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NASA NTRS1976

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Klimas, A. J.↗

NASA NTRS2019

Statistical optical link budget analysis

In this paper, we describe work on extending statistical analysis methods to optical communications links, with a primary focus on intensity modulated, direct detected photon-counting channel utilizing pulse-position-modulation (PPM). We performed analysis on the relationship between bit error rate (BER) requirement, statistical characteristics of the received signal power and noise power, and the coded performance curves. We presented link analysis results with preliminary uncertainty quantifications of signal power and noise power. We used the Consultative Committee for Space Data Systems (CCSDS) Serially Concatenated convolutionally coded Pulse Position Modulation (SCPPM) prototype software [1] to obtain coded performance curves under different operating conditions with varying signal power, background noise power, code rates,and PPM modulation orders. Comparison with traditional, deterministic analysis shows that extra margin needs to be reserved to compensate for the performance losses caused by uncertainties of the link parameters.

Cheung, Kar-Ming↗

NASA NTRS2016

Consistent Practices for the Probability of Detection (POD) of Fracture Critical Metallic Components Project

NASA-STD-5009 requires that successful flaw detection by NDE methods be statistically qualified for use on fracture critical metallic components, but does not standardize practices. This task works towards standardizing calculations and record retention with a web-based tool, the NNWG POD Standards Library or NPSL. Test methods will also be standardized with an appropriately flexible appendix to -5009 identifying best practices. Additionally, this appendix will describe how specimens used to qualify NDE systems will be cataloged, stored and protected from corrosion, damage, or loss.

Hughitt, Brian↗

NASA NTRS2005

The Influence of Roughness on Gear Surface Fatigue

Gear working surfaces are subjected to repeated rolling and sliding contacts, and often designs require loads sufficient to cause eventual fatigue of the surface. This research provides experimental data and analytical tools to further the understanding of the causal relationship of gear surface roughness to surface fatigue. The research included evaluations and developments of statistical tools for gear fatigue data, experimental evaluation of the surface fatigue lives of superfinished gears with a near-mirror quality, and evaluations of the experiments by analytical methods and surface inspections. Alternative statistical methods were evaluated using Monte Carlo studies leading to a final recommendation to describe gear fatigue data using a Weibull distribution, maximum likelihood estimates of shape and scale parameters, and a presumed zero-valued location parameter. A new method was developed for comparing two datasets by extending the current methods of likelihood-ratio based statistics. The surface fatigue lives of superfinished gears were evaluated by carefully controlled experiments, and it is shown conclusively that superfinishing of gears can provide for significantly greater lives relative to ground gears. The measured life improvement was approximately a factor of five. To assist with application of this finding to products, the experimental condition was evaluated. The fatigue life results were expressed in terms of specific film thickness and shown to be consistent with bearing data. Elastohydrodynamic and stress analyses were completed to relate the stress condition to fatigue. Smooth-surface models do not adequately explain the improved fatigue lives. Based on analyses using a rough surface model, it is concluded that the improved fatigue lives of superfinished gears is due to a reduced rate of near-surface micropitting fatigue processes, not due to any reduced rate of spalling (sub-surface) fatigue processes. To complete the evaluations, surface inspection were completed. The surface topographies of the ground gears changed substantially due to running, but the topographies of the superfinished gears were essentially unchanged with running.

Krantz, Timothy↗

NASA NTRS2000

Development and Application of Computational/In Vitro Toxicological Methods for Chemical Hazard Risk Reduction of New Materials for Advanced Weapon Systems

