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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Random search optimization based on genetic algorithm and discriminant function

The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.

Kiciman, M. O.↗
NASA NTRS1986

Inference of stress and texture from angular dependence of ultrasonic plate mode velocities

The theory for the angular dependence of the ultrasonic wave velocity in a symmetry plane of an orthorhombic, stressed material is presented. The two waves having polarizations in this plane are shown to have velocities which can be estimated from measurements of the SH sub 0 and S sub 0 guided modes of a thin plate: the relationship being exact for the SH sub 0 mode and requiring a 10% correction for the S sub 0 mode at long wavelength. It is then shown how stress and texture can be independently inferred from various features of the angular dependence of these two velocities. From the SH sub 0 data, the ability to determine the directions and differences in magnitudes of principal stresses is described and supported by experimental data on several materials. From a combination of the SH sub 0 and S sub 0 data, a procedure is proposed for determining the coefficients W sub 400, W sub 420 and W sub 440 of an expansion of the crystallite orientation distribution function in terms of generalized Legendre functions. Possible applications in process control are indicated.

Thompson, R. B.↗
NASA NTRS1998

A Solution to the Fundamental Linear Fractional Order Differential Equation

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Hartley, Tom T.↗
NASA NTRS1984

Generalization of the subsonic kernel function in the s-plane, with applications to flutter analysis

A generalized subsonic unsteady aerodynamic kernel function, valid for both growing and decaying oscillatory motions, is developed and applied in a modified flutter analysis computer program to solve the boundaries of constant damping ratio as well as the flutter boundary. Rates of change of damping ratios with respect to dynamic pressure near flutter are substantially lower from the generalized-kernel-function calculations than from the conventional velocity-damping (V-g) calculation. A rational function approximation for aerodynamic forces used in control theory for s-plane analysis gave rather good agreement with kernel-function results, except for strongly damped motion at combinations of high (subsonic) Mach number and reduced frequency.

Cunningham, H. J.↗
NASA NTRS2000

R-Function Relationships for Application in the Fractional Calculus

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Lorenzo, Carl F.↗
NASA NTRS2009

Modeling and Simulation of Variable Mass, Flexible Structures

The advent of the new Ares I launch vehicle has highlighted the need for advanced dynamic analysis tools for variable mass, flexible structures. This system is composed of interconnected flexible stages or components undergoing rapid mass depletion through the consumption of solid or liquid propellant. In addition to large rigid body configuration changes, the system simultaneously experiences elastic deformations. In most applications, the elastic deformations are compatible with linear strain-displacement relationships and are typically modeled using the assumed modes technique. The deformation of the system is approximated through the linear combination of the products of spatial shape functions and generalized time coordinates. Spatial shape functions are traditionally composed of normal mode shapes of the system or even constraint modes and static deformations derived from finite element models of the system. Equations of motion for systems undergoing coupled large rigid body motion and elastic deformation have previously been derived through a number of techniques [1]. However, in these derivations, the mode shapes or spatial shape functions of the system components were considered constant. But with the Ares I vehicle, the structural characteristics of the system are changing with the mass of the system. Previous approaches to solving this problem involve periodic updates to the spatial shape functions or interpolation between shape functions based on system mass or elapsed mission time. These solutions often introduce misleading or even unstable numerical transients into the system. Plus, interpolation on a shape function is not intuitive. This paper presents an approach in which the shape functions are held constant and operate on the changing mass and stiffness matrices of the vehicle components. Each vehicle stage or component finite element model is broken into dry structure and propellant models. A library of propellant models is used to describe the distribution of mass in the fuel tank or Solid Rocket Booster (SRB) case for various propellant levels. Based on the mass consumed by the liquid engine or SRB, the appropriate propellant model is coupled with the dry structure model for the stage. Then using vehicle configuration data, the integrated vehicle model is assembled and operated on by the constant system shape functions. The system mode shapes and frequencies can then be computed from the resulting generalized mass and stiffness matrices for that mass configuration. The rigid body mass properties of the vehicle are derived from the integrated vehicle model. The coupling terms between the vehicle rigid body motion and elastic deformation are also updated from the constant system shape functions and the integrated vehicle model. This approach was first used to analyze variable mass spinning beams and then prototyped into a generic dynamics simulation engine. The resulting code was tested against Crew Launch Vehicle (CLV-)class problems worked in the TREETOPS simulation package and by Wilson [2]. The Ares I System Integration Laboratory (SIL) is currently being developed at the Marshall Space Flight Center (MSFC) to test vehicle avionics hardware and software in a hardware-in-the-loop (HWIL) environment and certify that the integrated system is prepared for flight. The Ares I SIL utilizes the Ares Real-Time Environment for Modeling, Integration, and Simulation (ARTEMIS) tool to simulate the launch vehicle and stimulate avionics hardware. Due to the presence of vehicle control system filters and the thrust oscillation suppression system, which are tuned to the structural characteristics of the vehicle, ARTEMIS must incorporate accurate structural models of the Ares I launch vehicle. The ARTEMIS core dynamics simulation models the highly coupled nature of the vehicle flexible body dynamics, propellant slosh, and vehicle nozzle inertia effects combined with mass and flexible body properties that vary significant with time during the flight. All forces that act on the vehicle during flight must be simulated, including deflected engine thrust force, spatially distributed aerodynamic forces, gravity, and reaction control jet thrust forces. These forces are used to excite an integrated flexible vehicle, slosh, and nozzle dynamics model for the vehicle stack that simulates large rigid body translations and rotations along with small elastic deformations. Highly effective matrix math operations on a distributed, threaded high-performance simulation node allow ARTEMIS to retain up to 30 modes of flex for real-time simulation. Stage elements that separate from the stack during flight are propagated as independent rigid six degrees of freedom (6DOF) bodies. This paper will present the formulation of the resulting equations of motion, solutions to example problems, and describe the resulting dynamics simulation engine within ARTEMIS.

