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All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS2014

Autonomous Flight Rules Concept: User Implementation Costs and Strategies

The costs to implement Autonomous Flight Rules (AFR) were examined for estimates in acquisition, installation, training and operations. The user categories were airlines, fractional operators, general aviation and unmanned aircraft systems. Transition strategies to minimize costs while maximizing operational benefits were also analyzed. The primary cost category was found to be the avionics acquisition. Cost ranges for AFR equipment were given to reflect the uncertainty of the certification level for the equipment and the extent of existing compatible avionics in the aircraft to be modified.

Cotton, William B.↗
NASA NTRS1997

Performance Analysis of the NAS Y-MP Workload

This paper describes the performance characteristics of the computational workloads on the NAS Cray Y-MP machines, a Y-MP 832 and later a Y-MP 8128. Hardware measurements indicated that the Y-MP workload performance matured over time, ultimately sustaining an average throughput of 0.8 GFLOPS and a vector operation fraction of 87%. The measurements also revealed an operation rate exceeding 1 per clock period, a well-balanced architecture featuring a strong utilization of vector functional units, and an efficient memory organization. Introduction of the larger memory 8128 increased throughput by allowing a more efficient utilization of CPUs. Throughput also depended on the metering of the batch queues; low-idle Saturday workloads required a buffer of small jobs to prevent memory starvation of the CPU. UNICOS required about 7% of total CPU time to service the 832 workloads; this overhead decreased to 5% for the 8128 workloads. While most of the system time went to service I/O requests, efficient scheduling prevented excessive idle due to I/O wait. System measurements disclosed no obvious bottlenecks in the response of the machine and UNICOS to the workloads. In most cases, Cray-provided software tools were- quite sufficient for measuring the performance of both the machine and operating, system.

Bergeron, Robert J.↗
NASA NTRS1981

Local effects of partly cloudy skies on solar and emitted radiations

Solar radiation measurements are made on a routine basis. Global solar, atmospheric emitted, downwelled diffuse solar, and direct solar radiation measurement systems are fully operational with the first two in continuous operation. Fractional cloud cover measurements are made from GOES imagery or from ground based whole sky photographs. Normalized global solar irradiance values for partly cloudy skies were correlated to fractional cloud cover.

Whitney, D. A.↗
NASA NTRS1987

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗
NASA NTRS1987

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. I - Theory

In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.

Padovan, Joe↗
NASA NTRS1986

Balancing High-Speed Rotors at Low Speed

Flexible balancing reduces vibrations at operating speeds. Highspeed rotors in turbomachines dynamically balanced at fraction of operating rotor speed. New method takes into account rotor flexible rather than rigid.

Giordano, J.↗
NASA NTRS2018

Identification of Safety Metrics for Airport Surface Operations

A large fraction of safety incidents occurs on the ground during airport surface operations. Although these incidents are mostly non-fatal with a few exceptions, they are high profile incidents that remain a source of concern for the National Transportation Safety Board (NTSB), the Federal Aviation Administration (FAA), major airlines, and other stakeholders of the National Airspace System (NAS). These incidents have historically been mitigated by implementing changes to regulations, policies, and procedures over time. This approach has minimized but not eliminated the risk of occurrences. It is thus important to develop integrated techniques to assess, model, and prevent these incidents by analyzing the risk and likelihood of occurrence and communicating results of the analysis to decision-making personnel who can mitigate and prevent incidents in real time. The research presented in this report builds on prior work of researchers at the NASA Ames Research Center who developed an automated framework, Real-Time Safety Monitoring (RTSM), to enable monitoring and prediction of the safety of the NAS. In the RTSM framework, hazards to flight are translated to safety metrics such as wake vortex encounters or loss of separation, that can be modeled and analyzed offline and also predicted and monitored in real time (online). The intent of this report is to integrate predictable incidents that occur during surface and ground operations into the safety portfolio of the RTSM project by (i) identifying suitable information sources from which ground incidents can be studied, (ii) developing safety metrics correlated with surface operations, and (iii) recommending suitable data sources that can be quantified and used for the computation of pertinent safety metrics.

