Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Derived Matrices”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 1: Engineering and usage

The LOADS program L218, a digital computer program that calculates dynamic load coefficient matrices utilizing the force summation method, is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: translational and rotational accelerations, velocities, and displacements; panel aerodynamic forces; net panel forces; shears and moments. Program usage and a brief description of the analysis used are presented. A description of the design and structure of the program to aid those who will maintain and/or modify the program in the future is included.

Miller, R. D.↗

Power series evaluation of transition and covariance matrices.

Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.

Bierman, G. J.↗

Design of nonpolarizing achromatic beamsplitters with dielectric multilayer coatings

A novel design approach is presented for nominally nonpolarizing beamsplitters with very low polarization over an extended wavelength range, with low angular sensitivity. A high degree of intensity matching for s and p polarization in a given wavelength interval, from 500 to 600 nm, has been obtained for multilayer stacks derived from an initial graded-index film design by matching of the characteristic matrices. This graded-index film design maintains a very low polarization ratio for almost the complete visible region, covering a wavelength range about twice that covered by the derived homogeneous multilayer stack.

Zukic, Muamer↗

On the equinoctial orbit elements.

This paper investigates the equinoctial orbit elements for the two-body problem, showing that the associated matrices are free from singularities for zero eccentricities and zero and ninety degree inclinations. The matrix of the partial derivatives of the position and velocity vectors with respect to the orbit elements is given explicitly, together with the matrix of inverse partial derivatives, in order to facilitate construction of the matrizant (state transition matrix) corresponding to these elements. The Lagrange and Poisson bracket matrices are also given. The application of the equinoctial orbit elements to general and special perturbations is discussed.

Broucke, R. A.↗

Development of a solid hexahedron finite dynamic element

This paper presents the pertinent details of a newly developed solid rectangular hexahedron finite dynamic element, involving the derivation of the higher order stiffness and inertia dynamic correction matrices. Numerical results of a test case are also presented which indicate that adoption of the dynamic elements significantly improves the solution convergence, when compared with the related performance of the corresponding finite elements.

Gupta, K. K.↗

On the eigenvalue and eigenvector derivatives of a non-defective matrix

A novel approach is introduced to address the problem of existence of differentiable eigenvectors for a nondefective matrix which may have repeated eigenvalues. The existence of eigenvector derivatives for a unique set of continuous eigenvectors corresponding to a repeated eigenvalue is rigorously established for nondefective and analytic matrices. A numerically implementable method is then developed to compute the differentiable eigenvectors associated with repeated eigenvalues. The solutions of eigenvalue and eigenvector derivatives for repeated eigenvalues are then derived. An example is given to illustrate the validity of formulations developed in this paper.

Juang, Jer-Nan↗

Interval prediction in structural dynamic analysis

Methods for assessing the predictive accuracy of structural dynamic models are examined with attention given to the effects of modal mass, stiffness, and damping uncertainties. The methods are based on a nondeterministic analysis called 'interval prediction' in which interval variables are used to describe parameters and responses that are unknown. Statistical databases for generic modeling uncertainties are derived from experimental data and incorporated analytically to evaluate responses. Covariance matrices of modal mass, stiffness, and damping parameters are propagated numerically in models of large space structures by means of three methods. The test data tend to fall within the predicted intervals of uncertainty determined by the statistical databases. The present findings demonstrate the suitability of using data from previously analyzed and tested space structures for assessing the predictive accuracy of an analytical model.

Hasselman, Timothy K.↗

Probabilistic evaluation of on-line checks in fault-tolerant multiprocessor systems

The analysis of fault-tolerant multiprocessor systems that use concurrent error detection (CED) schemes is much more difficult than the analysis of conventional fault-tolerant architectures. Various analytical techniques have been proposed to evaluate CED schemes deterministically. However, these approaches are based on worst-case assumptions related to the failure of system components. Often, the evaluation results do not reflect the actual fault tolerance capabilities of the system. A probabilistic approach to evaluate the fault detecting and locating capabilities of on-line checks in a system is developed. The various probabilities associated with the checking schemes are identified and used in the framework of the matrix-based model. Based on these probabilistic matrices, estimates for the fault tolerance capabilities of various systems are derived analytically.

Nair, V. S. S.↗

Adaptation of a matrix parameterization of the middle atmospheric radiative cooling for an arbitrary vertical coordinate grid

Matrices corresponding to a revised vertical grid are shown to be derived from the original grid by integrating the radiative cooling rate over model layers. The method is applied to temperature profiles that represent average or extreme atmospheric conditions and a range of vertical resolutions. The example makes use of the 15-micron CO2 band parameterization proposed by Akmaev and Shved (1982) for the LTE region of the middle atmosphere. Cooling rate errors provided by the present method are not more than 0.11 K/day for a vertical grid spacing of less than 5 km. The matrix transformation method is shown to be valuable for adapting effective matrix parameterizations of middle atmosphere cooling to atmospheric models with arbitrary vertical resolutions.

