SEARCH · Search NASA

Results for “Inverse Optimization”

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 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS2003

A Blind Test of Hapke's Photometric Model

Hapke's bidirectional reflectance equation is a versatile analytical tool for predicting (i.e. forward modeling) the photometric behavior of a particulate surface from the observed optical and structural properties of its constituents. Remote sensing applications of Hapke s model, however, generally seek to predict the optical and structural properties of particulate soil constituents from the observed photometric behavior of a planetary surface (i.e. inverse-modeling). Our confidence in the latter approach can be established only if we ruthlessly test and optimize it. Here, we summarize preliminary results from a blind-test of the Hapke model using laboratory measurements obtained with the Bloomsburg University Goniometer (B.U.G.). The first author selected eleven well-characterized powder samples and measured the spectrophotometric behavior of each. A subset of twenty undisclosed examples of the photometric measurement sets were sent to the second author who fit the data using the Hapke model and attempted to interpret their optical and mechanical properties from photometry alone.

Helfenstein, P.↗

NASA NTRS2013

GRAIL Refinements to Lunar Seismic Structure

Weber, Renee C.↗

NASA NTRS2013

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps to reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co‐located at one corner. Due to this limited geographical extent, near‐surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine‐ or Lunar Prospector‐derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explore the density/velocity relationship. These efforts typically search for the best fitting thermodynamically calculated velocity/density model, allowing variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles previously derived from the Apollo seismic data through inversion of travel times vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocities and density as a function of latitude, longitude, and depth within the Moon. We will relate density to seismic velocity using a linear relationship that is allowed to be depth‐dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of density, velocity, and B‐coefficient perturbations that minimize (in a least‐squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

NASA NTRS2014

Grail Refinements to Lunar Seismic Structure

To probe a planet's interior, seismology provides the most direct constraints on the variables that govern the dynamic properties of the body. However, the GRAIL (Gravity Recovery and Interior Laboratory) mission's high-resolution measurements of the lunar gravity field provide constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten). These data complement seismic investigations, and joint interpretation permits improved constraints on the Moon's internal structure. Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

NASA NTRS2014

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude, and depth within the Moon. We relate density (p) to seismic velocity (v) using a depth-dependent linear relationship. The corresponding coefficient (B) can reflect a variety of material properties, including temperature and composition. The inversion seeks to recover the set of p, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗

NASA NTRS2016

Satellite-Based Spatiotemporal Trends in PM2.5 Concentrations: China 2004-2013

Three decades of rapid economic development is causing severe and widespread PM2.5(particulate matter (is) less than 2.5 ) pollution in China. However, research on the health impacts of PM2.5 exposure has been hindered by limited historical PM2.5 concentration data. We estimated ambient PM2.5 concentrations from 2004 to 2013 in China at 0.1 deg resolution using the most recent satellite data and evaluated model performance with available ground observations. We developed a two-stage spatial statistical model using the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 aerosol optical depth (AOD) and assimilated meteorology, land use data, and PM2.5 concentrations from China's recently established ground monitoring network. An inverse variance weighting (IVW) approach was developed to combine MODIS Dark Target and Deep Blue AOD to optimize data coverage. We evaluated model predicted PM2.5 concentrations from 2004 to early 2014 using ground observations. The overall model cross-validation R(sup 2) and relative prediction error were 0.79 and 35.6%, respectively. Validation beyond the model year (2013) indicated that it accurately predicted PM(sub 2.5) concentrations with little bias at the monthly (R(sup 2) = 0.73), regression slope = 0.91) and seasonal (R(sup 2) = 0.79), regression slope = 0.92) levels. Seasonal variations revealed that winter was the most polluted season and that summer was the cleanest season. Analysis of predicted PM2.5 levels showed a mean annual increase of 1.97 micro-g/cu cm between 2004 and 2007 and a decrease of 0.46 micro-g/cu cm between 2008 and 2013. Our satellite-driven model can provide reliable historical PM2.5 estimates in China at a resolution comparable to those used in epidemiologic studies on the health effects of long-term PM2.5 exposure in North America. This data source can potentially advance research on PM2.5 health effects in China.

satellite remote sensing↗

NASA NTRS1988

Inversion of the Solar Rotation Rate Versus Depth and Latitude

Three differential inversion techniques were used to compute the internal solar rotation rate from several sets of n-averaged frequency splittings. An iterative variation of the spectral expansion method; the optimal averaging kernel method; and a piecewise constant constrained least square method were used to invert the data. Each computation was carried out independently. While they present similar trends, each of the solutions differs in detail. A consistent feature in all the inversions is the disappearance of differential rotation below the base of the convection zone. Also, a strong differential signature in the deeper part of the convection zone is present in most of the solutions. A slow decrease of the rotation rate with depth for the equatorial and midlatitude curves is significant in the spectral expansion and the least square results but only marginally apparent in the averaging kernel results.

