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NASA NTRS1979

On the Performance of the Martin Digital Filter for High- and Low-pass Applications

A nonrecursive numerical filter is described in which the weighting sequence is optimized by minimizing the excursion from the ideal rectangular filter in a least squares sense over the entire domain of normalized frequency. Additional corrections to the weights in order to reduce overshoot oscillations (Gibbs phenomenon) and to insure unity gain at zero frequency for the low pass filter are incorporated. The filter is characterized by a zero phase shift for all frequencies (due to a symmetric weighting sequence), a finite memory and stability, and it may readily be transformed to a high pass filter. Equations for the filter weights and the frequency response function are presented, and applications to high and low pass filtering are examined. A discussion of optimization of high pass filter parameters for a rather stringent response requirement is given in an application to the removal of aircraft low frequency oscillations superimposed on remotely sensed ocean surface profiles. Several frequency response functions are displayed, both in normalized frequency space and in period space. A comparison of the performance of the Martin filter with some other commonly used low pass digital filters is provided in an application to oceanographic data.

Mcclain, C. R.↗

NASA NTRS2000

Combustion Response of AP Composite Propellants

The Cohen & Strand model for AP composite propellants is applied as boundary conditions, one for AP and one for binder, in solving the heat conduction equation in each to compute linear and non-linear combustion response properties for each and for the aggregate propellant. Iterations couple AP and binder through the quasi-steady flame processes. Illustrative results for linear response functions (pressure-coupled and velocity-coupled) are presented for a monomodal AP propellant varying AP size, pressure and crossflow speed, and examples of non-linear responses to arbitrary waveforms are shown. A quantitative comparison with response function data is limited to one well-characterized research formulation. Mechanistic implications are discussed, including recommendations for future modeling work.

Shusser, Michael↗

NASA NTRS2024

X-57 Cruise Motor GVT Using Fixed-Base Correction Technique

The National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC) completed a modal survey of the X-57 Maxwell aircraft cruise motor system to help inform cruise motor redesign efforts. X-57 Maxwell was an electric propulsion demonstrator aircraft developed by NASA to inform airworthiness standards for electrified-aircraft. The cruise motor system modal survey was completed in spring of 2023 utilizing the fixed-base correction (FBC) ground vibration test (GVT) technique developed by ATA Engineering, to decouple the motor modes from the aircraft modes. Previously during the full aircraft GVT, a detailed modal assessment of the cruise motors was not performed. Owing to the X-57 project’s phase in the aircraft development cycle when the motor redesign effort occurred, the cruise motor GVT could only be performed with the cruise motor system installed on the aircraft, with most of its installation hardware (wiring, baffling, sensors, etc.) attached. An impact hammer was used to provide excitation input at various locations within the tight confines of the cruise motor installation. To better support motor redesign efforts, the FBC methodology was utilized to fix, separate and de-couple the cruise motor modes from aircraft modal response. During the GVT, this required additional impact tap tests on candidate fixed-boundary points for each degree of freedom (DOF) to be fixed. Additional triaxial accelerometers installed at the candidate points were used to compute frequency response functions (FRFs) in X, Y, and Z directions to enable those DOFs to be numerically fixed. Test data was acquired using Hottinger Brüel & Kjær’s LAN-XI data acquisition hardware and BK Connect software. FBC post-test processing was performed using the Structural Modification Using Frequency Response Functions (SMURF) technique with ATA Engineering’s Interface between MATLAB, Analysis, Test (IMAT) software. Utilizing the FBC technique relieved test engineers from having to instrument the entire aircraft to identify and separate aircraft response from cruise motor modes of interest. The FBC technique also permitted structural analysis engineers to omit secondary components from their finite element model (FEM) of the cruise motor system. This FBC modal survey was successful, and the first time NASA AFRC utilized the FBC method on an aircraft rather than a test fixture, and also using an impact hammer rather than multiple shakers allowing significant project schedule and cost savings

Modal Survey↗

NASA NTRS1992

Pulsed laser spectral measurement using a Fabry-Perot interferometer: Limits to resolution

