SEARCH · Search NASA

Results for “linear inverse modeling”

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.

SourceResearch connectionFrom yearThrough year

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

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS2017

Imaging a Free-Geometry Magma Reservoir Using FEM-Based Linear Inverse Modeling of InSAR Data: Application to Rabaul Caldera, Papua New Guinea

We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluidfilled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.

Inverse theory↗

NASA NTRS2017

Imaging the Complex Geometry of a Magma Reservoir Using Fem-Based Linear Inverse Modeling of InSAR Data: Application to Rabaul Caldera, Papua New Guinea

We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.

Inverse theory↗

NASA NTRS2002

Low-Cost Evaluation of EO-1 Hyperion and ALI for Detection and Biophysical Characterization of Forest Logging in Amazonia (NCC5-481)

Major uncertainties exist regarding the rate and intensity of logging in tropical forests worldwide: these uncertainties severely limit economic, ecological, and biogeochemical analyses of these regions. Recent sawmill surveys in the Amazon region of Brazil show that the area logged is nearly equal to total area deforested annually, but conversion of survey data to forest area, forest structural damage, and biomass estimates requires multiple assumptions about logging practices. Remote sensing could provide an independent means to monitor logging activity and to estimate the biophysical consequences of this land use. Previous studies have demonstrated that the detection of logging in Amazon forests is difficult and no studies have developed either the quantitative physical basis or remote sensing approaches needed to estimate the effects of various logging regimes on forest structure. A major reason for these limitations has been a lack of sufficient, well-calibrated optical satellite data, which in turn, has impeded the development and use of physically-based, quantitative approaches for detection and structural characterization of forest logging regimes. We propose to use data from the EO-1 Hyperion imaging spectrometer to greatly increase our ability to estimate the presence and structural attributes of selective logging in the Amazon Basin. Our approach is based on four "biogeophysical indicators" not yet derived simultaneously from any satellite sensor: 1) green canopy leaf area index; 2) degree of shadowing; 3) presence of exposed soil and; 4) non-photosynthetic vegetation material. Airborne, field and modeling studies have shown that the optical reflectance continuum (400-2500 nm) contains sufficient information to derive estimates of each of these indicators. Our ongoing studies in the eastern Amazon basin also suggest that these four indicators are sensitive to logging intensity. Satellite-based estimates of these indicators should provide a means to quantify both the presence and degree of structural disturbance caused by various logging regimes. Our quantitative assessment of Hyperion hyperspectral and ALI multi-spectral data for the detection and structural characterization of selective logging in Amazonia will benefit from data collected through an ongoing project run by the Tropical Forest Foundation, within which we have developed a study of the canopy and landscape biophysics of conventional and reduced-impact logging. We will add to our base of forest structural information in concert with an EO-1 overpass. Using a photon transport model inversion technique that accounts for non-linear mixing of the four biogeophysical indicators, we will estimate these parameters across a gradient of selective logging intensity provided by conventional and reduced impact logging sites. We will also compare our physical ly-based approach to both conventional (e.g., NDVI) and novel (e.g., SWIR-channel) vegetation indices as well as to linear mixture modeling methods. We will cross-compare these approaches using Hyperion and ALI imagers to determine the strengths and limitations of these two sensors for applications of forest biophysics. This effort will yield the first physical ly-based, quantitative analysis of the detection and intensity of selective logging in Amazonia, comparing hyperspectral and improved multi-spectral approaches as well as inverse modeling, linear mixture modeling, and vegetation index techniques.

Asner, Gregory P.↗

NASA NTRS1993

Linearization of manipulator dynamics using spatial operators

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.

Jain, A.↗

NASA NTRS1989

Simplified Linear Multivariable Control Of Robots

Simplified method developed to design control system that makes joints of robot follow reference trajectories. Generic design includes independent multivariable feedforward and feedback controllers. Feedforward controller based on inverse of linearized model of dynamics of robot and implements control law that contains only proportional and first and second derivatives of reference trajectories with respect to time. Feedback controller, which implements control law of proportional, first-derivative, and integral terms, makes tracking errors converge toward zero as time passes.

