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At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
NASA NTRS1967

Investigation to define the propagation characteristics of a finite amplitude acoustic pressure wave

A theoretical analysis of the propagation characteristics of a finite amplitude pressure wave is presented. The analysis attempts to study the contribution of entropy-producing regions to the mechanism of aerodynamic noise generation. It results in a nonlinear convective wave equation in terms of entropy and a thermodynamic 'J' function. A direct analogy between the derived governing equation and those used in classical literature is obtained. An idealization of the processes considered permits the uncoupling of the equations of motion with a consequent construction of an acoustic analogy treating shock wave emission of finite amplitude acoustic waves. An engineering approach is reflected in the concept of an extended plug nozzle whose function is to facilitate aerodynamic noise attenuation by modifying the entropy-producing regions.

Peter, A. C.↗
NASA NTRS1971

Approximate optimal atmospheric entry trajectories

Reentry glider approximate optimal atmospheric entry trajectories for maximizing function of terminal velocity, altitude, flight path and heading angle under terminal nonlinear constraints

Speyer, J. L.↗
NASA NTRS1972

Bounded state space

This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.

Eyman, E. D.↗
NASA NTRS1976

Four-dimensional guidance problem with control delays

This paper, assuming steady wind and zero sideslip, presents a discrete-time mathematical model to obtain a control law and three-dimensional flight path to guide an aircraft in a given time from a given initial state (position, velocity and heading) to a prescribed final state subject to the constraints on airspeed acceleration, and pitch and bank angles of the aircraft. For ease in implementing the control law, the control inputs are assumed to be delayed and are applied in a sequential fashion. The guidance problem is formulated as a discrete nonlinear optimal control problem with time delays in dynamics and a cost functional of Bolza form. With a quadratic penalty function to handle terminal constraints on velocity and heading, a solution technique to the control problem based on conjugate gradient algorithm is investigated. Numerical examples are presented to illustrate the applicability of this approach to solution of a terminal area guidance problem in an automated air traffic control environment.

Nagarajan, N.↗
NASA NTRS1976

Construction of analytically solvable models for interacting species

The basic form of a model representation for systems of n interacting biological species is a set of essentially nonlinear autonomous ordinary differential equations. A generic canonical expression for the rate functions in the equations is reported which permits the analytical general solution to be obtained by elementary computation. It is shown that a general analytical solution is directly obtainable for models where the rate functions are prescribed by the generic canonical expression from the outset. Some illustrative examples are given which demonstrate that the generic canonical expression can be used to construct analytically solvable models for two interacting species with limit-cycle dynamics as well as for a three-species interdependence.

Rosen, G.↗
NASA NTRS1984

Mapping magnetized geologic structures from space: The effect of orbital and body parameters

When comparing previous satellite magnetometer missions (such as MAGSAT) with proposed new programs (for example, Geopotential Research Mission, GRM) it is important to quantify the difference in scientific information obtained. The ability to resolve separate magnetic blocks (simulating geological units) is used as a parameter for evaluating the expected geologic information from each mission. The effect of satellite orbital altitude on the ability to resolve two magnetic blocks with varying separations is evaluated and quantified. A systematic, nonlinear, relationship exists between resolution and distance between magnetic blocks as a function of orbital altitude. The proposed GRM would provide an order-of-magnitude greater anomaly resolution than the earlier MAGSAT mission for widely separated bodies. The resolution achieved at any particular altitude varies depending on the location of the bodies and orientation.

Schnetzler, C. C.↗
NASA NTRS1985

Polynomic nonlinear dynamical systems - A residual sensitivity method for model reduction

The motivation for using polynomic combinations of system states and inputs to model nonlinear dynamics systems is founded upon the classical theories of analysis and function representation. A feature of such representations is the need to make available all possible monomials in these variables, up to the degree specified, so as to provide for the description of widely varying functions within a broad class. For a particular application, however, certain monomials may be quite superfluous. This paper examines the possibility of removing monomials from the model in accordance with the level of sensitivity displayed by the residuals to their absence. Critical in these studies is the effect of system input excitation, and the effect of discarding monomial terms, upon the model parameter set. Therefore, model reduction is approached iteratively, with inputs redesigned at each iteration to ensure sufficient excitation of remaining monomials for parameter approximation. Examples are reported to illustrate the performance of such model reduction approaches.

Yurkovich, S.↗
NASA NTRS1986

Variable structure control of nonlinear systems through simplified uncertain models

A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.

