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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. IV: Coherent Backscattering

The problem of backscattering of light by a discrete random medium illuminated by an obliquely incident plane electromagnetic wave is considered.The analysis is performed in a linear-polarization basis and includes a complete derivation of the cross reflection matrix for a layer with densely and sparsely distributed particles, the design of an approximate method for computing the ladder and cross reflection matrices in the case of a semi-infinite medium with a sparse distribution of particles, the derivation of the relations between the elements of the ladder and cross reflection matrices in the exact backscattering direction for dense and sparse media, and the development of practical algorithms for solving the underlying integral equations by the method of Picard iterations and the discrete ordinate method. Simulation results for particles with large size parameters are also presented.

Adrian Doicu↗
NASA NTRS2018

Optimal Control Prediction Method for Control Allocation

This paper proposes a novel prediction method for online optimal control allocation that extends the volume of moments achievable with the Moore-Penrose generalized inverse to the entire Attainable Moment Set. This method formulates the control allocation problem using selected basis vectors and associated gains which reduces the optimization problem dimensions and provides physical insight into the resulting optimal solutions. The proposed algorithm finds the entire family of unique optimal control solutions along the desired moment vector from the origin to the boundary of the Attainable Moment Set. Numerical results for the Moore-Penrose prediction method show that the unique minimal controls obtained yield the desired moment with near machine precision accuracy while maintaining control effectors within specified position limits. This method has been fully validated against the unique solution obtained on the boundary of the Attainable Moment Set using the Durham Direct Allocation method. Minimal control solutions obtained for moments in the interior of the Attainable Moment Set, similarly yield the desired moment to near machine precision while providing control solutions that are smaller (i.e. 2-norm) than solutions found with traditional control allocation algorithms (e.g. interior point methods) applied to the minimal control problem. Numerical simulations using a Matlab® autocoded executable (MEX) for the representative real world problem of 3-moments with 20 individual control effectors and prescribed control position limits show a mean computation speed of approximately 125 Hz which is sufficient to enable real-time flight allocation.

Acheson, Michael J.↗
NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗
NASA NTRS2021

Transition Analysis for the CRM-NLF Wind Tunnel Configuration

This paper reports the results of a comprehensive linear stability analysis of the boundary layer flow over the common research model with natural laminar flow (CRM-NLF) aircraft configuration. The flow conditions match selected test conditions from a recent wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. Previous work has shown that the measured onset of laminar-turbulent transition during the experiments can be correlated with the linear amplification of Tollmien-Schlichting (TS) and stationary crossflow (CF) instabilities in the swept wing boundary layer. However, a significant scatter ( N ∈ (4,9)) was observed in the values of the logarithmic amplification factor along the measured transition front. This previous analysis was based on an approximate basic state (based on a boundary layer code with conical flow approximation) and parallel stability computations without surface curvature effects. Here, we examine the effects of these various approximations with the goal of quantifying the resulting changes in the N-factor correlations. Specifically, both linear stability theory (LST) and the parabolized stability equations (PSE)are used in conjunction with an accurate definition of the laminar boundary layer flow as computed with a Navier-Stokes solver with a Reynolds-Averaged-Navier-Stokes (RANS) based turbulence model within the turbulent parts of the flow. Furthermore, the effects of instability wave propagation within a fully three-dimensional boundary layer are also evaluated by integrating the disturbance growth rates along suitably chosen, curvilinear (i.e., nonplanar) propagation trajectories. The results of this analysis are also used in an accompanying paper by Venkatachari et al. to develop improved, physics based transition predictions for the same CRM-NLF configuration.

Boundary layer transition↗
NASA NTRS1998

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Simpson, Timothy W.↗
NASA NTRS1972

The selection of approximating functions for tabulated numerical data

A computer program was developed that selects, from a list of candidate functions, the approximating functions and associated coefficients which result in the best curve fit of a given set of numerical data. The advantages of the approach used here are: (1) Multivariable approximations can be performed. (2) Flexibility with respect to the type of approximations used is available. (3) The program is designed to choose the best terms to be used in the approximation from an arbitrary list of possible terms so that little knowledge of the proper approximating form is required. (4) Recursion relations are used in determining the coefficients of the approximating functions, which reduces the computer execution time of the program.

Ingram, H. L.↗
NASA NTRS1987

Approximations to eigenvalues of modified general matrices

The reanalysis of non-self-adjoint dynamic models is computationally very expensive in design optimization applications. This paper describes several approximations that can be applied to eigenvalues of non-hermitian matrices to reduce that computational cost. Approximations based on eigenvalue derivatives, generalized Rayleigh quotient and the trace theorem are presented and their accuracy and computational cost are estimated. The accuracy and cost estimates are verified by applying the approximations to random matrices and matrices arising in flutter analysis of compressor blades. Recommendations are made for selection of the best approximation when the derivatives are available and when they are not. In particular, it is concluded that the quadratic approximation for eigenvalues should never be used as higher order approximations are always more accurate as well as more efficient.

