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Conditional parameter identification with different losses of under- and overestimation

APPLIED MATHEMATICAL MODELLING 2013年第4期37卷 2166-2177页

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Polish Acad Sci Syst Res Inst Ctr Informat Technol Data Anal Methods PL-00901 Warsaw Poland Cracow Univ Technol Dept Automat Control & Informat Technol Krakow Poland Catholic Univ Lublin Inst Math & Comp Sci Lublin Poland

In many scientific and practical tasks, the classical concepts for parameter identification are satisfactory and generally applied with success, although many specialized problems necessitate the use of methods created with specifically defined assumptions and conditions. This paper investigates the method of parameter identification for the case where losses resulting from estimation errors can be described in polynomial form with additional asymmetry representing different results of under- and overestimation. Most importantly, the method presented here considers the conditionality of this parameter, which in practice means its significant dependence on other quantities whose values can be obtained metrologically. To solve a problem in this form the Bayes approach was used, allowing a minimum expected value of losses to be achieved. The methodology was based on the nonparametric technique of statistical kernel estimators, which freed the investigated procedure from forms of probability distributions characterizing both the parameter under investigation and conditioning quantities. As a result an algorithm is presented, ready for direct use without further intensive research and calculations. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Parameter identification Asymmetrical losses of estimation errors Conditional factors Nonparametric estimation Statistical kernel estimators numerical algorithm

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ast forward kinematics algorithm for real-time and ligh-precision control of the 3-RPS parallel mechanism

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Frontiers of Mechanical Engineering 2018年第3期13卷 368-375页

作者： Yue WANG Jingjun YU Xu PEI Robotics Institute Beihang University Beijing 100191 China Department of Mechanical Design Beihang University Beijing 100191 China

A new forward kinematics algorithm for the mechanism of 3-RPS （R： Revolute; P： Prismatic; S： Spherical） parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10 6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

关键词： 3-RPS parallel mechanism forward kinematics numerical algorithm parasitic motion

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NEW QUASI-NEWTON METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

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APPLICATIONS OF MATHEMATICS 2017年第2期62卷 121-134页

作者： Luksan, Ladislav Vlcek, Jan Czech Acad Sci Inst Comp Sci Pod Vodarenskou Vezi 2 Prague 18207 8 Czech Republic

We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n(2)) arithmetic operations per iteration in contrast with the Newton method, which requires O(n(3)) operations per iteration. Computational experiments confirm the high efficiency of the new method.

关键词： nonlinear equation system of equations trust-region method quasi-Newton method adjoint Broyden method numerical algorithm numerical experiment

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1-out-of-N multi-state standby systems with state-dependent random replacement times

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY 2017年第6期231卷 750-760页

作者： Levitin, Gregory Jia, Heping Ding, Yi Song, Yonghua Univ Elect Sci & Technol China Sch Comp Sci Collaborat Auton Comp Lab Chengdu Sichuan Peoples R China Israel Elect Corp Ltd Haifa Israel Zhejiang Univ Coll Elect Engn Hangzhou 310027 Zhejiang Peoples R China

Research on analysis of replacement time in standby systems has focused on systems with binary-state standby components. However, when the standby components are multi-state, the replacement time depends on the state of the standby component when it is activated for replacement. This article considers the impacts of state-dependent random replacement times on 1-out-of-N systems consisting of multi-state standby components. numerical algorithms for evaluating the multi-state standby system's instantaneous availability, expected availability over system mission time and the expected mission completion time are proposed. A Markov state transition model is used to describe the component behaviour in standby mode. The time-to-failure of the operating component and the replacement time of the standby component can obey arbitrary types of distributions. Illustrative examples are provided to demonstrate the proposed numerical algorithms. The effects of the number of standby components, different replacement time distributions and activation sequences are also discussed.

关键词： Random replacement time 1-out-of-N system multi-state standby system instantaneous availability numerical algorithm

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Simple algorithms for solving steady-state frictional rolling contact problems in two and three dimensions

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2013年第6期50卷 843-852页

作者： Zehil, Gerard-Philippe Gavin, Henri P. Duke Univ Dept Civil & Environm Engn Durham NC 27708 USA

This paper presents simple, yet robust and efficient algorithms for solving steady-state, frictional, rolling/sliding contact problems, in two and three dimensions. These are alternatives to powerful, well established, but in particular instances, possibly 'cumbersome' general-purpose numerical techniques, such as finite-element approaches based on constrained optimization. The cores of the solvers rely on very general principles: (i) resolving motional conflicts, and (ii) eliminating unacceptable surface tractions. The proposed algorithms are formulated in the context of small deformations and applied to the cases of a rigid cylinder and a rigid sphere rolling on a linear viscoelastic layer of finite thickness, in two and three dimensions, respectively. The underlying principles are elucidated, relevant mathematical expressions derived and details given about corresponding implementation techniques. The proposed contact algorithms can be extended to more general settings involving a deformable indenter, material nonlinearities and large deformations. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Rolling contact Cylinder Sphere Viscoelastic layer Coulomb's friction Stick/slip contact numerical algorithm

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Analysis and algorithms for the computation of the excited states of helium

