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NASA NTRS1992

A boundary integral method for an inverse problem in thermal imaging

An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data.

Bryan, Kurt↗

NASA NTRS1991

Joint inversion of shear wave travel time residuals and geoid and depth anomalies for long-wavelength variations in upper mantle temperature and composition along the Mid-Atlantic Ridge

Measurements were carried out for SS-S differential travel time residuals for nearly 500 paths crossing the northern Mid-Atlantic Ridge, assuming that the residuals are dominated by contributions from the upper mantle near the surface bounce point of the reflected phase SS. Results indicate that the SS-S travel time residuals decrease linearly with square root of age, to an age of 80-100 Ma, in general agreement with the plate cooling model. A joint inversion was formulated of travel time residuals and geoid and bathymetric anomalies for lateral variation in the upper mantle temperature and composition. The preferred inversion solutions were found to have variations in upper mantle temperature along the Mid-Atlantic Ridge of about 100 K. It was calculated that, for a constant bulk composition, such a temperature variation would produce about a 7-km variation in crustal thickness, larger than is generally observed.

Sheehan, Anne F.↗

NASA NTRS1991

Cold equation of state in a strong magnetic field - Effects of inverse beta-decay

The influence of a high magnetic field (B is greater than 10 exp 12 G) on the degenerate matter equation of state appropriate to a neutron star is studied. The regime dominated by relativistic electrons up to the neutron drip density is highlighted. The equilibrium matter composition and equation of state, allowing for inverse beta-decay. Two different equilibrium models are determined: an ideal neutron-proton-electron (npe) gas and the more realistic model of Baym, Pethick, and Sutherland (1971) consisting of a Coulomb lattice of heavy nuclei embedded in an electron gas. For a sufficiently high field strength, the magnetic field has an appreciable effect, changing the adiabatic index of the matter and the nuclear transition densities. The influence of a strong field on some simple nonequilibrium processes, including beta-decay and inverse beta-decay (electron capture) is also considered. The effects produced by the magnetic field are mainly due to the changes in the transverse electron quantum orbits and the allowed electron phase space induced by the field.

Lai, Dong↗

NASA NTRS1990

Validation of Earth Radiation Budget Experiment scanning radiometer data inversion procedures

Validation techniques were implemented in the inversion of scanner radiometer data to assess the accuracy of the top of atmosphere radiant fluxes. An evaluation of SW radiant flux standard deviations for the same scene type shows that they contribute about 6.0 W/sq m for viewing zenith angles less than 55 deg and can reach values of up to 17.6 W/sq m for larger zenith angles in the backward scanning position. Three-channel intercomparison results, presented as color graphic displays and histograms, effectively validate the radiance measurements and the spectral factors. Along-track data were used to validate limb-darkening models and showed good agreement with current ERBE models. These validation techniques were found to be very effective in assessing the quality of the radiant fluxes generated by the ERBE inversion algorithm.

Manalo, Natividad D.↗

NASA NTRS1992

Weighted current sheets supported in normal and inverse configurations - A model for prominence observations

A technique which incorporates both photospheric and prominence magnetic field observations is used to analyze the magnetic support of solar prominences in two dimensions. The prominence is modeled by a mass-loaded current sheet which is supported against gravity by magnetic fields from a bipolar source in the photosphere and a massless line current in the corona. It is found that prominence support can be achieved in three different kinds of configurations: an arcade topology with a normal polarity; a helical topology with a normal polarity; and a helical topology with an inverse polarity. In all cases the important parameter is the variation of the horizontal component of the prominence field with height. Adding a line current external to the prominence eliminates the nonsupport problem which plagues virtually all previous prominence models with inverse polarity.

Demoulin, P.↗

NASA NTRS1992

'Wrong' bond interactions at inversion domain boundaries in GaAs

Electronic structure calculations of GaAs inversion-domain boundaries (IDBs) on different planes are reported. The resulting interface energies are analyzed in terms of the number of 'wrong' bonds (Ga-Ga and As-As) and their mutual compensation. The compensation energy varies roughly inversely proportionally to the distance between the wrong bonds. This favors local compensation in stoichiometric material. This automatically occurs for 110-plane planes or by chemical reconstruction for other planes. Ga-rich IDBs are predicted to have low energy in either Ga-rich or n-type material.

Lambrecht, W. R. L.↗

NASA NTRS1991

Efficient control with an order (n) recursive inversion of the Jacobian for an n-link serial manipulator

A method is presented to order (n) recursively invert the Jacobian matrix for a serial n-link manipulator. By realizing that the Jacobian relationship involving accelerations is a special case for the forward dynamics problem, it is possible to obtain the Jacobian inverse by directly applying Rodriguez's (1987) recursive forward dynamics algorithm. In this technique, the n-link robot equation is formulated as a spatially recursive algorithm in the form of a filtering and smoothing problem. To compute the Jacobian inverse via this algorithm, the n-link manipulator is modeled with only a unit end-point mass and zero applied torques.

Meldrum, D. R.↗

NASA NTRS1992

Spatial operator factorization and inversion of the manipulator mass matrix

This paper advances two linear operator factorizations of the manipulator mass matrix. Embedded in the factorizations are many of the techniques that are regarded as very efficient computational solutions to inverse and forward dynamics problems. The operator factorizations provide a high-level architectural understanding of the mass matrix and its inverse, which is not visible in the detailed algorithms. They also lead to a new approach to the development of computer programs or organize complexity in robot dynamics.

