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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) is described for fitting single-input single-output transfer function models to empirical frequency response data. The program is interactive in that the user specifies ``elementary factors'' (gain, delay, pure differentiators and integrators, and first- and second-order zeros and poles) by entering numerical values or moving sliders in a graphical user interface. A nonlinear optimization can then be performed to obtain maximum likelihood estimates of transfer function parameters and uncertainties to provide feedback on the modeling and refine estimates. Several examples are discussed, including the identification of aircraft pitch dynamics from simulation data and data reported in the literature, approximating Theodorsen's function of unsteady aerodynamics, and obtaining a reduced-order model of a computational fluid dynamics code describing the unsteady aerodynamics around an aeroelastic wing. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and simple system identification problems. The program was written in MATLAB and is planned for public release through the NASA Software Catalog.

System identification↗
NASA NTRS1984

Exploring the use of structural models to improve remote sensing agricultural estimates

Satellite estimates of agricultural characteristics often are not sufficiently precise for reliable use in small geographical regions. The precision of estimates of agricultural characteristics such as crop proportions and leaf area indexes can be increased by modeling ground observations as a function of satellite estimates. Linear regression models using least squares estimators of the model parameters are most often advocated as an appropriate methodology; however, least squares estimation requires that the predictor variables are measured without error, an unreasonable assumption for this application. An alternative estimation methodology which assumes that both the response variables (ground observations) and the predictor variables (satellite estimates) are measured with error involves the use of linear structural models. The application of linear structural models to the estimation of agricultural characteristics using satellite spectral measurements is examined.

Gunst, R. F.↗
DOE OSTI2021

Transforming a Simple Structure Model to Represent a Complex Dynamic System with Unknown Boundary Restraints

Imposing a boundary condition on a structure can significantly alter its dynamic properties. However, sometimes the specifics of the new boundary conditions are not known. When the effects of a boundary condition are uncertain or there is not enough information, engineers need to excite the complex structure to obtain these modified properties. In order to experimentally obtain the new properties, engineers need multiple experiments and many outputs for interpolation in order to sufficiently represent the entire structure. In this study, the researchers attached a stinger to a cantilever beam, acting as a new transverse restraint of unknown properties. This paper presents a conversion expression that predicts the dynamic behavior of any point in the system with the new boundary condition. This expression relies only on one impact hammer experiment with one output and the model of the stinger-free cantilever beam, referred to as the simple structure. Researchers estimated the Transfer Function (TRF) of the beam and compared it with an experimentally measured TRF to validate the method. The mean absolute error of the estimated TRF compared to the experimental TRF is 1.99 dB. This demonstrates the use of the proposed method for estimating unmeasured TRFs in a system with an uncertain boundary condition using a single input, single output (SISO) test and a model of the simple structure.

42 ENGINEERING↗
NASA NTRS1986

Fourier transform techniques for the evaluation of the Thematic Mapper line spread function

An endeavor was made to use Fourier transform techniques to estimate the line spread function (LSF) of the Thematic Mapper (TM) from processed data. Data near the boundary of small fields from TM scenes were sampled, fitted to a theoretical curve, lowpass filtered, and then deconvolved to obtain the LSF. Lowpass filtering improved the truncation effect and eliminated the discontinuity at both ends of the data sequence.The selection of the cutoff frequency and the order of a lowpass filter is based on a newly defined criterion which tests the distortion of the processed edge by comparing it with the original edge. A parameter of the LSF, the equivalent width, is used to compare these LSF's deconvolved from sampled edge data with those evaluated by the derivative techniques. The calculated equivalent widths using the Fourier transform techniques for infrared bands are very close to TM design specifications.

Carnahan, W. H.↗
NASA NTRS1986

An analysis at mesospheric coherent-scatter power enhancements during solar flare events

Solar flares produce increases in coherent-scatter power from the mesosphere due to the increase in free electrons produced by X-ray photoionization. Thirteen such power enhancements were observed at Urbana. When such an enhancement occurs at an altitude containing a turbulence layer with constant strength, the relative enhancement of electon density is estimated from the enhancement in power. Such estimates of enchanced electron density are compared with estimates of the X-ray photoionization at that altitude, deduced from geostationary satellite measurements. It is found that possible types ion-chemical reaction scheme may be distinguished, and the nonflare ion-pair production function may be estimated. The type of ion-chemical scheme and the nonflare ion-production function are shown to depend on the solar zenith angle.

Parker, J.↗
NASA NTRS1994

Performance of mean-frequency estimators for Doppler radar and lidar

The performance of mean-frequency estimators for Doppler radar and lidar measurements of winds is presented in terms of two basic parameters: Phi, the ratio of the average signal energy per estimate to the spectral noise level; and Omega, which is proportional to the number of independent samples per estimate. For fixed Phi and Omega, the Cramer-Rao bound (CRB) (theoretical best performance) for unbiased estimators of mean frequency (normalized by the spectral width of the signal), signal power, and spectral width are essentially independent of the number of data samples M. For large Phi, the estimators of mean frequency are unbiased and the performance is independent of M. The spectral domain estimators and covariance based estimators are bounded by the approximate period of M. The spectral domain estimators and covariance based estimators are bounded by the approximate periodogram CRB. The standard deviation of the maximum-likelihood estimator approaches the exact CRB, which can be more than a factor of 2 better than the performance of the spectral domain estimators or covariance-based estimators for typical Omega. For small Phi, the estimators are biased due to the effects of the uncorrelated noise (white noise), which results in uniformly distributed 'bad' estimates. The fraction of bad estimates is a function of Phi and M with weak dependence on the parameter Omega. Simple empirical models describe the standard deviation of the good estimates and the fraction of bad estimates. For Doppler lidar and for large Phi, better performance is obtained by using many low-energy pulses instead of one pulse with the same total energy. For small Phi, the converse is true.

