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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

A Modified Linear-Mixing Method for Calculating Atmospheric Path Radiances of Aerosol Mixtures

The top-of-atmosphere (TOA) path radiance generated by an aerosol mixture can be synthesized by linearly adding the contributions of the individual aerosol components, weighted by their fractional optical depths. The method, known as linear mixing, is exact in the single-scattering limit. When multiple scattering is significant, the method reproduces the atmospheric path radiance of the mixture with less than 3% errors for weakly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors are much larger. This is due to neglecting the effect of multiple interactions between the aerosol components, especially when the values of the single-scattering albedos of these components are so different that the parameter epsilon = (Sigma)f(sub i) absolute value of bar omega(sub i) - bar omega(sub mix)/bar omega(sub i), is larger than approx. 0.1, where bar omega(sub i) and f(sub i) are the single-scattering albedo and the fractional abundance of the i th component, and bar omega(sub i) is the effective single-scattering albedo of the mixture. We describe an empirical, modified linear-mixing method which effectively accounts for the multiple interactions between aerosol components. The modified and standard methods are identical when epsilon = 0.0 and give similar results when epsilon less than or equal to 0.05. For optical depths larger than approx. 0.5, or when epsilon greater than 0.05, only the modified method can reproduce the radiances within 5% error for common aerosol types up to optical thickness of 2.0. Because this method facilitates efficient and accurate atmospheric path radiance calculations for mixtures of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), scheduled for launch into polar orbit in 1998.

Abdou, W. A.↗
NASA NTRS1997

A Modified Linear-Mixing Method for Calculating Atmospheric Path Radiances of Aerosol Mixtures

The top-of-atmosphere (TOA) path radiance generated by an aerosol mixture can be synthesized by linearly adding the contributions of the individual aerosol components, weighted by their fractional optical depths. The method, known as linear mixing, is exact in the single-scattering limit. When multiple scattering is significant, the method reproduces the atmospheric path radiance of the mixture with less than 3% errors for weakly absorbing aerosols up to optical thickness of 0.5. However, when strongly absorbing aerosols are included in the mixture, the errors are much larger. This is due to neglecting the effect of multiple interactions between the aerosol components, especially when the values of the single-scattering albedos of these components are so different that the parameter e = the sum of f(sub i)[(bar)omega(sub i) - (bar)omega(sub mix)]/(bar)omega(sub i) is larger than approximately 0.1, where (bar)omega(sub i)and f(sub i) are the single-scattering albedo and the fractional abundance of the ith component, and (bar)omega(sub mix) is the effective single-scattering albedo of the Mixture. We describe an empirical, modified linear-mixing method which effectively accounts for the multiple interactions between aerosol components. The modified and standard methods are identical when epsilon = 0.0 and give similar results when epsilon is less than or equal to 0.05. For optical depths larger than approximately 0.5, or when epsilon is greater than 0.05, only the modified method can reproduce the radiances within 5% error for common aerosol types up to optical thickness of 2.0. Because this method facilitates efficient and accurate atmospheric path radiance calculations for mixtures of a wide variety of aerosol types, it will be used as part of the aerosol retrieval methodology for the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), scheduled for launch into polar orbit in 1998.

Abdou, W. A.↗
NASA NTRS1998

Application of the Probabilistic Dynamic Synthesis Method to Realistic Structures

The Probabilistic Dynamic Synthesis method is a technique for obtaining the statistics of a desired response engineering quantity for a structure with non-deterministic parameters. The method uses measured data from modal testing of the structure as the input random variables, rather than more "primitive" quantities like geometry or material variation. This modal information is much more comprehensive and easily measured than the "primitive" information. The probabilistic analysis is carried out using either response surface reliability methods or Monte Carlo simulation. In previous work, the feasibility of the PDS method applied to a simple seven degree-of-freedom spring-mass system was verified. In this paper, extensive issues involved with applying the method to a realistic three-substructure system are examined, and free and forced response analyses are performed. The results from using the method are promising, especially when the lack of alternatives for obtaining quantitative output for probabilistic structures is considered.

Brown, Andrew M.↗
NASA NTRS1999

Structural Embeddings: Mechanization with Method

The most powerful tools for analysis of formal specifications are general-purpose theorem provers and model checkers, but these tools provide scant methodological support. Conversely, those approaches that do provide a well-developed method generally have less powerful automation. It is natural, therefore, to try to combine the better-developed methods with the more powerful general-purpose tools. An obstacle is that the methods and the tools often employ very different logics. We argue that methods are separable from their logics and are largely concerned with the structure and organization of specifications. We, propose a technique called structural embedding that allows the structural elements of a method to be supported by a general-purpose tool, while substituting the logic of the tool for that of the method. We have found this technique quite effective and we provide some examples of its application. We also suggest how general-purpose systems could be restructured to support this activity better.

Munoz, Cesar↗
NASA NTRS1996

The Newton Modified Barrier Method for QP Problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.

