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Creep constitutive models for viscoelastic materials based on fractional derivatives

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2017年第6期73卷 1377-1384页

作者： Xu, Huanying Jiang, Xiaoyun Shandong Univ Sch Math Jinan 250100 Peoples R China Shandong Univ Sch Math & Stat Weihai 264209 Peoples R China

To describe the time-dependent creep behavior of viscoelastic material, fractional constitutive relation models which are represented by the fractional element networks are studied. Three sets of creep experimental data for polymer and rock are employed to demonstrate the effectiveness of these fractional derivative models. The corresponding constrained problem of nonlinear optimization is solved with an interior-point algorithm to obtain best fitting parameters of these fractional derivative models. The comparison results of measured values and calculated values versus time are displayed through graphics. The results demonstrate that the fractional Poynting Thomson model is optimal in simulating the creep behavior of viscoelastic materials. And it also shows that the interior-point method is effective in the inverse problem to estimate parameters of fractional viscoelastic models. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Fractional viscoelastic models Viscoelastic material Poynting-Thomson model Parameter estimation interior-point algorithm

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SURFACE RECONSTRUCTION AND IMAGE ENHANCEMENT VIA L¹-MINIMIZATION

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2010年第3期32卷 1591-1616页

作者： Dobrev, Veselin Guermond, Jean-Luc Popov, Bojan Lawrence Livermore Natl Lab Livermore CA 94551 USA Texas A&M Univ Dept Math College Stn TX 77843 USA CNRS LIMSI UPRR 3251 F-91403 Orsay France Texas A&M Univ Dept Math College Stn TX 77843 USA

A surface reconstruction technique based on minimization of the total variation of the gradient is introduced. Convergence of the method is established, and an interior-point algorithm solving the associated linear programming problem is introduced. The reconstruction algorithm is illustrated on various test cases including natural and urban terrain data, and enhancement of low-resolution or aliased images.

关键词： finite elements L-1-minimization interior-point algorithm data reconstruction digital elevation models image enhancement

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Improving the axial compression capacity prediction of elliptical CFST columns using a hybrid ANN-IP model

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STEEL AND COMPOSITE STRUCTURES 2021年第3期39卷 319-335页

作者： Viet-Linh Tran Jang, Yun Kim, Seung-Eock Sejong Univ Dept Civil & Environm Engn 98 Gunja Dong Seoul 05006 South Korea Sejong Univ Dept Comp Engn 98 Gunja Dong Seoul 05006 South Korea Vinh Univ Dept Civil Engn Vinh 461010 Vietnam

This study proposes a new and highly-accurate artificial intelligence model, namely ANN-IP, which combines an interior-point (IP) algorithm and artificial neural network (ANN), to improve the axial compression capacity prediction of elliptical concrete-filled steel tubular (CFST) columns. For this purpose, 145 tests of elliptical CFST columns extracted from the literature are used to develop the ANN-IP model. In this regard, axial compression capacity is considered as a function of the column length, the major axis diameter, the minor axis diameter, the thickness of the steel tube, the yield strength of the steel tube, and the compressive strength of concrete. The performance of the ANN-IP model is compared with the ANN-LM model, which uses the robust Levenberg-Marquardt (LM) algorithm to train the ANN model. The comparative results show that the ANN-IP model obtains more magnificent precision (R-2 = 0.983, RMSE = 59.963 kN, a20-index = 0.979) than the ANN-LM model (R-2 = 0.938, RMSE = 116.634 kN, a20-index = 0.890). Finally, a new Graphical User Interface (GUI) tool is developed to use the ANN-IP model for the practical design. In conclusion, this study reveals that the proposed ANN -IP model can properly predict the axial compression capacity of elliptical CFST columns and eliminate the need for conducting costly experiments to some extent.