Akmaev, R. A.↗

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS (Energy-Corrected Sudden) and IOS (Infinite-Order Sudden) models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

Formalism↗

Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems

Systems of linear equations with Toeplitz coefficient matrices arise in many important applications. The classical Levinson algorithm computes solutions of Toeplitz systems with only O(n(sub 2)) arithmetic operations, as compared to O(n(sub 3)) operations that are needed for solving general linear systems. However, the Levinson algorithm in its original form requires that all leading principal submatrices are nonsingular. An extension of the Levinson algorithm to general Toeplitz systems is presented. The algorithm uses look-ahead to skip over exactly singular, as well as ill-conditioned leading submatrices, and, at the same time, it still fully exploits the Toeplitz structure. In our derivation of this algorithm, we make use of the intimate connection of Toeplitz matrices with formally biorthogonal polynomials.

Freund, Roland W.↗

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗

Improved orthogonality check for measured modes

A method is proposed for performing an orthogonality check for normal modes derived from ground vibration testing. The method utilizes partitioned mass and stiffness matrices for a linear undamped representation of a structure. The normalization of the modes by the proposed method inherently includes the effects of significant displacements which were not measured; and the method may allow the use of fewer measurement points than would be necessary with the conventional method.

Berman, A.↗

Dynamic mechanical analysis and organization/storage of data for polymetric materials

Dynamic mechanical analysis was performed on a variety of temperature resistant polymers and composite resin matrices. Data on glass transition temperatures and degree of cure attained were derived. In addition a laboratory based computer system was installed and data base set up to allow entry of composite data. The laboratory CPU termed TYCHO is based on a DEC PDP 11/44 CPU with a Datatrieve relational data base. The function of TYCHO is integration of chemical laboratory analytical instrumentation and storage of chemical structures for modeling of new polymeric structures and compounds

Rosenberg, M.↗

A Study of Feature Extraction Using Divergence Analysis of Texture Features

An empirical study of texture analysis for feature extraction and classification of high spatial resolution remotely sensed imagery (10 meters) is presented in terms of specific land cover types. The principal method examined is the use of spatial gray tone dependence (SGTD). The SGTD method reduces the gray levels within a moving window into a two-dimensional spatial gray tone dependence matrix which can be interpreted as a probability matrix of gray tone pairs. Haralick et al (1973) used a number of information theory measures to extract texture features from these matrices, including angular second moment (inertia), correlation, entropy, homogeneity, and energy. The derivation of the SGTD matrix is a function of: (1) the number of gray tones in an image; (2) the angle along which the frequency of SGTD is calculated; (3) the size of the moving window; and (4) the distance between gray tone pairs. The first three parameters were varied and tested on a 10 meter resolution panchromatic image of Maryville, Tennessee using the five SGTD measures. A transformed divergence measure was used to determine the statistical separability between four land cover categories forest, new residential, old residential, and industrial for each variation in texture parameters.

Hallada, W. A.↗

A frequency domain analysis for damped space structures

A method is presented for the analysis of damped structural systems in which the structural components are represented by impedance models and analyzed in the frequency domain. Methods are presented to assemble and condense system impedance matrices, and then to identify approximate mass, stiffness, and damping matrices for systems whose impedances are complicated functions of frequency. Formulas are derived for determination of approximate values for system natural frequencies and damping using frequency domain quantities. The sensitivities of these approximate values to system parameter changes are analyzed. The implementation of these analysis tools is discussed and applied to a simple mechanical system.

Hagood, Nesbitt W.↗

Kinematic sensitivity of robot manipulators

Kinematic sensitivity vectors and matrices for open-loop, n degrees-of-freedom manipulators are derived. First-order sensitivity vectors are defined as partial derivatives of the manipulator's position and orientation with respect to its geometrical parameters. The four-parameter kinematic model is considered, as well as the five-parameter model in case of nominally parallel joint axes. Sensitivity vectors are expressed in terms of coordinate axes of manipulator frames. Second-order sensitivity vectors, the partial derivatives of first-order sensitivity vectors, are also considered. It is shown that second-order sensitivity vectors can be expressed as vector products of the first-order sensitivity vectors.

Vuskovic, Marko I.↗

Hierarchical flux-based thermal-structural finite element analysis method

A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.

Polesky, Sandra P.↗