Direct calculation of first- and second-order density matrices - The higher RPA method
First and second order density matrices calculation of pure state N fermion systems, using higher random phase approximation
Simons, J.↗
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Random harmonic analysis program, L221 (TEV156). Volume 1: Engineering and usage
A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented.
Miller, R. D.↗
Identification of terrain cover using the optimum polarimetric classifier
A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.
Kong, J. A.↗
Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method
Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.
Uncertainty Quantification↗
Remote sensing of earth terrain
A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain cover are computed from theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.
Kong, J. A.↗
Application of the target decomposition theorem to a polarimetric random media model
With advances in polarimetric radar measurements of land surfaces, the need for understanding the underlying scattering mechanisms and dominant target features has become the focus of many studies. In particular, the maximum use of the polarimetric information to identify and/or separate parameters related to the surface features such as vegetation thickness, structure, water content, and soil surface characteristics will enhance the possibility of using polarimetric radars for monitoring the earth's surface from space. In this paper, Cloude's decomposition theorem is applied to a polarimetric random media model to simulate the radar measurements of vegetated canopies. The vegetated canopies are modeled as a three layer discrete random medium with leaves and branches in the first layer, tree trunks in the second layer, and a half space of homogeneous ground with rough interface as the bottom layer. The distorted born approximation (DBA) has been used to compute full Mueller matrix of the canopy, using canonical dielectric objects such as thin discs and cylinders as leaves, branches, and trunks, respectively. The Mueller matrix and the derived covariance matrix contain information on the second order statistics of radar signals at various polarizations from the canopy. To decompose the covariance matrix to its constituent targets, the eigenvalues and eigenvectors of the covariance matrix are computed in terms of the physical parameters of the canopy. In addition, each eigenvector explicitly shows the scattering mechanisms such as odd and even reflections in the canopy. Cloude's decomposition theorem is applied using the Pauli spin matrices as a basis and an expression for the degree of disorder or the entropy for the vegetated surface is found. Then, the physical parameters estimated from in situ measurements are used in the random media to obtain realistic covariance matrices. As a result, the sensitivity of the eigenvalue spectrums and the coefficients resulting from the target decomposition theorem to the physical parameters of the canopy are examined and the possible use of Cloude's theorem to estimate vegetation and soil parameters is discussed.
Saatchi, Sasan S.↗
Equation modifying program, L219 (EQMOD). Volume 2: Supplemental system design and maintenance document
A digital computer program, L219 (EQMOD), available for execution on the CDC 6600 is described. The program modifies matrices according to card input instructions and prepares magnetic files of matrices suitable for use in the linear systems analysis program (QR) and the random harmonic analysis program L221 (TEV156). The particular field of application of the program is the modification of the theoretical equations of motion and load equations generated in DYLOFLEX by the equation of motion program (L217) and the load equation program (L218), respectively.
Hirayama, M. Y.↗
Remote sensing of earth terrain
A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain covers are computed from the theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements. A systematic approach is presented for obtaining the optimal polarimetric matched filter which produces maximum contrast between two scattering classes, each represented by its respective covariance matrix.
Kong, J. A.↗
Theoretical models for polarimetric microwave remote sensing of earth terrain
Using the two-layer anisotropic random medium, a mathematically rigorous, fully polarimetric model is developed to compute the Mueller and covariance matrices in the backscattering direction for various kinds of earth terrain. The electric field is first written in the form of an integral equation involving the unperturbed dyadic Green's function in the absence of the permittivity fluctuations. The integral equation is then solved by an iterative series known as the Born series. With only the first term of the series, which physically describes a single scattering process, the fully polarimetric backscattering coefficients are derived. Four different kinds of upgoing and downgoing waves exist due to the excitation of both ordinary and extraordinary waves in the anisotropic random medium. An averaging scheme over the azimuthal direction is used to simulate the effects on the radar backscattering due to the azimuthal randomness in the growth direction of leaves in tree and grass fields.
Borgeaud, M.↗
BCH codes for large IC random-access memory systems
In this report some shortened BCH codes for possible applications to large IC random-access memory systems are presented. These codes are given by their parity-check matrices. Encoding and decoding of these codes are discussed.
Lin, S.↗
Radar scene generation for tactical decision aids
The Mueller matrix and polarization covariance matrix for polarimetric radar systems was studied. The clutter was modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model was applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. Theoretical predictions are matched with experimental data for vegetation fields. The strong fluctuation theory was used to derive the backscattering cross sections. A two-layer anisotropic random medium model was developed for the active and passive microwave remote sensing of ice fields. A three-layer random medium model was adopted to study the volume scattering effects for the active and passive microwave remote sensing of snow-covered ice fields.
Kong, J. A.↗
Modeling and observation of the radar polarization signature of forested areas
To understand radar measurements of forested areas, the authors have developed a model of L-band (25-cm) microwave scattering from a forest. The forest floor is modeled as a rough dielectric surface above which is a layer of nearly vertical dielectric cylinders representing tree trunks. Above this layer is a second layer consisting of randomly oriented cylinders which represent branches. The authors identify several scattering mechanisms and calculate the corresponding Stokes matrices, which combine to give the total Stokes matrix and resulting polarization signature. It is found that this simple model permits accurate prediction of the polarization of the scattered waves and that additional mechanisms, including the effects of leaves and twigs, are not required for the 25-cm observation of the forests studied. The authors present measurements of the polarization signature acquired over a forested area and show comparisons with model calculations.
