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CONVERGENCE OF A REGULARIZED EUCLIDEAN RESIDUAL ALGORITHM FOR NONLINEAR LEAST-SQUARES

SIAM JOURNAL ON numerical ANALYSIS 2010年第1期48卷 1-29页

作者： Bellavia, S. Cartis, C. Gould, N. I. M. Morini, B. Toint, Ph. L. Univ Florence Dipartimento Energet S Stecco I-50134 Florence Italy Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland Rutherford Appleton Lab Dept Comp Sci & Engn Chilton OX11 0QX Oxon England FUNDP Univ Namur Dept Math B-5000 Namur Belgium

The convergence properties of the new regularized Euclidean residual method for solving general nonlinear least-squares and nonlinear equation problems are investigated. This method, derived from a proposal by Nesterov [Optim. Methods Softw., 22 (2007), pp. 469-483], uses a model of the objective function consisting of the unsquared Euclidean linearized residual regularized by a quadratic term. At variance with previous analysis, its convergence properties are here considered without assuming uniformly nonsingular globally Lipschitz continuous Jacobians nor an exact sub-problem solution. It is proved that the method is globally convergent to first-order critical points and, under stronger assumptions, to roots of the underlying system of nonlinear equations. The rate of convergence is also shown to be quadratic under stronger assumptions.

关键词： nonlinear least-squares systems of nonlinear equations numerical algorithms global convergence

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DUCTILE FAILURE SIMULATION IN SPHERODIZED STEEL USING A CONTINUUM DAMAGE MECHANICS COUPLED FINITE ELEMENT FORMULATION

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INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS 2010年第2期7卷 319-348页

作者： Gautam, Sachin S. Dixit, P. M. Indian Inst Technol Kanpur Dept Mech Engn Kanpur 208016 Uttar Pradesh India

Ductile fracture occurs due to microvoid nucleation, growth and, finally, coalescence into microcracks. These microcracks grow in the presence of stresses leading to fracture. In this work, a criterion based on this phenomenon is used to simulate ductile fracture in a class of steel specimens. A critical value of the damage variable, estimated from experimental results, is used as an indicator of fracture initiation. A continuum damage mechanics model is employed to incorporate the damage in the constitutive relation of the material. A damage growth law based on experimental results is used. It is observed that the damage reaches the critical value first at the center in both the cylindrical and prenotched specimens. Thus, the failure begins at the center and then grows radially outward toward the free surface. The analysis is carried out till the damage reaches the critical value across the whole cross-section, at which point the specimen is considered to have failed.

关键词： Fracture continuum damage mechanics finite elements numerical algorithms

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A binary-tree based model for rate-independent polycrystals

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INTERNATIONAL JOURNAL OF PLASTICITY 2010年第1期26卷 42-64页

作者： Mahesh, Sivasambu Indian Inst Technol Dept Mech & Aerosp Engn Kanpur 208016 Uttar Pradesh India

A model of a rigid-plastic rate-independent polycrystalline aggregate wherein sub-aggregates are represented as the nodes of a binary tree is proposed. The lowest nodes of the binary tree represent grains. Higher binary tree nodes represent increasingly larger sub-aggregates of grains. culminating with the root of the tree, which represents the entire polycrystalline aggregate. Planar interfaces are assumed to separate the sub-aggregates represented by nodes in the binary tree. Equivalence between the governing equations of the model and a standard linear program is established. The objective function of the linear program is given by the plastic power associated with polycrystal deformation and the linear constraints are given by compatibility requirements between the sub-aggregates represented by sibling nodes in the binary tree. The deviatoric part of the Cauchy stress in each sub-aggregate is deduced as linear combinations of the Lagrange multipliers associated with the constraints. It is shown that the present model allows a generalization of Taylor's principle to polycrystals. The proposed model is applied to simulate tensile, compressive, torsional, and plane-strain deformation of copper polycrystals. The predicted macroscopic response is in good agreement with published experimental data. The effect of the initial distribution of the planar interfaces separating the sub-aggregates represented by the binary tree on the predicted mechanical response in tension, compression and torsion is studied. Also, the role of constraints relaxation in simulations of plane strain compression is investigated in detail. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Crystal plasticity Binary tree Texture modeling numerical algorithms

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Reduced-Order Filter Design for Discrete-Time Systems Corrupted with Multiplicative Noise

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第4期33卷 1287-1293页

作者： Stoica, Adrian-Mihail Barbelian, Mihai Pana, Valentin Dragasanu, Claudiu Univ Politehn Bucuresti Fac Aerosp Engn Bucharest 011061 Romania Romanian Space Agcy Bucharest 010362 Romania

The reduced-order filtering problem for discrete-time systems corrupted with multiplicative noise is solved. Two situations discussed include one when the system output does not include multiplicative noise terms and the other when the output is corrupted with state-dependent noise. Necessary and sufficient solvability conditions are derived in terms of feasibility of some specific systems of matrix inequalities. numerical aspects are analyzed for the two approaches showing how the semi-definite programming based algorithms can be used to solve the filtering problems. The design approach proposed in this paper allows a more direct gain scheduling procedure for the filter. It is also found that the filtering properties severely deteriorates due to the multiplicative noise which was ignored at the Kalman filter (KF) design.