The development of quantitative structure-activity relationship (QSAR) is essential for reducing the chemical hazards of new weapon systems. The current collaboration between HEST (toxicology research and testing), MLPJ (computational chemistry) and PRS (computational chemistry, new propellant synthesis) is focusing R&D efforts on basic research goals that will rapidly transition to useful products for propellant development. Computational methods are being investigated that will assist in forecasting cellular toxicological end-points. Models developed from these chemical structure-toxicity relationships are useful for the prediction of the toxicological endpoints of new related compounds. Research is focusing on the evaluation tools to be used for the discovery of such relationships and the development of models of the mechanisms of action. Combinations of computational chemistry techniques, in vitro toxicity methods, and statistical correlations, will be employed to develop and explore potential predictive relationships; results for series of molecular systems that demonstrate the viability of this approach are reported. A number of hydrazine salts have been synthesized for evaluation. Computational chemistry methods are being used to elucidate the mechanism of action of these salts. Toxicity endpoints such as viability (LDH) and changes in enzyme activity (glutahoione peroxidase and catalase) are being experimentally measured as indicators of cellular damage. Extrapolation from computational/in vitro studies to human toxicity, is the ultimate goal. The product of this program will be a predictive tool to assist in the development of new, less toxic propellants.

Frazier, John M.↗

NASA NTRS1977

Optimum coherent imaging of a limited field of view in the presence of angular and aperture noise

The question of image distribution reconstruction for coherent illumination of an object located in the aperture far zone is considered from first principles without postulating any particular optical spread function. The object function is mathematically modeled as a complex random function of angular coordinates, and it is assumed that the object distribution of interest is angularly limited to a certain a priori assigned field of view (FOV). A linear reconstruction procedure that is uniformly optimal in the FOV is established by using the methods of statistical estimation. Two special cases are examined: imaging a limited sector of a wide-angle random scene and objects in the FOV immersed in a wide-angle background of angular noise. It is noted that the domain of application of the reconstruction method is restricted to microwave frequencies.

Borgiotti, G. V.↗

NASA NTRS1960

A Self-Adaptive Missile Guidance System for Statistical Inputs

A method of designing a self-adaptive missile guidance system is presented. The system inputs are assumed to be known in a statistical sense only. Newton's modified Wiener theory is utilized in the design of the system and to establish the performance criterion. The missile is assumed to be a beam rider, to have a g limiter, and to operate over a flight envelope where the open-loop gain varies by a factor of 20. It is shown that the percent of time that missile acceleration limiting occurs can be used effectively to adjust the coefficients of the Wiener filter. The result is a guidance system which adapts itself to a changing environment and gives essentially optimum filtering and minimum miss distance.

Peery, H. Rodney↗

NASA NTRS1973

A variation of the Davis-Smith method for in-flight determination of spacecraft magnetic fields.

A variation of a procedure developed by Davis and Smith (1968) is presented for the in-flight determination of spacecraft magnetic fields. Both methods take statistical advantage of the observation that fluctuations in the interplanetary magnetic field over short periods of time are primarily changes in direction rather than in magnitude. During typical solar wind conditions between 0.8 and 1.0 AU, a statistical analysis of 2-3 days of continuous interplanetary field measurements yields an estimate of a constant spacecraft field with an uncertainty of plus or minus 0.25 gamma in the direction radial to the sun and plus or minus 15 gammas in the directions transverse to the radial. The method is also of use in estimating variable spacecraft fields with gradients of the order of 0.1 gamma/day and less and in other special circumstances.

Belcher, J. W.↗

NASA NTRS1988

Kuhn-Tucker optimization based reliability analysis for probabilistic finite elements

The fusion of probability finite element method (PFEM) and reliability analysis for fracture mechanics is considered. Reliability analysis with specific application to fracture mechanics is presented, and computational procedures are discussed. Explicit expressions for the optimization procedure with regard to fracture mechanics are given. The results show the PFEM is a very powerful tool in determining the second-moment statistics. The method can determine the probability of failure or fracture subject to randomness in load, material properties and crack length, orientation, and location.