Tobbe, Patrick A.↗
NASA NTRS1984

Generic Karman-Rostovstev plate equations in an affine space

The Karman-Rostovstev plate equations are affinely transformed into equations that depend on the generic plate constants generalized rigidity, generalized extensional rigidity, and generalized Poisson ratio associated with the well-known linearized orthotropic plate/slab equations. Furthermore, since the generalized extensional rigidity is a function of generalized rigidity and generalized Poisson ratio only, with generalized Poisson ratio being a weak parameter, the only fundamental constant is generalized rigidity. This means that regardless of what analysis technique is used, the results can be cast in terms of only one strong material parameter (whose range is from zero to one). The affine stretching is performed on the dependent variables as well as the independent variables, so that the dependence of all quantities of interest on generalized rigidity and generalized Poisson ratio are easily calculated (e.g., even auxiliary quantities such as stress, strain, all weighted stress resultants, etc.). Some typical results (static side load response, collapse load limited by rib buckling) are presented by modifying an approximate technique due to Donnell (1976).

Brunelle, E. J.↗
NASA NTRS2012

New Vary-Chap Profile of the Topside Ionosphere Electron Density Distribution for use with the IRI Model and the GIRO Real-Time Data

A new Vary-Chap function is introduced for the empirical modeling of the electron density N(h) profile in the topside ionosphere that uses a shape function S(h) in the generalized Chapman function. The Vary-Chap profile extends the bottomside profile that is specified by the IRI model or measured by the Global Ionospheric Radio Observatory (GIRO) to the altitude of the ISIS-2 satellite. Some 80,000 topside profiles, measured by the topside sounder on the ISIS-2 satellite were analyzed, and the shape function S(h) was calculated for each profile. A parameterized function S*(h), composed of two sub-functions S1(h) and S2(h), is fitted to the measured S(h) profile using three free parameters. At altitudes just above the F2 layer peak height hmF2, the shape function S1 controls S(h), and at greater altitudes S2 controls S(h). The height of the intersection of S1 and S2 is defined as the transition height h(sub T) indicating the transition from an O(+) to an H(+)-dominated profile shape. The observed transition heights range from approx.500 km to 800 km.

Nsumei, Patrick↗
NASA NTRSDate not supplied

A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications

Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.

GC99↗
NASA NTRS2010

Uterine Contraction Modeling and Simulation

Building a training system for medical personnel to properly interpret fetal heart rate tracing requires developing accurate models that can relate various signal patterns to certain pathologies. In addition to modeling the fetal heart rate signal itself, the change of uterine pressure that bears strong relation to fetal heart rate and provides indications of maternal and fetal status should also be considered. In this work, we have developed a group of parametric models to simulate uterine contractions during labor and delivery. Through analysis of real patient records, we propose to model uterine contraction signals by three major components: regular contractions, impulsive noise caused by fetal movements, and low amplitude noise invoked by maternal breathing and measuring apparatus. The regular contractions are modeled by an asymmetric generalized Gaussian function and least squares estimation is used to compute the parameter values of the asymmetric generalized Gaussian function based on uterine contractions of real patients. Regular contractions are detected based on thresholding and derivative analysis of uterine contractions. Impulsive noise caused by fetal movements and low amplitude noise by maternal breathing and measuring apparatus are modeled by rational polynomial functions and Perlin noise, respectively. Experiment results show the synthesized uterine contractions can mimic the real uterine contractions realistically, demonstrating the effectiveness of the proposed algorithm.

