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At least 289 records · Page 16

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NASA NTRS1983

A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. The theorem proved here allows one to obtain the structure function (covariances of the nth differences) of such a process in terms of the differences of a single function of one time variable. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.

Greenhall, C. A.↗

NASA NTRS1984

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗

NASA NTRS1984

On Choosing Between Two Probabilistic Choice Sub-models in a Dynamic Multitask Environment

An independent random utility model based on Thurstone's Theory of Comparative Judgment and a constant utility model based on Luce's Choice Axiom are reviewed in detail. Predictions from the two models are shown to be equivalent under certain restrictions on the distribution of the underlying random process. Each model is applied as a stochastic choice submodel in a dynamic, multitask, environment. Resulting choice probabilities are nearly identical, indicating that, despite their conceptual differences, neither model may be preferred over the other based solely on its predictive capability.

Soulsby, E. P.↗

NASA NTRS1984

Kalman filter modeling

The formulation of appropriate state-space models for Kalman filtering applications is studied. The so-called model is completely specified by four matrix parameters and the initial conditions of the recursive equations. Once these are determined, the die is cast, and the way in which the measurements are weighted is determined foreverafter. Thus, finding a model that fits the physical situation at hand is all important. Also, it is often the most difficult aspect of designing a Kalman filter. Formulation of discrete state models from the spectral density and ARMA random process descriptions is discussed. Finally, it is pointed out that many common processes encountered in applied work (such as band-limited white noise) simply do not lend themselves very well to Kalman filter modeling.

Brown, R. G.↗

NASA NTRS1985

Observation of arrival times of EAS with energies or = 6 x 10 (14) eV

The Earth's atmosphere is continually being bombarded by primary cosmic ray particles which are generally believed to be high-energy nuclei. The fact that the majority of cosmic ray primaries are charged particles and that space is permeated with random magnetic fields, means that the particles do not travel in straight lines. The arrival time distribution of EAS may also transfer some information about the primary particles. Actually, if the particles come to our Earth in a completely random process, the arrival time distribution of pairs of successive particles should fit an exponential law. The work reported here was arried out at Sydney University from May 1982 to January 1983. All the data are used to plot the arrival-time distribution of the events, that is, the distribution of time-separation between consecutive events on a 1 minute bin size. During this period more than 2300 showers were recorded. The results are discussed and compared with that of some other experiments.

Sun, L.↗

NASA NTRS1986

Nonlinear response - A time domain approach

The present paper reviews the basic concepts of nonlinear response of panels to surface flow and acoustic pressures, simulation of random processes, time domain solutions and the Monte Carlo Method. Applications of this procedure to the orbit-on-demand space vehicles, acoustic fatigue and composite materials are discussed. Numerical examples are included for a variety of nonlinear problems to illustrate the applicability of this method.

Vaicaitis, R.↗

NASA NTRS1986

Noise transmission into enclosures

This paper describes analytical and experimental studies of noise transmission into rectangular and cylindrical enclosures. The solutions of the governing acoustic-structural equations are developed by modal decomposition of structural vibrations and the interior acoustic field. Particular attention is directed toward the low frequencies, that is, frequencies up through the first few structural and cavity resonant modes. The structural vibrations are driven by the external acoustic and/or mechanical point loads which are taken to be Gaussian stationary random processes. The structural models include rectangular panels and cylindrical shells.

Vaicaitis, R.↗

NASA NTRS1987

Acoustic fatigue - A Monte Carlo approach

The present paper reviews the basic concepts of nonlinear structural response to surface flow and acoustic pressure inputs. A time domain solution and the Monte Carlo method are utilized to estimate the required statistics of the nonlinear response. Simulation procedures of multi-dimensional and multi-variate random processes are discussed. Application of these procedures to acoustic fatigue of flight structures are considered. Numerical examples are included to illustrate the applicability of this method for the solution of nonlinear problems.

Vaicaitis, R.↗

NASA NTRS1987

Irregular and diurnal variability in asynoptic measurements of stratospheric trace species

The consequences of irregular and diurnal variability on the interpretation of asynoptic measurements of stratospheric trace species are explored. In particular, the fidelity with which the continuous behavior may be recovered from discrete asynoptic measurements is examined. Dynamically created tracer variability in the form of an advected space-time random process is discussed. Diagnostics such as power spectra and time-mean fields are derived asynoptically and compared with the true behavior. Diurnal variations of a photochemically active species are considered, describing variability in terms of a solar waveform which propagates through a latitudinal envelope. Several diagnostics of the behavior are derived asynoptically and compared with the true variability.

Salby, Murry L.↗

NASA NTRS1988

Karhunen-Loeve expansion of Burgers' model of turbulence

The properties of the Karhunen-Loeve expansion of a strongly inhomogeneous random process are examined with emphasis on applications to turbulent flow fields. The ability of the KL expansion to represent functions that have both slow and rapid variations in a relatively small number of expansion terms is tested on a one-dimensional model based on the forced Burgers' equation. The rate of the convergence of the expansion is evaluated, and its dependence on the Reynolds number is determined. It is shown that the KL eigenfunctions possess wall boundary layers attached to outer structures that are independent of the Reynolds number (at high Reynolds numbers). It is also shown that the spectrum of eigenvalues is broad at large Reynolds numbers, requiring many terms to represent higher-order derivatives of the function.

