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At least 37 records · Page 2

Phasing of a space based segmented submillimeter wavelength telescope using focal plane measurements

As part of a technology development program for realizing a space based submillimeter telescope, two different approaches to the absolute phasing of a segmented primary mirror using focal plane measurements have been implemented for feasibility. The method of optimization by simulated annealing evaluates the image quality of a point spread function after all the telescope segments have been randomly moved. It accepts each iteration which improves the image quality, as well as a random number of iterations which do not, thus keeping the Strehl in the initialization procedure from falling into local maxima. Methods for determining the annealing schedule, and the step size for random segment movements are presented and discussed. Using phase diversity and a model for the telescope imaging system, a nonlinear least squares algorithm has also been implemented which parameterizes each of the segment actuator movements. Using multiple out of focus images, the segment actuator positions are estimated using an iterative procedure. Nonlinear least squares, although computationally intensive, offers a large savings in the actuator movements over simulated annealing and pairwise phasing methods for large numbers of segments. These algorithms have been integrated into a general simulation program which models the behavior of the telescope under anticipated space conditions.

Levine, B. M.↗

Analysis of pressure-broadened ozone spectra in the 3 micron region

The Molecular Spectroscopy Lab at NASA-Langley has been involved in a long term effort to carefully characterize the infrared spectra of small molecules of atmospheric interest, including methane, water vapor, ozone, and their isotopic counterparts. High resolution gas phase infrared spectra are obtained using both a tunable diode laser system, and the McMath Fourier transform spectrometer at the Kitt Peak Solar Observatory. Spectra are obtained at various pressures and temperatures for pure gas samples, and for samples containing mixtures of the species of interest in nitrogen, oxygen, or air. From these spectra, using a nonlinear least squares fitting technique, spectral parameters of position, intensity, and half-width were determined for varying laboratory conditions that approximate atmospheric conditions experienced in remote sensing situations. These parameters are of interest in theoretical studies of these species, as well as in allowing more accurate interpretation of remote sensing data. The current work involves the analysis of a series of McMath FTIR spectra of ozone broadened by mixing with air, nitrogen, or oxygen. Each spectrum covers the region from 2396 to 4057/cm. Each vibrational band is analyzed by first diving its region into small intervals containing a few well isolated absorption lines of reasonable intensity. Each of these small intervals is fit by multiple iterations of the nonlinear least square program until residuals are minimized to a reasonable value which corresponds to the noise level of the measured spectrum. Intervals for the 3 nu(sub 3) ozone band in the region from 3000 to 3060 wavenumbers are being examined.

Prochaska, Eleanor S.↗

Stratospheric HNO3 quantification from line-by-line nonlinear least-squares analysis of high-resolution balloon-borne solar absorption spectra in the 870/cm region

Line parameters for the nu(5) and 2nu(9) bands and associated hot bands of HNO3 have been calculated and compared with laboratory spectra, and the results are presented. Spectral intervals near 870/cm for which best agreement was obtained are used to quantitatively analyze HNO3 absorption features in 0.02/cm resolution stratospheric solar absorption spectra.

Goldman, A.↗

A Newton algorithm for complex curve fitting

The problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type which converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions.

Spanos, J. T.↗

Newton algorithm for fitting transfer functions to frequency response measurements

In this paper the problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type that converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second-order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions. Two numerical examples demonstrate the effectiveness of the algorithm.

Spanos, J. T.↗

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Tzikang, Chen↗

Least-squares sequential parameter and state estimation for large space structures

