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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗
NASA NTRS1955

From linear mechanics to nonlinear mechanics

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

RESEARCH TECHNIQUE, MATHEMATICS↗
NASA NTRS1991

Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.

Rao, S. S.↗
NASA NTRS1972

Dynamic response of a plane-symmetrical exothermic reaction center.

?sger,An analysis of the dynamic behavior of an idealized, plane-symmetrical exothermic reaction center is presented. The conservation equations for the reaction center are combined and yield a single integral equation expressing a nonlinear transfer function of the system for which the input is provided by a given time profile of the heat released per unit mass while the output gives the pressure pulse it generates under the restriction of plane-symmetrical motion. The solution is governed by a Daumk]hler number. For a given form of the exothermic power pulse profile, the dynamic behavior of the system is completely specified in terms of only this Daumk]hler number and the heat of reaction per unit mass of the combustible medium. Specific solutions are worked out for a set of typical elementary power pulse profiles, and the practical significance of the results is illustrated by their application to the problem of transition to detonation in an explosive gas.

Meyer, J. W.↗
NASA NTRS1972

Effects of propellant composition variables on acceleration-induced burning-rate augmentation of solid propellants

This work was conducted to define further the effects of propellant composition variables on the acceleration-induced burning rate augmentation of solid propellants. The rate augmentation at a given acceleration was found to be a nonlinear inverse function of the reference burning rate and not controlled by binder or catalyst type at a given reference rate. A nonaluminized propellant and a low rate double-base propellant exhibited strong transient rate augmentation due to surface pitting resulting from the retention of hot particles on the propellant surface.

Northam, G. B.↗
NASA NTRS1973

Effects of composition on acceleration induced burning-rate augmentation.

The objective of this work was to better define the effects of propellant composition variables on the acceleration induced burning-rate augmentation of solid propellants. The rate augmentation of an aluminized propellant at a given acceleration level was found to be a nonlinear inverse function of the reference or static burning rate and not controlled by binder or catalyst type at a given reference rate. A nonaluminized and a low rate double-base propellant exhibited strong transient rate augmentation due to surface pitting resulting from the retention of hot particles on the propellant surface.

Northam, G. B.↗
NASA NTRS1973

Transmission of radiometer data from the Synchronous Meteorological Satellite

The Synchronous Meteorological Satellite uses a spin scanner radiometer which generates eight visual signals and two infrared signals. These signals are multiplexed and converted into a 28-Mbps data stream. This signal is transmitted to ground by quadriphase modulation at 1686.1 MHz. On the ground, the digital signal is reconstructed to an analog signal. To conserve bandwidth, an analog-to-digital converter with a nonlinear transfer function was used for the visual signals. The size of the quantization step was made proportional to the noise output of the scanner photomultiplier tube which increases as the square root of incident light. The radiometer data transmission link was simulated on a digital computer to determine the transfer function. Some results of the simulation are shown.

Davies, R. S.↗
NASA NTRS1976

Optimization of multi-constrained structures based on optimality criteria

A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.

Rizzi, P.↗
NASA NTRS1979

Parameter estimation in X-ray astronomy using maximum likelihood

Methods of estimation of parameter values and confidence regions by maximum likelihood and Fisher efficient scores starting from Poisson probabilities are developed for the nonlinear spectral functions commonly encountered in X-ray astronomy. It is argued that these methods offer significant advantages over the commonly used alternatives called minimum chi-squared because they rely on less pervasive statistical approximations and so may be expected to remain valid for data of poorer quality. Extensive numerical simulations of the maximum likelihood method are reported which verify that the best-fit parameter value and confidence region calculations are correct over a wide range of input spectra.

Wachter, K.↗
NASA NTRS1980

In-flight calibration of the fine pointing Sun sensor on the solar maximum mission

The attitude control objectives of solar maximum mission are to point the boresight of the payload fine pointing sun sensor (FPSS) to any point within 30 arc-minutes of the Sun's center with an accuracy of 5 arc-seconds (3 sigma, pitch and yaw) and a jitter of less than 3 arc-seconds (3 sigma). To meet these stringent accuracy requirements, a procedure was developed for in-flight calibration of the FPSS. The spacecraft was maneuvered using FPSS offset commands to position the Sun at different points within the FPSS field of view. The coefficients of the FPSS digital to analog nonlinear transfer function were determined by minimizing the residuals between the pitch and yaw angles computed from the FPSS measurements and the corresponding reference angles obtained from inertial reference unit measurements. The actual in-flight calibration and the calibration algorithm are discussed.

