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At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Shebalin, John V.↗
NASA NTRS1990

Minimum Weight Design of a Leaf Spring Tapered in Thickness and Width for the Hubble Space Telescope-Space Support Equipment

A linear elastic solution to the problem of minimum weight design of cantilever beams with variable width and depth is presented. The solution shown is for the specific application of the Hubble Space Telescope maintenance mission hardware. During these maintenance missions, delicate instruments must be isolated from the potentially damaging vibration environment of the space shuttle cargo bay during the ascent and descent phases. The leaf springs are designed to maintain the isolation system natural frequency at a level where load transmission to the instruments in a minimum. Nonlinear programming is used for the optimization process. The weight of the beams is the objective function with the deflection and allowable bending stress as the constraint equations. The design variables are the width and depth of the beams at both the free and the fixed ends.

Rodriguez, P. I.↗
NASA NTRS1990

Simulation and analysis of flexibly jointed manipulators

Modeling, simulation, and analysis of robot manipulators with non-negligible joint flexibility are studied. A recursive Newton-Euler model of the flexibly jointed manipulator is developed with many advantages over the traditional Lagrange-Euler methods. The Newton-Euler approach leads to a method for the simulation of a flexibly jointed manipulator in which the number of computations grows linearly with the number of links. Additionally, any function for the flexibility between the motor and link may be used permitting the simulation of nonlinear effects, such as backlash, in a uniform manner for all joints. An analysis of the control problems for flexibly jointed manipulators is presented by converting the Newton-Euler model to a Lagrange-Euler form. The detailed structure available in the model is used to examine linearizing controllers and shows the dependency of the control on the choice of flexible model and structure of the manipulator.

Murphy, Steve H.↗
NASA NTRS1992

A decomposition method for optimization of large-system reliability

This paper considers a decomposition approach for optimization of the reliability of a large system with a general network structure. A 3-level methodology is developed for optimal allocation of available resources among subsystems in order to ensure maximization of system-reliability. The decentralized nature of this methodology greatly reduces the complexity of the large problem and facilitates seeking the optimal solution. Two examples show that the complexity of a large system can be greatly reduced by solving several smaller-dimensional sub-problems iteratively. Sub-problems whose dimensions are small can be efficiently solved by any existing nonlinear programming method. Another important feature of this approach is the possible simplification of the objective function during the solution. This leads in some cases to an analytic solution for the lower-level optimization problems in a 3-level decomposition solution.

Li, Duan↗
NASA NTRS1994

Optimizing the Zeldovich approximation

We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities produced by TZA.

Melott, Adrian L.↗
NASA NTRS1994

Neural network applications in telecommunications

Neural network capabilities include automatic and organized handling of complex information, quick adaptation to continuously changing environments, nonlinear modeling, and parallel implementation. This viewgraph presentation presents Bellcore work on applications, learning chip computational function, learning system block diagram, neural network equalization, broadband access control, calling-card fraud detection, software reliability prediction, and conclusions.

Alspector, Joshua↗
NASA NTRS1994

Optimizations on Designing High-Resolution Finite-Difference Schemes

We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.

Liu, Yen↗
NASA NTRS1998

Stochastic feedback and the regulation of biological rhythms

We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of "stochastic feedback". We illustrate this approach by considering at a coarse-grained level the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully acounts for key characteristics of cardiac variability, including the l/f power spectrum, the functional form and scaling of the distribution of variations, and correlations in the Fourier phases indicating nonlinear dynamics.

NASA Discipline Cardiopulmonary↗
NASA NTRS2004

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Sullivan, Roy M.↗
NASA NTRS2016

Exhibition of Stochastic Resonance in Vestibular Perception

Astronauts experience sensorimotor changes during spaceflight, particularly during G-transitions. Post flight sensorimotor changes include spatial disorientation, along with postural and gait instability that may degrade operational capabilities of the astronauts and endanger the crew. A sensorimotor countermeasure that mitigates these effects would improve crewmember safety and decrease risk. The goal of this research is to investigate the potential use of stochastic vestibular stimulation (SVS) as a technology to improve sensorimotor function. We hypothesize that low levels of SVS will improve sensorimotor perception through the phenomenon of stochastic resonance (SR), when the response of a nonlinear system to a weak input signal is enhanced by the application of a particular nonzero level of noise. This study aims to advance the development of SVS as a potential countermeasure by 1) demonstrating the exhibition of stochastic resonance in vestibular perception, a vital component of sensorimotor function, 2) investigating the repeatability of SR exhibition, and 3) determining the relative contribution of the semicircular canals (SCC) and otolith (OTO) organs to vestibular perceptual SR. A constant current stimulator was used to deliver bilateral bipolar SVS via electrodes placed on each of the mastoid processes, as previously done. Vestibular perceptual motion recognition thresholds were measured using a 6-degree of freedom MOOG platform and a 150 trial 3-down/1-up staircase procedure. In the first test session, we measured vestibular perceptual thresholds in upright roll-tilt at 0.2 Hz (SCC+OTO) with SVS ranging from 0-700 μA. In a second test session a week later, we re-measured roll-tilt thresholds with 0, optimal (from test session 1), and 1500 μA SVS levels. A subset of these subjects, plus naive subjects, participated in two additional test sessions in which we measured thresholds in supine roll-rotation at 0.2 Hz (SCC) and upright y-translation at 1 Hz (OTO) with SVS up to 700 μA. A sinusoidal galvanic vestibular stimulation (GVS) perceptual threshold was also measured on each test day and used to normalize the SVS levels across subjects. In roll-tilt thresholds with SVS, the characteristic SR curve was qualitatively exhibited in 10 of 12 subjects, and the improvement in motion threshold was significant in 6 subjects, indicating that optimal SVS improved passive body motion perception in a way that is consistent with classical SR theory. A probabilistic comparison to numeric simulations further validated these experimental results. On the second test session, 4 out of the 10 SR exhibitors showed repeated improvement with SVS compared to the no SVS condition. Data collection is ongoing for the last two test sessions in which SCC and OTO only perceptual motion recognition thresholds are being measured with SVS. The final results of these test sessions will give insight into whether vestibular perceptual SR can occur when only one type of vestibular sensor is sensing motion or if it is more evident when sensory integration between the SCC and OTO is occurring during the motion. The overall purpose of this research is to further quantify the effects of SVS on various sensorimotor tasks and to gain a more fundamental understanding of how SVS causes SR in the vestibular system. In the context of human space flight, results from this research will help in understanding how SVS may be practically implemented in the future as a component of a comprehensive countermeasure plan for G-transition adaptation.