We are developing a Doppler lidar system using the edge technique to measure atmospheric wind profiles. The edge technique requires a laser with a narrow spectral bandwidth and a high resolution optical filter. The lidar system will use a Nd:YAG laser operating at 1.064 microns and a high resolution Fabry-Perot interferometer for the edge filter. The Doppler shift measurement is made by locating the laser on the edge of the filter's spectral response function. Due to the steep slope on the edge, large changes in the filter transmission will be observed for small changes in frequency. The Doppler shift can be determined from a measurement of this change in filter transmission if the filter spectral response function in the region of the measurement is well known. Recently developed injection seeded solid state lasers have made near transform limited laser output readily available for lidar work. Injection-seeded Nd:YAG laser exhibit single mode output with smooth Gaussian temporal pulse shapes. Results of an experiment we conducted to evaluate the effects of a short Gaussian temporal input pulse on the spectral response of a high resolution Fabry-Perot interferometer are presented.

Notari, Anthony↗

NASA NTRS2017

X-Ray Spectro-Polarimetry with Photoelectric Polarimeters

We derive a generalization of forward fitting for X-ray spectroscopy to include linear polarization of X-ray sources, appropriate for the anticipated next generation of space-based photoelectric polarimeters. We show that the inclusion of polarization sensitivity requires joint fitting to three observed spectra, one for each of the Stokes parameters, I(E), U(E), and Q(E). The equations for StokesI (E) (the total intensity spectrum) are identical to the familiar case with no polarization sensitivity, and for which the model-predicted spectrum is obtained by a convolution of the source spectrum, F (E), with the familiar energy response function,(E) R(E,E), where (E) and R(E,E) are the effective area and energy redistribution matrix, respectively. In addition to the energy spectrum, the two new relations for U(E) and Q(E) include the source polarization fraction and position angle versus energy, a(E), and 0(E), respectively, and the model-predicted spectra for these relations are obtained by a convolution with the modulated energy response function, (E)(E) R(E,E), where(E) is the energy-dependent modulation fraction that quantifies a polarimeters angular response to 100 polarized radiation. We present results of simulations with response parameters appropriate for the proposed PRAXyS Small Explorer observatory to illustrate the procedures and methods, and we discuss some aspects of photoelectric polarimeters with relevance to understanding their calibration and operation.

polarization↗

NASA NTRS1976

A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust

A uniformly valid second-order theory is developed for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulas for the airfoil response functions (i.e., fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.

Goldstein, M. E.↗

NASA NTRS2003

Piezoelectric Actuator Modeling Using MSC/NASTRAN and MATLAB

This paper presents a procedure for modeling structures containing piezoelectric actuators using MSCMASTRAN and MATLAB. The paper describes the utility and functionality of one set of validated modeling tools. The tools described herein use MSCMASTRAN to model the structure with piezoelectric actuators and a thermally induced strain to model straining of the actuators due to an applied voltage field. MATLAB scripts are used to assemble the dynamic equations and to generate frequency response functions. The application of these tools is discussed using a cantilever aluminum beam with a surface mounted piezoelectric actuator as a sample problem. Software in the form of MSCINASTRAN DMAP input commands, MATLAB scripts, and a step-by-step procedure to solve the example problem are provided. Analysis results are generated in terms of frequency response functions from deflection and strain data as a function of input voltage to the actuator.

Reaves, Mercedes C.↗

NASA NTRS1985

Statistical Signal Analysis for Systems with Interferenced Inputs

A new approach is introduced, based on statistical signal analysis, which overcomes the error due to input signal interference. The model analyzed is given. The input signals u sub 1 (t) and u sub 2 (t) are assumed to be unknown. The measurable signals x sub 1 (t) and x sub 2 (t) are interferened according to the frequency response functions, H sub 12 (f) and H sub 21 (f). The goal of the analysis was to evaluate the power output due to each input, u sub 1 (t) and u sub 2 (t), for the case where both are applied to the same time. In addition, all frequency response functions are calculated. The interferenced system is described by a set of five equations with six unknown functions. An IBM XT Personal Computer, which was interfaced with the FFT, was used to solve the set of equations. The software was tested on an electrical two-input, one-output system. The results were excellent. The research presented includes the analysis of the acoustic radiation from a rectangular plate with two force inputs and the sound pressure as an output signal.

