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Results for “inverse problem solving”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Solving inversion problems with neural networks

A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

Kamgar-Parsi, Behzad↗
NASA NTRS1992

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗
NASA NTRS1991

Energy functions for regularization algorithms

Regularization techniques are widely used for inverse problem solving in computer vision such as surface reconstruction, edge detection, or optical flow estimation. Energy functions used for regularization algorithms measure how smooth a curve or surface is, and to render acceptable solutions these energies must verify certain properties such as invariance with Euclidean transformations or invariance with parameterization. The notion of smoothness energy is extended here to the notion of a differential stabilizer, and it is shown that to void the systematic underestimation of undercurvature for planar curve fitting, it is necessary that circles be the curves of maximum smoothness. A set of stabilizers is proposed that meet this condition as well as invariance with rotation and parameterization.

Delingette, H.↗
NASA NTRS2012

A Review of Low Frequency Electromagnetic Wave Phenomena Related to Tropospheric-Ionospheric Coupling Mechanisms

Investigation of coupling mechanisms between the troposphere and the ionosphere requires a multidisciplinary approach involving several branches of atmospheric sciences, from meteorology, atmospheric chemistry, and fulminology to aeronomy, plasma physics, and space weather. In this work, we review low frequency electromagnetic wave propagation in the Earth-ionosphere cavity from a troposphere-ionosphere coupling perspective. We discuss electromagnetic wave generation, propagation, and resonance phenomena, considering atmospheric, ionospheric and magnetospheric sources, from lightning and transient luminous events at low altitude to Alfven waves and particle precipitation related to solar and magnetospheric processes. We review in situ ionospheric processes as well as surface and space weather phenomena that drive troposphere-ionosphere dynamics. Effects of aerosols, water vapor distribution, thermodynamic parameters, and cloud charge separation and electrification processes on atmospheric electricity and electromagnetic waves are reviewed. We also briefly revisit ionospheric irregularities such as spread-F and explosive spread-F, sporadic-E, traveling ionospheric disturbances, Trimpi effect, and hiss and plasma turbulence. Regarding the role of the lower boundary of the cavity, we review transient surface phenomena, including seismic activity, earthquakes, volcanic processes and dust electrification. The role of surface and atmospheric gravity waves in ionospheric dynamics is also briefly addressed. We summarize analytical and numerical tools and techniques to model low frequency electromagnetic wave propagation and solving inverse problems and summarize in a final section a few challenging subjects that are important for a better understanding of tropospheric-ionospheric coupling mechanisms.

Simoes, Fernando↗
NASA NTRS1991

Inverse problems in the design, modeling and testing of engineering systems

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

Alifanov, Oleg M.↗
NASA NTRS2022

A Novel Approach to Solve Forward/Inverse Problems in Remote Sensing Applications

Inversion of electromagnetic (EM) signals reflected from or transmitted through a medium, or emitted by it due to internal sources can be used to investigate the optical and physical properties of a variety of scattering/absorbing/emitting materials. Such media encompass planetary atmospheres and surfaces (including water/snow/ice), and plant canopies. In many situations the signals emerging from such media can be described by a linear transport equation which in the case of EM radiation is the radiative transfer equation (RTE). Solutions of the RTE can be used as a forward model to solve the inverse problem to determine the medium state parameters giving rise to the emergent (reflected/transmitted/emitted) EM signals. A novel method is developed to determine layer-by-layer contributions to the emergent signals from such stratified, multilayered media based on the solution of the pertinent RTE. As a specific example of how this approach may be applied, the radiation reflected from a multilayered atmosphere is used to solve the problem relevant for EM probing by a space-based lidar system. The solutions agree with those obtained using the standard lidar approach for situations in which single scattering prevails, but this novel approach also yields reliable results for optically thick, multiple scattering aerosol and cloud layers that cannot be provided by the traditional lidar approach.

forward modeling↗
NASA NTRS2021

Inversion of Magnetic Measurements of the Swarm A Satellite of the Bangui Magnetic Anomaly

We wanted to make a satellite altitude magnetic anomaly map of the large magnetic anomaly in the Central African Republic, the Bangui magnetic anomaly, with data from the Swarm satellites. In the first part of our study, we summarize the earlier investigations and their interpretation. In the second we discuss our data processing applied to produce a magnetic anomaly map. We used the IGRF 12th to remove the long-wavelength regional anomalies. We will use an inverse procedure, which always requires a solution of the direct problem, and a horizontal polygonal prism given in the Descartes coordinate system. For this, reason the total magnetic anomaly was transformed into the Descartes coordinate system. The magnetization and its direction were used from our previous paper. The inverse problem is solved by the Simplex procedure. Our selected polygon has 14 geometrical parameters however, the inverse problem that is the numerical determination of the minimum problem is solved in the 14 dimensions. The result of our inverse problem was the 12 horizontal coordinates and the two upper and lower data of the polygon. The origin of the Bangui anomaly has been discussed in several scientific reports, either as a deep crustal tectonic feature or the result of a large external impactor. However, according to our inversion computations we cannot make any unambiguous finding for the origin of this feature. The inaccuracy in our total anomaly map is given by the Gaussian error propagation.

