Results for “Parameterization method” — Page 6

NASA NTRS1989

Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).

Patten, W. N.↗

NASA NTRS1992

Satellite-derived surface latent heat fluxes in a rapidly intensifying marine cyclone

Surface latent heat fluxes are estimated in the vicinity of a rapidly deepening cyclone before and during its period of most rapid intensification. This was done with a bulk parameterization scheme and remotely sensed input data. A method is studied for estimating the difference in specific humidity between the surface and a ten meter height using the Special Sensor Microwave/Imager (SSM/I) observed integrated water vapor field and a sea surface temperature analysis. The surface latent heat flux fields generally have estimated errors below 40 pct. south of 40 deg. N and outside the region of high integrated water vapor values associated with frontal bands. The method of estimating surface latent heat fluxes for the case study was found to be usable in most regions of the Northwest Atlantic Ocean except for those locations directly adjacent to coastlines in instances of offshore flow and in the vicinity of surface fronts.

Miller, Douglas K.↗

NASA NTRS1992

Satellite-derived surface latent heat fluxes in a rapidly intensifying marine cyclone

The aim of this article is to estimate surface latent heat fluxes in the vicinity of a rapidly deepening cyclone before and during its period of most rapid intensification. This is done with a bulk parameterization scheme and remotely sensed input data. A method for estimating the difference in specific humidity between the surface and a 10-m height is investigated using the Special Sensor Microwave/Imager-observed integrated water vapor field and a sea surface temperature analysis. The surface latent heat flux fields generally have estimated errors below 40 percent south of 40 deg N and outside the region of high integrated water vapor values associated with frontal bands. The method of estimating surface latent heat fluxes for the case study was found to be usable in most regions of the northwest Atlantic Ocean except for those locations directly adjacent to coastlines in instances of offshore flow and in the vicinity of surface fronts.

Miller, Douglas K.↗

NASA NTRS1993

A new method for the identification of non-Gaussian line profiles in elliptical galaxies

A new parameterization for the line profiles of elliptical galaxies, the Gauss-Hermite series, is proposed. This approach expands the line profile as a sum of orthogonal functions which minimizes the correlations between the errors in the parameters of the fit. This method also make use of the fact that Gaussians provide good low-order fits to observed line profiles. The method yields measurements of the line strength, mean radial velocity, and the velocity dispersion as well as two extra parameters, h3 and h4, that measure asymmetric and symmetric deviations of the line profiles from a Gaussian, respectively. The new method was used to derive profiles for three elliptical galaxies which all have asymmetric line profiles on the major axis with symmetric deviations from a Gaussian. Results confirm that elliptical galaxies have complex structures due to their complex formation history.

Van Der Marel, Roeland P.↗

NASA NTRS1981

Instability of non-zonal baroclinic flows - Multiple-scale analysis

The linear instability of a non-zonal flow can be reduced to an eigenvalue-eigenfunction problem, governed by a nonseparable partial differential equation (Niehaus, 1980). Approximate solutions, found by the method of multiple scales, are derived here and compared with earlier results found using a spectral method. The amplitude maxima are correctly located. The zonal variations of local wavenumber and of amplitude are qualitatively correct, but not sufficiently extreme. Because the method is oversensitive to local conditions, and less sensitive to global constraints, this comparison provides theoretical limits to the possibility of parameterizing transient eddies in terms of the local time mean state of the atmosphere. The method can be extended easily to flows with more realistic vertical structure.

Niehaus, M. C. W.↗

NASA NTRS1994

Theoretical Investigation of Wave-Vector-Dependent Analytical and Numerical Formulations of the Interband Impact-Ionization Transition Rate for Electron in Bulk Silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E Scholl, and M. Rudan, and a more exact, numerical method of Y. Wang and K. F. Brennan. Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formula, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with (he completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to (he overlap integrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such [he transition rate may be overestimated at those points for which "near vertical," small change in k, transitions occur.

Kolnik, Jan↗

NASA NTRS1994

Theoretical investigation of wave-vector-dependent analytical and numerical formulations of the interband impact-ionization transition rate for electrons in bulk silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E. Scholl, and M. Rudan (1993), and a more exact, numerical method of Y. Wang and K. F. Brennan (1994). Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formular, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with the completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to the overlap intergrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such the transition rate may be overestimated at those points for which 'near vertical,' small change in k, transitions occur.

Kolnik, Jan↗

NASA NTRS1985

MAP-oriented research in the People's Republic of China

A brief accounting of MAP oriented research in the Republic of China is given. A stratosphere balloon launching facility and its capabilities are reviewed. Observations of the stratospheric aerosols with a balloon-borne aerosol computer were made. Long term monitoring of stratospheric aerosols induced by volcanic eruptions are made with a ruby lidar. The main parameters of an ST radar system are given. The ionospheric D region is investigated with the method of ionospheric absorption. And photochemical modeling and radiation parameterization of the middle atmosphere are made.

Lu, D.↗

NASA NTRSDate not supplied

Efficient and Singularity-Aware Inverse Kinematics for 6-DOF and 7-DOF Revolute Manipulators

Inverse kinematics (IK) for 6-DOF and 7-DOF revolute robot manipulators may be decomposed into canonical subproblems which find the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems. We demonstrate significant performance improvements over existing IK methods. 7-DOF manipulators have one redundant DOF to parameterize, so we introduce the general SEW angle, which generalizes the conventional SEW angle but with an arbitrary reference direction function. One special choice, the stereographic SEW angle, has a singularity when the wrist is on a half-line instead of a full line.

