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NASA NTRS1984

Preliminary results in implementing a model of the world economy on the CYBER 205: A case of large sparse nonsymmetric linear equations

A brief description of the Model of the World Economy implemented at the Institute for Economic Analysis is presented, together with our experience in converting the software to vector code. For each time period, the model is reduced to a linear system of over 2000 variables. The matrix of coefficients has a bordered block diagonal structure, and we show how some of the matrix operations can be carried out on all diagonal blocks at once.

Szyld, D. B.↗

NASA NTRS1985

Parameter identification in distributed systems

This paper describes a method for the identification of the parameters entering into the equations of motion of distributed systems. Because the motion of distributed systems is described in terms of partial differential equations, these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. In this paper, these distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. It is assumed that the nature of the equations of motion is known and that a limited number of eigenvalues and eigenfunctions is identified in advance. Use is then made of the least squares method, in conjunction with the eigenfunctions' orthogonality, to compute the undetermined coefficients, thus identifying the system distributed parameters. A method for the identification of the eigensolution is also presented. The procedure for the identification of the eigensolution and of the system parameters is demonstrated via a numerical example.

Baruh, H.↗

NASA NTRS1984

Applications of CONMIN to wing design optimization with vortex flow effect

Slender wings on supersonic cruise configurations are expected to be thin and highly swept. As a result, edge-separated vortex flow is inevitable and must be accounted for in aerodynamic analysis and design. The present method is based on the method of suction analogy to calculate the total aerodynamic characteristics. The method requires the solution of the attached flow problem, the latter being solved by a low-order panel method in subsonic and supersonic flow. In essence, the lifting pressure is calculated by using a pressure-doublet distribution satisfying the Prandtl-Glauert equation. From the pressure distribution, the leading-edge suction is calculated. The latter is assumed to be the vortex lift through the method of suction analogy. For a cambered wing, the location of vortex-lift action point is important in predicting the aerodynamic characteristics. It is also seen that the effect of camber shape appears nonlinearly in all aerodynamic expressions. To design the camber shape, the camber slope is represented by a cosine Fourier series at each of several spanwise stations. The Fourier coefficients are the design variables. To design a leading-edge flap in the vortex flow (i.e., a vortex flap), the coordinates of corner points and the deflection angle are the design variables. The process of wing design is to determine the camber shape and twist distribution such that an objective function, typically the drag, is minimized, subject to various constraints.

Lan, C. E.↗

NASA NTRS1991

Scaling of spanwise length scales in a turbulent boundary layer

The results from an experimental investigation at IIT were combined with Spalart's (1988) Direct Numerical Simulation data base to investigate the scaling of the spanwise length scales of the dominant structures in the near-wall region of a turbulent boundary layer. To achieve this goal, the scaling of the spanwise correlation coefficient between the wall-shear stress and the streamwise velocity, at various heights in the boundary layer, was studied over the Reynolds number range, 670 to 5961. In addition, the scaling of the conditional velocity field associated with high and low wall-shear stress events was examined. The results indicate that the spanwise correlation coefficient scales with inner variables for 'small' spanwise offsets.

Wark, C. E.↗

NASA NTRS1992

Eigenvalue error analysis of viscously damped structures using a Ritz reduction method

The efficient solution of the eigenvalue problem that results from inserting passive dampers with variable stiffness and damping coefficients into a structure is addressed. Eigenanalysis of reduced models obtained by retaining a number of normal modes augmented with Ritz vectors corresponding to the static solutions resulting from the load patterns introduced by the dampers has been empirically shown to yield excellent approximations to the full eigenvalue problem. An analysis of this technique in the case of a single damper is presented. A priori and a posteriori error estimates are generated and tested on numerical examples. Comparison theorems with modally truncated models and a Markov parameter matching reduced-order model are derived. These theorems corroborate the heuristic that residual flexibility methods improve low-frequency approximation of the system. The analysis leads to other techniques for eigenvalue approximation. Approximate closed-form solutions are derived that include a refinement to eigenvalue derivative methods for approximation. An efficient Newton scheme is also developed. A numerical example is presented demonstrating the effectiveness of each of these methods.

