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Structural analysis and design of multivariable control systems: An algebraic approach

The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

Tsay, Yih Tsong

Method and apparatus for filtering visual documents

A method and apparatus for producing an abstract or condensed version of a visual document is presented. The frames comprising the visual document are first sampled to reduce the number of frames required for processing. The frames are then subjected to a structural decomposition process that reduces all information in each frame to a set of values. These values are in turn normalized and further combined to produce only one information content value per frame. The information content values of these frames are then compared to a selected distribution cutoff point. This effectively selects those values at the tails of a normal distribution, thus filtering key frames from their surrounding frames. The value for each frame is then compared with the value from the previous frame, and the respective frame is finally stored only if the values are significantly different. The method filters or compresses a visual document with a reduction in digital storage on the ratio of up to 700 to 1 or more, depending on the content of the visual document being filtered.

Rorvig, Mark E.

ICER-3D: A Progressive Wavelet-Based Compressor for Hyperspectral Images

ICER-3D is a progressive, wavelet-based compressor for hyperspectral images. ICER-3D is derived from the ICER image compressor. ICER-3D can provide lossless and lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The three-dimensional wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of hyperspectral data sets, while facilitating elimination of spectral ringing artifacts. Correlation is further exploited by a context modeler that effectively exploits spectral dependencies in the wavelet-transformed hyperspectral data. Performance results illustrating the benefits of these features are presented.

Kiely, A.

ICER-3D Hyperspectral Image Compression Software

Software has been developed to implement the ICER-3D algorithm. ICER-3D effects progressive, three-dimensional (3D), wavelet-based compression of hyperspectral images. If a compressed data stream is truncated, the progressive nature of the algorithm enables reconstruction of hyperspectral data at fidelity commensurate with the given data volume. The ICER-3D software is capable of providing either lossless or lossy compression, and incorporates an error-containment scheme to limit the effects of data loss during transmission. The compression algorithm, which was derived from the ICER image compression algorithm, includes wavelet-transform, context-modeling, and entropy coding subalgorithms. The 3D wavelet decomposition structure used by ICER-3D exploits correlations in all three dimensions of sets of hyperspectral image data, while facilitating elimination of spectral ringing artifacts, using a technique summarized in "Improving 3D Wavelet-Based Compression of Spectral Images" (NPO-41381), NASA Tech Briefs, Vol. 33, No. 3 (March 2009), page 7a. Correlation is further exploited by a context-modeling subalgorithm, which exploits spectral dependencies in the wavelet-transformed hyperspectral data, using an algorithm that is summarized in "Context Modeler for Wavelet Compression of Hyperspectral Images" (NPO-43239), which follows this article. An important feature of ICER-3D is a scheme for limiting the adverse effects of loss of data during transmission. In this scheme, as in the similar scheme used by ICER, the spatial-frequency domain is partitioned into rectangular error-containment regions. In ICER-3D, the partitions extend through all the wavelength bands. The data in each partition are compressed independently of those in the other partitions, so that loss or corruption of data from any partition does not affect the other partitions. Furthermore, because compression is progressive within each partition, when data are lost, any data from that partition received prior to the loss can be used to reconstruct that partition at lower fidelity. By virtue of the compression improvement it achieves relative to previous means of onboard data compression, this software enables (1) increased return of hyperspectral scientific data in the presence of limits on the rates of transmission of data from spacecraft to Earth via radio communication links and/or (2) reduction in spacecraft radio-communication power and/or cost through reduction in the amounts of data required to be downlinked and stored onboard prior to downlink. The software is also suitable for compressing hyperspectral images for ground storage or archival purposes.

Xie, Hua

Data Structure and Parallel Decomposition Considerations on a Fibonacci Grid

The Fibonacci grid, proposed by Swinbank and Purser (see companion abstract), provides attractive properties for global numerical atmospheric prediction by offering an optimally homogeneous, geometrically regular, and approximately isotropic discretization, with only the polar regions requiring special numerical treatment. It is a mathematical idealization, applied to the sphere, of the multi-spiral patterns often found in botanical structures, such as in pine cones and sunflower heads. Computationally, it is natural to organize the domain, into zones, in each of which the same pair, or triple, of "Fibonacci spirals" dominate. But the further subdivision of such zones into "tiles" of a shape and size suitable for distribution to the processors of a massively parallel computer requires very careful consideration if the subsequent spatial computations along the respective spirals, especially those computations (such as compact differencing schemes) that involve recursion, can be implemented in an efficient "load-balanced "manner without requiring excessive amounts of inter-processor communications. In this paper we show how certain "number theoretic" properties of the Fibonacci sequence (whose numbers prescribe the multiplicity of successive spirals) may be exploited in the decomposition of grid zones into tidy arrangements of triangular grid tiles, each tile possessing one side approximately parallel to the constant-latitude zone boundary. We also describe how the spatially recursive processes may be decomposed across such a tiling, and the directionality of the recursions reversed on alternate grid lines, to ensure a very high degree of load balancing throughout the execution of the computations required for one time step of a global model.

