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NASA NTRS1983

Constrained Self-adaptive Solutions Procedures for Structure Subject to High Temperature Elastic-plastic Creep Effects

This paper will develop a new solution strategy which can handle elastic-plastic-creep problems in an inherently stable manner. This is achieved by introducing a new constrained time stepping algorithm which will enable the solution of creep initiated pre/postbuckling behavior where indefinite tangent stiffnesses are encountered. Due to the generality of the scheme, both monotone and cyclic loading histories can be handled. The presentation will give a thorough overview of current solution schemes and their short comings, the development of constrained time stepping algorithms as well as illustrate the results of several numerical experiments which benchmark the new procedure.

Padovan, J.↗

NASA NTRS1982

Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

Various aspects of the convergence, uniqueness, and existence properties associated with solutions generated via the elliptically constrained incremental Newton-Raphson (ECINR) algorithm are analyzed. Several theorems are developed, and the formal behavior of the elliptically constrained scheme developed by Padovan (1981) is discussed in detail. Consideration is given to global and local rates of convergence, to the determination of the occurrence of safety zones wherein the algorithm yields inherently convergent results, to formal limitations on the class of functions which the scheme can be applied to solve, and to single and multidimensional formalisms on existence uniqueness and convergence. Special attention is given to functions whose Jacobian matrix exhibit positive, negative, semi and indefinite properties. Several significant advantages of ECINR over the classical INR are mentioned.

Padovan, J.↗

NASA NTRS1983

Pseudo-updated constrained solution algorithm for nonlinear heat conduction

This paper develops efficiency and stability improvements in the incremental successive substitution (ISS) procedure commonly used to generate the solution to nonlinear heat conduction problems. This is achieved by employing the pseudo-update scheme of Broyden, Fletcher, Goldfarb and Shanno in conjunction with the constrained version of the ISS. The resulting algorithm retains the formulational simplicity associated with ISS schemes while incorporating the enhanced convergence properties of slope driven procedures as well as the stability of constrained approaches. To illustrate the enhanced operating characteristics of the new scheme, the results of several benchmark comparisons are presented.

Tovichakchaikul, S.↗

NASA NTRS1985

Constrained optimization for image restoration using nonlinear programming

The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.

Yeh, C.-L.↗

NASA NTRS1986

Constrained hierarchical least square nonlinear equation solvers

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

Padovan, J.↗

NASA NTRS1987

Constrained sheath optics for high thrust density, low specific impulse ion thrusters

The results of an experimental study showing that a contoured, fine wire mesh attached to the screen grid can be used to control the divergence characteristics of ion beamlets produced at low net-to-total accelerating voltage ratios are presented. The influence of free and constrained-sheath optics systems on beamlet divergence characteristics are found to be similar in the operating regime investigated, but it was found that constrained-sheath optics systems can be operated at higher perveance levels than free-sheath ones. The concept of a fine wire interference probe that can be used to study ion beamlet focusing behavior is introduced. This probe is used to demonstrate beamlet focusing to a diameter about one hundreth of the screen grid extraction aperture diameter. Additional testing is suggested to define an optimally contoured mesh that could yield well focused beamlets at net-to-total accelerating voltage ratios below about 0.1.

Wilbur, Paul J.↗

NASA NTRS1987

Inadequacy of single-impulse transfers for path constrained rendezvous

The use of single-impulse techniques to maneuver from point to point about a large space structure (LSS) with an arbitrary geometrical configuration and spin is examined. Particular consideration is given to transfers with both endpoints on the forbidden zone surface. Clohessy-Wiltshire equations of relative motion are employed to solve path constrained rendezvous problems. External and internal transfers between arbitrary points are analyzed in terms of tangential departure and arrival conditions. It is observed that single-impulse techniques are inadequate for transferring about the exterior of any LSS; however, single-impulse transfers are applicable for transfers in the interior of LSSs. It is concluded that single-impulse transducers are not applicable for path constrained rendezvous guidance.

