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NASA NTRS2005

Tools for Basic Statistical Analysis

Statistical Analysis Toolset is a collection of eight Microsoft Excel spreadsheet programs, each of which performs calculations pertaining to an aspect of statistical analysis. These programs present input and output data in user-friendly, menu-driven formats, with automatic execution. The following types of calculations are performed: Descriptive statistics are computed for a set of data x(i) (i = 1, 2, 3 . . . ) entered by the user. Normal Distribution Estimates will calculate the statistical value that corresponds to cumulative probability values, given a sample mean and standard deviation of the normal distribution. Normal Distribution from two Data Points will extend and generate a cumulative normal distribution for the user, given two data points and their associated probability values. Two programs perform two-way analysis of variance (ANOVA) with no replication or generalized ANOVA for two factors with four levels and three repetitions. Linear Regression-ANOVA will curvefit data to the linear equation y=f(x) and will do an ANOVA to check its significance.

Luz, Paul L.↗

DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

NASA NTRS1987

Dual laser gyro test program

This paper addresses the results of a comparative test evaluation of two similar-sized but otherwise dissimilar ring laser gyroscopes (RLG's). Both units were tested side by side, with the input axes (IA's) parallel, on the same test table. This report describes the rationale and design factors considered important to the test objectives. Emphasis was placed upon the evaluation of the scale factor (SF) linearity, drift rate stability (short term and long term), and derived rate. Conclusions drawn were (1) that dual operation had an observable but insignificant effect on the test results, (2) that the benefits of dual operation outweighed the additional design and analysis efforts required at the outset of the program, and (3) that the performance characteristics of the two test articles were significantly different. The differences between the two test articles (1) led to suggestions which could direct one vendor toward obtaining improved performance and (2) resulted in the creation of a conceptually new method (DELTA TIME-COUNT histogram) for quickly assessing the quality of laser gyros (or any digital sensor device for that matter).

Jones, Malcolm E.↗

NASA NTRS2017

Improvement of Automated POST Case Success Rate Using Support Vector Machines

Zwack, Mathew R.↗

NASA NTRS2018

Hawkeye Ocean Color Instrument – Performance Summary

Hawkeye is an ocean color instrument that is part of the SeaHawk satellite developed for SOCON, the Sustained Ocean Color Observations using Nanosatellites program funded by the Gordon and Betty Moore Foundation and managed by the University of North Carolina – Wilmington (UNC-W). HawkEye has spectral characteristics similar to SeaWiFS, but with 8 times finer resolution and a smaller field of view more appropriate for lakes, rivers, and near-shore terrestrial environments. With a volume of only 10 X 10 X 10 cm (a CubeSat 1U), it can produce 8 bands of image data in a single pass, each with 1800 x 6000 pixels, with a resolution of 120 meters per pixel. This paper will present a short summary of instrument design, the spacecraft interface, and “lessons learned” during this effort. Scientists considering using linear arrays in a pushbroom mode for remote sensing will find this useful. Much of the discussion will center on optical performance, such as flat field calibration, polarization effects, stray light, out-of-band response, and exposure linearity. Images from field tests will be shown.The Hawkeye instrument is an ocean color measuring instrument designed to fly on the SeaHawk satellite developed for SOCON, the Sustained Ocean Color Observations using Nanosatellites program funded by the Gordon and Betty Moore Foundation and managed by the University of North Carolina – Wilmington (UNC-W). The Hawkeye instrument measures ocean color in 8 spectral bands, similar to SeaWiFS, except Band 7, which is shifted to a slightly lower wavelength to avoid the oxygen absorption feature that a wider band overlapped on SeaWiFS. The instrument is approximately 1/3rd the volume of the entire satellite, which is a 3U Cubesat manufactured by Clydespace in Glasgow, Scotland. The purpose of this instrument is to ascertain the quality of ocean color data possible with such a small, inexpensive instrument and bus. The nominal orbit is 540 km, and the nominal pixel geometric instantaneous field of view (GIFOV) 120 meters on a side. Each band will produce an image 1800 x 6000 pixels in size, for a total field of view of 216 X 720 km.2) DESIGN CONCEPTThe Hawkeye instrument uses linear arrays in pushbroom mode to collect data over a two dimensional area. The instrument has 4 linear CCD arrays, the Onsemi KLI-4104, to collect the 8 bands of data. Figure 1 illustrates the optical design for two bands, sharing a single array.

Hawkeye↗

NASA NTRS2017

Improvement of Automated POST Case Success Rate Using Support Vector Machines

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.

