Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear problems”

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.

At least 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles

A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.

Korte, John J.↗
NASA NTRS1992

Recursive Filtering And Smoothing In Robot Dynamics

Techniques developed originally for electronic systems also useful for multibody mechanical systems. Report summarizes methods developed to solve nonlinear forward-dynamics problem for robot of multiple-link arms connected by joints. Primary objective to show equivalence between recursive methods of dynamical analysis and some filtering and smoothing techniques from state-estimation theory.

Rodriguez, Guillermo↗
NASA NTRS1991

A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids

A solution procedure for solving nonlinear time-marching problems is presented. The nonsymmetric systems of equations arising from a Newton-type linearization of these time-marching problems are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms.

Johan, Zdenek↗
NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗
NASA NTRS1992

High-resolution gravity model of Venus

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter has been evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Reasenberg, R. D.↗
NASA NTRS1993

Further development towards a new virtual-pulse time integral methodology for general nonlinear transient thermal analysis

New developments describing the theoretical basis towards an effective virtual-pulse time integral procedure are presented for general nonlinear transient heat transfer problems. To validate the proposed methodology of computation, numerical test examples are given and comparisons are drawn with the implicit second-order accurate Crank-Nicolson technique. The proposed method shows superior or improved accuracy and stability characteristics for the models tested.

Tamma, K. K.↗
NASA NTRS1993

Dynamics of aging magnetic clouds

The dynamics of radially expanding magnetic clouds is rigorously analyzed within the framework of ideal MHD. The cloud is modelled as a cylindrically symmetric magnetic flux rope. In the force balance we include the gas pressure gradient and the Lorentz force. Interaction with the ambient solar wind due to expansion of the magnetic cloud is represented by a drag force proportional to the bulk velocity. We consider the self-similar expansion of a polytrope, and reduce the problem to an ordinary nonlinear differential equation for the evolution function. Analyzing the asymptotic behavior of the evolution function, we formulate theoretical expectations for the long-term behavior of cloud parameters. We focus on the temporal evolution of (1) the magnetic field strength; (2) the twist of the field lines; (3) the asymmetry of the total field profile; and (4) the bulk flow speed. We present data from two magnetic clouds observed at 1 AU and 2 AU, respectively, and find good agreement with theoretical expectations. For a peak magnetic field strength at 1 AU of 25 nT and a polytropic index of 0.5, we find that a magnetic cloud can be distinguished from the background interplanetary field up to a distance of about 5 AU. Taking larger magnetic fields and bigger polytropic indices this distance can double.

Osherovich, V. A.↗
NASA NTRS1993

Venus gravity

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter (PVO) by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter was evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Reasenberg, Robert D.↗
NASA NTRS1995

Estimating errors in least-squares fitting

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Richter, P. H.↗
NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗
NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗
NASA NTRS1997

Regularization for Atmospheric Temperature Retrieval Problems

Passive remote sensing of the atmosphere is used to determine the atmospheric state. A radiometer measures microwave emissions from earth's atmosphere and surface. The radiance measured by the radiometer is proportional to the brightness temperature. This brightness temperature can be used to estimate atmospheric parameters such as temperature and water vapor content. These quantities are of primary importance for different applications in meteorology, oceanography, and geophysical sciences. Depending on the range in the electromagnetic spectrum being measured by the radiometer and the atmospheric quantities to be estimated, the retrieval or inverse problem of determining atmospheric parameters from brightness temperature might be linear or nonlinear. In most applications, the retrieval problem requires the inversion of a Fredholm integral equation of the first kind making this an ill-posed problem. The numerical solution of the retrieval problem requires the transformation of the continuous problem into a discrete problem. The ill-posedness of the continuous problem translates into ill-conditioning or ill-posedness of the discrete problem. Regularization methods are used to convert the ill-posed problem into a well-posed one. In this paper, we present some results of our work in applying different regularization techniques to atmospheric temperature retrievals using brightness temperatures measured with the SSM/T-1 sensor. Simulation results are presented which show the potential of these techniques to improve temperature retrievals. In particular, no statistical assumptions are needed and the algorithms were capable of correctly estimating the temperature profile corner at the tropopause independent of the initial guess.

Velez-Reyes, Miguel↗
NASA NTRS2002

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

Hughes, Steven P.↗
NASA NTRS1999

Numerical System Solver Developed for the National Cycle Program

As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

Binder, Michael P.↗
NASA NTRS2008

Helios Prototype Vehicle Mishap: Technical Findings, Recommendations, and Lessons Learned

Instability associated with the Helios Prototype HPO3-2 vehicle was a nonlinear stability and control problem involving complex interactions among the flexible structure, the unsteady aerodynamics, the flight control system, the environmental conditions, and vehicle flight dynamics. Analysis tools and solution techniques were constrained by conventional and segmented linear methodologies that did not provide the proper level of complexity to understand the technology interactions on the vehicle s stability and control characteristics. More advanced, multidisciplinary (structures, aeroelastic, aerodynamics, atmospheric, materials, propulsion, controls, etc) "time-domain" analysis methods appropriate to highly flexible, "morphing" vehicles are required. Ground-test procedures and techniques appropriate to this class of vehicle are needed to validate new analysis methods and predictions

DelFrate, John H.↗
NASA NTRS2009

Control of Systems With Slow Actuators Using Time Scale Separation

This paper addresses the problem of controlling a nonlinear plant with a slow actuator using singular perturbation method. For the known plant-actuator cascaded system the proposed scheme achieves tracking of a given reference model with considerably less control demand than would otherwise result when using conventional design techniques. This is the consequence of excluding the small parameter from the actuator dynamics via time scale separation. The resulting tracking error is within the order of this small parameter. For the unknown system the adaptive counterpart is developed based on the prediction model, which is driven towards the reference model by the control design. It is proven that the prediction model tracks the reference model with an error proportional to the small parameter, while the prediction error converges to zero. The resulting closed-loop system with all prediction models and adaptive laws remains stable. The benefits of the approach are demonstrated in simulation studies and compared to conventional control approaches.

Stepanyan, Vehram↗
NASA NTRS1988

Does the resistive tearing instability nonlinearly evolve to a fast reconnection mode

A fundamental problem in applying linear tearing instability theory to the rapid processes (particle acceleration, heating) in flares was the characteristically slow rate of reconnection. This problem can be at least partially overcome if the tearin mode nonlinearly evolves to a regime in which the reconnection rate is substantially enhanced, such as that for the Petschek configuration. This possibility was often suggested, and some numerical simulations appear to provide support for such a view. Numerical simulation are used to study the nonlinear evolution of the tearing stability and show that a fast Petschek-like regime may not be achieved. This conclusion follows when there are sufficient grid points within the diffusion region to completely resolve the nonlinear dynamic interactions in the diffusion layer. When the numerical resolution is not adequate, the solution does appear to approach a Petschek configuration. The resolved solution contains reverse flow vortices and current sheets, terminated with a current reversal, similar to those obtained by Syrovatsky (JEPT, 33, 933, 1971).

Steinolfson, R. S.↗