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At least 1,657 records · Page 92

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NASA NTRS1976

On signal design by the R sub 0 criterion for non-white Gaussian noise channels

The use of the R sub 0 criterion for modulation system design is investigated for channels with non-white Gaussian noise. A signal space representation of the waveform channel is developed, and the cut-off rate R sub 0 for vector channels with additive nonwhite Gaussian noise and unquantized demodulation is derived. When the signal unput to the channel is a continuous random vector, maximization of R sub 0 with constrained average signal energy leads to a water-filling interpretation of optimal energy distribution in signal space. The necessary condition for a finite signal set to maximize R sub 0 with constrained energy and an equally likely probability assignment of signal vectors is presented, and an algorithm is outlined for numerically computing the optimum signal set. A necessary condition on a constrained energy, finite signal set is found which maximizes a Taylor series approximation of R sub 0. This signal set is compared with the finite signal set which has the water-filling average energy distribution.

Bordelon, D. L.↗

NASA NTRS1984

Element-by-element Solution Procedures for Nonlinear Structural Analysis

Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.

Hughes, T. J. R.↗

NASA NTRS1984

Dual approximations in optimal control

A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.

Hager, W. W.↗

NASA NTRS1985

Marching iterative methods for the parabolized and thin layer Navier-Stokes equations

Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.

Israeli, M.↗

NASA NTRS1986

On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed parameter systems

A series of numerical examples is reported and several algorithms compared for estimation of coefficients in differential equation models. Unconstrained, constrained and Tikhonov regularization methods are tested for their behavior with regard to both convergence (of approximation methods for the states and parameters) and stability (continuity of the estimates with respect to perturbations in the data or observed states).

Banks, H. T.↗

NASA NTRS1985

Marching iterative methods for the Parabolized and Thin Layer Navier-Stokes equations

Israeli, M.↗

NASA NTRS1987

Adaptive finite element methods for high-speed compressible flows

An adaptive finite element algorithm for solving the unsteady Euler equations is described. The finite element algorithm is based on a Taylor/Galerkin formulation and uses a very fast and efficient data structure to refine and unrefine the grid in order to optimize the approximation. A general version of the method which can be applied to moving grids with sliding interfaces is given, and results for a transient supersonic calculation of rotor-stator interaction are presented.

Oden, J. T.↗

NASA NTRS1994

The classification of the Arctic Sea ice types and the determination of surface temperature using advanced very high resolution radiometer data

The accurate quantification of new ice and open water areas and surface temperatures within the sea ice packs is a key to the realistic parameterization of heat, moisture, and turbulence fluxes between ocean and atmosphere in the polar regions. Multispectral NOAA advanced very high resolution radiometer/2 (AVHRR/2) satellite images are analyzed to evaluate how effectively the data can be used to characterize sea ice in the Bering and Greenland seas, both in terms of surface type and physical temperature. The basis of the classification algorithm, which is developed using a late wintertime Bering Sea ice cover data, is that frequency distributions of 10.8- micrometers radiances provide four distinct peaks, represeting open water, new ice, young ice, and thick ice with a snow cover. The results are found to be spatially and temporally consistent. Possible sources of ambiguity, especially associated with wider temporal and spatial application of the technique, are discussed. An ice surface temperature algorithm is developed for the same study area by regressing thermal infrared data from 10.8- and 12.0- micrometers channels against station air temperatures, which are assumed to approximate the skin temperatures of adjacent snow and ice. The standard deviations of the results when compared with in situ data are about 0.5 K over leads and polynyas to about 0.5-1.5 K over thick ice. This study is based upon a set of in situ data limited in scope and coverage. Cloud masks are applied using a thresholding technique that utilizes 3.74- and 10.8- micrometers channel data. The temperature maps produced show coherence with surface features like new ice and leads, and consistency with corresponding surface type maps. Further studies are needed to better understand the effects of both the spatial and temporal variability in emissivity, aerosol and precipitable atmospheric ice particle distribution, and atmospheric temperature inversions.

Massom, Robert↗

NASA NTRS1997

Convergence Estimates for Multidisciplinary Analysis and Optimization

A quantitative analysis of coupling between systems of equations is introduced. This analysis is then applied to problems in multidisciplinary analysis, sensitivity, and optimization. For the sensitivity and optimization problems both multidisciplinary and single discipline feasibility schemes are considered. In all these cases a "convergence factor" is estimated in terms of the Jacobians and Hessians of the system, thus it can also be approximated by existing disciplinary analysis and optimization codes. The convergence factor is identified with the measure for the "coupling" between the disciplines in the system. Applications to algorithm development are discussed. Demonstration of the convergence estimates and numerical results are given for a system composed of two non-linear algebraic equations, and for a system composed of two PDEs modeling aeroelasticity.

Arian, Eyal↗

NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗

NASA NTRS2000

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

Jones, Robert L.↗

NASA NTRSDate not supplied

Uncertainty Estimation for SMAP Level-1 Brightness Temperature Assimilation at Different Timescales

In this study, we assimilate Soil Moisture Active Passive (SMAP) mission brightness temperature (Tb) observations into NASA’s Catchment Land Surface Model using an Ensemble Kalman filter to update surface and root-zone soil moisture simulations. Different time series components of the Tb observations are assimilated including anomalies, inter-annual variations, and high-frequency variations. To optimize the weights that the data assimilation (DA) puts on the observations, the ratio between the un-certainties of modeled and observed Tb is approximated using modeled and observed soil moisture uncertainties estimated using triple collocation analysis. Results are compared to a benchmark experiment that mimics the operational SMAP Level-4 algorithm, which assimilates Tb observations using a spatially-constant 4 Kelvin (K) observation uncertainty. All DA experiments exhibit notable skill improvements in most regions. Improvements are greatest for the inter-annual variations in the simulations of both surface and root-zone soil moisture (mean improvements in terms of Pearson correlation (-) are 0.08 and 0.06, respectively). Anomaly simulations improve similarly (0.07), and improvements in the high-frequency variations are only observed for sur-face soil moisture simulations (0.06). Strikingly, however, no notable difference in skill—neither improvement nor deterioration—is observed between the experiments that use optimized observation uncertainty parameters and the 4 K benchmark experiment. We show, analytically, that this may be explained by the presence of large observation operator errors, which have the potential to render post-update uncertainty insensitive to inaccuracies in the Kalman gain.

