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NASA NTRS1974

Nonparametric maximum likelihood estimation of probability densities by penalty function methods

When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the nonparametric maximum likelihood procedure is undefined. A very general theory of maximum penalized likelihood estimation which should avoid many of these difficulties is presented. It is demonstrated that each reproducing kernel Hilbert space leads, in a very natural way, to a maximum penalized likelihood estimator and that a well-known class of reproducing kernel Hilbert spaces gives polynomial splines as the nonparametric maximum penalized likelihood estimates.

Demontricher, G. F.↗

NASA NTRS1976

On least-squares design of recursive digital filters

Time-domain methods for the design of recursive digital filters using a squared error criterion are compared with a frequency-domain technique. Levy's method, which has been used to estimate transfer functions of continuous-time systems is modified to obtain design equations for digital filters. A special case of Levy's method is shown to be essentially equivalent to the time-domain methods.

Shenoi, K.↗

NASA NTRS1976

Modal density function and number of propagating modes in ducts

The question of the number of propagating modes within a small range of mode cut off ratio was raised. The population density of modes were shown to be greatest near cut off and least for the well propagating modes. It was shown that modes of nearly the same cut off ratio behave nearly the same in a sound absorbing duct as well as in the way they propagate to the far. Handling all of the propagating modes individually, they can be grouped into several cut off ratio ranges. It is important to know the modal density function to estimate acoustic power distribution.

Rice, E. J.↗

NASA NTRS1979

Turbulent density fluctuations in a subsonic and transonic free jet using crossed-beam schlieren techniques

Scalar density fluctuations were measured nonintrusively in the shear layer of a 5.08-cm (2-in.) cold air jet using a crossed-beam schlieren method. Two statistics, covariance and three-dimensional spectrum function, were estimated for an exit Mach number range of 0.3 to 0.97. The density fluctuation intensity, integral scale, and eddy convection speed were calculated and compared to available data where possible. Spectra were found to change significantly in shape becoming less peaked between 3 and 9 jet diameters downstream from the orifice, but they consistently exhibited a -5/3 power law decay at 3, 6, and 9 diameters for frequencies above the peak.

Martin, R. A.↗

NASA NTRS1979

Aircraft control by propeller cyclic blades

A theory is developed for aircraft control obtained from the propeller forces and moments generated by blade angle variation during a blade revolution. The propeller blade is pitched harmonically one cycle per propeller revolution which results in vehicle control forces and moments, termed cyclic-control. Using a power series respresentation of an arbitrary function of cyclic-blade angle, cyclic-control theory is developed which leads to exact solutions in terms of derivatives of steady-state thrust and power with respect to blade angle. An alternative solution, when the cyclic-blade angle function is limited to a sinusoidal cycle, is in terms of Bessel functions. An estimate of non-steady azimuth angle change or lag is presented. Cyclic-control analysis applied to the counter-rotating propeller shows that control forces or moments can be uniquely isolated from each other. Thus the dual rotor, in hovering mode, has propulsion without rotor tilt or moments, or, when in propeller mode at the tail of an air ship or submarine, vehicle control with no vehicle movement. Control isolation is also attainable from three or more propellers in-line.

Deyoung, J.↗

NASA NTRS1982

Computing the Power-Density Spectrum for an Engineering Model

Computer program for calculating of power-density spectrum (PDS) from data base generated by Advanced Continuous Simulation Language (ACSL) uses algorithm that employs fast Fourier transform (FFT) to calculate PDS of variable. Accomplished by first estimating autocovariance function of variable and then taking FFT of smoothed autocovariance function to obtain PDS. Fast-Fourier-transform technique conserves computer resources.

Dunn, H. J.↗

NASA NTRS1981

JPL antenna technology development

Plans for evaluating, designing, fabricating, transporting and deploying cost effective and STS compatible offset wrap rib antennas up to 300 meters in diameter for mobile communications, Earth resources observation, and for the orbiting VLBI are reviewed. The JPL surface measurement system, intended for large mesh deployable antenna applications will be demonstrated and validated as part of the antenna ground based demonstration program. Results of the offset wrap rib deployable antenna technology development will include: (1) high confidence structural designs for antennas up to 100 meters in diameter; (2) high confidence estimates of functional performance and fabrication cost for a wide range of antenna sizes (up to 300 meters in diameter); (3) risk assessment for fabricating the large size antennas; and (4) 55 meter diameter flight quality hardware that can be cost effectively completed toto accommodate a flight experiment and/or application.

Freeland, R. E.↗

NASA NTRS1982

An IUE survey of the Hyades star cluster

To date 11 of the brightest X-Ray stars (F-K dwarfs) in the Hyades have been observed with the IUE satellite with the short wavelength spectrograph. The IUE results and the X-Ray observations from the Hyades survey with the Einstein Observatory were combined. The differential emission measure function was estimated for each of the 7 stars which showed evidence of emission lines. Constraints on stellar atmospheric parameters (chromospheric pressure, coronal temperature and filling factor were derived. The implications of these results in the context of loop models for the corona and transition region (TR) of these stars are discussed.