Bai, R. M.↗

NASA NTRS1997

PLATSIM: A Simulation and Analysis Package for Large-Order Flexible Systems

The software package PLATSIM provides efficient time and frequency domain analysis of large-order generic space platforms. PLATSIM can perform open-loop analysis or closed-loop analysis with linear or nonlinear control system models. PLATSIM exploits the particular form of sparsity of the plant matrices for very efficient linear and nonlinear time domain analysis, as well as frequency domain analysis. A new, original algorithm for the efficient computation of open-loop and closed-loop frequency response functions for large-order systems has been developed and is implemented within the package. Furthermore, a novel and efficient jitter analysis routine which determines jitter and stability values from time simulations in a very efficient manner has been developed and is incorporated in the PLATSIM package. In the time domain analysis, PLATSIM simulates the response of the space platform to disturbances and calculates the jitter and stability values from the response time histories. In the frequency domain analysis, PLATSIM calculates frequency response function matrices and provides the corresponding Bode plots. The PLATSIM software package is written in MATLAB script language. A graphical user interface is developed in the package to provide convenient access to its various features.

Maghami, Peiman G.↗

NASA NTRS1979

The analytical design of spectral measurements for multispectral remote sensor systems

The author has identified the following significant results. In order to choose a design which will be optimal for the largest class of remote sensing problems, a method was developed which attempted to represent the spectral response function from a scene as accurately as possible. The performance of the overall recognition system was studied relative to the accuracy of the spectral representation. The spectral representation was only one of a set of five interrelated parameter categories which also included the spatial representation parameter, the signal to noise ratio, ancillary data, and information classes. The spectral response functions observed from a stratum were modeled as a stochastic process with a Gaussian probability measure. The criterion for spectral representation was defined by the minimum expected mean-square error.

Wiersma, D. J.↗

NASA NTRS2000

Comparison of Dynamic Characteristics for an Inflatable Solar Concentrator in Atmospheric and Thermal Vacuum Conditions

Dynamic testing of an inflatable solar concentrator structure in a thermal vacuum chamber as well as in ambient laboratory conditions is described in detail. Unique aspects of modal testing for the extremely lightweight inflatable are identified, including the use of a noncontacting laser vibrometer measurement system. For the thermal vacuum environment, mode shapes and frequency response functions are compared for three different test article inflation pressures at room temperature. Modes that persist through all the inflation pressure regimes are identified, as well as modes that are unique for each pressure. In atmospheric pressure and room temperature conditions, dynamic measurements were obtained for the expected operational inflation pressure of 0.5 psig. Experimental mode shapes and frequency response functions for ambient conditions are described and compared to the 0.5 psig results from the thermal vacuum tests. Only a few mode shapes were identified that occurred in both vacuum and atmospheric environments. This somewhat surprising result is discussed in detail, and attributed at least partly to 1.) large differences in modal damping, and 2.) significant differences in the mass of air contained by the structure, in the two environments. Results of this investigation point out the necessity of testing inflatable space structures in vacuum conditions before they can be launched. Ground testing in atmospheric pressure is not sufficient for predicting on-orbit dynamics of non-rigidized inflatable systems.

Slade, Kara N.↗

NASA NTRS1987

Optimal application of Morrison's iterative noise removal for deconvolution. Appendices

Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given.

Ioup, George E.↗

NASA NTRS2003

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

Howell, L. W., Jr.↗

NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗

NASA NTRS1991

How to observe the gyre to global-scale variability in satellite altimetry - Signal attenuation by orbit error removal

Formulas analogous to the frequency response functions for commonly used filters in orbit error removal are analytically derived to devise observational strategies for the large-scale oceanic variability and to decipher the signal contents of previous results. These include the polynomial orbit error approximations, i.e., the linear, bias-only and quadratic corrections, and the sinusoidal orbit error approximations (the purely sinusoidal correction, and the sinusoid-and-bias correction). It is shown that the frequency response function for a polynomial correction is a function of the ratio of wavelength/track length and to retain 90 percent or more of the signal at a certain wavelength, the ratio must be less than 0.65 (for the quadratic case), 0.90 (linear), and 1.54 (bias-only).