关键词： artificial neural network axial compression capacity elliptical concrete-filled steel tubular column interior-point algorithm graphical user interface

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Shakedown analysis of engineering structures with limited kinematical hardening

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2012年第15-16期49卷 2177-2186页

作者： Simon, J. -W. Weichert, D. Rhein Westfal TH Aachen Inst Gen Mech D-52056 Aachen Germany

We present a numerical method for the computation of shakedown loads of engineering structures with limited kinematical hardening under thermo-mechanical loading. The method is based on Melan's statical shakedown theorem, which results in a nonlinear convex optimization problem. This is solved by an interior-point algorithm recently developed by the authors, specially designed for lower bound shakedown analysis of large-scale problems. Limited kinematical hardening is taken into account by use of a two-surface model, such that both alternating plasticity and incremental collapse can be captured. For the yield surface as well as for the bounding surface the von Mises criterion is used. The proposed method is. validated by two examples, where numerical results are compared to those of literature where available. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Shakedown analysis Lower bound approach Limited kinematical hardening interior-point algorithm Convex optimization Nonlinear programming

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Shakedown analysis with multidimensional loading spaces

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COMPUTATIONAL MECHANICS 2012年第4期49卷 477-485页

作者： Simon, Jaan-Willem Weichert, Dieter Rhein Westfal TH Aachen Inst Gen Mech D-52056 Aachen Germany

A numerical method for the computation of shakedown loads of structures subjected to varying thermal and mechanical loading is proposed for the case of multidimensional loading spaces. The shakedown loading factors are determined based on the lower bound direct method using the von Mises yield criterion. The resulting nonlinear convex optimization problem is solved by use of the interior-point method. Although the underlying theory allows for the consideration of arbitrary numbers of loadings in principle, until now applications have been restricted to special cases, where either one or two loads vary independently. In this article, former formulations of the optimization problem are generalized for the case of arbitrary numbers of loadings. The method is implemented into an interior-point algorithm specially designed for this method. For illustration, numerical results are presented for a three-dimensional loading space applied to a square plate with a central circular hole.

关键词： Direct method Shakedown analysis interior-point algorithm Large-scale problem Multidimensional loading space

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Copula density estimation by finite mixture of parametric copula densities

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第11期50卷 3315-3337页

作者： Qu, Leming Lu, Yang Boise State Univ Dept Math Boise ID 83725 USA Boise State Univ Dept Civil Engn Boise ID 83725 USA

A copula density estimation method that is based on a finite mixture of heterogeneous parametric copula densities is proposed here. More specifically, the mixture components are Clayton, Frank, Gumbel, T, and normal copula densities, which are capable of capturing lower tail, strong central, upper tail, heavy tail, and symmetrical elliptical dependence, respectively. The model parameters are estimated by an interior-point algorithm for the constrained maximum likelihood problem. The interior-point algorithm is compared with the commonly used EM algorithm. Simulation and real data application show that the proposed approach is effective to model complex dependencies for data in dimensions beyond two or three.

关键词： Copula Dependence modeling Mixture model Maximum likelihood estimation interior-point algorithm

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Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden-Fowler model

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SOFT COMPUTING 2022年第24期26卷 13693-13708页

作者： Sabir, Zulqurnain Raja, Muhammad Asif Zahoor Baleanu, Dumitru Guirao, Juan L. G. Hazara Univ Dept Math & Stat Mansehra Pakistan Natl Yunlin Univ Sci & Technol Future Technol Res Ctr 123 Univ RdSect 3 Touliu 64002 Yunlin Taiwan Cankaya Univ Turkey Inst Space Sci Dept Math Ankara Magurele Romania Inst Space Sci Magurele Romania Tech Univ Cartagena Hosp Marina Dept Appl Math & Stat Cartagena 30203 Spain

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden-Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden-Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.