Seraji, Homayoun↗

NASA NTRS1975

Comparison of some biased estimation methods (including ordinary subset regression) in the linear model

Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.

Sidik, S. M.↗

NASA NTRS1986

Design of multivariable controllers for robot manipulators

The paper presents a simple method for the design of linear multivariable controllers for multi-link robot manipulators. The control scheme consists of multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and achieves pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. The two controllers are independent of each other and are designed separately based on the linearized robot model and then integrated in the overall control scheme. The proposed scheme is simple and can be implemented for real-time control of robot manipulators.

Seraji, H.↗

NASA NTRS1986

Linear multivariable control of robot manipulators

The paper presents a simple scheme for the linear multivariable control of multi-link robot manipulators. The control scheme consists of multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative terms. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-derivative type and achieves stability and pole placement. This controller reduces any initial tracking error to zero as desired. The two controllers are independent of each other and are designed separately based on the linearized robot model and then integrated in an overall control scheme.

Seraji, H.↗

NASA NTRS1987

An approach to multivariable control of manipulators

The paper presents simple schemes for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates. The joint control scheme consists of two independent multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms - implying feedforward from the desired position, velocity and acceleration. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and is designed to achieve pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. Simple and explicit expressions of computation of the feedforward and feedback gains are obtained based on the linearized model of robot dynamics. This leads to computationally efficient schemes for either on-line gain computation or off-line gain scheduling to account for variations in the linearized robot model due to changes in the operating point. The joint control scheme is extended to direct control of the end-effector motion in Cartesian space. Simulation results are given for illustration.

Seraji, H.↗

NASA NTRS1989

Method and apparatus for adaptive force and position control of manipulators

The present invention discloses systematic methods and apparatus for the design of real time controllers. Real-time control employs adaptive force/position by use of feedforward and feedback controllers, with the feedforward controller being the inverse of the linearized model of robot dynamics and containing only proportional-double-derivative terms is disclosed. The feedback controller, of the proportional-integral-derivative type, ensures that manipulator joints follow reference trajectories and the feedback controller achieves robust tracking of step-plus-exponential trajectories, all in real time. The adaptive controller includes adaptive force and position control within a hybrid control architecture. The adaptive controller, for force control, achieves tracking of desired force setpoints, and the adaptive position controller accomplishes tracking of desired position trajectories. Circuits in the adaptive feedback and feedforward controllers are varied by adaptation laws.

Seraji, Homayoun↗

NASA NTRS1987

An equivalent layer magnetization model for Australia based on Magsat data

An equivalent layer magnetization model for Australia and adjacent oceanic areas is presented. The model is obtained by linear inversion of Magsat anomaly data measured in the altitude range 325-550 km. The anomaly data set has been isolated from the raw data set by use of models of the core field and very long wavelength external fields, and is internally consistent. Certain major structural features of the Australian continent are geographically associated with magnetization anomalies. A first-order difference is seen between the Tasman Zone and the Precambrian cratonic areas: magnetization anomalies are much more subdued in the former, possibly reflecting a shallowing of the Curie isotherm within the crust. A profile of the vertical integral of magnetization is presented for a crustal section extending from the Gawler Block to the southeast coast. It is shown that the magnetization variations are probably due partly, but not wholly, to depth to Curie isotherm variations; gross magnetization variations among at least three distinct crustal units must be involved.

Mayhew, M. A.↗

NASA NTRS1993

Steady induction effects in geomagnetism. Part 1C: Geomagnetic estimation of steady surficial core motions: Application to the definitive geomagnetic reference field models