Liu, Miao↗
NASA NTRS1981

Generic functional requirements for a NASA general-purpose data base management system

Generic functional requirements for a general-purpose, multi-mission data base management system (DBMS) for application to remotely sensed scientific data bases are detailed. The motivation for utilizing DBMS technology in this environment is explained. The major requirements include: (1) a DBMS for scientific observational data; (2) a multi-mission capability; (3) user-friendly; (4) extensive and integrated information about data; (5) robust languages for defining data structures and formats; (6) scientific data types and structures; (7) flexible physical access mechanisms; (8) ways of representing spatial relationships; (9) a high level nonprocedural interactive query and data manipulation language; (10) data base maintenance utilities; (11) high rate input/output and large data volume storage; and adaptability to a distributed data base and/or data base machine configuration. Detailed functions are specified in a top-down hierarchic fashion. Implementation, performance, and support requirements are also given.

Lohman, G. M.↗
NASA NTRS1975

Aerodynamic sound generation due to the interaction of an unsteady wake with a rigid surface

Some aspects of sound generation by the interaction between a wedge and the wake of a circular cylinder in a uniform incompressible stream are studied experimentally. There is a minimum separation distance between the cylinder and the wedge when a tone is first generated. As the separation distance increases beyond the minimum, the frequency increases and asymptotically approaches the frequency normally present in the free wake. The Strouhal number defined as the ratio fd/U where f is the frequency, d is the cylinder diameter and U the free-stream speed is found to be in general a function of the Reynolds number (based on d) and h/d, where h is the separation distance. The minimum distance is in general a function of the Reynolds number. Flow visualization studies show that considerable differences exist between the flow below the minimum separation distance and just above it.

Smith, C. A.↗
NASA NTRS1990

A characterization of associativity

A necessary and sufficient condition for associativity of a function is given, in terms of a particular relation being a function. The concept of an associative function is generalized to the concept of a function being asssociative relative to a sequence and a characterization of such relative associativity is also given. These two characteristics are applied to the problem of proving the associativity, or relative associativity, of a function.

Charlesworth, Arthur↗
NASA NTRS1990

Identification of aerodynamic models for maneuvering aircraft

Due to the requirement of increased performance and maneuverability, the flight envelope of a modern fighter is frequently extended to the high angle-of-attack regime. Vehicles maneuvering in this regime are subjected to nonlinear aerodynamic loads. The nonlinearities are due mainly to three-dimensional separated flow and concentrated vortex flow that occur at large angles of attack. Accurate prediction of these nonlinear airloads is of great importance in the analysis of a vehicle's flight motion and in the design of its flight control system. A satisfactory evaluation of the performance envelope of the aircraft may require a large number of coupled computations, one for each change in initial conditions. To avoid the disadvantage of solving the coupled flow-field equations and aircraft's motion equations, an alternate approach is to use a mathematical modeling to describe the steady and unsteady aerodynamics for the aircraft equations of motion. Aerodynamic forces and moments acting on a rapidly maneuvering aircraft are, in general, nonlinear functions of motion variables, their time rate of change, and the history of maneuvering. A numerical method was developed to analyze the nonlinear and time-dependent aerodynamic response to establish the generalized indicial function in terms of motion variables and their time rates of change.

Chin, Suei↗
NASA NTRS1999

Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes

The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various nonhomogeneity ratios, crack lengths. crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

Shbeeb, N.↗
NASA NTRS1988

The topology of fractal universes

It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.

Hamilton, A. J. S.↗
NASA NTRS1972

Some efficient methods for obtaining infinite series solutions of n-th order linear ordinary differential equations

The use of the theta-operator method and generalized hypergeometric functions in obtaining solutions to nth-order linear ordinary differential equations is explained. For completeness, the analysis of the differential equation to determine whether the point of expansion is an ordinary point or a regular singular point is included. The superiority of the two methods shown over the standard method is demonstrated by using all three of the methods to work out several examples. Also included is a compendium of formulae and properties of the theta operator and generalized hypergeometric functions which is complete enough to make the report self-contained.

Allen, G.↗