Solution of linear system of equations when the matrix is circulant
The general circulant matrix is introduced, and its inversion is shown.
Balgovind, R. C.↗
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The San Fernando Observatory video Stokes polarimeter
A study was conducted to determine the suitability of the San Fernando Observatory's 61 cm (24 inch) aperture vacuum solar telescope and 3 m (118 inch) focal length vacuum spectroheliograph for Stokes Polarimetry measurements. The polarization characteristics of these two instruments was measured by determining their Mueller matrices as a function of telescope orientation, field angle, wavelength, grating type, and position of the measuring beam in the telescope entrance window. In general, the polarizing and depolarizing properties are small so that inversion of the system Mueller matrix will permit the accurate measurement of Stokes profiles for vector magnetic field determination. A proposed polarimeter design based on the use of a TV camera system to simultaneously scan six different polarization components of a given line profile is described. This design, which uses no rotating optics or electronic modulators and makes efficient use of the available irradiance, promises to yield high quality vector magnetograms.
Richter, P. H.↗
Computationally efficient multibody simulations
Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.
Ramakrishnan, Jayant↗
3D Navier-Stokes Time Accurate Solutions Using Multipartitioning Parallel Computation Methodology
A parallel CFD code solving 3D time accurate Navier-Stokes equations with multipartitioning parallel Methodology is being developed in collaboration with Ohio State University within the Air Vehicle Directorate, at Wright Patterson Air Force Base. The advantage of the multipartitioning parallel method is that the domain decomposition will not introduce domain boundaries for the implicit operators. A ring structure data communication is employed so that the implicit time accurate method can be implemented for multi-processors with the same accuracy as for the single processor. No sub-iteration is needed at the domain boundaries. The code has been validated for some typical unsteady flows, which include Coutte Flow, flow passing a cylinder. The code now is being employed for a large scale time accurate wall jet transient flow computation. 'ne preliminary results are promising. The mesh has been refined to capture more details of the flow field. The mesh refinement computation is in progress and would be difficult to successfully implement without the parallel computation techniques used. A modified version of the code with more efficient inversion of the diagonalized block matrix is currently being tested.
Zha, Ge-Cheng↗
Using Dual-wavelength Fiber Bragg Gratings for Temperature and Strain Sensing at Cryogenic Temperature
By using dual-wavelength fiber-optic Bragg gratings, a new technique has been developed for sensing both temperature and strain simultaneously in cryogenic temperature range. Two Bragg gratings with different wavelengths were inscribed at the same location in an optical fiber to form a dual-wavelength sensor. By measuring the wavelength shifts that resulted from the fiber being subjected to different temperatures and strains, the wavelength-dependent thermo-optic coefficients and photoelastic coefficients of the fiber were determined. These coefficients were used to construct the elements of the K matrix, which enables to determine inversely the strain and temperature changes by measuring the wavelength shifts of the dual-wavelength Bragg grating. In this study, measurements were made over the temperature range from room temperature down to about 10 K, addressing much of the low temperature range of cryogenic tanks. A structure transition of the optical fiber during the temperature change was found from about 70 K to 140 K. This transition caused splitting of the waveforms characterizing the Bragg gratings, and the determination of wavelength shifts was consequently complicated. Several alternatives are proposed to resolve this problem. The effectiveness and sensitivities of these measurements in different temperature ranges are discussed. The separation of two wavelengths for the dual-wavelength Bragg grating has been widened to increase the sensitivities of measurement; however, this separation can still be covered in the scanning range from single scanning laser.
Wu, Meng-Chou↗
Solar Sail Attitude Control Performance Comparison
Performance of two solar sail attitude control implementations is evaluated. One implementation employs four articulated reflective vanes located at the periphery of the sail assembly to generate control torque about all three axes. A second attitude control configuration uses mass on a gimbaled boom to alter the center-of-mass location relative to the center-of-pressure producing roll and pitch torque along with a pair of articulated control vanes for yaw control. Command generation algorithms employ linearized dynamics with a feedback inversion loop to map desired vehicle attitude control torque into vane and/or gimbal articulation angle commands. We investigate the impact on actuator deflection angle behavior due to variations in how the Jacobian matrix is incorporated into the feedback inversion loop. Additionally, we compare how well each implementation tracks a commanded thrust profile, which has been generated to follow an orbit trajectory from the sun-earth L1 point to a sub-L1 station.
Bladt, Jeff J.↗
Scalar gain interpretation of large order filters
A technique is developed which demonstrates how to interpret a large fully-populated filter gain matrix as a set of scalar gains. The inverse problem is also solved, namely, how to develop a large-order filter gain matrix from a specified set of scalar gains. Examples are given to illustrate the method.