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Thau, F. E.↗

Reaction Wheel Disturbance Model Extraction Software - RWDMES

The RWDMES is a tool for modeling the disturbances imparted on spacecraft by spinning reaction wheels. Reaction wheels are usually the largest disturbance source on a precision pointing spacecraft, and can be the dominating source of pointing error. Accurate knowledge of the disturbance environment is critical to accurate prediction of the pointing performance. In the past, it has been difficult to extract an accurate wheel disturbance model since the forcing mechanisms are difficult to model physically, and the forcing amplitudes are filtered by the dynamics of the reaction wheel. RWDMES captures the wheel-induced disturbances using a hybrid physical/empirical model that is extracted directly from measured forcing data. The empirical models capture the tonal forces that occur at harmonics of the spin rate, and the broadband forces that arise from random effects. The empirical forcing functions are filtered by a physical model of the wheel structure that includes spin-rate-dependent moments (gyroscopic terms). The resulting hybrid model creates a highly accurate prediction of wheel-induced forces. It accounts for variation in disturbance frequency, as well as the shifts in structural amplification by the whirl modes, as the spin rate changes. This software provides a point-and-click environment for producing accurate models with minimal user effort. Where conventional approaches may take weeks to produce a model of variable quality, RWDMES can create a demonstrably high accuracy model in two hours. The software consists of a graphical user interface (GUI) that enables the user to specify all analysis parameters, to evaluate analysis results and to iteratively refine the model. Underlying algorithms automatically extract disturbance harmonics, initialize and tune harmonic models, and initialize and tune broadband noise models. The component steps are described in the RWDMES user s guide and include: converting time domain data to waterfall PSDs (power spectral densities); converting PSDs to order analysis data; extracting harmonics; initializing and simultaneously tuning a harmonic model and a wheel structural model; initializing and tuning a broadband model; and verifying the harmonic/broadband/structural model against the measurement data. Functional operation is through a MATLAB GUI that loads test data, performs the various analyses, plots evaluation data for assessment and refinement of analysis parameters, and exports the data to documentation or downstream analysis code. The harmonic models are defined as specified functions of frequency, typically speed-squared. The reaction wheel structural model is realized as mass, damping, and stiffness matrices (typically from a finite element analysis package) with the addition of a gyroscopic forcing matrix. The broadband noise model is realized as a set of speed-dependent filters. The tuning of the combined model is performed using nonlinear least squares techniques. RWDMES is implemented as a MATLAB toolbox comprising the Fit Manager for performing the model extraction, Data Manager for managing input data and output models, the Gyro Manager for modifying wheel structural models, and the Harmonic Editor for evaluating and tuning harmonic models. This software was validated using data from Goodrich E wheels, and from GSFC Lunar Reconnaissance Orbiter (LRO) wheels. The validation testing proved that RWDMES has the capability to extract accurate disturbance models from flight reaction wheels with minimal user effort.

Blaurock, Carl↗

Rotational Raman-Based Temperature Measurements in a High-Velocity Turbulent Jet

Spontaneous rotational Raman scattering spectroscopy is used to acquire the first ever high quality, spatially-resolved measurements of the mean and root mean square (rms) temperature fluctuations in turbulent, high-velocity heated jets. Raman spectra in air were obtained across a matrix of radial and axial locations downstream from a 50 mm diameter nozzle operating from subsonic to supersonic conditions over a wide range of temperatures and Mach numbers, in accordance with the Tanna matrix frequently used in jet noise studies. These data were acquired in the hostile, high noise (115 dB) environment of a large scale open air test facility at NASA Glenn Research Center (GRC). Temperature estimates were determined by performing nonlinear least squares fitting of the single shot spectra to the theoretical rotational Stokes spectra of N2 and O2, using a custom in-house code developed specifically for this investigation. The laser employed in this study was a high energy, long-pulsed, frequency doubled Nd:YAG laser. One thousand single-shot spectra were acquired at each spatial coordinate. Mean temperature and rms temperature variations were calculated at each measurement location. Excellent agreement between the averaged and single-shot temperatures was observed with an accuracy better than 2.5 percent for temperature, and rms variations in temperature between +/-2.2 percent at 296 K and +/-4.5 percent at 850 K. The results of this and planned follow-on studies will support NASA GRC's development of physics-based jet noise prediction, turbulence modeling and aeroacoustic source modeling codes.

Randy J Locke↗

Rotational Raman-Based Temperature Measurements in a High-Velocity Turbulent Jet

Spontaneous rotational Raman scattering spectroscopy is used to acquire the first ever high quality, spatially-resolved measurements of the mean and root mean square (rms) temperature fluctuations in turbulent, high-velocity heated jets. Raman spectra in air were obtained across a matrix of radial and axial locations downstream from a 50 mm diameter nozzle operating from subsonic to supersonic conditions over a wide range of temperatures and Mach numbers, in accordance with the Tanna matrix frequently used in jet noise studies. These data were acquired in the hostile, high noise (115 dB) environment of a large scale open air test facility at NASA Glenn Research Center (GRC). Temperature estimates were determined by performing nonlinear least squares fitting of the single shot spectra to the theoretical rotational Stokes spectra of N2 and O2, using a custom in-house code developed specifically for this investigation. The laser employed in this study was a high energy, long-pulsed, frequency doubled Nd:YAG laser. One thousand single-shot spectra were acquired at each spatial coordinate. Mean temperature and rms temperature variations were calculated at each measurement location. Excellent agreement between the averaged and single-shot temperatures was observed with an accuracy better than 2.5 percent for temperature, and rms variations in temperature between +/-2.2 percent at 296 K and +/-4.5 percent at 850 K. The results of this and planned follow-on studies will support NASA GRC's development of physics-based jet noise prediction, turbulence modeling and aeroacoustic source modeling codes.

