Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inversion theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Volume 1: Theory development and parametric studies

Typical analytical models for interaction between rotor and stator in a turbofan analyze the effect of wakes from the rotor impinging on the stator, producing unsteady loading, and thereby generating noise. Reflection/transmission characteristics of the rotor are sometimes added in a separate calculation. In those models, there is a one-to-one relationship between wake harmonics and noise harmonics; that is, the BPF (blade passing frequency) wake harmonic causes only the BPF noise harmonic, etc. This report presents a more complete model in which flow tangency boundary conditions are satisfied on two cascades in relative motion for several harmonics simultaneously. By an extension of S.N. Smith's code for two dimensional flat plate cascades, the noise generation/frequency scattering/blade row reflection problem is solved in a single matrix inversion. It is found that the BPF harmonic excitation of the stator scatters considerable energy in the higher BPF harmonics due to relative motion between the blade rows. Furthermore, when swirl between the rotor and stator is modeled, a 'mode trapping' effect occurs which explains observations on fans operating at rotational speeds below BFP cuton: the BPF mode amplifies between blade rows by multiple reflections but cannot escape to the inlet and exit ducts. However, energy scattered into higher harmonics does propagate and dominates the spectrum at two and three times BPF. This report presents the complete derivation of the theory, comparison with a previous (more limited) coupled rotor/stator interaction theory due to Kaji and Okazaki, exploration of the mode trapping phenomenon, and parametric studies showing the effects of vane/blade ratio and rotor/stator interaction. For generality, the analysis applies to stages where the rotor is either upstream or downstream of the stator and to counter rotation stages. The theory has been coded in a FORTRAN program called CUP2D, documented in Volume 2 of this report. It is concluded that the new features of this analysis - unsteady coupling, frequency scattering, and flow turning between rotor and stator - have a profound effect on noise generation caused by rotor/stator interaction. Treating rotors and stators as isolated cascades is not adequate for noise analysis and prediction.

Hanson, Donald B.↗
NASA NTRS1989

Inverse dynamics of a 3 degree of freedom spatial flexible manipulator

A technique is presented for solving the inverse dynamics and kinematics of 3 degree of freedom spatial flexible manipulator. The proposed method finds the joint torques necessary to produce a specified end effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested through simulation analysis. Results show the potential use of this method for the smooth motion control of space telerobots.

Bayo, Eduardo↗
NASA NTRS1989

Absorption line profiles in a moving atmosphere - A single scattering linear perturbation theory

An integral equation is derived which linearly relates Doppler perturbations in the spectrum of atmospheric absorption features to the wind system which creates them. The perturbation theory is developed using a single scattering model, which is validated against a multiple scattering calculation. The nature and basic properties of the kernels in the integral equation are examined. It is concluded that the kernels are well behaved and that wind velocity profiles can be recovered using standard inversion techniques.

Hays, P. B.↗
NASA NTRS1990

Observation of a strong inverse temperature dependence for the opacity of atmospheric water vapor in the mm continuum near 280 GHz

Results are presented of the field measurements of atmospheric opacity at 278 GHz (9.3/cm) conducted at the McMurdo Station (Antarctica) during the austral springs of 1986 and 1987, in conjunction with balloon measurements of water vapor profile and total column density, showing a strong inverse temperature dependence when normalized to precipitable water vapor. The value of measured opacity per mm of precipitable water vapor (PWV) is roughly two times greater at -35 C than at -10 C and three times greater than measurements at +25 C reported by Zammit and Ade (1981). Various theories proposed to explain excess absorption in continuum regions are reviewed.

Emmons, Louisa K.↗
NASA NTRS1936

Correction of downwash in wind tunnels of circular and elliptic sections

The downwash velocity distribution behind the wing was determined for the free jet and for the closed tunnel of both circular and elliptic cross sections. The wing was placed at the center of the tunnel. The theory makes it possible to determine the downwash at any point in the jet. The computations were performed for points in the plane determined by the jet axis and the center-of-pressure line of the wing. The downwash proved to be proportional to the wing lift and inversely proportional to the cross-sectional area of the tunnel.

Lotz, Irmgard↗
NASA NTRS1980

Aerodynamic coefficients in generalized unsteady thin airfoil theory

Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).

Williams, M. H.↗
NASA NTRS1993

Data analysis and interpretation of lunar dust exosphere

The lunar horizon glow observed by Apollo astronauts and recorded during the Surveyor missions is believed to result from the scattering of sunlight off lunar fines suspended in a dust layer above the lunar surface. For scale heights of tens of kilometers, theory and astronaut's observations suggest that the size of the dust particles will be smaller than 0.1 microns in radius and will act as Rayleigh scatters. This means that the dust scattered light will be 100 percent polarized at a 90 degree scattering angle and will depend on wavelength to the inverse fourth power ('bluing'). Believing these signatures to be observable from ground based telescopes, observational data in the form of CCD images has been collected from McDonald Observatory's 36 in. telescope, and the reduction and analysis of this data is the focus of the present report.