Zwack, Matthew R.↗

NASA NTRS1975

Prediction of elemental creep

Cyclic and steady-state creep tests were performed to provide data which were used to develop predictive equations. These equations, describing creep as a function of stress, temperature, and time, were developed through the use of a least squares regression analyses computer program for both the steady-state and cyclic data sets. Comparison of the data from the two types of tests, revealed that there was no significant difference between the cyclic and steady-state creep strains for the L-605 sheet under the experimental conditions investigated (for the same total time at load). Attempts to develop a single linear equation describing the combined steady-state and cyclic creep data resulted in standard errors of estimates higher than obtained for the individual data sets. A proposed approach to predict elemental creep in metals uses the cyclic creep equation and a computer program which applies strain and time hardening theories of creep accumulation.

Davis, J. W.↗

NASA NTRS1989

Probabilistic analysis for fatigue strength degradation of materials

This report presents the results of the first year of a research program conducted for NASA-LeRC by the University of Texas at San Antonio. The research included development of methodology that provides a probabilistic treatment of lifetime prediction of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Linear elastic fracture mechanics is utilized in the latter model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs, RANDOM2, RANDOM3, and RANDOM4. These programs determine the random lifetime of an engine component, in mechanical load cycles, to reach a critical fatigue strength or crack size. The material considered was a cast nickel base superalloy, one typical of those used in the Space Shuttle Main Engine.

Royce, Lola↗

NASA NTRS1990

High Tc superconducting materials and devices

The high Tc Y1Ba2Cu3O(7-x) ceramic materials, initially developed in 1987, are now being extensively investigated for a variety of engineering applications. The superconductor applications which are presently identified as of most interest to NASA-LaRC are low-noise, low thermal conductivity grounding links; large-area linear Meissner-effect bearings; and sensitive, low-noise sensors and leads. Devices designed for these applications require the development of a number of processing and fabrication technologies. Included among the technologies most specific to the present needs are tapecasting, melt texturing, magnetic field grain alignment, superconductor/polymer composite fabrication, thin film MOD (metal-organic decomposition) processing, screen printing of thick films, and photolithography of thin films. The overall objective of the program was to establish a high Tc superconductivity laboratory capability at NASA-LaRC and demonstrate this capability by fabricating superconducting 123 material via bulk and thin film processes. Specific objectives include: order equipment and set up laboratory; prepare 1 kg batches of 123 material via oxide raw material; construct tapecaster and tapecaster 123 material; fabricate 123 grounding link; fabricate 123 composite for Meissner linear bearing; develop 123 thin film processes (nitrates, acetates); establish Tc and Jc measurement capability; and set up a commercial use of space program in superconductivity at LaRC. In general, most of the objectives of the program were met. Finally, efforts to implement a commercial use of space program in superconductivity at LaRC were completed and at least two industrial companies have indicated their interest in participating.

Haertling, Gene H.↗

NASA NTRS1975

An experimental and analytical investigation of axisymmetric diffusers

A finite difference computer program for turbulent compressible flow was used to establish the performance of several diffuser shapes for experimental testing. The diffusers were designed to have a linear change in Mach number, a linear change in pressure, or a curvature fitted by a quadratic equation. Testing was performed with M = 0.1 to 0.9 with and without boundary layer bleed. Above M = 0.6, data were obtained with a normal shock upstream of the diffuser entrance. Peak static pressure recovery occurred with a diffuser inlet M0.75. The quadratic diffuser yielded the highest total pressure recovery.

Povinelli, L. A.↗

NASA NTRS1974

HAL/S - The programming language for Shuttle

HAL/S is a higher order language and system, now operational, adopted by NASA for programming Space Shuttle on-board software. Program reliability is enhanced through language clarity and readability, modularity through program structure, and protection of code and data. Salient features of HAL/S include output orientation, automatic checking (with strictly enforced compiler rules), the availability of linear algebra, real-time control, a statement-level simulator, and compiler transferability (for applying HAL/S to additional object and host computers). The compiler is described briefly.

Martin, F. H.↗

NASA NTRS1975

An experimental and analytical investigation of axisymmetric diffusers

A finite difference computer program for turbulent compressible flow was used to establish the performance of several diffuser shapes for experimental testing. The diffusers were designed to have a linear change in Mach number, a linear change in pressure or a curvature fitted by a quadratic equation. Testing was performed with M = 0.1 to 0.9 with and without boundary layer bleed. Above M = 0.6, data were obtained with a normal shock upstream of the diffuser entrance. Peak static pressure recovery occurred with a diffuser inlet M-0.75. The quadratic diffuser yielded the highest total pressure recovery.

Povinelli, L. A.↗

NASA NTRS1989

Topology of modified helical gears

The topology of several types of modified surfaces of helical gears is proposed. The modified surfaces allow absorption of a linear or almost linear function of transmission errors. These errors are caused by gear misalignment and an improvement of the contact of gear tooth surfaces. Principles and corresponding programs for computer aided simulation of meshing and contact of gears have been developed. The results of this investigation are illustrated with numerical examples.