关键词： Kalman Filter State Space Representation Aerospace Engineering numerical Simulation numerical algorithms Optical Sensor White Noise

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New Lambert Algorithm Using the Hamilton-Jacobi-Bellman Equation

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第3期33卷 1000-1008页

作者： Bando, Mai Yamakawa, Hiroshi Kyoto Univ Kyoto 6110011 Japan

A study was conducted to demonstrate the formulation of the new Lambert Algorithm using the Hamilton-Jacobi-Bellman Equation (HJB). The two-point boundary-value problem (TPBVP) of the Hamiltonian system was treated as an optimal control problem where the Lagrangian function played a role as a performance index. The approach demonstrated in the study was based on the expansion of the value function in the Chebyshev series with unknown coefficients, considering the computational advantages of the use of Chebyshev polynomials. The differential expressions that arose in the HJB equation were expanded in Chebyshev series with the unknown coefficients. The new algorithm had the potential to provide a solution to the TPVBP using the spectral information about the gravitation potential function and was applicable to the problem under a higher-order perturbed potential function without any modification.

关键词： Hamilton Jacobi Bellman (HJB) Equations Lambert Algorithm Earth Lagrange Multipliers Kinetic Energy Boundary Value Problems Nonlinear Dynamics Nonlinear Systems Finite Difference Method numerical algorithms

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Microstructure Effects in Aluminized Solid Rocket Propellants

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JOURNAL OF PROPULSION AND POWER 2010年第4期26卷 724-733页

作者： De Luca, L. T. Galfetti, L. Colombo, G. Maggi, F. Bandera, A. Babuk, V. A. Sinditskii, V. P. Politecn Milan I-20156 Milan Italy Balt State Tech Univ St Petersburg 190005 Russia Mendeleev Univ Chem Technol Moscow 125047 Russia

Experiments concerning the ballistic characterization of several nanoaluminum (nAl) powders are reported. Most studies were performed with laboratory composite solid rocket propellants based on ammonium perchlorate as oxidizer and hydroxyl-terminated polybutadiene as inert binder. The ultimate objective is to understand the flame structure of differently metallized formulations and improve their specific impulse efficiency by mitigating the two-phase losses. Ballistic results confirm, for increasing nAl mass fraction or decreasing nAl size, higher steady burning rates with essentially the same pressure sensitivity and reduced average size of condensed combustion products. However, aggregation and agglomeration phenomena near the burning surface appear noticeably different for microaluminum (mu Al) and nAl powders. By contrasting the associated flame structures, a particle-laden flame zone with a sensibly reduced particle size is disclosed in the case of nAl. Propellant microstructure is considered the main controlling factor. A way to predict the incipient agglomerate size for mu Al propellants is proposed and verified by testing several additional ammonium perchlorate/hydroxyl-terminated polybutadiene/aluminum formulations of industrial manufacture.

关键词： High Energy Material Aluminized Composite Solid Propellant Propellant Storage Combustion Inefficiency Condensation Statistical Analysis Polypropylene Solid Rocket Motor Thermal Conductivity numerical algorithms

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Maximum Torque and Momentum Envelopes for Reaction-Wheel Arrays

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第5期33卷 1606-1614页

作者： Markley, F. Landis Reynolds, Reid G. Liu, Frank X. Lebsock, Kenneth L. NASA Goddard Space Flight Ctr Attitude Control Syst Engn Branch Greenbelt MD 20771 USA Millennium Space Syst Inc Torrance CA 90503 USA Stinger Ghaffarian Technol Inc Greenbelt MD 20770 USA Orbital Sci Corp Greenbelt MD 20770 USA

Spacecraft reaction-wheel maneuvers are limited by the maximum torque and/or angular momentum that the wheels can provide. The torque or momentum envelope for an n-wheel configuration can be obtained by projecting the n-dimensional hypercube, representing the domain boundary of individual wheel torques or momenta, into three-dimensional space via the 3 x n matrix of wheel axes. This paper elucidates the properties of the projected hypercube and presents algorithms for determining this maximal torque or momentum envelope for general wheel configurations and for distributing a prescribed torque or momentum among the n wheels. We show that these algorithms provide 22, 27, and 33% more capability than the more conventional pseudoinverse algorithm for configurations of four, five, and six wheels, respectively. Analysis of a representative slew using six wheels shows that these algorithms can provide either a 25% reduction in maximum wheel momentum or a 30% reduction in slew time when compared with the pseudoinverse algorithm.