Chu, Cheng-Chih↗

NASA NTRS1995

Linear and nonlinear trending and prediction for AVHRR time series data

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

Smid, J.↗

NASA NTRS1995

Optical characterization of the oceanic unicellular cyanobacterium Synechococcus grown under a day-night cycle in natural irradiance

The optical properties of the ocenanic cyanobacterium Synechococcus (clone WH8103) were examined in a nutrient-replete laboratory culture grown under a day-night cycle in natural irradiance. Measurements of the spectral absorption and beam attenuation coefficients, the size distribution of cells in suspension, and microscopic analysis of samples were made at intervals of 2-4 hours for 2 days. These measurements were used to calculate the optical properties at the level of a single 'mean' cell representative of the acutal population, specifically, the optical cross sections for spectral absorption bar-(sigma(sub a)), scattering bar-sigma(sub b))(lambda), and attentuation bar-(sigma(sub c))(lambda). In addition, concurrent determinations of chlorophyll a and particulate organic carbon allowed calculation of the Chl a- and C-specific optical coefficients. The refractive index of cells was derived from the observed data using a theory of light absorption and scattering by homogeneous spheres. Low irradiance because of cloudy skies resulted in slow division rates of cells in the culture. The percentage of dividing cells was unusually high (greater than 30%) throughout the experiment. The optical cross sections varied greatly over a day-night cycle, with a minimum near dawn or midmorning and maximum near dusk. During daylight hours, bar-(sigma(sub b)) and bar-(sigma(sub c)) can increase more than twofold and bar-(sigma(sub a) by as much as 45%. The real part of the refractive index n increaed during the day; changes in n had equal or greater effect than the varying size distribution on changes in bar-(sigma(sub c)) and bar-(sigma(sub b)). The contribution of changes in n to the increase of bar-(sigma(sub c))(660) during daylight hours was 65.7% and 45.1% on day 1 and 2, respectively. During the dark period, when bar-(sigma(sub c))(660) decreased by a factor of 2.9, the effect of decreasing n was dominant (86.3%). With the exception of a few hours during the second light period, the imaginary part of the refractive index n' showed little variation over a day-night cycle, and bar-(sigma(sub a)) was largely controlled by variations in cell size. The real part of the refractive index at lambda = 660 nm was correlated with the intracellular C concentration and the imaginary part at lambda = 678 nm with the intracellular Chl a concentration. The C-specfic attenuation coefficient showed significant diel variability, which has implications for the estimation of oceanic primary production from measurements of diel variability in beam attenuation. This study provides strong evidence that diel variability is an important component of the optical characterization of marine phytoplankton.

Stramski, Dariusz↗

NASA NTRS1960

The Influence of Silicon Additions on Friction and Wear of Nickel Alloys at Temperatures to 1000 Degrees Fahrenheit

Small additions of silicon have considerable beneficial effect on performance on slider alloys. This effect has most frequently been attributed to increased hardness. The research reported was conducted to consider a hypothesis that the primary role of silicon in slider alloys is one of supporting the formation of protective surface films. Friction and wear data were obtained at temperatures from 75 to 1000 degrees Fahrenheit with a series of binary silicon-nickel alloys containing up to 10 percent silicon. Pertinent hot hardness, metallurgical and surface-film analysis data are included. Atmospheres used were air, mixtures of oxygen and argon, a mixture of hydrogen and nitrogen, and a halogenated methane gas lubricant. The results show the role of silicon as a film former to be of great importance in success of silicon-containing alloys as slider materials for extreme temperatures. The range of variables studied gave friction coefficients from 0.05 to greater than 10.00 depending on film formation tendencies. Alloys with 5 percent or more silicon having a duplex structure showed the best results. Film formation resulted from surface reactions or the smearing of the softer phase from the alloys having duplex structure.