Andrews, George A., Jr.↗
NASA NTRS1988

A unified framework for approximation in inverse problems for distributed parameter systems

A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results.

Banks, H. T.↗
NASA NTRS1990

An approximation theory for the identification of linear thermoelastic systems

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Rosen, I. G.↗
NASA NTRS1982

The GLAS physical inversion method for analysis of HIRS2/MSU sounding data

Goddard Laboratory for Atmospheric Sciences has developed a method to derive atmospheric temperature profiles, sea or land surface temperatures, sea ice extent and snow cover, and cloud heights and fractional cloud, from HIRS2/MSU radiance data. Chapter 1 describes the physics used in the radiative transfer calculations and demonstrates the accuracy of the calculations. Chapter 2 describes the rapid transmittance algorithm used and demonstrates its accuracy. Chapter 3 describes the theory and application of the techniques used to analyze the satellite data. Chapter 4 shows results obtained for January 1979.

Susskind, J.↗
NASA NTRS1984

Reflectance spectroscopy - Quantitative analysis techniques for remote sensing applications

The empirical methods and scattering theories that are important for solving remote sensing problems are among the methods for remotely sensed reflectance data analysis presently compared. In the case of the photon mean optical path length concept's implications for reflectance spectra modeling, it is shown that the mean optical path length in a particulate surface is in roughly inverse proportion to the square root of the absorption coefficient. Absorption bands, which are Gaussian in shape when plotted as true absorptance vs photon energy, are also Gaussians in apparent absorptance, although they have a smaller intensity. An apparent continuum in a reflectance spectrum is modeled as a mathematical function that is used to isolate a particular absorption feature for analysis, and it is noted that this continuum should be removed by dividing it into the reflectance spectrum.

Clark, R. N.↗
NASA NTRS1992

Botswana water and surface energy balance research program. Part 2: Large scale moisture and passive microwaves

The Botswana water and surface energy balance research program was developed to study and evaluate the integrated use of multispectral satellite remote sensing for monitoring the hydrological status of the Earth's surface. The research program consisted of two major, mutually related components: a surface energy balance modeling component, built around an extensive field campaign; and a passive microwave research component which consisted of a retrospective study of large scale moisture conditions and Nimbus scanning multichannel microwave radiometer microwave signatures. The integrated approach of both components are explained in general and activities performed within the passive microwave research component are summarized. The microwave theory is discussed taking into account: soil dielectric constant, emissivity, soil roughness effects, vegetation effects, optical depth, single scattering albedo, and wavelength effects. The study site is described. The soil moisture data and its processing are considered. The relation between observed large scale soil moisture and normalized brightness temperatures is discussed. Vegetation characteristics and inverse modeling of soil emissivity is considered.

Vandegriend, A. A.↗
NASA NTRS2021

Integration of an Arm Kinematics Hot Patch onboard the Curiosity Rover

NASA's Mars Science Laboratory (MSL) mission has updated the Curiosity rover's flight software multiple times since landing on Mars on August 6, 2012. The most common patching method has been a hot patch, in which running flight software is modified after being copied into RAM from its persistent storage. The latest hot patch to be installed on Curiosity fixed an issue in the robotic arm software that computes generalized inverse kinematics. Additional unit testing performed since the start of the surface mission revealed that this software can sometimes produce erroneous solutions.The cause was identified as numerical instability in a quartic root finder. When the inputs to that solver are not well conditioned, floating-point numerical issuescan cause erroneous roots to be reported. In theory, this could result in the robotic arm turret instruments being commanded to unintended positions, for example, below the terrain surface. Out of approximately 3.7 million unit test cases, 97.2\% of the position errors were below 5 mm. However, there were 16 test cases where theposition error was greater than 20 cm, and the maximum position error was 1.2 meters.The patch was uploaded to Curiosity on sol 2642 (January 11, 2020) after the solution was developed, re-implemented as a hot patch, and validated and verified using Earth-based Curiosity testbeds. A checkout test of the patch was performed on Curiosity on sol 2657, and nominal use of the patch began on sol 2658. In this paper, we describe the steps that led to integrating the arm kinematic hot patch into Curiosity's flight software, from the discovery of the bug to the nominal use of the patch in flight.

Maimone, Mark↗
NASA NTRS1991

Lateral variation in upper mantle temperature and composition beneath mid-ocean ridges inferred from shear-wave propagation, geoid, and bathymetry

Resolution of both the extent and mechanism of lateral heterogeneity in the upper mantle constraints the nature and scales of mantle convection. Oceanic regions are of particular interest as they are likely to provide the closest glimpse at the patterns of temperature anomalies and convective flow in the upper mantle because of their young age and simple crustal structure relative to continental regions. Lateral variations were determined in the seismic velocity and attenuation structure of the lithosphere and astenosphere beneath the oceans, and these seismological observations were combined with the data and theory of geoid and bathymetry anomalies in order to test and improve current models for seafloor spreading and mantle convection. Variations were determined in mantle properties on a scale of about 1000 km, comparable to the thickness of the upper mantle. Seismic velocity, geoid, and bathymetry anomalies are all sensitive to variations in upper mantle density, and inversions were formulated to combine quantitatively these different data and to search for a common origin. Variations in mantle density can be either of thermal or compositional origin and are related to mantle convection or differentiation.

