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Reachability analysis using dissipation inequalities for uncertain nonlinear systems

SYSTEMS & CONTROL LETTERS 2020年 142卷 104736-104736页

作者： Yin, He Packard, Andrew Arcak, Murat Seiler, Peter Univ Calif Berkeley Dept Mech Engn Berkeley CA 94720 USA Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation inequalities that account for time-varying uncertain parameters, L-2 disturbances, and perturbations Delta characterized by integral quadratic constraints (IQCs) with both hard and soft factorizations. The use of IQCs in forward reachability analysis allows for various types of uncertainty, including unmodeled dynamics. The generalized S-procedure and Sum-of-Squares techniques are used to derive algorithms with the goal of finding the tightest outer bound with a desired shape. Both pedagogical and practically motivated examples are presented, including a 7-state F-18 aircraft model. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Analysis of systems with uncertainties numerical algorithms Reachable set estimation

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Modeling of the thermo-mechanical response and texture evolution of WE43 Mg alloy in the dynamic recrystallization regime using a viscoplastic self-consistent formulation

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INTERNATIONAL JOURNAL OF PLASTICITY 2020年 130卷 102705-102705页

作者： Zecevic, Miroslav Knezevic, Marko McWilliams, Brandon Lebensohn, Ricardo A. Lso Alamos Natl Lab Theoret Div Los Alamos NM 87544 USA Univ New Hampshire Dept Mech Engn Durham NH 03824 USA CCDC Army Res Lab Aberdeen Proving Ground MD 21005 USA

This paper presents a microstructure sensitive model for predicting mechanical response and texture evolution of metals in the dynamic recrystallization regime. A recently proposed viscoplastic self-consistent (VPSC) formulation for the prediction of recrystallization driven by strain energy and intragranular misorientation is extended to hexagonal close-packed (hcp) metals. The model is applied to the dynamic recrystallization of magnesium alloy WE43 at different temperatures and strain rates. Model predictions in terms of stress-strain response and texture evolution are compared to the experimental measurements and acceptable agreement is achieved. According to the model predictions, superplastic behavior of nuclei was found to be the dominant softening mechanism at high temperatures and low strain rates. High concentration of precipitates at the grain boundaries and presence of alloying elements are the likely causes of low boundary mobility, resulting in nucleation dominated dynamic recrystallization. Relatively strong basal compression textures indicate dominant activity of basal slip, which can be achieved only through large difference in slip resistance between soft basal and hard prismatic and pyramidal modes.

关键词： microstructures thermomechanical processes constitutive behavior numerical algorithms VPSC model

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Closed-Form Solution for Secondary Perturbation Displacement in Finite-Element-Implemented Koiter's Theory

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AIAA JOURNAL 2020年第4期58卷 1785-1795页

作者： Yan, Jiayi Li, Shuguang Univ Nottingham Fac Engn Nottingham NG7 2RD England Univ Nottingham Fac Engn Aerosp Composites Nottingham NG7 2RD England Zhuzhou China Railway Rolling Corp Ltd Times Elect UK Innovat Ctr 2650 Kings CourtBirmingham Business Pk Solihull B37 7YE W Midlands England

The finite-element-implemented Koiter's initial postbuckling analysis has not managed to convince commercial finite element code developers to incorporate it into their codes to benefit structural designers and analysts. Three key obstacles have been identified. With two of them being resolved recently, the present paper addressed the remaining one, namely, the efficient solution of the second-order perturbation equation. A closed-form solution is obtained, which is more computationally efficient than any approach adopted in the past. The closed-form solution is obtained mathematically rigorously, and in the meantime it is computational efficient. The approach applies also to problems where buckling is of multiple modes. The solution procedure established in this paper has been verified and demonstrated through a structural application.