Liu, W. K.↗

NASA NTRS2010

A GPS-Based Pitot-Static Calibration Method Using Global Output-Error Optimization

Pressure-based airspeed and altitude measurements for aircraft typically require calibration of the installed system to account for pressure sensing errors such as those due to local flow field effects. In some cases, calibration is used to meet requirements such as those specified in Federal Aviation Regulation Part 25. Several methods are used for in-flight pitot-static calibration including tower fly-by, pacer aircraft, and trailing cone methods. In the 1990 s, the introduction of satellite-based positioning systems to the civilian market enabled new inflight calibration methods based on accurate ground speed measurements provided by Global Positioning Systems (GPS). Use of GPS for airspeed calibration has many advantages such as accuracy, ease of portability (e.g. hand-held) and the flexibility of operating in airspace without the limitations of test range boundaries or ground telemetry support. The current research was motivated by the need for a rapid and statistically accurate method for in-flight calibration of pitot-static systems for remotely piloted, dynamically-scaled research aircraft. Current calibration methods were deemed not practical for this application because of confined test range size and limited flight time available for each sortie. A method was developed that uses high data rate measurements of static and total pressure, and GPSbased ground speed measurements to compute the pressure errors over a range of airspeed. The novel application of this approach is the use of system identification methods that rapidly compute optimal pressure error models with defined confidence intervals in nearreal time. This method has been demonstrated in flight tests and has shown 2- bounds of approximately 0.2 kts with an order of magnitude reduction in test time over other methods. As part of this experiment, a unique database of wind measurements was acquired concurrently with the flight experiments, for the purpose of experimental validation of the optimization method. This paper describes the GPS-based pitot-static calibration method developed for the AirSTAR research test-bed operated as part of the Integrated Resilient Aircraft Controls (IRAC) project in the NASA Aviation Safety Program (AvSP). A description of the method will be provided and results from recent flight tests will be shown to illustrate the performance and advantages of this approach. Discussion of maneuver requirements and data reduction will be included as well as potential applications.

Foster, John V.↗

NASA NTRS1984

Lagrangian least-squares prediction of solar flux (F-bar 10.7)

The result of a study on the application of an improved statistical prediction method for estimating the intermediate-term (months) and long-term (years) behavior of solar flux is discussed. The study indicates that better predictions, in a chi square sense, are possible by selecting sets of the solar flux data such that each set (cycle) starts and ends at the maxima (or minima) for the data base and initialization point of the procedure. Then one applies a Lagrangian least-squares statistical technique. Evidence is also presented to support the existence of an aperiodic variation in the periods as well as the amplitudes.

Holland, R. L.↗

NASA NTRS2021

Nonlinear Navigation Analysis for a Europa Lander Mission Concept

Navigation strategies typically use linearized techniques to predict maneuver statistics. This method has been successfully employed on numerous high-energy trajectories, but may not be valid for low-energy ones due to the highly non-linear environment. We explore nonlinear navigational techniques applied to a Europa Lander concept by assessing trajectory sensitivity. The linearity assumption is tested at different phases of the endgame trajectory. Maneuver strategies and placement are considered to improve the delivery to Europa. Several cases of non-linear statistical maneuver Monte Carlo simulations are conducted to optimize maneuvers and compare ∆V statistics against conventional linear simulations.

Hernandez, Sonia↗

NASA NTRS1994

Automatic generation of efficient orderings of events for scheduling applications

In scheduling a set of tasks, it is often not known with certainty how long a given event will take. We call this duration uncertainty. Duration uncertainty is a primary obstacle to the successful completion of a schedule. If a duration of one task is longer than expected, the remaining tasks are delayed. The delay may result in the abandonment of the schedule itself, a phenomenon known as schedule breakage. One response to schedule breakage is on-line, dynamic rescheduling. A more recent alternative is called proactive rescheduling. This method uses statistical data about the durations of events in order to anticipate the locations in the schedule where breakage is likely prior to the execution of the schedule. It generates alternative schedules at such sensitive points, which can be then applied by the scheduler at execution time, without the delay incurred by dynamic rescheduling. This paper proposes a technique for making proactive error management more effective. The technique is based on applying a similarity-based method of clustering to the problem of identifying similar events in a set of events.