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第8期235卷 2041-2062页

作者： Ding, Zhonghai Chen, Goong Univ Nevada Dept Math Sci Las Vegas NV 89154 USA Texas A&M Univ Dept Math College Stn TX 77843 USA Texas A&M Univ Inst Quantum Studies College Stn TX 77843 USA

In this paper, we study a dimensionally scaled helium atom model for excited states of helium. The mathematical analysis of the corresponding effective energy potential is presented. Two simple numerical algorithms are developed for the computation of the excited states of helium. Comparison between our numerical results and those in the existing literature is given to indicate the accuracy and efficiency of the proposed algorithms. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Helium atom Schrodinger equation Excited states Dimensional scaling numerical algorithm

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A three-dimensional plasticity-damage constitutive model for timber under cyclic loads

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COMPUTERS & STRUCTURES 2018年 195卷 47-63页

作者： Sirumbal-Zapata, Luis F. Malaga-Chuquitaype, Christian Elghazouli, Ahmed Y. Imperial Coll London Dept Civil & Environm Engn London England

The performance of timber structures is governed by the nonlinear response at their connections, where high deformation levels and stress concentrations are developed, particularly when subjected to load reversals. To date, no constitutive model for wood under cyclic load exists which is able to incorporate its most important failure modes while considering plastic deformations and cyclic stiffness and strength degradation simultaneously. This paper presents the formulation and implementation of a plasticity damage model with these characteristics within a continuum mechanics approach. The theoretical framework of both plasticity and damage models is described, and a detailed derivation of the constitutive equations required for their computational implementation and coupling as well as the return mapping and iterative algorithms for their integration are presented. The damage evolution process is handled by two independent scalar variables for tension and compression. A general orthotropic plasticity yield surface with isotropic hardening is employed to incorporate timber plastic flow in compression. A closed-form expression for the plasticity-damage consistent tangent operator is derived. It is demonstrated that the proposed constitutive model captures all the key characteristics required for an accurate modelling of timber under large deformation levels until failure. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Timber Plasticity Continuum damage mechanics Orthotropy Cyclic loading numerical algorithm

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When can forward stable algorithms be composed stably?

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IMA JOURNAL OF numerical ANALYSIS 2024年第2期44卷 886-919页

作者： Beltran, Carlos Noferini, Vanni Vannieuwenhoven, Nick Univ Cantabria Dept MATESCO Avda Los Castros S-N Santander 39005 Spain Aalto Univ Dept Math & Syst Anal POB 11100 FI-00076 Aalto Finland Katholieke Univ Leuven Dept Comp Sci Celestijnenlaan 200A B-3001 Leuven Belgium

We state some widely satisfied hypotheses, depending only on two functions g and h, under which the composition of a forward stable algorithm for g and a forward stable algorithm for h is a forward stable algorithm for the composition g ? h. We show that the failure of these conditions can potentially lead to unstable algorithms. Finally, we list a number of examples to illustrate the new concepts and the usability of the results.

关键词： Condition number numerical stability numerical algorithm composition theorem amenability relative error

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Simulation of damage evolution in ductile metals undergoing dynamic loading conditions

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INTERNATIONAL JOURNAL OF PLASTICITY 2011年第10期27卷 1598-1617页

作者： Bruenig, Michael Gerke, Steffen Univ Bundeswehr Munchen Inst Mech & Stat D-85577 Neubiberg Germany

A set of constitutive equations for large rate-dependent elastic-plastic-damage materials at elevated temperatures is presented to be able to analyze adiabatic high strain rate deformation processes for a wide range of stress triaxialities. The model is based on the concepts of continuum damage mechanics. Since the material macroscopic thermo-mechanical response under large strain and high strain rate deformation loading is governed by different physical mechanisms, a multi-dissipative approach is proposed. It incorporates thermo-mechanical coupling effects as well as internal dissipative mechanisms through rate-dependent constitutive relations with a set of internal variables. In addition, the effect of stress triaxiality on the onset and evolution of plastic flow, damage and failure is discussed. Furthermore, the algorithm for numerical integration of the coupled constitutive rate equations is presented. It relies on operator split methodology resulting in an inelastic predictor-elastic corrector technique. The explicit finite element program LS-DYNA augmented by an user-defined material subroutine is used to approximate boundary-value problems under dynamic loading conditions. numerical simulations of dynamic experiments with different specimens are performed and good correlation of numerical results and published experimental data is achieved. Based on numerical studies modified specimens geometries are proposed to be able to detect complex damage and failure mechanisms in Hopkinson-Bar experiments. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Damage and fracture Stress triaxiality dependence Dynamic loading numerical algorithm numerical simulations

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Seiche modes of elongated natural basins

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COASTAL ENGINEERING JOURNAL 2003年第3期45卷 421-438页

作者： Sobey, RJ Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

numerical algorithms are formulated for the prediction of seiche modes (eigen frequencies and mode shapes) in elongated natural basins. Confirmation is provided by an analytical solution for a basin with a linear variation in surface width and a parabolic variation in cross-section. Spatial variations in geometry are shown to have a significant influence on modal frequencies and especially modal shapes. In particular, local modal amplitudes axe significantly enhanced by extensive regions of shallower water. Applications are given to the Caspian Sea and the Adriatic Sea.

关键词： seiche mode shapes elongated basins natural basins normal modes spatial variability analytical solution numerical algorithm Adriatic Sea Caspian Sea

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