关键词： Prebuckling Deformations Finite Element Modeling Aspect Ratio Airy Stress Function numerical Analysis Poisson's Ratio Plane Stress Structural Stability numerical algorithms Iterative Algorithm

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Asymptotic Optimality of a Time Optimal Path Parametrization Algorithm

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IEEE CONTROL SYSTEMS LETTERS 2019年第4期3卷 835-840页

作者： Spasojevic, Igor Murali, Varun Karaman, Sertac MIT Lab Informat & Decis Syst 77 Massachusetts Ave Cambridge MA 02139 USA

The time optimal path parametrization problem addresses minimizing the traversal time of a specified path by an actuation constrained agent. Recently, an efficient numerical algorithm for solving this problem has been proposed. This letter theoretically establishes convergence of the former algorithm to the optimum for the whole class of problems solved optimally by computationally more demanding approaches based on convex programming. Additionally, we provide a characterization of the optimum, which may be of independent interest.

关键词： numerical algorithms optimal control robotics

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The influence of hydrogen on cyclic plasticity of <001> oriented nickel single crystal. Part II: Stability of edge dislocation dipoles

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INTERNATIONAL JOURNAL OF PLASTICITY 2020年 129卷 102667-102667页

作者： Hachet, G. Metsue, A. Oudriss, A. Feaugas, X. La Rochelle Univ LaSIE UMR CNRS 7356 Ave Michel Crepeau F-17000 La Rochelle France CEA Saclay Serv Rech Met Phys F-91191 Gif Sur Yvette France

A competition between hardening and softening hydrogen effects on the cyclic behaviour of oriented nickel single crystal has been observed and discussed in terms of effective and back stresses partitioning. Moreover,... 详细信息

A competition between hardening and softening hydrogen effects on the cyclic behaviour of <001> oriented nickel single crystal has been observed and discussed in terms of effective and back stresses partitioning. Moreover, the consequences of hydrogen have been studied in terms of composite model which illustrates the interaction between hydrogen and dislocation organisation. The hydrogen hardening associated with dislocation wall phase is a key feature which has been discussed and elucidated at edge dislocation dipoles scale using atomic calculations in nickel single crystal. The aim of our study was to evaluate the stability of this dislocation organisation in the presence of hydrogen, vacancies and vacancy clusters. As the main result, we noted that hydrogen in Cottrell's atmosphere hardens dipole configurations following solid solution strengthening and vacancies induced by hydrogen incorporation and cyclic loading attenuate this result. Moreover, the consequences of vacancies are more important when they are regrouped as clusters than when they are homogeneously distributed in the Cottrell's atmosphere. Such results can explain the complex behaviour of the wall phase and the consequence on long-range internal stresses observed in the first part of this study.

关键词： Edge dislocation dipole Fatigue Crystal plasticity numerical algorithms Hydrogen

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Constitutive-damage modeling and computational implementation for simulation of elasto-viscoplastic-damage behavior of polymeric foams over a wide range of strain rates and temperatures

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INTERNATIONAL JOURNAL OF PLASTICITY 2020年 130卷 102712-102712页

作者： Lee, Jeong-Ho Ryu, Dong-Man Lee, Chi-Seung Boston Univ Dept Mech Engn Boston MA 02215 USA Michigan State Univ Dept Mech Engn E Lansing MI 48824 USA Pusan Natl Univ Hosp Biomed Res Inst Busan 49241 South Korea Pusan Natl Univ Sch Med Dept Convergence Med Busan 49241 South Korea Pusan Natl Univ Sch Med Dept Biomed Engn Busan 49241 South Korea

The material behavior and damage of polymeric foams (e.g., polyurethane foam and polystyrene foam) are extremely complex under compression, depending on strain rates and temperatures. In the present study, the elasto-viscoplastic-damage behavior of polymeric foams over a wide range of strain rates and temperature is evaluated and predicted using the modified Gurson-TvergaardNeedleman-Lemaitre (GTNL) model and the modified Khan-Huang-Liang (KHL) model. A modified GTNL model is introduced to describe phenomena of decreasing void volume fraction and elastic modulus for polymeric foams under uniaxial compression. The modified KHL model is proposed to evaluate the nonlinear strain rate- and temperature-dependent material behavior of polymeric foams. The full derivation of the implicit integration algorithm of the proposed modified GTNL-KHL model is introduced, and a user-defined material (UMAT) subroutine for commercial finite element analysis code (i.e., ABAQUS) is established. Using the UMAT, the damage characteristics (e.g., void volume fraction and elastic modulus changes) and the nonlinear material behavior (e.g., linear elastic, softening/plateau and densification) of polymeric foams under uniaxial compression with various strain rates and temperatures are successfully simulated.