Melman, A.↗
NASA NTRS2000

Application of Statistical Methods of Rain Rate Estimation to Data From The TRMM Precipitation Radar

The TRMM Precipitation Radar is well suited to statistical methods in that the measurements over any given region are sparsely sampled in time. Moreover, the instantaneous rain rate estimates are often of limited accuracy at high rain rates because of attenuation effects and at light rain rates because of receiver sensitivity. For the estimation of the time-averaged rain characteristics over an area both errors are relevant. By enlarging the space-time region over which the data are collected, the sampling error can be reduced. However. the bias and distortion of the estimated rain distribution generally will remain if estimates at the high and low rain rates are not corrected. In this paper we use the TRMM PR data to investigate the behavior of 2 statistical methods the purpose of which is to estimate the rain rate over large space-time domains. Examination of large-scale rain characteristics provides a useful starting point. The high correlation between the mean and standard deviation of rain rate implies that the conditional distribution of this quantity can be approximated by a one-parameter distribution. This property is used to explore the behavior of the area-time-integral (ATI) methods where fractional area above a threshold is related to the mean rain rate. In the usual application of the ATI method a correlation is established between these quantities. However, if a particular form of the rain rate distribution is assumed and if the ratio of the mean to standard deviation is known, then not only the mean but the full distribution can be extracted from a measurement of fractional area above a threshold. The second method is an extension of this idea where the distribution is estimated from data over a range of rain rates chosen in an intermediate range where the effects of attenuation and poor sensitivity can be neglected. The advantage of estimating the distribution itself rather than the mean value is that it yields the fraction of rain contributed by the light and heavy rain rates. This is useful in estimating the fraction of rainfall contributed by the rain rates that go undetected by the radar. The results at high rain rates provide a cross-check on the usual attenuation correction methods that are applied at the highest resolution of the instrument.

Meneghini, R.↗
NASA NTRS2000

A Bridge Health Monitoring Method Using the Hilbert-Huang Transform: A Case Study

We have developed a new method for nondestructive instrument method to monitor the health of a bridge. This new method is based on a transient test load and simple data collection. The nuclear of the method is the new invented nonstationary and nonlinear time series analysis method, the Empirical Mode Decomposition and Hilbert Spectral Analysis. The final decision on the health of the bridge structure is based on the nonlinear characteristic of the data, and on the comparison between the free and the forced vibration frequencies. Thus this alternative method enjoys many advantages: (1) no a priori data required, (2) simple data collection, and (3) minimum traffic disruption. Results from a case study of the Shing-Nan Bridge in Hou-Wei will be reported.

Huang, Norden E.↗
NASA NTRS2000

Microencapsulation and Electrostatic Processing Method

Methods are provided for forming spherical multilamellar microcapsules having alternating hydrophilic and hydrophobic liquid layers, surrounded by flexible, semi-permeable hydrophobic or hydrophilic outer membranes which can be tailored specifically to control the diffusion rate. The methods of the invention rely on low shear mixing and liquid-liquid diffusion process and are particularly well suited for forming microcapsules containing both hydrophilic and hydrophobic drugs. These methods can be carried out in the absence of gravity and do not rely on density-driven phase separation, mechanical mixing or solvent evaporation phases. The methods include the process of forming, washing and filtering microcapsules. In addition, the methods contemplate coating microcapsules with ancillary coatings using an electrostatic field and free fluid electrophoresis of the microcapsules. The microcapsules produced by such methods are particularly useful in the delivery of pharmaceutical compositions.

Morrison, Dennis R.↗
NASA NTRS2000

Alternative Methods of the Thermospheric Atomic Oxygen Density Determination

Atomic oxygen density in the upper thermosphere (approximately 300 km) can be calculated using ground based incoherent scatter radar and Fabry-Perot interferometer measurements. Burnside et al. [1991] was the first to try this method, but Buonsanto et al. provided an extensive treatment of the method in 1997. This paper further examines the method using 46 nights of data collected over six years and the latest information on the oxygen collision frequency. The method is compared with the MSIS-86 atomic oxygen prediction values, which are based upon in situ rocket born and satellite measurements from the 70's to the mid-80's In general, the method supports the MSIS-86 model, but indicates several areas of discrepancy. Furthermore, no direct correlation is found between the geomagnetic conditions and the difference between the method and MSIS-86 predictions.

Bennett. Adam C.↗
NASA NTRS2000

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗
NASA NTRS2001

Alternative Method for the Thermospheric Atomic Oxygen Density Determination

Atomic oxygen density in the upper thermosphere (approximately 300 km) can be calculated using ground based incoherent scatter radar and Fabry-Perot interferometer measurements. Burnside et al. was the first to try this method, but Buonsanto et al. provided an extensive treatment of the method in 1997. This paper further examines the method using 46 nights of data collected over six years and the latest information on the oxygen collision frequency. The method is compared with the MSIS (Mass Spectrometer Incoherent Scatter)-86 atomic oxygen prediction values, which are based upon in situ rocket born and satellite measurements from the 70s to the mid-80s. In general, the method supports the MSIS-86 model, but indicates several areas of discrepancy. Furthermore, no direct correlation is found between the geomagnetic conditions and the difference between the method and MSIS-86 predictions.