Frehlich, R. G.↗
NASA NTRS2017

Methods of Constructing a Blended Performance Function Suitable for Formation Flight

This paper presents two methods for constructing an approximate performance function of a desired parameter using correlated parameters. The methods are useful when real-time measurements of a desired performance function are not available to applications such as extremum-seeking control systems. The first method approximates an a priori measured or estimated desired performance function by combining real-time measurements of readily available correlated parameters. The parameters are combined using a weighting vector determined from a minimum-squares optimization to form a blended performance function. The blended performance function better matches the desired performance function mini- mum than single-measurement performance functions. The second method expands upon the first by replacing the a priori data with near-real-time measurements of the desired performance function. The resulting blended performance function weighting vector is up- dated when measurements of the desired performance function are available. Both methods are applied to data collected during formation- flight-for-drag-reduction flight experiments.

control systems↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗
NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗
NASA NTRS1983

Estimation of delays and other parameters in nonlinear functional differential equations

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Banks, H. T.↗
NASA NTRS1984

Viking bistatic radar experiment - Summary of results in near-equatorial regions

Viking bistatic radar have been processed using Hagfors' scattering function to obtain estimates of rms surface roughness from ground tracks primarily in the equatorial region of Mars. Roughness varies from as little as 0.75 deg rms east of Solis and Sinai Plana to at least 8 deg on the western slope of Arsia Mons. Estimated roughness in cratered terrain is generally about 5 deg or less, implying the existence of smoothing processes on scales less than 100 m. There is good agreement between bistatic roughness estimates and earth-based results at ground track intersections near the equator in both cratered terrain and plains. Surface tilt probability density functions derived from these observations are usually more sharply peaked than the Hagfors function for similar values of rms surface roughness. Earlier results using the Gaussian model appear to have overestimated the surface roughness by 30-40 percent.

Simpson, R. A.↗
DOE OSTI2019

Bootstrapping the 3d Ising model at finite temperature

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions (σσ) and (ϵϵ). As a result, we estimate the one-point functions of the lowest-dimension $\mathbb{Z}_2$-even scalar ϵ and the stress energy tensor T μν . Our result for (σσ) at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1968

Application of a truncated normal failure distribution in reliability testing

Statistical truncated normal distribution function is applied as a time-to-failure distribution function in equipment reliability estimations. Age-dependent characteristics of the truncated function provide a basis for formulating a system of high-reliability testing that effectively merges statistical, engineering, and cost considerations.

Groves, C., Jr.↗
NASA NTRS1980

Heating of the moon by heterogeneous accretion

Monte Carlo models of lunar accretion are developed by randomly sampling mass and velocity distributions of objects in the solar nebula in circumsolar and circumterrestrial orbits. The thermal effect of an impact is expressed as the volume of melt produced; the melt volumes produced by each Monte Carlo case are sorted into regions to produce percentage melt estimates as a function of radius. One-hundred cases are calculated to obtain a range of plausible thermal histories for lunar accretion. The average melt percentage estimates show substantial deep melting, but the spread of melt percentage values about the mean from the random sampling procedure is wide enough to include 0% melting for radii below 100 km and 100% melting for radii below 500 km.

Ransford, G. A.↗
NASA NTRS1985

Admittance functions from Venus vertical gravity and modes of topographic support

Two-dimensional Fourier admittance functions have been estimated for various regions of Venus, using as input the Pioneer Venus topography data and the Venus vertical gravity model of Sjogren. Model admittance functions are computed for various cases, such as lithospheric loading from above, and support from below, for comparison. These models are functions of depth of compensation, flexural rigidity, and crust and mantle densities. The long wavelength topography and gravity signals contain most of the spectral power in the Venus data, and the admittances at these wavelengths are compatible with deep compensation of surface topography.

Williams, D. R.↗
DOE OSTI2019

Heisenberg-scaling measurement protocol for analytic functions with quantum sensor networks

Here we generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean-squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and we conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Signal sequence detection given noisy, common background image sets.

The optimum processing (likelihood functional) is found for a set of M images, each the sum of a member of a signal sequence due to an object to be detected and its parameters estimated, a sample function of a noise field, and a sample function of a common background field. The noise fields are independent, zero mean, white Gaussian fields, all independent of the background field. The latter is assumed to be either (1) completely unknown or of known mean and covariance functions with (2) a certain fluctuation property or (3) Gaussian. Three equivalent forms of the optimum processing are found: (1) a summation of generalized matched filterings of the images, (2) a summation of matched filtering of certain generalized differences of the images, and (3) a summation of 'estimator-correlator' type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given, and is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability.

Harger, R. O.↗
NASA NTRS2007

Propagation of Computational Uncertainty Using the Modern Design of Experiments

This paper describes the use of formally designed experiments to aid in the error analysis of a computational experiment. A method is described by which the underlying code is approximated with relatively low-order polynomial graduating functions represented by truncated Taylor series approximations to the true underlying response function. A resource-minimal approach is outlined by which such graduating functions can be estimated from a minimum number of case runs of the underlying computational code. Certain practical considerations are discussed, including ways and means of coping with high-order response functions. The distributional properties of prediction residuals are presented and discussed. A practical method is presented for quantifying that component of the prediction uncertainty of a computational code that can be attributed to imperfect knowledge of independent variable levels. This method is illustrated with a recent assessment of uncertainty in computational estimates of Space Shuttle thermal and structural reentry loads attributable to ice and foam debris impact on ascent.

DeLoach, Richard↗