Search NASA⌕ Search

SEARCH · Search NASA

Results for “Inverse problems”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

An inverse method with regularity condition for transonic airfoil design

It is known from Lighthill's exact solution of the incompressible inverse problem that in the inverse design problem, the surface pressure distribution and the free stream speed cannot both be prescribed independently. This implies the existence of a constraint on the prescribed pressure distribution. The same constraint exists at compressible speeds. Presented here is an inverse design method for transonic airfoils. In this method, the target pressure distribution contains a free parameter that is adjusted during the computation to satisfy the regularity condition. Some design results are presented in order to demonstrate the capabilities of the method.

Zhu, Ziqiang↗
NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗
NASA NTRS1995

Hydromagnetic conditions near the core-mantle boundary

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

Backus, George E.↗
NASA NTRS1986

Studies of acoustic emission from point and extended sources

The use of simulated and controlled acoustic emission signals forms the basis of a powerful tool for the detailed study of various deformation and wave interaction processes in materials. The results of experiments and signal analyses of acoustic emission resulting from point sources such as various types of indentation-produced cracks in brittle materials and the growth of fatigue cracks in 7075-T6 aluminum panels are discussed. Recent work dealing with the modeling and subsequent signal processing of an extended source of emission in a material is reviewed. Results of the forward problem and the inverse problem are presented with the example of a source distributed through the interior of a specimen.

Sachse, W.↗
NASA NTRS1991

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗
NASA NTRS2018

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of ~45 deg between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

Connerney, J. E. P.↗
NASA NTRS2005

Bayesian Inference in Satellite Gravity Inversion

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Kis, K. I.↗
NASA NTRS1988

Bayesian inference in geomagnetism

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

Backus, George E.↗
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 NTRS2001

Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

NASA Discipline Cardiopulmonary↗
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 NTRS2022

Real-time rapid leakage estimation for deep space habitats using exponentially-weighted adaptively-refined search

The recent accelerated growth in space-related research and development activities makes the near-term need for long-term extraterrestrial habitats evident. Such habitats must operate under continuous disruptive conditions arising from extreme environments like meteoroid impacts, extreme temperature fluctuations, galactic cosmic rays, destructive dust, and seismic events. Loss of air or atmospheric leakage from a habitat poses safety challenges that demand proper attention. Such leakage may arise from micro-meteoroid impacts, crack growth, bolt/rivet loosening, and seal deterioration. In this paper, leakage estimation in deep space habitats is posed as an inverse problem. A forward pressure-based dynamical model is formulated for atmospheric leakage. Experiments are performed on a small-scaled pressure chamber where different leakage scenarios are emulated and corresponding pressure values are measured. An exponentially-weighted adaptively-refined search (EWARS) algorithm is developed and validated for the inverse problem of real-time leakage estimation. It is demonstrated that the proposed methodology can achieve real-time estimation and tracking of constant and variable leaks with accuracy.

Deep space habitats↗
NASA NTRS1991

The turbomachine blading design using S2-S1 approach

The boundary conditions corresponding to the design problem when the blades being simulated by the bound vorticity distribution are presented. The 3D flow is analyzed by the two steps S2 - S1 approach. In the first step, the number of blades is supposed to be infinite, the vortex distribution is transformed into an axisymmetric one, so that the flow field can be analyzed in a meridional plane. The thickness distribution of the blade producing the flow channel striction is taken into account by the modification of metric tensor in the continuity equation. Using the meridional stream function to define the flow field, the mass conservation is satisfied automatically. The governing equation is deduced from the relation between the azimuthal component of the vorticity and the meridional velocity. The value of the azimuthal component of the vorticity is provided by the hub to shroud equilibrium condition. This step leads to the determination of the axisymmetric stream sheets as well as the approximate camber surface of the blade. In the second step, the finite number of blades is taken into account, the inverse problem corresponding to the blade to blade flow confined in each stream sheet is analyzed. The momentum equation implies that the free vortex of the absolute velocity must be tangential to the stream sheet. The governing equation for the blade to blade flow stream function is deduced from this condition. At the beginning, the upper and the lower surfaces of the blades are created from the camber surface obtained from the first step with the assigned thickness distribution. The bound vorticity distribution and the penetrating flux conservation applied on the presumed blade surface constitute the boundary conditions of the inverse problem. The detection of this flux leads to the rectification of the geometry of the blades.

Luu, T. S.↗
NASA NTRS1975

Remote monitoring of environmental particulate pollution - A problem in inversion of first-kind integral equations

The determination of the microstructure, chemical nature, and dynamical evolution of scattering particulates in the atmosphere is considered. A description is given of indirect sampling techniques which can circumvent most of the difficulties associated with direct sampling techniques, taking into account methods based on scattering, extinction, and diffraction of an incident light beam. Approaches for reconstructing the particulate size distribution from the direct and the scattered radiation are discussed. A new method is proposed for determining the chemical composition of the particulates and attention is given to the relevance of methods of solution involving first kind Fredholm integral equations.

Fymat, A. L.↗
NASA NTRS1983

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