Mason, Paul A. C.↗
Two-polarity magnetization in the Manson impact breccia
A preliminary paleomagnetic study of the impact breccia matrix and clasts has produced surprising results--nearly antipodal normal and reversed polarity magnetic vectors are observed in different portions of the core. Near-antipodal magnetizations within a segment of matrix and within individual samples rule out core inversion as the explanation of the dual polarity. In both the dense and the sandy matrix breccias, the magnetizations of clasts and matrix within the same core segment are identical; this negative 'conglomerate test' indicates that magnetization originated after impact. Paleomagnetic study of the Manson Impact Structure is an attempt to refine the Ar-40/Ar-39 age (65.7 +/- 1 m.y.) that suggests Manson to be a Cretaceous-Tertiary boundary impact. Refinement is possible because the boundary occurs within a reversed polarity interval (29R) of only 0.5 m.y. duration. The two breccia types in the Manson structure were both examined: one of a very dense matrix and apparently partially melted, and the breccia stratigraphically below it of granular or 'sandy' chloritic matrix. Samples were taken from the matrixes and a wide variety of clast compositions, including granite, diabase, gneiss, amphibolite, and melted granite. Currently, measurements have been made on 22 samples, using 30-35 steps of either alternating field (AF) or thermal demagnetization.
Steiner, M. B.↗
Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP
The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.
Gupta, V. K.↗
Unified formulation of dynamics for serial rigid multibody systems
There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.
Jain, Abhinandan↗
On the role of dimensionality and sample size for unstructured and structured covariance matrix estimation
The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.
Morgera, S. D.↗
The Influence of Shallow Subsurface Properties on Particle Motion in Acoustic-Seismic Coupling
Atmospheric acoustic waves transmit energy into the solid Earth through air-to-ground coupling. These waves are recorded by seismic sensors and provide insight into both atmospheric phenomena and subsurface properties. Interpreting these signals is often challenging because they are modulated by subsurface structure and the incidence angle of the acoustic wave. This study examines acoustic--seismic coupling generated by the 2012 Camp Minden Explosion, which was recorded by hundreds of seismoacoustic stations. We apply a novel technique to quantify the seismic particle motion, model coupled waves with a propagator matrix approach, and apply a Bayesian inversion to infer properties of the shallow subsurface. Our analysis reveals that prograde motion is widespread and focused in low shear-wave velocity regions, such as the Mississippi Embayment, and retrograde motion is more common in higher shear-velocity areas. Inversion results at some stations produce plausible subsurface models with strong waveform fits, while inversions at other sites are less successful. These results indicate prograde particle motion in air-to-ground coupled waves is more prevalent than previously recognized and may serve as a diagnostic for shallow velocity structure. Our comprehensive modeling and inversion framework provides a potential method to extract layered near-surface properties from acoustic-seismic coupling observations.
58 GEOSCIENCES↗
Complex eigenvalue analysis of rotating structures
A FORTRAN subroutine to NASTRAN which constructs coriolis and centripetal acceleration matrices, and a centrifugal load vector due to spin about a selected point or about the mass center of the structure is discussed. The rigid translational degrees of freedom can be removed by using a transformation matrix T and its explicitly given inverse. These matrices are generated in the subroutine and their explicit expressions are given.
Patel, J. S.↗
Inventory estimation on the massively parallel processor
This paper describes algorithms for efficiently computing inventory estimates from satellite based images. The algorithms incorporate a one dimensional feature extraction which optimizes the pairwise sum of Fisher distances. Biases are eliminated with a premultiplication by the inverse of the analytically derived error matrix. The technique is demonstrated with a numerical example using statistics obtained from an actual Landsat scene. Attention was given to implementation of the Massively Parallel processor (MPP). A timing analysis demonstrates that the inventory estimation can be performed an order of magnitude faster on the MPP than on a conventional serial machine.
Argentiero, P. D.↗
Optimal Sensor Locations for Structural Identification
The optimum sensor location problem, OSLP, may be thought of in terms of the set of systems, S, the class of input time functions, I, and the identification algorithm (estimator) used, E. Thus, for a given time history of input, the technique of determining the OSL requires, in general, the solution of the optimization and the identification problems simultaneously. A technique which uncouples the two problems is introduced. This is done by means of the concept of an efficient estimator for which the covariance of the parameter estimates is inversely proportional to the Fisher Information Matrix.
Udwadia, F. E.↗
Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes
In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.
Lin, Shu↗
Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization
Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.
Casarin, Mario↗
Affine Generalized Inverse for Optimal Control Allocation
This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set.
Acheson, Michael J.↗