Computational Geometry↗

NASA NTRS2005

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗

NASA NTRS2006

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗

NASA NTRS1998

Attitude/attitude-rate estimation from GPS differential phase measurements using integrated-rate parameters

A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.

Oshman, Yaakov↗

NASA NTRS1997

Vector Observation-Aided/Attitude-Rate Estimation Using Global Positioning System Signals

A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.

Oshman, Yaakov↗

NASA NTRS1992

Adaptation of a matrix parameterization of the middle atmospheric radiative cooling for an arbitrary vertical coordinate grid

Matrices corresponding to a revised vertical grid are shown to be derived from the original grid by integrating the radiative cooling rate over model layers. The method is applied to temperature profiles that represent average or extreme atmospheric conditions and a range of vertical resolutions. The example makes use of the 15-micron CO2 band parameterization proposed by Akmaev and Shved (1982) for the LTE region of the middle atmosphere. Cooling rate errors provided by the present method are not more than 0.11 K/day for a vertical grid spacing of less than 5 km. The matrix transformation method is shown to be valuable for adapting effective matrix parameterizations of middle atmosphere cooling to atmospheric models with arbitrary vertical resolutions.

Akmaev, R. A.↗

NASA NTRSDate not supplied

Structured Covariance Gaussian Networks for Orion Crew Module Aerodynamic Uncertainty Quantification

In this paper we propose a new approach for nonlinear regression and uncertainty quantification. The method is based on a pair of neural networks which parameterize mean and dense covariance functions of a multivariate Gaussian process, trained together to maximize the log-likelihood of observing the given data. The covariance matrix is made positive definite at every input by construction. We also propose a sampling approach that produces viable surrogate function realizations from the Gaussian process. We call the proposed model a Structured Covariance Gaussian Network (SCGN). We illustrate the use of SCGNs for learning an aerodynamic response surface with built-in uncertainty for the Orion crew module. We find that SCGN provides an efficient and systematic way to learn nonlinear functional relationships and dense covariances. We compare results to a baseline Gaussian process regressor and observe that the SCGN provides comparable uncertainty descriptions with improved scalability to dataset size. The sample functions generated by SCGN are fast to evaluate online and are therefore convenient for use in trajectory simulations. These results suggest that SCGN may be a viable computational method for aerodynamic uncertainty quantification.

machine learning↗

NASA NTRSDate not supplied

Structured Covariance Gaussian Networks for Orion Crew Module Aerodynamic Uncertainty Quantification

In this paper we propose a new approach for nonlinear regression and uncertainty quantification. The method is based on a pair of neural networks which parameterize mean and dense covariance functions of a multivariate Gaussian process, trained together to maximize the log-likelihood of observing the given data. The covariance matrix is made positive definite at every input by construction. We also propose a sampling approach that produces viable surrogate function realizations from the Gaussian process. We call the proposed model a Structured Covariance Gaussian Network (SCGN). We illustrate the use of SCGNs for learning an aerodynamic response surface with built-in uncertainty for the Orion crew module. We find that SCGN provides an efficient and systematic way to learn nonlinear functional relationships and dense covariances. We compare results to a baseline Gaussian process regressor and observe that the SCGN provides comparable uncertainty descriptions with improved scalability to dataset size. The sample functions generated by SCGN are fast to evaluate online and are therefore convenient for use in trajectory simulations. These results suggest that SCGN may be a viable computational method for aerodynamic uncertainty quantification.

machine learning↗

NASA NTRS2013

A Comparison Between Gravity Wave Momentum Fluxes in Observations and Climate Models

For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations,MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.

mathematical models↗

NASA NTRS2002

Evaluation of Methods to Estimate the Surface Downwelling Longwave Flux during Arctic Winter

Surface longwave radiation fluxes dominate the energy budget of nighttime polar regions, yet little is known about the relative accuracy of existing satellite-based techniques to estimate this parameter. We compare eight methods to estimate the downwelling longwave radiation flux and to validate their performance with measurements from two field programs in thc Arctic: the Coordinated Eastern Arctic Experiment (CEAREX ) conducted in the Barents Sea during the autumn and winter of 1988, and the Lead Experiment performed in the Beaufort Sea in the spring of 1992. Five of the eight methods were developed for satellite-derived quantities, and three are simple parameterizations based on surface observations. All of the algorithms require information about cloud fraction, which is provided from the NASA-NOAA Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) polar pathfinder dataset (Path-P): some techniques ingest temperature and moisture profiles (also from Path-P): one-half of the methods assume that clouds are opaque and have a constant geometric thickness of 50 hPa, and three include no thickness information whatsoever. With a somewhat limited validation dataset, the following primary conclusions result: (1) all methods exhibit approximately the same correlations with measurements and rms differences, but the biases range from -34 W sq m (16% of the mean) to nearly 0; (2) the error analysis described here indicates that the assumption of a 50-hPa cloud thickness is too thin by a factor of 2 on average in polar nighttime conditions; (3) cloud-overlap techniques. which effectively increase mean cloud thickness, significantly improve the results; (4) simple Arctic-specific parameterizations performed poorly, probably because they were developed with surface-observed cloud fractions; and (5) the single algorithm that includes an estimate of cloud thickness exhibits the smallest differences from observations.

Chiacchio, Marc↗