Sira-Ramirez, Hebertt↗
NASA NTRS1989

Nonlinear Curve-Fitting Program

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Everhart, Joel L.↗
NASA NTRS1992

Multiwavelength pyrometry for nongray bodies

A multiwavelength technique was developed and applied to measure the temperatures of nongray surfaces. The instruments required are a spectral radiometer, a dedicated auxiliary radiation source, and a computer. In general, three radiation spectra are recorded: (1) spectrum S sub 0 of the auxiliary radiation source; (2) spectrum S sub 1 of the surface-emitted radiation; and (3) spectrum S sub 2, the sum of the radiation of S sub 1 plus the reflected radiation due to the incidence of the auxiliary radiation source on the surface. Subtracting spectrum S sub 1 from spectrum Sub 2 yields the reflection spectrum resulting from the incidence radiation. From these spectra, a quantity z(lambda) is derived and is related to the reflectivity r(lambda) by r(lambda) = z(lambda)/f, where f is a constant. Spectrum S sub 1 is represented mathematically as the product of a wavelength-dependent emissivity obtained from Kirchhoff's law and a Planck function of temperature T. Application of two-variable (lambda and z), nonlinear, least-squares curve-fitting computer software to fit spectrum S sub 1 to this mathematical expression yielded the surface temperature. This technique also measured the spectral reflectivity and emissivity of the surface. Instrumentation necessary to extend measurement to elevated temperatures and in the presence of reflective interference is discussed.

Ng, Daniel↗
NASA NTRS1996

Low-Dimensional Dynamical Models of Thermal Convection

A low-dimensional dynamic model for transitional buoyancy-driven flow in a differentially heated tall enclosure is presented. The full governing partial differential equations with the associated boundary conditions are solved by a spectral element method for a cavity of aspect ratio A=20. Proper orthogonal decomposition is applied to the oscillatory solution at Prandtl number Pr=P tau (omega) = 0.71 and Grashof number G tau (omega) = 3.2 x 10 (exp 4) to construct empirical eigenfunctions. Using the four most energetic empirical eigenfunctions for the velocity and temperature as basis functions and applying Galerkin's method, a reduced model consisting of eight nonlinear ordinary differential equations is obtained. Close to the 'design' conditions (P tau(omega) G tau(omega)), the low-order model (LOM) predictions are in excellent agreement with the predictions of the full model. In particular, the critical Grashof number at the onset of the first temporal flow instability (Hopf bifurcation) was well as the frequency and amplitude of oscillations at supercritical conditions are in excellent agreement with the predictions of the full model. Far from the 'design' conditions, the LOM predicts the existence of multiple stable steady solutions at large values of G tau, and a unique stable steady solution at small values of G tau, and exhibits hysteretic behavior that is qualitatively similar to that observed in direct numerical simulations based on the full model.

Liakopoulos, Anthony↗
NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗
NASA NTRS2005

Shock Waves in a Bose-Einstein Condensate

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Kulikov, Igor↗
NASA NTRS2013

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Architecture and Performance Predictions

A peak-seeking control approach for real-time trim configuration optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control approach is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are controlled for optimization of fuel flow. This paper presents the design and integration of this peak-seeking controller on a modified NASA F/A-18 airplane with research flight control computers. A research flight was performed to collect data to build a realistic model of the performance function and characterize measurement noise. This model was then implemented into a nonlinear six-degree-of-freedom F/A-18 simulation along with the peak-seeking control algorithm. With the goal of eventual flight tests, the algorithm was first evaluated in the improved simulation environment. Results from the simulation predict good convergence on minimum fuel flow with a 2.5-percent reduction in fuel flow relative to the baseline trim of the aircraft.

performance optimization↗
NASA NTRS2013

Peak-Seeking Optimization of Trim for Reduced Fuel Consumption: Architecture and Performance Predictions

A peak-seeking control approach for real-time trim configuration optimization for reduced fuel consumption has been developed by researchers at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center to address the goals of the NASA Environmentally Responsible Aviation project to reduce fuel burn and emissions. The peak-seeking control approach is based on a steepest-descent algorithm using a time-varying Kalman filter to estimate the gradient of a performance function of fuel flow versus control surface positions. In real-time operation, deflections of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of an FA-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) are controlled for optimization of fuel flow. This presentation presents the design and integration of this peak-seeking controller on a modified NASA FA-18 airplane with research flight control computers. A research flight was performed to collect data to build a realistic model of the performance function and characterize measurement noise. This model was then implemented into a nonlinear six-degree-of-freedom FA-18 simulation along with the peak-seeking control algorithm. With the goal of eventual flight tests, the algorithm was first evaluated in the improved simulation environment. Results from the simulation predict good convergence on minimum fuel flow with a 2.5-percent reduction in fuel flow relative to the baseline trim of the aircraft.

peak-seeking↗