Design and global analysis of spacecraft attitude control systems
Mathematical model of global spacecraft attitude control system based on three dimensional motion
Meyer, G.↗
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Results for “Mathematical analysis”
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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Sensitivity analysis as an aid in modelling and control of (poorly-defined) ecological systems
A literature review of the use of sensitivity analyses in modelling nonlinear, ill-defined systems, such as ecological interactions is presented. Discussions of previous work, and a proposed scheme for generalized sensitivity analysis applicable to ill-defined systems are included. This scheme considers classes of mathematical models, problem-defining behavior, analysis procedures (especially the use of Monte-Carlo methods), sensitivity ranking of parameters, and extension to control system design.
Hornberger, G. M.↗
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
Baker, A. J.↗
Design and Analysis of Precise Pointing Systems
The mathematical models of Glovebox Integrated Microgravity Isolation Technology (g- LIMIT) dynamics/control system, which include six degrees of freedom (DOF) equations of motion, mathematical models of position sensors, accelerometers and actuators, and acceleration and position controller, were developed using MATLAB and TREETOPS simulations. Optimal control parameters of G-LIMIT control system were determined through sensitivity studies and its performance were evaluated with the TREETOPS model of G-LIMIT dynamics and control system. The functional operation and performance of the Tektronix DTM920 digital thermometer were studied and the inputs to the crew procedures and training of the DTM920 were documented.
Kim, Young K.↗
Analysis of thermal stress and metal movement during welding
Objectives of study were: investigation of temperature changes caused by welding arc with analysis of temperature distribution; development of system of mathematical statements describing thermal stresses and plastic strains during welding; and development of system of mathematical solutions and computer programs for one-dimensional analysis.
Andrews, J. B.↗
Decomposition-Based Failure Mode Identification Method for Risk-Free Design of Large Systems
When designing products, it is crucial to assure failure and risk-free operation in the intended operating environment. Failures are typically studied and eliminated as much as possible during the early stages of design. The few failures that go undetected result in unacceptable damage and losses in high-risk applications where public safety is of concern. Published NASA and NTSB accident reports point to a variety of components identified as sources of failures in the reported cases. In previous work, data from these reports were processed and placed in matrix form for all the system components and failure modes encountered, and then manipulated using matrix methods to determine similarities between the different components and failure modes. In this paper, these matrices are represented in the form of a linear combination of failures modes, mathematically formed using Principal Components Analysis (PCA) decomposition. The PCA decomposition results in a low-dimensionality representation of all failure modes and components of interest, represented in a transformed coordinate system. Such a representation opens the way for efficient pattern analysis and prediction of failure modes with highest potential risks on the final product, rather than making decisions based on the large space of component and failure mode data. The mathematics of the proposed method are explained first using a simple example problem. The method is then applied to component failure data gathered from helicopter, accident reports to demonstrate its potential.
Tumer, Irem Y.↗
Reliability growth during a development testing program
Binomial and trinomial mathematical models for reliability growth studies - statistical analysis of system failures
MATHEMATICAL MODEL↗
Considerations for the Extension of Gas Path Analysis to Electrified Aircraft Propulsion Systems
Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to Electrified Aircraft Propulsion (EAP) systems is also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware is provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach towards the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.
Electrified Aircraft Propulsion↗
Considerations for the Extension of Gas Path Analysis to Electrified Aircraft Propulsion Systems
Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to Electrified Aircraft Propulsion (EAP) systems is also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware is provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach towards the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.
Electrified Aircraft Propulsion↗
Considerations for the Extension of Gas Path Analysis to Electrified Aircraft Propulsion Systems
Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to Electrified Aircraft Propulsion (EAP) systems is also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware is provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach towards the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.
Electrified Aircraft Propulsion↗
Introduction to abstract analysis
This book, which grew out of lectures given at the NASA Lewis Research Center, introduces the scientist and engineer with the usual background in applied mathematics to the concepts of abstract analysis. The emphasis is not on preparing the reader to do research in the field but on giving him some of the background necessary for reading the literature of pure mathematics. Although the material here is by no means original, the presentation differs in some respects from texts on material of this nature. The proofs are more detailed herein and quite easy to follow. We have attempted to indicate how the material relates to and serves as a foundation for more advanced sub- jects. We have also attempted at several places to show how the material covered here relates to the more familiar “real mathematics.” Enough examples are included to illustrate the concepts. No attempt is made to indicate the original sources of the material or even to point out the originators of all the concepts. Contrary to the usual practice, the relation between convergence and continuity on the one hand and algebraic operations on the other is dis- cussed in the abstract setting of linear spaces. This is done principally to familiarize the reader with these very important concepts in a reasonably simple way.