Korzennik, Sylvain G.↗

NASA NTRS2012

Top-down Estimate of Dust Emissions Through Integration of MODIS and MISR Aerosol Retrievals With the Geos-chem Adjoint Model

Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOSChem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.

MODIS aerosol retrievals↗

NASA NTRSDate not supplied

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

entry↗

NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗

NASA NTRS1981

A procedure for estimating the information content of SBUV ozone profiles

A description is presented of a new procedure for determining ozone mixing ratios in the upper stratosphere from satellite observations of backscattered ultraviolet (SBUV) radiance. The employed approach is based on a SBUV inversion procedure. The inversion algorithm can best be described as a series of sequentially performed operations, taking into account the determination of a first guess profile, the representation of the ozone profile by a polynomial, the extension of the profile outside the measurement region, error assessment, the optimal ozone profile, and the utilization of iteration. It is found that the described ozone profiling algorithm can be implemented with sufficient computational speed to be used operationally for the inversion of SBUV data.

Cunnold, D. M.↗

NASA NTRS1965

Method of characteristic constants and retro- thrust optimality in a gravitational field - necessary and sufficient conditions.

Intermediate thrust sub-arcs analyzed by method of characteristic constants for optimum retrothrust program in inverse-square-law force field

BOUNDARY VALUE↗

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

Structural control design based on reduced-order observer

An observer-based structural control design method is proposed in this paper. The method is a semi-inverse design procedure in that the control law is not designed before the observer system, but is a result that comes from the observer design. However, the observer design is not completely independent of the control design either, but seeks to yield a control law that is close to a prescribed control law. First, the observer design problem is considered as the reconstruction of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the optimal feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. The semi-inverse design procedure can yield a reduced-order observer with dimension considerably smaller than that of the system. Two examples are used to demonstrate the proposed design procedure.

Su, Tzu-Jeng↗

NASA NTRS1998

Numerical Procedures for Inlet/Diffuser/Nozzle Flows

Two primitive variable, pressure based, flux-split, RNS/NS solution procedures for viscous flows are presented. Both methods are uniformly valid across the full Mach number range, Le., from the incompressible limit to high supersonic speeds. The first method is an 'optimized' version of a previously developed global pressure relaxation RNS procedure. Considerable reduction in the number of relatively expensive matrix inversion, and thereby in the computational time, has been achieved with this procedure. CPU times are reduced by a factor of 15 for predominantly elliptic flows (incompressible and low subsonic). The second method is a time-marching, 'linearized' convection RNS/NS procedure. The key to the efficiency of this procedure is the reduction to a single LU inversion at the inflow cross-plane. The remainder of the algorithm simply requires back-substitution with this LU and the corresponding residual vector at any cross-plane location. This method is not time-consistent, but has a convective-type CFL stability limitation. Both formulations are robust and provide accurate solutions for a variety of internal viscous flows to be provided herein.

Rubin, Stanley G.↗

NASA NTRS1998

Accelerated Training for Large Feedforward Neural Networks

In this paper we introduce a new training algorithm, the scaled variable metric (SVM) method. Our approach attempts to increase the convergence rate of the modified variable metric method. It is also combined with the RBackprop algorithm, which computes the product of the matrix of second derivatives (Hessian) with an arbitrary vector. The RBackprop method allows us to avoid computationally expensive, direct line searches. In addition, it can be utilized in the new, 'predictive' updating technique of the inverse Hessian approximation. We have used directional slope testing to adjust the step size and found that this strategy works exceptionally well in conjunction with the Rbackprop algorithm. Some supplementary, but nevertheless important enhancements to the basic training scheme such as improved setting of a scaling factor for the variable metric update and computationally more efficient procedure for updating the inverse Hessian approximation are presented as well. We summarize by comparing the SVM method with four first- and second- order optimization algorithms including a very effective implementation of the Levenberg-Marquardt method. Our tests indicate promising computational speed gains of the new training technique, particularly for large feedforward networks, i.e., for problems where the training process may be the most laborious.