Bennett, A. C.↗
NASA NTRS2001

A New Method to Cross Calibrate and Validate TOMS, SBUV/2, and SCIAMACHY Measurements

A unique method to validate back scattered ultraviolet (buv) type satellite data that complements the measurements from existing ground networks is proposed. The method involves comparing the zenith sky radiance measurements from the ground to the nadir radiance measurements taken from space. Since the measurements are compared directly, the proposed method is superior to any other method that involves comparing derived products (for example, ozone), because comparison of derived products involve inversion algorithms which are susceptible to several type of errors. Forward radiative transfer (RT) calculations show that for an aerosol free atmosphere, the ground-based zenith sky radiance measurement and the satellite nadir radiance measurements can be predicted with an accuracy of better than 1 percent. The RT computations also show that for certain values of the solar zenith angles, the radiance comparisons could be better than half a percent. This accuracy is practically independent of ozone amount and aerosols in the atmosphere. Experiences with the Shuttle Solar Backscatter Ultraviolet (SSBUV) program show that the accuracy of the ground-based zenith sky radiance measuring instrument can be maintained at a level of a few tenth of a percent. This implies that the zenith sky radiance measurements can be used to validate Total Ozone Mapping Spectrometer (TOMS), Solar Backscatter Ultraviolet (SBUV/2), and The SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) radiance data. Also, this method will help improve the long term precision of the measurements for better trend detection and the accuracy of other BUV products such as tropospheric ozone and aerosols. Finally, in the long term, this method is a good candidate to inter-calibrate and validate long term observations of upcoming operational instruments such as Global Ozone Monitoring Experiment (GOME-2), Ozone Mapping Instrument (OMI), Ozone Dynamics Ultraviolet Spectrometer (ODUS), and Ozone Mapping and Profiler Suite (OMPS).

Ahmad, Ziauddin↗
NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗
NASA NTRS1996

Hyperbolic Methods for Surface and Field Grid Generation

This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.

Chan, William M.↗
NASA NTRS2001

SGBEM-FEM Alternating Method for Analyzing 3D Non-Planar Cracks and Their Growth in Structural Components

The highly accurate and efficient Symmetric Galerkin Boundary Element Method (SGBEM), a Finite Element Method (FEM)-based alternating method, is proposed for analyzing three-dimensional non-planar cracks and their growth. The cracks are modeled using the symmetric Galerkin boundary element method as a distribution of displacement discontinuities, simulating an infinite medium. The finite element method only analyzes the stress for the uncracked body. The solution for the cracked structural component is determined by an iteration procedure. This process alternates between an FEM solution for the uncracked body and the SGBEM solution for a crack in an infinite body. Numerical analysis, and the Java code used, evaluate stress intensity factors and model fatigue crack growth. Examples of non-planar cracks in infinite media and planar cracks in finite bodies, as well as growth under fatigue, show the accuracy of the method.

Nikishkov, G. P.↗
NASA NTRS2002

Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum- exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Mei, Renwei↗
NASA NTRS2002

Measurement of Trailing Edge Noise Using Directional Array and Coherent Output Power Methods

The use of a directional (or phased) array of microphones for the measurement of trailing edge (TE) noise is described and tested. The capabilities of this method arc evaluated via measurements of TE noise from a NACA 63-215 airfoil model and from a cylindrical rod. This TE noise measurement approach is compared to one that is based on thc cross spectral analysis of output signals from a pair of microphones placed on opposite sides of an airframe model (COP method). Advantages and limitations of both methods arc examined. It is shown that the microphone array can accurately measures TE noise and captures its two-dimensional characteristic over a large frequency range for any TE configuration as long as noise contamination from extraneous sources is within bounds. The COP method is shown to also accurately measure TE noise but over a more limited frequency range that narrows for increased TE thickness. Finally, the applicability and generality of an airfoil self-noise prediction method was evaluated via comparison to the experimental data obtained using the COP and array measurement methods. The predicted and experimental results are shown to agree over large frequency ranges.

Hutcheson, Florence V.↗
NASA NTRS2002

Measurement Of Trailing Edge Noise using Directional Array and Coherent Output Power Methods

The use of a directional array of microphones for the measurement of trailing edge (TE) noise is described. The capabilities of this method are evaluated via measurements of TE noise from a NACA 63-215 airfoil model and from a cylindrical rod. This TE noise measurement approach is compared to one that is based on the cross spectral analysis of output signals from a pair of microphones (COP method). Advantages and limitations of both methods are examined. It is shown that the microphone array can accurately measures TE noise and captures its two-dimensional characteristic over a large frequency range for any TE configuration as long as noise contamination from extraneous sources is within bounds. The COP method is shown to also accurately measure TE noise but over a more limited frequency range that narrows for increased TE thickness. Finally, the applicability and generality of an airfoil self-noise prediction method was evaluated via comparison to the experimental data obtained using the COP and array measurement methods. The predicted and experimental results are shown to agree over large frequency ranges.

Hutcheson, Florence V.↗