关键词： Polymeric foams Constitutive behavior Elastic-viscoplastic material Finite elements numerical algorithms

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Exascale applications: skin in the game

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2020年第2166期378卷 20190056-20190056页

作者： Alexander, Francis Almgren, Ann Bell, John Bhattacharjee, Amitava Chen, Jacqueline Colella, Phil Daniel, David DeSlippe, Jack Diachin, Lori Draeger, Erik Dubey, Anshu Dunning, Thom Evans, Thomas Foster, Ian Francois, Marianne Germann, Tim Gordon, Mark Habib, Salman Halappanavar, Mahantesh Hamilton, Steven Hart, William Huang, Zhenyu (Henry) Hungerford, Aimee Kasen, Daniel Kent, Paul R. C. Kolev, Tzanio Kothe, Douglas B. Kronfeld, Andreas Luo, Ye Mackenzie, Paul McCallen, David Messer, Bronson Mniszewski, Sue Oehmen, Chris Perazzo, Amedeo Perez, Danny Richards, David Rider, William J. Rieben, Rob Roche, Kenneth Siegel, Andrew Sprague, Michael Steefel, Carl Stevens, Rick Syamlal, Madhava Taylor, Mark Turner, John Vay, Jean-Luc Voter, Artur F. Windus, Theresa L. Yelick, Katherine Brookhaven Natl Lab Upton NY 11973 USA Lawrence Berkeley Natl Lab Berkeley CA USA Princeton Plasma Phys Lab POB 451 Princeton NJ 08543 USA Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA Los Alamos Natl Lab Los Alamos NM USA Lawrence Livermore Natl Lab Livermore CA 94550 USA Argonne Natl Lab 9700 S Cass Ave Argonne IL 60439 USA Pacific Northwest Natl Lab Richland WA 99352 USA Oak Ridge Natl Lab Oak Ridge TN 37830 USA Ames Lab Ames IA USA Fermilab Natl Accelerator Lab POB 500 Batavia IL 60510 USA SLAC Natl Accelerator Lab Menlo Pk CA USA Natl Renewable Energy Lab Golden CO USA Natl Energy Technol Lab Morgantown WV USA

As noted in Wikipedia, skin in the game refers to having 'incurred risk by being involved in achieving a goal', where 'skin is a synecdoche for the person involved, and game is the metaphor for actions on the field of play under discussion'. For exascale applications under development in the US Department of Energy Exascale Computing Project, nothing could be more apt, with the skin being exascale applications and the game being delivering comprehensive science-based computational applications that effectively exploit exascale high-performance computing technologies to provide breakthrough modelling and simulation and data science solutions. These solutions will yield high-confidence insights and answers to the most critical problems and challenges for the USA in scientific discovery, national security, energy assurance, economic competitiveness and advanced healthcare. This article is part of a discussion meeting issue 'numerical algorithms for high-performance computational science'.

关键词： exascale high-performance computing computational science applications numerical algorithms machine learning modelling and simulation

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Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

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JOURNAL OF CHEMICAL PHYSICS 2020年第21期153卷 211101页

作者： Choi, Seonghoon Vanicek, Jiri Ecole Polytech Fed Lausanne EPFL Lab Theoret Phys Chem Inst Sci & Ingn Chim CH-1015 Lausanne Switzerland

Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations are exact and unitary transforms of each other, whereas the approximate quasidiabatic Hamiltonian ignores the residual nonadiabatic couplings in the exact quasidiabatic Hamiltonian. A rigorous numerical comparison of the four different representations is difficult because of the exceptional nature of systems where the four representations can be defined exactly and the necessity of an exceedingly accurate numerical algorithm that avoids mixing numerical errors with errors due to the different forms of the Hamiltonian. Using the quadratic Jahn-Teller model and high-order geometric integrators, we are able to perform this comparison and find that only the rarely employed exact quasidiabatic Hamiltonian yields nearly identical results to the benchmark results of the strictly diabatic Hamiltonian, which is not available in general. In this Jahn-Teller model and with the same Fourier grid, the commonly employed approximate quasidiabatic Hamiltonian led to inaccurate wavepacket dynamics, while the Hamiltonian in the adiabatic basis was the least accurate, due to the singular nonadiabatic couplings at the conical intersection.