关键词： Coupled Emden-Fowler model interior-point algorithm Neural networks Numerical computing

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POLYNOMIAL-TIME algorithmS FOR LINEAR-PROGRAMMING BASED ONLY ON PRIMAL SCALING AND PROJECTED GRADIENTS OF A POTENTIAL FUNCTION

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MATHEMATICAL PROGRAMMING 1991年第2期51卷 203-222页

作者： FREUND, RM 1. Sloan School of Management Massachusetts Institute of Technology 02139 Cambridge MA USA

This paper presents extensions and further analytical properties of algorithms for linear programming based only on primal scaling and projected gradients of a potential function. The paper contains extensions and analysis of two polynomial-time algorithms for linear programming. We first present an extension of Gonzaga's O(nL) iteration algorithm, that computes dual variables and does not assume a known optimal objective function value. This algorithm uses only affine scaling, and is based on computing the projected gradient of the potential function [GRAPHICS] where x is the vector of primal variables and s is the vector of dual slack variables, and q = n + square-root n. The algorithm takes either a primal step or recomputes dual variables at each iteration. We next present an alternate form of Ye's O(square-root n L) iteration algorithm, that is an extension of the first algorithm of the paper, but uses the potential function [GRAPHICS] where q = n + square-root n. We use this alternate form of Ye's algorithm to show that Ye's algorithm is optimal with respect to the choice of the parameter q in the following sense. Suppose that q = n + n(t) where t greater-than-or-equal-to 0. Then the algorithm will solve the linear program in O(n(r)L) iterations, where r = max{t, 1-t}. Thus the value of t that minimizes the complexity bound is t = 1/2, yielding Ye's O(square-root n L) iteration bound.

关键词： LINEAR PROGRAM POLYNOMIAL TIME BOUND AFFINE SCALING interior-point algorithm

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Novel design of Morlet wavelet neural network for solving second order Lane-Emden equation

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MATHEMATICS AND COMPUTERS IN SIMULATION 2020年第0期172卷 1-14页

作者： Sabir, Zulqurnain Wahab, Hafiz Abdul Umar, Muhammad Sakar, Mehmet Giyas Raja, Muhammad Asif Zahoor Hazara Univ Dept Math & Stat Mansehra Pakistan Yuzuncu Yil Univ Fac Sci Dept Math Van Turkey COMSATS Univ Islamabad Dept Elect & Comp Engn Attock Campus Attock 43600 Pakistan

In this study, a novel computational paradigm based on Morlet wavelet neural network (MWNN) optimized with integrated strength of genetic algorithm (GAs) and interior-point algorithm (IPA) is presented for solving second order Lane-Emden equation (LEE). The solution of the LEE is performed by using modelling of the system with MWNNs aided with a hybrid combination of global search of GAs and an efficient local search of IPA. Three variants of the LEE have been numerically evaluated and their comparison with exact solutions demonstrates the correctness of the presented methodology. The statistical analyses are performed to establish the accuracy and convergence via the Theil's inequality coefficient, mean absolute deviation, and Nash Sutcliffe efficiency based metrics. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Lane-Emden equation Artificial neural networks Singular Genetic algorithm Nonlinear interior-point algorithm

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A Finite Mixture Three-Parameter Weibull Model for the Analysis of Wind Speed Data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2012年第12期41卷 2160-2171页

作者： Qin, Xu Zhang, Jiang-She Yan, Xiao-Dong Univ Elect Sci & Technol China Sch Math Sci Chengdu 610054 Peoples R China Xi An Jiao Tong Univ Fac Sci Xian 710049 Peoples R China Xi An Jiao Tong Univ State Key Lab Mfg Syst Engn Xian 710049 Peoples R China Chinese Acad Sci Inst Atmospher Phys Key Lab Reg Climate Environm Res Temp E Asia Beijing Peoples R China

This article presents a mixture three-parameter Weibull distribution to model wind speed data. The parameters are estimated by using maximum likelihood (ML) method in which the maximization problem is regarded as a nonlinear programming with only inequality constraints and is solved numerically by the interior-point method. By applying this model to four lattice-point wind speed sequences extracted from National Centers for Environmental Prediction (NCEP) reanalysis data, it is observed that the mixture three-parameter Weibull distribution model proposed in this paper provides a better fit than the existing Weibull models for the analysis of wind speed data under study.

关键词： interior-point algorithm Maximum likelihood estimation Mixture Weibull distribution Wind speed

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