Stern, S. A.↗

NASA NTRS1987

Dynamics formulations for the real-time simulation of constrained motion

The Space Shuttle program has relied heavily on simulation throughout all phases of development and operation. Real-time, man-in-the-loop simulation has served the NASA manned space flight program by providing the means to evaluate systems design and integrated systems performance in a simulated flight environment as well as provide a means to train flight crews. New challenges are presented by the development and operation of a permanently manned space station. The assembly of the space station, the transferral of payloads and the use of the space station manipulator to berth the Orbiter are operations critical to the success of the space station. All these operations are examples of constrained motion among the bodies associated with the Orbiter and space station system. The state of the art of formulating the governing dynamical equations of motion for constrained systems are described. The uses of the two basic problems in multibody dynamics are discussed. The most efficient formulations of the equations of motion are addressed from the point of view of completeness. The issues surrounding incorporating the constraints into the equation of motion are presented.

Kelly, Frederick A.↗

NASA NTRS1991

Lithium in halo stars - Constraining the effects of helium diffusion on globular cluster ages and cosmology

Stellar evolutionary models with diffusion are used to show that observations of lithium in extreme halo stars provide crucial constraints on the magnitude of the effects of helium diffusion. The flatness of the observed Li-T(eff) relation severely constrains diffusion Li isochrones, which tend to curve downward toward higher T(eff). It is argued that Li observations at the hot edge of the plateau are particularly important in constraining the effects of helium diffusion; yet, they are currently few in number. It is proposed that additional observations are required there, as well as below 5500 K, to define more securely the morphology of the halo Li abundances. Implications for the primordial Li abundance are considered. It is suggested that a conservative upper limit to the initial Li abundance, due to diffusive effects alone, is 2.35.

Deliyannis, Constantine P.↗

NASA NTRS1992

Constrained modes in control theory - Transmission zeros of uniform beams

Mathematical arguments are presented demonstrating that the well-established control system concept of the transmission zero is very closely related to the structural concept of the constrained mode. It is shown that the transmission zeros of a flexible structure form a set of constrained natural frequencies for it, with the constraints depending explicitly on the locations and the types of sensors and actuators used for control. Based on this formulation, an algorithm is derived and used to produce dimensionless plots of the zero of a uniform beam with a compatible sensor/actuator pair.

Williams, T.↗

NASA NTRS1992

Constrained control allocation

This paper addresses the problem of the allocation of several flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The controls are assumed to be individually linear in their effect throughout their ranges of motion, and independent of one another in their effects. The geometries of the subset of the constrained controls and of its image in moment space are examined. A direct method of allocating these several controls is presented, that guarantees the maximum possible moment is generated within the constraints of the controls. The results are illustrated by an example problem involving three controls and two moments.

Durham, Wayne C.↗

NASA NTRS1993

Image coding using entropy-constrained residual vector quantization

The residual vector quantization (RVQ) structure is exploited to produce a variable length codeword RVQ. Necessary conditions for the optimality of this RVQ are presented, and a new entropy-constrained RVQ (ECRVQ) design algorithm is shown to be very effective in designing RVQ codebooks over a wide range of bit rates and vector sizes. The new EC-RVQ has several important advantages. It can outperform entropy-constrained VQ (ECVQ) in terms of peak signal-to-noise ratio (PSNR), memory, and computation requirements. It can also be used to design high rate codebooks and codebooks with relatively large vector sizes. Experimental results indicate that when the new EC-RVQ is applied to image coding, very high quality is achieved at relatively low bit rates.

Kossentini, Faouzi↗

NASA NTRS1994

Constrained minimization of smooth functions using a genetic algorithm

The use of genetic algorithms for minimization of differentiable functions that are subject to differentiable constraints is considered. A technique is demonstrated for converting the solution of the necessary conditions for a constrained minimum into an unconstrained function minimization. This technique is extended as a global constrained optimization algorithm. The theory is applied to calculating minimum-fuel ascent control settings for an energy state model of an aerospace plane.