Michalakes, John

Structural optimization by multilevel decomposition

The application of formal optimization techniques to the design of large engineering structures such as aircraft is presently hindered in connection with the large number of design variables involved. According to an approach which attempts to overcome the difficulties, the problem is broken up into several smaller subproblems. This approach has, however, weaknesses which may prevent a determination of the minimum structural weight. Schmit and Ramanathan (1973) have developed a method, which is designed to incorporate control of the material distribution among the finite elements of an assembled structure for a two-level optimization. However, the optimization schemes considered would not be suitable to optimization schemes considered would not be suitable to multidisciplinary optimization of large engineering systems. Sobieszczanski-Sobieski (1982) proposed a method for decomposing a large multidisciplinary optimization problem into a number of small subproblems. The present investigation is concerned with the implementation of this method.

Sobieszczanski-Sobieski, J.

Noise transmission into enclosures

This paper describes analytical and experimental studies of noise transmission into rectangular and cylindrical enclosures. The solutions of the governing acoustic-structural equations are developed by modal decomposition of structural vibrations and the interior acoustic field. Particular attention is directed toward the low frequencies, that is, frequencies up through the first few structural and cavity resonant modes. The structural vibrations are driven by the external acoustic and/or mechanical point loads which are taken to be Gaussian stationary random processes. The structural models include rectangular panels and cylindrical shells.

Vaicaitis, R.

Structural optimization by multilevel decomposition

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Sobieszczanski-Sobieski, J.

Multilevel optimization using a continuum model for structures

The new concept of using a continuum model in the multilevel decomposition of structural optimization problems is presented. The practicality of this concept is demonstrated by application in a scheme for the optimization of beam-like space structures. This scheme is tested against traditional optimization procedures for savings in computational cost. Results from both optimization methods are presented for comparison.

Yates, K.

Structural optimization by generalized, multilevel decomposition

The developments toward a general multilevel optimization capability and results for a three-level structural optimization are described. The method partitions a structure into a number of substructuring levels where each substructure corresponds to a subsystem in the general case of an engineering system. The method is illustrated by a portal framework that decomposes into individual beams. Each beam is a box that can be further decomposed into stiffened plates. Substructuring for this example spans three different levels: (1) the bottom level of finite elements representing the plates; (2) an intermediate level of beams treated as substructures; and (3) the top level for the assembled structure. The three-level case is now considered to be qualitatively complete.

Sobieszczanski-Sobieski, J.

Studies in turbulence

Various papers on turbulence are presented. Individual topics addressed include: modeling the dissipation rate in rotating turbulent flows, mapping closures for turbulent mixing and reaction, understanding turbulence in vortex dynamics, models for the structure and dynamics of near-wall turbulence, complexity of turbulence near a wall, proper orthogonal decomposition, propagating structures in wall-bounded turbulence flows. Also discussed are: constitutive relation in compressible turbulence, compressible turbulence and shock waves, direct simulation of compressible turbulence in a shear flow, structural genesis in wall-bounded turbulence flows, vortex lattice structure of turbulent shear slows, etiology of shear layer vortices, trilinear coordinates in fluid mechanics.

Gatski, Thomas B.

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Sobieszczanskisobieski, Jaroslaw

Multilevel decomposition of complete vehicle configuration in a parallel computing environment

This research summarizes various approaches to multilevel decomposition to solve large structural problems. A linear decomposition scheme based on the Sobieski algorithm is selected as a vehicle for automated synthesis of a complete vehicle configuration in a parallel processing environment. The research is in a developmental state. Preliminary numerical results are presented for several example problems.

Bhatt, Vinay

A parallel algorithm for global routing

A Parallel Hierarchical algorithm for Global Routing (PHIGURE) is presented. The router is based on the work of Burstein and Pelavin, but has many extensions for general global routing and parallel execution. Main features of the algorithm include structured hierarchical decomposition into separate independent tasks which are suitable for parallel execution and adaptive simplex solution for adding feedthroughs and adjusting channel heights for row-based layout. Alternative decomposition methods and the various levels of parallelism available in the algorithm are examined closely. The algorithm is described and results are presented for a shared-memory multiprocessor implementation.

Brouwer, Randall J.

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Sobieszczanski-Sobieski, Jaroslaw

Re-engineering the mission life cycle with ABC and IDEF

The theory behind re-engineering a business process is to remove the non-value added activities thereby lowering the process cost. In order to achieve this, one must be able to identify where the non-value added elements are located which is not a trivial task. This is because the non-value added elements are often hidden in the form of overhead and/or pooled resources. In order to be able to isolate these non-value added processes from among the other processes, one must first decompose the overall top level process into lower layers of sub-processes. In addition, costing data must be assigned to each sub-process along with the value the sub-process adds towards the final product. IDEF0 is a Federal Information Processing Standard (FIPS) process-modeling tool that allows for this functional decomposition through structured analysis. In addition, it illustrates the relationship of the process and the value added to the product or service. The value added portion is further defined in IDEF1X which is an entity relationship diagramming tool. The entity relationship model is the blueprint of the product as it moves along the 'assembly line' and therefore relates all of the parts to each other and the final product. It also relates the parts to the tools that produce the product and all of the paper work that is used in their acquisition. The use of IDEF therefore facilitates the use of Activity Based Costing (ABC). ABC is an essential method in a high variety, product-customizing environment, to facilitate rapid response to externally caused change. This paper describes the work being done in the Mission Operations Division to re-engineer the development and operation life cycle of Mission Operations Centers using these tools.

Mandl, Daniel