关键词： Reaction Wheels James Webb Space Telescope Gamma Ray Bursts Spacecraft Structures Resonant Frequencies Earth Mathematical Analysis numerical algorithms Attitude Control Lagrange Points

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Decentralized estimation and control of graph connectivity for mobile sensor networks

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AUTOMATICA 2010年第2期46卷 390-396页

作者： Yang, P. Freeman, R. A. Gordon, G. J. Lynch, K. M. Srinivasa, S. S. Sukthankar, R. Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Carnegie Mellon Univ Sch Comp Sci Pittsburgh PA 15213 USA Intel Res Pittsburgh PA 15213 USA

The ability of a robot team to reconfigure itself is useful in many applications: for metamorphic robots to change shape, for swarm motion towards a goal, for biological systems to avoid predators, or for mobile buoys to clean up oil spills. In many situations, auxiliary constraints, such as connectivity between team members or limits on the maximum hop-count, must be satisfied during reconfiguration. In this paper, we show that both the estimation and control of the graph connectivity can be accomplished in a decentralized manner. We describe a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimator, we further propose a decentralized gradient controller for each agent to maintain global connectivity during motion. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Connectivity Decentralized control Graph theory numerical algorithms Autonomous mobile robots

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Sensitivity analysis of the moments of the profit on an Income Protection Policy

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2010年第1期26卷 50-70页

作者： Cordeiro, Isabel Maria Magalhaes, Pedro Manuel Univ Minho Escola Econ & Gestao P-4710057 Braga Portugal Inst Super Econ & Gestao CAMAPRE Lisbon Portugal Inst Gestao Fundos Capitalizacao Seguranca Social Oporto Portugal

The main purpose of this paper is to perform a sensitivity analysis where we quantify and analyse the effects on the mean of the profit on an Income Protection policy and two risk measures of changing the values of the transition intensities. All the calculations carried out are based on a multiple state model for Income Protection proposed in Continuous Mortality Investigation Committee (Continuous Mortality Investigation Reports 1991;12). Within this model, we derive a formula for the mean of the profit, which enables to evaluate it more efficiently. In order to calculate the two risk measures we use the numerical algorithms for the calculation of the moments of the profit proposed by Waters (Insurance: Mathematics and Economics 1990;9:101-113). We carry out the sensitivity analysis considering two different situations: in the first situation, we update the premium rates used to calculate the moments of the profit, according to the changes in the values of the transition intensities;in the second one, we do not update the premium rates. Both analyses are of practical interest to insurance companies selling Income Protection policies. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： Income Protection sensitivity analysis multiple state models profit on a policy numerical algorithms premium rates

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A generic approach towards finite growth with examples of athlete's heart, cardiac dilation, and cardiac wall thickening

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2010年第10期58卷 1661-1680页

作者： Goktepe, Serdar Abilez, Oscar John Kuhl, Ellen Stanford Univ Dept Mech Engn Stanford CA 94305 USA Dept Bioengn Stanford CA 94305 USA Stanford Univ Med Ctr Dept Surg Stanford CA 94305 USA Dept Cardiothorac Surg Stanford CA 94305 USA

The objective of this work is to establish a generic continuum-based computational concept for finite growth of living biological tissues. The underlying idea is the introduction of an incompatible growth configuration which naturally introduces a multiplicative decomposition of the deformation gradient into an elastic and a growth part. The two major challenges of finite growth are the kinematic characterization of the growth tensor and the identification of mechanical driving forces for its evolution. Motivated by morphological changes in cell geometry, we illustrate a micromechanically motivated ansatz for the growth tensor for cardiac tissue that can capture both strain-driven ventricular dilation and stress-driven wall thickening. Guided by clinical observations, we explore three distinct pathophysiological cases: athlete's heart, cardiac dilation, and cardiac wall thickening. We demonstrate the computational solution of finite growth within a fully implicit incremental iterative Newton-Raphson based finite element solution scheme. The features of the proposed approach are illustrated and compared for the three different growth pathologies in terms of a generic bi-ventricular heart model. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Biological growth Biological material Constitutive behavior Finite elements numerical algorithms

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