and life. The practical aspects of gear lubrication are presented, including mechanical and service variables which must be considered to obtain optimum gear performance under severe operating conditions.

Townsend, D. P.↗
NASA NTRS1973

Statistical turbulence theory and turbulence phenomenology

The application of deductive turbulence theory for validity determination of turbulence phenomenology at the level of second-order, single-point moments is considered. Particular emphasis is placed on the phenomenological formula relating the dissipation to the turbulence energy and the Rotta-type formula for the return to isotropy. Methods which deal directly with most or all the scales of motion explicitly are reviewed briefly. The statistical theory of turbulence is presented as an expansion about randomness. Two concepts are involved: (1) a modeling of the turbulence as nearly multipoint Gaussian, and (2) a simultaneous introduction of a generalized eddy viscosity operator.

Herring, J. R.↗
NASA NTRS1987

Predictive monitoring research: Summary of the PREMON system

Traditional approaches to monitoring are proving inadequate in the face of two important issues: the dynamic adjustment of expectations about sensor values when the behavior of the device is too complex to enumerate beforehand, and the selective but effective interpretation of sensor readings when the number of sensors becomes overwhelming. This system addresses these issues by building an explicit model of a device and applying common-sense theories of physics to model causality in the device. The resulting causal simulation of the device supports planning decisions about how to efficiently yet reliably utilize a limited number of sensors to verify correct operation of the device.

Doyle, Richard J.↗
NASA NTRS1988

Development of a coded 16-ary CPFSK coherent demodulator

Theory and hardware are described for a proof-of-concept 16-ary continuous phase frequency shift keying (16-CPFSK) digital modem. The 16 frequencies are spaced every 1/16th baud rate for 2 bits/sec/Hz operation. Overall rate 3/4 convolutional coding is incorporated. The demodulator differs significantly from typical quadrature phase detector approaches in that phase is coherently measured by processing the baseband output of a frequency discriminator. Baud rate phase samples from the baseband processor are decoded to yield the original data stream. The method of encoding onto the 16-ary phase nodes, together with convolutional coding gain, results in near quad PSK (QPSK) performance. The modulated signal is of constant envelope; thus the power amplifier can be saturated for peak performance. The spectrum is inherently bandlimited and requires no RF filter.

Clarke, Ken↗
NASA NTRS1992

The early Martian atmosphere

Atmospheric noble gases on Mars, Earth, and Venus are severely and variably depleted with respect to solar abundances, and are characterized by isotopic signatures that differ from planet to planet and from meteoritic and inferred solar compositions. Earlier theories based on simple accretion of meteoritic veneers as planetary volatile sources are unable to replicate these distributions, and so attention is now focusing on evolutionary processes that can fractionate both elements and isotopes, operating either on the early planets themselves or in large preplanetary planetesimals.

Pepin, Robert O.↗
NASA NTRS1991

Hybrid neural network and fuzzy logic approaches for rendezvous and capture in space

The nonlinear behavior of many practical systems and unavailability of quantitative data regarding the input-output relations makes the analytical modeling of these systems very difficult. On the other hand, approximate reasoning-based controllers which do not require analytical models have demonstrated a number of successful applications such as the subway system in the city of Sendai. These applications have mainly concentrated on emulating the performance of a skilled human operator in the form of linguistic rules. However, the process of learning and tuning the control rules to achieve the desired performance remains a difficult task. Fuzzy Logic Control is based on fuzzy set theory. A fuzzy set is an extension of a crisp set. Crisp sets only allow full membership or no membership at all, whereas fuzzy sets allow partial membership. In other words, an element may partially belong to a set.

Berenji, Hamid R.↗
NASA NTRS1993

Phase of the quantum harmonic oscillator with applications to optical polarization

The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.

Shepard, Scott R.↗
NASA NTRS2004

Induced Power of the Helicopter Rotor

A simplified rotor model was used to explore fundamental behavior of lifting rotor induced power at moderate and high advance ratios. Several rotor inflow theories, including dynamic inflow theory and prescribed-wake vortex theory, together with idealized notional airfoil stall models were employed. A number of unusual results were encountered at high advance ratios including trim control reversal and multiple trim solutions. Significant increases in rotor induced power (torque) above the ideal minimum were observed for moderately high advance ratio. Very high induced power was observed near and above unity advance ratio. The results were sensitive to the stall characteristics of the airfoil models used. An equivalent wing analysis was developed to determine induced power from Prandtl lifting line theory and help interpret the rotor induced power behavior in terms of the spanwise airload distribution. The equivalent wing approach was successful in capturing the principal variations of induced power for different configurations and operating conditions. The effects blade root cutout were found to have a significant effect on rotor trim and induced power at high advance ratios.