ground operations↗
NASA NTRS2018

Identification of Safety Metrics for Airport Surface Operations

A large fraction of safety incidents occurs on the ground during airport surface operations. Although these incidents are mostly non-fatal with a few exceptions, they are high profile incidents that remain a source of concern for the National Transportation Safety Board (NTSB), the Federal Aviation Administration (FAA), major airlines, and other stakeholders of the National Airspace System (NAS). These incidents have historically been mitigated by implementing changes to regulations, policies, and procedures over time. This approach has minimized but not eliminated the risk of occurrence of safety incidents. It is thus important to develop integrated techniques to assess, model, and prevent these incidents by analyzing the risk and likelihood of occurrence and communicating results of the analysis to decision-making personnel who can mitigate and prevent incidents in real time. The work presented in this paper builds on a previously developed architecture for safety, Real-Time Safety Monitoring (RTSM), to enable monitoring and prediction of the safety of the NAS. In the RTSM framework, hazards to flight are translated to safety metrics such as wake vortex encounters or loss of separation, that can be modeled and analyzed offline and also predicted and monitored in real time (online). The intent of this paper is to integrate predictable incidents that occur during surface and ground operations into the safety portfolio of the RTSM project by (i) identifying suitable information sources from which ground incidents can be studied, (ii) developing safety metrics correlated with surface operations, and (iii) recommending suitable data sources that can be quantified and used for the computation of pertinent safety metrics.

safety↗
NASA NTRS1986

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. Part 1: Theory

In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.

Padovan, Joe↗
NASA NTRS1983

Two hundred passage three-way valve: Fraction collector

This paper describes the design and operation of a fraction collector used to direct flow of separated biological materials from 197 capillary tubes to either a collection tray or to a waste tank. This mechanism uses a 28-volt dc gear motor driving twin cams to force 197 needles through a self-sealing silicone rubber septum, where they inject the material in 197 separate pockets in a collection tray. The position of the collector tray is sensed by two optical limit switches. The time sequences are controlled automatically by an electronics control monitoring module.

Keffer, J. L.↗
NASA NTRS1988

The geology and petrogenesis of the southern closepet granite

The Archaean Closepet Granite is a polyphase body intruding the Peninsular Gneiss Complex and the associated supracrustal rocks. The granite out-crop runs for nearly 500 km with an approximate width of 20 to 25 km and cut across the regional metamorphic structure passing from granulite facies in the South and green schist facies in the north. In the amphibolite-granulite facies transition zone the granite is intimately mixed with migmatites and charnockite. Field observations suggests that anatexis of Peninsular gneisses led to the formation of granite melt, and there is a space relationship between migmatite formation, charnockite development and production and emplacement of granite magma. Based on texture and cross cutting relationships four major granite phases are recognized: (1) Pyroxene bearing dark grey granite; (2) Porphyritec granite; (3) Equigranular grey granite; and (4) Equigranular pink granite. The granite is medium to coarse grained and exhibit hypidiomorphic granular to porphyritic texture. The modal composition varies from granite granodiorite to quartz monzonite. Geochemical variation of the granite suite is consistent with either fractional crystallization or partial melting, but in both the cases biotite plus feldspar must be involved as fractionating or residual phases during melting to account trace element chemistry. The trace element data has been plotted on discriminant diagrams, where majority of samples plot in volcanic arc and within plate, tectonic environments. The granite show distinct REE patterns with variable total REE content. The REE patterns and overall abundances suggests that the granite suite represents a product of partial melting of crustal source in which fractional crystallization operated in a limited number of cases.

Jayananda, M.↗
NASA NTRS1998

Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems

This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.

Hartley, Tom T.↗
NASA NTRS2002

Experiments and Spectral Studies of Martian Volcanic Rocks: Implications for the Origin of Pathfinder Rocks and Soils

The composition and spectral properties of the Mars Pathfinder rocks and soils together with the identification of basaltic and andesitic Mars terrains based on Thermal Emission Spectrometer (TES) data raised interesting questions regarding the nature and origin of Mars surface rocks. We have investigated the following questions: (1) are the Pathfinder rocks igneous and is it possible these rocks could have formed by known igneous processes, such as equilibrium or fractional crystallization, operating within SNC magmas known to exist on Mars? If it is possible, what P (depth) and PH2O conditions are required? (2) whether TES-based interpretations of plagioclase-rich basalt and andesitic terrains in the south and north regions of Mars respectively are unique. Are the surface compositions of these regions plagioclase-rich, possibly indicating the presence of old AI-rich crust of Mars, or are the spectra being affected by something like surface weathering processes that might determine the spectral pyroxene to plagioclase ratio?