KI Kis↗
NASA NTRS1991

Inverse problems in diffraction

A two-dimensional problem of diffraction of a plane electromagnetic wave on a smooth 2 pi-periodic surface is considered. A numerical algorithm solving this problem is developed. An inverse problem of determination of the shape of 2 pi-periodic surface using the performance data of reverse scattering is considered. The inverse problem was solved by means of minimization of the residual functional with the help of the gradient descent method. The initial data were calculated with the help of the numerical method. On each step of the iterative method of minimization, the residual functional was calculated approximately with the help of the small slope method. The examples of the shape determination are considered.

Mikheev, Andrew G.↗
NASA NTRS2013

Thick Galactic Cosmic Radiation Shielding Using Atmospheric Data

NASA is concerned with protecting astronauts from the effects of galactic cosmic radiation and has expended substantial effort in the development of computer models to predict the shielding obtained from various materials. However, these models were only developed for shields up to about 120 g!cm2 in thickness and have predicted that shields of this thickness are insufficient to provide adequate protection for extended deep space flights. Consequently, effort is underway to extend the range of these models to thicker shields and experimental data is required to help confirm the resulting code. In this paper empirically obtained effective dose measurements from aircraft flights in the atmosphere are used to obtain the radiation shielding function of the earth's atmosphere, a very thick shield. Obtaining this result required solving an inverse problem and the method for solving it is presented. The results are shown to be in agreement with current code in the ranges where they overlap. These results are then checked and used to predict the radiation dosage under thick shields such as planetary regolith and the atmosphere of Venus.

Youngquist, Robert C.↗
NASA NTRS1979

Improvements in surface singularity analysis and design methods

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Bristow, D. R.↗
NASA NTRS1991

Numerical recovery of certain discontinuous electrical conductivities

The inverse problem of recovering an electrical conductivity of the form Gamma(x) = 1 + (k-1)(sub Chi(D)) (Chi(D) is the characteristic function of D) on a region omega is a subset of 2-dimensional Euclid space from boundary data is considered, where D is a subset of omega and k is some positive constant. A linearization of the forward problem is formed and used in a least squares output method for approximately solving the inverse problem. Convergence results are proved and some numerical results presented.

Bryan, Kurt↗
NASA NTRS1981

Space Shuttle Orbiter flight heating rate measurement sensitivity to thermal protection system uncertainties

A study was completed to determine the sensitivity of computed convective heating rates to uncertainties in the thermal protection system thermal model. Those parameters considered were: density, thermal conductivity, and specific heat of both the reusable surface insulation and its coating; coating thickness and emittance; and temperature measurement uncertainty. The assessment used a modified version of the computer program to calculate heating rates from temperature time histories. The original version of the program solves the direct one dimensional heating problem and this modified version of The program is set up to solve the inverse problem. The modified program was used in thermocouple data reduction for shuttle flight data. Both nominal thermal models and altered thermal models were used to determine the necessity for accurate knowledge of thermal protection system's material thermal properties. For many thermal properties, the sensitivity (inaccuracies created in the calculation of convective heating rate by an altered property) was very low.

Bradley, P. F.↗
NASA NTRS1991

Inverse problem in incompressible, irrotational axisymmetric flow

A vortex-sheet method for solving the axisymmetric inverse problem is presented, and an iterative, interactive computer program for computing the body shape starting from an assumed shape is developed. The method eliminates the calculation of the direct problem at every iteration using the given velocity. The singular integral that arises in the problem formulation has been integrated analytically. The efficiency of the vortex-sheet method is demonstrated using three test cases, and the obtained body shapes and the corresponding surface velocity distributions are presented.

Dinavahi, Surya P. G.↗
NASA NTRS1977

A spectral domain method for remotely probing stratified media

The problem of remotely probing a stratified, lossless, dielectric medium is formulated using the spectral domain method of probing. The response of the medium to a spectrum of plane waves incident at various angles is used to invert the unknown profile. For TE polarization, the electric field satisfies a Helmholtz equation. The inverse problem is solved by means of a new representation for the wave function. The principal step in this inversion is solving a second kind Fredholm equation which is very amenable to numerical computations. Several examples are presented including some which indicate that the method can be used with experimentally obtained data. When the fields exhibit a surface wave behavior, a unique inversion can be obtained only if information about the magnetic field is also available. In this case, the inversion is accomplished by a two-step procedure which employs a formula of Jost and Kohn. Some examples are presented, and an approach which greatly shortens the computations without greatly deteriorating the results is discussed.

Schaubert, D. H.↗
NASA NTRS1972

The inverse scattering problem for transmission lines

A number of exact and approximate methods for solving the inverse scattering problem for transmission lines are reviewed. In particular, the application to transmission lines of Marcenko's version of the Gelfand-Levitan exact method for the quantum mechanical problem is compared with a more direct approach based on a different version of the Gelfand-Levitan method. In addition, some aspects of the lack of uniqueness of solutions are discussed, and some open questions related to the inverse scattering problem are suggested.

Kay, I.↗
NASA NTRS1958

A method of computing the transient temperature of thick walls from arbitrary variation of adiabatic-wall temperature and heat-transfer coefficient

A method of calculating the temperature of thick walls has been developed in which the time series and the response to a unit triangle variation of surface temperature concepts are used, together with essentially standard formulas for transient temperature and heat flow into thick walls. The method can be used without knowledge of the mathematical tools of its development. The method is particularly suitable for determining the wall temperature in one-dimensional thermal problems in aeronautics where there is a continuous variation of the heat-transfer coefficient and adiabatic-wall temperature. The method also offers a convenient means for solving the inverse problem of determining the heat-flow history when temperature history is known.

Hill, P R↗