Durden, Stephen L.↗
NASA-UVA light aerospace alloy and structures technology program
The report on progress achieved in accomplishing of the NASA-UVA Light Aerospace Alloy and Structures Technology Program is presented. The objective is to conduct interdisciplinary graduate student research on the performance of next generation, light weight aerospace alloys and associated thermal gradient structures in close collaboration with researchers. The efforts will produce basic understanding of material behavior, new monolithic and composite alloys, processing methods, solid and fluid mechanics analyses, measurement advances, and a pool of educated graduate students. The presented accomplishments include: research on corrosion fatigue of Al-Li-Cu alloy 2090; research on the strengthening effect of small In additions to Al-Li-Cu alloys; research on localized corrosion of Al-Li alloys; research on stress corrosion cracking of Al-Li-Cu alloys; research on fiber-matrix reaction studies (Ti-1100 and Ti-15-3 matrices containing SCS-6, SCS-9, and SCS-10 fibers); and research on methods for quantifying non-random particle distribution in materials that has led to generation of a set of computer programs that can detect and characterize clusters in particles.
Gangloff, Richard P.↗
SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method
Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.
Uncertainty Quantification↗
Modified radiative transfer theory for a two-layer anisotropic random medium
The modified radiative transfer (MRT) equations which describe propagation and scattering of the electromagnetic field intensity in a layered anisotropic random medium are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The extinction matrices and scattering phase matrices for both mean and incoherent field intensities are obtained. Backscattering enhancement is observed due to the spatial coherent effect between upward and downward propagating waves. It also occurs for the half-space case, because of coupling between ordinary and extraordinary waves. The depolarization effect is predicted in the first-order renormalization approximation to the MRT equation.
Lee, J. K.↗
Combining Acceleration and Displacement Dependent Modal Frequency Responses Using an MSC/NASTRAN DMAP Alter
Solving for dynamic responses of free-free launch vehicle/spacecraft systems acted upon by buffeting winds is commonly performed throughout the aerospace industry. Due to the unpredictable nature of this wind loading event, these problems are typically solved using frequency response random analysis techniques. To generate dynamic responses for spacecraft with statically-indeterminate interfaces, spacecraft contractors prefer to develop models which have response transformation matrices developed for mode acceleration data recovery. This method transforms spacecraft boundary accelerations and displacements into internal responses. Unfortunately, standard MSC/NASTRAN modal frequency response solution sequences cannot be used to combine acceleration- and displacement-dependent responses required for spacecraft mode acceleration data recovery. External user-written computer codes can be used with MSC/NASTRAN output to perform such combinations, but these methods can be labor and computer resource intensive. Taking advantage of the analytical and computer resource efficiencies inherent within MS C/NASTRAN, a DMAP Alter has been developed to combine acceleration- and displacement-dependent modal frequency responses for performing spacecraft mode acceleration data recovery. The Alter has been used successfully to efficiently solve a common aerospace buffeting wind analysis.
Barnett, Alan R.↗
A scattering model for forested area
A forested area is modeled as a volume of randomly oriented and distributed disc-shaped, or needle-shaped leaves shading a distribution of branches modeled as randomly oriented finite-length, dielectric cylinders above an irregular soil surface. Since the radii of branches have a wide range of sizes, the model only requires the length of a branch to be large compared with its radius which may be any size relative to the incident wavelength. In addition, the model also assumes the thickness of a disc-shaped leaf or the radius of a needle-shaped leaf is much smaller than the electromagnetic wavelength. The scattering phase matrices for disc, needle, and cylinder are developed in terms of the scattering amplitudes of the corresponding fields which are computed by the forward scattering theorem. These quantities along with the Kirchoff scattering model for a randomly rough surface are used in the standard radiative transfer formulation to compute the backscattering coefficient. Numerical illustrations for the backscattering coefficient are given as a function of the shading factor, incidence angle, leaf orientation distribution, branch orientation distribution, and the number density of leaves. Also illustrated are the properties of the extinction coefficient as a function of leaf and branch orientation distributions. Comparisons are made with measured backscattering coefficients from forested areas reported in the literature.
Karam, M. A.↗
Numerical synthesis of tri-variate velocity realizations of turbulence
An approach for synthesizing trivariate turbulence velocity field spatial realizations is presented. Some of the spatial frequency characteristics of the random velocity field are described by the von Karman spectrum. The simulation algorithm is based on an efficient autoregressive-moving average (ARMA) scheme involving coefficient square matrices of order three. The determination of the efficient low order ARMA algorithm is preceded by the determination of a suitable high order autoregressive (AR) simulation algorithm. The numerical results are presented in a dimensionless form. Thus, they are applicable for any scale of turbulence.
Spanos, P.-T. D.↗