Buckley, Donald H.↗

NASA NTRS2016

Lidar-Based Estimates of Above-Ground Biomass in the Continental US and Mexico Using Ground, Airborne, and Satellite Observations

Existing national forest inventory plots, an airborne lidar scanning (ALS) system, and a space profiling lidar system (ICESat-GLAS) are used to generate circa 2005 estimates of total aboveground dry biomass (AGB) in forest strata, by state, in the continental United States (CONUS) and Mexico. The airborne lidar is used to link ground observations of AGB to space lidar measurements. Two sets of models are generated, the first relating ground estimates of AGB to airborne laser scanning (ALS) measurements and the second set relating ALS estimates of AGB (generated using the first model set) to GLAS measurements. GLAS then, is used as a sampling tool within a hybrid estimation framework to generate stratum-, state-, and national-level AGB estimates. A two-phase variance estimator is employed to quantify GLAS sampling variability and, additively, ALS-GLAS model variability in this current, three-phase (ground-ALS-space lidar) study. The model variance component characterizes the variability of the regression coefficients used to predict ALS-based estimates of biomass as a function of GLAS measurements. Three different types of predictive models are considered in CONUS to determine which produced biomass totals closest to ground-based national forest inventory estimates - (1) linear (LIN), (2) linear-no-intercept (LNI), and (3) log-linear. For CONUS at the national level, the GLAS LNI model estimate (23.95 +/- 0.45 Gt AGB), agreed most closely with the US national forest inventory ground estimate, 24.17 +/- 0.06 Gt, i.e., within 1%. The national biomass total based on linear ground-ALS and ALS-GLAS models (25.87 +/- 0.49 Gt) overestimated the national ground-based estimate by 7.5%. The comparable log-linear model result (63.29 +/-1.36 Gt) overestimated ground results by 261%. All three national biomass GLAS estimates, LIN, LNI, and log-linear, are based on 241,718 pulses collected on 230 orbits. The US national forest inventory (ground) estimates are based on 119,414 ground plots. At the US state level, the average absolute value of the deviation of LNI GLAS estimates from the comparable ground estimate of total biomass was 18.8% (range: Oregon,−40.8% to North Dakota, 128.6%). Log-linear models produced gross overestimates in the continental US, i.e., N2.6x, and the use of this model to predict regional biomass using GLAS data in temperate, western hemisphere forests is not appropriate. The best model form, LNI, is used to produce biomass estimates in Mexico. The average biomass density in Mexican forests is 53.10 +/- 0.88 t/ha, and the total biomass for the country, given a total forest area of 688,096 sq km, is 3.65 +/- 0.06 Gt. In Mexico, our GLAS biomass total underestimated a 2005 FAO estimate (4.152 Gt) by 12% and overestimated a 2007/8 radar study's figure (3.06 Gt) by 19%.

Hybrid 3-Phase sampling↗

NASA NTRSDate not supplied

Optimization of Plug Nozzles Using CFD Informed Design Space Querying

This paper presents an axisymmetric CFD approach based on Reynolds-averaged Navier-Stokes (RANS) calculations for the shape optimization of plug nozzle contours for both supersonic cruise and landing/takeoff (LTO) conditions. Three key external plug design parameters were defined as independent variables in the optimization scheme, while nozzle performance was evaluated using thrust coefficient (Cfg) and discharge coefficient (Cd) as the primary dependent variables. By varying these parameters, a wide range of axisymmetric conic section plug profiles can be achieved, simplifying the problem. The paper also discusses the supersonic plug nozzle optimization approach, design space seeding, meshing, and CFD simulations for the optimization process. The results demonstrate that the approach is effective in exploring the parameter space and reducing computational expenses, making it a viable option for optimizing nozzle plug contours. Using this optimization toolchain, the study yielded preliminary designs for LTO, cruise, and LTO-cruise balanced plug nozzles.

nozzles↗

NASA NTRSDate not supplied

Optimization of Plug Nozzles Using CFD Informed Design Space Querying

CFD↗

NASA NTRS1996

Is the Non-Dipole Magnetic Field Random?

Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.

Walker, Andrew D.↗

NASA NTRS2011

Some Insights of Spectral Optimization in Ocean Color Inversion

In the past decades various algorithms have been developed for the retrieval of water constituents from the measurement of ocean color radiometry, and one of the approaches is spectral optimization. This approach defines an error target (or error function) between the input remote sensing reflectance and the output remote sensing reflectance, with the latter modeled with a few variables that represent the optically active properties (such as the absorption coefficient of phytoplankton and the backscattering coefficient of particles). The values of the variables when the error reach a minimum (optimization is achieved) are considered the properties that form the input remote sensing reflectance; or in other words, the equations are solved numerically. The applications of this approach implicitly assume that the error is a monotonic function of the various variables. Here, with data from numerical simulation and field measurements, we show the shape of the error surface, in a way to justify the possibility of finding a solution of the various variables. In addition, because the spectral properties could be modeled differently, impacts of such differences on the error surface as well as on the retrievals are also presented.