Moerder, Daniel D.↗

NASA NTRS1994

A brief survey of constrained mechanics and variational problems in terms of differential forms

There has been considerable interest recently in constrained mechanics and variational problems. This is in part due to applied interests (such as 'non-holonomic mechanics in robotics') and in other part due to the fact that several schools of 'pure' mathematics have found that this classical subject is of importance for what they are trying to do. I have made various attempts at developing these subjects since my Lincoln lab days of the late 1950's. In this Chapter, I will sketch a Unified point of view, using Cartan's approach with differential forms. This has the advantage from the C-O-R viewpoint being developed in this Volume that the extension from 'smooth' to 'generalized' data is very systematic and algebraic. (I will only deal with the 'smooth' point of view in this Chapter; I will develop the 'generalized function' material at a later point.) The material presented briefly here about Variational Calculus and Constrained Mechanics can be found in more detail in my books, 'Differential Geometry and the Calculus of Variations', 'Lie Algebras and Quantum Mechanics', and 'Geometry, Physics and Systems'.

Hermann, Robert↗

NASA NTRS1994

High-energy gamma-ray emission from solar flares: Constraining the accelerated proton spectrum

Using a multi-component model to describe the gamma-ray emission, we investigate the flares of December 16, 1988 and March 6, 1989 which exhibited unambiguous evidence of neutral pion decay. The observations are then combined with theoretical calculations of pion production to constrain the accelerated proton spectra. The detection of pi(sup 0) emission alone can indicate much about the energy distribution and spectral variation of the protons accelerated to pion producing energies. Here both the intensity and detailed spectral shape of the Doppler-broadened pi(sup 0) decay feature are used to determine the spectral form of the accelerated proton energy distribution. The Doppler width of this gamma-ray emission provides a unique diagnostic of the spectral shape at high energies, independent of any normalisation. To our knowledge, this is the first time that this diagnostic has been used to constrain the proton spectra. The form of the energetic proton distribution is found to be severely limited by the observed intensity and Doppler width of the pi(sup 0) decay emission, demonstrating effectively the diagnostic capabilities of the pi(sup 0) decay gamma-rays. The spectral index derived from the gamma-ray intensity is found to be much harder than that derived from the Doppler width. To reconcile this apparent discrepancy we investigate the effects of introducing a high-energy cut-off in the accelerated proton distribution. With cut-off energies of around 0.5-0.8 GeV and relatively hard spectra, the observed intensities and broadening can be reproduced with a single energetic proton distribution above the pion production threshold.

Alexander, David↗

NASA NTRS1995

Mass-Additive Vibration Testing Of Constrained Structures

Report describes study of mass-additive method of modal survey testing of flexible structures that, in normal use, constrained by other structures. Structure normally constrained by another structure is suspended freely and extra masses attached to boundary.

Admire, John R.↗

NASA NTRS1996

Pattern Search Algorithms for Bound Constrained Minimization

We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexibility present in pattern search methods for unconstrained problems. We prove global convergence despite the fact that pattern search methods do not have explicit information concerning the gradient and its projection onto the feasible region and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.

Lewis, Robert Michael↗

NASA NTRS1995

Optical Correlation of Images With Signal-Dependent Noise Using Constrained-Modulation Filter Devices

Images with signal-dependent noise present challenges beyond those of images with additive white or colored signal-independent noise in terms of designing the optimal 4-f correlation filter that maximizes correlation-peak signal-to-noise ratio, or combinations of correlation-peak metrics. Determining the proper design becomes more difficult when the filter is to be implemented on a constrained-modulation spatial light modulator device. The design issues involved for updatable optical filters for images with signal-dependent film-grain noise and speckle noise are examined. It is shown that although design of the optimal linear filter in the Fourier domain is impossible for images with signal-dependent noise, proper nonlinear preprocessing of the images allows the application of previously developed design rules for optimal filters to be implemented on constrained-modulation devices. Thus the nonlinear preprocessing becomes necessary for correlation in optical systems with current spatial light modulator technology. These results are illustrated with computer simulations of images with signal-dependent noise correlated with binary-phase-only filters and ternary-phase-amplitude filters.

Downie, John D.↗