Morris, Robert A.↗

NASA NTRS2008

Near-infrared Variability in the 2MASS Calibration Fields: A Search for Planetary Transit Candidates

The Two Micron All Sky Survey (2MASS) photometric calibration observations cover approximately 6 square degrees on the sky in 35 'calibration fields,' each sampled in nominal photometric conditions between 562 and 3692 times during the 4 years of the 2MASS mission. We compile a catalog of variables from the calibration observations to search for M dwarfs transited by extrasolar planets. We present our methods for measuring periodic and nonperiodic flux variability. From 7554 sources with apparent K(sub s) magnitudes between 5.6 and 16.1, we identify 247 variables, including extragalactic variables and 23 periodic variables. We have discovered three M dwarf eclipsing systems, including two candidates for transiting extrasolar planets.

statistical methods↗

NASA NTRS2008

Metrology Optical Power Budgeting in SIM Using Statistical Analysis Techniques

The Space Interferometry Mission (SIM) is a space-based stellar interferometry instrument, consisting of up to three interferometers, which will be capable of micro-arc second resolution. Alignment knowledge of the three interferometer baselines requires a three-dimensional, 14-leg truss with each leg being monitored by an external metrology gauge. In addition, each of the three interferometers requires an internal metrology gauge to monitor the optical path length differences between the two sides. Both external and internal metrology gauges are interferometry based, operating at a wavelength of 1319 nanometers. Each gauge has fiber inputs delivering measurement and local oscillator (LO) power, split into probe-LO and reference-LO beam pairs. These beams experience power loss due to a variety of mechanisms including, but not restricted to, design efficiency, material attenuation, element misalignment, diffraction, and coupling efficiency. Since the attenuation due to these sources may degrade over time, an accounting of the range of expected attenuation is needed so an optical power margin can be book kept. A method of statistical optical power analysis and budgeting, based on a technique developed for deep space RF telecommunications, is described in this paper and provides a numerical confidence level for having sufficient optical power relative to mission metrology performance requirements.

stellar interferometry↗

NASA NTRS1996

Numerical Modeling of Spray Combustion with an Unstructured-Grid Method

The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.

Shang, H. M.↗

NASA NTRS1985

Use of observational and model-derived fields and regime model output statistics in mesoscale forecasting

Various empirical and statistical weather-forecasting studies which utilize stratification by weather regime are described. Objective classification was used to determine weather regime in some studies. In other cases the weather pattern was determined on the basis of a parameter representing the physical and dynamical processes relevant to the anticipated mesoscale phenomena, such as low level moisture convergence and convective precipitation, or the Froude number and the occurrence of cold-air damming. For mesoscale phenomena already in existence, new forecasting techniques were developed. The use of cloud models in operational forecasting is discussed. Models to calculate the spatial scales of forcings and resultant response for mesoscale systems are presented. The use of these models to represent the climatologically most prevalent systems, and to perform case-by-case simulations is reviewed. Operational implementation of mesoscale data into weather forecasts, using both actual simulation output and method-output statistics is discussed.

Forbes, G. S.↗

NASA NTRS2017

Improved Reference Sampling and Subtraction: A Technique for Reducing the Read Noise of Near-Infrared Detector Systems

Near-infrared array detectors, like the James Webb Space Telescope (JWST) NIRSpec's Teledyne's H2RGs, often provide reference pixels and a reference output. These are used to remove correlated noise. Improved reference sampling and subtraction (IRS(exp 2)) is a statistical technique for using this reference information optimally in a leastsquares sense. Compared with the traditional H2RG readout, IRS(exp 2) uses a different clocking pattern to interleave many more reference pixels into the data than is otherwise possible. Compared with standard reference correction techniques, IRS(exp 2) subtracts the reference pixels and reference output using a statistically optimized set of frequency dependent weights. The benefits include somewhat lower noise variance and much less obvious correlated noise. NIRSpec's IRS(exp 2) images are cosmetically clean, with less 1/f banding than in traditional data from the same system. This article describes the IRS(exp 2) clocking pattern and presents the equations needed to use IRS(exp 2) in systems other than NIRSpec. For NIRSpec, applying these equations is already an option in the calibration pipeline. As an aid to instrument builders, we provide our prototype IRS(exp 2) calibration software and sample JWST NIRSpec data. The same techniques are applicable to other detector systems, including those based on Teledyne's H4RG arrays. The H4RG's interleaved reference pixel readout mode is effectively one IRS(exp 2) pattern.

Methods-statistical↗