Randy J Locke↗

Zr-92(d,p)Zr-93 and Zr-92(d,t)Zr-91

The structures of Zr-93 and Zr-91 were studied by the stripping reaction Zr-92(d,p)Zr-93 and the pick-up reaction Zr-92(d,t)Zr-91 using 13 MeV incident deuterons. The reaction product particles were detected by counter telescope. Typical spectra from the reactions were analyzed by a nonlinear least squares peak fitting program which included a background search. Spin and parity assignments to observed excited levels were made by comparing experimental angular distributions with distorted wave Born approximation calculations.

Baron, N.↗

Slosh testing of a spherical mercury propellant tank with positive-expulsion diaphragm

A preliminary investigation was conducted to evaluate the lateral slosh characteristics of a 23-cm diameter mercury propellant tank with a positive-expulsion diaphragm and 17.5% ullage. Data are presented for tank sinusoidal acceleration levels between 0.05 and 0.5 g at frequencies ranging from 5 to 50 Hz. Results indicate that slosh characteristics are highly nonlinear at acceleration levels approaching those in flight, and depend heavily on the shape and stiffness of the diaphragm. Nyquist plots of driving force over acceleration are shown to be a useful tool for determining natural frequency, damping, and modal mass characteristics. A computerized nonlinear least squares method for extracting the modal parameters from the Nyquist plots is described and results of applying the method are presented.

Ross, R. G., Jr.↗

An efficiency study on obtaining the minimum weight of a thermal protection system

Three minimizing techniques are evaluated to determine the most efficient method for minimizing the weight of a thermal protection system and for reducing computer usage time. The methods used (numerical optimization and nonlinear least squares) for solving the minimum-weight problem involving more than one material and more than one constraint are discussed. In addition, the one material and one constraint problem is discussed.

Williams, S. D.↗

A study on characterization of stratospheric aerosol and gas parameters with the spacecraft solar occultation experiment

Spacecraft remote sensing of stratospheric aerosol and ozone vertical profiles using the solar occultation experiment has been analyzed. A computer algorithm has been developed in which a two step inversion of the simulated data can be performed. The radiometric data are first inverted into a vertical extinction profile using a linear inversion algorithm. Then the multiwavelength extinction profiles are solved with a nonlinear least square algorithm to produce aerosol and ozone vertical profiles. Examples of inversion results are shown illustrating the resolution and noise sensitivity of the inversion algorithms.

Chu, W. P.↗

Effective thermal conductivity determination for low-density insulating materials

That nonlinear least squares can be used to determine effective thermal conductivity was demonstrated, and a method for assessing the relative error associated with these predicted values was provided. The differences between dynamic and static determination of effective thermal conductivity of low-density materials that transfer heat by a combination of conduction, convection, and radiation were discussed.

Williams, S. D.↗

Microprocessor utilization in search and rescue missions

The position of an emergency transmitter may be determined by measuring the Doppler shift of the distress signal as received by an orbiting satellite. This requires the computation of an initial estimate and refinement of this estimate through an iterative, nonlinear, least squares estimation. A version of the algorithm was implemented and tested by locating a transmitter on the premises and obtaining observations from a satellite. The computer used was an IBM 360/95. The position was determined within the desired 10 km radius accuracy. The feasibility of performing the same task in real time using microprocessor technology, was determined. The least squares algorithm was implemented on an Intel 8080 microprocessor. The results indicate that a microprocessor can easily match the IBM implementation in accuracy and be performed inside the time limitations set.

Schwartz, M.↗

Maximum likelihood estimation for life distributions with competing failure modes

The general model for the competing failure modes assuming that location parameters for each mode are expressible as linear functions of the stress variables and the failure modes act independently is presented. The general form of the likelihood function and the likelihood equations are derived for the extreme value distributions, and solving these equations using nonlinear least squares techniques provides an estimate of the asymptotic covariance matrix of the estimators. Monte-Carlo results indicate that, under appropriate conditions, the location parameters are nearly unbiased, the scale parameter is slightly biased, and the asymptotic covariances are rapidly approached.

Sidik, S. M.↗