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NASA NTRS1991

Second-order discrete Kalman filtering equations for control-structure interaction simulations

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.

Park, K. C.↗

NASA NTRS1989

Probabilistic boundary element method

The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.

Cruse, T. A.↗

NASA NTRS1991

Development and verification of global/local analysis techniques for laminated composites

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.

Thompson, Danniella Muheim↗

NASA NTRS1990

Orthogonal series generalized likelihood ratio test for failure detection and isolation

A new failure detection and isolation algorithm for linear dynamic systems is presented. This algorithm, the Orthogonal Series Generalized Likelihood Ratio (OSGLR) test, is based on the assumption that the failure modes of interest can be represented by truncated series expansions. This assumption leads to a failure detection algorithm with several desirable properties. Computer simulation results are presented for the detection of the failures of actuators and sensors of a C-130 aircraft. The results show that the OSGLR test generally performs as well as the GLR test in terms of time to detect a failure and is more robust to failure mode uncertainty. However, the OSGLR test is also somewhat more sensitive to modeling errors than the GLR test.

Hall, Steven R.↗

NASA NTRS1990

The 27-28 October 1986 FIRE IFO cirrus case study - A five lidar overview of cloud structure and evolution

During the case study from the First ISCCP (International Satellite Cloud Climatology Program) Regional Experiment (FIRE) Intensive Field Observation (IFO), one airborne lidar system and four ground-based systems collected linear depolarization, intrinsically calibrated backscatter, and Doppler velocity information. Data presented describe the temporal evolution and spatial distribution of cirrus clouds over an area encompassing southern and central Wisconsin. Cirrus cloud types include dissipating subvisual and thin fibrous cirrus cloud bands, an isolated mesoscale uncinus complex, a large-scale, deep cloud that developed into an organized cirrus structure within the lidar array, and a series of intensifying mesoscale cirrus cloud masses. It is noted that the cirrus frequently developed in the vertical from particle fallstreaks emanating from generating regions at or near cloud tops; however, glaciating supercooled altocumulus clouds contributed to the production of ice mass at the base of the deep cirrus cloud.

Sassen, Kenneth↗

NASA NTRS1990

Implementation of two projection methods on a shared memory multiprocessor - DEC VAX 6240

The relative performance of two iterative schemes, based on projection techniques, is compared on a shared memory multiprocessor - VAX 6240. The CG accelerated Block-SSOR method and the CG accelerated Symmetric-Kaczmarz method are considered for the solution of large sparse nonsymmetric systems of linear equations. It is shown that the regular structure of many matrices can be exploited by the CG-accelerated Block-SSOR method to provide good speedup in a multiprocessing environment. However, the CG accelerated Symmetric-Kaczmarz method, while being a viable alternative on a scalar machine, is unable to benefit from multiprocessing.

Kamath, C.↗

NASA NTRS1991

Efficient use of direct solvers for the calculation of compressible flows

While the direct solution of systems of linear equations resulting from fluid dynamic problems has generally not been practical in the past, it is presently demonstrated that the direct method is often more efficient than the most popular iterative schemes when constructed in such a way as to take advantage of presently available vector processing capabilities and large memory. The vertical line Gauss-Seidel algorithm was chosen as the iterative method to be compared with the direct method. It is fond that the direct method becomes efficient only when large residual reductions are desired.

Riggins, David W.↗

NASA NTRS1992

An incremental strategy for calculating consistent discrete CFD sensitivity derivatives

In this preliminary study involving advanced computational fluid dynamic (CFD) codes, an incremental formulation, also known as the 'delta' or 'correction' form, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods appear to be needed for future 3D applications; however, because direct solver methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form result in certain difficulties, such as ill-conditioning of the coefficient matrix, which can be overcome when these equations are cast in the incremental form; these and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two laminar sample problems: (1) transonic flow through a double-throat nozzle; and (2) flow over an isolated airfoil.

Korivi, Vamshi Mohan↗

NASA NTRS1992

Minimization of deviations of gear real tooth surfaces determined by coordinate measurements

The deviations of a gear's real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method was developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

Litvin, F. L.↗

NASA NTRS1992

Asymptotic modal analysis and statistical energy analysis

Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well.

Dowell, Earl H.↗

NASA NTRS1990

Calibration of optical detectors using discrete Fourier transform techniques

A method for determining the detector electrooptical transfer function (DEOTF) at different discrete frequencies simultaneously is presented. It involves simulation of the detector with a waveform of unknown frequency composition, such as a square wave or impulse function. The DEOTF is calculated as the ratio of the discrete Fourier transform of the detector output to the transform of the input waveform. This technique was successfully applied to Golay cell and bolometer detectors and can be used for other linear detector systems.

Hagopian, John G.↗

NASA NTRS1992

Large-amplitude finite element flutter analysis of composite panels in hypersonic flow

Consideration is given to a finite-element approach for determining the nonlinear flutter characteristics of 3D thin laminated composite panels using the full third-order-piston transverse-loading aerodynamic theory. The unsteady hypersonic aerodynamic theory and the von Karman large-deflection-plate theory are used to formulate the aeroelasticity problem. Nonlinear flutter analyses are performed to assess the influence of the higher-order aerodynamic theory on the structure's limit-cycle amplitude and the dynamic pressure of the flow velocity. A solution procedure is presented to solve the nonlinear panel flutter and large-amplitude free-vibration finite-element equations. Nonlinear flutter analyses are performed for different boundary support-conditions and for various system parameters. Linear finite-element flutter for isotropic and composite panels and large-amplitude isotropic panel flutter results are compared with existing classical solutions. The large-amplitude panel flutter results using the full third-order piston aerodynamic theory are presented to assess the influence of the nonlinear aerodynamic theory.

Gray, Carl E., Jr.↗

NASA NTRS1993

Efficient Minimum-Polynomial And Reduced-Rank Extrapolation

MPERRE computer program accelerates convergence of sequence of vectors by use of minimum-polynomial extrapolation (MPE) and reduced-rank extrapolation (RRE). Effective in accelerating convergences of such sequences of vectors as those obtained from iterative solution of systems of linear and nonlinear equations. In conjunction with various iterative techniques, successfully employed in finite-difference solution of large-scale elliptic boundary-value problems and problems in computational-fluid-dynamics. Only input required is sequence of vectors, convergence of which is accelerated. Program economical and easy to use. Written in FORTRAN 77.

Sidi, Avram↗

NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗

NASA NTRS1992

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Korivi, V. M.↗

NASA NTRS1993

Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers

Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.

Baddourah, Majdi A.↗

NASA NTRS1991

Sequential design of linear quadratic state regulators with prescribed eigenvalues and specified relative stability

This paper considers the problem of optimal regulator design of linear multivariable systems with prescribed pole locations and/or poles corresponding to specified relative stability. A sequential method based on the frequency-domain optimality condition is proposed for achieving the desired pole assignment and determination of the corresponding quadratic performance index. This design method enables the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

Ganesan, Sekar↗

NASA NTRS1993

Linear, multivariable robust control with a mu perspective

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Packard, Andy↗