Analysis and design of space vehicle flight control systems. Volume XIII - Adaptive control
Mathematical models used for space vehicle flight adaptive control systems
MATHEMATICAL MODEL↗
SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Sunspot analysis and prediction
Evaluation of several procedures that apply rarely used and exotic mathematical functions yields a unique method of application of common trigonometric functions. These functions appear to produce results in the development of a mathematical model capable of describing all available sunspot data.
Source record↗
Acoustic spectral analysis and testing techniques
Subjects covered in four reports are described including: (1) mathematical techniques for combining decibel levels of octaves or constant bandwidth: (2) techniques for determining equation for power spectral density function; (3) computer program to analyze acoustical test data; and (4) computer simulation of horn responses utilizing hyperbolic horn theory.
Hayes, C. D.↗
A new sensitivity analysis for structural optimization of composite rotor blades
This paper presents a detailed mathematical derivation of the sensitivity derivatives for the structural dynamic, aeroelastic stability and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semianalytical approach, because certain derivatives have to be evaluated by a finite difference scheme. Using the present formulation, sensitivity derivatives for the structural dynamic and aeroelastic stability characteristics, were evaluated for both isotropic and composite rotor blades. Based on the results, useful conclusions are obtained regarding the relative merits of the semi-analytical approach, for calculating sensitivity derivatives, when compared to a pure finite difference approach.
Venkatesan, C.↗
Sensitivity Analysis for Multibody Dynamics Using Spatial Operators
Illustrate use of spatial operators as mathematical tools to make the inherently complex multibody dynamics tractable.
multibody dynamics algorithms↗
Some statistical analysis techniques for the effect of systematic instrument errors on the results of measurements in a space experiment
Mathematical models of certain systematic telemetry signal errors arising during the passage of the signal through the recording and transmitting blocks of the physical instruments aboard the spacecraft are classified and constructed. Statistical analysis methods are used to determine the background function and relative sensitivity coefficients of the channels of a charged particle detector. Results are presented. A block diagram for a method taking into account the effect of distortions is given.
Kondakov, S. P.↗
Trends in computerized structural analysis and synthesis; Proceedings of the Symposium, Washington, D.C., October 30-November 1, 1978
The subjects considered are related to future directions of structural applications and potential of new computing systems, advances and trends in data management and engineering software development, advances in applied mathematics and symbolic computing, computer-aided instruction and interactive computer graphics, nonlinear analysis, dynamic analysis and transient response, structural synthesis, structural analysis and design systems, advanced structural applications, supercomputers, numerical analysis, and trends in software systems. Attention is given to the reliability and optimality of the finite element method, computerized symbolic manipulation in structural mechanics, a standard computer graphics subroutine package, and a drag method as a finite element mesh generation scheme.
Noor, A. K.↗
On determining important aspects of mathematical models: Application to problems in physics and chemistry
The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.
Rabitz, Herschel↗
Design sensitivity analysis of rotorcraft airframe structures for vibration reduction
Optimization of rotorcraft structures for vibration reduction was studied. The objective of this study is to develop practical computational procedures for structural optimization of airframes subject to steady-state vibration response constraints. One of the key elements of any such computational procedure is design sensitivity analysis. A method for design sensitivity analysis of airframes under vibration response constraints is presented. The mathematical formulation of the method and its implementation as a new solution sequence in MSC/NASTRAN are described. The results of the application of the method to a simple finite element stick model of the AH-1G helicopter airframe are presented and discussed. Selection of design variables that are most likely to bring about changes in the response at specified locations in the airframe is based on consideration of forced response strain energy. Sensitivity coefficients are determined for the selected design variable set. Constraints on the natural frequencies are also included in addition to the constraints on the steady-state response. Sensitivity coefficients for these constraints are determined. Results of the analysis and insights gained in applying the method to the airframe model are discussed. The general nature of future work to be conducted is described.
Murthy, T. Sreekanta↗
SAVS: A Space Analysis and Visualization System
We propose to develop, test, demonstrate, and deliver to NASA a powerful and versatile data acquisition, manipulation, analysis and visualization system which will enhance scientific capabilities in the display and interpretation of diverse and distributed data within an integrated user-friendly environment. Our approach exploits existing technologies and combines three major elements into an easy-to-use interactive package: (1) innovative visualization software; (2) advanced database techniques; and (3) a rich set of mathematical and image processing tools. Visualization capabilities will include one-, two-, and three-dimensional displays, along with animation, compression, warping and slicing functions. Analysis tools will include generic mathematical and statistical techniques along with the ability to use large scale models for interactive interpretation of large volume data sets. Our system will be implemented on Sun and DEC UNIX workstations and on the Stardent Graphics Super computer. Our final deliverable will include complete documentation and a NASA/NSF-CDAW/SUNDIAL campaign demonstration.
Szuszczewicz, Edward P.↗
SAVS: A Space Analysis and Visualization System
We propose to develop, test, demonstrate, and deliver to NASA a powerful and versatile data acquisition, manipulation, analysis and visualization system which will enhance scientific capabilities in the display and interpretation of diverse and distributed data within an integrated user-friendly environment. Our approach exploits existing technologies and combines three major elements into an easy-to-use interactive package: (1) innovative visualization software; (2) advanced database techniques; and (3) a rich set of mathematical and image processing tools. Visualization capabilities will include one-, two-, and three-dimensinal displays, along with animation, compression, warping and slicing functions. Analysis tools will include generic mathematical and statistical techniques along with the ability to use large scale models for interactive interpretation of large volume data sets. Our system will be implemented on Sun and EC UNIX workstations and on the Stardent Graphics Supercomputer. Our final deliverable will include complete documentation and a NASA/NSF-CDAW/SUNDIAL campaign demonstration.
