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    易平

    • 教授       硕士生导师
    • 性别:女
    • 毕业院校:大连理工大学
    • 学位:博士
    • 所在单位:土木工程学院
    • 学科:结构工程. 防灾减灾工程及防护工程
    • 办公地点:大连理工大学综合实验三号楼524
    • 联系方式:yiping@dlut.edu.cn
    • 电子邮箱:yiping@dlut.edu.cn

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    Convergence control of the iterative procedure for performance-measure-based probabilistic structural design optimization

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    论文类型:期刊论文

    第一作者:Yi, Ping

    通讯作者:Yang, DX (reprint author), Dalian Univ Technol, Dept Engn Mech, State Key Lab Struct Anal Ind Equipment, Dalian, Peoples R China.

    合写作者:Yang, Dixiong

    发表时间:2009-12-01

    发表刊物:ENGINEERING OPTIMIZATION

    收录刊物:SCIE、EI、Scopus

    卷号:41

    期号:12

    页面范围:1145-1161

    ISSN号:0305-215X

    关键字:AMV iterative procedure; numerical instability; probabilistic structural design optimization; performance measure approach; chaotic dynamics; stability transformation method

    摘要:The advanced mean value (AMV) iterative scheme is commonly used to evaluate probabilistic constraints in the performance measure approach (PMA) for probabilistic structural design optimization (PSDO). However, the iterative procedure of PSDO may fail to converge. In this article, the chaotic dynamics theory is suggested to investigate and attack the non-convergence difficulties of PMA-based PSDO. Essentially, the AMV iterative formula forms a discrete dynamical system with control parameters. If the AMV iterative sequences present the numerical instabilities of periodic oscillation, bifurcation, and even chaos in some control parameter interval, then the outer optimization loop in PSDO cannot converge and acquire the correct optimal design. Furthermore, the stability transformation method (STM) of chaos feedback control is applied to perform the convergence control of AMV, in order to capture the desired fixed points in the whole control parameter interval. Meanwhile, PSDO is solved by the approaches of PMA two-level and PMA with the sequential approximate programming (SAP)-PMA with SAP. Numerical results of several examples illustrate that STM can smoothly overcome the convergence failure of PSDO resulting from the periodic oscillation, bifurcation, and chaotic solutions of AMV iterative procedure for evaluating the probabilistic constraints. Moreover, the probabilistic optimization with uniform random variables, which is widely recognized as a highly nonlinear and fairly difficult problem, can be attacked through introducing the strategy of chaos control. In addition, the approach of PMA with SAP combining with STM is quite effective and efficient.