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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗
NASA NTRS1974

Indirect synthesis of multi-degree of freedom transient systems

An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.

Pilkey, W. D.↗
NASA NTRS1991

Aerospace plane guidance using time-scale decomposition - A geometric approach

A method is proposed for developing the necessary guidance logic to steer single-stage vehicles into orbit. The minimum-fuel ascent problem is first considered to analyze the effects of dynamic pressure, acceleration, and heating constraints on guidance systems to thereby develop the guidance logic. The optimal solution consists of behavior with two time scales, and the control law is used to develop near-optimal guidance. The solution uses the slow manifold to delineate the control for minimum-fuel reduced-order trajectory and a separate control for tracking the optimal reduced-order trajectory. A family of fast manifolds is then employed to resolve the tracking problem via the feedback linearization methodology from nonlinear geometric control theory. The two-time-scale decomposition is found to produce a near-optimal ascent by tracking the applicable state-constraint boundary, as well as to simplify the control-design task.

Van Buren, Mark A.↗
NASA NTRS1975

Estimation of transonic aircraft aerodynamics to high angles of attack

A recently developed method for estimating transonic aircraft aerodynamics to high angles of attack which is especially suited to computerized aircraft design and optimization studies is described. Following theoretical and empirical guidelines, explicit nonlinear equations are formulated for subsonic, transonic, and supersonic speeds; new algorithms are used for assessing compressibility effects and for analyzing transonic, shock-dominated flows which adhere to Laitone's limit Mach-number criterion. Viscous dominated flows are not analyzed. The transonic influence of viscosity is indirectly accommodated by assigning designated inputs rather than extracted solutions for the chordwise locations of shock and separation. The method is extended to complete aircraft configurations by including accounts for nose lift, the wing downwash field, and tail lift. Several comparisons of experiment and estimate are included.

Axelson, J. A.↗
NASA NTRS1976

Formulation of a methodology for power circuit design optimization

A methodology for optimizing power-processor designs is described which achieves optimization with respect to some power-processor characteristic deemed particularly desirable by the designer, such as weight or efficiency. Optimization theory based on Lagrange multipliers is reviewed together with nonlinear programming techniques employing penalty functions. The methodology, the task of which is to minimize an objective function subject to design constraints, is demonstrated with the aid of four examples: optimum-weight core selection for an inductor with a predetermined winding size, optimum-weight inductor design with a given loss constraint, optimum-loss inductor design with a given weight constraint, and a comparison of optimum-weight single- and two-stage input-filter designs with identical loss and other requirement constraints. Closed-form solutions for the first three examples are obtained by applying the Lagrange-multiplier method, but solutions for the last example are found numerically through the use of the sequential unconstrained minimization technique.

Yu, Y.↗
NASA NTRS1979

Preliminary design procedure for insulated structures subjected to transient heating

Minimum-mass designs were obtained for insulated structural panels loaded by a general set of inplane forces and a time dependent temperature. Temperature and stress histories in the structure are given by closed-form solutions, and optimization of the insulation and structural thicknesses is performed by nonlinear mathematical programming techniques. Design calculations are described to evaluate the structural efficiency of eight materials under combined heating and mechanical loads: graphite/polyimide, graphite/epoxy, boron/aluminum, titanium, aluminum, Rene 41, carbon/carbon, and Lockalloy. The effect on design mass of intensity and duration of heating were assessed. Results indicate that an optimum structure may have a temperature response well below the recommended allowable temperature for the material.

Adelman, H. M.↗
NASA NTRS1983

Programming the gradient projection algorithm

The gradient projection method of numerical optimization which is applied to problems having linear constraints but nonlinear objective functions is described and analyzed. The algorithm is found to be efficient and thorough for small systems, but requires the addition of auxiliary methods and programming for large scale systems with severe nonlinearities. In order to verify the theoretical results a digital computer is used to simulate the algorithm.

Hargrove, A.↗
NASA NTRS1987

Mathematical programming formulations for satellite synthesis

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Bhasin, Puneet↗
NASA NTRS1992

Neural networks in structural analysis and design - An overview

The present paper provides an overview of the state-of-the-art in the application of neural networks in problems of structural analysis and design, including a survey of published applications in structural engineering. Such applications have included, among others, the use of neural networks in modeling nonlinear analysis of structures, as a rapid reanalysis capability in optimal design, and in developing problem parameter sensitivity of optimal solutions for use in multilevel decomposition based design. While most of the applications reported in the literature have been restricted to the use of the multilayer perceptron architecture and minor variations thereof, other network architectures have also been successfully explored, including the ART network, the counterpropagation network and the Hopfield-Tank model.

Hajela, P.↗
NASA NTRS1993

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.

Storaasli, Olaf O.↗
NASA NTRS1993

Computational mechanics analysis tools for parallel-vector supercomputers

Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.

Storaasli, O. O.↗
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 NTRS1989

The dynamics and control of large flexible space structures - 12, supplement 11

The rapid 2-D slewing and vibrational control of the unsymmetrical flexible SCOLE (Spacecraft Control Laboratory Experiment) with multi-bounded controls is considered. Pontryagin's Maximum Principle is applied to the nonlinear equations of the system to derive the necessary conditions for the optimal control. The resulting two point boundary value problem is then solved by using the quasilinearization technique, and the near minimum time is obtained by sequentially shortening the slewing time until the controls are near the bang-bang type. The tradeoff between the minimum time and the minimum flexible amplitude requirements is discussed. The numerical results show that the responses of the nonlinear system are significantly different from those of the linearized system for rapid slewing. The SCOLE station-keeping closed loop dynamics are re-examined by employing a slightly different method for developing the equations of motion in which higher order terms in the expressions for the mast modal shape functions are now included. A preliminary study on the effect of actuator mass on the closed loop dynamics of large space systems is conducted. A numerical example based on a coupled two-mass two-spring system illustrates the effect of changes caused in the mass and stiffness matrices on the closed loop system eigenvalues. In certain cases the need for redesigning control laws previously synthesized, but not accounting for actuator masses, is indicated.

Bainum, Peter M.↗
NASA NTRS1985

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Murphy, Patrick Charles↗
NASA NTRS1999

Development of a Multiobjective Optimization Procedure for Sonic Boom Minimization

A design optimization procedure for improved sonic boom and aerodynamic performance of high speed aircraft is presented. The multiobjective optimization procedure simultaneously minimizes the sonic boom at a given distance from the aircraft and the drag-to-lift ratio (C(sub D)/C(sub L)) Of the aircraft. Upper and lower bounds are also imposed on the lift coefficient. The Kreisselmeier - Steinhauser function is used for the multiobjective optimization formulation. A discrete semi-analytical aerodynamic sensitivity analysis procedure coupled with an analytical grid sensitivity analysis technique is used for evaluating design sensitivities. The use of the semi-analytical sensitivity analysis techniques results in significant computational savings. The flow equations are solved using a three-dimensional parabolized Navier-Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. A nonlinear programming technique and an approximate analysis procedure are used for the optimization. The optimization procedure developed is applied to the design of two high speed configurations, namely, a doubly swept wing-body configuration and a delta wing-body configuration. For the two sweep case only, minimization of the first peak in the pressure signature is performed first by optimizing only the nose radius and length of the aircraft. Minimization of the second peak in the pressure signature is performed next by optimizing only the wing geometric parameters. Significant improvements are obtained in the sonic boom characteristics and the aerodynamic performance of the wing-body configurations.

Narayan, J. R.↗