关键词： Communications Topics Diabatic states Quantum chemical dynamics Time-dependent Schrodinger equation Potential energy surfaces Geometric phases Geometrical methods Jahn-Teller distortion Non-adiabatic molecular dynamics numerical algorithms Molecular Hamiltonian

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Inertial-Based Derivative-Free Method for System of Monotone Nonlinear Equations and Application

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IEEE ACCESS 2020年 8卷 226921-226930页

作者： Awwal, Aliyu Muhammed Kumam, Poom Wang, Lin Huang, Shuang Kumam, Wiyada King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Ctr Excellence Theoret & Computat Sci Ctr TaCS CO Fixed Point Theory & Applicat Res Grp Bangkok 10140 Thailand Gombe State Univ Fac Sci Dept Math Gombe 760214 Nigeria King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math KMUTT Fixed Point Res Lab Room SCL 802Sci Lab Bldg Bangkok 10140 Thailand Yunnan Univ Finance & Econ Off Sci & Res Kunming 650221 Yunnan Peoples R China Rajamangala Univ Technol Thanyaburi Fac Sci & Technol Dept Math & Comp Sci Program Appl Stat Pathum Thani 12110 Thailand China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan

Iterative methods for solving nonlinear problems are of great importance due to their appearance in various areas of applications. In this paper, based on the inertial effect, we propose two projection derivative-free iterative methods for solving system of nonlinear equations. For the purpose of improving the numerical performance, the two methods incorporated the inertial step into the modified Barzilai and Borwein (BB) spectral parameters to generate the sequence of their respective search directions. The two spectral parameters are shown to be well-defined. For each method, the sequence of the search direction is bounded and satisfies the sufficient descent property. We establish the convergence analysis of the two methods based on the assumption that the underlying mapping is Lipschitzian and monotone. We demonstrate the efficiencies of the two methods on some collection of monotone system of nonlinear equations test problems. Finally, we apply the two methods to solve motion control problem involving a two planar robot.

关键词： Nonlinear equations Iterative methods Convergence Nonlinear systems Search problems Scientific computing Robots Inertial effect line search nonlinear monotone equations nonlinear problems numerical algorithms projection method spectral parameters

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Certifying Global Optimality for the L ∞ -Norm Computation of Large-Scale Descriptor Systems ⁎

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IFAC-PapersOnLine 2020年第2期53卷 4279-4284页

作者： P. Schwerdtner E. Mengi M. Voigt Technische Universität Berlin Institut für Mathematik FG Numerische Mathematik Straße des 17. Juni 136 10623 Berlin Germany Koç University Department of Mathematics Rumeli Feneri Yolu 34450 Sanyer Istanbul Turkey University of Hamburg Department of Mathematics Center for Optimization and Approximation Bundesstraβe 55 20146 Hamburg Germany

We present a method for the certification of algorithms that approximate the L ∞ - or H ∞ -norm of transfer functions of large-scale (descriptor) systems. This certification is needed because such algorithms depend heavily on user input, and may converge to a local maximizer of the related singular value function leading to an incorrect value, much lower than the actual norm. Hence, we design an algorithm that determines whether a given value is less than the L ∞ -norm of the transfer function under consideration, and that does not require user input other than the system matrices. In the algorithm, we check whether a certain structured matrix pencil has any purely imaginary eigenvalues by repeatedly applying a structure-preserving shift-and-invert Arnoldi iteration combined with an appropriate shifting strategy. Our algorithm consists of two stages. First, an interval on the imaginary axis which may contain imaginary eigenvalues is determined. Then, in the second stage, a shift is chosen on this interval and the eigenvalues closest to this shift are computed. If none of these eigenvalues is purely imaginary, then an imaginary interval around the shift of appropriate length is removed such that two subintervals remain. This second stage is then repeated on the remaining two subintervals until either a purely imaginary eigenvalue is found or no critical subintervals are left. We show the effectiveness of our method by testing it without any parameter adaptation on a benchmark collection of large-scale systems.

关键词： Computer-aided control systems design descriptor systems eigenvalue problems H ∞ control linear control systems norms numerical algorithms robust control

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