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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Kullback-Leibler information function and the sequential selection of experiments to discriminate among several linear models

A sequential adaptive experimental design procedure for a related problem is studied. It is assumed that a finite set of potential linear models relating certain controlled variables to an observed variable is postulated, and that exactly one of these models is correct. The problem is to sequentially design most informative experiments so that the correct model equation can be determined with as little experimentation as possible. Discussion includes: structure of the linear models; prerequisite distribution theory; entropy functions and the Kullback-Leibler information function; the sequential decision procedure; and computer simulation results. An example of application is given.

Sidik, S. M.↗
NASA NTRS1974

Quasi-linear theory via the cumulant expansion approach

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

Jones, F. C.↗
NASA NTRS1974

Evaluation of magnetic refocusing in linear-beam microwave tubes

Magnetic field configurations in which the axial component of the field decays linearly to a constant plateau field are evaluated for use in refocusing the output beam of linear beam microwave tubes. The slope of the decay and the value of the plateau field are parameters in this study. A uniform beam with a space charge force only in the radial direction is assumed, and the electron trajectories are computed for various classes. For a given magnetic configuration (slope and plateau value) the plateau length is calculated for a specified class and the rms deviation of the output angles for all classes is computed at the end of this plateau length. A minimum condition for a refocused beam is defined to be one in which the rms value of the output angles is less than the rms input. Many of the configurations satisfied this criteria and successfully reduced the rms value by half.

Stankiewicz, N.↗
NASA NTRS1974

Optimal compensator structure for linear time-invariant plant with inaccessible states

The problem is considered of designing an optimal linear time-invariant dynamic compensator for the regulation of an n-th order linear time-invariant plant with m independent outputs. The initial plant state is characterized by its first and second moments, and the cost is usual quadratic infinite-time penalty on the state and control, averaged over the initial plant and compensator states. The compensator is based on a minimal-order Luenberger observer and consequently has fixed dimension n-m. Necessary and sufficient conditions are derived for optimality of the compensator gains. The optimal compensator is shown to be unique if the plant has a particular canonical form, and, in general, for any arbitrary plant, the class of all optimal compensators is precisely determined.

Blanvillain, P. J. P.↗
NASA NTRS1974

Optimal output feedback control of linear systems in presence of forcing and measurement noise

The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.

Joshi, S. M.↗
NASA NTRS1973

Deformation and burst of a liquid droplet freely suspended in a linear shear field

A theoretical method is presented for predicting the deformation and the conditions for breakup of a liquid droplet freely suspended in a general linear shear field. This is achieved by expanding the solution to the creeping-flow equations in powers of the deformation parameter epsilon and using linear stability theory to determine the onset of bursting. When compared with numerical solutions and with the available experimental data, the theoretical results are generally found to be of acceptable accuracy although, in some cases, the agreement is only qualitative.

Barthes-Biesel, D.↗
NASA NTRS1974

Viscous-fluid reaction to a torsionally oscillating spheroid Linearized steady-state weak-separation solution

For both the linearized prolate and oblate problems, perturbation series for all orders of eccentricity are obtained. The 'weak separation' method of solving partial-differential-equation boundary-value problems assumes that each linearly independent solution is a sum of products of single-variable functions. The method is applied to a hierarchy of partial differential equations. The weak-separation solutions are constructed by generalizing only the Bessel functions of the homogeneous solution.

Tompkins, D. R., Jr.↗
NASA NTRS1974

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

Michalopoulos, C. D.↗
NASA NTRS1974

A stable, linear frequency-modulated oscillator, part 1

The development of a push-pull frequency-modulated oscillator employing field-effect transistors is described. The advantages of field-effect transistors for use in a frequency-stable oscillator are presented. Linearization of the frequency deviation was accomplished by utilizing the square-law characteristic of an FET used as a modulating amplifier. The push-pull oscillator model produced a linear frequency deviation of more than 10 MHz at a center frequency of approximately 100 MHz. Output power is within 0.6 db of a nominal +8.5 dBm over the desired frequency range, and the modulation bandwidth is dc to 10 MHz. Frequency variation with temperature after compensation with a negative-temperature-coefficient capacitor is within + or - 0.05% from 0 to 60 C.

Honnell, M. A.↗
NASA NTRS1973

A linear stochastic model of the human operator

A linear stochastic model of the human operator is developed and applied to the problem of piloted control of an aircraft. The pilot and aircraft are modeled as linear time-invariant systems containing both process and measurement noise. The loop closure by the pilot is determined by formulating the problem as an optimal stochastic control problem. The solution to the optimal control problem yields not only the pilot's optimal control output which he uses to control the vehicle, but also the optimal combination of his observations of the vehicle states upon which the pilot bases his control. A method is presented so that, using experimental pilot vehicle data, the cost functional which is minimized in the optimal control problem will be numerically equal to the pilot rating that the pilot would associate with the given vehicle and task.