Szuszczewicz, Edward P.↗
Axially grooved heat pipes - 1976
This paper summarizes the 'state-of-the-art' of axially grooved heat pipes. Applications are identified and the related heat pipe design and performance are defined. Recent developments in the analysis, design and fabrication of axially grooved hardware are also discussed. A mathematical model which predicts the hydrodynamic behavior and accounts for liquid recession, liquid/vapor shear interaction and 1-g puddle flow is also presented. Performance data for various fluids in the 100-500 K range is compared to predictions from the Groove Analysis Program (GAP). Finally, a simplified closed form solution which accounts for gravity effects, self-priming and composite pumping by the grooves as well as all of the hydrodynamic losses is also discussed.
Brennan, P. J.↗
Analysis, Simulation, and Verification of Knowledge-Based, Rule-Based, and Expert Systems
Mathematically sound techniques are used to view a knowledge-based system (KBS) as a set of processes executing in parallel and being enabled in response to specific rules being fired. The set of processes can be manipulated, examined, analyzed, and used in a simulation. The tool that embodies this technology may warn developers of errors in their rules, but may also highlight rules (or sets of rules) in the system that are underspecified (or overspecified) and need to be corrected for the KBS to operate as intended. The rules embodied in a KBS specify the allowed situations, events, and/or results of the system they describe. In that sense, they provide a very abstract specification of a system. The system is implemented through the combination of the system specification together with an appropriate inference engine, independent of the algorithm used in that inference engine. Viewing the rule base as a major component of the specification, and choosing an appropriate specification notation to represent it, reveals how additional power can be derived from an approach to the knowledge-base system that involves analysis, simulation, and verification. This innovative approach requires no special knowledge of the rules, and allows a general approach where standardized analysis, verification, simulation, and model checking techniques can be applied to the KBS.
Hinchey, Mike↗
INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION
Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.
computational mathematics↗
General MACOS Interface for Modeling and Analysis for Controlled Optical Systems
The General MACOS Interface (GMI) for Modeling and Analysis for Controlled Optical Systems (MACOS) enables the use of MATLAB as a front-end for JPL s critical optical modeling package, MACOS. MACOS is JPL s in-house optical modeling software, which has proven to be a superb tool for advanced systems engineering of optical systems. GMI, coupled with MACOS, allows for seamless interfacing with modeling tools from other disciplines to make possible integration of dynamics, structures, and thermal models with the addition of control systems for deformable optics and other actuated optics. This software package is designed as a tool for analysts to quickly and easily use MACOS without needing to be an expert at programming MACOS. The strength of MACOS is its ability to interface with various modeling/development platforms, allowing evaluation of system performance with thermal, mechanical, and optical modeling parameter variations. GMI provides an improved means for accessing selected key MACOS functionalities. The main objective of GMI is to marry the vast mathematical and graphical capabilities of MATLAB with the powerful optical analysis engine of MACOS, thereby providing a useful tool to anyone who can program in MATLAB. GMI also improves modeling efficiency by eliminating the need to write an interface function for each task/project, reducing error sources, speeding up user/modeling tasks, and making MACOS well suited for fast prototyping.
Sigrist, Norbert↗
A Simple Engineering Analysis of Solar Particle Event High Energy Tails and Their Impact on Vehicle Design
The mathematical models for Solar Particle Event (SPE) high energy tails are constructed with several di erent algorithms. Since limited measured data exist above energies around 400 MeV, this paper arbitrarily de nes the high energy tail as any proton with an energy above 400 MeV. In order to better understand the importance of accurately modeling the high energy tail for SPE spectra, the contribution to astronaut whole body e ective dose equivalent of the high energy portions of three di erent SPE models has been evaluated. To ensure completeness of this analysis, simple and complex geometries were used. This analysis showed that the high energy tail of certain SPEs can be relevant to astronaut exposure and hence safety. Therefore, models of high energy tails for SPEs should be well analyzed and based on data if possible.
Singleterry, Robert C., Jr.↗
Annual Research Briefs, 2004: Center for Turbulence Research
This report contains the 2004 annual progress reports of the Research Fellows and students of the Center for Turbulence Research in its eighteenth year of operation. Since its inception in 1987, the objective of the CTR has been to advance the physical understanding of turbulent flows and development of physics based predictive tools for engineering analysis and turbulence control. Turbulence is ubiquitous in nature and in engineering devices. The studies at CTR have been motivated by applications where turbulence effects are significant; these include a broad range of technical areas such as planetary boundary layers, formation of planets, solar convection, magnetohydrodynamics, environmental and eco systems, aerodynamic noise, propulsion systems and high speed transportation. Numerical simulation has been the predominant research tool at CTR which has required a critical mass of researchers in numerical analysis and computer science in addition to core disciplines such as applied mathematics, chemical kinetics and fluid mechanics. Maintaining and promoting this interdisciplinary culture has been a hallmark of CTR and has been responsible for the realization of the results of its basic research in applications. The first group of reports in this volume are directed towards development, analysis and application of novel numerical methods for ow simulations. Development of methods for large eddy simulation of complex flows has been a central theme in this group. The second group is concerned with turbulent combustion, scalar transport and multi-phase ows. The nal group is devoted to geophysical turbulence where the problem of solar convection has been a new focus of considerable attention recently at CTR.
Moin, Parviz↗
Scattering from surfaces with different roughness scales, analysis and interpretation
Statistical analysis and physical interpretation of scattering from surfaces with different roughness scales
ELECTROMAGNETIC SCATTERING↗