Ormiston, Robert A.↗
NASA NTRS2005

Inertial Motion-Tracking Technology for Virtual 3-D

In the 1990s, NASA pioneered virtual reality research. The concept was present long before, but, prior to this, the technology did not exist to make a viable virtual reality system. Scientists had theories and ideas they knew that the concept had potential, but the computers of the 1970s and 1980s were not fast enough, sensors were heavy and cumbersome, and people had difficulty blending fluidly with the machines. Scientists at Ames Research Center built upon the research of previous decades and put the necessary technology behind them, making the theories of virtual reality a reality. Virtual reality systems depend on complex motion-tracking sensors to convey information between the user and the computer to give the user the feeling that he is operating in the real world. These motion-tracking sensors measure and report an object s position and orientation as it changes. A simple example of motion tracking would be the cursor on a computer screen moving in correspondence to the shifting of the mouse. Tracking in 3-D, necessary to create virtual reality, however, is much more complex. To be successful, the perspective of the virtual image seen on the computer must be an accurate representation of what is seen in the real world. As the user s head or camera moves, turns, or tilts, the computer-generated environment must change accordingly with no noticeable lag, jitter, or distortion. Historically, the lack of smooth and rapid tracking of the user s motion has thwarted the widespread use of immersive 3-D computer graphics. NASA uses virtual reality technology for a variety of purposes, mostly training of astronauts. The actual missions are costly and dangerous, so any opportunity the crews have to practice their maneuvering in accurate situations before the mission is valuable and instructive. For that purpose, NASA has funded a great deal of virtual reality research, and benefited from the results.

Source record↗
NASA NTRS2008

The Dissipation Mechanism of Magnetic Reconnection

Magnetic reconnection is arguably the most efficient transport and energy conversion mechanism in almost ideal plasmas. Reconnection controls the overall dynamics in space and astrophysics plasmas, as well as in many laboratory plasma systems. Reconnection operates by means of a localized diffusion region, where deviations from the plasma idealness condition generate electric fields and permit plasma transport even far away from the diffusion region itself. Recent advances in analytic theory and computer modeling have begun to shed light on the internal dynamics of the diffusion region. In particular, we begin to understand the delicate nature of the force balance in the inner diffusion region, where particles can become unmagnetized and where electric field forces are important. This presentation will provide a brief introduction of the reconnection process and its applications. This introduction will be followed by a detailed analysis of the current understanding of dissipation region physics, and by an outlook toward future research.

Hesse, Michael↗
NASA NTRS2008

The Dissipation Mechanism of Magnetic Reconnection

Magnetic reconnection is arguably the most efficient transport and energy conversion mechanism in almost ideal plasmas. Reconnection controls the overall dynamics in space and astrophysics plasmas, as well as in many laboratory plasma systems. Reconnection operates by means of a localized diffusion region, where deviations from the plasma idealness condition generate electric fields and permit plasma transport even far away from the diffusion region itself. Recent advances in analytic theory and computer modeling have begun to shed light on the internal dynamics of the diffusion region. In particular, we begin to understand the delicate nature of the force balance in the inner diffusion region, where particles can become unmagnetized and where electric field forces are important. This presentation will provide a brief introduction of the reconnection process and its applications. This introduction will be followed by a detailed analysis of the current understanding of dissipation region physics, and by an outlook toward future research.

Hesse, Michael↗
NASA NTRS2007

The Inner Workings of Magnetic Reconnection

Magnetic reconnection is arguably the most efficient transport and energy conversion mechanism in almost ideal plasmas. Reconnection controls the overall dynamics in space and astrophysics plasmas, as well as in many laboratory plasma systems. Reconnection operates by means of a localized diffusion region, where deviations from the plasma idealness condition generate electric fields and permit plasma transport even far away from the diffusion region itself. Recent advances in analytic theory and computer modeling have begun to shed light on the internal dynamics of the diffusion region. In particular, we begin to understand the delicate nature of the force balance in the inner diffusion region, where particles can become unmagnetized and where electric field forces are important. This presentation will provide a brief introduction of the reconnection process and its applications. This introduction will be followed by a detailed analysis of the current understanding of dissipation region physics, and by an outlook toward future research.

Hesse, Michael↗