Tai, Chang-Kou↗

NASA NTRS1977

Role of condensed phase details in the oscillatory combustion of composite propellants

The response functions of composite propellants are theoretically derived, including explicitly the pressure-dependent degradation term in the condensed phase, hypothesizing that the overall rate-limiting reactions are in the relatively low temperature condensed phase. The method of 'inner' and 'outer' expansions with the reduced activation energy as the singular perturbation parameter has been employed. The results cover subsurface reactions with and without surface reactions, adiabatic and uniform-combustion models for the quasi-steady gas phase processes. The response functions display several experimentally observed features like dependence on mean pressure and the instability behavior of some 'zero-n' propellants.

Kumar, R. N.↗

NASA NTRSDate not supplied

Deriving Broadband Radiances from Geostationary Satellite Visible Radiance Channels for Use in the CERES SYN1deg Product

The NASA CERES project was designed to monitor the Earth’s radiation budget, both at the regional and global scale. The CERES SSF1deg single satellite product provides TOA flux observations from Aqua, Terra, NPP, and NOAA-20. The SYN1deg product incorporates observations from Terra, Aqua, and geostationary (GEO) satellites. The GEO observations are included in the SYN1deg product to infer the regional diurnal cycle between CERES observations. GEO satellites throughout the CERES record have different narrowband spectral response functions and do not directly observe radiances over the broadband spectra of CERES instruments. Hence the emphasis of this study is improving the process of deriving broadband radiances from the myriad GEO visible channel observations. We present a new method for converting the narrowband radiances observed from GEO operational satellites. This study relies on radiative transfer model hyper-spectral radiances for many cloud and surface conditions under all angular conditions observed by GEO sensors. First, the hyper-spectral radiances from a radiative transfer model must be convolved with the spectral response function of the visible imager for each GEO sensor in the CERES record. For each angular bin and surface type, the clear-sky and multiple optical depth and phase cloudy-sky narrowband and broadband reflectance pairs are linearly regressed. This study found that, no matter how the scene conditions are stratified, for example the all-sky, clear-sky, ice or water clouds, they all provide similar linear regressions. This includes ocean glint conditions, where the clear-sky reflectance exceeds cloudy conditions and yet the relationship was found to be linear in the given angular bin. This infers that no GEO retrieved cloud information is necessary in the narrowband to broadband conversion process, which relies only on visible channel reflectance. Over land, most of the GEO visible channels do not observe the NIR vegetation reflectance. We intend to use land adjustment factors developed using the TOA reflectance difference between the real-time MODIS .86um and the .64um channel. We validate this approach by using coincident observational data between CERES and MODIS aboard Aqua and Terra as well as GEO and CERES observations .

CERES↗

NASA NTRS1996

Research concerning the net flux of radiation in the atmosphere of Jupiter

The plan of the NFR (Net Flux of Radiation) team is for the data from the two solar channels (B and E) of NFR to be reduced with the goal of determining the solar heating rate. In order to determine the solar heating rate from the NFR measurements, effects due to the instrument's spatial and spectral response functions, to the temperature variation of the instrument (and associated drift of calibration), to the setting sun, and to the rotation of the probe (initially at a rate comparable to the NFR sampling frequency), all must be well modelled. In the past year, a forward modeling routine was created to simulate NFR data return in the B and E channels. The effects of varying parameters describing the atmospheric model (such as cloud location and thickness) and the descent profile (such as rotation rate) were investigated and an inversion routine was developed. For the forward modeling, existing radiative transfer codes were used to determine intensity fields within the Jovian atmosphere. A routine was developed to determine instantaneous instrument response by integrating the intensity field over the instrument response functions. A second routine was developed to determine the actual output of the NFR by integrating along an arbitrary descent trajectory. Near the top of the atmosphere, the upflux data alone are used to constrain the cloud structure of he atmosphere. To accomplish this, models are used to describe the variation in up flux between consecutive measurements in terms of variations of cloud opacity and variations in known parameters such as the solar zenith angle. This allows us to develop a zero-order model of cloud structure. Lower in the atmosphere, at levels where there is little or no azimuthal structure to the net flux measurements, both the up flux and net flux are used to derive layer transmission and reflection functions, which then determine layer opacity and single scattering albedo. A preliminary analysis of the data began in December 1995. In these data we could see the rapid oscillations expected at the beginning of the data due to probe rotation and the sun passing through the edge of the field of view. In addition, the time when this oscillation stopped was clearly visible. This sets the rough optical depth above the probe at this time.

Tomasko, M. G.↗