Sheehan, Anne Francis↗
NASA NTRS1993

Retrieval of temperature profiles from Martian infrared spectra

In theory, a thermal emission spectrum of Mars (220-1600 cm(exp -1)) contains a wealth of information about the composition and thermal structure of the atmosphere and surface. However, in practice, the ability to retrieve quantitative information from the spectrum is limited by a number of factors including (1) the ill-posed nature of the spectral inversion problem and the resulting nonuniqueness of all solutions; (2) assumptions built into any spectral inversion program; (3) uncertainties in surface pressure, temperature, and emissivity; and (4) uncertainties in the optical properties of atmospheric aerosols. Below, factors (1) and (2) are discussed as fundamental limitations on temperature retrievals from Mariner 9 Infrared Interferometer Spectrometer (IRIS) spectra. In preparation for the Mars Observer mission and the return of tens of thousands of infrared spectra per day from the Thermal Emission Spectrometer (TES), we have developed a fast inversion algorithm to retrieve temperature structure and aerosol opacity from the infrared spectra. The derived atmospheric models will be used to provide the atmospheric contribution to the TES spectra, so that the thermal emission spectra of the underlying surface can be determined for making mineralogical identifications. As a test of our algorithm, we are undertaking a systematic analysis of the entire Mariner 9 Infrared Interferometric Spectrometer (IRIS) dataset of 21,000 plus spectra. While portions of the IRIS dataset have been previously analyzed, the lack of a speedy and robust algorithm to invert the IRIS spectra to retrieve temperature profiles and aerosol opacities has been a major impediment to a truly comprehensive analysis.

Mcmillan, W. Wallace↗
NASA NTRS2018

An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells

The inverse Finite Element Method (iFEM) is a revolutionary methodology for real-time reconstruction of full-field structural displacements and stresses in structures that are instrumented with strain sensors. This inverse problem is commonly referred to as shape and stress sensing, which is well-recognized as an enabling technology for structural health monitoring systems. In this study, an improved iFEM formulation is proposed for shape and stress sensing of laminated composite and sandwich plates and shells. The formulation includes the kinematics of a shear deformation plate theory known as Refined Zigzag Theory (RZT) as its baseline. The present iFEM formulation is based upon the minimization of a weighted-least-squares functional that uses the complete set of section strains of RZT. The improved iFEM methodology is applicable for shape and stress sensing of thin and moderately thick plate and shell structures involving a relatively small number of strain gauges. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. A three-node inverseshell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. For both problems, the experimental strain data are generated numerically by the direct finite element analysis using high-fidelity discretizations. These strains are then regarded as the experimental strains obtained from surface mounted strain gauges or embedded fiber Bragg grating (FBG) sensors. The numerical results demonstrate the superior capability and potential applicability of the i3- RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures.

Kefal, Adnan↗
NASA NTRS1971

Feasibility study for automatic reduction of phase change imagery

The feasibility of automatically reducing a form of pictorial aerodynamic heating data is discussed. The imagery, depicting the melting history of a thin coat of fusible temperature indicator painted on an aerodynamically heated model, was previously reduced by manual methods. Careful examination of various lighting theories and approaches led to an experimentally verified illumination concept capable of yielding high-quality imagery. Both digital and video image processing techniques were applied to reduction of the data, and it was demonstrated that either method can be used to develop superimposed contours. Mathematical techniques were developed to find the model-to-image and the inverse image-to-model transformation using six conjugate points, and methods were developed using these transformations to determine heating rates on the model surface. A video system was designed which is able to reduce the imagery rapidly, economically and accurately. Costs for this system were estimated. A study plan was outlined whereby the mathematical transformation techniques developed to produce model coordinate heating data could be applied to operational software, and methods were discussed and costs estimated for obtaining the digital information necessary for this software.

Nossaman, G. O.↗
NASA NTRS1976

First order impulsive solutions

A mathematically rigorous derivation is given of first order corrections to multi-impulse approximations to the solutions to space flight optimization problems with bang-bang control. The rocket was subjected to an inverse square gravitational force and to a thrust force with constant magnitude. The mass decreased linearly with time. An optimal impulsive solution was obtained for a problem with given initial and final conditions. The method was then used to obtain first-order corrections to the initial values of the costate variables. Indications are given on how the theory may be extended to higher order corrections. The theory was applied to intercept and rendezvous problems.

Andrus, J. F.↗