Marvin E Goldstein↗
Common radiation analysis model for 75,000 pound thrust NERVA engine (1137400E)
The mathematical model and sources of radiation used for the radiation analysis and shielding activities in support of the design of the 1137400E version of the 75,000 lbs thrust NERVA engine are presented. The nuclear subsystem (NSS) and non-nuclear components are discussed. The geometrical model for the NSS is two dimensional as required for the DOT discrete ordinates computer code or for an azimuthally symetrical three dimensional Point Kernel or Monte Carlo code. The geometrical model for the non-nuclear components is three dimensional in the FASTER geometry format. This geometry routine is inherent in the ANSC versions of the QAD and GGG Point Kernal programs and the COHORT Monte Carlo program. Data are included pertaining to a pressure vessel surface radiation source data tape which has been used as the basis for starting ANSC analyses with the DASH code to bridge into the COHORT Monte Carlo code using the WANL supplied DOT angular flux leakage data. In addition to the model descriptions and sources of radiation, the methods of analyses are briefly described.
Warman, E. A.↗
Dual-Use Space Technology Transfer Conference and Exhibition
This is the second volume of papers presented at the Dual-Use Space Technology Transfer Conference and Exhibition held at the Johnson Space Center February 1-3, 1994. Possible technology transfers covered during the conference were in the areas of information access; innovative microwave and optical applications; materials and structures; marketing and barriers; intelligent systems; human factors and habitation; communications and data systems; business process and technology transfer; software engineering; biotechnology and advanced bioinstrumentation; communications signal processing and analysis; medical care; applications derived from control center data systems; human performance evaluation; technology transfer methods; mathematics, modeling, and simulation; propulsion; software analysis and decision tools; systems/processes in human support technology; networks, control centers, and distributed systems; power; rapid development; perception and vision technologies; integrated vehicle health management; automation technologies; advanced avionics; and robotics technologies.
Krishen, Kumar↗
Nonstandard Analysis and Jump Conditions for Converging Shock Waves
Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.
Baty, Roy S.↗
Tape recorder - reproducer mechanism - worst - case analysis Final report
Failure analysis of tape recorder-producer mechanism - mathematical model for functional design specifications
FUNCTIONAL ANALYSIS↗
Apollo spacecraft systems analysis program. Landing radar altimeter beam bandwidth and Doppler equations for mathematical model use
Lunar reflectivity, acquisition altitude, landing radar altimeter beam bandwidth, and Doppler equations verified for use in mathematical model
Blakely, C. E.↗
Affine Transformations to Correlate Experimental and Simulated EDS Spectra for Multi-Element Systems
Energy Dispersive X-ray Spectroscopy (EDS) is an essential technique for determining elemental concentrations and distributions within microstructures, critical for materials discovery, optimization, and qualification. However, most published EDS data is qualitative because current quantitative EDS analysis methods require extensive calibration and post-processing, limiting their practicality and widespread adoption. This work seeks to establish a framework for accelerated EDS characterization and spectrum analysis that can leverage ML to analyze correlations between various elemental compositions and resulting EDS spectra. The complex physics and data result in a high-dimensional problem that grows exponentially with the number of elements in the system and the complexity of the spectrum analysis. ML provides a way to compute and optimize the results of this highly dimensional problem in a flexible way to tailor it to the user’s specific needs and material system. However, the framework emphasizes transparency through a strictly mathematical affine transformation, so the analysis remains understandable and reviewable to facilitate adoption by the scientific community. While currently implemented methods are simplistic and unvalidated, further development and demonstration of this framework could enable high-throughput, accurate, and accessible EDS characterization.
11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
A retrospective review of von Neumann’s analysis of hidden variables in quantum mechanics
This article reviews the history of J. von Neumann’s analysis of hidden variables in quantum mechanics and the subsequent analysis by others. In his book The Mathematical Foundations of Quantum Mechanics , published in 1932, von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He arrived at two principal conclusions: first, hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and second, if they did exist, the theory would have already failed in situations where it has been successfully applied. This analysis has been taken as an “incorrect proof” against the existence of hidden variables, possibly due to a mistranslation of the German word prufen . von Neumann’s so-called proof isn’t even wrong as such a proof does not exist, but it is an examination of the limitations imposed by internal consistency of the Hilbert space formulation of the theory. One of the earliest attempts to eliminate uncertainty, by D. Bohm, requires a major modification of quantum mechanics (observables are not represented by Hermitian operators), which supports von Neumann’s first principal conclusion. However, testing the Bohm theory requires constructing a physically impossible initial state. As such, the theory has no experimental consequences, so W. Pauli referred to it as an “uncashable check”. As there are no observable consequences, the Bohm theory is possibly a counterexample to von Neumann’s second conclusion that hidden variables in particular would have already led to a failure of the theory.
density matrix↗