Durrett, J. C.↗
NASA NTRS1975

Digital program for solving the linear stochastic optimal control and estimation problem

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

Geyser, L. C.↗
NASA NTRS1975

LFSPMC: Linear feature selection program using the probability of misclassification

The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.

Guseman, L. F., Jr.↗
NASA NTRS1975

A counter example in linear feature selection theory

The linear feature selection problem in multi-class pattern recognition is described as that of linearly transforming statistical information from n-dimensional (real Euclidean) space into k-dimensional space, while requiring that average interclass divergence in the transformed space decrease as little as possible. Divergence is the expected interclass divergence derived from Hajek two-class divergence; it is known that there always exists a k x n matrix B such that the transformation determined by B maximizes the divergence in k-dimensional space. It is known that, if Q is any k x k invertible matrix, and B is as defined above, then QB again maximizes the divergence in k-space. It is shown that the converse of this result is false: two matrices exist, B sub 1 and B sub 2, each of which maximizes transformed divergence, which are not related in the fashion B sub 2 = QB sub 1 for any k x k matrix Q.

Brown, D. R.↗
NASA NTRS1975

Investigation of relationships between linears, total and hazy areas, and petroleum production in the Williston Basin: An ERTS approach

The author has identified the following significant results. ERTS-1 imagery in a variety of formats was used to locate linear, tonal, and hazy features and to relate them to areas of hydrocarbon production in the Williston Basin of North Dakota, eastern Montana, and northern South Dakota. Derivative maps of rectilinear, curvilinear, tonal, and hazy features were made using standard laboratory techniques. Mapping of rectilinears on both bands 5 and 7 over the entire region indicated the presence of a northeast-southwest and a northwest-southeast regional trend which is indicative of the bedrock fracture pattern in the basin. Curved lines generally bound areas of unique tone, maps of tonal patterns repeat many of the boundaries seen on curvilinear maps. Tones were best analyzed on spring and fall imagery in the Williston Basin. It is postulated that hazy areas are caused by atmospheric phenomena. The ability to use ERTS imagery as an exploration tool was examined where petroleum and gas are presently produced (Bottineau Field, Nesson and Antelope anticlines, Redwing Creek, and Cedar Creek anticline). It is determined that some tonal and linear features coincide with location of present production in Redwing and Cedar Creeks. In the remaining cases, targets could not be sufficiently well defined to justify this method.

Erickson, J. M.↗
NASA NTRS1975

Modulation linearization of a frequency-modulated voltage controlled oscillator, part 3

An analysis is presented for the voltage versus frequency characteristics of a varactor modulated VHF voltage controlled oscillator in which the frequency deviation is linearized by using the nonlinear characteristics of a field effect transistor as a signal amplifier. The equations developed are used to calculate the oscillator output frequency in terms of pertinent circuit parameters. It is shown that the nonlinearity exponent of the FET has a pronounced influence on frequency deviation linearity, whereas the junction exponent of the varactor controls total frequency deviation for a given input signal. A design example for a 250 MHz frequency modulated oscillator is presented.

Honnell, M. A.↗
NASA NTRS1974

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Yu, Y.-Y.↗
NASA NTRS1975

Application of visible linear array technology to earth observation sensors

The present paper identifies the systems engineering aspects of applying solid-state technology to earth observations applications being traditionally performed by point (or multiple-point) detector line scanned mechanisms. It is shown that the translation from a basically serial data flow point-detector mechanically-scanned sensor to a solid state highly parallel linear-array pushbroom sensor results in minimizing mechanical complexity and maximizing electronics complexity, with increased demands upon optical performance in some applications. Technical aspects relevant to highly parallel photodiode linear-array pushbroom applications are discussed. Examples of systems engineering applications are provided.

Noll, R. E.↗
NASA NTRS1975

Linear polarization variations modulo 5.6 days in HDE 226868

Results are reported for observations of variations in the linear polarization in HDE 226868 (the optical counterpart of Cyg X-1) made with a photoelastic polarimeter and a U-filter. The UV linear-polarization variations, as folded on the 5.6-day orbital period, are found to have amplitudes of 0.25% and position-angle changes of 2.7 deg. These results are shown to be consistent with the geometry and phasing required by the model of the binary system.

Nolt, I. G.↗