Rutherford, Malcolm J.↗
NASA NTRS2014

Investigation of the Effects of Cathode Flow Fraction and Position on the Performance and Operation of the High Voltage Hall Accelerator

The National Aeronautics and Space Administration (NASA) Science Mission Directorate In- Space Propulsion Technology office is sponsoring NASA Glenn Research Center (GRC) to develop a 4 kW-class Hall thruster propulsion system for implementation in NASA science missions. Tests were performed within NASA GRC Vacuum Facility 5 at background pressure levels that were six times lower than what has previously been attained in other vacuum facilities. A study was conducted to assess the impact of varying the cathode-to-anode flow fraction and cathode position on the performance and operational characteristics of the High Voltage Hall Accelerator (HiVHAc) thruster. In addition, the impact of injecting additional xenon propellant in the vicinity of the cathode was also assessed. Cathode-to-anode flow fraction sensitivity tests were performed for power levels between 1.0 and 3.9 kW. It was found that varying the cathode flow fraction from 5 to approximately 10% of the anode flow resulted in the cathode-to-ground voltage becoming more positive. For an operating condition of 3.8 kW and 500 V, varying the cathode position from a distance of closest approach to 600 mm away did not result in any substantial variation in thrust but resulted in the cathode-to-ground changing from -17 to -4 V. The change in the cathode-to-ground voltage along with visual observations indicated a change in how the cathode plume was coupling to the thruster discharge. Finally, the injection of secondary xenon flow in the vicinity of the cathode had an impact similar to increasing the cathode-to-anode flow fraction, where the cathode-to-ground voltage became more positive and discharge current and thrust increased slightly. Future tests of the HiVHAc thruster are planned with a centrally mounted cathode in order to further assess the impact of cathode position on thruster performance.

Cathode Coupling↗
NASA NTRS1978

A single user efficiency measure for evaluation of parallel or pipeline computer architectures

A precise statement of the relationship between sequential computation at one rate, parallel or pipeline computation at a much higher rate, the data movement rate between levels of memory, the fraction of inherently sequential operations or data that must be processed sequentially, the fraction of data to be moved that cannot be overlapped with computation, and the relative computational complexity of the algorithms for the two processes, scalar and vector, was developed. The relationship should be applied to the multirate processes that obtain in the employment of various new or proposed computer architectures for computational aerodynamics. The relationship, an efficiency measure that the single user of the computer system perceives, argues strongly in favor of separating scalar and vector processes, sometimes referred to as loosely coupled processes, to achieve optimum use of hardware.

Jones, W. P.↗
NASA NTRS2004

Thermodynamic Vent System Test in a Low Earth Orbit Simulation

A thermodynamic vent system for a cryogenic nitrogen tank was tested in a vacuum chamber simulating oxygen storage in low earth orbit. The nitrogen tank was surrounded by a cryo-shroud at -40 F. The tank was insulated with two layers of multi-layer insulation. Heat transfer into cryogenic tanks causes phase change and increases tank pressure which must be controlled. A thermodynamic vent system was used to control pressure as the location of vapor is unknown in low gravity and direct venting would be wasteful. The thermodynamic vent system consists of a Joule-Thomson valve and heat exchanger installed on the inlet side of the tank mixer-pump. The combination is used to extract thermal energy from the tank fluid, reducing temperature and ullage pressure. The system was sized so that the tank mixer-pump operated a small fraction of the time to limit motor heating. Initially the mixer used sub-cooled liquid to cool the liquid-vapor interface inducing condensation and pressure reduction. Later, the thermodynamic vent system was used. Pressure cycles were performed until steady-state operation was demonstrated. Three test runs were conducted at tank fills of 97, 80, and 63 percent. Each test was begun with a boil-off test to determine heat transfer into the tank. The lower tank fills had time averaged vent rates very close to steady-state boil-off rates showing the thermodynamic vent system was nearly as efficient as direct venting in normal gravity.

VanOverbeke, Thomas J.↗