Rodriguez, Guillermo↗

NASA NTRS1991

The inverse Compton gamma-ray spectrum of the Crab nebula

The observed TeV flux from the Crab can be explained by inverse Compton scattering in the nebula if the average nebular field is indeed approximately equal to 0.0003 G as is predicted by the spectral break between radio and optical. The estimated spectral index at TeV energies also agrees with the observed value. The unpulsed high energy gamma-rays seen by COS-B are not explained by this inverse Compton component but can be explained by synchrotron radiation requiring electrons up to at least 10 exp 16 eV, most likely accelerated at the shock in the pulsar wind. The detection of a spectral depression at about 1 GeV would allow an estimate of the maximum electron energy. The flux estimates also predict the detection of a steady flux of unpulsed UHE gamma-rays from near the shock with sensitive detectors if the field strength increases downstream with increasing radius as is predicted by MHD theory.

De Jager, O. C.↗

NASA NTRS1991

Microwave polarization inversion observed

Observations of an inversion of solar-active-region microwave polarization are described as they occurred during the Coronal Magnetic Structures Observing Campaign. Data regarding the microwave frequencies, soft X-ray emissions, brightness temperatures, and column emissions are obtained with the observations. The data are employed in the potential-field extrapolation procedure by Sakurai (1982) to calculate the coronal magnetic-field vector, and the microwave polarization observations yield reasonable coronal densities and evidence of an inversion.

Brosius, Jeffrey W.↗

NASA NTRS1992

An inverse dynamics approach to trajectory optimization for an aerospace plane

An inverse dynamics approach for trajectory optimization is proposed. This technique can be useful in many difficult trajectory optimization and control problems. The application of the approach is exemplified by ascent trajectory optimization for an aerospace plane. Both minimum-fuel and minimax types of performance indices are considered. When rocket augmentation is available for ascent, it is shown that accurate orbital insertion can be achieved through the inverse control of the rocket in the presence of disturbances.

Lu, Ping↗

NASA NTRS1992

Inverse kinematics problem in robotics using neural networks

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

Choi, Benjamin B.↗

NASA NTRS1993

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Voorhies, Coerte V.↗

NASA NTRS1992

Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model

Simultaneous inversion of the three parameters was performed which included mean-grain size of ice particles in snow, snow density, and snow temperatures from five brightness temperatures. Good results for the inversion of parameters were obtained using the neural network based on the simulated data computed from the dense media radiative transfer equation that takes into account the effects of multiple scattering.

Tsang, Leung↗

NASA NTRS1993

Feasibility of determining surface emissions of trace gases using an inverse method in a three-dimensional chemical transport model

The paper investigates the feasibility of using an inverse method based on a linear Kalman filter in a three-dimensional atmospheric transport model, for the determination of regional surface fluxes with rapid convergence, using data from a finite number of observation sites. It was found that the inverse method used was capable to accurately determine regional surface fluxes using the present ALE/GALE sites, and to converge to the correct solution within a year or two, using initial conditions very different from the final solution.

Hartley, Dana↗

NASA NTRS1993

An inverse method for computation of structural stiffness distributions of aeroelastically optimized wings

An inverse method has been developed to compute the structural stiffness properties of wings given a specified wing loading and aeroelastic twist distribution. The method directly solves for the bending and torsional stiffness distribution of the wing using a modal representation of these properties. An aeroelastic design problem involving the use of a computational aerodynamics method to optimize the aeroelastic twist distribution of a tighter wing operating at maneuver flight conditions is used to demonstrate the application of the method. This exercise verifies the ability of the inverse scheme to accurately compute the structural stiffness distribution required to generate a specific aeroelastic twist under a specified aeroelastic load.

Schuster, David M.↗

NASA NTRS1992

Error analysis applied to several inversion techniques used for the retrieval of middle atmospheric constituents from limb-scanning MM-wave spectroscopic measurements

The formal retrieval error analysis of Rodgers (1990) allows the quantitative determination of such retrieval properties as measurement error sensitivity, resolution, and inversion bias. This technique was applied to five numerical inversion techniques and two nonlinear iterative techniques used for the retrieval of middle atmospheric constituent concentrations from limb-scanning millimeter-wave spectroscopic measurements. It is found that the iterative methods have better vertical resolution, but are slightly more sensitive to measurement error than constrained matrix methods. The iterative methods converge to the exact solution, whereas two of the matrix methods under consideration have an explicit constraint, the sensitivity of the solution to the a priori profile. Tradeoffs of these retrieval characteristics are presented.

Puliafito, E.↗

NASA NTRS1993

Deduction of emissions of source gases using an objective inversion algorithm and a chemical transport model

An inversion algorithm, constructed to deduce the emissions of a source gas required to produce a specified surface concentration, is applied to the observed surface concentrations of CFC 11, methylchloroform, and methane, using a two-dimensional chemical transport model. The information utilized for this deduction process is limited to the measured atmospheric concentration of the source gas, including the associated standard deviations of these measurements. In this way the amount of objective information available in these measurements is assessed. The algorithm is shown to be capable of producing a latitudinal emissions distribution as well as the error bounds on the deduced emission distribution. The 'ill posed' nature of this inverse problem is discussed as well as the implications this has on the spatial and temporal resolution at which emissions can be resolved. Finally, a methane emission distribution is deduced which has the expected seasonal variations and consistent with results from other, more subjective, deduction studies.

Brown, Margaret↗