Murthy, Durbha V.↗
NASA NTRS1989

Approximation algorithms for planning and control

A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.

Boddy, Mark↗
NASA NTRS1983

Development and evaluation of a Kalman-filter algorithm for terminal area navigation using sensors of moderate accuracy

Translational state estimation in terminal area operations, using a set of commonly available position, air data, and acceleration sensors, is described. Kalman filtering is applied to obtain maximum estimation accuracy from the sensors but feasibility in real-time computations requires a variety of approximations and devices aimed at minimizing the required computation time with only negligible loss of accuracy. Accuracy behavior throughout the terminal area, its relation to sensor accuracy, its effect on trajectory tracking errors and control activity in an automatic flight control system, and its adequacy in terms of existing criteria for various terminal area operations are examined. The principal investigative tool is a simulation of the system.

Kanning, G.↗
NASA NTRS1983

A Kalman filter algorithm for terminal-area navigation with sensors of moderate accuracy

Translational state estimation in terminal area operations, using a set of commonly available position, air data, nd acceleration sensors, is described. Kalman filtering is applied to obtain maximum estimation occuracy from the sensors but feasibility in real-time computations requires a variety of approximations and devices aimed at minimizing the required computation time with only negligible loss of accuracy. Accuracy behavior throughout the terminal area, its relation to sensor accuracy, its effect on trajectory tracking errors and control activity in an automatic flight control system, and its adequacy in terms of existing criteria for various terminal area operations are examined. The principal investigative tool is a simulation of the system. Previously announced in STAR as N83-29193

Cicolani, L. S.↗
NASA NTRS1989

CSM research: Methods and application studies

Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.

Knight, Norman F., Jr.↗
NASA NTRS1992

Radiation Transport Around Axisymmetric Blunt Body Vehicles Using a Modified Differential Approximation

A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Hartung, Lin C.↗
NASA NTRS2019

A Neural Network Correction to the Scalar Approximation in Radiative Transfer

The next generation of advanced high-resolution sensors in geostationary orbit will gather detailed information for studying the Earth system. There is an increasing desire to perform observing system simulation experiments (OSSEs) for new sensors during the development phase of the mission in order to better leverage information content from the new and existing sensors. Forward radiative transfer calculations that simulate the observing characteristics of a new instrument are the first step to an OSSE, and they are computationally intensive. The scalar approximation to the radiative transfer equation, a simplification of the vector representation, can save considerable computational cost, but produces errors in top of the atmosphere (TOA) radiance as large as 10% due to neglecting polarization effects. This article presents an artificial neural network technique to correct scalar TOA radiance over both land and ocean surfaces to within 1% of vector-calculated radiance. A neural network was trained on a database of scalar-vector TOA radiance differences at a large range of solar and viewing angles for several thousand realistic atmospheric vertical profiles that were sampled from a high resolution (7 km) global atmospheric transport model. The profiles include Rayleigh scattering and aerosol scattering and absorption. Training and validation of the neural network was demonstrated for two wavelengths in the ultraviolet-visible (US-Vis) spectral range (354 nm and 670 nm). The significant computational savings accrued from using a scalar approximation plus neural network correction approach to simulating TOA radiance will make feasible hyperspectral forward simulations of high-resolution sensors on geostationary satellites, such as TEMPO, GOES-R, GEMS, and SENTINEL-4.

TOA↗
NASA NTRS1991

Computation of atmospheric cooling rates by exact and approximate methods

Infrared fluxes and cooling rates for several standard model atmospheres, with and without water vapor, carbon dioxide, and ozone, have been calculated using a line-by-line method at 0.01/cm resolution. The sensitivity of the results to the vertical integration scheme and to the model for water vapor continuum absorption is shown. Comparison with similar calculations performed at NOAA/GFDL shows agreement to within 0.5 W/sq m in fluxes at various levels and 0.05 K/d in cooling rates. Comparison with a fast, parameterized radiation code used in climate models reveals a worst case difference, when all gases are included, of 3.7 W/sq m in flux; cooling rate differences are 0.1 K/d or less when integrated over a substantial layer with point differences as large as 0.3 K/d.

Ridgway, William L.↗
NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗
NASA NTRS1985

Calculation of pressure-broadened linewidths for CO in Ar

Calculations of the pressure-broadening cross sections of CO in Ar have been made within the infinite-order sudden (IOS) and coupled states (CS) quantum scattering approximations. Two intermolecular potentials were used, a pairwise additive atom-atom potential which has been employed previously in semiclassical (modified Anderson theory) studies of this system and one calculated ab initio within an electron gas formalism. Predictions from the two potentials generally agree within about 25 percent and bracket experimental values (except for some recent high temperature data obtained in shock tube experiments). The CS approximation appears to be quite accurate although computationally expensive. The much cheaper IOS approximation is accurate for the J = 0-1 line but does not properly predict the dependence on line number. The quantum results are also compared with earlier semiclassical values.

Green, S.↗
NASA NTRS1996

Sensing Position With Approximately Constant Contact Force

Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary.

Sturdevant, Jay↗