Litvin, F. L.↗

NASA NTRS1989

Nonlinear and distributed parameter models of the mini-mast truss

Large spacecraft such as Space Station Freedom employ large trusses in their construction. The structural dynamics of such trusses often exhibit nonlinear behavior and little damping which can impact significantly the performance of control systems. The Mini-MAST truss was constructed to research such structural dynamics and control systems. The Mini-MAST truss is an object of study for the guest investigator program as part of NASA's controls-structures interaction program. The Mini-MAST truss is deployable and about 65 ft long. Although the bending characteristics of the Mini-MAST truss are essentially linear, the angular deflection under torsional loading has exhibited significant hysteresis and nonlinear stiffness. It is the purpose to develop nonlinear and distributed parameter models of the truss and to compare the model dynamics with actual measurements. Distributed parameter models have the advantage of requiring fewer model parameters. A tangent function is used to describe the nonlinear stiffness in torsion, partly because of the convenience of its easily expressed inverse. Hysteretic slip elements are introduced and extended to a continuum to account for the observed hysteresis in torsion. The contribution of slipping to the structural damping is analyzed and found to be strongly dependent on the applied loads. Because of the many factors which affect the damping and stiffness in a truss, it is risky to assume linearity.

Taylor, Lawrence W., Jr.↗

NASA NTRS1989

Topology of modified helical gears

Litvin, F. L.↗

NASA NTRS2008

ISIS Topside-Sounder Plasma-Wave Investigations as Guides to Desired Virtual Wave Observatory (VWO) Data Search Capabilities

Many plasma-wave phenomena, observed by space-borne radio sounders, cannot be properly explained in terms of wave propagation in a cold plasma consisting of mobile electrons and infinitely massive positive ions. These phenomena include signals known as plasma resonances. The principal resonances at the harmonics of the electron cyclotron frequency, the plasma frequency, and the upper-hybrid frequency are well explained by the warm-plasma propagation of sounder-generated electrostatic waves, Other resonances have been attributed to sounder-stimulated plasma instability and non-linear effects, eigenmodes of cylindrical electromagnetic plasma oscillations, and plasma memory processes. Data from the topside sounders of the International Satellites for Ionospheric Studies (ISIS) program played a major role in these interpretations. A data transformation and preservation effort at the Goddard Space Flight Center has produced digital ISIS topside ionograms and a metadata search program that has enabled some recent discoveries pertaining to the physics of these plasma resonances. For example, data records were obtained that enabled the long-standing question (several decades) of the origin of the plasma resonance at the fundamental electron cyclotron frequency to be explained [Muldrew, Radio Sci., 2006]. These data-search capabilities, and the science enabled by them, will be presented as a guide to desired data search capabilities to be included in the Virtual Wave Observatory (VWO).

Benson, Robert F.↗

NASA NTRS2010

Design and Evaluation of a Dynamic Programming Flight Routing Algorithm Using the Convective Weather Avoidance Model

The optimization of traffic flows in congested airspace with varying convective weather is a challenging problem. One approach is to generate shortest routes between origins and destinations while meeting airspace capacity constraint in the presence of uncertainties, such as weather and airspace demand. This study focuses on development of an optimal flight path search algorithm that optimizes national airspace system throughput and efficiency in the presence of uncertainties. The algorithm is based on dynamic programming and utilizes the predicted probability that an aircraft will deviate around convective weather. It is shown that the running time of the algorithm increases linearly with the total number of links between all stages. The optimal routes minimize a combination of fuel cost and expected cost of route deviation due to convective weather. They are considered as alternatives to the set of coded departure routes which are predefined by FAA to reroute pre-departure flights around weather or air traffic constraints. A formula, which calculates predicted probability of deviation from a given flight path, is also derived. The predicted probability of deviation is calculated for all path candidates. Routes with the best probability are selected as optimal. The predicted probability of deviation serves as a computable measure of reliability in pre-departure rerouting. The algorithm can also be extended to automatically adjust its design parameters to satisfy the desired level of reliability.

Ng, Hok K.↗

NASA NTRS2014

Amine Swingbed Payload Technology Demonstration

The Amine Swingbed is an amine-based, vacuum-regenerated adsorption technology for removing carbon dioxide and humidity from a habitable spacecraft environment, and is the baseline technology for the Orion Program’s Multi-Purpose Crew Vehicle (MPCV). It uses a pair of interleaved-layer beds filled with SA9T, the amine sorbent, and a linear multiball valve rotates 270° back and forth to control the flow of air and vacuum to adsorbing and desorbing beds. One bed adsorbs CO2 and H2O from cabin air while the other bed is exposed to vacuum for regeneration by venting the CO2 and H2O. The two beds are thermally linked, so no additional heating or cooling is required. The technology can be applied to habitable environments where recycling CO2 and H2O is not required such as short duration missions.

Sweterlitsch, Jeffrey↗