Lee, Zhongping↗

NASA NTRS2004

Meteor44 Video Meteor Photometry

Meteor44 is a software system developed at MSFC for the calibration and analysis of video meteor data. The dynamic range of the (8bit) video data is extended by approximately 4 magnitudes for both meteors and stellar images using saturation compensation. Camera and lens specific saturation compensation coefficients are derived from artificial variable star laboratory measurements. Saturation compensation significantly increases the number of meteors with measured intensity and improves the estimation of meteoroid mass distribution. Astrometry is automated to determine each image's plate coefficient using appropriate star catalogs. The images are simultaneously intensity calibrated from the contained stars to determine the photon sensitivity and the saturation level referenced above the atmosphere. The camera s spectral response is used to compensate for stellar color index and typical meteor spectra in order to report meteor light curves in traditional visual magnitude units. Recent efforts include improved camera calibration procedures, long focal length 'streak' meteor photometry and two-station track determination. Meteor44 has been used to analyze data from the 2001, 2002 and 2003 MSFC Leonid observational campaigns as well as several lesser showers. The software is interactive and can be demonstrated using data from recent Leonid campaigns.

Swift, Wesley R.↗

NASA NTRS2004

Meteor44 Video Meteor Photometry

Meteor44 is a software system developed at MSFC for the calibration and analysis of video meteor data. The dynamic range of the (8bit) video data is extended by approximately 4 magnitudes for both meteors and stellar images using saturation compensation. Camera and lens specific saturation compensation coefficients are derived from artificial variable star laboratory measurements. Saturation compensation significantly increases the number of meteors with measured intensity and improves the estimation of meteoroid mass distribution. Astrometry is automated to determine each image s plate coefficient using appropriate star catalogs. The images are simultaneously intensity calibrated from the contained stars to determine the photon sensitivity and the saturation level referenced above the atmosphere. The camera s spectral response is used to compensate for stellar color index and typical meteor spectra in order to report meteor light curves in traditional visual magnitude units. Recent efforts include improved camera calibration procedures, long focal length "streak" meteor photome&y and two-station track determination. Meteor44 has been used to analyze data from the 2001.2002 and 2003 MSFC Leonid observational campaigns as well as several lesser showers. The software is interactive and can be demonstrated using data from recent Leonid campaigns.

Swift, Wesley R.↗

NASA NTRS2015

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

Schaefer, John↗

NASA NTRS1976

Meteorological adjustment of yearly mean values for air pollutant concentration comparison

Using multiple linear regression analysis, models which estimate mean concentrations of Total Suspended Particulate (TSP), sulfur dioxide, and nitrogen dioxide as a function of several meteorologic variables, two rough economic indicators, and a simple trend in time are studied. Meteorologic data were obtained and do not include inversion heights. The goodness of fit of the estimated models is partially reflected by the squared coefficient of multiple correlation which indicates that, at the various sampling stations, the models accounted for about 23 to 47 percent of the total variance of the observed TSP concentrations. If the resulting model equations are used in place of simple overall means of the observed concentrations, there is about a 20 percent improvement in either: (1) predicting mean concentrations for specified meteorological conditions; or (2) adjusting successive yearly averages to allow for comparisons devoid of meteorological effects. An application to source identification is presented using regression coefficients of wind velocity predictor variables.

Sidik, S. M.↗

NASA NTRS2010

Coherent Eigenmodes in Homogeneous MHD Turbulence

The statistical mechanics of Fourier models of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence is discussed, along with their relevance for dissipative magnetofluids. Although statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation, i.e., we have coherent structure. We use eigenanalysis of the modal covariance matrices in the probability density function to explain this phenomena in terms of `broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We provide examples from 2-D and 3-D magnetohydrodynamic simulations of homogeneous turbulence, and show new results from long-time simulations of MHD turbulence with and without a mean magnetic field

Shebalin, John V.↗