Chambers, D. H.↗

NASA NTRS1988

Modelling the SIR-B image response to partially coherent seas

A mathematical model of transient seas modulated by coherent swells is developed as a Rayleigh-Poisson random process subject to deterministic correlations of scattering sites, as they appear in a time window defined by a SAR's range-Doppler measurements of the surface coordinates. This model of SAR response to sea surface dynamics is discussed as a Fourier domain predictor/corrector of a dynamic motion blur.

Tilley, D. G.↗

NASA NTRS1989

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed.

Noll, Thomas E.↗

NASA NTRS1988

Sampling inhomogeneous turbulent fields

The reconstruction of an inhomogeneous random process from a finite number of discrete samples can be performed in terms of the Karhunen-Loeve (KL) expansion for that process. The n(th) eigenfunction has n - 1 zero crossings which are the sampling points for the inhomogeneous process. The rapid variation of the KL eigenfunctions makes it unnecessary to have a high density of sampling (or grid points) near the wall. However, this result should not be construed to indicate that with spectral simulations significantly fewer grid points are required with the KL expansion as compared to other orthogonal expansions. Moin and Moser (1989) have shown that the advantage of the KL expansion over Chebychev expansion rapidly diminishes when high percentage (say 90 percent) energy recovery is demanded.

Adrian, R. J.↗

NASA NTRS1990

Aeroservoelasticity

Accomplishments and current research projects along four main thrusts in aeroservoelasticity at the NASA Langley Research Center are described. One activity focuses on enhancing the modelling and the analysis procedures to accurately predict aeroservoelastic interactions. In the area of modelling, improvements to the minimum-state method of approximating unsteady aerodynamics are shown to provide precise, low-order models for design and simulation tasks. Recent extensions in aerodynamic correction factor methodology are also described. With respect to analysis procedures, the paper reviews novel enhancements to Matched Filter Theory and Random Process Theory for predicting the critical gust profile and the associated time-correlated gust loads for structural design considerations. In another activity, two research projects leading towards improved design capability are summarized. The first program involves the development of an integrated structure/control design capability; the second provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. Experimental validation of new theoretical developments is the third activity. As such, a short description of the Active Flexible Wing Project is presented, and recent wind-tunnel test accomplishments are summarized. Finally within the area of application, a study performed to assess the state-of-the-art of aeroelastic and aeroservoelastic analysis and design technology with respect to hot, hypersonic flight vehicles is reviewed.

Noll, Thomas E.↗

NASA NTRS1990

Aeroservoelasticity

The paper describes recent accomplishments and current research projects along four main thrusts in aeroservoelasticity at NASA Langley. One activity focuses on enhancing the modeling and analysis procedures to accurately predict aeroservoelastic interactions. Improvements to the minimum-state method of approximating unsteady aerodynamics are shown to provide precise low-order models for design and simulation tasks. Recent extensions in aerodynamic correction-factor methodology are also described. With respect to analysis procedures, the paper reviews novel enhancements to matched filter theory and random process theory for predicting the critical gust profile and the associated time-correlated gust loads for structural design considerations. Two research projects leading towards improved design capability are also summarized: (1) an integrated structure/control design capability and (2) procedures for obtaining low-order robust digital control laws for aeroelastic applications.

Noll, Thomas E.↗

NASA NTRS1990

Stationary and nonstationary random vibrations of laminated composite plates via a higher order theory

Higher order shear deformation theory is utilized to study he weakly stationary and nonstationary random vibrations of cross-ply laminated plates. Normal mode method, in conjunction with the biorthogonality condition, for the nonsymmetric differential equations is applied. Detailed derivation is given for the governing equations, biorthogonality condition, the generalized mass and the generalized forces. Results are listed for a plate which is simply supported at all the edges, and subjected to a point load which is either timewise stationary or nonstationary random process.

Elishakoff, Isaac↗

NASA NTRS1989

Recent activities within the aeroservoelasticity branch at the NASA Langley Research Center

Noll, Thomas↗

NASA NTRS1990

Noise power spectral density of the Sundstrand QA-2000 accelerometer

There are no good data on low frequency (less than 0.1 Hz) power spectral density (PSD) for the Q-Flex accelerometer. However, some preliminary stability measurements were made over periods of 12 to 24 hours and demonstrated stability less than 0.5 micro-g over greater than 12 hours. The test data appear to contain significant contributions from temperature variations at that level, so the true sensor contribution may be less than that. If what was seen could be construed as a true random process, it would correspond to about 0.1 micro-g rms over a bandwidth from 10(exp -5) Hz to about 1 Hz. Other studies of low frequency PSD in flexure accelerometers have indicated that material aging effects tend to approximate a first order Markhov process. If we combine such a model with the spectrum obtained at higher frequencies, it suggests the spectrum shown here as a conservative estimate of Q-Flex noise performance.

Peters, Rex↗