Stepniewski, Slawomir W.↗

NASA NTRS2017

Remote Sensing of Precipitation from Airborne and Spaceborne Radar

Weather radar measurements from airborne or satellite platforms can be an effective remote sensing tool for examining the three-dimensional structures of clouds and precipitation. This chapter describes some fundamental properties of radar measurements and their dependence on the particle size distribution (PSD) and radar frequency. The inverse problem of solving for the vertical profile of PSD from a profile of measured reflectivity is stated as an optimal estimation problem for single- and multi-frequency measurements. Phenomena that can change the measured reflectivity Z(sub m) from its intrinsic value Z(sub e), namely attenuation, non-uniform beam filling, and multiple scattering, are described and mitigation of these effects in the context of the optimal estimation framework is discussed. Finally, some techniques involving the use of passive microwave measurements to further constrain the retrieval of the PSD are presented.

cloud↗

NASA NTRS2016

Consistent Evaluation of ACOS-GOSAT, BESD-SCIAMACHY, CarbonTracker, and MACC Through Comparisons to TCCON

Consistent validation of satellite CO2 estimates is a prerequisite for using multiple satellite CO2 measurements for joint flux inversion, and for establishing an accurate long-term atmospheric CO2 data record. Harmonizing satellite CO2 measurements is particularly important since the differences in instruments, observing geometries, sampling strategies, etc. imbue different measurement characteristics in the various satellite CO2 data products. We focus on validating model and satellite observation attributes that impact flux estimates and CO2 assimilation, including accurate error estimates, correlated and random errors, overall biases, biases by season and latitude, the impact of coincidence criteria, validation of seasonal cycle phase and amplitude, yearly growth, and daily variability. We evaluate dry-air mole fraction (X(sub CO2)) for Greenhouse gases Observing SATellite (GOSAT) (Atmospheric CO2 Observations from Space, ACOS b3.5) and SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) (Bremen Optimal Estimation DOAS, BESD v2.00.08) as well as the CarbonTracker (CT2013b) simulated CO2 mole fraction fields and the Monitoring Atmospheric Composition and Climate (MACC) CO2 inversion system (v13.1) and compare these to Total Carbon Column Observing Network (TCCON) observations (GGG2012/2014). We find standard deviations of 0.9, 0.9, 1.7, and 2.1 parts per million vs. TCCON for CT2013b, MACC, GOSAT, and SCIAMACHY, respectively, with the single observation errors 1.9 and 0.9 times the predicted errors for GOSAT and SCIAMACHY, respectively. We quantify how satellite error drops with data averaging by interpreting according to (error(sup 2) equals a(sup 2) plus b(sup 2) divided by n (with n being the number of observations averaged, a the systematic (correlated) errors, and b the random (uncorrelated) errors). a and b are estimated by satellites, coincidence criteria, and hemisphere. Biases at individual stations have year-to-year variability of 0.3 parts per million, with biases larger than the TCCON predicted bias uncertainty of 0.4 parts per million at many stations. We find that GOSAT and CT2013b under-predict the seasonal cycle amplitude in the Northern Hemisphere (NH) between 46 and 53 degrees North latitude, MACC over-predicts between 26 and 37 degrees North latitude, and CT2013b under-predicts the seasonal cycle amplitude in the Southern Hemisphere (SH). The seasonal cycle phase indicates whether a data set or model lags another data set in time. We find that the GOSAT measurements improve the seasonal cycle phase substantially over the prior while SCIAMACHY measurements improve the phase significantly for just two of seven sites. The models reproduce the measured seasonal cycle phase well except for at Lauder_125HR (CT2013b) and Darwin (MACC). We compare the variability within 1 day between TCCON and models in June-July-August; there is correlation between 0.2 and 0.8 in the NH, with models showing 10-50 percent the variability of TCCON at different stations and CT2013b showing more variability than MACC. This paper highlights findings that provide inputs to estimate flux errors in model assimilations, and places where models and satellites need further investigation, e.g., the SH for models and 45-67 degrees North latitude for GOSAT and CT2013b.

ACOS-GOSAT↗