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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

A variational technique for smoothing flight-test and accident data

The problem of determining aircraft motions along a trajectory is solved using a variational algorithm that generates unmeasured states and forcing functions, and estimates instrument bias and scale-factor errors. The problem is formulated as a nonlinear fixed-interval smoothing problem, and is solved as a sequence of linear two-point boundary value problems, using a sweep method. The algorithm has been implemented for use in flight-test and accident analysis. Aircraft motions are assumed to be governed by a six-degree-of-freedom kinematic model; forcing functions consist of body accelerations and winds, and the measurement model includes aerodynamic and radar data. Examples of the determination of aircraft motions from typical flight-test and accident data are presented.

Bach, R. E., Jr.↗
NASA NTRS1980

Vertical slender jets

The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface tension effects are neglected. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from orifices in various shapes including an ellipse, a rectangle, and an equilateral triangle. Computational results are presented illustrating the propagation of discontinuities and the formation of thin sheets of fluid.

Geer, J. F.↗
NASA NTRS1987

Optimal reconfiguration strategy for a degradable multimodule computing system

The present quantitative approach to the problem of reconfiguring a degradable multimode system assigns some modules to computation and arranges others for reliability. By using expected total reward as the optimal criterion, there emerges an active reconfiguration strategy based not only on the occurrence of failure but the progression of the given mission. This reconfiguration strategy requires specification of the times at which the system should undergo reconfiguration, and the configurations to which the system should change. The optimal reconfiguration problem is converted to integer nonlinear knapsack and fractional programming problems.

Lee, Yann-Hang↗
NASA NTRS1982

A Variational Technique for Smoothing Flight-Test and Accident Data

The problem of determining aircraft motions along a trajectory is solved using a variational algorithm that generates unmeasured states and forcing functions, and estimates instrument bias and scale-factor errors. The problem is formulated as a nonlinear fixed-interval smoothing problem, and is solved as a sequence or linear two-point boundary value problems, using a sweep method. The algorithm has been implemented for use in flight-test and accident analysis. Aircraft motions are assumed to be governed by a six-degree-of-freedom kinematic model; forcing functions consist of body accelerations and winds, and the measurement model includes aerodynamic and radar data. Examples of the determination of aircraft motions from typical flight-test and accident data are presented.

Bach, Ralph E. , Jr.↗
NASA NTRS1973

An interative solution of an integral equation for radiative transfer by using variational technique

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

Yoshikawa, K. K.↗
NASA NTRS1991

Trajectory optimization and guidance for a hypersonic vehicle

The optimal ascent problem for a hypersonic vehicle is formulated as an inverse dynamic problem. This formulation is essential in solving the trajectory optimization problem via the nonlinear programming approach. Both minimum-fuel and minimax type of performance indices are considered. The results reveal important features of the optimal trajectory and controls, and they are subsequently used to construct a nonlinear feedback midcourse control law. This control law not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suitable for onboard implementation. Finally, off-nominal trajectory guidance is addressed using combination of feedback compensation and onboard generation of control through the inverse dynamics approach.

Lu, Ping↗
NASA NTRS1996

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Cai, Xiao-Chuan↗
NASA NTRS1987

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.

Sather, Duane P.↗
NASA NTRS2017

Coronagraph Design Optimization for Segmented Aperture Telescopes

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-o between planet light throughput and di racted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) di racted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, speci cally ctitious "auxiliary" electric elds which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured o -axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

Redding, Dave↗
NASA NTRS1982

Rapid approximate determination of nonlinear solutions - Application to aerodynamic flows and design/optimization problems

Stahara et al. (1978) have considered the use of an approximation technique which employs two or more nonlinear base solutions determined by the full computational method to predict entire families of related nonlinear solutions. The present investigation provides results for several applications of that method which demonstrate both its accuracy and its utility for engineering applications. Attention is given to the perturbation concept and methods, aspects of coordinate straining, aspects of analytical formulation, and an application to surface properties. In a discussion of the results, single and multiple parameter perturbations are considered along with a combination of the approximation method with optimization procedures. The results show that it is possible to combine in certain cases large savings in computational cost with improved optimization.

Stahara, S. S.↗
NASA NTRS1990

An averaging approach to optimal adaptive control of large space structures

Averaging methods are applied to analyzing the transient response associated with adaptive control of large space structures. Using a dominant mode approximation to the plant, an analytical bound is found on the envelope of the adaptive response, characterizing many of the features of the response useful for control design (e.g., peak values, quadratic costs, settling times, etc.). An optimal adaptive design problem is formulated based on minimizing the product of the settling time and peak torque requirement. The resulting nonlinear constrained optimization problem is solved in closed form, and several properties of the optimal adaptive design are discussed.

Bayard, D. S.↗
NASA NTRS1993

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

Bless, Robert R.↗
NASA NTRS1979

Modern estimation techniques applied to microwave sensing of the marine boundary layer

Previous efforts in the area of satellite microwave sensing of the marine boundary layer have relied upon linear regression techniques to extract geophysical parameters from the microwave measurement data. The approach used in the present paper shifts emphasis away from the generation of regression weighting matrices which implicitly assume that the data are linear in the parameters to be determined and that the problem is statistically stationary. The idea is simply to employ modern computational estimation techniques to obtain parameter estimates from nonlinear noisy measurements. The approach is limited only to the region of validity of Grody's (1976) model. Attention is focused on documenting how estimation techniques, in particular the square root information filter (SRIF), are used to solve a nonlinear function optimization problem.

Bierman, G. J.↗
NASA NTRS1972

Optimal horizontal guidance law for aircraft in the terminal area.

Study of the horizontal guidance of aircraft in and near the terminal area. The problem of guiding an aircraft in minimum time from an arbitrary point to the outer marker is formulated as a nonlinear optimal control problem, and the control law solution is obtained by the application of the maximum principle. It is found that for some initial states the problem is singular. Furthermore, the extremal controls for this problem are not unique. Consequently, the optimal controls must be obtained on the basis of the value of the performance index. The control law is implemented in the form of a digital computer program which computes the optimal trajectory for arbitrary initial conditions.

Pecsvaradi, T.↗
NASA NTRS2000

Validation of a High-Order Prefactored Compact Scheme on Nonlinear Flows with Complex Geometries

Three benchmark problems are solved using a sixth-order prefactored compact scheme employing an explicit 10th-order filter with optimized fourth-order Runge-Kutta time stepping. The problems solved are the following: (1) propagation of sound waves through a transonic nozzle; (2) shock-sound interaction; and (3) single airfoil gust response. In the first two problems, the spatial accuracy of the scheme is tested on a stretched grid, and the effectiveness of boundary conditions is shown. The solution stability and accuracy near a shock discontinuity is shown as well. Also, 1-D nonlinear characteristic boundary conditions will be evaluated. In the third problem, a nonlinear Euler solver will be used that solves the equations in generalized curvilinear coordinates using the chain rule transformation. This work, continuing earlier work on flat-plate cascades and Joukowski airfoils, will focus mainly on the effect of the grid and boundary conditions on the accuracy of the solution. The grids were generated using a commercially available grid generator, GridPro/az3000.

Hixon, Ray↗