| 基于功能度量法的概率优化设计的收敛控制 |
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| 引用本文： | 易平,杨迪雄.基于功能度量法的概率优化设计的收敛控制[J].力学学报,2008,40(1):128-134. |
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| 作者姓名： | 易平 杨迪雄 |
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| 作者单位： | 大连理工大学土木水利学院 大连理工大学工程力学系工业装备结构分析国家重点实验室 |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划(973计划) |
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| 摘 要： | 概率结构优化设计(PSDO)中概率约束的评定可以采用最近提出的、被认为更
高效、稳定的功能度量法(PMA). 改进均值(AMV)迭代格式经常在PMA中使用，但它对一些非
线性功能函数或非正态随机变量，搜索最小功能目标点时可能陷入周期振荡或混沌解，从而
使PSDO的两层次算法或序列近似规划算法优化计算失败. 利用混沌反馈控制的稳定
转换法对功能度量法的AMV迭代格式实施了收敛控制，使嵌入周期和混沌轨道的不稳定不动点
稳定化，获得稳定收敛解，从而使概率约束的评定能正常进行；再由两层次算法或序列
近似规划算法进行结构优化设计. 算例结果表明了稳定转换法实施收敛控制的有效性，以及
序列近似规划算法相对高效的优点.
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| 关 键 词： | 概率结构优化设计 功能度量法 AMV迭代格式 序列近似规划 混沌动力学 稳定转换法 |
| 文章编号： | 0459-1879（2008）01-0128-07 |
| 收稿时间： | 2007-04-18 |
| 修稿时间： | 2007-11-09 |
CONVERGENCE CONTROL OF PROBABILISTIC STRUCTURAL DESIGN OPTIMIZATION BASED ON PERFORMANCE MEASURE APPROACH |
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| Yi Ping,Yang Dixiong.CONVERGENCE CONTROL OF PROBABILISTIC STRUCTURAL DESIGN OPTIMIZATION BASED ON PERFORMANCE MEASURE APPROACH[J].chinese journal of theoretical and applied mechanics,2008,40(1):128-134. |
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| Authors: | Yi Ping Yang Dixiong |
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| Affiliation: | Institute of Civil and Hydraulic Engineering, Dalian University of
Technology, Dalian 116024, China
State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, China |
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| Abstract: | The evaluation of probabilistic constraints in
Probabilistic Structural Design Optimization (PSDO) can be carried out using
the recently proposed performance measure approach (PMA). The advanced
mean-value (AMV) method is well suitable for PMA due to its simplicity and
efficiency. However, when the AMV iterative scheme is applied to search for
the minimum performance target point for some nonlinear performance
functions, the iterative sequences could fall into the periodic oscillation
and even chaos. Then both PMA Two-level and PMA with SAP (Sequential
Approximate Programming), which are based on this evaluation of
probabilistic constraints, could yield convergent failure. In the present
paper, the convergence control of AMV iterative procedure is first
implemented by using the stability transformation method of chaos feedback
control. The unstable fixed points embedded in the periodic and chaotic
orbit are stabilized and the expected stable convergent solutions are
obtained. Once the evaluation of probabilistic constraints can be carried
out successfully, the design optimization is performed by PMA Two-level or
PMA with SAP. The numerical results demonstrate that the convergence control
using stability transformation method is effective and PMA with SAP is more
efficient. |
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| Keywords: | probabilistic structural design optimization performance measure approach AMV iterative procedure sequential approximate programming chaotic dynamics stability transformation method |
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