Zolcinski, M. C.↗

NASA NTRS1981

Recursive algorithms for two-dimensional smoothing using bicubic hermite polynomial

It is noted that in the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines gives an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. A derivation is presented here of quarter-plane filtering algorithms that provide smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure sheds light on specific problems encountered in two-dimensional filtering problems. What is more, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Because of certain approximations introduced in its derivation, this recursive processor becomes suboptimal.

Kim, C. S.↗

NASA NTRS1982

Theory of design using nonlinear transformations

This paper is presenting an overview of the theory of transformations from nonlinear systems to linear systems. Topics covered include (1) necessary and sufficient conditions for transformations to exist, (2) a method of constructing transformations (3) robustness in design (based on transformations theory) and Liapunov functions, (4) estimation theory, and (5) the relationship between transformation theory and 'nonlinear zeros'. Application of these results to automatic flight control is presented in another paper at this session.

Su, R.↗

NASA NTRS1984

LANDSAT-4 image data quality analysis

Reformatting software to handle LANDSAT 5 data in quadrant format was completed and tested. The sensor two-dimensional point spread function was estimated from scene data. Budget recalculations are discussed. Two publications done under this contract are named.

Anuta, P. E.↗

NASA NTRS1985

A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies

An approximation scheme is developed for the identification of hybrid systems describing the transverse vibrations of flexible beams with attached tip bodies. In particular, problems involving the estimation of functional parameters are considered. The identification problem is formulated as a least squares fit to data subject to the coupled system of partial and ordinary differential equations describing the transverse displacement of the beam and the motion of the tip bodies respectively. A cubic spline-based Galerkin method applied to the state equations in weak form and the discretization of the admissible parameter space yield a sequence of approximating finite dimensional identification problems. It is shown that each of the approximating problems admits a solution and that from the resulting sequence of optimal solutions a convergent subsequence can be extracted, the limit of which is a solution to the original identification problem. The approximating identification problems can be solved using standard techniques and readily available software.

Banks, H. T.↗

NASA NTRS1984

Observations and theory of the solar semidiurnal tide in the mesosphere of Venus

The 1978 Pioneer Venus mission, in addition to producing strong IR radiometer experiment evidence for the existence of a semidiurnal solar tide in the Venus mesosphere, has yielded radiative flux and cloud particle distribution data about the structure of solar heating and IR cooling which facilitate calculations of tidal forcing functions and estimates of radiative dissipation rates. It is presently shown that a physically reasonable mean flow can be found which leads to theoretically predicted tides that are in excellent agreement with those observed. The zonal mean flow obtained exhibits a maximum velocity of about 130 m/sec at 70 km altitude, decreasing to about zero at 88 km, together with a jet-like meridional structure that strongly deviates from solid body rotation.

Fels, S. B.↗

NASA NTRS1986

Computational methods for the identification of spatially varying stiffness and damping in beams

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Banks, H. T.↗

NASA NTRS1987

Monitoring the environment by remote sensing

Structural features of ecosystems, such as leaf area index, phytomass and canopy chemical contents, are beginning to be estimated from remotely sensed data. This development, in combination with ecological modeling, is permitting the estimation of functional features of ecosystems including primary productivity and nutrient cycling. Such techniques are also being applied to the problem of monitoring the effects of air or water pollutants on biota. Sensors that obtain data at a coarse spatial scale (1 km2 or more) are also permitting the observation of biospheric patterns at a large regional or global scale for the first time. When coupled with atmospheric measurements, field data and simulation models, such data may serve to address ecological processes, including pollution effects, at large regional or global scales.

Westman, Walter E.↗

NASA NTRS1988

Theoretical study of the nitrogen atom hyperfine coupling constant

The nitrogen-atom isotropic hyperfine coupling constant A(iso) is studied as a function of improvements in both the one-particle and n-particle basis sets. The study underscores the importance of diffuse basis functions. For example, the (9s 5p) primitive set of Huzinaga (1965) augmented with an even-tempered diffuse s function yields values for A(iso) that are virtually identical to an energy-optimized (23s 12p) even-tempered set. The A(iso) constant is found to converge relatively quickly with increasing l quantum numbers: d, f, and g functions are estimated to contribute 2.5 + or - 0.2, 0.4 + or - 0.1, and 0.05 + or - 0.05 MHz, respectively. Full CI calibration calculations indicate that very high levels of correlation treatment are required for quantitative results. In addition, a strong coupling is observed between the one-particle and n-particle requirements. The best result, 10.4 MHz, is in excellent agreement with the accurate experimental value of 10.4509 MHz.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1991

Comparison of laser transit anemometry data analysis techniques

Two techniques for the extraction of two-dimensional flow information from laser transit anemometry (LTA) data sets are presented and compared via a simulation study and experimental investigation. The methods are a probability density function (PDF) estimation technique and a marginal distribution analysis technique. The simulation study builds on the results of previous work and provides a quantification of the accuracy of both techniques for various LTA data acquisition scenarios. The experimental comparison consists of using an LTA system to survey the flow downstream of a turbulence generator in a small low-speed wind tunnel. The collected data sets are analyzed and compared.

Humphreys, William M., Jr.↗

NASA NTRS1988

On-orbit system parameter identification

Viewgraphs and discussion on on-orbit system parameter identification are included. Topics covered include: dynamic programming filter (DPF); cost function and estimator; frequency domain formulation structrual dynamic identification; and attributes of DPF.

Simonian, Stepan S.↗