Alexander Gruber↗

DOE OSTI2020

Experimental Validation of Approximate Dynamic Programming Based Optimization and Convergence on Microgrid Applications

Stochastic optimization can better address uncertainties in power system problems. However, when state space and action space become large, many existing approaches become computationally expensive and even infeasible. Approximate dynamic programming (ADP) attracts researchers’ attention as a powerful tool for solving power system optimization problems with reduced computational cost. In this paper, in light of the existing literature, we investigate how the ADP approach with post-decision value function approximation converges to the nearly optimal solution with improved computational speed and experimentally validate the performance of the approach for a microgrid energy optimization problem. The approximation error versus the number of iteration is studied for convergence analysis of the post-decision ADP. A flowchart is provided to illustrate the proposed ADP algorithm for a microgrid energy optimization problem. The performance of ADP and dynamic programming (DP) is compared in terms of optimization error and computational time. It has found that the post-decision ADP approach can achieve competitive optimality with improved computational speed compared to the traditional DP.

Das, Avijit↗

DOE OSTI2022

Stout Smearing on a Quantum Computer

Smearing of gauge-field configurations in lattice field theory improves the results of lattice simulations by suppressing high energy modes from correlation functions. In quantum simulations, high kinetic energy eigenstates are introduced when the time evolution operator is approximated such as Trotterization. While improved Trotter product formulae exist to reduce the errors, they have diminishing accuracy returns with respect to resource costs. Therefore having an algorithm that has fewer resources than an improved Trotter formula is desirable. In this work I develop a representation agnostic method for quantum smearing and show that it reduces the coupling to high energy modes in the discrete nonabelian gauge theory $D_4$

Gustafson, Erik J.↗

NASA NTRS2005

Radiative Studies of Planetary Atmospheres

Retrieval algorithms and associated software for application to CIRS infrared spectral data have been developed and coded. A general forward radiative transfer code has been written that runs efficiently on a Macintosh, even at high spectral resolution (0.5 per centimeter). It makes use of the correlated-k approach for representation of the gaseous absorption and can include those gases listed in the HITRAN and GEISA atlases, along with collision-induced absorption. Cloud effects are included as spectrally dependent absorbers. Provision has been made for future extension to include particle scattering in an n-stream approximation. The primary purpose of the code is to produce synthetic data and to serve as the forward calculating element in gas and cloud retrieval programs developed for the Mac as well as other platforms. Initial development of algorithms and production software suitable for application to CIRS data to be obtained from Jupiter, Saturn and Titan has been completed, and production versions of the software for application to the spectral data are in place. This includes temperature, gaseous constituent, and cloud opacity retrieval, algorithms that can be applied to both nadir and limb data. This work has been done as a cooperative effort between Conrath and Matcheva (Cornell), Achterberg (GSFWSSAI), and Flasar (GSFC).

Conrath, Barney J.↗

DOE OSTI2021

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction

In this paper, we investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C 6 H 4 S 2 ) 2 ] z in two oxidation states ( z = –2, –1) using density-functional theory (DFT) with Fermi–Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3 d orbitals. The FLO-SIC method relies on optimization of Fermi–Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3 d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO–LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3 d -element-based systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2010

Analyzing Non Stationary Processes in Radiometers

The lack of well-developed techniques for modeling changing statistical moments in our observations has stymied the application of stochastic process theory for many scientific and engineering applications. Non linear effects of the observation methodology is one of the most perplexing aspects to modeling non stationary processes. This perplexing problem was encountered when modeling the effect of non stationary receiver fluctuations on the performance of radiometer calibration architectures. Existing modeling approaches were found not applicable; particularly problematic is modeling processes across scales over which they begin to exhibit non stationary behavior within the time interval of the calibration algorithm. Alternatively, the radiometer output is modeled as samples from a sequence random variables; the random variables are treated using a conditional probability distribution function conditioned on the use of the variable in the calibration algorithm. This approach of treating a process as a sequence of random variables with non stationary stochastic moments produce sensible predictions of temporal effects of calibration algorithms. To test these model predictions, an experiment using the Millimeter wave Imaging Radiometer (MIR) was conducted. The MIR with its two black body calibration references was configured in a laboratory setting to observe a third ultra-stable reference (CryoTarget). The MIR was programmed to sequentially sample each of the three references in approximately a 1 second cycle. Data were collected over a six-hour interval. The sequence of reference measurements form an ensemble sample set comprised of a series of three reference measurements. Two references are required to estimate the receiver response. A third reference is used to estimate the uncertainty in the estimate. Typically, calibration algorithms are designed to suppress the non stationary effects of receiver fluctuations. By treating the data sequence as an ensemble collection, it is possible to apply temporal algorithms which exacerbate the non stationary effects. By varying the algorithm, information about the properties of the non stationary receiver fluctuations is obtained. Comparisons of analytical calculations and statistical analysis of data demonstrate impressive agreement.

Racette, Paul↗

NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux-difference splitting method has been extended to treat two-dimensional viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-stage Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