In the source-free mantle/frozen-flux core magnetic earth model, the non-linear inverse steady motional induction problem was solved using the method presented in Part 1B. How that method was applied to estimate steady, broad-scale fluid velocity fields near the top of Earth's core that induce the secular change indicated by the Definitive Geomagnetic Reference Field (DGRF) models from 1945 to 1980 are described. Special attention is given to the derivation of weight matrices for the DGRF models because the weights determine the apparent significance of the residual secular change. The derived weight matrices also enable estimation of the secular change signal-to-noise ratio characterizing the DGRF models. Two types of weights were derived in 1987-88: radial field weights for fitting the evolution of the broad-scale portion of the radial geomagnetic field component at Earth's surface implied by the DGRF's, and general weights for fitting the evolution of the broad-scale portion of the scalar potential specified by these models. The difference is non-trivial because not all the geomagnetic data represented by the DGRF's constrain the radial field component. For radial field weights (or general weights), a quantitatively acceptable explication of broad-scale secular change relative to the 1980 Magsat epoch must account for 99.94271 percent (or 99.98784 percent) of the total weighted variance accumulated therein. Tolerable normalized root-mean-square weighted residuals of 2.394 percent (or 1.103 percent) are less than the 7 percent errors expected in the source-free mantle/frozen-flux core approximation.

Voorhies, Coerte V.↗

NASA NTRS1980

Inversion of multiwavelength radiometer measurements by three-dimensional filtering

Remote sensing data from satellites typically have three dimensions: scan position, spacecraft position, and wavelength. Inversion of the radiometric data to infer geophysical parameters is a filtering problem in which the dimension of wavelength (or channel number) is transformed into a dimension of geophysical parameters, and the most general solution is a three-dimensional filter. Linear filters have the advantages of computational speed and easily described transfer functions; but often the measurements are nonlinear functions of the parameters to be inferred. To the extent that the nonlinear inversion problem is overdetermined, it can be modeled by a critically determined linear problem. As an example, inversion of Scanning Multichannel Microwave Radiometer (SMMR) data by means of a three-dimensional Wiener Filter is described. Atmospheric water vapor content, rain liquid water content, surface wind speed and surface temperature are the parameters inferred from the measurements. Nonprecipitating liquid water and water vapor scale height are also modeled but not retrieved. The a priori statistics on which the filter is trained have the effect of governing the selection of a trade-off point of noise as a function of resolution (in all three retrieval dimensions).

Rosenkranz, P. W.↗

NASA NTRS1994

Microbial community structure at the U.S.-Joint Global Ocean Flux Study Station ALOHA: Inverse methods for estimating biochemical indicator ratios

Modeling biogeochemical fluxes in the marine plankton requires the application of factors for extrapolation of biomass indicators measured in the field (chlorophyll a, adenosine triphosphate, bacterial counts) to biomass carbon or nitrogen. These are often inferred from culture studies and are poorly constrained for natural populations. At least squares inverse method with a simple linear model constrains the values of several common indicator ratios, giving self-consistent solutions that provide useful information about the structure of the microbial community at our North Pacific Ocean study site (Station ALOHA (A Long-term Oligotrophic Habitat Assessment)). These results indicate that the fraction of the microbial biomass that is autotrophic (pigmented) is greater in the mixed layer than at the deep chlorophyll maximum layer and that heterotrophic bacteria are a significant but not necessarily predominant component of the microbial community in the euphotic zone.

Christian, James R.↗

NASA NTRSDate not supplied

A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty

When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.

Luke J Miller↗

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 NTRS1997

Evaluation of a Neural Adaptive Flight Controller

The objective of this paper is to present results from the evaluation of a direct adaptive tracking controller. The control architecture employs both pre-trained and an on-line neural networks to represent the non-linear aircraft dynamics in the model inversion portion of the controller. The aircraft model used for this evaluation is representative of the F-15 Advanced Control Technology for Integrated Vehicles (ACTIVE) aircraft. The controller was evaluated for three cases: (1) nominal conditions; (2) loss of control power; and (3) loss of control power in the presence of atmospheric turbulence. The results were compared with the existing F-15 ACTIVE conventional mode controller in all cases. The results indicate extremely desirable airframe stabilization characteristics for case (1) that do not degrade significantly for case (2) or (3) as does the conventional mode controller. It was concluded that this controller exhibits both stable and robust adaptive characteristics when subjected to mild and extreme loss of control power conditions. Integration of this neural adaptive flight controller into the full non-linear six degree-of-freedom F-15 ACTIVE simulation is recommended for evaluation in a real-time high fidelity piloted simulation environment.

Totah, Joseph J.↗

NASA NTRS1985

Variability simulations with a steady, linearized primitive equations model

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.

Kinter, J. L., III↗