Gambardella, P. J.↗
NASA NTRS1982

The stability of quasi-geostrophic fields induced by potential vorticity sources

A determination of the conditions leading to instabilities which grow in place in quasi-geostrophic fields induced by localized potential vorticity sources is presented. The analysis considers a quasi-geostrophic barotropic flow in a horizontally open domain, and a nondimensional quasi-geostrophic vorticity equation is defined which governs the deviation stream function. Weak forcing is considered, and it is shown that the field induced by the topography is stable while the field induced by the potential vorticity source can be unstable. The growth rate is exponential and a function of nonlinearity and friction, which, if absent, indicates an unstable flowfield. The instability is shown to be capable of changing the flowfield from one quasi-steady state to another, with energy extraction occurring at the source

Merkine, L.-O.↗
NASA NTRS1983

Torque Compensator for Mirror Mountings

Device nulls flexural distributions of pivotal torques. Magnetic compensator for flexing pivot torque consists of opposing fixed and movable magnet bars. Magnetic torque varies nonlinearly as function of angle of tilt of movable bar. Positions of fixed magnets changed to improve magnetic torque linearity.

Howe, S. D.↗
NASA NTRS1983

A theory of rotating stall of multistage axial compressors. III - Limit cycles

A theory of rotating stall, based on single parameters for blade-passage lag and external-flow lag and a given compressor characteristic yields limit cycles in velocity space. These limit cycles are governed by Lienard's equation with the characteristic playing the role of nonlinear damping function. Cyclic integrals of the solution determine stall propagation speed and the effect of rotating stall on average performance. Solution with various line-segment characteristics and various throttle settings are found and discussed. There is generally a limiting flow coefficient beyond which no solution is possible; this probably represents stall recovery. This recovery point is independent of internal compressor lag, but does depend on external lags and on the height-to-width ratio of the diagram. Tall diagrams and small external lags (inlet and diffusor) favor recovery. Suggestions for future theoretical and experimental research are discussed.

Moore, F. K.↗
NASA NTRS1984

A shock-capturing finite element method

Finite element methods are developed for a one-dimensional singular perturbation problem involving a nonlinear flux function. In the limit of vanishing dissipation, the numerical flux is found to be almost identical to that due to Engquist and Osher, the only difference being in the treatment of transonic compression. This facilitates sharper resolution of stationary shocks, but is accompanied by loss of smoothness and monotonicity.

Hughes, T. J. R.↗
NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗
NASA NTRS1986

Bifurcations in unsteady aerodynamics

Nonlinear algebraic functional expansions are used to create a form for the unsteady aerodynamic response that is consistent with solutions of the time dependent Navier-Stokes equations. An enumeration of means of invalidating Frechet differentiability of the aerodynamic response, one of which is aerodynamic bifurcation, is proposed as a way of classifying steady and unsteady aerodynamic phenomena that are important in flight dynamics applications. Accomodating bifurcation phenomena involving time dependent equilibrium states within a mathematical model of the aerodynamic response raises an issue of memory effects that becomes more important with each successive bifurcation.

Tobak, M.↗
NASA NTRS1986

Analytical formulation of orbiter-payload coupled by trunnion joints with Coulomb friction

An orbiter and its payload substructure are linked together by five trunnion joints which have thirty degrees-of-freedom. Geometric compatibility conditions require fourteen of the interface physical coordinates of the orbiter and payload to be equal to each other and the remaining sixteen are free to have relative motions under Coulomb friction. The component modes synthesis method using fourteen inertia relief attachment modes for the formulation of the coupled system is presented. The exact nonlinear friction function is derived based on the characteristics of the joints. Formulation is applicable to an orbiter that carries any number of payload substructures.

Liu, Frank C.↗