Galvan-Garza, R. C.↗
NASA NTRS2022

A Framework for Deep Learning Emulation of Numerical Models With a Case Study in Satellite Remote Sensing

Numerical models based on physics represent the state of the art in Earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model resolutions overwhelms the latest generation computers, reducing the ability of modelers to generate simulations for understanding parameter sensitivities and characterizing variability and uncertainty. Thus, surrogate models are often developed to capture the essential attributes of the full-blown numerical models. Recent successes of machine learning methods, especially deep learning (DL), across many disciplines offer the possibility that complex nonlinear connectionist representations may be able to capture the underlying complex structures and nonlinear processes in Earth systems. A difficult test for DL-based emulation, which refers to function approximation of numerical models, is to understand whether they can be comparable to traditional forms of surrogate models in terms of computational efficiency while simultaneously reproducing model results in a credible manner. A DL emulation that passes this test may be expected to perform even better than simple models with respect to capturing complex processes and spatiotemporal dependencies. Here, we examine, with a case study in satellite-based remote sensing, the hypothesis that DL approaches can credibly represent the simulations from a surrogate model with comparable computational efficiency. Our results are encouraging in that the DL emulation reproduces the results with acceptable accuracy and often even faster performance. We discuss the broader implications of our results in light of the pace of improvements in high-performance implementations of DL and the growing desire for higher resolution simulations in the Earth sciences.

Bayesian Deep Learning↗
NASA NTRS1994

Multilevel algorithms for nonlinear optimization

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Alexandrov, Natalia↗
NASA NTRS2006

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Kukreja, Sunil L.↗
NASA NTRS1982

Gain optimization with nonlinear controls

An algorithm has been developed for the analysis and design of controls for nonlinear systems. The technical approach is to use statistical linearization to model the nonlinear dynamics of a system. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this report is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general however and numerical computation requires only that the specific nonlinearity be considered in the analysis.

Slater, G. L.↗
NASA NTRS1989

A penalty approach for nonlinear optimization with discrete design variables

Introduced here is a simple approach to minimization problems with discrete design variables by modifying the penaly function approach of converting the constrained problems into sequential unconstrained minimization technique (SUMT) problems. It was discovered, during the course of the present work, that a similar idea was suggested by Marcal and Gellatly. However, no further work has been encountered. A brief description of the SUMT is presented. The form of the penalty function for the discrete-valued design variables and strategy used for the implementation of the procedure is discussed next. Finally, several design examples are used to demonstrate the procedure, and results are compared with the ones available in the literature.

Shin, Dong K.↗
NASA NTRS1989

The distribution of solar magnetic fluxes and the nonlinearity of stellar flux-flux relations

Synoptic maps for the 1975-1984 period are used to determine the time-dependent distribution function of magnetic flux densities in the solar atmosphere. The distribution function depends only on the global level of magnetic activity, and it is used to study how relations between magnetic flux densities and radiative flux densities from different temperature regimes in the outer atmosphere (derived from spatially resolved solar observations) transform into relations between surface-averaged flux densities. It is found that the transformation to surface-averaged fluxes preserves the power-law character of relations between radiative and magnetic flux densities for spatially resolved data.

Schrijver, C. J.↗
NASA NTRS1982

Nonlinear constitutive theory for turbine engine structural analysis

A number of viscoplastic constitutive theories and a conventional constitutive theory are evaluated and compared in their ability to predict nonlinear stress-strain behavior in gas turbine engine components at elevated temperatures. Specific application of these theories is directed towards the structural analysis of combustor liners undergoing transient, cyclic, thermomechanical load histories. The combustor liner material considered in this study is Hastelloy X. The material constants for each of the theories (as a function of temperature) are obtained from existing, published experimental data. The viscoplastic theories and a conventional theory are incorporated into a general purpose, nonlinear, finite element computer program. Several numerical examples of combustor liner structural analysis using these theories are given to demonstrate their capabilities. Based on the numerical stress-strain results, the theories are evaluated and compared.

Thompson, R. L.↗
NASA NTRS1999

Structural Optimization for Reliability Using Nonlinear Goal Programming

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

El-Sayed, Mohamed E.↗